diff --git a/annotated.html b/annotated.html
index 2bfefd3e7..31a2561f8 100644
--- a/annotated.html
+++ b/annotated.html
@@ -141,7 +141,7 @@ $(document).ready(function(){initNavTree('annotated.html',''); initResizable();
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 <div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
   <ul>
-    <li class="footer">Generated on Sun Jun 21 2020 19:43:38 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:41 for Algorithms_in_C++ by
     <a href="http://www.doxygen.org/index.html">
     <img class="footer" src="doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
   </ul>
diff --git a/classes.html b/classes.html
index 783478e4e..47f21a030 100644
--- a/classes.html
+++ b/classes.html
@@ -184,7 +184,7 @@ $(document).ready(function(){initNavTree('classes.html',''); initResizable(); })
 <!-- start footer part -->
 <div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
   <ul>
-    <li class="footer">Generated on Sun Jun 21 2020 19:43:38 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:41 for Algorithms_in_C++ by
     <a href="http://www.doxygen.org/index.html">
     <img class="footer" src="doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
   </ul>
diff --git a/d0/d01/smallest__circle_8cpp.html b/d0/d01/smallest__circle_8cpp.html
index 9e9b96298..3b62b29ad 100644
--- a/d0/d01/smallest__circle_8cpp.html
+++ b/d0/d01/smallest__circle_8cpp.html
@@ -563,7 +563,7 @@ Here is the call graph for this function:</div>
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     <li class="navelem"><a class="el" href="../../dir_9510827d0b234b3cc54b29892f217477.html">others</a></li><li class="navelem"><a class="el" href="../../d0/d01/smallest__circle_8cpp.html">smallest_circle.cpp</a></li>
-    <li class="footer">Generated on Sun Jun 21 2020 19:43:37 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:39 for Algorithms_in_C++ by
     <a href="http://www.doxygen.org/index.html">
     <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
   </ul>
diff --git a/d0/d08/realtime__stats_8cpp.html b/d0/d08/realtime__stats_8cpp.html
index 33b3553a2..145ffe24a 100644
--- a/d0/d08/realtime__stats_8cpp.html
+++ b/d0/d08/realtime__stats_8cpp.html
@@ -304,7 +304,7 @@ Here is the call graph for this function:</div>
 <div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
   <ul>
     <li class="navelem"><a class="el" href="../../dir_296d53ceaeaa7e099814a6def439fe8a.html">math</a></li><li class="navelem"><a class="el" href="../../d0/d08/realtime__stats_8cpp.html">realtime_stats.cpp</a></li>
-    <li class="footer">Generated on Sun Jun 21 2020 19:43:36 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:38 for Algorithms_in_C++ by
     <a href="http://www.doxygen.org/index.html">
     <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
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diff --git a/d0/d0d/structmst-members.html b/d0/d0d/structmst-members.html
index 0f46635db..0cfaf11db 100644
--- a/d0/d0d/structmst-members.html
+++ b/d0/d0d/structmst-members.html
@@ -105,7 +105,7 @@ $(document).ready(function(){initNavTree('d1/d77/structmst.html','../../'); init
 <!-- start footer part -->
 <div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
   <ul>
-    <li class="footer">Generated on Sun Jun 21 2020 19:43:37 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:40 for Algorithms_in_C++ by
     <a href="http://www.doxygen.org/index.html">
     <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
   </ul>
diff --git a/d0/d55/classcll-members.html b/d0/d55/classcll-members.html
index 577ff29d1..10a4e2d25 100644
--- a/d0/d55/classcll-members.html
+++ b/d0/d55/classcll-members.html
@@ -113,7 +113,7 @@ $(document).ready(function(){initNavTree('d5/d15/classcll.html','../../'); initR
 <!-- start footer part -->
 <div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
   <ul>
-    <li class="footer">Generated on Sun Jun 21 2020 19:43:37 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:40 for Algorithms_in_C++ by
     <a href="http://www.doxygen.org/index.html">
     <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
   </ul>
diff --git a/d0/d78/classstatistics_1_1stats__computer1-members.html b/d0/d78/classstatistics_1_1stats__computer1-members.html
index 0e0d6b651..05ddaf7e0 100644
--- a/d0/d78/classstatistics_1_1stats__computer1-members.html
+++ b/d0/d78/classstatistics_1_1stats__computer1-members.html
@@ -111,7 +111,7 @@ $(document).ready(function(){initNavTree('d7/d7c/classstatistics_1_1stats__compu
 <!-- start footer part -->
 <div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
   <ul>
-    <li class="footer">Generated on Sun Jun 21 2020 19:43:38 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:41 for Algorithms_in_C++ by
     <a href="http://www.doxygen.org/index.html">
     <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
   </ul>
diff --git a/d0/da2/number__of__positive__divisors_8cpp.html b/d0/da2/number__of__positive__divisors_8cpp.html
index a1d5195da..d60f2cf20 100644
--- a/d0/da2/number__of__positive__divisors_8cpp.html
+++ b/d0/da2/number__of__positive__divisors_8cpp.html
@@ -232,7 +232,7 @@ Here is the call graph for this function:</div>
 <div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
   <ul>
     <li class="navelem"><a class="el" href="../../dir_296d53ceaeaa7e099814a6def439fe8a.html">math</a></li><li class="navelem"><a class="el" href="../../d0/da2/number__of__positive__divisors_8cpp.html">number_of_positive_divisors.cpp</a></li>
-    <li class="footer">Generated on Sun Jun 21 2020 19:43:36 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:38 for Algorithms_in_C++ by
     <a href="http://www.doxygen.org/index.html">
     <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
   </ul>
diff --git a/d0/db6/non__recursive__merge__sort_8cpp.html b/d0/db6/non__recursive__merge__sort_8cpp.html
index c7e82a9fe..8dfe5891a 100644
--- a/d0/db6/non__recursive__merge__sort_8cpp.html
+++ b/d0/db6/non__recursive__merge__sort_8cpp.html
@@ -144,7 +144,7 @@ int&#160;</td><td class="memItemRight" valign="bottom"><b>main</b> (int argc, ch
 <div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
   <ul>
     <li class="navelem"><a class="el" href="../../dir_bb1b521853a9c46347182a9d10420771.html">sorting</a></li><li class="navelem"><a class="el" href="../../d0/db6/non__recursive__merge__sort_8cpp.html">non_recursive_merge_sort.cpp</a></li>
-    <li class="footer">Generated on Sun Jun 21 2020 19:43:37 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:40 for Algorithms_in_C++ by
     <a href="http://www.doxygen.org/index.html">
     <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
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diff --git a/d0/dc4/struct_point-members.html b/d0/dc4/struct_point-members.html
index 314c3bc15..5570bb98e 100644
--- a/d0/dc4/struct_point-members.html
+++ b/d0/dc4/struct_point-members.html
@@ -107,7 +107,7 @@ $(document).ready(function(){initNavTree('d8/dc8/struct_point.html','../../'); i
 <!-- start footer part -->
 <div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
   <ul>
-    <li class="footer">Generated on Sun Jun 21 2020 19:43:37 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:40 for Algorithms_in_C++ by
     <a href="http://www.doxygen.org/index.html">
     <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
   </ul>
diff --git a/d0/dd2/class_queue___array.html b/d0/dd2/class_queue___array.html
index fde90fdea..15f307b3c 100644
--- a/d0/dd2/class_queue___array.html
+++ b/d0/dd2/class_queue___array.html
@@ -139,7 +139,7 @@ int&#160;</td><td class="memItemRight" valign="bottom"><b>size</b></td></tr>
 <div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
   <ul>
     <li class="navelem"><a class="el" href="../../d0/dd2/class_queue___array.html">Queue_Array</a></li>
-    <li class="footer">Generated on Sun Jun 21 2020 19:43:37 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:40 for Algorithms_in_C++ by
     <a href="http://www.doxygen.org/index.html">
     <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
   </ul>
diff --git a/d0/de2/gaussian__elimination_8cpp.html b/d0/de2/gaussian__elimination_8cpp.html
index 953be1501..826aa6c4f 100644
--- a/d0/de2/gaussian__elimination_8cpp.html
+++ b/d0/de2/gaussian__elimination_8cpp.html
@@ -217,7 +217,7 @@ Here is the call graph for this function:</div>
 <div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
   <ul>
     <li class="navelem"><a class="el" href="../../dir_9c6faab82c22511b50177aa2e38e2780.html">numerical_methods</a></li><li class="navelem"><a class="el" href="../../d0/de2/gaussian__elimination_8cpp.html">gaussian_elimination.cpp</a></li>
-    <li class="footer">Generated on Sun Jun 21 2020 19:43:36 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:38 for Algorithms_in_C++ by
     <a href="http://www.doxygen.org/index.html">
     <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
   </ul>
diff --git a/d0/dff/structlinkedlist.html b/d0/dff/structlinkedlist.html
index 5d0222ab0..5d0ac2ebf 100644
--- a/d0/dff/structlinkedlist.html
+++ b/d0/dff/structlinkedlist.html
@@ -122,7 +122,7 @@ int&#160;</td><td class="memItemRight" valign="bottom"><b>data</b></td></tr>
 <div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
   <ul>
     <li class="navelem"><a class="el" href="../../d0/dff/structlinkedlist.html">linkedlist</a></li>
-    <li class="footer">Generated on Sun Jun 21 2020 19:43:37 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:40 for Algorithms_in_C++ by
     <a href="http://www.doxygen.org/index.html">
     <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
   </ul>
diff --git a/d1/d07/class_solution-members.html b/d1/d07/class_solution-members.html
index 56242c5ef..401ad65ad 100644
--- a/d1/d07/class_solution-members.html
+++ b/d1/d07/class_solution-members.html
@@ -110,7 +110,7 @@ $(document).ready(function(){initNavTree('dd/d4f/class_solution.html','../../');
 <!-- start footer part -->
 <div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
   <ul>
-    <li class="footer">Generated on Sun Jun 21 2020 19:43:38 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:40 for Algorithms_in_C++ by
     <a href="http://www.doxygen.org/index.html">
     <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
   </ul>
diff --git a/d1/d11/gcd__of__n__numbers_8cpp.html b/d1/d11/gcd__of__n__numbers_8cpp.html
index 5245973e3..576de3eaa 100644
--- a/d1/d11/gcd__of__n__numbers_8cpp.html
+++ b/d1/d11/gcd__of__n__numbers_8cpp.html
@@ -214,7 +214,7 @@ Here is the call graph for this function:</div>
 <div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
   <ul>
     <li class="navelem"><a class="el" href="../../dir_296d53ceaeaa7e099814a6def439fe8a.html">math</a></li><li class="navelem"><a class="el" href="../../d1/d11/gcd__of__n__numbers_8cpp.html">gcd_of_n_numbers.cpp</a></li>
-    <li class="footer">Generated on Sun Jun 21 2020 19:43:36 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:38 for Algorithms_in_C++ by
     <a href="http://www.doxygen.org/index.html">
     <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
   </ul>
diff --git a/d1/d1d/class_graph-members.html b/d1/d1d/class_graph-members.html
index 7471d5c2b..693d71d03 100644
--- a/d1/d1d/class_graph-members.html
+++ b/d1/d1d/class_graph-members.html
@@ -144,7 +144,7 @@ $(document).ready(function(){initNavTree('da/d9a/class_graph.html','../../'); in
 <!-- start footer part -->
 <div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
   <ul>
-    <li class="footer">Generated on Sun Jun 21 2020 19:43:37 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:40 for Algorithms_in_C++ by
     <a href="http://www.doxygen.org/index.html">
     <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
   </ul>
diff --git a/d1/d21/quick__sort_8cpp.html b/d1/d21/quick__sort_8cpp.html
index 3755bcaed..69b21b021 100644
--- a/d1/d21/quick__sort_8cpp.html
+++ b/d1/d21/quick__sort_8cpp.html
@@ -191,7 +191,7 @@ Here is the call graph for this function:</div>
 <div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
   <ul>
     <li class="navelem"><a class="el" href="../../dir_bb1b521853a9c46347182a9d10420771.html">sorting</a></li><li class="navelem"><a class="el" href="../../d1/d21/quick__sort_8cpp.html">quick_sort.cpp</a></li>
-    <li class="footer">Generated on Sun Jun 21 2020 19:43:37 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:40 for Algorithms_in_C++ by
     <a href="http://www.doxygen.org/index.html">
     <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
   </ul>
diff --git a/d1/d76/buzz__number_8cpp.html b/d1/d76/buzz__number_8cpp.html
index ebbae3fc1..8d8c9651f 100644
--- a/d1/d76/buzz__number_8cpp.html
+++ b/d1/d76/buzz__number_8cpp.html
@@ -160,7 +160,7 @@ Here is the call graph for this function:</div>
 <div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
   <ul>
     <li class="navelem"><a class="el" href="../../dir_9510827d0b234b3cc54b29892f217477.html">others</a></li><li class="navelem"><a class="el" href="../../d1/d76/buzz__number_8cpp.html">buzz_number.cpp</a></li>
-    <li class="footer">Generated on Sun Jun 21 2020 19:43:37 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:38 for Algorithms_in_C++ by
     <a href="http://www.doxygen.org/index.html">
     <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
   </ul>
diff --git a/d1/d77/structmst.html b/d1/d77/structmst.html
index a6b3bf481..07907fb7d 100644
--- a/d1/d77/structmst.html
+++ b/d1/d77/structmst.html
@@ -119,7 +119,7 @@ int&#160;</td><td class="memItemRight" valign="bottom"><b>near</b></td></tr>
 <div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
   <ul>
     <li class="navelem"><a class="el" href="../../d1/d77/structmst.html">mst</a></li>
-    <li class="footer">Generated on Sun Jun 21 2020 19:43:37 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:40 for Algorithms_in_C++ by
     <a href="http://www.doxygen.org/index.html">
     <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
   </ul>
diff --git a/d1/db3/structcompare.html b/d1/db3/structcompare.html
index 67de0f9a9..6d2fac40e 100644
--- a/d1/db3/structcompare.html
+++ b/d1/db3/structcompare.html
@@ -113,7 +113,7 @@ bool&#160;</td><td class="memItemRight" valign="bottom"><b>operator()</b> (<a cl
 <div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
   <ul>
     <li class="navelem"><a class="el" href="../../d1/db3/structcompare.html">compare</a></li>
-    <li class="footer">Generated on Sun Jun 21 2020 19:43:37 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:40 for Algorithms_in_C++ by
     <a href="http://www.doxygen.org/index.html">
     <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
   </ul>
diff --git a/d1/dc2/classstack.html b/d1/dc2/classstack.html
index ed2ca22ef..0447188fd 100644
--- a/d1/dc2/classstack.html
+++ b/d1/dc2/classstack.html
@@ -511,7 +511,7 @@ template&lt;class Type &gt; </div>
 <div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
   <ul>
     <li class="navelem"><a class="el" href="../../d1/dc2/classstack.html">stack</a></li>
-    <li class="footer">Generated on Sun Jun 21 2020 19:43:38 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:41 for Algorithms_in_C++ by
     <a href="http://www.doxygen.org/index.html">
     <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
   </ul>
diff --git a/d1/df2/structnode-members.html b/d1/df2/structnode-members.html
index e93fa1303..4ad661d35 100644
--- a/d1/df2/structnode-members.html
+++ b/d1/df2/structnode-members.html
@@ -118,7 +118,7 @@ $(document).ready(function(){initNavTree('d5/da1/structnode.html','../../'); ini
 <!-- start footer part -->
 <div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
   <ul>
-    <li class="footer">Generated on Sun Jun 21 2020 19:43:37 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:40 for Algorithms_in_C++ by
     <a href="http://www.doxygen.org/index.html">
     <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
   </ul>
diff --git a/d1/df3/hash__search_8cpp.html b/d1/df3/hash__search_8cpp.html
index d36227881..02cc4fed5 100644
--- a/d1/df3/hash__search_8cpp.html
+++ b/d1/df3/hash__search_8cpp.html
@@ -397,7 +397,7 @@ Here is the call graph for this function:</div>
 <div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
   <ul>
     <li class="navelem"><a class="el" href="../../dir_19b2bf9199a15c634a08b1ede1dd896a.html">search</a></li><li class="navelem"><a class="el" href="../../d1/df3/hash__search_8cpp.html">hash_search.cpp</a></li>
-    <li class="footer">Generated on Sun Jun 21 2020 19:43:37 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:39 for Algorithms_in_C++ by
     <a href="http://www.doxygen.org/index.html">
     <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
   </ul>
diff --git a/d2/d05/class_min_heap.html b/d2/d05/class_min_heap.html
index 8e84286bf..9e2fdb026 100644
--- a/d2/d05/class_min_heap.html
+++ b/d2/d05/class_min_heap.html
@@ -469,7 +469,7 @@ Here is the call graph for this function:</div>
 <div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
   <ul>
     <li class="navelem"><a class="el" href="../../d2/d05/class_min_heap.html">MinHeap</a></li>
-    <li class="footer">Generated on Sun Jun 21 2020 19:43:37 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:40 for Algorithms_in_C++ by
     <a href="http://www.doxygen.org/index.html">
     <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
   </ul>
diff --git a/d2/d0b/fast__power_8cpp.html b/d2/d0b/fast__power_8cpp.html
index 8b95223ba..e8f7fc81f 100644
--- a/d2/d0b/fast__power_8cpp.html
+++ b/d2/d0b/fast__power_8cpp.html
@@ -292,7 +292,7 @@ Here is the call graph for this function:</div>
 <div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
   <ul>
     <li class="navelem"><a class="el" href="../../dir_296d53ceaeaa7e099814a6def439fe8a.html">math</a></li><li class="navelem"><a class="el" href="../../d2/d0b/fast__power_8cpp.html">fast_power.cpp</a></li>
-    <li class="footer">Generated on Sun Jun 21 2020 19:43:36 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:38 for Algorithms_in_C++ by
     <a href="http://www.doxygen.org/index.html">
     <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
   </ul>
diff --git a/d2/d22/jump__search_8cpp.html b/d2/d22/jump__search_8cpp.html
index faa9592ac..10fde2205 100644
--- a/d2/d22/jump__search_8cpp.html
+++ b/d2/d22/jump__search_8cpp.html
@@ -200,7 +200,7 @@ Here is the call graph for this function:</div>
 <div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
   <ul>
     <li class="navelem"><a class="el" href="../../dir_19b2bf9199a15c634a08b1ede1dd896a.html">search</a></li><li class="navelem"><a class="el" href="../../d2/d22/jump__search_8cpp.html">jump_search.cpp</a></li>
-    <li class="footer">Generated on Sun Jun 21 2020 19:43:37 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:39 for Algorithms_in_C++ by
     <a href="http://www.doxygen.org/index.html">
     <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
   </ul>
diff --git a/d2/d2c/structtower.html b/d2/d2c/structtower.html
index 43735ea02..0fe62adc7 100644
--- a/d2/d2c/structtower.html
+++ b/d2/d2c/structtower.html
@@ -120,7 +120,7 @@ int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../..
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   <ul>
     <li class="navelem"><a class="el" href="../../d2/d2c/structtower.html">tower</a></li>
-    <li class="footer">Generated on Sun Jun 21 2020 19:43:38 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:41 for Algorithms_in_C++ by
     <a href="http://www.doxygen.org/index.html">
     <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
   </ul>
diff --git a/d2/d36/structqueue.html b/d2/d36/structqueue.html
index 1d3d44bc9..3b8df03a3 100644
--- a/d2/d36/structqueue.html
+++ b/d2/d36/structqueue.html
@@ -508,7 +508,7 @@ template&lt;class Kind &gt; </div>
 <div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
   <ul>
     <li class="navelem"><a class="el" href="../../d2/d36/structqueue.html">queue</a></li>
-    <li class="footer">Generated on Sun Jun 21 2020 19:43:37 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:40 for Algorithms_in_C++ by
     <a href="http://www.doxygen.org/index.html">
     <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
   </ul>
diff --git a/d2/d3b/namespaceqr__algorithm.html b/d2/d3b/namespaceqr__algorithm.html
index 70fd78f3d..4b54c8aa8 100644
--- a/d2/d3b/namespaceqr__algorithm.html
+++ b/d2/d3b/namespaceqr__algorithm.html
@@ -625,7 +625,7 @@ template&lt;typename T &gt; </div>
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   <ul>
     <li class="navelem"><a class="el" href="../../d2/d3b/namespaceqr__algorithm.html">qr_algorithm</a></li>
-    <li class="footer">Generated on Sun Jun 21 2020 19:43:38 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:41 for Algorithms_in_C++ by
     <a href="http://www.doxygen.org/index.html">
     <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
   </ul>
diff --git a/d2/d52/heap__sort_8cpp.html b/d2/d52/heap__sort_8cpp.html
index 6dc3cfb7d..885feffd2 100644
--- a/d2/d52/heap__sort_8cpp.html
+++ b/d2/d52/heap__sort_8cpp.html
@@ -256,7 +256,7 @@ Here is the call graph for this function:</div>
 <div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
   <ul>
     <li class="navelem"><a class="el" href="../../dir_bb1b521853a9c46347182a9d10420771.html">sorting</a></li><li class="navelem"><a class="el" href="../../d2/d52/heap__sort_8cpp.html">heap_sort.cpp</a></li>
-    <li class="footer">Generated on Sun Jun 21 2020 19:43:37 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:40 for Algorithms_in_C++ by
     <a href="http://www.doxygen.org/index.html">
     <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
   </ul>
diff --git a/d2/dc4/classstack__linked_list.html b/d2/dc4/classstack__linked_list.html
index 5938995e8..18226ed71 100644
--- a/d2/dc4/classstack__linked_list.html
+++ b/d2/dc4/classstack__linked_list.html
@@ -135,7 +135,7 @@ Public Attributes</h2></td></tr>
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   <ul>
     <li class="navelem"><a class="el" href="../../d2/dc4/classstack__linked_list.html">stack_linkedList</a></li>
-    <li class="footer">Generated on Sun Jun 21 2020 19:43:38 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:41 for Algorithms_in_C++ by
     <a href="http://www.doxygen.org/index.html">
     <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
   </ul>
diff --git a/d2/dcf/namespacestatistics.html b/d2/dcf/namespacestatistics.html
index 8cadcbe91..4898ad25a 100644
--- a/d2/dcf/namespacestatistics.html
+++ b/d2/dcf/namespacestatistics.html
@@ -115,7 +115,7 @@ Classes</h2></td></tr>
 <div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
   <ul>
     <li class="navelem"><a class="el" href="../../d2/dcf/namespacestatistics.html">statistics</a></li>
-    <li class="footer">Generated on Sun Jun 21 2020 19:43:38 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:41 for Algorithms_in_C++ by
     <a href="http://www.doxygen.org/index.html">
     <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
   </ul>
diff --git a/d3/d06/ode__semi__implicit__euler_8cpp.html b/d3/d06/ode__semi__implicit__euler_8cpp.html
index 4947cc381..43c907bfa 100644
--- a/d3/d06/ode__semi__implicit__euler_8cpp.html
+++ b/d3/d06/ode__semi__implicit__euler_8cpp.html
@@ -405,7 +405,7 @@ Here is the call graph for this function:</div>
 <div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
   <ul>
     <li class="navelem"><a class="el" href="../../dir_9c6faab82c22511b50177aa2e38e2780.html">numerical_methods</a></li><li class="navelem"><a class="el" href="../../d3/d06/ode__semi__implicit__euler_8cpp.html">ode_semi_implicit_euler.cpp</a></li>
-    <li class="footer">Generated on Sun Jun 21 2020 19:43:37 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:38 for Algorithms_in_C++ by
     <a href="http://www.doxygen.org/index.html">
     <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
   </ul>
diff --git a/d3/d19/sparse__matrix_8cpp.html b/d3/d19/sparse__matrix_8cpp.html
index ca0f983a4..552b97c68 100644
--- a/d3/d19/sparse__matrix_8cpp.html
+++ b/d3/d19/sparse__matrix_8cpp.html
@@ -179,7 +179,7 @@ Functions</h2></td></tr>
 <div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
   <ul>
     <li class="navelem"><a class="el" href="../../dir_9510827d0b234b3cc54b29892f217477.html">others</a></li><li class="navelem"><a class="el" href="../../d3/d19/sparse__matrix_8cpp.html">sparse_matrix.cpp</a></li>
-    <li class="footer">Generated on Sun Jun 21 2020 19:43:37 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:39 for Algorithms_in_C++ by
     <a href="http://www.doxygen.org/index.html">
     <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
   </ul>
diff --git a/d3/d24/qr__decomposition_8cpp.html b/d3/d24/qr__decomposition_8cpp.html
index 240bf0363..5c5086bf4 100644
--- a/d3/d24/qr__decomposition_8cpp.html
+++ b/d3/d24/qr__decomposition_8cpp.html
@@ -194,7 +194,7 @@ Here is the call graph for this function:</div>
 <div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
   <ul>
     <li class="navelem"><a class="el" href="../../dir_9c6faab82c22511b50177aa2e38e2780.html">numerical_methods</a></li><li class="navelem"><a class="el" href="../../d3/d24/qr__decomposition_8cpp.html">qr_decomposition.cpp</a></li>
-    <li class="footer">Generated on Sun Jun 21 2020 19:43:37 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:38 for Algorithms_in_C++ by
     <a href="http://www.doxygen.org/index.html">
     <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
   </ul>
diff --git a/d3/d26/binary__search__tree_8cpp.html b/d3/d26/binary__search__tree_8cpp.html
index c4f25334f..209db77bd 100644
--- a/d3/d26/binary__search__tree_8cpp.html
+++ b/d3/d26/binary__search__tree_8cpp.html
@@ -165,7 +165,7 @@ Variables</h2></td></tr>
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     <li class="navelem"><a class="el" href="../../dir_2e746e9d06bf2d8ff842208bcc6ebcfc.html">data_structures</a></li><li class="navelem"><a class="el" href="../../d3/d26/binary__search__tree_8cpp.html">binary_search_tree.cpp</a></li>
-    <li class="footer">Generated on Sun Jun 21 2020 19:43:35 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:38 for Algorithms_in_C++ by
     <a href="http://www.doxygen.org/index.html">
     <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
   </ul>
diff --git a/d3/d61/vector__important__functions_8cpp.html b/d3/d61/vector__important__functions_8cpp.html
index 5ded0e197..52e069cef 100644
--- a/d3/d61/vector__important__functions_8cpp.html
+++ b/d3/d61/vector__important__functions_8cpp.html
@@ -188,7 +188,7 @@ Here is the call graph for this function:</div>
 <div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
   <ul>
     <li class="navelem"><a class="el" href="../../dir_9510827d0b234b3cc54b29892f217477.html">others</a></li><li class="navelem"><a class="el" href="../../d3/d61/vector__important__functions_8cpp.html">vector_important_functions.cpp</a></li>
-    <li class="footer">Generated on Sun Jun 21 2020 19:43:37 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:39 for Algorithms_in_C++ by
     <a href="http://www.doxygen.org/index.html">
     <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
   </ul>
diff --git a/d3/d7d/brute__force__string__searching_8cpp.html b/d3/d7d/brute__force__string__searching_8cpp.html
index f545d7ca8..437cf0092 100644
--- a/d3/d7d/brute__force__string__searching_8cpp.html
+++ b/d3/d7d/brute__force__string__searching_8cpp.html
@@ -197,7 +197,7 @@ Here is the call graph for this function:</div>
 <div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
   <ul>
     <li class="navelem"><a class="el" href="../../dir_73a3cc5065b223eb41b02873c0e19f0e.html">strings</a></li><li class="navelem"><a class="el" href="../../d3/d7d/brute__force__string__searching_8cpp.html">brute_force_string_searching.cpp</a></li>
-    <li class="footer">Generated on Sun Jun 21 2020 19:43:37 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:40 for Algorithms_in_C++ by
     <a href="http://www.doxygen.org/index.html">
     <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
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diff --git a/d3/da3/classstatistics_1_1stats__computer2-members.html b/d3/da3/classstatistics_1_1stats__computer2-members.html
index 24668af20..9a06f3200 100644
--- a/d3/da3/classstatistics_1_1stats__computer2-members.html
+++ b/d3/da3/classstatistics_1_1stats__computer2-members.html
@@ -111,7 +111,7 @@ $(document).ready(function(){initNavTree('d8/dab/classstatistics_1_1stats__compu
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 <div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
   <ul>
-    <li class="footer">Generated on Sun Jun 21 2020 19:43:38 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:41 for Algorithms_in_C++ by
     <a href="http://www.doxygen.org/index.html">
     <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
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diff --git a/d3/dbb/class_cycle_check.html b/d3/dbb/class_cycle_check.html
index a7a2a0b09..738e6828e 100644
--- a/d3/dbb/class_cycle_check.html
+++ b/d3/dbb/class_cycle_check.html
@@ -388,7 +388,7 @@ Here is the call graph for this function:</div>
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   <ul>
     <li class="navelem"><a class="el" href="../../d3/dbb/class_cycle_check.html">CycleCheck</a></li>
-    <li class="footer">Generated on Sun Jun 21 2020 19:43:37 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:40 for Algorithms_in_C++ by
     <a href="http://www.doxygen.org/index.html">
     <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
   </ul>
diff --git a/d3/dce/linkedlist__implentation__usingarray_8cpp.html b/d3/dce/linkedlist__implentation__usingarray_8cpp.html
index d9fad20a7..ababc22d8 100644
--- a/d3/dce/linkedlist__implentation__usingarray_8cpp.html
+++ b/d3/dce/linkedlist__implentation__usingarray_8cpp.html
@@ -298,7 +298,7 @@ Here is the call graph for this function:</div>
 <div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
   <ul>
     <li class="navelem"><a class="el" href="../../dir_2e746e9d06bf2d8ff842208bcc6ebcfc.html">data_structures</a></li><li class="navelem"><a class="el" href="../../d3/dce/linkedlist__implentation__usingarray_8cpp.html">linkedlist_implentation_usingarray.cpp</a></li>
-    <li class="footer">Generated on Sun Jun 21 2020 19:43:35 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:38 for Algorithms_in_C++ by
     <a href="http://www.doxygen.org/index.html">
     <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
   </ul>
diff --git a/d4/d1f/class_min_heap-members.html b/d4/d1f/class_min_heap-members.html
index 5b2a3a598..9df1dbe60 100644
--- a/d4/d1f/class_min_heap-members.html
+++ b/d4/d1f/class_min_heap-members.html
@@ -115,7 +115,7 @@ $(document).ready(function(){initNavTree('d2/d05/class_min_heap.html','../../');
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 <div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
   <ul>
-    <li class="footer">Generated on Sun Jun 21 2020 19:43:37 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:40 for Algorithms_in_C++ by
     <a href="http://www.doxygen.org/index.html">
     <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
   </ul>
diff --git a/d4/d21/least__common__multiple_8cpp.html b/d4/d21/least__common__multiple_8cpp.html
index 4b12524da..ea69348c9 100644
--- a/d4/d21/least__common__multiple_8cpp.html
+++ b/d4/d21/least__common__multiple_8cpp.html
@@ -284,7 +284,7 @@ Here is the call graph for this function:</div>
 <div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
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     <li class="navelem"><a class="el" href="../../dir_296d53ceaeaa7e099814a6def439fe8a.html">math</a></li><li class="navelem"><a class="el" href="../../d4/d21/least__common__multiple_8cpp.html">least_common_multiple.cpp</a></li>
-    <li class="footer">Generated on Sun Jun 21 2020 19:43:36 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:38 for Algorithms_in_C++ by
     <a href="http://www.doxygen.org/index.html">
     <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
   </ul>
diff --git a/d4/d32/fibonacci__fast_8cpp.html b/d4/d32/fibonacci__fast_8cpp.html
index e5051d9ef..65ab5dcea 100644
--- a/d4/d32/fibonacci__fast_8cpp.html
+++ b/d4/d32/fibonacci__fast_8cpp.html
@@ -237,7 +237,7 @@ Here is the call graph for this function:</div>
 <div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
   <ul>
     <li class="navelem"><a class="el" href="../../dir_296d53ceaeaa7e099814a6def439fe8a.html">math</a></li><li class="navelem"><a class="el" href="../../d4/d32/fibonacci__fast_8cpp.html">fibonacci_fast.cpp</a></li>
-    <li class="footer">Generated on Sun Jun 21 2020 19:43:36 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:38 for Algorithms_in_C++ by
     <a href="http://www.doxygen.org/index.html">
     <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
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diff --git a/d4/d45/gcd__recursive__euclidean_8cpp.html b/d4/d45/gcd__recursive__euclidean_8cpp.html
