From 008ae67aedf8880f79824bc9bd914ff346172edd Mon Sep 17 00:00:00 2001 From: github-actions <${GITHUB_ACTOR}@users.noreply.github.com> Date: Fri, 30 Oct 2020 11:37:21 +0000 Subject: [PATCH] Documentation for 0c223567067fa2fbac7c5cf2afeb743f4682b48d --- d1/dbe/lu__decomposition_8h_source.html | 10 +- d1/de0/namespacenumerical__methods.html | 114 ++++ da/df2/durand__kerner__roots_8cpp.html | 3 +- dc/de2/false__position_8cpp__incl.map | 8 +- dc/de2/false__position_8cpp__incl.md5 | 2 +- dc/de2/false__position_8cpp__incl.svg | 58 +- dd/d29/false__position_8cpp.html | 297 +++++++---- dd/d29/false__position_8cpp.js | 7 +- ...003b5b2dcfff0769b957ab5c968b03d_cgraph.map | 4 - ...003b5b2dcfff0769b957ab5c968b03d_cgraph.md5 | 1 - ...003b5b2dcfff0769b957ab5c968b03d_cgraph.svg | 37 -- ...d69b49dc37da1c02b3ab8c7fe783494_cgraph.map | 4 + ...d69b49dc37da1c02b3ab8c7fe783494_cgraph.md5 | 1 + ...d69b49dc37da1c02b3ab8c7fe783494_cgraph.svg | 51 ++ ...5a6ec58b5064d63d4f0df3854496713_cgraph.map | 3 + ...5a6ec58b5064d63d4f0df3854496713_cgraph.md5 | 1 + ...5a6ec58b5064d63d4f0df3854496713_cgraph.svg | 29 + ...5cb7bfb90abc898e042d624372c5345_cgraph.map | 3 + ...5cb7bfb90abc898e042d624372c5345_cgraph.md5 | 1 + ...5cb7bfb90abc898e042d624372c5345_cgraph.svg | 29 + ...66f6b31b5ad750f1fe042a706a4e3d4_cgraph.map | 7 - ...66f6b31b5ad750f1fe042a706a4e3d4_cgraph.md5 | 1 - ...66f6b31b5ad750f1fe042a706a4e3d4_cgraph.svg | 82 --- df/dea/namespacefalse__position.html | 112 ++++ globals_defs.html | 5 +- globals_e.html | 9 +- globals_func_e.html | 7 +- globals_func_i.html | 6 +- globals_func_s.html | 7 +- globals_i.html | 8 +- globals_m.html | 15 +- globals_p.html | 6 +- globals_s.html | 7 +- namespaces.html | 88 ++-- namespaces_dup.js | 2 + navtreedata.js | 8 +- navtreeindex0.js | 14 +- navtreeindex1.js | 20 +- navtreeindex2.js | 22 +- navtreeindex3.js | 24 +- navtreeindex4.js | 14 +- navtreeindex5.js | 18 +- navtreeindex6.js | 19 +- search/all_10.js | 138 ++--- search/all_11.js | 235 ++++----- search/all_12.js | 42 +- search/all_13.js | 213 ++++---- search/all_14.js | 494 +++++++++--------- search/all_15.js | 220 ++++---- search/all_16.js | 128 ++--- search/all_17.js | 92 ++-- search/all_18.js | 170 +++--- search/all_19.js | 12 +- search/all_1a.js | 8 +- search/all_1b.js | 6 +- search/all_1c.js | 186 +++---- search/all_6.js | 2 +- search/all_7.js | 231 ++++---- search/all_8.js | 152 +++--- search/all_9.js | 88 ++-- search/all_a.js | 378 +++++++------- search/all_b.js | 16 +- search/all_c.js | 36 +- search/all_d.js | 162 +++--- search/all_e.js | 252 ++++----- search/all_f.js | 145 ++--- search/classes_0.js | 40 +- search/classes_1.js | 78 +-- search/classes_10.js | 6 +- search/classes_11.js | 80 +-- search/classes_12.js | 96 ++-- search/classes_13.js | 46 +- search/classes_14.js | 64 +-- search/classes_15.js | 38 +- search/classes_16.js | 62 +-- search/classes_17.js | 4 +- search/classes_18.js | 2 +- search/classes_2.js | 70 +-- search/classes_3.js | 32 +- search/classes_4.js | 34 +- search/classes_5.js | 34 +- search/classes_6.js | 12 +- search/classes_7.js | 18 +- search/classes_8.js | 196 +++---- search/classes_9.js | 2 +- search/classes_a.js | 4 +- search/classes_b.js | 36 +- search/classes_c.js | 76 +-- search/classes_d.js | 36 +- search/classes_e.js | 24 +- search/classes_f.js | 34 +- search/defines_0.js | 4 +- search/defines_1.js | 4 +- search/defines_2.js | 4 +- search/defines_3.js | 2 +- search/defines_4.js | 4 +- search/defines_5.js | 4 +- search/defines_6.js | 4 +- search/files_0.js | 2 +- search/files_1.js | 8 +- search/files_10.js | 26 +- search/files_11.js | 14 +- search/files_12.js | 6 +- search/files_13.js | 36 +- search/files_14.js | 10 +- search/files_15.js | 6 +- search/files_16.js | 4 +- search/files_17.js | 2 +- search/files_2.js | 26 +- search/files_3.js | 20 +- search/files_4.js | 18 +- search/files_5.js | 6 +- search/files_6.js | 18 +- search/files_7.js | 14 +- search/files_8.js | 16 +- search/files_9.js | 8 +- search/files_a.js | 6 +- search/files_b.js | 10 +- search/files_c.js | 26 +- search/files_d.js | 20 +- search/files_e.js | 14 +- search/files_f.js | 8 +- search/functions_0.js | 6 +- search/functions_1.js | 162 +++--- search/functions_10.js | 165 +++--- search/functions_11.js | 18 +- search/functions_12.js | 155 +++--- search/functions_13.js | 378 +++++++------- search/functions_14.js | 164 +++--- search/functions_15.js | 84 +-- search/functions_16.js | 46 +- search/functions_17.js | 150 +++--- search/functions_18.js | 6 +- search/functions_19.js | 2 +- search/functions_1a.js | 4 +- search/functions_1b.js | 186 +++---- search/functions_2.js | 122 ++--- search/functions_3.js | 162 +++--- search/functions_4.js | 188 +++---- search/functions_5.js | 114 ++-- search/functions_6.js | 208 ++++---- search/functions_7.js | 128 ++--- search/functions_8.js | 44 +- search/functions_9.js | 190 +++---- search/functions_a.js | 6 +- search/functions_b.js