index 179317b7c..a62414913 100644
--- a/d4/d45/gcd__recursive__euclidean_8cpp.html
+++ b/d4/d45/gcd__recursive__euclidean_8cpp.html
@@ -216,7 +216,7 @@ Here is the call graph for this function:</div>
 <div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
   <ul>
     <li class="navelem"><a class="el" href="../../dir_296d53ceaeaa7e099814a6def439fe8a.html">math</a></li><li class="navelem"><a class="el" href="../../d4/d45/gcd__recursive__euclidean_8cpp.html">gcd_recursive_euclidean.cpp</a></li>
-    <li class="footer">Generated on Sun Jun 21 2020 19:43:36 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:38 for Algorithms_in_C++ by
     <a href="http://www.doxygen.org/index.html">
     <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
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diff --git a/d4/d68/qr__decompose_8h.html b/d4/d68/qr__decompose_8h.html
index 7fc2a64f6..ab08aa1e0 100644
--- a/d4/d68/qr__decompose_8h.html
+++ b/d4/d68/qr__decompose_8h.html
@@ -158,7 +158,7 @@ Functions</h2></td></tr>
 <div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
   <ul>
     <li class="navelem"><a class="el" href="../../dir_9c6faab82c22511b50177aa2e38e2780.html">numerical_methods</a></li><li class="navelem"><a class="el" href="../../d4/d68/qr__decompose_8h.html">qr_decompose.h</a></li>
-    <li class="footer">Generated on Sun Jun 21 2020 19:43:37 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:38 for Algorithms_in_C++ by
     <a href="http://www.doxygen.org/index.html">
     <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
   </ul>
diff --git a/d4/d68/qr__decompose_8h_source.html b/d4/d68/qr__decompose_8h_source.html
index 40c62faec..e85cc0e50 100644
--- a/d4/d68/qr__decompose_8h_source.html
+++ b/d4/d68/qr__decompose_8h_source.html
@@ -318,7 +318,7 @@ $(document).ready(function(){initNavTree('d4/d68/qr__decompose_8h_source.html','
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 <div class="ttc" id="afalse__position_8cpp_html_a0a3abbca80bc98e7abcb3ae73abe0f14"><div class="ttname"><a href="../../dd/d29/false__position_8cpp.html#a0a3abbca80bc98e7abcb3ae73abe0f14">MAX_ITERATIONS</a></div><div class="ttdeci">#define MAX_ITERATIONS</div><div class="ttdoc">Maximum number of iterations to check.</div><div class="ttdef"><b>Definition:</b> false_position.cpp:24</div></div>
 <div class="ttc" id="aclassstatistics_1_1stats__computer2_html_a7e7a1a2b0a03df0a70cac40d193421d2"><div class="ttname"><a href="../../d8/dab/classstatistics_1_1stats__computer2.html#a7e7a1a2b0a03df0a70cac40d193421d2">statistics::stats_computer2::operator&gt;&gt;</a></div><div class="ttdeci">friend std::istream &amp; operator&gt;&gt;(std::istream &amp;input, stats_computer2 &amp;stat)</div><div class="ttdef"><b>Definition:</b> realtime_stats.cpp:97</div></div>
-<div class="ttc" id="anewton__raphson__method_8cpp_html_a0a3abbca80bc98e7abcb3ae73abe0f14"><div class="ttname"><a href="../../de/dd3/newton__raphson__method_8cpp.html#a0a3abbca80bc98e7abcb3ae73abe0f14">MAX_ITERATIONS</a></div><div class="ttdeci">#define MAX_ITERATIONS</div><div class="ttdoc">Maximum number of iterations to check.</div><div class="ttdef"><b>Definition:</b> newton_raphson_method.cpp:22</div></div>
+<div class="ttc" id="anewton__raphson__method_8cpp_html_a0a3abbca80bc98e7abcb3ae73abe0f14"><div class="ttname"><a href="../../de/dd3/newton__raphson__method_8cpp.html#a0a3abbca80bc98e7abcb3ae73abe0f14">MAX_ITERATIONS</a></div><div class="ttdeci">#define MAX_ITERATIONS</div><div class="ttdoc">Maximum number of iterations to check.</div><div class="ttdef"><b>Definition:</b> newton_raphson_method.cpp:21</div></div>
 <div class="ttc" id="abasic_string_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a></div><div class="ttdoc">STL class.</div></div>
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 <div class="ttc" id="auniform_int_distribution_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/random/uniform_int_distribution.html">std::uniform_int_distribution</a></div></div>
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 <div class="ttc" id="aclock_t_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/chrono/c/clock_t.html">std::clock_t</a></div></div>
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-<div class="ttc" id="anewton__raphson__method_8cpp_html_a2003b5b2dcfff0769b957ab5c968b03d"><div class="ttname"><a href="../../de/dd3/newton__raphson__method_8cpp.html#a2003b5b2dcfff0769b957ab5c968b03d">eq</a></div><div class="ttdeci">static double eq(double i)</div><div class="ttdef"><b>Definition:</b> newton_raphson_method.cpp:26</div></div>
+<div class="ttc" id="aordinary__least__squares__regressor_8cpp_html_a67249e31221231cf3aaf3cfd870372d0"><div class="ttname"><a href="../../dc/d38/ordinary__least__squares__regressor_8cpp.html#a67249e31221231cf3aaf3cfd870372d0">operator+</a></div><div class="ttdeci">std::vector&lt; T &gt; operator+(std::vector&lt; T &gt; const &amp;A, std::vector&lt; T &gt; const &amp;B)</div><div class="ttdef"><b>Definition:</b> ordinary_least_squares_regressor.cpp:196</div></div>
+<div class="ttc" id="anewton__raphson__method_8cpp_html_a2003b5b2dcfff0769b957ab5c968b03d"><div class="ttname"><a href="../../de/dd3/newton__raphson__method_8cpp.html#a2003b5b2dcfff0769b957ab5c968b03d">eq</a></div><div class="ttdeci">static double eq(double i)</div><div class="ttdef"><b>Definition:</b> newton_raphson_method.cpp:29</div></div>
 <div class="ttc" id="apair_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/utility/pair.html">std::pair</a></div></div>
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+<div class="ttc" id="anewton__raphson__method_8cpp_html_a3d3f7f41977394680af6ebbed96f3386"><div class="ttname"><a href="../../de/dd3/newton__raphson__method_8cpp.html#a3d3f7f41977394680af6ebbed96f3386">eq_der</a></div><div class="ttdeci">static double eq_der(double i)</div><div class="ttdef"><b>Definition:</b> newton_raphson_method.cpp:39</div></div>
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 <div class="ttc" id="aatof_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/byte/atof.html">std::atof</a></div><div class="ttdeci">T atof(T... args)</div></div>
 <div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a></div><div class="ttdoc">STL class.</div></div>
@@ -346,13 +346,13 @@ $(document).ready(function(){initNavTree('d4/d68/qr__decompose_8h_source.html','
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-<div class="ttc" id="aordinary__least__squares__regressor_8cpp_html_a4921874435266592b222e3f2eda0e01f"><div class="ttname"><a href="../../dc/d38/ordinary__least__squares__regressor_8cpp.html#a4921874435266592b222e3f2eda0e01f">is_square</a></div><div class="ttdeci">bool is_square(std::vector&lt; std::vector&lt; T &gt;&gt; const &amp;A)</div><div class="ttdef"><b>Definition:</b> ordinary_least_squares_regressor.cpp:54</div></div>
+<div class="ttc" id="aordinary__least__squares__regressor_8cpp_html_a4921874435266592b222e3f2eda0e01f"><div class="ttname"><a href="../../dc/d38/ordinary__least__squares__regressor_8cpp.html#a4921874435266592b222e3f2eda0e01f">is_square</a></div><div class="ttdeci">bool is_square(std::vector&lt; std::vector&lt; T &gt;&gt; const &amp;A)</div><div class="ttdef"><b>Definition:</b> ordinary_least_squares_regressor.cpp:55</div></div>
 <div class="ttc" id="aprime__factorization_8cpp_html_ae66f6b31b5ad750f1fe042a706a4e3d4"><div class="ttname"><a href="../../db/d0d/prime__factorization_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a></div><div class="ttdeci">int main()</div><div class="ttdef"><b>Definition:</b> prime_factorization.cpp:62</div></div>
 <div class="ttc" id="amiller__rabin_8cpp_html_a798398d5bfd375a3c0ce68100842f6f5"><div class="ttname"><a href="../../d6/d42/miller__rabin_8cpp.html#a798398d5bfd375a3c0ce68100842f6f5">reverse_binary</a></div><div class="ttdeci">std::vector&lt; T &gt; reverse_binary(T num)</div><div class="ttdef"><b>Definition:</b> miller_rabin.cpp:19</div></div>
 <div class="ttc" id="asqrt_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/math/sqrt.html">std::sqrt</a></div><div class="ttdeci">T sqrt(T... args)</div></div>
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+<div class="ttc" id="aordinary__least__squares__regressor_8cpp_html_ab6171f4db68a5e50ae0f3500a63acd26"><div class="ttname"><a href="../../dc/d38/ordinary__least__squares__regressor_8cpp.html#ab6171f4db68a5e50ae0f3500a63acd26">operator*</a></div><div class="ttdeci">std::vector&lt; std::vector&lt; T &gt; &gt; operator*(std::vector&lt; std::vector&lt; T &gt;&gt; const &amp;A, std::vector&lt; std::vector&lt; T &gt;&gt; const &amp;B)</div><div class="ttdef"><b>Definition:</b> ordinary_least_squares_regressor.cpp:72</div></div>
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 <div class="ttc" id="amersenne_twister_engine_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/random/mersenne_twister_engine.html">std::mt19937</a></div></div>
@@ -360,7 +360,7 @@ $(document).ready(function(){initNavTree('d4/d68/qr__decompose_8h_source.html','
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 <div class="ttc" id="aclock_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a></div><div class="ttdeci">T clock(T... args)</div></div>
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@@ -384,10 +384,10 @@ $(document).ready(function(){initNavTree('d4/d68/qr__decompose_8h_source.html','
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 <div class="ttc" id="aopen_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ofstream/open.html">std::ofstream::open</a></div><div class="ttdeci">T open(T... args)</div></div>
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@@ -406,21 +406,22 @@ $(document).ready(function(){initNavTree('d4/d68/qr__decompose_8h_source.html','
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+<div class="ttc" id="akohonen__som__topology_8cpp_html_a1440a7779ac56f47a3f355ce4a8c7da0"><div class="ttname"><a href="../../d4/def/kohonen__som__topology_8cpp.html#a1440a7779ac56f47a3f355ce4a8c7da0">test1</a></div><div class="ttdeci">void test1()</div><div class="ttdef"><b>Definition:</b> kohonen_som_topology.cpp:359</div></div>
 <div class="ttc" id="asize_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">std::string::size</a></div><div class="ttdeci">T size(T... args)</div></div>
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+<div class="ttc" id="aclassmachine__learning_1_1adaline_html_a74e3c6c037b67895014414c5d75465e5"><div class="ttname"><a href="../../d6/d30/classmachine__learning_1_1adaline.html#a74e3c6c037b67895014414c5d75465e5">machine_learning::adaline::fit</a></div><div class="ttdeci">double fit(const std::vector&lt; double &gt; &amp;x, const int &amp;y)</div><div class="ttdef"><b>Definition:</b> adaline_learning.cpp:112</div></div>
 <div class="ttc" id="amatrix__exponentiation_8cpp_html_ad8389ed58fd0ec66df248014775ad1fa"><div class="ttname"><a href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a></div><div class="ttdeci">ll ans(ll n)</div><div class="ttdef"><b>Definition:</b> matrix_exponentiation.cpp:94</div></div>
 <div class="ttc" id="astack_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/stack.html">std::stack</a></div><div class="ttdoc">STL class.</div></div>
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@@ -433,7 +433,7 @@ $(document).ready(function(){initNavTree('d4/d86/large__number_8h_source.html','
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 <div class="ttc" id="aemplace_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/queue/emplace.html">std::queue::emplace</a></div><div class="ttdeci">T emplace(T... args)</div></div>
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@@ -453,17 +453,17 @@ $(document).ready(function(){initNavTree('d4/d86/large__number_8h_source.html','
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 <div class="ttc" id="aback_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/back.html">std::vector::back</a></div><div class="ttdeci">T back(T... args)</div></div>
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 <div class="ttc" id="anamespacemachine__learning_html"><div class="ttname"><a href="../../d8/d77/namespacemachine__learning.html">machine_learning</a></div><div class="ttdoc">Machine learning algorithms.</div></div>
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-<div class="ttc" id="anamespacemachine__learning_html_ac4010fe3a52a74e8b5b1aaadfe38b46f"><div class="ttname"><a href="../../d8/d77/namespacemachine__learning.html#ac4010fe3a52a74e8b5b1aaadfe38b46f">machine_learning::update_weights</a></div><div class="ttdeci">double update_weights(const std::valarray&lt; double &gt; &amp;X, std::vector&lt; std::vector&lt; std::valarray&lt; double &gt;&gt;&gt; *W, std::vector&lt; std::valarray&lt; double &gt;&gt; *D, double alpha, int R)</div><div class="ttdef"><b>Definition:</b> kohonen_som_topology.cpp:191</div></div>
+<div class="ttc" id="anamespacemachine__learning_html_ac4010fe3a52a74e8b5b1aaadfe38b46f"><div class="ttname"><a href="../../d8/d77/namespacemachine__learning.html#ac4010fe3a52a74e8b5b1aaadfe38b46f">machine_learning::update_weights</a></div><div class="ttdeci">double update_weights(const std::valarray&lt; double &gt; &amp;X, std::vector&lt; std::vector&lt; std::valarray&lt; double &gt;&gt;&gt; *W, std::vector&lt; std::valarray&lt; double &gt;&gt; *D, double alpha, int R)</div><div class="ttdef"><b>Definition:</b> kohonen_som_topology.cpp:193</div></div>
 <div class="ttc" id="aqueue_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/queue.html">std::queue</a></div><div class="ttdoc">STL class.</div></div>
 <div class="ttc" id="aclass_graph_html"><div class="ttname"><a href="../../da/d9a/class_graph.html">Graph</a></div><div class="ttdef"><b>Definition:</b> bellman_ford.cpp:13</div></div>
 <div class="ttc" id="aclass_solution_html"><div class="ttname"><a href="../../dd/d4f/class_solution.html">Solution</a></div><div class="ttdef"><b>Definition:</b> bridge_finding_with_tarjan_algorithm.cpp:13</div></div>
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+<div class="ttc" id="agroup__machine__learning_html_gab53c14440b2b2dd3172c66afc5c2f63f"><div class="ttname"><a href="../../d9/d66/group__machine__learning.html#gab53c14440b2b2dd3172c66afc5c2f63f">get_min_2d</a></div><div class="ttdeci">void get_min_2d(const std::vector&lt; std::valarray&lt; double &gt;&gt; &amp;X, double *val, int *x_idx, int *y_idx)</div><div class="ttdef"><b>Definition:</b> kohonen_som_topology.cpp:99</div></div>
 <div class="ttc" id="afront_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/queue/front.html">std::queue::front</a></div><div class="ttdeci">T front(T... args)</div></div>
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+<div class="ttc" id="aclassmachine__learning_1_1adaline_html_ac8a9c2aaaa63b0f27ea176857e1e7d56"><div class="ttname"><a href="../../d6/d30/classmachine__learning_1_1adaline.html#ac8a9c2aaaa63b0f27ea176857e1e7d56">machine_learning::adaline::check_size_match</a></div><div class="ttdeci">bool check_size_match(const std::vector&lt; double &gt; &amp;x)</div><div class="ttdef"><b>Definition:</b> adaline_learning.cpp:176</div></div>
 <div class="ttc" id="asqrt_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/math/sqrt.html">std::sqrt</a></div><div class="ttdeci">T sqrt(T... args)</div></div>
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 <div class="ttc" id="akohonen__som__trace_8cpp_html_a1440a7779ac56f47a3f355ce4a8c7da0"><div class="ttname"><a href="../../d9/d49/kohonen__som__trace_8cpp.html#a1440a7779ac56f47a3f355ce4a8c7da0">test1</a></div><div class="ttdeci">void test1()</div><div class="ttdef"><b>Definition:</b> kohonen_som_trace.cpp:225</div></div>
@@ -484,7 +484,7 @@ $(document).ready(function(){initNavTree('d4/d86/large__number_8h_source.html','
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 <div class="ttc" id="aclass_cycle_check_html_ad9a270ffba3a68539b92272c702e3474"><div class="ttname"><a href="../../d3/dbb/class_cycle_check.html#ad9a270ffba3a68539b92272c702e3474">CycleCheck::isCyclicDFS</a></div><div class="ttdeci">static bool isCyclicDFS(Graph const &amp;graph)</div><div class="ttdef"><b>Definition:</b> cycle_check_directed_graph.cpp:206</div></div>
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+<div class="ttc" id="akohonen__som__topology_8cpp_html_a6d0455dd5c30adda100e95f0423c786e"><div class="ttname"><a href="../../d4/def/kohonen__som__topology_8cpp.html#a6d0455dd5c30adda100e95f0423c786e">test3</a></div><div class="ttdeci">void test3()</div><div class="ttdef"><b>Definition:</b> kohonen_som_topology.cpp:523</div></div>
 <div class="ttc" id="aavltree_8cpp_html_a1ecfaaea49d452772dbb2b28133e36e0"><div class="ttname"><a href="../../d8/dee/avltree_8cpp.html#a1ecfaaea49d452772dbb2b28133e36e0">createNode</a></div><div class="ttdeci">node * createNode(int data)</div><div class="ttdef"><b>Definition:</b> avltree.cpp:21</div></div>
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 <div class="ttc" id="aclass_cycle_check_html_a2f4485c08b45e7a21a2e86f9c3f01d8b"><div class="ttname"><a href="../../d3/dbb/class_cycle_check.html#a2f4485c08b45e7a21a2e86f9c3f01d8b">CycleCheck::isCyclicDFSHelper</a></div><div class="ttdeci">static bool isCyclicDFSHelper(AdjList const &amp;adjList, std::vector&lt; nodeStates &gt; *state, unsigned int node)</div><div class="ttdef"><b>Definition:</b> cycle_check_directed_graph.cpp:165</div></div>
@@ -495,7 +495,7 @@ $(document).ready(function(){initNavTree('d4/d86/large__number_8h_source.html','
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 <div class="ttc" id="aavltree_8cpp_html_aa7cd8a68075fae1c33df41233c1bed6a"><div class="ttname"><a href="../../d8/dee/avltree_8cpp.html#aa7cd8a68075fae1c33df41233c1bed6a">insert</a></div><div class="ttdeci">node * insert(node *root, int item)</div><div class="ttdef"><b>Definition:</b> avltree.cpp:66</div></div>
 <div class="ttc" id="afprintf_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/c/fprintf.html">std::printf</a></div><div class="ttdeci">T printf(T... args)</div></div>
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 <div class="ttc" id="amatrix__exponentiation_8cpp_html_afcf0d19607cd0edd8ae333d2b9c220c0"><div class="ttname"><a href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a></div><div class="ttdeci">ll k</div><div class="ttdef"><b>Definition:</b> matrix_exponentiation.cpp:48</div></div>
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+<div class="ttc" id="aclassmachine__learning_1_1adaline_html_a4cd8fe438032fedaa66f93bfd66f5492"><div class="ttname"><a href="../../d6/d30/classmachine__learning_1_1adaline.html#a4cd8fe438032fedaa66f93bfd66f5492">machine_learning::adaline::weights</a></div><div class="ttdeci">std::vector&lt; double &gt; weights</div><div class="ttdoc">weights of the neural network</div><div class="ttdef"><b>Definition:</b> adaline_learning.cpp:189</div></div>
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+<div class="ttc" id="akohonen__som__topology_8cpp_html_ab3081e021270ba21a9fd88646f6a6e26"><div class="ttname"><a href="../../d4/def/kohonen__som__topology_8cpp.html#ab3081e021270ba21a9fd88646f6a6e26">test_3d_classes1</a></div><div class="ttdeci">void test_3d_classes1(std::vector&lt; std::valarray&lt; double &gt;&gt; *data)</div><div class="ttdef"><b>Definition:</b> kohonen_som_topology.cpp:399</div></div>
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+<div class="ttc" id="akohonen__som__topology_8cpp_html_a0283886819c7c140a023582b7269e2d0"><div class="ttname"><a href="../../d4/def/kohonen__som__topology_8cpp.html#a0283886819c7c140a023582b7269e2d0">test2</a></div><div class="ttdeci">void test2()</div><div class="ttdef"><b>Definition:</b> kohonen_som_topology.cpp:439</div></div>
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@@ -545,7 +545,7 @@ $(document).ready(function(){initNavTree('d4/d86/large__number_8h_source.html','
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+<div class="ttc" id="agroup__machine__learning_html_ga6c606bc85a3e9fd9d010f874ad760336"><div class="ttname"><a href="../../d9/d66/group__machine__learning.html#ga6c606bc85a3e9fd9d010f874ad760336">save_2d_data</a></div><div class="ttdeci">int save_2d_data(const char *fname, const std::vector&lt; std::valarray&lt; double &gt;&gt; &amp;X)</div><div class="ttdef"><b>Definition:</b> kohonen_som_topology.cpp:62</div></div>
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@@ -560,10 +560,10 @@ $(document).ready(function(){initNavTree('d4/d86/large__number_8h_source.html','
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 <div class="ttc" id="agreater_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/utility/functional/greater.html">std::greater</a></div></div>
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@@ -573,7 +573,7 @@ $(document).ready(function(){initNavTree('d4/d86/large__number_8h_source.html','
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 <div class="ttc" id="async_with_stdio_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/ios_base/sync_with_stdio.html">std::ios_base::sync_with_stdio</a></div><div class="ttdeci">T sync_with_stdio(T... args)</div></div>
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@@ -601,31 +601,31 @@ $(document).ready(function(){initNavTree('d4/d86/large__number_8h_source.html','
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-<div class="ttc" id="aclassmachine__learning_1_1adaline_html_aa23d60262f917f35836ef4b1c1d9f7d3"><div class="ttname"><a href="../../d6/d30/classmachine__learning_1_1adaline.html#aa23d60262f917f35836ef4b1c1d9f7d3">machine_learning::adaline::accuracy</a></div><div class="ttdeci">const double accuracy</div><div class="ttdoc">model fit convergence accuracy</div><div class="ttdef"><b>Definition:</b> adaline_learning.cpp:186</div></div>
+<div class="ttc" id="aclassmachine__learning_1_1adaline_html_aa23d60262f917f35836ef4b1c1d9f7d3"><div class="ttname"><a href="../../d6/d30/classmachine__learning_1_1adaline.html#aa23d60262f917f35836ef4b1c1d9f7d3">machine_learning::adaline::accuracy</a></div><div class="ttdeci">const double accuracy</div><div class="ttdoc">model fit convergence accuracy</div><div class="ttdef"><b>Definition:</b> adaline_learning.cpp:188</div></div>
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+<div class="ttc" id="akohonen__som__topology_8cpp_html_a6b5e744876fd980a3451cbb385d4e755"><div class="ttname"><a href="../../d4/def/kohonen__som__topology_8cpp.html#a6b5e744876fd980a3451cbb385d4e755">test_2d_classes</a></div><div class="ttdeci">void test_2d_classes(std::vector&lt; std::valarray&lt; double &gt;&gt; *data)</div><div class="ttdef"><b>Definition:</b> kohonen_som_topology.cpp:320</div></div>
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+<div class="ttc" id="aadaline__learning_8cpp_html_a992bdf1fdb0b9d414bcf7981d2d87aa9"><div class="ttname"><a href="../../d5/db0/adaline__learning_8cpp.html#a992bdf1fdb0b9d414bcf7981d2d87aa9">test3</a></div><div class="ttdeci">void test3(double eta=0.01)</div><div class="ttdef"><b>Definition:</b> adaline_learning.cpp:289</div></div>
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+<div class="ttc" id="aadaline__learning_8cpp_html_a3c04138a5bfe5d72780bb7e82a18e627"><div class="ttname"><a href="../../d5/db0/adaline__learning_8cpp.html#a3c04138a5bfe5d72780bb7e82a18e627">main</a></div><div class="ttdeci">int main(int argc, char **argv)</div><div class="ttdef"><b>Definition:</b> adaline_learning.cpp:333</div></div>
 <div class="ttc" id="astructlist_html"><div class="ttname"><a href="../../d8/d10/structlist.html">list&lt; int &gt;</a></div></div>
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:35 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:38 for Algorithms_in_C++ by
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     <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:36 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:38 for Algorithms_in_C++ by
     <a href="http://www.doxygen.org/index.html">
     <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
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diff --git a/d4/da0/gcd__iterative__euclidean_8cpp.html b/d4/da0/gcd__iterative__euclidean_8cpp.html
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:36 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:38 for Algorithms_in_C++ by
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     <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
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+    <li class="footer">Generated on Mon Jun 22 2020 11:53:40 for Algorithms_in_C++ by
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     <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
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diff --git a/d4/db4/struct_segment_intersection.html b/d4/db4/struct_segment_intersection.html
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:38 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:40 for Algorithms_in_C++ by
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     <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:37 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:40 for Algorithms_in_C++ by
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     <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:38 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:41 for Algorithms_in_C++ by
     <a href="http://www.doxygen.org/index.html">
     <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
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     <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
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@@ -165,8 +165,8 @@ Functions</h2></td></tr>
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 <div class="textblock"><p><a href="https://en.wikipedia.org/wiki/Self-organizing_map">Kohonen self organizing map</a> (topological map) </p>
-<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/kvedala">Krishna Vedala</a> This example implements a powerful unsupervised learning algorithm called as a self organizing map. The algorithm creates a connected network of weights that closely follows the given data points. This thus creates a topological map of the given data i.e., it maintains the relationship between varipus data points in a much higher dimesional space by creating an equivalent in a 2-dimensional space. <img src="https://raw.githubusercontent.com/TheAlgorithms/C-Plus-Plus/docs/images/machine_learning/2D_Kohonen_SOM.svg" alt="Trained topological maps for the test cases in the program" style="pointer-events: none;" class="inline"/> </dd></dl>
-<dl class="section note"><dt>Note</dt><dd>This C++ version of the program is considerable slower than its <a href="https://github.com/kvedala/C/blob/master/machine_learning/kohonen_som_trace.c">C counterpart</a> </dd>
+<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/kvedala">Krishna Vedala</a></dd></dl>
+<p>This example implements a powerful unsupervised learning algorithm called as a self organizing map. The algorithm creates a connected network of weights that closely follows the given data points. This thus creates a topological map of the given data i.e., it maintains the relationship between varipus data points in a much higher dimesional space by creating an equivalent in a 2-dimensional space. <img src="https://raw.githubusercontent.com/TheAlgorithms/C-Plus-Plus/docs/images/machine_learning/2D_Kohonen_SOM.svg" alt="Trained topological maps for the test cases in the program" style="pointer-events: none;" class="inline"/> </p><dl class="section note"><dt>Note</dt><dd>This C++ version of the program is considerable slower than its <a href="https://github.com/kvedala/C/blob/master/machine_learning/kohonen_som_trace.c">C counterpart</a> </dd>
 <dd>
 The compiled code is much slower when compiled with MS Visual C++ 2019 than with GCC on windows </dd></dl>
 <dl class="section see"><dt>See also</dt><dd><a class="el" href="../../d9/d49/kohonen__som__trace_8cpp.html" title="Kohonen self organizing map (data tracing)">kohonen_som_trace.cpp</a> </dd></dl>
@@ -205,9 +205,9 @@ The compiled code is much slower when compiled with MS Visual C++ 2019 than with
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>time difference in seconds </dd></dl>
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-<div class="line"><a name="l00561"></a><span class="lineno">  561</span>&#160;}</div>
+<div class="fragment"><div class="line"><a name="l00561"></a><span class="lineno">  561</span>&#160;                                                      {</div>
+<div class="line"><a name="l00562"></a><span class="lineno">  562</span>&#160;    <span class="keywordflow">return</span> <span class="keyword">static_cast&lt;</span><span class="keywordtype">double</span><span class="keyword">&gt;</span>(end_t - start_t) / CLOCKS_PER_SEC;</div>
+<div class="line"><a name="l00563"></a><span class="lineno">  563</span>&#160;}</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -237,38 +237,38 @@ The compiled code is much slower when compiled with MS Visual C++ 2019 than with
       </table>
 </div><div class="memdoc">
 <p>Main function </p>
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-<div class="line"><a name="l00569"></a><span class="lineno">  569</span>&#160;<span class="preprocessor">#endif</span></div>
-<div class="line"><a name="l00570"></a><span class="lineno">  570</span>&#160; </div>
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+<div class="fragment"><div class="line"><a name="l00566"></a><span class="lineno">  566</span>&#160;                                {</div>
+<div class="line"><a name="l00567"></a><span class="lineno">  567</span>&#160;<span class="preprocessor">#ifdef _OPENMP</span></div>
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+<div class="line"><a name="l00569"></a><span class="lineno">  569</span>&#160;<span class="preprocessor">#else</span></div>
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+<div class="line"><a name="l00571"></a><span class="lineno">  571</span>&#160;<span class="preprocessor">#endif</span></div>
 <div class="line"><a name="l00572"></a><span class="lineno">  572</span>&#160; </div>
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-<div class="line"><a name="l00574"></a><span class="lineno">  574</span>&#160;    <a class="code" href="../../d4/def/kohonen__som__topology_8cpp.html#a1440a7779ac56f47a3f355ce4a8c7da0">test1</a>();</div>
-<div class="line"><a name="l00575"></a><span class="lineno">  575</span>&#160;    <span class="keyword">auto</span> end_clk = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
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-<div class="line"><a name="l00577"></a><span class="lineno">  577</span>&#160;              &lt;&lt; <span class="stringliteral">&quot; sec\n&quot;</span>;</div>
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-<div class="line"><a name="l00583"></a><span class="lineno">  583</span>&#160;              &lt;&lt; <span class="stringliteral">&quot; sec\n&quot;</span>;</div>
-<div class="line"><a name="l00584"></a><span class="lineno">  584</span>&#160; </div>
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-<div class="line"><a name="l00586"></a><span class="lineno">  586</span>&#160;    <a class="code" href="../../d4/def/kohonen__som__topology_8cpp.html#a6d0455dd5c30adda100e95f0423c786e">test3</a>();</div>
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-<div class="line"><a name="l00588"></a><span class="lineno">  588</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 3 completed in &quot;</span> &lt;&lt; <a class="code" href="../../d4/def/kohonen__som__topology_8cpp.html#a2256c10b16edba377b64a44b6c656908">get_clock_diff</a>(start_clk, end_clk)</div>
-<div class="line"><a name="l00589"></a><span class="lineno">  589</span>&#160;              &lt;&lt; <span class="stringliteral">&quot; sec\n&quot;</span>;</div>
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-<div class="line"><a name="l00591"></a><span class="lineno">  591</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div>
-<div class="line"><a name="l00592"></a><span class="lineno">  592</span>&#160;        &lt;&lt; <span class="stringliteral">&quot;(Note: Calculated times include: creating test sets, training &quot;</span></div>
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-<div class="line"><a name="l00595"></a><span class="lineno">  595</span>&#160;}</div>
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+<div class="line"><a name="l00580"></a><span class="lineno">  580</span>&#160; </div>
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 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
@@ -297,36 +297,36 @@ Here is the call graph for this function:</div>
 <li><code>w11.csv</code>: initial random map</li>
 <li><code>w12.csv</code>: trained SOM map </li>
 </ul>
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-<div class="line"><a name="l00383"></a><span class="lineno">  383</span>&#160;    <a class="code" href="../../d8/d77/namespacemachine__learning.html#a1d577f5d95b774ae97eb6838852d0df5">save_u_matrix</a>(<span class="stringliteral">&quot;w11.csv&quot;</span>, W);   <span class="comment">// save initial random weights</span></div>
-<div class="line"><a name="l00384"></a><span class="lineno">  384</span>&#160;    <a class="code" href="../../d8/d77/namespacemachine__learning.html#adc731720947b4bc2ab047c141e7d0299">kohonen_som</a>(X, &amp;W, 1e-4);      <span class="comment">// train the SOM</span></div>
-<div class="line"><a name="l00385"></a><span class="lineno">  385</span>&#160;    <a class="code" href="../../d8/d77/namespacemachine__learning.html#a1d577f5d95b774ae97eb6838852d0df5">save_u_matrix</a>(<span class="stringliteral">&quot;w12.csv&quot;</span>, W);   <span class="comment">// save the resultant weights</span></div>
-<div class="line"><a name="l00386"></a><span class="lineno">  386</span>&#160;}</div>
+<div class="fragment"><div class="line"><a name="l00359"></a><span class="lineno">  359</span>&#160;             {</div>
+<div class="line"><a name="l00360"></a><span class="lineno">  360</span>&#160;    <span class="keywordtype">int</span> j, N = 300;</div>
+<div class="line"><a name="l00361"></a><span class="lineno">  361</span>&#160;    <span class="keywordtype">int</span> features = 2;</div>
+<div class="line"><a name="l00362"></a><span class="lineno">  362</span>&#160;    <span class="keywordtype">int</span> num_out = 30;</div>
+<div class="line"><a name="l00363"></a><span class="lineno">  363</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::valarray&lt;double&gt;</a>&gt; X(N);</div>
+<div class="line"><a name="l00364"></a><span class="lineno">  364</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;std::valarray&lt;double&gt;</a>&gt;&gt; W(num_out);</div>
+<div class="line"><a name="l00365"></a><span class="lineno">  365</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a>(num_out, N); i++) {</div>
+<div class="line"><a name="l00366"></a><span class="lineno">  366</span>&#160;        <span class="comment">// loop till max(N, num_out)</span></div>
+<div class="line"><a name="l00367"></a><span class="lineno">  367</span>&#160;        <span class="keywordflow">if</span> (i &lt; N)  <span class="comment">// only add new arrays if i &lt; N</span></div>
+<div class="line"><a name="l00368"></a><span class="lineno">  368</span>&#160;            X[i] = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a>(features);</div>
+<div class="line"><a name="l00369"></a><span class="lineno">  369</span>&#160;        <span class="keywordflow">if</span> (i &lt; num_out) {  <span class="comment">// only add new arrays if i &lt; num_out</span></div>
+<div class="line"><a name="l00370"></a><span class="lineno">  370</span>&#160;            W[i] = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::valarray&lt;double&gt;</a>&gt;(num_out);</div>
+<div class="line"><a name="l00371"></a><span class="lineno">  371</span>&#160;            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a> = 0; <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a> &lt; num_out; <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a>++) {</div>
+<div class="line"><a name="l00372"></a><span class="lineno">  372</span>&#160;                W[i][<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a>] = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a>(features);</div>
+<div class="line"><a name="l00373"></a><span class="lineno">  373</span>&#160;<span class="preprocessor">#ifdef _OPENMP</span></div>
+<div class="line"><a name="l00374"></a><span class="lineno">  374</span>&#160;<span class="preprocessor">#pragma omp for</span></div>
+<div class="line"><a name="l00375"></a><span class="lineno">  375</span>&#160;<span class="preprocessor">#endif</span></div>
+<div class="line"><a name="l00376"></a><span class="lineno">  376</span>&#160;                <span class="keywordflow">for</span> (j = 0; j &lt; features; j++)</div>
+<div class="line"><a name="l00377"></a><span class="lineno">  377</span>&#160;                    <span class="comment">// preallocate with random initial weights</span></div>
+<div class="line"><a name="l00378"></a><span class="lineno">  378</span>&#160;                    W[i][<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a>][j] = <a class="code" href="../../d9/d66/group__machine__learning.html#gaf5ce14f026d6d231bef29161bac2b485">_random</a>(-10, 10);</div>
+<div class="line"><a name="l00379"></a><span class="lineno">  379</span>&#160;            }</div>
+<div class="line"><a name="l00380"></a><span class="lineno">  380</span>&#160;        }</div>
+<div class="line"><a name="l00381"></a><span class="lineno">  381</span>&#160;    }</div>
+<div class="line"><a name="l00382"></a><span class="lineno">  382</span>&#160; </div>
+<div class="line"><a name="l00383"></a><span class="lineno">  383</span>&#160;    <a class="code" href="../../d4/def/kohonen__som__topology_8cpp.html#a6b5e744876fd980a3451cbb385d4e755">test_2d_classes</a>(&amp;X);  <span class="comment">// create test data around circumference of a circle</span></div>
+<div class="line"><a name="l00384"></a><span class="lineno">  384</span>&#160;    <a class="code" href="../../d9/d66/group__machine__learning.html#ga6c606bc85a3e9fd9d010f874ad760336">save_2d_data</a>(<span class="stringliteral">&quot;test1.csv&quot;</span>, X);  <span class="comment">// save test data points</span></div>
+<div class="line"><a name="l00385"></a><span class="lineno">  385</span>&#160;    <a class="code" href="../../d8/d77/namespacemachine__learning.html#a1d577f5d95b774ae97eb6838852d0df5">save_u_matrix</a>(<span class="stringliteral">&quot;w11.csv&quot;</span>, W);   <span class="comment">// save initial random weights</span></div>
+<div class="line"><a name="l00386"></a><span class="lineno">  386</span>&#160;    <a class="code" href="../../d8/d77/namespacemachine__learning.html#adc731720947b4bc2ab047c141e7d0299">kohonen_som</a>(X, &amp;W, 1e-4);      <span class="comment">// train the SOM</span></div>
+<div class="line"><a name="l00387"></a><span class="lineno">  387</span>&#160;    <a class="code" href="../../d8/d77/namespacemachine__learning.html#a1d577f5d95b774ae97eb6838852d0df5">save_u_matrix</a>(<span class="stringliteral">&quot;w12.csv&quot;</span>, W);   <span class="comment">// save the resultant weights</span></div>
+<div class="line"><a name="l00388"></a><span class="lineno">  388</span>&#160;}</div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
@@ -355,36 +355,36 @@ Here is the call graph for this function:</div>
 <li><code>w21.csv</code>: initial random map</li>
 <li><code>w22.csv</code>: trained SOM map </li>
 </ul>
-<div class="fragment"><div class="line"><a name="l00437"></a><span class="lineno">  437</span>&#160;             {</div>
-<div class="line"><a name="l00438"></a><span class="lineno">  438</span>&#160;    <span class="keywordtype">int</span> j, N = 300;</div>
-<div class="line"><a name="l00439"></a><span class="lineno">  439</span>&#160;    <span class="keywordtype">int</span> features = 3;</div>
-<div class="line"><a name="l00440"></a><span class="lineno">  440</span>&#160;    <span class="keywordtype">int</span> num_out = 30;</div>
-<div class="line"><a name="l00441"></a><span class="lineno">  441</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::valarray&lt;double&gt;</a>&gt; X(N);</div>
-<div class="line"><a name="l00442"></a><span class="lineno">  442</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;std::valarray&lt;double&gt;</a>&gt;&gt; W(num_out);</div>
-<div class="line"><a name="l00443"></a><span class="lineno">  443</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a>(num_out, N); i++) {</div>
-<div class="line"><a name="l00444"></a><span class="lineno">  444</span>&#160;        <span class="comment">// loop till max(N, num_out)</span></div>
-<div class="line"><a name="l00445"></a><span class="lineno">  445</span>&#160;        <span class="keywordflow">if</span> (i &lt; N)  <span class="comment">// only add new arrays if i &lt; N</span></div>
-<div class="line"><a name="l00446"></a><span class="lineno">  446</span>&#160;            X[i] = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a>(features);</div>
-<div class="line"><a name="l00447"></a><span class="lineno">  447</span>&#160;        <span class="keywordflow">if</span> (i &lt; num_out) {  <span class="comment">// only add new arrays if i &lt; num_out</span></div>
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-<div class="line"><a name="l00449"></a><span class="lineno">  449</span>&#160;            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a> = 0; <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a> &lt; num_out; <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a>++) {</div>
-<div class="line"><a name="l00450"></a><span class="lineno">  450</span>&#160;                W[i][<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a>] = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a>(features);</div>
-<div class="line"><a name="l00451"></a><span class="lineno">  451</span>&#160;<span class="preprocessor">#ifdef _OPENMP</span></div>
-<div class="line"><a name="l00452"></a><span class="lineno">  452</span>&#160;<span class="preprocessor">#pragma omp for</span></div>
-<div class="line"><a name="l00453"></a><span class="lineno">  453</span>&#160;<span class="preprocessor">#endif</span></div>
-<div class="line"><a name="l00454"></a><span class="lineno">  454</span>&#160;                <span class="keywordflow">for</span> (j = 0; j &lt; features; j++)</div>
-<div class="line"><a name="l00455"></a><span class="lineno">  455</span>&#160;                    <span class="comment">// preallocate with random initial weights</span></div>
-<div class="line"><a name="l00456"></a><span class="lineno">  456</span>&#160;                    W[i][<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a>][j] = <a class="code" href="../../d9/d66/group__machine__learning.html#gaf5ce14f026d6d231bef29161bac2b485">_random</a>(-10, 10);</div>
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-<div class="line"><a name="l00458"></a><span class="lineno">  458</span>&#160;        }</div>
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-<div class="line"><a name="l00460"></a><span class="lineno">  460</span>&#160; </div>
-<div class="line"><a name="l00461"></a><span class="lineno">  461</span>&#160;    <a class="code" href="../../d4/def/kohonen__som__topology_8cpp.html#ab3081e021270ba21a9fd88646f6a6e26">test_3d_classes1</a>(&amp;X);  <span class="comment">// create test data around circumference of a circle</span></div>
-<div class="line"><a name="l00462"></a><span class="lineno">  462</span>&#160;    <a class="code" href="../../d9/d66/group__machine__learning.html#ga6c606bc85a3e9fd9d010f874ad760336">save_2d_data</a>(<span class="stringliteral">&quot;test2.csv&quot;</span>, X);  <span class="comment">// save test data points</span></div>
-<div class="line"><a name="l00463"></a><span class="lineno">  463</span>&#160;    <a class="code" href="../../d8/d77/namespacemachine__learning.html#a1d577f5d95b774ae97eb6838852d0df5">save_u_matrix</a>(<span class="stringliteral">&quot;w21.csv&quot;</span>, W);   <span class="comment">// save initial random weights</span></div>
-<div class="line"><a name="l00464"></a><span class="lineno">  464</span>&#160;    <a class="code" href="../../d8/d77/namespacemachine__learning.html#adc731720947b4bc2ab047c141e7d0299">kohonen_som</a>(X, &amp;W, 1e-4);      <span class="comment">// train the SOM</span></div>
-<div class="line"><a name="l00465"></a><span class="lineno">  465</span>&#160;    <a class="code" href="../../d8/d77/namespacemachine__learning.html#a1d577f5d95b774ae97eb6838852d0df5">save_u_matrix</a>(<span class="stringliteral">&quot;w22.csv&quot;</span>, W);   <span class="comment">// save the resultant weights</span></div>
-<div class="line"><a name="l00466"></a><span class="lineno">  466</span>&#160;}</div>
+<div class="fragment"><div class="line"><a name="l00439"></a><span class="lineno">  439</span>&#160;             {</div>
+<div class="line"><a name="l00440"></a><span class="lineno">  440</span>&#160;    <span class="keywordtype">int</span> j, N = 300;</div>
+<div class="line"><a name="l00441"></a><span class="lineno">  441</span>&#160;    <span class="keywordtype">int</span> features = 3;</div>
+<div class="line"><a name="l00442"></a><span class="lineno">  442</span>&#160;    <span class="keywordtype">int</span> num_out = 30;</div>
+<div class="line"><a name="l00443"></a><span class="lineno">  443</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::valarray&lt;double&gt;</a>&gt; X(N);</div>
+<div class="line"><a name="l00444"></a><span class="lineno">  444</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;std::valarray&lt;double&gt;</a>&gt;&gt; W(num_out);</div>
+<div class="line"><a name="l00445"></a><span class="lineno">  445</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a>(num_out, N); i++) {</div>
+<div class="line"><a name="l00446"></a><span class="lineno">  446</span>&#160;        <span class="comment">// loop till max(N, num_out)</span></div>
+<div class="line"><a name="l00447"></a><span class="lineno">  447</span>&#160;        <span class="keywordflow">if</span> (i &lt; N)  <span class="comment">// only add new arrays if i &lt; N</span></div>
+<div class="line"><a name="l00448"></a><span class="lineno">  448</span>&#160;            X[i] = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a>(features);</div>
+<div class="line"><a name="l00449"></a><span class="lineno">  449</span>&#160;        <span class="keywordflow">if</span> (i &lt; num_out) {  <span class="comment">// only add new arrays if i &lt; num_out</span></div>
+<div class="line"><a name="l00450"></a><span class="lineno">  450</span>&#160;            W[i] = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::valarray&lt;double&gt;</a>&gt;(num_out);</div>
+<div class="line"><a name="l00451"></a><span class="lineno">  451</span>&#160;            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a> = 0; <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a> &lt; num_out; <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a>++) {</div>
+<div class="line"><a name="l00452"></a><span class="lineno">  452</span>&#160;                W[i][<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a>] = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a>(features);</div>
+<div class="line"><a name="l00453"></a><span class="lineno">  453</span>&#160;<span class="preprocessor">#ifdef _OPENMP</span></div>
+<div class="line"><a name="l00454"></a><span class="lineno">  454</span>&#160;<span class="preprocessor">#pragma omp for</span></div>
+<div class="line"><a name="l00455"></a><span class="lineno">  455</span>&#160;<span class="preprocessor">#endif</span></div>
+<div class="line"><a name="l00456"></a><span class="lineno">  456</span>&#160;                <span class="keywordflow">for</span> (j = 0; j &lt; features; j++)</div>
+<div class="line"><a name="l00457"></a><span class="lineno">  457</span>&#160;                    <span class="comment">// preallocate with random initial weights</span></div>
+<div class="line"><a name="l00458"></a><span class="lineno">  458</span>&#160;                    W[i][<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a>][j] = <a class="code" href="../../d9/d66/group__machine__learning.html#gaf5ce14f026d6d231bef29161bac2b485">_random</a>(-10, 10);</div>
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+<div class="line"><a name="l00460"></a><span class="lineno">  460</span>&#160;        }</div>
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+<div class="line"><a name="l00462"></a><span class="lineno">  462</span>&#160; </div>
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+<div class="line"><a name="l00464"></a><span class="lineno">  464</span>&#160;    <a class="code" href="../../d9/d66/group__machine__learning.html#ga6c606bc85a3e9fd9d010f874ad760336">save_2d_data</a>(<span class="stringliteral">&quot;test2.csv&quot;</span>, X);  <span class="comment">// save test data points</span></div>
+<div class="line"><a name="l00465"></a><span class="lineno">  465</span>&#160;    <a class="code" href="../../d8/d77/namespacemachine__learning.html#a1d577f5d95b774ae97eb6838852d0df5">save_u_matrix</a>(<span class="stringliteral">&quot;w21.csv&quot;</span>, W);   <span class="comment">// save initial random weights</span></div>
+<div class="line"><a name="l00466"></a><span class="lineno">  466</span>&#160;    <a class="code" href="../../d8/d77/namespacemachine__learning.html#adc731720947b4bc2ab047c141e7d0299">kohonen_som</a>(X, &amp;W, 1e-4);      <span class="comment">// train the SOM</span></div>
+<div class="line"><a name="l00467"></a><span class="lineno">  467</span>&#160;    <a class="code" href="../../d8/d77/namespacemachine__learning.html#a1d577f5d95b774ae97eb6838852d0df5">save_u_matrix</a>(<span class="stringliteral">&quot;w22.csv&quot;</span>, W);   <span class="comment">// save the resultant weights</span></div>
+<div class="line"><a name="l00468"></a><span class="lineno">  468</span>&#160;}</div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
@@ -413,36 +413,36 @@ Here is the call graph for this function:</div>
 <li><code>w31.csv</code>: initial random map</li>
 <li><code>w32.csv</code>: trained SOM map </li>
 </ul>
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-<div class="line"><a name="l00528"></a><span class="lineno">  528</span>&#160;        <span class="comment">// loop till max(N, num_out)</span></div>
-<div class="line"><a name="l00529"></a><span class="lineno">  529</span>&#160;        <span class="keywordflow">if</span> (i &lt; N)  <span class="comment">// only add new arrays if i &lt; N</span></div>
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-<div class="line"><a name="l00538"></a><span class="lineno">  538</span>&#160;                <span class="keywordflow">for</span> (j = 0; j &lt; features; j++)</div>
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-<div class="line"><a name="l00542"></a><span class="lineno">  542</span>&#160;        }</div>
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-<div class="line"><a name="l00546"></a><span class="lineno">  546</span>&#160;    <a class="code" href="../../d9/d66/group__machine__learning.html#ga6c606bc85a3e9fd9d010f874ad760336">save_2d_data</a>(<span class="stringliteral">&quot;test3.csv&quot;</span>, X);  <span class="comment">// save test data points</span></div>
-<div class="line"><a name="l00547"></a><span class="lineno">  547</span>&#160;    <a class="code" href="../../d8/d77/namespacemachine__learning.html#a1d577f5d95b774ae97eb6838852d0df5">save_u_matrix</a>(<span class="stringliteral">&quot;w31.csv&quot;</span>, W);   <span class="comment">// save initial random weights</span></div>
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-<div class="line"><a name="l00549"></a><span class="lineno">  549</span>&#160;    <a class="code" href="../../d8/d77/namespacemachine__learning.html#a1d577f5d95b774ae97eb6838852d0df5">save_u_matrix</a>(<span class="stringliteral">&quot;w32.csv&quot;</span>, W);   <span class="comment">// save the resultant weights</span></div>
-<div class="line"><a name="l00550"></a><span class="lineno">  550</span>&#160;}</div>
+<div class="fragment"><div class="line"><a name="l00523"></a><span class="lineno">  523</span>&#160;             {</div>
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+<div class="line"><a name="l00526"></a><span class="lineno">  526</span>&#160;    <span class="keywordtype">int</span> num_out = 30;</div>
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+<div class="line"><a name="l00528"></a><span class="lineno">  528</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;std::valarray&lt;double&gt;</a>&gt;&gt; W(num_out);</div>
+<div class="line"><a name="l00529"></a><span class="lineno">  529</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a>(num_out, N); i++) {</div>
+<div class="line"><a name="l00530"></a><span class="lineno">  530</span>&#160;        <span class="comment">// loop till max(N, num_out)</span></div>
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+<div class="line"><a name="l00533"></a><span class="lineno">  533</span>&#160;        <span class="keywordflow">if</span> (i &lt; num_out) {  <span class="comment">// only add new arrays if i &lt; num_out</span></div>
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+<div class="line"><a name="l00537"></a><span class="lineno">  537</span>&#160;<span class="preprocessor">#ifdef _OPENMP</span></div>
+<div class="line"><a name="l00538"></a><span class="lineno">  538</span>&#160;<span class="preprocessor">#pragma omp for</span></div>
+<div class="line"><a name="l00539"></a><span class="lineno">  539</span>&#160;<span class="preprocessor">#endif</span></div>
+<div class="line"><a name="l00540"></a><span class="lineno">  540</span>&#160;                <span class="keywordflow">for</span> (j = 0; j &lt; features; j++)</div>
+<div class="line"><a name="l00541"></a><span class="lineno">  541</span>&#160;                    <span class="comment">// preallocate with random initial weights</span></div>
+<div class="line"><a name="l00542"></a><span class="lineno">  542</span>&#160;                    W[i][<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a>][j] = <a class="code" href="../../d9/d66/group__machine__learning.html#gaf5ce14f026d6d231bef29161bac2b485">_random</a>(-10, 10);</div>
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+<div class="line"><a name="l00544"></a><span class="lineno">  544</span>&#160;        }</div>
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+<div class="line"><a name="l00546"></a><span class="lineno">  546</span>&#160; </div>
+<div class="line"><a name="l00547"></a><span class="lineno">  547</span>&#160;    <a class="code" href="../../d4/def/kohonen__som__topology_8cpp.html#a0e7435446ed7c763f7de79a468add2e0">test_3d_classes2</a>(&amp;X);  <span class="comment">// create test data around circumference of a circle</span></div>
+<div class="line"><a name="l00548"></a><span class="lineno">  548</span>&#160;    <a class="code" href="../../d9/d66/group__machine__learning.html#ga6c606bc85a3e9fd9d010f874ad760336">save_2d_data</a>(<span class="stringliteral">&quot;test3.csv&quot;</span>, X);  <span class="comment">// save test data points</span></div>
+<div class="line"><a name="l00549"></a><span class="lineno">  549</span>&#160;    <a class="code" href="../../d8/d77/namespacemachine__learning.html#a1d577f5d95b774ae97eb6838852d0df5">save_u_matrix</a>(<span class="stringliteral">&quot;w31.csv&quot;</span>, W);   <span class="comment">// save initial random weights</span></div>
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+<div class="line"><a name="l00551"></a><span class="lineno">  551</span>&#160;    <a class="code" href="../../d8/d77/namespacemachine__learning.html#a1d577f5d95b774ae97eb6838852d0df5">save_u_matrix</a>(<span class="stringliteral">&quot;w32.csv&quot;</span>, W);   <span class="comment">// save the resultant weights</span></div>
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 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
@@ -479,36 +479,36 @@ Here is the call graph for this function:</div>
   </table>
   </dd>
 </dl>
-<div class="fragment"><div class="line"><a name="l00318"></a><span class="lineno">  318</span>&#160;                                                           {</div>
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-<div class="line"><a name="l00321"></a><span class="lineno">  321</span>&#160;    <span class="keywordtype">int</span> i;</div>
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+<div class="line"><a name="l00340"></a><span class="lineno">  340</span>&#160;        <span class="comment">// create random coordinates (x,y,z) around the centre of the class</span></div>
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+<div class="line"><a name="l00342"></a><span class="lineno">  342</span>&#160;        <a class="code" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>[0][i][1] = <a class="code" href="../../d9/d66/group__machine__learning.html#gaf5ce14f026d6d231bef29161bac2b485">_random</a>(centres[cls][1] - R, centres[cls][1] + R);</div>
+<div class="line"><a name="l00343"></a><span class="lineno">  343</span>&#160; </div>
+<div class="line"><a name="l00344"></a><span class="lineno">  344</span>&#160;        <span class="comment">/* The follosing can also be used</span></div>
+<div class="line"><a name="l00345"></a><span class="lineno">  345</span>&#160;<span class="comment">        for (int j = 0; j &lt; 2; j++)</span></div>
+<div class="line"><a name="l00346"></a><span class="lineno">  346</span>&#160;<span class="comment">            data[i][j] = _random(centres[class][j] - R, centres[class][j] + R);</span></div>
+<div class="line"><a name="l00347"></a><span class="lineno">  347</span>&#160;<span class="comment">        */</span></div>
+<div class="line"><a name="l00348"></a><span class="lineno">  348</span>&#160;    }</div>
+<div class="line"><a name="l00349"></a><span class="lineno">  349</span>&#160;}</div>
 </div><!-- fragment --><div class="dynheader">
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@@ -545,37 +545,37 @@ Here is the call graph for this function:</div>
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-<div class="fragment"><div class="line"><a name="l00397"></a><span class="lineno">  397</span>&#160;                                                            {</div>
-<div class="line"><a name="l00398"></a><span class="lineno">  398</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">int</span> N = <a class="code" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>-&gt;size();</div>
-<div class="line"><a name="l00399"></a><span class="lineno">  399</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">double</span> R = 0.3;  <span class="comment">// radius of cluster</span></div>
-<div class="line"><a name="l00400"></a><span class="lineno">  400</span>&#160;    <span class="keywordtype">int</span> i;</div>
-<div class="line"><a name="l00401"></a><span class="lineno">  401</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">int</span> num_classes = 4;</div>
-<div class="line"><a name="l00402"></a><span class="lineno">  402</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">double</span> centres[][3] = {</div>
-<div class="line"><a name="l00403"></a><span class="lineno">  403</span>&#160;        <span class="comment">// centres of each class cluster</span></div>
-<div class="line"><a name="l00404"></a><span class="lineno">  404</span>&#160;        {.5, .5, .5},    <span class="comment">// centre of class 1</span></div>
-<div class="line"><a name="l00405"></a><span class="lineno">  405</span>&#160;        {.5, -.5, -.5},  <span class="comment">// centre of class 2</span></div>
-<div class="line"><a name="l00406"></a><span class="lineno">  406</span>&#160;        {-.5, .5, .5},   <span class="comment">// centre of class 3</span></div>
-<div class="line"><a name="l00407"></a><span class="lineno">  407</span>&#160;        {-.5, -.5 - .5}  <span class="comment">// centre of class 4</span></div>
-<div class="line"><a name="l00408"></a><span class="lineno">  408</span>&#160;    };</div>
-<div class="line"><a name="l00409"></a><span class="lineno">  409</span>&#160; </div>
-<div class="line"><a name="l00410"></a><span class="lineno">  410</span>&#160;<span class="preprocessor">#ifdef _OPENMP</span></div>
-<div class="line"><a name="l00411"></a><span class="lineno">  411</span>&#160;<span class="preprocessor">#pragma omp for</span></div>
-<div class="line"><a name="l00412"></a><span class="lineno">  412</span>&#160;<span class="preprocessor">#endif</span></div>
-<div class="line"><a name="l00413"></a><span class="lineno">  413</span>&#160;    <span class="keywordflow">for</span> (i = 0; i &lt; N; i++) {</div>
-<div class="line"><a name="l00414"></a><span class="lineno">  414</span>&#160;        <span class="comment">// select a random class for the point</span></div>
-<div class="line"><a name="l00415"></a><span class="lineno">  415</span>&#160;        <span class="keywordtype">int</span> cls = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % num_classes;</div>
-<div class="line"><a name="l00416"></a><span class="lineno">  416</span>&#160; </div>
-<div class="line"><a name="l00417"></a><span class="lineno">  417</span>&#160;        <span class="comment">// create random coordinates (x,y,z) around the centre of the class</span></div>
-<div class="line"><a name="l00418"></a><span class="lineno">  418</span>&#160;        <a class="code" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>[0][i][0] = <a class="code" href="../../d9/d66/group__machine__learning.html#gaf5ce14f026d6d231bef29161bac2b485">_random</a>(centres[cls][0] - R, centres[cls][0] + R);</div>
-<div class="line"><a name="l00419"></a><span class="lineno">  419</span>&#160;        <a class="code" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>[0][i][1] = <a class="code" href="../../d9/d66/group__machine__learning.html#gaf5ce14f026d6d231bef29161bac2b485">_random</a>(centres[cls][1] - R, centres[cls][1] + R);</div>
-<div class="line"><a name="l00420"></a><span class="lineno">  420</span>&#160;        <a class="code" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>[0][i][2] = <a class="code" href="../../d9/d66/group__machine__learning.html#gaf5ce14f026d6d231bef29161bac2b485">_random</a>(centres[cls][2] - R, centres[cls][2] + R);</div>
-<div class="line"><a name="l00421"></a><span class="lineno">  421</span>&#160; </div>
-<div class="line"><a name="l00422"></a><span class="lineno">  422</span>&#160;        <span class="comment">/* The follosing can also be used</span></div>
-<div class="line"><a name="l00423"></a><span class="lineno">  423</span>&#160;<span class="comment">        for (int j = 0; j &lt; 3; j++)</span></div>
-<div class="line"><a name="l00424"></a><span class="lineno">  424</span>&#160;<span class="comment">            data[i][j] = _random(centres[class][j] - R, centres[class][j] + R);</span></div>
-<div class="line"><a name="l00425"></a><span class="lineno">  425</span>&#160;<span class="comment">        */</span></div>
-<div class="line"><a name="l00426"></a><span class="lineno">  426</span>&#160;    }</div>
-<div class="line"><a name="l00427"></a><span class="lineno">  427</span>&#160;}</div>
+<div class="fragment"><div class="line"><a name="l00399"></a><span class="lineno">  399</span>&#160;                                                            {</div>
+<div class="line"><a name="l00400"></a><span class="lineno">  400</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">int</span> N = <a class="code" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>-&gt;size();</div>
+<div class="line"><a name="l00401"></a><span class="lineno">  401</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">double</span> R = 0.3;  <span class="comment">// radius of cluster</span></div>
+<div class="line"><a name="l00402"></a><span class="lineno">  402</span>&#160;    <span class="keywordtype">int</span> i;</div>
+<div class="line"><a name="l00403"></a><span class="lineno">  403</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">int</span> num_classes = 4;</div>
+<div class="line"><a name="l00404"></a><span class="lineno">  404</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">double</span> centres[][3] = {</div>
+<div class="line"><a name="l00405"></a><span class="lineno">  405</span>&#160;        <span class="comment">// centres of each class cluster</span></div>
+<div class="line"><a name="l00406"></a><span class="lineno">  406</span>&#160;        {.5, .5, .5},    <span class="comment">// centre of class 1</span></div>
+<div class="line"><a name="l00407"></a><span class="lineno">  407</span>&#160;        {.5, -.5, -.5},  <span class="comment">// centre of class 2</span></div>
+<div class="line"><a name="l00408"></a><span class="lineno">  408</span>&#160;        {-.5, .5, .5},   <span class="comment">// centre of class 3</span></div>
+<div class="line"><a name="l00409"></a><span class="lineno">  409</span>&#160;        {-.5, -.5 - .5}  <span class="comment">// centre of class 4</span></div>
+<div class="line"><a name="l00410"></a><span class="lineno">  410</span>&#160;    };</div>
+<div class="line"><a name="l00411"></a><span class="lineno">  411</span>&#160; </div>
+<div class="line"><a name="l00412"></a><span class="lineno">  412</span>&#160;<span class="preprocessor">#ifdef _OPENMP</span></div>
+<div class="line"><a name="l00413"></a><span class="lineno">  413</span>&#160;<span class="preprocessor">#pragma omp for</span></div>
+<div class="line"><a name="l00414"></a><span class="lineno">  414</span>&#160;<span class="preprocessor">#endif</span></div>
+<div class="line"><a name="l00415"></a><span class="lineno">  415</span>&#160;    <span class="keywordflow">for</span> (i = 0; i &lt; N; i++) {</div>
+<div class="line"><a name="l00416"></a><span class="lineno">  416</span>&#160;        <span class="comment">// select a random class for the point</span></div>
+<div class="line"><a name="l00417"></a><span class="lineno">  417</span>&#160;        <span class="keywordtype">int</span> cls = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % num_classes;</div>
+<div class="line"><a name="l00418"></a><span class="lineno">  418</span>&#160; </div>
+<div class="line"><a name="l00419"></a><span class="lineno">  419</span>&#160;        <span class="comment">// create random coordinates (x,y,z) around the centre of the class</span></div>
+<div class="line"><a name="l00420"></a><span class="lineno">  420</span>&#160;        <a class="code" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>[0][i][0] = <a class="code" href="../../d9/d66/group__machine__learning.html#gaf5ce14f026d6d231bef29161bac2b485">_random</a>(centres[cls][0] - R, centres[cls][0] + R);</div>
+<div class="line"><a name="l00421"></a><span class="lineno">  421</span>&#160;        <a class="code" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>[0][i][1] = <a class="code" href="../../d9/d66/group__machine__learning.html#gaf5ce14f026d6d231bef29161bac2b485">_random</a>(centres[cls][1] - R, centres[cls][1] + R);</div>
+<div class="line"><a name="l00422"></a><span class="lineno">  422</span>&#160;        <a class="code" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>[0][i][2] = <a class="code" href="../../d9/d66/group__machine__learning.html#gaf5ce14f026d6d231bef29161bac2b485">_random</a>(centres[cls][2] - R, centres[cls][2] + R);</div>
+<div class="line"><a name="l00423"></a><span class="lineno">  423</span>&#160; </div>
+<div class="line"><a name="l00424"></a><span class="lineno">  424</span>&#160;        <span class="comment">/* The follosing can also be used</span></div>
+<div class="line"><a name="l00425"></a><span class="lineno">  425</span>&#160;<span class="comment">        for (int j = 0; j &lt; 3; j++)</span></div>
+<div class="line"><a name="l00426"></a><span class="lineno">  426</span>&#160;<span class="comment">            data[i][j] = _random(centres[class][j] - R, centres[class][j] + R);</span></div>
+<div class="line"><a name="l00427"></a><span class="lineno">  427</span>&#160;<span class="comment">        */</span></div>
+<div class="line"><a name="l00428"></a><span class="lineno">  428</span>&#160;    }</div>
+<div class="line"><a name="l00429"></a><span class="lineno">  429</span>&#160;}</div>
 </div><!-- fragment --><div class="dynheader">
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 <div class="dyncontent">
@@ -612,41 +612,41 @@ Here is the call graph for this function:</div>
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   </dd>
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-<div class="fragment"><div class="line"><a name="l00477"></a><span class="lineno">  477</span>&#160;                                                            {</div>
-<div class="line"><a name="l00478"></a><span class="lineno">  478</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">int</span> N = <a class="code" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>-&gt;size();</div>
-<div class="line"><a name="l00479"></a><span class="lineno">  479</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">double</span> R = 0.2;  <span class="comment">// radius of cluster</span></div>
-<div class="line"><a name="l00480"></a><span class="lineno">  480</span>&#160;    <span class="keywordtype">int</span> i;</div>
-<div class="line"><a name="l00481"></a><span class="lineno">  481</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">int</span> num_classes = 8;</div>
-<div class="line"><a name="l00482"></a><span class="lineno">  482</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">double</span> centres[][3] = {</div>
-<div class="line"><a name="l00483"></a><span class="lineno">  483</span>&#160;        <span class="comment">// centres of each class cluster</span></div>
-<div class="line"><a name="l00484"></a><span class="lineno">  484</span>&#160;        {.5, .5, .5},    <span class="comment">// centre of class 1</span></div>
-<div class="line"><a name="l00485"></a><span class="lineno">  485</span>&#160;        {.5, .5, -.5},   <span class="comment">// centre of class 2</span></div>
-<div class="line"><a name="l00486"></a><span class="lineno">  486</span>&#160;        {.5, -.5, .5},   <span class="comment">// centre of class 3</span></div>
-<div class="line"><a name="l00487"></a><span class="lineno">  487</span>&#160;        {.5, -.5, -.5},  <span class="comment">// centre of class 4</span></div>
-<div class="line"><a name="l00488"></a><span class="lineno">  488</span>&#160;        {-.5, .5, .5},   <span class="comment">// centre of class 5</span></div>
-<div class="line"><a name="l00489"></a><span class="lineno">  489</span>&#160;        {-.5, .5, -.5},  <span class="comment">// centre of class 6</span></div>
-<div class="line"><a name="l00490"></a><span class="lineno">  490</span>&#160;        {-.5, -.5, .5},  <span class="comment">// centre of class 7</span></div>
-<div class="line"><a name="l00491"></a><span class="lineno">  491</span>&#160;        {-.5, -.5, -.5}  <span class="comment">// centre of class 8</span></div>
-<div class="line"><a name="l00492"></a><span class="lineno">  492</span>&#160;    };</div>
-<div class="line"><a name="l00493"></a><span class="lineno">  493</span>&#160; </div>
-<div class="line"><a name="l00494"></a><span class="lineno">  494</span>&#160;<span class="preprocessor">#ifdef _OPENMP</span></div>
-<div class="line"><a name="l00495"></a><span class="lineno">  495</span>&#160;<span class="preprocessor">#pragma omp for</span></div>
-<div class="line"><a name="l00496"></a><span class="lineno">  496</span>&#160;<span class="preprocessor">#endif</span></div>
-<div class="line"><a name="l00497"></a><span class="lineno">  497</span>&#160;    <span class="keywordflow">for</span> (i = 0; i &lt; N; i++) {</div>
-<div class="line"><a name="l00498"></a><span class="lineno">  498</span>&#160;        <span class="comment">// select a random class for the point</span></div>
-<div class="line"><a name="l00499"></a><span class="lineno">  499</span>&#160;        <span class="keywordtype">int</span> cls = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % num_classes;</div>
-<div class="line"><a name="l00500"></a><span class="lineno">  500</span>&#160; </div>
-<div class="line"><a name="l00501"></a><span class="lineno">  501</span>&#160;        <span class="comment">// create random coordinates (x,y,z) around the centre of the class</span></div>
-<div class="line"><a name="l00502"></a><span class="lineno">  502</span>&#160;        <a class="code" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>[0][i][0] = <a class="code" href="../../d9/d66/group__machine__learning.html#gaf5ce14f026d6d231bef29161bac2b485">_random</a>(centres[cls][0] - R, centres[cls][0] + R);</div>
-<div class="line"><a name="l00503"></a><span class="lineno">  503</span>&#160;        <a class="code" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>[0][i][1] = <a class="code" href="../../d9/d66/group__machine__learning.html#gaf5ce14f026d6d231bef29161bac2b485">_random</a>(centres[cls][1] - R, centres[cls][1] + R);</div>
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-<div class="line"><a name="l00505"></a><span class="lineno">  505</span>&#160; </div>
-<div class="line"><a name="l00506"></a><span class="lineno">  506</span>&#160;        <span class="comment">/* The follosing can also be used</span></div>
-<div class="line"><a name="l00507"></a><span class="lineno">  507</span>&#160;<span class="comment">        for (int j = 0; j &lt; 3; j++)</span></div>
-<div class="line"><a name="l00508"></a><span class="lineno">  508</span>&#160;<span class="comment">            data[i][j] = _random(centres[class][j] - R, centres[class][j] + R);</span></div>
-<div class="line"><a name="l00509"></a><span class="lineno">  509</span>&#160;<span class="comment">        */</span></div>
-<div class="line"><a name="l00510"></a><span class="lineno">  510</span>&#160;    }</div>
-<div class="line"><a name="l00511"></a><span class="lineno">  511</span>&#160;}</div>
+<div class="fragment"><div class="line"><a name="l00479"></a><span class="lineno">  479</span>&#160;                                                            {</div>
+<div class="line"><a name="l00480"></a><span class="lineno">  480</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">int</span> N = <a class="code" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>-&gt;size();</div>
+<div class="line"><a name="l00481"></a><span class="lineno">  481</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">double</span> R = 0.2;  <span class="comment">// radius of cluster</span></div>
+<div class="line"><a name="l00482"></a><span class="lineno">  482</span>&#160;    <span class="keywordtype">int</span> i;</div>
+<div class="line"><a name="l00483"></a><span class="lineno">  483</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">int</span> num_classes = 8;</div>
+<div class="line"><a name="l00484"></a><span class="lineno">  484</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">double</span> centres[][3] = {</div>
+<div class="line"><a name="l00485"></a><span class="lineno">  485</span>&#160;        <span class="comment">// centres of each class cluster</span></div>
+<div class="line"><a name="l00486"></a><span class="lineno">  486</span>&#160;        {.5, .5, .5},    <span class="comment">// centre of class 1</span></div>
+<div class="line"><a name="l00487"></a><span class="lineno">  487</span>&#160;        {.5, .5, -.5},   <span class="comment">// centre of class 2</span></div>
+<div class="line"><a name="l00488"></a><span class="lineno">  488</span>&#160;        {.5, -.5, .5},   <span class="comment">// centre of class 3</span></div>
+<div class="line"><a name="l00489"></a><span class="lineno">  489</span>&#160;        {.5, -.5, -.5},  <span class="comment">// centre of class 4</span></div>
+<div class="line"><a name="l00490"></a><span class="lineno">  490</span>&#160;        {-.5, .5, .5},   <span class="comment">// centre of class 5</span></div>
+<div class="line"><a name="l00491"></a><span class="lineno">  491</span>&#160;        {-.5, .5, -.5},  <span class="comment">// centre of class 6</span></div>
+<div class="line"><a name="l00492"></a><span class="lineno">  492</span>&#160;        {-.5, -.5, .5},  <span class="comment">// centre of class 7</span></div>
+<div class="line"><a name="l00493"></a><span class="lineno">  493</span>&#160;        {-.5, -.5, -.5}  <span class="comment">// centre of class 8</span></div>
+<div class="line"><a name="l00494"></a><span class="lineno">  494</span>&#160;    };</div>
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+    <li class="footer">Generated on Mon Jun 22 2020 11:53:38 for Algorithms_in_C++ by
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:37 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:39 for Algorithms_in_C++ by
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+    <li class="footer">Generated on Mon Jun 22 2020 11:53:40 for Algorithms_in_C++ by
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:38 for Algorithms_in_C++ by
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:37 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:40 for Algorithms_in_C++ by
     <a href="http://www.doxygen.org/index.html">
     <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
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diff --git a/d5/db0/adaline__learning_8cpp.html b/d5/db0/adaline__learning_8cpp.html
index 8af34c29a..db24b0003 100644
--- a/d5/db0/adaline__learning_8cpp.html
+++ b/d5/db0/adaline__learning_8cpp.html
@@ -148,7 +148,8 @@ Functions</h2></td></tr>
 <a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
 <div class="textblock"><p><a href="https://en.wikipedia.org/wiki/ADALINE">Adaptive Linear Neuron (ADALINE)</a> implementation </p>
 <dl class="section author"><dt>Author</dt><dd><a href="https://github.com/kvedala">Krishna Vedala</a></dd></dl>
-<p><img src="https://upload.wikimedia.org/wikipedia/commons/b/be/Adaline_flow_chart.gif" alt="" width="200px" class="inline"/> <a href="https://commons.wikimedia.org/wiki/File:Adaline_flow_chart.gif">source</a> ADALINE is one of the first and simplest single layer artificial neural network. The algorithm essentially implements a linear function </p><p class="formulaDsp">
+<p><a href="https://commons.wikimedia.org/wiki/File:Adaline_flow_chart.gif"><img src="https://upload.wikimedia.org/wikipedia/commons/b/be/Adaline_flow_chart.gif" alt="Structure of an ADALINE network. Source: Wikipedia" style="width:200px; float:right;" class="inline"/></a></p>
+<p>ADALINE is one of the first and simplest single layer artificial neural network. The algorithm essentially implements a linear function </p><p class="formulaDsp">
 \[ f\left(x_0,x_1,x_2,\ldots\right) = \sum_j x_jw_j+\theta \]
 </p>
 <p> where \(x_j\) are the input features of a sample, \(w_j\) are the coefficients of the linear function and \(\theta\) is a constant. If we know the \(w_j\), then for any given set of features, \(y\) can be computed. Computing the \(w_j\) is a supervised learning algorithm wherein a set of features and their corresponding outputs are given and weights are computed using stochastic gradient descent method. </p>
@@ -179,27 +180,27 @@ Functions</h2></td></tr>
       </table>
 </div><div class="memdoc">
 <p>Main function </p>
-<div class="fragment"><div class="line"><a name="l00331"></a><span class="lineno">  331</span>&#160;                                {</div>
-<div class="line"><a name="l00332"></a><span class="lineno">  332</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/srand.html">std::srand</a>(<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/time.html">std::time</a>(<span class="keyword">nullptr</span>));  <span class="comment">// initialize random number generator</span></div>
-<div class="line"><a name="l00333"></a><span class="lineno">  333</span>&#160; </div>
-<div class="line"><a name="l00334"></a><span class="lineno">  334</span>&#160;    <span class="keywordtype">double</span> eta = 0.1;  <span class="comment">// default value of eta</span></div>
-<div class="line"><a name="l00335"></a><span class="lineno">  335</span>&#160;    <span class="keywordflow">if</span> (argc == 2)     <span class="comment">// read eta value from commandline argument if present</span></div>
-<div class="line"><a name="l00336"></a><span class="lineno">  336</span>&#160;        eta = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/byte/strtof.html">strtof</a>(argv[1], <span class="keyword">nullptr</span>);</div>
-<div class="line"><a name="l00337"></a><span class="lineno">  337</span>&#160; </div>
-<div class="line"><a name="l00338"></a><span class="lineno">  338</span>&#160;    <a class="code" href="../../d5/db0/adaline__learning_8cpp.html#a52053d88ea1bcbbed9aca67ab4eeb499">test1</a>(eta);</div>
+<div class="fragment"><div class="line"><a name="l00333"></a><span class="lineno">  333</span>&#160;                                {</div>
+<div class="line"><a name="l00334"></a><span class="lineno">  334</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/srand.html">std::srand</a>(<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/time.html">std::time</a>(<span class="keyword">nullptr</span>));  <span class="comment">// initialize random number generator</span></div>
+<div class="line"><a name="l00335"></a><span class="lineno">  335</span>&#160; </div>
+<div class="line"><a name="l00336"></a><span class="lineno">  336</span>&#160;    <span class="keywordtype">double</span> eta = 0.1;  <span class="comment">// default value of eta</span></div>
+<div class="line"><a name="l00337"></a><span class="lineno">  337</span>&#160;    <span class="keywordflow">if</span> (argc == 2)     <span class="comment">// read eta value from commandline argument if present</span></div>
+<div class="line"><a name="l00338"></a><span class="lineno">  338</span>&#160;        eta = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/byte/strtof.html">strtof</a>(argv[1], <span class="keyword">nullptr</span>);</div>
 <div class="line"><a name="l00339"></a><span class="lineno">  339</span>&#160; </div>
-<div class="line"><a name="l00340"></a><span class="lineno">  340</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Press ENTER to continue...&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a name="l00341"></a><span class="lineno">  341</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a>.get();</div>
-<div class="line"><a name="l00342"></a><span class="lineno">  342</span>&#160; </div>
-<div class="line"><a name="l00343"></a><span class="lineno">  343</span>&#160;    <a class="code" href="../../d5/db0/adaline__learning_8cpp.html#a379f7488a305f2571f2932b319931f82">test2</a>(eta);</div>
+<div class="line"><a name="l00340"></a><span class="lineno">  340</span>&#160;    <a class="code" href="../../d5/db0/adaline__learning_8cpp.html#a52053d88ea1bcbbed9aca67ab4eeb499">test1</a>(eta);</div>
+<div class="line"><a name="l00341"></a><span class="lineno">  341</span>&#160; </div>
+<div class="line"><a name="l00342"></a><span class="lineno">  342</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Press ENTER to continue...&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00343"></a><span class="lineno">  343</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a>.get();</div>
 <div class="line"><a name="l00344"></a><span class="lineno">  344</span>&#160; </div>
-<div class="line"><a name="l00345"></a><span class="lineno">  345</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Press ENTER to continue...&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a name="l00346"></a><span class="lineno">  346</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a>.get();</div>
-<div class="line"><a name="l00347"></a><span class="lineno">  347</span>&#160; </div>
-<div class="line"><a name="l00348"></a><span class="lineno">  348</span>&#160;    <a class="code" href="../../d5/db0/adaline__learning_8cpp.html#a992bdf1fdb0b9d414bcf7981d2d87aa9">test3</a>(eta);</div>
+<div class="line"><a name="l00345"></a><span class="lineno">  345</span>&#160;    <a class="code" href="../../d5/db0/adaline__learning_8cpp.html#a379f7488a305f2571f2932b319931f82">test2</a>(eta);</div>
+<div class="line"><a name="l00346"></a><span class="lineno">  346</span>&#160; </div>
+<div class="line"><a name="l00347"></a><span class="lineno">  347</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Press ENTER to continue...&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00348"></a><span class="lineno">  348</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a>.get();</div>
 <div class="line"><a name="l00349"></a><span class="lineno">  349</span>&#160; </div>
-<div class="line"><a name="l00350"></a><span class="lineno">  350</span>&#160;    <span class="keywordflow">return</span> 0;</div>
-<div class="line"><a name="l00351"></a><span class="lineno">  351</span>&#160;}</div>
+<div class="line"><a name="l00350"></a><span class="lineno">  350</span>&#160;    <a class="code" href="../../d5/db0/adaline__learning_8cpp.html#a992bdf1fdb0b9d414bcf7981d2d87aa9">test3</a>(eta);</div>
+<div class="line"><a name="l00351"></a><span class="lineno">  351</span>&#160; </div>
+<div class="line"><a name="l00352"></a><span class="lineno">  352</span>&#160;    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><a name="l00353"></a><span class="lineno">  353</span>&#160;}</div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
@@ -230,32 +231,32 @@ Here is the call graph for this function:</div>
   </table>
   </dd>
 </dl>
-<div class="fragment"><div class="line"><a name="l00202"></a><span class="lineno">  202</span>&#160;                              {</div>
-<div class="line"><a name="l00203"></a><span class="lineno">  203</span>&#160;    <a class="code" href="../../d6/d30/classmachine__learning_1_1adaline.html">adaline</a> ada(2, eta);  <span class="comment">// 2 features</span></div>
-<div class="line"><a name="l00204"></a><span class="lineno">  204</span>&#160; </div>
-<div class="line"><a name="l00205"></a><span class="lineno">  205</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">int</span> N = 10;  <span class="comment">// number of sample points</span></div>
+<div class="fragment"><div class="line"><a name="l00204"></a><span class="lineno">  204</span>&#160;                              {</div>
+<div class="line"><a name="l00205"></a><span class="lineno">  205</span>&#160;    <a class="code" href="../../d6/d30/classmachine__learning_1_1adaline.html">adaline</a> ada(2, eta);  <span class="comment">// 2 features</span></div>
 <div class="line"><a name="l00206"></a><span class="lineno">  206</span>&#160; </div>
-<div class="line"><a name="l00207"></a><span class="lineno">  207</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;double&gt;</a> X[N] = {{0, 1},  {1, -2},   {2, 3},   {3, -1},</div>
-<div class="line"><a name="l00208"></a><span class="lineno">  208</span>&#160;                                {4, 1},  {6, -5},   {-7, -3}, {-8, 5},</div>
-<div class="line"><a name="l00209"></a><span class="lineno">  209</span>&#160;                                {-9, 2}, {-10, -15}};</div>
-<div class="line"><a name="l00210"></a><span class="lineno">  210</span>&#160;    <span class="keywordtype">int</span> y[] = {1, -1, 1, -1, -1, -1, 1, 1, 1, -1};  <span class="comment">// corresponding y-values</span></div>
-<div class="line"><a name="l00211"></a><span class="lineno">  211</span>&#160; </div>
-<div class="line"><a name="l00212"></a><span class="lineno">  212</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;------- Test 1 -------&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a name="l00213"></a><span class="lineno">  213</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Model before fit: &quot;</span> &lt;&lt; ada &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a name="l00214"></a><span class="lineno">  214</span>&#160; </div>
-<div class="line"><a name="l00215"></a><span class="lineno">  215</span>&#160;    ada.fit(X, y);</div>
-<div class="line"><a name="l00216"></a><span class="lineno">  216</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Model after fit: &quot;</span> &lt;&lt; ada &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a name="l00217"></a><span class="lineno">  217</span>&#160; </div>
-<div class="line"><a name="l00218"></a><span class="lineno">  218</span>&#160;    <span class="keywordtype">int</span> predict = ada.predict({5, -3});</div>
-<div class="line"><a name="l00219"></a><span class="lineno">  219</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Predict for x=(5,-3): &quot;</span> &lt;&lt; predict;</div>
-<div class="line"><a name="l00220"></a><span class="lineno">  220</span>&#160;    assert(predict == -1);</div>
-<div class="line"><a name="l00221"></a><span class="lineno">  221</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot; ...passed&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a name="l00222"></a><span class="lineno">  222</span>&#160; </div>
-<div class="line"><a name="l00223"></a><span class="lineno">  223</span>&#160;    predict = ada.predict({5, 8});</div>
-<div class="line"><a name="l00224"></a><span class="lineno">  224</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Predict for x=(5,8): &quot;</span> &lt;&lt; predict;</div>
-<div class="line"><a name="l00225"></a><span class="lineno">  225</span>&#160;    assert(predict == 1);</div>
-<div class="line"><a name="l00226"></a><span class="lineno">  226</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot; ...passed&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a name="l00227"></a><span class="lineno">  227</span>&#160;}</div>
+<div class="line"><a name="l00207"></a><span class="lineno">  207</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">int</span> N = 10;  <span class="comment">// number of sample points</span></div>
+<div class="line"><a name="l00208"></a><span class="lineno">  208</span>&#160; </div>
+<div class="line"><a name="l00209"></a><span class="lineno">  209</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;double&gt;</a> X[N] = {{0, 1},  {1, -2},   {2, 3},   {3, -1},</div>
+<div class="line"><a name="l00210"></a><span class="lineno">  210</span>&#160;                                {4, 1},  {6, -5},   {-7, -3}, {-8, 5},</div>
+<div class="line"><a name="l00211"></a><span class="lineno">  211</span>&#160;                                {-9, 2}, {-10, -15}};</div>
+<div class="line"><a name="l00212"></a><span class="lineno">  212</span>&#160;    <span class="keywordtype">int</span> y[] = {1, -1, 1, -1, -1, -1, 1, 1, 1, -1};  <span class="comment">// corresponding y-values</span></div>
+<div class="line"><a name="l00213"></a><span class="lineno">  213</span>&#160; </div>
+<div class="line"><a name="l00214"></a><span class="lineno">  214</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;------- Test 1 -------&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00215"></a><span class="lineno">  215</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Model before fit: &quot;</span> &lt;&lt; ada &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00216"></a><span class="lineno">  216</span>&#160; </div>
+<div class="line"><a name="l00217"></a><span class="lineno">  217</span>&#160;    ada.fit(X, y);</div>
+<div class="line"><a name="l00218"></a><span class="lineno">  218</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Model after fit: &quot;</span> &lt;&lt; ada &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00219"></a><span class="lineno">  219</span>&#160; </div>
+<div class="line"><a name="l00220"></a><span class="lineno">  220</span>&#160;    <span class="keywordtype">int</span> predict = ada.predict({5, -3});</div>
+<div class="line"><a name="l00221"></a><span class="lineno">  221</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Predict for x=(5,-3): &quot;</span> &lt;&lt; predict;</div>
+<div class="line"><a name="l00222"></a><span class="lineno">  222</span>&#160;    assert(predict == -1);</div>
+<div class="line"><a name="l00223"></a><span class="lineno">  223</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot; ...passed&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00224"></a><span class="lineno">  224</span>&#160; </div>
+<div class="line"><a name="l00225"></a><span class="lineno">  225</span>&#160;    predict = ada.predict({5, 8});</div>
+<div class="line"><a name="l00226"></a><span class="lineno">  226</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Predict for x=(5,8): &quot;</span> &lt;&lt; predict;</div>
+<div class="line"><a name="l00227"></a><span class="lineno">  227</span>&#160;    assert(predict == 1);</div>
+<div class="line"><a name="l00228"></a><span class="lineno">  228</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot; ...passed&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00229"></a><span class="lineno">  229</span>&#160;}</div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
@@ -286,45 +287,45 @@ Here is the call graph for this function:</div>
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   </dd>
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-<div class="line"><a name="l00238"></a><span class="lineno">  238</span>&#160; </div>
-<div class="line"><a name="l00239"></a><span class="lineno">  239</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">int</span> N = 50;  <span class="comment">// number of sample points</span></div>
+<div class="fragment"><div class="line"><a name="l00238"></a><span class="lineno">  238</span>&#160;                              {</div>
+<div class="line"><a name="l00239"></a><span class="lineno">  239</span>&#160;    <a class="code" href="../../d6/d30/classmachine__learning_1_1adaline.html">adaline</a> ada(2, eta);  <span class="comment">// 2 features</span></div>
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-<div class="line"><a name="l00241"></a><span class="lineno">  241</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;double&gt;</a> X[N];</div>
-<div class="line"><a name="l00242"></a><span class="lineno">  242</span>&#160;    <span class="keywordtype">int</span> Y[N];  <span class="comment">// corresponding y-values</span></div>
-<div class="line"><a name="l00243"></a><span class="lineno">  243</span>&#160; </div>
-<div class="line"><a name="l00244"></a><span class="lineno">  244</span>&#160;    <span class="comment">// generate sample points in the interval</span></div>
-<div class="line"><a name="l00245"></a><span class="lineno">  245</span>&#160;    <span class="comment">// [-range2/100 , (range2-1)/100]</span></div>
-<div class="line"><a name="l00246"></a><span class="lineno">  246</span>&#160;    <span class="keywordtype">int</span> range = 500;          <span class="comment">// sample points full-range</span></div>
-<div class="line"><a name="l00247"></a><span class="lineno">  247</span>&#160;    <span class="keywordtype">int</span> range2 = range &gt;&gt; 1;  <span class="comment">// sample points half-range</span></div>
-<div class="line"><a name="l00248"></a><span class="lineno">  248</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; N; i++) {</div>
-<div class="line"><a name="l00249"></a><span class="lineno">  249</span>&#160;        <span class="keywordtype">double</span> x0 = ((<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % range) - range2) / 100.f;</div>
-<div class="line"><a name="l00250"></a><span class="lineno">  250</span>&#160;        <span class="keywordtype">double</span> x1 = ((<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % range) - range2) / 100.f;</div>
-<div class="line"><a name="l00251"></a><span class="lineno">  251</span>&#160;        X[i] = {x0, x1};</div>
-<div class="line"><a name="l00252"></a><span class="lineno">  252</span>&#160;        Y[i] = (x0 + 3. * x1) &gt; -1 ? 1 : -1;</div>
-<div class="line"><a name="l00253"></a><span class="lineno">  253</span>&#160;    }</div>
-<div class="line"><a name="l00254"></a><span class="lineno">  254</span>&#160; </div>
-<div class="line"><a name="l00255"></a><span class="lineno">  255</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;------- Test 2 -------&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a name="l00256"></a><span class="lineno">  256</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Model before fit: &quot;</span> &lt;&lt; ada &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a name="l00257"></a><span class="lineno">  257</span>&#160; </div>
-<div class="line"><a name="l00258"></a><span class="lineno">  258</span>&#160;    ada.fit(X, Y);</div>
-<div class="line"><a name="l00259"></a><span class="lineno">  259</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Model after fit: &quot;</span> &lt;&lt; ada &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a name="l00260"></a><span class="lineno">  260</span>&#160; </div>
-<div class="line"><a name="l00261"></a><span class="lineno">  261</span>&#160;    <span class="keywordtype">int</span> N_test_cases = 5;</div>
-<div class="line"><a name="l00262"></a><span class="lineno">  262</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; N_test_cases; i++) {</div>
-<div class="line"><a name="l00263"></a><span class="lineno">  263</span>&#160;        <span class="keywordtype">double</span> x0 = ((<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % range) - range2) / 100.f;</div>
-<div class="line"><a name="l00264"></a><span class="lineno">  264</span>&#160;        <span class="keywordtype">double</span> x1 = ((<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % range) - range2) / 100.f;</div>
-<div class="line"><a name="l00265"></a><span class="lineno">  265</span>&#160; </div>
-<div class="line"><a name="l00266"></a><span class="lineno">  266</span>&#160;        <span class="keywordtype">int</span> predict = ada.predict({x0, x1});</div>
+<div class="line"><a name="l00241"></a><span class="lineno">  241</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">int</span> N = 50;  <span class="comment">// number of sample points</span></div>
+<div class="line"><a name="l00242"></a><span class="lineno">  242</span>&#160; </div>
+<div class="line"><a name="l00243"></a><span class="lineno">  243</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;double&gt;</a> X[N];</div>
+<div class="line"><a name="l00244"></a><span class="lineno">  244</span>&#160;    <span class="keywordtype">int</span> Y[N];  <span class="comment">// corresponding y-values</span></div>
+<div class="line"><a name="l00245"></a><span class="lineno">  245</span>&#160; </div>
+<div class="line"><a name="l00246"></a><span class="lineno">  246</span>&#160;    <span class="comment">// generate sample points in the interval</span></div>
+<div class="line"><a name="l00247"></a><span class="lineno">  247</span>&#160;    <span class="comment">// [-range2/100 , (range2-1)/100]</span></div>
+<div class="line"><a name="l00248"></a><span class="lineno">  248</span>&#160;    <span class="keywordtype">int</span> range = 500;          <span class="comment">// sample points full-range</span></div>
+<div class="line"><a name="l00249"></a><span class="lineno">  249</span>&#160;    <span class="keywordtype">int</span> range2 = range &gt;&gt; 1;  <span class="comment">// sample points half-range</span></div>
+<div class="line"><a name="l00250"></a><span class="lineno">  250</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; N; i++) {</div>
+<div class="line"><a name="l00251"></a><span class="lineno">  251</span>&#160;        <span class="keywordtype">double</span> x0 = ((<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % range) - range2) / 100.f;</div>
+<div class="line"><a name="l00252"></a><span class="lineno">  252</span>&#160;        <span class="keywordtype">double</span> x1 = ((<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % range) - range2) / 100.f;</div>
+<div class="line"><a name="l00253"></a><span class="lineno">  253</span>&#160;        X[i] = {x0, x1};</div>
+<div class="line"><a name="l00254"></a><span class="lineno">  254</span>&#160;        Y[i] = (x0 + 3. * x1) &gt; -1 ? 1 : -1;</div>
+<div class="line"><a name="l00255"></a><span class="lineno">  255</span>&#160;    }</div>
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+<div class="line"><a name="l00257"></a><span class="lineno">  257</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;------- Test 2 -------&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00258"></a><span class="lineno">  258</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Model before fit: &quot;</span> &lt;&lt; ada &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00259"></a><span class="lineno">  259</span>&#160; </div>
+<div class="line"><a name="l00260"></a><span class="lineno">  260</span>&#160;    ada.fit(X, Y);</div>
+<div class="line"><a name="l00261"></a><span class="lineno">  261</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Model after fit: &quot;</span> &lt;&lt; ada &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00262"></a><span class="lineno">  262</span>&#160; </div>
+<div class="line"><a name="l00263"></a><span class="lineno">  263</span>&#160;    <span class="keywordtype">int</span> N_test_cases = 5;</div>
+<div class="line"><a name="l00264"></a><span class="lineno">  264</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; N_test_cases; i++) {</div>
+<div class="line"><a name="l00265"></a><span class="lineno">  265</span>&#160;        <span class="keywordtype">double</span> x0 = ((<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % range) - range2) / 100.f;</div>
+<div class="line"><a name="l00266"></a><span class="lineno">  266</span>&#160;        <span class="keywordtype">double</span> x1 = ((<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % range) - range2) / 100.f;</div>
 <div class="line"><a name="l00267"></a><span class="lineno">  267</span>&#160; </div>
-<div class="line"><a name="l00268"></a><span class="lineno">  268</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Predict for x=(&quot;</span> &lt;&lt; x0 &lt;&lt; <span class="stringliteral">&quot;,&quot;</span> &lt;&lt; x1 &lt;&lt; <span class="stringliteral">&quot;): &quot;</span> &lt;&lt; predict;</div>
+<div class="line"><a name="l00268"></a><span class="lineno">  268</span>&#160;        <span class="keywordtype">int</span> predict = ada.predict({x0, x1});</div>
 <div class="line"><a name="l00269"></a><span class="lineno">  269</span>&#160; </div>
-<div class="line"><a name="l00270"></a><span class="lineno">  270</span>&#160;        <span class="keywordtype">int</span> expected_val = (x0 + 3. * x1) &gt; -1 ? 1 : -1;</div>
-<div class="line"><a name="l00271"></a><span class="lineno">  271</span>&#160;        assert(predict == expected_val);</div>
-<div class="line"><a name="l00272"></a><span class="lineno">  272</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot; ...passed&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a name="l00273"></a><span class="lineno">  273</span>&#160;    }</div>
-<div class="line"><a name="l00274"></a><span class="lineno">  274</span>&#160;}</div>
+<div class="line"><a name="l00270"></a><span class="lineno">  270</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Predict for x=(&quot;</span> &lt;&lt; x0 &lt;&lt; <span class="stringliteral">&quot;,&quot;</span> &lt;&lt; x1 &lt;&lt; <span class="stringliteral">&quot;): &quot;</span> &lt;&lt; predict;</div>
+<div class="line"><a name="l00271"></a><span class="lineno">  271</span>&#160; </div>
+<div class="line"><a name="l00272"></a><span class="lineno">  272</span>&#160;        <span class="keywordtype">int</span> expected_val = (x0 + 3. * x1) &gt; -1 ? 1 : -1;</div>
+<div class="line"><a name="l00273"></a><span class="lineno">  273</span>&#160;        assert(predict == expected_val);</div>
+<div class="line"><a name="l00274"></a><span class="lineno">  274</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot; ...passed&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00275"></a><span class="lineno">  275</span>&#160;    }</div>
+<div class="line"><a name="l00276"></a><span class="lineno">  276</span>&#160;}</div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
@@ -356,48 +357,48 @@ Here is the call graph for this function:</div>
   </table>
   </dd>
 </dl>
-<div class="fragment"><div class="line"><a name="l00287"></a><span class="lineno">  287</span>&#160;                              {</div>
-<div class="line"><a name="l00288"></a><span class="lineno">  288</span>&#160;    <a class="code" href="../../d6/d30/classmachine__learning_1_1adaline.html">adaline</a> ada(6, eta);  <span class="comment">// 2 features</span></div>
-<div class="line"><a name="l00289"></a><span class="lineno">  289</span>&#160; </div>
-<div class="line"><a name="l00290"></a><span class="lineno">  290</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">int</span> N = 100;  <span class="comment">// number of sample points</span></div>
+<div class="fragment"><div class="line"><a name="l00289"></a><span class="lineno">  289</span>&#160;                              {</div>
+<div class="line"><a name="l00290"></a><span class="lineno">  290</span>&#160;    <a class="code" href="../../d6/d30/classmachine__learning_1_1adaline.html">adaline</a> ada(6, eta);  <span class="comment">// 2 features</span></div>
 <div class="line"><a name="l00291"></a><span class="lineno">  291</span>&#160; </div>
-<div class="line"><a name="l00292"></a><span class="lineno">  292</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;double&gt;</a> X[N];</div>
-<div class="line"><a name="l00293"></a><span class="lineno">  293</span>&#160;    <span class="keywordtype">int</span> Y[N];  <span class="comment">// corresponding y-values</span></div>
-<div class="line"><a name="l00294"></a><span class="lineno">  294</span>&#160; </div>
-<div class="line"><a name="l00295"></a><span class="lineno">  295</span>&#160;    <span class="comment">// generate sample points in the interval</span></div>
-<div class="line"><a name="l00296"></a><span class="lineno">  296</span>&#160;    <span class="comment">// [-range2/100 , (range2-1)/100]</span></div>
-<div class="line"><a name="l00297"></a><span class="lineno">  297</span>&#160;    <span class="keywordtype">int</span> range = 200;          <span class="comment">// sample points full-range</span></div>
-<div class="line"><a name="l00298"></a><span class="lineno">  298</span>&#160;    <span class="keywordtype">int</span> range2 = range &gt;&gt; 1;  <span class="comment">// sample points half-range</span></div>
-<div class="line"><a name="l00299"></a><span class="lineno">  299</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; N; i++) {</div>
-<div class="line"><a name="l00300"></a><span class="lineno">  300</span>&#160;        <span class="keywordtype">double</span> x0 = ((<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % range) - range2) / 100.f;</div>
-<div class="line"><a name="l00301"></a><span class="lineno">  301</span>&#160;        <span class="keywordtype">double</span> x1 = ((<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % range) - range2) / 100.f;</div>
-<div class="line"><a name="l00302"></a><span class="lineno">  302</span>&#160;        <span class="keywordtype">double</span> x2 = ((<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % range) - range2) / 100.f;</div>
-<div class="line"><a name="l00303"></a><span class="lineno">  303</span>&#160;        X[i] = {x0, x1, x2, x0 * x0, x1 * x1, x2 * x2};</div>
-<div class="line"><a name="l00304"></a><span class="lineno">  304</span>&#160;        Y[i] = ((x0 * x0) + (x1 * x1) + (x2 * x2)) &lt;= 1.f ? 1 : -1;</div>
-<div class="line"><a name="l00305"></a><span class="lineno">  305</span>&#160;    }</div>
-<div class="line"><a name="l00306"></a><span class="lineno">  306</span>&#160; </div>
-<div class="line"><a name="l00307"></a><span class="lineno">  307</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;------- Test 3 -------&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a name="l00308"></a><span class="lineno">  308</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Model before fit: &quot;</span> &lt;&lt; ada &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a name="l00309"></a><span class="lineno">  309</span>&#160; </div>
-<div class="line"><a name="l00310"></a><span class="lineno">  310</span>&#160;    ada.fit(X, Y);</div>
-<div class="line"><a name="l00311"></a><span class="lineno">  311</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Model after fit: &quot;</span> &lt;&lt; ada &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a name="l00312"></a><span class="lineno">  312</span>&#160; </div>
-<div class="line"><a name="l00313"></a><span class="lineno">  313</span>&#160;    <span class="keywordtype">int</span> N_test_cases = 5;</div>
-<div class="line"><a name="l00314"></a><span class="lineno">  314</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; N_test_cases; i++) {</div>
-<div class="line"><a name="l00315"></a><span class="lineno">  315</span>&#160;        <span class="keywordtype">double</span> x0 = ((<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % range) - range2) / 100.f;</div>
-<div class="line"><a name="l00316"></a><span class="lineno">  316</span>&#160;        <span class="keywordtype">double</span> x1 = ((<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % range) - range2) / 100.f;</div>
-<div class="line"><a name="l00317"></a><span class="lineno">  317</span>&#160;        <span class="keywordtype">double</span> x2 = ((<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % range) - range2) / 100.f;</div>
-<div class="line"><a name="l00318"></a><span class="lineno">  318</span>&#160; </div>
-<div class="line"><a name="l00319"></a><span class="lineno">  319</span>&#160;        <span class="keywordtype">int</span> predict = ada.predict({x0, x1, x2, x0 * x0, x1 * x1, x2 * x2});</div>
+<div class="line"><a name="l00292"></a><span class="lineno">  292</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">int</span> N = 100;  <span class="comment">// number of sample points</span></div>
+<div class="line"><a name="l00293"></a><span class="lineno">  293</span>&#160; </div>
+<div class="line"><a name="l00294"></a><span class="lineno">  294</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;double&gt;</a> X[N];</div>
+<div class="line"><a name="l00295"></a><span class="lineno">  295</span>&#160;    <span class="keywordtype">int</span> Y[N];  <span class="comment">// corresponding y-values</span></div>
+<div class="line"><a name="l00296"></a><span class="lineno">  296</span>&#160; </div>
+<div class="line"><a name="l00297"></a><span class="lineno">  297</span>&#160;    <span class="comment">// generate sample points in the interval</span></div>
+<div class="line"><a name="l00298"></a><span class="lineno">  298</span>&#160;    <span class="comment">// [-range2/100 , (range2-1)/100]</span></div>
+<div class="line"><a name="l00299"></a><span class="lineno">  299</span>&#160;    <span class="keywordtype">int</span> range = 200;          <span class="comment">// sample points full-range</span></div>
+<div class="line"><a name="l00300"></a><span class="lineno">  300</span>&#160;    <span class="keywordtype">int</span> range2 = range &gt;&gt; 1;  <span class="comment">// sample points half-range</span></div>
+<div class="line"><a name="l00301"></a><span class="lineno">  301</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; N; i++) {</div>
+<div class="line"><a name="l00302"></a><span class="lineno">  302</span>&#160;        <span class="keywordtype">double</span> x0 = ((<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % range) - range2) / 100.f;</div>
+<div class="line"><a name="l00303"></a><span class="lineno">  303</span>&#160;        <span class="keywordtype">double</span> x1 = ((<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % range) - range2) / 100.f;</div>
+<div class="line"><a name="l00304"></a><span class="lineno">  304</span>&#160;        <span class="keywordtype">double</span> x2 = ((<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % range) - range2) / 100.f;</div>
+<div class="line"><a name="l00305"></a><span class="lineno">  305</span>&#160;        X[i] = {x0, x1, x2, x0 * x0, x1 * x1, x2 * x2};</div>
+<div class="line"><a name="l00306"></a><span class="lineno">  306</span>&#160;        Y[i] = ((x0 * x0) + (x1 * x1) + (x2 * x2)) &lt;= 1.f ? 1 : -1;</div>
+<div class="line"><a name="l00307"></a><span class="lineno">  307</span>&#160;    }</div>
+<div class="line"><a name="l00308"></a><span class="lineno">  308</span>&#160; </div>
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+<div class="line"><a name="l00310"></a><span class="lineno">  310</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Model before fit: &quot;</span> &lt;&lt; ada &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00311"></a><span class="lineno">  311</span>&#160; </div>
+<div class="line"><a name="l00312"></a><span class="lineno">  312</span>&#160;    ada.fit(X, Y);</div>
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+<div class="line"><a name="l00314"></a><span class="lineno">  314</span>&#160; </div>
+<div class="line"><a name="l00315"></a><span class="lineno">  315</span>&#160;    <span class="keywordtype">int</span> N_test_cases = 5;</div>
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+<div class="line"><a name="l00317"></a><span class="lineno">  317</span>&#160;        <span class="keywordtype">double</span> x0 = ((<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % range) - range2) / 100.f;</div>
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+<div class="ttc" id="aclassmachine__learning_1_1adaline_html"><div class="ttname"><a href="../../d6/d30/classmachine__learning_1_1adaline.html">machine_learning::adaline</a></div><div class="ttdef"><b>Definition:</b> adaline_learning.cpp:44</div></div>
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     <li class="navelem"><a class="el" href="../../dir_3343723ae086de42ee4ca9774da3a13f.html">machine_learning</a></li><li class="navelem"><a class="el" href="../../d5/db0/adaline__learning_8cpp.html">adaline_learning.cpp</a></li>
-    <li class="footer">Generated on Sun Jun 21 2020 19:43:35 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:38 for Algorithms_in_C++ by
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     <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:37 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:40 for Algorithms_in_C++ by
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   <ul>
-    <li class="footer">Generated on Sun Jun 21 2020 19:43:37 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:40 for Algorithms_in_C++ by
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     <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
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diff --git a/d5/de2/structtower-members.html b/d5/de2/structtower-members.html
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   <ul>
-    <li class="footer">Generated on Sun Jun 21 2020 19:43:38 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:41 for Algorithms_in_C++ by
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     <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:37 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:39 for Algorithms_in_C++ by
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:37 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:40 for Algorithms_in_C++ by
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:37 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:39 for Algorithms_in_C++ by
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-<div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160;    }</div>
+<div class="fragment"><div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160;        : <a class="code" href="../../d6/d30/classmachine__learning_1_1adaline.html#a28160d17e492597a2f112e0d38551cda">eta</a>(<a class="code" href="../../d6/d30/classmachine__learning_1_1adaline.html#a28160d17e492597a2f112e0d38551cda">eta</a>), <a class="code" href="../../d6/d30/classmachine__learning_1_1adaline.html#aa23d60262f917f35836ef4b1c1d9f7d3">accuracy</a>(<a class="code" href="../../d6/d30/classmachine__learning_1_1adaline.html#aa23d60262f917f35836ef4b1c1d9f7d3">accuracy</a>) {</div>
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+<div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160;                      &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00059"></a><span class="lineno">   59</span>&#160;            <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/program/exit.html">std::exit</a>(EXIT_FAILURE);</div>
+<div class="line"><a name="l00060"></a><span class="lineno">   60</span>&#160;        }</div>
+<div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160; </div>
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+<div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160;            num_features +</div>
+<div class="line"><a name="l00064"></a><span class="lineno">   64</span>&#160;            1);  <span class="comment">// additional weight is for the constant bias term</span></div>
+<div class="line"><a name="l00065"></a><span class="lineno">   65</span>&#160; </div>
+<div class="line"><a name="l00066"></a><span class="lineno">   66</span>&#160;        <span class="comment">// initialize with random weights in the range [-50, 49]</span></div>
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+<div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160;        <span class="comment">// weights[i] = (static_cast&lt;double&gt;(std::rand() % 100) - 50);</span></div>
+<div class="line"><a name="l00069"></a><span class="lineno">   69</span>&#160;    }</div>
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@@ -252,16 +252,16 @@ Here is the call graph for this function:</div>
 <dl class="section return"><dt>Returns</dt><dd><code>true</code> size matches </dd>
 <dd>
 <code>false</code> size does not match </dd></dl>
-<div class="fragment"><div class="line"><a name="l00174"></a><span class="lineno">  174</span>&#160;                                                      {</div>
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+<div class="fragment"><div class="line"><a name="l00176"></a><span class="lineno">  176</span>&#160;                                                      {</div>
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+<div class="line"><a name="l00178"></a><span class="lineno">  178</span>&#160;            <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; __func__ &lt;&lt; <span class="stringliteral">&quot;: &quot;</span></div>
+<div class="line"><a name="l00179"></a><span class="lineno">  179</span>&#160;                      &lt;&lt; <span class="stringliteral">&quot;Number of features in x does not match the feature &quot;</span></div>
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@@ -312,23 +312,23 @@ Here is the call graph for this function:</div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>correction factor </dd></dl>
-<div class="fragment"><div class="line"><a name="l00110"></a><span class="lineno">  110</span>&#160;                                                         {</div>
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+<div class="line"><a name="l00121"></a><span class="lineno">  121</span>&#160;        <span class="comment">/* update each weight, the last weight is the bias term */</span></div>
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+<div class="line"><a name="l00127"></a><span class="lineno">  127</span>&#160;        <span class="keywordflow">return</span> correction_factor;</div>
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@@ -380,35 +380,35 @@ template&lt;int N&gt; </div>
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@@ -453,20 +453,20 @@ template&lt;int N&gt; </div>
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-<div class="line"><a name="l00097"></a><span class="lineno">   97</span>&#160;        y = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/inner_product.html">std::inner_product</a>(x.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/begin.html">begin</a>(), x.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/end.html">end</a>(), <a class="code" href="../../d6/d30/classmachine__learning_1_1adaline.html#a4cd8fe438032fedaa66f93bfd66f5492">weights</a>.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/begin.html">begin</a>(), y);</div>
-<div class="line"><a name="l00098"></a><span class="lineno">   98</span>&#160; </div>
-<div class="line"><a name="l00099"></a><span class="lineno">   99</span>&#160;        <span class="keywordflow">if</span> (out != <span class="keyword">nullptr</span>)  <span class="comment">// if out variable is provided</span></div>
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-<div class="line"><a name="l00102"></a><span class="lineno">  102</span>&#160;        <span class="keywordflow">return</span> activation(y);  <span class="comment">// quantizer: apply ADALINE threshold function</span></div>
-<div class="line"><a name="l00103"></a><span class="lineno">  103</span>&#160;    }</div>
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+<div class="line"><a name="l00097"></a><span class="lineno">   97</span>&#160; </div>
+<div class="line"><a name="l00098"></a><span class="lineno">   98</span>&#160;        <span class="comment">// for (int i = 0; i &lt; x.size(); i++) y += x[i] * weights[i];</span></div>
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+<div class="line"><a name="l00100"></a><span class="lineno">  100</span>&#160; </div>
+<div class="line"><a name="l00101"></a><span class="lineno">  101</span>&#160;        <span class="keywordflow">if</span> (out != <span class="keyword">nullptr</span>)  <span class="comment">// if out variable is provided</span></div>
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+<div class="line"><a name="l00104"></a><span class="lineno">  104</span>&#160;        <span class="keywordflow">return</span> activation(y);  <span class="comment">// quantizer: apply ADALINE threshold function</span></div>
+<div class="line"><a name="l00105"></a><span class="lineno">  105</span>&#160;    }</div>
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 <p>Operator to print the weights of the model </p>
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diff --git a/d6/d42/miller__rabin_8cpp.html b/d6/d42/miller__rabin_8cpp.html
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:36 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:38 for Algorithms_in_C++ by
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diff --git a/d6/d48/structtrie-members.html b/d6/d48/structtrie-members.html
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:38 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:41 for Algorithms_in_C++ by
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diff --git a/d6/d4a/addition__rule_8cpp.html b/d6/d4a/addition__rule_8cpp.html
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:37 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:39 for Algorithms_in_C++ by
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:37 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:40 for Algorithms_in_C++ by
     <a href="http://www.doxygen.org/index.html">
     <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
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diff --git a/d6/d9d/large__factorial_8cpp.html b/d6/d9d/large__factorial_8cpp.html
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:36 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:38 for Algorithms_in_C++ by
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diff --git a/d6/db0/binomial__dist_8cpp.html b/d6/db0/binomial__dist_8cpp.html
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:37 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:39 for Algorithms_in_C++ by
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:37 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:40 for Algorithms_in_C++ by
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diff --git a/d6/dce/rabin__karp_8cpp.html b/d6/dce/rabin__karp_8cpp.html
index 113dc7cbd..ca4e5b646 100644
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:37 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:40 for Algorithms_in_C++ by
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diff --git a/d6/dd3/ode__midpoint__euler_8cpp.html b/d6/dd3/ode__midpoint__euler_8cpp.html
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+    <li class="footer">Generated on Mon Jun 22 2020 11:53:38 for Algorithms_in_C++ by
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+    <li class="footer">Generated on Mon Jun 22 2020 11:53:38 for Algorithms_in_C++ by
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:37 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:40 for Algorithms_in_C++ by
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:35 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:38 for Algorithms_in_C++ by
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:37 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:40 for Algorithms_in_C++ by
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     <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
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diff --git a/d8/d53/modular__inverse__fermat__little__theorem_8cpp.html b/d8/d53/modular__inverse__fermat__little__theorem_8cpp.html
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:36 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:38 for Algorithms_in_C++ by
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:37 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:40 for Algorithms_in_C++ by
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     <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:35 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:38 for Algorithms_in_C++ by
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-<div class="line"><a name="l00296"></a><span class="lineno">  296</span>&#160;                  &lt;&lt; <span class="stringliteral">&quot;\t d_min: &quot;</span> &lt;&lt; dmin_ratio &lt;&lt; <span class="stringliteral">&quot;\r&quot;</span>;</div>
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-<div class="line"><a name="l00300"></a><span class="lineno">  300</span>&#160;}</div>
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+<div class="line"><a name="l00291"></a><span class="lineno">  291</span>&#160;        <span class="comment">// termination condition variable -&gt; % change in minimum distance</span></div>
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 <dl class="section return"><dt>Returns</dt><dd>0 if all ok </dd>
 <dd>
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-<div class="line"><a name="l00136"></a><span class="lineno">  136</span>&#160;    <span class="keywordflow">if</span> (!fp) {  <span class="comment">// error with fopen</span></div>
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-<div class="line"><a name="l00146"></a><span class="lineno">  146</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; W.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); i++) {         <span class="comment">// for each x</span></div>
-<div class="line"><a name="l00147"></a><span class="lineno">  147</span>&#160;        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; W[0].<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); j++) {  <span class="comment">// for each y</span></div>
-<div class="line"><a name="l00148"></a><span class="lineno">  148</span>&#160;            <span class="keywordtype">double</span> <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/distance.html">distance</a> = 0.f;</div>
-<div class="line"><a name="l00149"></a><span class="lineno">  149</span>&#160; </div>
-<div class="line"><a name="l00150"></a><span class="lineno">  150</span>&#160;            <span class="keywordtype">int</span> from_x = std::max&lt;int&gt;(0, i - R);</div>
-<div class="line"><a name="l00151"></a><span class="lineno">  151</span>&#160;            <span class="keywordtype">int</span> to_x = std::min&lt;int&gt;(W.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(), i + R + 1);</div>
-<div class="line"><a name="l00152"></a><span class="lineno">  152</span>&#160;            <span class="keywordtype">int</span> from_y = std::max&lt;int&gt;(0, j - R);</div>
-<div class="line"><a name="l00153"></a><span class="lineno">  153</span>&#160;            <span class="keywordtype">int</span> to_y = std::min&lt;int&gt;(W[0].size(), j + R + 1);</div>
-<div class="line"><a name="l00154"></a><span class="lineno">  154</span>&#160;            <span class="keywordtype">int</span> l, m;</div>
-<div class="line"><a name="l00155"></a><span class="lineno">  155</span>&#160;<span class="preprocessor">#ifdef _OPENMP</span></div>
-<div class="line"><a name="l00156"></a><span class="lineno">  156</span>&#160;<span class="preprocessor">#pragma omp parallel for reduction(+ : distance)</span></div>
-<div class="line"><a name="l00157"></a><span class="lineno">  157</span>&#160;<span class="preprocessor">#endif</span></div>
-<div class="line"><a name="l00158"></a><span class="lineno">  158</span>&#160;            <span class="keywordflow">for</span> (l = from_x; l &lt; to_x; l++) {      <span class="comment">// scan neighborhoor in x</span></div>
-<div class="line"><a name="l00159"></a><span class="lineno">  159</span>&#160;                <span class="keywordflow">for</span> (m = from_y; m &lt; to_y; m++) {  <span class="comment">// scan neighborhood in y</span></div>
-<div class="line"><a name="l00160"></a><span class="lineno">  160</span>&#160;                    <span class="keyword">auto</span> d = W[i][j] - W[l][m];</div>
-<div class="line"><a name="l00161"></a><span class="lineno">  161</span>&#160;                    <span class="keywordtype">double</span> d2 = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a>(d, 2).sum();</div>
-<div class="line"><a name="l00162"></a><span class="lineno">  162</span>&#160;                    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/distance.html">distance</a> += <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/sqrt.html">std::sqrt</a>(d2);</div>
-<div class="line"><a name="l00163"></a><span class="lineno">  163</span>&#160;                    <span class="comment">// distance += d2;</span></div>
-<div class="line"><a name="l00164"></a><span class="lineno">  164</span>&#160;                }</div>
-<div class="line"><a name="l00165"></a><span class="lineno">  165</span>&#160;            }</div>
-<div class="line"><a name="l00166"></a><span class="lineno">  166</span>&#160; </div>
-<div class="line"><a name="l00167"></a><span class="lineno">  167</span>&#160;            <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/distance.html">distance</a> /= R * R;          <span class="comment">// mean distance from neighbors</span></div>
-<div class="line"><a name="l00168"></a><span class="lineno">  168</span>&#160;            fp &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/distance.html">distance</a>;             <span class="comment">// print the mean separation</span></div>
-<div class="line"><a name="l00169"></a><span class="lineno">  169</span>&#160;            <span class="keywordflow">if</span> (j &lt; W[0].size() - 1) {  <span class="comment">// if not the last column</span></div>
-<div class="line"><a name="l00170"></a><span class="lineno">  170</span>&#160;                fp &lt;&lt; <span class="charliteral">&#39;,&#39;</span>;              <span class="comment">// suffix comma</span></div>
-<div class="line"><a name="l00171"></a><span class="lineno">  171</span>&#160;            }</div>
-<div class="line"><a name="l00172"></a><span class="lineno">  172</span>&#160;        }</div>
-<div class="line"><a name="l00173"></a><span class="lineno">  173</span>&#160;        <span class="keywordflow">if</span> (i &lt; W.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>() - 1)  <span class="comment">// if not the last row</span></div>
-<div class="line"><a name="l00174"></a><span class="lineno">  174</span>&#160;            fp &lt;&lt; <span class="charliteral">&#39;\n&#39;</span>;        <span class="comment">// start a new line</span></div>
-<div class="line"><a name="l00175"></a><span class="lineno">  175</span>&#160;    }</div>
-<div class="line"><a name="l00176"></a><span class="lineno">  176</span>&#160; </div>
-<div class="line"><a name="l00177"></a><span class="lineno">  177</span>&#160;    fp.close();</div>
-<div class="line"><a name="l00178"></a><span class="lineno">  178</span>&#160;    <span class="keywordflow">return</span> 0;</div>
-<div class="line"><a name="l00179"></a><span class="lineno">  179</span>&#160;}</div>
+<div class="fragment"><div class="line"><a name="l00136"></a><span class="lineno">  136</span>&#160;                                                                      {</div>
+<div class="line"><a name="l00137"></a><span class="lineno">  137</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream.html">std::ofstream</a> fp(fname);</div>
+<div class="line"><a name="l00138"></a><span class="lineno">  138</span>&#160;    <span class="keywordflow">if</span> (!fp) {  <span class="comment">// error with fopen</span></div>
+<div class="line"><a name="l00139"></a><span class="lineno">  139</span>&#160;        <span class="keywordtype">char</span> msg[120];</div>
+<div class="line"><a name="l00140"></a><span class="lineno">  140</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/c/fprintf.html">std::snprintf</a>(msg, <span class="keyword">sizeof</span>(msg), <span class="stringliteral">&quot;File error (%s): &quot;</span>, fname);</div>
+<div class="line"><a name="l00141"></a><span class="lineno">  141</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/c/perror.html">std::perror</a>(msg);</div>
+<div class="line"><a name="l00142"></a><span class="lineno">  142</span>&#160;        <span class="keywordflow">return</span> -1;</div>
+<div class="line"><a name="l00143"></a><span class="lineno">  143</span>&#160;    }</div>
+<div class="line"><a name="l00144"></a><span class="lineno">  144</span>&#160; </div>
+<div class="line"><a name="l00145"></a><span class="lineno">  145</span>&#160;    <span class="comment">// neighborhood range</span></div>
+<div class="line"><a name="l00146"></a><span class="lineno">  146</span>&#160;    <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> R = 1;</div>
+<div class="line"><a name="l00147"></a><span class="lineno">  147</span>&#160; </div>
+<div class="line"><a name="l00148"></a><span class="lineno">  148</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; W.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); i++) {         <span class="comment">// for each x</span></div>
+<div class="line"><a name="l00149"></a><span class="lineno">  149</span>&#160;        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; W[0].<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); j++) {  <span class="comment">// for each y</span></div>
+<div class="line"><a name="l00150"></a><span class="lineno">  150</span>&#160;            <span class="keywordtype">double</span> <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/distance.html">distance</a> = 0.f;</div>
+<div class="line"><a name="l00151"></a><span class="lineno">  151</span>&#160; </div>
+<div class="line"><a name="l00152"></a><span class="lineno">  152</span>&#160;            <span class="keywordtype">int</span> from_x = std::max&lt;int&gt;(0, i - R);</div>
+<div class="line"><a name="l00153"></a><span class="lineno">  153</span>&#160;            <span class="keywordtype">int</span> to_x = std::min&lt;int&gt;(W.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(), i + R + 1);</div>
+<div class="line"><a name="l00154"></a><span class="lineno">  154</span>&#160;            <span class="keywordtype">int</span> from_y = std::max&lt;int&gt;(0, j - R);</div>
+<div class="line"><a name="l00155"></a><span class="lineno">  155</span>&#160;            <span class="keywordtype">int</span> to_y = std::min&lt;int&gt;(W[0].size(), j + R + 1);</div>
+<div class="line"><a name="l00156"></a><span class="lineno">  156</span>&#160;            <span class="keywordtype">int</span> l, m;</div>
+<div class="line"><a name="l00157"></a><span class="lineno">  157</span>&#160;<span class="preprocessor">#ifdef _OPENMP</span></div>
+<div class="line"><a name="l00158"></a><span class="lineno">  158</span>&#160;<span class="preprocessor">#pragma omp parallel for reduction(+ : distance)</span></div>
+<div class="line"><a name="l00159"></a><span class="lineno">  159</span>&#160;<span class="preprocessor">#endif</span></div>
+<div class="line"><a name="l00160"></a><span class="lineno">  160</span>&#160;            <span class="keywordflow">for</span> (l = from_x; l &lt; to_x; l++) {      <span class="comment">// scan neighborhoor in x</span></div>
+<div class="line"><a name="l00161"></a><span class="lineno">  161</span>&#160;                <span class="keywordflow">for</span> (m = from_y; m &lt; to_y; m++) {  <span class="comment">// scan neighborhood in y</span></div>
+<div class="line"><a name="l00162"></a><span class="lineno">  162</span>&#160;                    <span class="keyword">auto</span> d = W[i][j] - W[l][m];</div>
+<div class="line"><a name="l00163"></a><span class="lineno">  163</span>&#160;                    <span class="keywordtype">double</span> d2 = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a>(d, 2).sum();</div>
+<div class="line"><a name="l00164"></a><span class="lineno">  164</span>&#160;                    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/distance.html">distance</a> += <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/sqrt.html">std::sqrt</a>(d2);</div>
+<div class="line"><a name="l00165"></a><span class="lineno">  165</span>&#160;                    <span class="comment">// distance += d2;</span></div>
+<div class="line"><a name="l00166"></a><span class="lineno">  166</span>&#160;                }</div>
+<div class="line"><a name="l00167"></a><span class="lineno">  167</span>&#160;            }</div>
+<div class="line"><a name="l00168"></a><span class="lineno">  168</span>&#160; </div>
+<div class="line"><a name="l00169"></a><span class="lineno">  169</span>&#160;            <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/distance.html">distance</a> /= R * R;          <span class="comment">// mean distance from neighbors</span></div>
+<div class="line"><a name="l00170"></a><span class="lineno">  170</span>&#160;            fp &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/distance.html">distance</a>;             <span class="comment">// print the mean separation</span></div>
+<div class="line"><a name="l00171"></a><span class="lineno">  171</span>&#160;            <span class="keywordflow">if</span> (j &lt; W[0].size() - 1) {  <span class="comment">// if not the last column</span></div>
+<div class="line"><a name="l00172"></a><span class="lineno">  172</span>&#160;                fp &lt;&lt; <span class="charliteral">&#39;,&#39;</span>;              <span class="comment">// suffix comma</span></div>
+<div class="line"><a name="l00173"></a><span class="lineno">  173</span>&#160;            }</div>
+<div class="line"><a name="l00174"></a><span class="lineno">  174</span>&#160;        }</div>
+<div class="line"><a name="l00175"></a><span class="lineno">  175</span>&#160;        <span class="keywordflow">if</span> (i &lt; W.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>() - 1)  <span class="comment">// if not the last row</span></div>
+<div class="line"><a name="l00176"></a><span class="lineno">  176</span>&#160;            fp &lt;&lt; <span class="charliteral">&#39;\n&#39;</span>;        <span class="comment">// start a new line</span></div>
+<div class="line"><a name="l00177"></a><span class="lineno">  177</span>&#160;    }</div>
+<div class="line"><a name="l00178"></a><span class="lineno">  178</span>&#160; </div>
+<div class="line"><a name="l00179"></a><span class="lineno">  179</span>&#160;    fp.close();</div>
+<div class="line"><a name="l00180"></a><span class="lineno">  180</span>&#160;    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><a name="l00181"></a><span class="lineno">  181</span>&#160;}</div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
@@ -525,62 +525,62 @@ Here is the call graph for this function:</div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>minimum distance of sample and trained weights </dd></dl>
-<div class="fragment"><div class="line"><a name="l00194"></a><span class="lineno">  194</span>&#160;                             {</div>
-<div class="line"><a name="l00195"></a><span class="lineno">  195</span>&#160;    <span class="keywordtype">int</span> x, y;</div>
-<div class="line"><a name="l00196"></a><span class="lineno">  196</span>&#160;    <span class="keywordtype">int</span> num_out_x = <span class="keyword">static_cast&lt;</span><span class="keywordtype">int</span><span class="keyword">&gt;</span>(W-&gt;<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>());       <span class="comment">// output nodes - in X</span></div>
-<div class="line"><a name="l00197"></a><span class="lineno">  197</span>&#160;    <span class="keywordtype">int</span> num_out_y = <span class="keyword">static_cast&lt;</span><span class="keywordtype">int</span><span class="keyword">&gt;</span>(W[0][0].<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>());  <span class="comment">// output nodes - in Y</span></div>
-<div class="line"><a name="l00198"></a><span class="lineno">  198</span>&#160;    <span class="keywordtype">int</span> num_features = <span class="keyword">static_cast&lt;</span><span class="keywordtype">int</span><span class="keyword">&gt;</span>(W[0][0][0].<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>());  <span class="comment">//  features = in Z</span></div>
-<div class="line"><a name="l00199"></a><span class="lineno">  199</span>&#160;    <span class="keywordtype">double</span> d_min = 0.f;</div>
-<div class="line"><a name="l00200"></a><span class="lineno">  200</span>&#160; </div>
-<div class="line"><a name="l00201"></a><span class="lineno">  201</span>&#160;<span class="preprocessor">#ifdef _OPENMP</span></div>
-<div class="line"><a name="l00202"></a><span class="lineno">  202</span>&#160;<span class="preprocessor">#pragma omp for</span></div>
-<div class="line"><a name="l00203"></a><span class="lineno">  203</span>&#160;<span class="preprocessor">#endif</span></div>
-<div class="line"><a name="l00204"></a><span class="lineno">  204</span>&#160;    <span class="comment">// step 1: for each output point</span></div>
-<div class="line"><a name="l00205"></a><span class="lineno">  205</span>&#160;    <span class="keywordflow">for</span> (x = 0; x &lt; num_out_x; x++) {</div>
-<div class="line"><a name="l00206"></a><span class="lineno">  206</span>&#160;        <span class="keywordflow">for</span> (y = 0; y &lt; num_out_y; y++) {</div>
-<div class="line"><a name="l00207"></a><span class="lineno">  207</span>&#160;            (*D)[x][y] = 0.f;</div>
-<div class="line"><a name="l00208"></a><span class="lineno">  208</span>&#160;            <span class="comment">// compute Euclidian distance of each output</span></div>
-<div class="line"><a name="l00209"></a><span class="lineno">  209</span>&#160;            <span class="comment">// point from the current sample</span></div>
-<div class="line"><a name="l00210"></a><span class="lineno">  210</span>&#160;            <span class="keyword">auto</span> d = ((*W)[x][y] - X);</div>
-<div class="line"><a name="l00211"></a><span class="lineno">  211</span>&#160;            (*D)[x][y] = (d * d).sum();</div>
-<div class="line"><a name="l00212"></a><span class="lineno">  212</span>&#160;            (*D)[x][y] = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/sqrt.html">std::sqrt</a>((*D)[x][y]);</div>
-<div class="line"><a name="l00213"></a><span class="lineno">  213</span>&#160;        }</div>
-<div class="line"><a name="l00214"></a><span class="lineno">  214</span>&#160;    }</div>
-<div class="line"><a name="l00215"></a><span class="lineno">  215</span>&#160; </div>
-<div class="line"><a name="l00216"></a><span class="lineno">  216</span>&#160;    <span class="comment">// step 2:  get closest node i.e., node with snallest Euclidian distance</span></div>
-<div class="line"><a name="l00217"></a><span class="lineno">  217</span>&#160;    <span class="comment">// to the current pattern</span></div>
-<div class="line"><a name="l00218"></a><span class="lineno">  218</span>&#160;    <span class="keywordtype">int</span> d_min_x, d_min_y;</div>
-<div class="line"><a name="l00219"></a><span class="lineno">  219</span>&#160;    <a class="code" href="../../d9/d66/group__machine__learning.html#gab53c14440b2b2dd3172c66afc5c2f63f">get_min_2d</a>(*D, &amp;d_min, &amp;d_min_x, &amp;d_min_y);</div>
-<div class="line"><a name="l00220"></a><span class="lineno">  220</span>&#160; </div>
-<div class="line"><a name="l00221"></a><span class="lineno">  221</span>&#160;    <span class="comment">// step 3a: get the neighborhood range</span></div>
-<div class="line"><a name="l00222"></a><span class="lineno">  222</span>&#160;    <span class="keywordtype">int</span> from_x = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a>(0, d_min_x - R);</div>
-<div class="line"><a name="l00223"></a><span class="lineno">  223</span>&#160;    <span class="keywordtype">int</span> to_x = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/min.html">std::min</a>(num_out_x, d_min_x + R + 1);</div>
-<div class="line"><a name="l00224"></a><span class="lineno">  224</span>&#160;    <span class="keywordtype">int</span> from_y = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a>(0, d_min_y - R);</div>
-<div class="line"><a name="l00225"></a><span class="lineno">  225</span>&#160;    <span class="keywordtype">int</span> to_y = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/min.html">std::min</a>(num_out_y, d_min_y + R + 1);</div>
-<div class="line"><a name="l00226"></a><span class="lineno">  226</span>&#160; </div>
-<div class="line"><a name="l00227"></a><span class="lineno">  227</span>&#160;    <span class="comment">// step 3b: update the weights of nodes in the</span></div>
-<div class="line"><a name="l00228"></a><span class="lineno">  228</span>&#160;    <span class="comment">// neighborhood</span></div>
-<div class="line"><a name="l00229"></a><span class="lineno">  229</span>&#160;<span class="preprocessor">#ifdef _OPENMP</span></div>
-<div class="line"><a name="l00230"></a><span class="lineno">  230</span>&#160;<span class="preprocessor">#pragma omp for</span></div>
-<div class="line"><a name="l00231"></a><span class="lineno">  231</span>&#160;<span class="preprocessor">#endif</span></div>
-<div class="line"><a name="l00232"></a><span class="lineno">  232</span>&#160;    <span class="keywordflow">for</span> (x = from_x; x &lt; to_x; x++) {</div>
-<div class="line"><a name="l00233"></a><span class="lineno">  233</span>&#160;        <span class="keywordflow">for</span> (y = from_y; y &lt; to_y; y++) {</div>
-<div class="line"><a name="l00234"></a><span class="lineno">  234</span>&#160;            <span class="comment">/* you can enable the following normalization if needed.</span></div>
-<div class="line"><a name="l00235"></a><span class="lineno">  235</span>&#160;<span class="comment">   personally, I found it detrimental to convergence */</span></div>
-<div class="line"><a name="l00236"></a><span class="lineno">  236</span>&#160;            <span class="comment">// const double s2pi = sqrt(2.f * M_PI);</span></div>
-<div class="line"><a name="l00237"></a><span class="lineno">  237</span>&#160;            <span class="comment">// double normalize = 1.f / (alpha * s2pi);</span></div>
-<div class="line"><a name="l00238"></a><span class="lineno">  238</span>&#160; </div>
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-<div class="line"><a name="l00242"></a><span class="lineno">  242</span>&#160;                (d_min_x - x) * (d_min_x - x) + (d_min_y - y) * (d_min_y - y);</div>
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-<div class="line"><a name="l00249"></a><span class="lineno">  249</span>&#160;}</div>
+<div class="fragment"><div class="line"><a name="l00196"></a><span class="lineno">  196</span>&#160;                             {</div>
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+<div class="line"><a name="l00199"></a><span class="lineno">  199</span>&#160;    <span class="keywordtype">int</span> num_out_y = <span class="keyword">static_cast&lt;</span><span class="keywordtype">int</span><span class="keyword">&gt;</span>(W[0][0].<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>());  <span class="comment">// output nodes - in Y</span></div>
+<div class="line"><a name="l00200"></a><span class="lineno">  200</span>&#160;    <span class="keywordtype">int</span> num_features = <span class="keyword">static_cast&lt;</span><span class="keywordtype">int</span><span class="keyword">&gt;</span>(W[0][0][0].<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>());  <span class="comment">//  features = in Z</span></div>
+<div class="line"><a name="l00201"></a><span class="lineno">  201</span>&#160;    <span class="keywordtype">double</span> d_min = 0.f;</div>
+<div class="line"><a name="l00202"></a><span class="lineno">  202</span>&#160; </div>
+<div class="line"><a name="l00203"></a><span class="lineno">  203</span>&#160;<span class="preprocessor">#ifdef _OPENMP</span></div>
+<div class="line"><a name="l00204"></a><span class="lineno">  204</span>&#160;<span class="preprocessor">#pragma omp for</span></div>
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+<div class="line"><a name="l00206"></a><span class="lineno">  206</span>&#160;    <span class="comment">// step 1: for each output point</span></div>
+<div class="line"><a name="l00207"></a><span class="lineno">  207</span>&#160;    <span class="keywordflow">for</span> (x = 0; x &lt; num_out_x; x++) {</div>
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+<div class="line"><a name="l00210"></a><span class="lineno">  210</span>&#160;            <span class="comment">// compute Euclidian distance of each output</span></div>
+<div class="line"><a name="l00211"></a><span class="lineno">  211</span>&#160;            <span class="comment">// point from the current sample</span></div>
+<div class="line"><a name="l00212"></a><span class="lineno">  212</span>&#160;            <span class="keyword">auto</span> d = ((*W)[x][y] - X);</div>
+<div class="line"><a name="l00213"></a><span class="lineno">  213</span>&#160;            (*D)[x][y] = (d * d).sum();</div>
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+<div class="line"><a name="l00218"></a><span class="lineno">  218</span>&#160;    <span class="comment">// step 2:  get closest node i.e., node with snallest Euclidian distance</span></div>
+<div class="line"><a name="l00219"></a><span class="lineno">  219</span>&#160;    <span class="comment">// to the current pattern</span></div>
+<div class="line"><a name="l00220"></a><span class="lineno">  220</span>&#160;    <span class="keywordtype">int</span> d_min_x, d_min_y;</div>
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+<div class="line"><a name="l00225"></a><span class="lineno">  225</span>&#160;    <span class="keywordtype">int</span> to_x = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/min.html">std::min</a>(num_out_x, d_min_x + R + 1);</div>
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+<div class="line"><a name="l00227"></a><span class="lineno">  227</span>&#160;    <span class="keywordtype">int</span> to_y = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/min.html">std::min</a>(num_out_y, d_min_y + R + 1);</div>
+<div class="line"><a name="l00228"></a><span class="lineno">  228</span>&#160; </div>
+<div class="line"><a name="l00229"></a><span class="lineno">  229</span>&#160;    <span class="comment">// step 3b: update the weights of nodes in the</span></div>
+<div class="line"><a name="l00230"></a><span class="lineno">  230</span>&#160;    <span class="comment">// neighborhood</span></div>
+<div class="line"><a name="l00231"></a><span class="lineno">  231</span>&#160;<span class="preprocessor">#ifdef _OPENMP</span></div>
+<div class="line"><a name="l00232"></a><span class="lineno">  232</span>&#160;<span class="preprocessor">#pragma omp for</span></div>
+<div class="line"><a name="l00233"></a><span class="lineno">  233</span>&#160;<span class="preprocessor">#endif</span></div>
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+<div class="line"><a name="l00247"></a><span class="lineno">  247</span>&#160;            (*W)[x][y] += (X - (*W)[x][y]) * alpha * scale_factor;</div>
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+<div class="ttc" id="anamespacemachine__learning_html_ac4010fe3a52a74e8b5b1aaadfe38b46f"><div class="ttname"><a href="../../d8/d77/namespacemachine__learning.html#ac4010fe3a52a74e8b5b1aaadfe38b46f">machine_learning::update_weights</a></div><div class="ttdeci">double update_weights(const std::valarray&lt; double &gt; &amp;X, std::vector&lt; std::vector&lt; std::valarray&lt; double &gt;&gt;&gt; *W, std::vector&lt; std::valarray&lt; double &gt;&gt; *D, double alpha, int R)</div><div class="ttdef"><b>Definition:</b> kohonen_som_topology.cpp:193</div></div>
+<div class="ttc" id="agroup__machine__learning_html_gab53c14440b2b2dd3172c66afc5c2f63f"><div class="ttname"><a href="../../d9/d66/group__machine__learning.html#gab53c14440b2b2dd3172c66afc5c2f63f">get_min_2d</a></div><div class="ttdeci">void get_min_2d(const std::vector&lt; std::valarray&lt; double &gt;&gt; &amp;X, double *val, int *x_idx, int *y_idx)</div><div class="ttdef"><b>Definition:</b> kohonen_som_topology.cpp:99</div></div>
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:36 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:38 for Algorithms_in_C++ by
     <a href="http://www.doxygen.org/index.html">
     <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
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diff --git a/d8/dee/avltree_8cpp.html b/d8/dee/avltree_8cpp.html
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@@ -743,7 +743,7 @@ Here is the call graph for this function:</div>
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:35 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:38 for Algorithms_in_C++ by
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diff --git a/d9/d00/factorial_8cpp.html b/d9/d00/factorial_8cpp.html
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:36 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:38 for Algorithms_in_C++ by
     <a href="http://www.doxygen.org/index.html">
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diff --git a/d9/d02/linear__search_8cpp.html b/d9/d02/linear__search_8cpp.html
index b9ae7ea71..d945e1188 100644
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@@ -231,7 +231,7 @@ Here is the call graph for this function:</div>
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:37 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:39 for Algorithms_in_C++ by
     <a href="http://www.doxygen.org/index.html">
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diff --git a/d9/d03/namespacestring__search.html b/d9/d03/namespacestring__search.html
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:38 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:41 for Algorithms_in_C++ by
     <a href="http://www.doxygen.org/index.html">
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diff --git a/d9/d1d/structqueue-members.html b/d9/d1d/structqueue-members.html
index 8d977fc48..3ff4ce963 100644
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   <ul>
-    <li class="footer">Generated on Sun Jun 21 2020 19:43:37 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:40 for Algorithms_in_C++ by
     <a href="http://www.doxygen.org/index.html">
     <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
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diff --git a/d9/d21/classmachine__learning_1_1adaline-members.html b/d9/d21/classmachine__learning_1_1adaline-members.html
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   <ul>
-    <li class="footer">Generated on Sun Jun 21 2020 19:43:38 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:41 for Algorithms_in_C++ by
     <a href="http://www.doxygen.org/index.html">
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diff --git a/d9/d24/poisson__dist_8cpp.html b/d9/d24/poisson__dist_8cpp.html
index 7abd3906d..ea62d0fbc 100644
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@@ -366,7 +366,7 @@ Here is the call graph for this function:</div>
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:37 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:39 for Algorithms_in_C++ by
     <a href="http://www.doxygen.org/index.html">
     <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
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diff --git a/d9/d49/kohonen__som__trace_8cpp.html b/d9/d49/kohonen__som__trace_8cpp.html
index 79a9ff027..a15ee68f8 100644
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+<div class="ttc" id="agroup__machine__learning_html_gaf5ce14f026d6d231bef29161bac2b485"><div class="ttname"><a href="../../d9/d66/group__machine__learning.html#gaf5ce14f026d6d231bef29161bac2b485">_random</a></div><div class="ttdeci">double _random(double a, double b)</div><div class="ttdef"><b>Definition:</b> kohonen_som_topology.cpp:50</div></div>
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 <!-- start footer part -->
 <div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
   <ul>
     <li class="navelem"><a class="el" href="../../dir_3343723ae086de42ee4ca9774da3a13f.html">machine_learning</a></li><li class="navelem"><a class="el" href="../../d9/d49/kohonen__som__trace_8cpp.html">kohonen_som_trace.cpp</a></li>
-    <li class="footer">Generated on Sun Jun 21 2020 19:43:35 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:38 for Algorithms_in_C++ by
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:36 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:38 for Algorithms_in_C++ by
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+<div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160;        <span class="comment">// for each feature in the array</span></div>
+<div class="line"><a name="l00078"></a><span class="lineno">   78</span>&#160;        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; num_features; j++) {</div>
+<div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160;            fp &lt;&lt; X[i][j];             <span class="comment">// print the feature value</span></div>
+<div class="line"><a name="l00080"></a><span class="lineno">   80</span>&#160;            <span class="keywordflow">if</span> (j &lt; num_features - 1)  <span class="comment">// if not the last feature</span></div>
+<div class="line"><a name="l00081"></a><span class="lineno">   81</span>&#160;                fp &lt;&lt; <span class="stringliteral">&quot;,&quot;</span>;             <span class="comment">// suffix comma</span></div>
+<div class="line"><a name="l00082"></a><span class="lineno">   82</span>&#160;        }</div>
+<div class="line"><a name="l00083"></a><span class="lineno">   83</span>&#160;        <span class="keywordflow">if</span> (i &lt; num_points - 1)  <span class="comment">// if not the last row</span></div>
+<div class="line"><a name="l00084"></a><span class="lineno">   84</span>&#160;            fp &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;          <span class="comment">// start a new line</span></div>
+<div class="line"><a name="l00085"></a><span class="lineno">   85</span>&#160;    }</div>
+<div class="line"><a name="l00086"></a><span class="lineno">   86</span>&#160; </div>
+<div class="line"><a name="l00087"></a><span class="lineno">   87</span>&#160;    fp.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream/close.html">close</a>();</div>
+<div class="line"><a name="l00088"></a><span class="lineno">   88</span>&#160;    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><a name="l00089"></a><span class="lineno">   89</span>&#160;}</div>
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:37 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:40 for Algorithms_in_C++ by
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     <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
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diff --git a/d9/d69/median__search_8cpp.html b/d9/d69/median__search_8cpp.html
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:37 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:39 for Algorithms_in_C++ by
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diff --git a/d9/d89/fibonacci_8cpp.html b/d9/d89/fibonacci_8cpp.html
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:36 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:38 for Algorithms_in_C++ by
     <a href="http://www.doxygen.org/index.html">
     <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
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diff --git a/d9/d90/struct_btree.html b/d9/d90/struct_btree.html
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@@ -125,7 +125,7 @@ struct <a class="el" href="../../d9/d90/struct_btree.html">Btree</a> *&#160;</td
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:37 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:40 for Algorithms_in_C++ by
     <a href="http://www.doxygen.org/index.html">
     <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
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diff --git a/d9/dd7/interpolation__search_8cpp.html b/d9/dd7/interpolation__search_8cpp.html
index e7f1ab1d8..1a0ac1307 100644
--- a/d9/dd7/interpolation__search_8cpp.html
+++ b/d9/dd7/interpolation__search_8cpp.html
@@ -241,7 +241,7 @@ Here is the call graph for this function:</div>
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     <li class="navelem"><a class="el" href="../../dir_19b2bf9199a15c634a08b1ede1dd896a.html">search</a></li><li class="navelem"><a class="el" href="../../d9/dd7/interpolation__search_8cpp.html">interpolation_search.cpp</a></li>
-    <li class="footer">Generated on Sun Jun 21 2020 19:43:37 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:39 for Algorithms_in_C++ by
     <a href="http://www.doxygen.org/index.html">
     <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
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diff --git a/d9/dee/classdouble__linked__list.html b/d9/dee/classdouble__linked__list.html
index fe72aa487..f2b0bcdf9 100644
--- a/d9/dee/classdouble__linked__list.html
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@@ -125,7 +125,7 @@ void&#160;</td><td class="memItemRight" valign="bottom"><b>reverseShow</b> ()</t
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   <ul>
     <li class="navelem"><a class="el" href="../../d9/dee/classdouble__linked__list.html">double_linked_list</a></li>
-    <li class="footer">Generated on Sun Jun 21 2020 19:43:37 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:40 for Algorithms_in_C++ by
     <a href="http://www.doxygen.org/index.html">
     <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
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diff --git a/da/d23/eulers__totient__function_8cpp.html b/da/d23/eulers__totient__function_8cpp.html
index f324643d3..04186dfe8 100644
--- a/da/d23/eulers__totient__function_8cpp.html
+++ b/da/d23/eulers__totient__function_8cpp.html
@@ -178,7 +178,7 @@ Some known values are:</p><ul>
 <div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
   <ul>
     <li class="navelem"><a class="el" href="../../dir_296d53ceaeaa7e099814a6def439fe8a.html">math</a></li><li class="navelem"><a class="el" href="../../da/d23/eulers__totient__function_8cpp.html">eulers_totient_function.cpp</a></li>
-    <li class="footer">Generated on Sun Jun 21 2020 19:43:35 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:38 for Algorithms_in_C++ by
     <a href="http://www.doxygen.org/index.html">
     <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
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diff --git a/da/d24/sqrt__double_8cpp.html b/da/d24/sqrt__double_8cpp.html
index b72f09f15..58b73d303 100644
--- a/da/d24/sqrt__double_8cpp.html
+++ b/da/d24/sqrt__double_8cpp.html
@@ -205,7 +205,7 @@ Here is the call graph for this function:</div>
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     <li class="navelem"><a class="el" href="../../dir_296d53ceaeaa7e099814a6def439fe8a.html">math</a></li><li class="navelem"><a class="el" href="../../da/d24/sqrt__double_8cpp.html">sqrt_double.cpp</a></li>
-    <li class="footer">Generated on Sun Jun 21 2020 19:43:36 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:38 for Algorithms_in_C++ by
     <a href="http://www.doxygen.org/index.html">
     <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
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diff --git a/da/d7b/primality__test_8cpp.html b/da/d7b/primality__test_8cpp.html
index d777abd6d..d161edabc 100644
--- a/da/d7b/primality__test_8cpp.html
+++ b/da/d7b/primality__test_8cpp.html
@@ -204,7 +204,7 @@ Here is the call graph for this function:</div>
 <div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
   <ul>
     <li class="navelem"><a class="el" href="../../dir_9510827d0b234b3cc54b29892f217477.html">others</a></li><li class="navelem"><a class="el" href="../../da/d7b/primality__test_8cpp.html">primality_test.cpp</a></li>
-    <li class="footer">Generated on Sun Jun 21 2020 19:43:37 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:39 for Algorithms_in_C++ by
     <a href="http://www.doxygen.org/index.html">
     <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
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diff --git a/da/d9a/class_graph.html b/da/d9a/class_graph.html
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--- a/da/d9a/class_graph.html
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@@ -572,7 +572,7 @@ int&#160;</td><td class="memItemRight" valign="bottom"><b>max_flow</b> = 0</td><
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   <ul>
     <li class="navelem"><a class="el" href="../../da/d9a/class_graph.html">Graph</a></li>
-    <li class="footer">Generated on Sun Jun 21 2020 19:43:37 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:40 for Algorithms_in_C++ by
     <a href="http://www.doxygen.org/index.html">
     <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
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diff --git a/da/d9a/palindrome__of__number_8cpp.html b/da/d9a/palindrome__of__number_8cpp.html
index 2972e3e40..0b736dd89 100644
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@@ -172,7 +172,7 @@ Here is the call graph for this function:</div>
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     <li class="navelem"><a class="el" href="../../dir_9510827d0b234b3cc54b29892f217477.html">others</a></li><li class="navelem"><a class="el" href="../../da/d9a/palindrome__of__number_8cpp.html">palindrome_of_number.cpp</a></li>
-    <li class="footer">Generated on Sun Jun 21 2020 19:43:37 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:39 for Algorithms_in_C++ by
     <a href="http://www.doxygen.org/index.html">
     <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
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diff --git a/da/de7/decimal__to__hexadecimal_8cpp.html b/da/de7/decimal__to__hexadecimal_8cpp.html
index 59025fbf5..2da2c719d 100644
--- a/da/de7/decimal__to__hexadecimal_8cpp.html
+++ b/da/de7/decimal__to__hexadecimal_8cpp.html
@@ -173,7 +173,7 @@ Here is the call graph for this function:</div>
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     <li class="navelem"><a class="el" href="../../dir_9510827d0b234b3cc54b29892f217477.html">others</a></li><li class="navelem"><a class="el" href="../../da/de7/decimal__to__hexadecimal_8cpp.html">decimal_to_hexadecimal.cpp</a></li>
-    <li class="footer">Generated on Sun Jun 21 2020 19:43:37 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:39 for Algorithms_in_C++ by
     <a href="http://www.doxygen.org/index.html">
     <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
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diff --git a/da/df2/durand__kerner__roots_8cpp.html b/da/df2/durand__kerner__roots_8cpp.html
index 3a18aac45..49a5728ba 100644
--- a/da/df2/durand__kerner__roots_8cpp.html
+++ b/da/df2/durand__kerner__roots_8cpp.html
@@ -577,7 +577,7 @@ Here is the call graph for this function:</div>
 <div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
   <ul>
     <li class="navelem"><a class="el" href="../../dir_9c6faab82c22511b50177aa2e38e2780.html">numerical_methods</a></li><li class="navelem"><a class="el" href="../../da/df2/durand__kerner__roots_8cpp.html">durand_kerner_roots.cpp</a></li>
-    <li class="footer">Generated on Sun Jun 21 2020 19:43:36 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:38 for Algorithms_in_C++ by
     <a href="http://www.doxygen.org/index.html">
     <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
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diff --git a/db/d07/spiral__print_8cpp.html b/db/d07/spiral__print_8cpp.html
index 3c544dc01..b88aa9646 100644
--- a/db/d07/spiral__print_8cpp.html
+++ b/db/d07/spiral__print_8cpp.html
@@ -299,7 +299,7 @@ Functions</h2></td></tr>
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:37 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:39 for Algorithms_in_C++ by
     <a href="http://www.doxygen.org/index.html">
     <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
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diff --git a/db/d0d/prime__factorization_8cpp.html b/db/d0d/prime__factorization_8cpp.html
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--- a/db/d0d/prime__factorization_8cpp.html
+++ b/db/d0d/prime__factorization_8cpp.html
@@ -321,7 +321,7 @@ Here is the call graph for this function:</div>
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:36 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:38 for Algorithms_in_C++ by
     <a href="http://www.doxygen.org/index.html">
     <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
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diff --git a/db/d3c/tower__of__hanoi_8cpp.html b/db/d3c/tower__of__hanoi_8cpp.html
index 7832b81d9..96c9830b8 100644
--- a/db/d3c/tower__of__hanoi_8cpp.html
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@@ -341,7 +341,7 @@ Here is the call graph for this function:</div>
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:37 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:39 for Algorithms_in_C++ by
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     <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:37 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:40 for Algorithms_in_C++ by
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:37 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:40 for Algorithms_in_C++ by
     <a href="http://www.doxygen.org/index.html">
     <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
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diff --git a/db/d8b/struct_node.html b/db/d8b/struct_node.html
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:37 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:40 for Algorithms_in_C++ by
     <a href="http://www.doxygen.org/index.html">
     <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
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diff --git a/db/d93/check__prime_8cpp.html b/db/d93/check__prime_8cpp.html
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:35 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:38 for Algorithms_in_C++ by
     <a href="http://www.doxygen.org/index.html">
     <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
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diff --git a/db/dd3/ode__forward__euler_8cpp.html b/db/dd3/ode__forward__euler_8cpp.html
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:36 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:38 for Algorithms_in_C++ by
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diff --git a/db/df3/happy__number_8cpp.html b/db/df3/happy__number_8cpp.html
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:37 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:39 for Algorithms_in_C++ by
     <a href="http://www.doxygen.org/index.html">
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diff --git a/dc/d1a/pascal__triangle_8cpp.html b/dc/d1a/pascal__triangle_8cpp.html
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:37 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:39 for Algorithms_in_C++ by
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diff --git a/dc/d38/ordinary__least__squares__regressor_8cpp.html b/dc/d38/ordinary__least__squares__regressor_8cpp.html
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 <a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
 <div class="textblock"><p>Linear regression example using <a href="https://en.wikipedia.org/wiki/Ordinary_least_squares">Ordinary least squares</a> </p>
-<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/kvedala">Krishna Vedala</a> Program that gets the number of data samples and number of features per sample along with output per sample. It applies OLS regression to compute the regression output for additional test data samples. </dd></dl>
+<p>Program that gets the number of data samples and number of features per sample along with output per sample. It applies OLS regression to compute the regression output for additional test data samples.</p>
+<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/kvedala">Krishna Vedala</a> </dd></dl>
 </div><h2 class="groupheader">Function Documentation</h2>
 <a id="a38ff1d954e9b7de93eb20e2dd101a045"></a>
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-<div class="fragment"><div class="line"><a name="l00310"></a><span class="lineno">  310</span>&#160;                                                            {</div>
-<div class="line"><a name="l00311"></a><span class="lineno">  311</span>&#160;    <span class="comment">// NxF</span></div>
-<div class="line"><a name="l00312"></a><span class="lineno">  312</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;T&gt;</a>&gt; X2 = X;</div>
-<div class="line"><a name="l00313"></a><span class="lineno">  313</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i &lt; X2.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); i++)</div>
-<div class="line"><a name="l00314"></a><span class="lineno">  314</span>&#160;        <span class="comment">// add Y-intercept -&gt; Nx(F+1)</span></div>
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-<div class="line"><a name="l00316"></a><span class="lineno">  316</span>&#160;    <span class="comment">// (F+1)xN</span></div>
-<div class="line"><a name="l00317"></a><span class="lineno">  317</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;T&gt;</a>&gt; Xt = <a class="code" href="../../dc/d38/ordinary__least__squares__regressor_8cpp.html#a889f9de199fa793497c864d8e493af05">get_transpose</a>(X2);</div>
-<div class="line"><a name="l00318"></a><span class="lineno">  318</span>&#160;    <span class="comment">// (F+1)x(F+1)</span></div>
-<div class="line"><a name="l00319"></a><span class="lineno">  319</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;T&gt;</a>&gt; tmp = <a class="code" href="../../dc/d38/ordinary__least__squares__regressor_8cpp.html#a98ab8f75d981088369b89b8be2182483">get_inverse</a>(Xt * X2);</div>
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-<div class="line"><a name="l00323"></a><span class="lineno">  323</span>&#160;    <span class="comment">//      &lt;&lt; &quot;Projection matrix: &quot; &lt;&lt; X2 * out &lt;&lt; endl;</span></div>
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+<div class="line"><a name="l00321"></a><span class="lineno">  321</span>&#160;    <span class="comment">// (F+1)xN</span></div>
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+<div class="line"><a name="l00323"></a><span class="lineno">  323</span>&#160;    <span class="comment">// cout &lt;&lt; endl</span></div>
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+<div class="line"><a name="l00325"></a><span class="lineno">  325</span>&#160; </div>
+<div class="line"><a name="l00326"></a><span class="lineno">  326</span>&#160;    <span class="comment">// Fx1,1    -&gt; (F+1)^th element is the independent constant</span></div>
+<div class="line"><a name="l00327"></a><span class="lineno">  327</span>&#160;    <span class="keywordflow">return</span> out * Y;</div>
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 <p>Get matrix inverse using Row-trasnformations. Given matrix must be a square and non-singular. </p><dl class="section return"><dt>Returns</dt><dd>inverse matrix </dd></dl>
-<div class="fragment"><div class="line"><a name="l00218"></a><span class="lineno">  218</span>&#160;                                      {</div>
-<div class="line"><a name="l00219"></a><span class="lineno">  219</span>&#160;    <span class="comment">// Assuming A is square matrix</span></div>
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-<div class="line"><a name="l00245"></a><span class="lineno">  245</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> row = 0; row &lt; N; row++) {</div>
-<div class="line"><a name="l00246"></a><span class="lineno">  246</span>&#160;        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> row2 = row; row2 &lt; N &amp;&amp; temp[row][row] == 0; row2++) {</div>
-<div class="line"><a name="l00247"></a><span class="lineno">  247</span>&#160;            <span class="comment">// this to ensure diagonal elements are not 0</span></div>
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-<div class="line"><a name="l00252"></a><span class="lineno">  252</span>&#160;        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> col2 = row; col2 &lt; N &amp;&amp; temp[row][row] == 0; col2++) {</div>
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-<div class="line"><a name="l00259"></a><span class="lineno">  259</span>&#160; </div>
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-<div class="line"><a name="l00263"></a><span class="lineno">  263</span>&#160;            <span class="keywordflow">return</span> inverse;</div>
-<div class="line"><a name="l00264"></a><span class="lineno">  264</span>&#160;        }</div>
-<div class="line"><a name="l00265"></a><span class="lineno">  265</span>&#160; </div>
-<div class="line"><a name="l00266"></a><span class="lineno">  266</span>&#160;        <span class="comment">// set diagonal to 1</span></div>
-<div class="line"><a name="l00267"></a><span class="lineno">  267</span>&#160;        <span class="keywordtype">float</span> divisor = <span class="keyword">static_cast&lt;</span><span class="keywordtype">float</span><span class="keyword">&gt;</span>(temp[row][row]);</div>
-<div class="line"><a name="l00268"></a><span class="lineno">  268</span>&#160;        temp[row] = temp[row] / divisor;</div>
-<div class="line"><a name="l00269"></a><span class="lineno">  269</span>&#160;        inverse[row] = inverse[row] / divisor;</div>
-<div class="line"><a name="l00270"></a><span class="lineno">  270</span>&#160;        <span class="comment">// Row transformations</span></div>
-<div class="line"><a name="l00271"></a><span class="lineno">  271</span>&#160;        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> row2 = 0; row2 &lt; N; row2++) {</div>
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-<div class="line"><a name="l00274"></a><span class="lineno">  274</span>&#160;            <span class="keywordtype">float</span> factor = temp[row2][row];</div>
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-<div class="line"><a name="l00279"></a><span class="lineno">  279</span>&#160; </div>
-<div class="line"><a name="l00280"></a><span class="lineno">  280</span>&#160;    <span class="keywordflow">return</span> inverse;</div>
-<div class="line"><a name="l00281"></a><span class="lineno">  281</span>&#160;}</div>
+<div class="fragment"><div class="line"><a name="l00219"></a><span class="lineno">  219</span>&#160;                                      {</div>
+<div class="line"><a name="l00220"></a><span class="lineno">  220</span>&#160;    <span class="comment">// Assuming A is square matrix</span></div>
+<div class="line"><a name="l00221"></a><span class="lineno">  221</span>&#160;    <span class="keywordtype">size_t</span> N = A.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();</div>
+<div class="line"><a name="l00222"></a><span class="lineno">  222</span>&#160; </div>
+<div class="line"><a name="l00223"></a><span class="lineno">  223</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;float&gt;</a>&gt; inverse(N);</div>
+<div class="line"><a name="l00224"></a><span class="lineno">  224</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> row = 0; row &lt; N; row++) {</div>
+<div class="line"><a name="l00225"></a><span class="lineno">  225</span>&#160;        <span class="comment">// preallocatae a resultant identity matrix</span></div>
+<div class="line"><a name="l00226"></a><span class="lineno">  226</span>&#160;        inverse[row] = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;float&gt;</a>(N);</div>
+<div class="line"><a name="l00227"></a><span class="lineno">  227</span>&#160;        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> col = 0; col &lt; N; col++)</div>
+<div class="line"><a name="l00228"></a><span class="lineno">  228</span>&#160;            inverse[row][col] = (row == col) ? 1.f : 0.f;</div>
+<div class="line"><a name="l00229"></a><span class="lineno">  229</span>&#160;    }</div>
+<div class="line"><a name="l00230"></a><span class="lineno">  230</span>&#160; </div>
+<div class="line"><a name="l00231"></a><span class="lineno">  231</span>&#160;    <span class="keywordflow">if</span> (!<a class="code" href="../../dc/d38/ordinary__least__squares__regressor_8cpp.html#a4921874435266592b222e3f2eda0e01f">is_square</a>(A)) {</div>
+<div class="line"><a name="l00232"></a><span class="lineno">  232</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;A must be a square matrix!&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00233"></a><span class="lineno">  233</span>&#160;        <span class="keywordflow">return</span> inverse;</div>
+<div class="line"><a name="l00234"></a><span class="lineno">  234</span>&#160;    }</div>
+<div class="line"><a name="l00235"></a><span class="lineno">  235</span>&#160; </div>
+<div class="line"><a name="l00236"></a><span class="lineno">  236</span>&#160;    <span class="comment">// preallocatae a temporary matrix identical to A</span></div>
+<div class="line"><a name="l00237"></a><span class="lineno">  237</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;float&gt;</a>&gt; temp(N);</div>
+<div class="line"><a name="l00238"></a><span class="lineno">  238</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> row = 0; row &lt; N; row++) {</div>
+<div class="line"><a name="l00239"></a><span class="lineno">  239</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;float&gt;</a> v(N);</div>
+<div class="line"><a name="l00240"></a><span class="lineno">  240</span>&#160;        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> col = 0; col &lt; N; col++)</div>
+<div class="line"><a name="l00241"></a><span class="lineno">  241</span>&#160;            v[col] = <span class="keyword">static_cast&lt;</span><span class="keywordtype">float</span><span class="keyword">&gt;</span>(A[row][col]);</div>
+<div class="line"><a name="l00242"></a><span class="lineno">  242</span>&#160;        temp[row] = v;</div>
+<div class="line"><a name="l00243"></a><span class="lineno">  243</span>&#160;    }</div>
+<div class="line"><a name="l00244"></a><span class="lineno">  244</span>&#160; </div>
+<div class="line"><a name="l00245"></a><span class="lineno">  245</span>&#160;    <span class="comment">// start transformations</span></div>
+<div class="line"><a name="l00246"></a><span class="lineno">  246</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> row = 0; row &lt; N; row++) {</div>
+<div class="line"><a name="l00247"></a><span class="lineno">  247</span>&#160;        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> row2 = row; row2 &lt; N &amp;&amp; temp[row][row] == 0; row2++) {</div>
+<div class="line"><a name="l00248"></a><span class="lineno">  248</span>&#160;            <span class="comment">// this to ensure diagonal elements are not 0</span></div>
+<div class="line"><a name="l00249"></a><span class="lineno">  249</span>&#160;            temp[row] = temp[row] + temp[row2];</div>
+<div class="line"><a name="l00250"></a><span class="lineno">  250</span>&#160;            inverse[row] = inverse[row] + inverse[row2];</div>
+<div class="line"><a name="l00251"></a><span class="lineno">  251</span>&#160;        }</div>
+<div class="line"><a name="l00252"></a><span class="lineno">  252</span>&#160; </div>
+<div class="line"><a name="l00253"></a><span class="lineno">  253</span>&#160;        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> col2 = row; col2 &lt; N &amp;&amp; temp[row][row] == 0; col2++) {</div>
+<div class="line"><a name="l00254"></a><span class="lineno">  254</span>&#160;            <span class="comment">// this to further ensure diagonal elements are not 0</span></div>
+<div class="line"><a name="l00255"></a><span class="lineno">  255</span>&#160;            <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> row2 = 0; row2 &lt; N; row2++) {</div>
+<div class="line"><a name="l00256"></a><span class="lineno">  256</span>&#160;                temp[row2][row] = temp[row2][row] + temp[row2][col2];</div>
+<div class="line"><a name="l00257"></a><span class="lineno">  257</span>&#160;                inverse[row2][row] = inverse[row2][row] + inverse[row2][col2];</div>
+<div class="line"><a name="l00258"></a><span class="lineno">  258</span>&#160;            }</div>
+<div class="line"><a name="l00259"></a><span class="lineno">  259</span>&#160;        }</div>
+<div class="line"><a name="l00260"></a><span class="lineno">  260</span>&#160; </div>
+<div class="line"><a name="l00261"></a><span class="lineno">  261</span>&#160;        <span class="keywordflow">if</span> (temp[row][row] == 0) {</div>
+<div class="line"><a name="l00262"></a><span class="lineno">  262</span>&#160;            <span class="comment">// Probably a low-rank matrix and hence singular</span></div>
+<div class="line"><a name="l00263"></a><span class="lineno">  263</span>&#160;            <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;Low-rank matrix, no inverse!&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00264"></a><span class="lineno">  264</span>&#160;            <span class="keywordflow">return</span> inverse;</div>
+<div class="line"><a name="l00265"></a><span class="lineno">  265</span>&#160;        }</div>
+<div class="line"><a name="l00266"></a><span class="lineno">  266</span>&#160; </div>
+<div class="line"><a name="l00267"></a><span class="lineno">  267</span>&#160;        <span class="comment">// set diagonal to 1</span></div>
+<div class="line"><a name="l00268"></a><span class="lineno">  268</span>&#160;        <span class="keywordtype">float</span> divisor = <span class="keyword">static_cast&lt;</span><span class="keywordtype">float</span><span class="keyword">&gt;</span>(temp[row][row]);</div>
+<div class="line"><a name="l00269"></a><span class="lineno">  269</span>&#160;        temp[row] = temp[row] / divisor;</div>
+<div class="line"><a name="l00270"></a><span class="lineno">  270</span>&#160;        inverse[row] = inverse[row] / divisor;</div>
+<div class="line"><a name="l00271"></a><span class="lineno">  271</span>&#160;        <span class="comment">// Row transformations</span></div>
+<div class="line"><a name="l00272"></a><span class="lineno">  272</span>&#160;        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> row2 = 0; row2 &lt; N; row2++) {</div>
+<div class="line"><a name="l00273"></a><span class="lineno">  273</span>&#160;            <span class="keywordflow">if</span> (row2 == row)</div>
+<div class="line"><a name="l00274"></a><span class="lineno">  274</span>&#160;                <span class="keywordflow">continue</span>;</div>
+<div class="line"><a name="l00275"></a><span class="lineno">  275</span>&#160;            <span class="keywordtype">float</span> factor = temp[row2][row];</div>
+<div class="line"><a name="l00276"></a><span class="lineno">  276</span>&#160;            temp[row2] = temp[row2] - factor * temp[row];</div>
+<div class="line"><a name="l00277"></a><span class="lineno">  277</span>&#160;            inverse[row2] = inverse[row2] - factor * inverse[row];</div>
+<div class="line"><a name="l00278"></a><span class="lineno">  278</span>&#160;        }</div>
+<div class="line"><a name="l00279"></a><span class="lineno">  279</span>&#160;    }</div>
+<div class="line"><a name="l00280"></a><span class="lineno">  280</span>&#160; </div>
+<div class="line"><a name="l00281"></a><span class="lineno">  281</span>&#160;    <span class="keywordflow">return</span> inverse;</div>
+<div class="line"><a name="l00282"></a><span class="lineno">  282</span>&#160;}</div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
@@ -334,17 +335,17 @@ template&lt;typename T &gt; </div>
       </table>
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 <p>matrix transpose </p><dl class="section return"><dt>Returns</dt><dd>resultant matrix </dd></dl>
-<div class="fragment"><div class="line"><a name="l00289"></a><span class="lineno">  289</span>&#160;                                      {</div>
-<div class="line"><a name="l00290"></a><span class="lineno">  290</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;T&gt;</a>&gt; result(A[0].size());</div>
-<div class="line"><a name="l00291"></a><span class="lineno">  291</span>&#160; </div>
-<div class="line"><a name="l00292"></a><span class="lineno">  292</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> row = 0; row &lt; A[0].<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); row++) {</div>
-<div class="line"><a name="l00293"></a><span class="lineno">  293</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;T&gt;</a> v(A.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>());</div>
-<div class="line"><a name="l00294"></a><span class="lineno">  294</span>&#160;        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> col = 0; col &lt; A.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); col++) v[col] = A[col][row];</div>
-<div class="line"><a name="l00295"></a><span class="lineno">  295</span>&#160; </div>
-<div class="line"><a name="l00296"></a><span class="lineno">  296</span>&#160;        result[row] = v;</div>
-<div class="line"><a name="l00297"></a><span class="lineno">  297</span>&#160;    }</div>
-<div class="line"><a name="l00298"></a><span class="lineno">  298</span>&#160;    <span class="keywordflow">return</span> result;</div>
-<div class="line"><a name="l00299"></a><span class="lineno">  299</span>&#160;}</div>
+<div class="fragment"><div class="line"><a name="l00290"></a><span class="lineno">  290</span>&#160;                                      {</div>
+<div class="line"><a name="l00291"></a><span class="lineno">  291</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;T&gt;</a>&gt; result(A[0].size());</div>
+<div class="line"><a name="l00292"></a><span class="lineno">  292</span>&#160; </div>
+<div class="line"><a name="l00293"></a><span class="lineno">  293</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> row = 0; row &lt; A[0].<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); row++) {</div>
+<div class="line"><a name="l00294"></a><span class="lineno">  294</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;T&gt;</a> v(A.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>());</div>
+<div class="line"><a name="l00295"></a><span class="lineno">  295</span>&#160;        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> col = 0; col &lt; A.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); col++) v[col] = A[col][row];</div>
+<div class="line"><a name="l00296"></a><span class="lineno">  296</span>&#160; </div>
+<div class="line"><a name="l00297"></a><span class="lineno">  297</span>&#160;        result[row] = v;</div>
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+<div class="line"><a name="l00299"></a><span class="lineno">  299</span>&#160;    <span class="keywordflow">return</span> result;</div>
+<div class="line"><a name="l00300"></a><span class="lineno">  300</span>&#160;}</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -374,14 +375,14 @@ template&lt;typename T &gt; </div>
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 <p>function to check if given matrix is a square matrix </p><dl class="section return"><dt>Returns</dt><dd>1 if true, 0 if false </dd></dl>
-<div class="fragment"><div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160;                                                        {</div>
-<div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160;    <span class="comment">// Assuming A is square matrix</span></div>
-<div class="line"><a name="l00056"></a><span class="lineno">   56</span>&#160;    <span class="keywordtype">size_t</span> N = A.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();</div>
-<div class="line"><a name="l00057"></a><span class="lineno">   57</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i &lt; N; i++)</div>
-<div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160;        <span class="keywordflow">if</span> (A[i].size() != N)</div>
-<div class="line"><a name="l00059"></a><span class="lineno">   59</span>&#160;            <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
-<div class="line"><a name="l00060"></a><span class="lineno">   60</span>&#160;    <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
-<div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160;}</div>
+<div class="fragment"><div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160;                                                        {</div>
+<div class="line"><a name="l00056"></a><span class="lineno">   56</span>&#160;    <span class="comment">// Assuming A is square matrix</span></div>
+<div class="line"><a name="l00057"></a><span class="lineno">   57</span>&#160;    <span class="keywordtype">size_t</span> N = A.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();</div>
+<div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i &lt; N; i++)</div>
+<div class="line"><a name="l00059"></a><span class="lineno">   59</span>&#160;        <span class="keywordflow">if</span> (A[i].size() != N)</div>
+<div class="line"><a name="l00060"></a><span class="lineno">   60</span>&#160;            <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
+<div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160;    <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
+<div class="line"><a name="l00062"></a><span class="lineno">   62</span>&#160;}</div>
 </div><!-- fragment -->
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@@ -400,56 +401,56 @@ template&lt;typename T &gt; </div>
       </table>
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 <p>main function </p>
-<div class="fragment"><div class="line"><a name="l00357"></a><span class="lineno">  357</span>&#160;           {</div>
-<div class="line"><a name="l00358"></a><span class="lineno">  358</span>&#160;    <span class="keywordtype">size_t</span> N, F;</div>
-<div class="line"><a name="l00359"></a><span class="lineno">  359</span>&#160; </div>
-<div class="line"><a name="l00360"></a><span class="lineno">  360</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter number of features: &quot;</span>;</div>
-<div class="line"><a name="l00361"></a><span class="lineno">  361</span>&#160;    <span class="comment">// number of features = columns</span></div>
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-<div class="line"><a name="l00397"></a><span class="lineno">  397</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;float&gt;</a> v(F);</div>
-<div class="line"><a name="l00398"></a><span class="lineno">  398</span>&#160;        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> cols = 0; cols &lt; F; cols++) std::cin &gt;&gt; v[cols];</div>
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+<div class="line"><a name="l00362"></a><span class="lineno">  362</span>&#160;    <span class="comment">// number of features = columns</span></div>
+<div class="line"><a name="l00363"></a><span class="lineno">  363</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; F;</div>
+<div class="line"><a name="l00364"></a><span class="lineno">  364</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter number of samples: &quot;</span>;</div>
+<div class="line"><a name="l00365"></a><span class="lineno">  365</span>&#160;    <span class="comment">// number of samples = rows</span></div>
+<div class="line"><a name="l00366"></a><span class="lineno">  366</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; N;</div>
+<div class="line"><a name="l00367"></a><span class="lineno">  367</span>&#160; </div>
+<div class="line"><a name="l00368"></a><span class="lineno">  368</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;float&gt;</a>&gt; <a class="code" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>(N);</div>
+<div class="line"><a name="l00369"></a><span class="lineno">  369</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;float&gt;</a> Y(N);</div>
+<div class="line"><a name="l00370"></a><span class="lineno">  370</span>&#160; </div>
+<div class="line"><a name="l00371"></a><span class="lineno">  371</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div>
+<div class="line"><a name="l00372"></a><span class="lineno">  372</span>&#160;        &lt;&lt; <span class="stringliteral">&quot;Enter training data. Per sample, provide features ad one output.&quot;</span></div>
+<div class="line"><a name="l00373"></a><span class="lineno">  373</span>&#160;        &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00374"></a><span class="lineno">  374</span>&#160; </div>
+<div class="line"><a name="l00375"></a><span class="lineno">  375</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> rows = 0; rows &lt; N; rows++) {</div>
+<div class="line"><a name="l00376"></a><span class="lineno">  376</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;float&gt;</a> v(F);</div>
+<div class="line"><a name="l00377"></a><span class="lineno">  377</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Sample# &quot;</span> &lt;&lt; rows + 1 &lt;&lt; <span class="stringliteral">&quot;: &quot;</span>;</div>
+<div class="line"><a name="l00378"></a><span class="lineno">  378</span>&#160;        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> cols = 0; cols &lt; F; cols++)</div>
+<div class="line"><a name="l00379"></a><span class="lineno">  379</span>&#160;            <span class="comment">// get the F features</span></div>
+<div class="line"><a name="l00380"></a><span class="lineno">  380</span>&#160;            <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; v[cols];</div>
+<div class="line"><a name="l00381"></a><span class="lineno">  381</span>&#160;        <a class="code" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>[rows] = v;</div>
+<div class="line"><a name="l00382"></a><span class="lineno">  382</span>&#160;        <span class="comment">// get the corresponding output</span></div>
+<div class="line"><a name="l00383"></a><span class="lineno">  383</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; Y[rows];</div>
+<div class="line"><a name="l00384"></a><span class="lineno">  384</span>&#160;    }</div>
+<div class="line"><a name="l00385"></a><span class="lineno">  385</span>&#160; </div>
+<div class="line"><a name="l00386"></a><span class="lineno">  386</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;float&gt;</a> beta = <a class="code" href="../../dc/d38/ordinary__least__squares__regressor_8cpp.html#a38ff1d954e9b7de93eb20e2dd101a045">fit_OLS_regressor</a>(<a class="code" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>, Y);</div>
+<div class="line"><a name="l00387"></a><span class="lineno">  387</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a> &lt;&lt; <span class="stringliteral">&quot;beta:&quot;</span> &lt;&lt; beta &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00388"></a><span class="lineno">  388</span>&#160; </div>
+<div class="line"><a name="l00389"></a><span class="lineno">  389</span>&#160;    <span class="keywordtype">size_t</span> T;</div>
+<div class="line"><a name="l00390"></a><span class="lineno">  390</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter number of test samples: &quot;</span>;</div>
+<div class="line"><a name="l00391"></a><span class="lineno">  391</span>&#160;    <span class="comment">// number of test sample inputs</span></div>
+<div class="line"><a name="l00392"></a><span class="lineno">  392</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; T;</div>
+<div class="line"><a name="l00393"></a><span class="lineno">  393</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;float&gt;</a>&gt; data2(T);</div>
+<div class="line"><a name="l00394"></a><span class="lineno">  394</span>&#160;    <span class="comment">// vector&lt;float&gt; Y2(T);</span></div>
+<div class="line"><a name="l00395"></a><span class="lineno">  395</span>&#160; </div>
+<div class="line"><a name="l00396"></a><span class="lineno">  396</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> rows = 0; rows &lt; T; rows++) {</div>
+<div class="line"><a name="l00397"></a><span class="lineno">  397</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Sample# &quot;</span> &lt;&lt; rows + 1 &lt;&lt; <span class="stringliteral">&quot;: &quot;</span>;</div>
+<div class="line"><a name="l00398"></a><span class="lineno">  398</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;float&gt;</a> v(F);</div>
+<div class="line"><a name="l00399"></a><span class="lineno">  399</span>&#160;        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> cols = 0; cols &lt; F; cols++) std::cin &gt;&gt; v[cols];</div>
+<div class="line"><a name="l00400"></a><span class="lineno">  400</span>&#160;        data2[rows] = v;</div>
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+<div class="line"><a name="l00403"></a><span class="lineno">  403</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;float&gt;</a> out = <a class="code" href="../../dc/d38/ordinary__least__squares__regressor_8cpp.html#a4bcaaf41c66da4d3a471dacef133def7">predict_OLS_regressor</a>(data2, beta);</div>
+<div class="line"><a name="l00404"></a><span class="lineno">  404</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> rows = 0; rows &lt; T; rows++) <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; out[rows] &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00405"></a><span class="lineno">  405</span>&#160; </div>
+<div class="line"><a name="l00406"></a><span class="lineno">  406</span>&#160;    <span class="keywordflow">return</span> 0;</div>
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 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
@@ -487,18 +488,18 @@ template&lt;typename T &gt; </div>
       </table>
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 <p>pre-multiplication of a vector by a scalar </p><dl class="section return"><dt>Returns</dt><dd>resultant vector </dd></dl>
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@@ -537,32 +538,32 @@ template&lt;typename T &gt; </div>
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 <p>Matrix multiplication such that if A is size (mxn) and B is of size (pxq) then the multiplication is defined only when n = p and the resultant matrix is of size (mxq)</p>
 <dl class="section return"><dt>Returns</dt><dd>resultant matrix </dd></dl>
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+<div class="line"><a name="l00098"></a><span class="lineno">   98</span>&#160;}</div>
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@@ -600,25 +601,25 @@ template&lt;typename T &gt; </div>
       </table>
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 <p>multiplication of a matrix with a column vector </p><dl class="section return"><dt>Returns</dt><dd>resultant vector </dd></dl>
-<div class="fragment"><div class="line"><a name="l00105"></a><span class="lineno">  105</span>&#160;                                                {</div>
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-<div class="line"><a name="l00107"></a><span class="lineno">  107</span>&#160;    <span class="keywordtype">size_t</span> N_A = A.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();</div>
-<div class="line"><a name="l00108"></a><span class="lineno">  108</span>&#160; </div>
-<div class="line"><a name="l00109"></a><span class="lineno">  109</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;T&gt;</a> result(N_A);</div>
-<div class="line"><a name="l00110"></a><span class="lineno">  110</span>&#160; </div>
-<div class="line"><a name="l00111"></a><span class="lineno">  111</span>&#160;    <span class="keywordflow">if</span> (A[0].size() != B.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>()) {</div>
-<div class="line"><a name="l00112"></a><span class="lineno">  112</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;Number of columns in A != Number of rows in B (&quot;</span></div>
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-<div class="line"><a name="l00114"></a><span class="lineno">  114</span>&#160;        <span class="keywordflow">return</span> result;</div>
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-<div class="line"><a name="l00118"></a><span class="lineno">  118</span>&#160;        result[row] = <span class="keyword">static_cast&lt;</span>T<span class="keyword">&gt;</span>(0);</div>
-<div class="line"><a name="l00119"></a><span class="lineno">  119</span>&#160;        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> j = 0; j &lt; B.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); j++) result[row] += A[row][j] * B[j];</div>
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-<div class="line"><a name="l00121"></a><span class="lineno">  121</span>&#160; </div>
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-<div class="line"><a name="l00123"></a><span class="lineno">  123</span>&#160;}</div>
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+<div class="line"><a name="l00113"></a><span class="lineno">  113</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;Number of columns in A != Number of rows in B (&quot;</span></div>
+<div class="line"><a name="l00114"></a><span class="lineno">  114</span>&#160;                  &lt;&lt; A[0].<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>() &lt;&lt; <span class="stringliteral">&quot;, &quot;</span> &lt;&lt; B.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>() &lt;&lt; <span class="stringliteral">&quot;)&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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@@ -656,17 +657,17 @@ template&lt;typename T &gt; </div>
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 <p>post-multiplication of a vector by a scalar </p><dl class="section return"><dt>Returns</dt><dd>resultant vector </dd></dl>
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-<div class="line"><a name="l00158"></a><span class="lineno">  158</span>&#160;}</div>
+<div class="fragment"><div class="line"><a name="l00149"></a><span class="lineno">  149</span>&#160;                                                                      {</div>
+<div class="line"><a name="l00150"></a><span class="lineno">  150</span>&#160;    <span class="comment">// Number of rows in A</span></div>
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@@ -756,21 +757,21 @@ template&lt;typename T &gt; </div>
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 <p>subtraction of two vectors of identical lengths </p><dl class="section return"><dt>Returns</dt><dd>resultant vector </dd></dl>
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@@ -808,9 +809,9 @@ template&lt;typename T &gt; </div>
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 <p>division of a vector by a scalar </p><dl class="section return"><dt>Returns</dt><dd>resultant vector </dd></dl>
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@@ -842,19 +843,19 @@ template&lt;typename T &gt; </div>
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 <p>operator to print a matrix </p>
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@@ -892,16 +893,16 @@ template&lt;typename T &gt; </div>
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 <p>operator to print a vector </p>
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@@ -949,18 +950,18 @@ template&lt;typename T &gt; </div>
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   <ul>
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:37 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:38 for Algorithms_in_C++ by
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diff --git a/dc/d93/trie__modern_8cpp.html b/dc/d93/trie__modern_8cpp.html
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+    <li class="footer">Generated on Mon Jun 22 2020 11:53:38 for Algorithms_in_C++ by
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:37 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:40 for Algorithms_in_C++ by
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     <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
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diff --git a/dc/dc5/paranthesis__matching_8cpp.html b/dc/dc5/paranthesis__matching_8cpp.html
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@@ -218,7 +218,7 @@ Implementation is C-type and does not utilize the C++ constructs </dd></dl>
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:37 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:39 for Algorithms_in_C++ by
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     <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:37 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:40 for Algorithms_in_C++ by
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     <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:37 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:40 for Algorithms_in_C++ by
     <a href="http://www.doxygen.org/index.html">
     <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:37 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:40 for Algorithms_in_C++ by
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+    <li class="footer">Generated on Mon Jun 22 2020 11:53:41 for Algorithms_in_C++ by
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diff --git a/dd/d3b/struct_entry.html b/dd/d3b/struct_entry.html
index fc541f325..aa5afbe5d 100644
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:37 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:40 for Algorithms_in_C++ by
     <a href="http://www.doxygen.org/index.html">
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diff --git a/dd/d4f/class_solution.html b/dd/d4f/class_solution.html
index aefaca98a..cf9f67283 100644
--- a/dd/d4f/class_solution.html
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:38 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:40 for Algorithms_in_C++ by
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index 926ba3a30..3b117e620 100644
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+    <li class="footer">Generated on Mon Jun 22 2020 11:53:41 for Algorithms_in_C++ by
     <a href="http://www.doxygen.org/index.html">
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diff --git a/dd/d65/lu__decompose_8cpp.html b/dd/d65/lu__decompose_8cpp.html
index 72e1a4bb5..eb381c449 100644
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:36 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:38 for Algorithms_in_C++ by
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+    <li class="footer">Generated on Mon Jun 22 2020 11:53:40 for Algorithms_in_C++ by
     <a href="http://www.doxygen.org/index.html">
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:37 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:40 for Algorithms_in_C++ by
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index f49a6a095..57b0702bd 100644
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:37 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:40 for Algorithms_in_C++ by
     <a href="http://www.doxygen.org/index.html">
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index de610ab06..4f461c87f 100644
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:37 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:40 for Algorithms_in_C++ by
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index a22b46ab4..11d61fdcc 100644
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+    <li class="footer">Generated on Mon Jun 22 2020 11:53:40 for Algorithms_in_C++ by
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index b942d02a1..89ae060c5 100644
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:37 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:40 for Algorithms_in_C++ by
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diff --git a/de/d29/class_fenwick_tree-members.html b/de/d29/class_fenwick_tree-members.html
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+    <li class="footer">Generated on Mon Jun 22 2020 11:53:40 for Algorithms_in_C++ by
     <a href="http://www.doxygen.org/index.html">
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diff --git a/de/d47/string__fibonacci_8cpp.html b/de/d47/string__fibonacci_8cpp.html
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:36 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:38 for Algorithms_in_C++ by
     <a href="http://www.doxygen.org/index.html">
     <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:38 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:41 for Algorithms_in_C++ by
     <a href="http://www.doxygen.org/index.html">
     <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
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diff --git a/de/d6a/knuth__morris__pratt_8cpp.html b/de/d6a/knuth__morris__pratt_8cpp.html
index d51890bea..f8ad47385 100644
--- a/de/d6a/knuth__morris__pratt_8cpp.html
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:37 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:40 for Algorithms_in_C++ by
     <a href="http://www.doxygen.org/index.html">
     <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
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diff --git a/de/d75/qr__eigen__values_8cpp.html b/de/d75/qr__eigen__values_8cpp.html
index 866f1d3a1..8208651ba 100644
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:37 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:38 for Algorithms_in_C++ by
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     <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
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index fb184eea0..4cca6ba89 100644
--- a/de/d7c/struct_trie_1_1_trie_node-members.html
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:38 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:41 for Algorithms_in_C++ by
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     <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
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diff --git a/de/d85/decimal__to__roman__numeral_8cpp.html b/de/d85/decimal__to__roman__numeral_8cpp.html
index 1b1776a03..28892a19a 100644
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:37 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:39 for Algorithms_in_C++ by
     <a href="http://www.doxygen.org/index.html">
     <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
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diff --git a/de/d8a/class_trie-members.html b/de/d8a/class_trie-members.html
index baca83c9d..ad5939018 100644
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:38 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:41 for Algorithms_in_C++ by
     <a href="http://www.doxygen.org/index.html">
     <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
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diff --git a/de/d91/class_queue___array-members.html b/de/d91/class_queue___array-members.html
index 353b47e5c..b073f1fe1 100644
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:37 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:40 for Algorithms_in_C++ by
     <a href="http://www.doxygen.org/index.html">
     <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
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--- a/de/d91/structlist-members.html
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:37 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:40 for Algorithms_in_C++ by
     <a href="http://www.doxygen.org/index.html">
     <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
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diff --git a/de/d9b/prime__numbers_8cpp.html b/de/d9b/prime__numbers_8cpp.html
index 6ab204e84..171979034 100644
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:36 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:38 for Algorithms_in_C++ by
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:37 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:40 for Algorithms_in_C++ by
     <a href="http://www.doxygen.org/index.html">
     <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
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diff --git a/de/dc3/binaryheap_8cpp.html b/de/dc3/binaryheap_8cpp.html
index 1319b16af..2d080eac7 100644
--- a/de/dc3/binaryheap_8cpp.html
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:35 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:38 for Algorithms_in_C++ by
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:37 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:40 for Algorithms_in_C++ by
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diff --git a/de/dcf/binary__exponent_8cpp.html b/de/dcf/binary__exponent_8cpp.html
index 6d790b240..423439219 100644
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:35 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:38 for Algorithms_in_C++ by
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index 690427fac..084ffc8da 100644
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+<tr class="memdesc:a002b2f4894492820fe708b1b7e7c5e70"><td class="mdescLeft">&#160;</td><td class="mdescRight">system accuracy limit <br /></td></tr>
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+#define&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../de/dd3/newton__raphson__method_8cpp.html#a0a3abbca80bc98e7abcb3ae73abe0f14">MAX_ITERATIONS</a>&#160;&#160;&#160;INT16_MAX</td></tr>
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-<p>define \(f(x)\) to find root for </p>
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+<p>define \(f(x)\) to find root for. Currently defined as: </p><p class="formulaDsp">
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-<p>define the derivative function \(f&#39;(x)\) </p>
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-<div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160;}</div>
+<p>define the derivative function \(f&#39;(x)\) For the current problem, it is: </p><p class="formulaDsp">
+\[ f&#39;(x) = 3x^2 - 4 \]
+</p>
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:39 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:41 for Algorithms_in_C++ by
     <a href="http://www.doxygen.org/index.html">
     <img class="footer" src="doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
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diff --git a/functions_rela.html b/functions_rela.html
index da4314f9c..4c427d791 100644
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:39 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:41 for Algorithms_in_C++ by
     <a href="http://www.doxygen.org/index.html">
     <img class="footer" src="doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
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diff --git a/functions_vars.html b/functions_vars.html
index 8734fa5ad..2e4ba9c55 100644
--- a/functions_vars.html
+++ b/functions_vars.html
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:39 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:41 for Algorithms_in_C++ by
     <a href="http://www.doxygen.org/index.html">
     <img class="footer" src="doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
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diff --git a/globals.html b/globals.html
index 1e588ab6d..e7839e98a 100644
--- a/globals.html
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:39 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:41 for Algorithms_in_C++ by
     <a href="http://www.doxygen.org/index.html">
     <img class="footer" src="doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
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diff --git a/globals_a.html b/globals_a.html
index acac601d4..e2f32ff44 100644
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:39 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:41 for Algorithms_in_C++ by
     <a href="http://www.doxygen.org/index.html">
     <img class="footer" src="doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
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diff --git a/globals_b.html b/globals_b.html
index 18b99b37f..a8bd18d1e 100644
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:39 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:41 for Algorithms_in_C++ by
     <a href="http://www.doxygen.org/index.html">
     <img class="footer" src="doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
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diff --git a/globals_c.html b/globals_c.html
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:39 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:41 for Algorithms_in_C++ by
     <a href="http://www.doxygen.org/index.html">
     <img class="footer" src="doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
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diff --git a/globals_d.html b/globals_d.html
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:39 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:41 for Algorithms_in_C++ by
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     <img class="footer" src="doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
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diff --git a/globals_defs.html b/globals_defs.html
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+<li>EPSILON
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+</li>
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+    <li class="footer">Generated on Mon Jun 22 2020 11:53:42 for Algorithms_in_C++ by
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     <img class="footer" src="doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
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diff --git a/globals_e.html b/globals_e.html
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+<li>EPSILON
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+: <a class="el" href="d3/d06/ode__semi__implicit__euler_8cpp.html#af3adf7b092a87868917ee5fb4255192b">ode_semi_implicit_euler.cpp</a>
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+    <li class="footer">Generated on Mon Jun 22 2020 11:53:41 for Algorithms_in_C++ by
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     <img class="footer" src="doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
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diff --git a/globals_f.html b/globals_f.html
index dc9192683..fd2e453ad 100644
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:39 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:41 for Algorithms_in_C++ by
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     <img class="footer" src="doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
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diff --git a/globals_func.html b/globals_func.html
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:39 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:41 for Algorithms_in_C++ by
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     <img class="footer" src="doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
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diff --git a/globals_func_a.html b/globals_func_a.html
index e105fbfd8..da2a856de 100644
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:39 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:41 for Algorithms_in_C++ by
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     <img class="footer" src="doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
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diff --git a/globals_func_b.html b/globals_func_b.html
index bc44774d9..86d91f587 100644
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:39 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:41 for Algorithms_in_C++ by
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     <img class="footer" src="doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
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diff --git a/globals_func_c.html b/globals_func_c.html
index 4a20040fe..6d1c3ae63 100644
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:39 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:42 for Algorithms_in_C++ by
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     <img class="footer" src="doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
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diff --git a/globals_func_d.html b/globals_func_d.html
index 56c039716..db7490459 100644
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:39 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:42 for Algorithms_in_C++ by
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     <img class="footer" src="doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
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diff --git a/globals_func_e.html b/globals_func_e.html
index 55232882f..5cf47c515 100644
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:39 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:42 for Algorithms_in_C++ by
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     <img class="footer" src="doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
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diff --git a/globals_func_f.html b/globals_func_f.html
index 30e9b1078..491967c29 100644
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:39 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:42 for Algorithms_in_C++ by
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     <img class="footer" src="doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
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diff --git a/globals_func_g.html b/globals_func_g.html
index 3cac0c5e7..aedabc788 100644
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:39 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:42 for Algorithms_in_C++ by
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     <img class="footer" src="doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
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diff --git a/globals_func_h.html b/globals_func_h.html
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:39 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:42 for Algorithms_in_C++ by
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     <img class="footer" src="doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
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diff --git a/globals_func_i.html b/globals_func_i.html
index 69050bcba..c3dd89b8f 100644
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:39 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:42 for Algorithms_in_C++ by
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     <img class="footer" src="doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
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diff --git a/globals_func_j.html b/globals_func_j.html
index 387cc6453..b15b8c4d5 100644
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:39 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:42 for Algorithms_in_C++ by
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     <img class="footer" src="doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
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diff --git a/globals_func_l.html b/globals_func_l.html
index b36433ae0..ae89e6ad8 100644
--- a/globals_func_l.html
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:39 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:42 for Algorithms_in_C++ by
     <a href="http://www.doxygen.org/index.html">
     <img class="footer" src="doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
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diff --git a/globals_func_m.html b/globals_func_m.html
index 7fcd5a633..9cdd2ed95 100644
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:39 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:42 for Algorithms_in_C++ by
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     <img class="footer" src="doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
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diff --git a/globals_func_n.html b/globals_func_n.html
index bd82ea6a3..f66f8cc4d 100644
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:39 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:42 for Algorithms_in_C++ by
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     <img class="footer" src="doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
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diff --git a/globals_func_o.html b/globals_func_o.html
index 2a4dd72e7..3acf6a739 100644
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-    <li class="footer">Generated on Sun Jun 21 2020 19:43:39 for Algorithms_in_C++ by
+    <li class="footer">Generated on Mon Jun 22 2020 11:53:42 for Algorithms_in_C++ by
     <a href="http://www.doxygen.org/index.html">
     <img class="footer" src="doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
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diff --git a/globals_func_p.html b/globals_func_p.html
index 17c6f31ae..c8c62bde9 100644
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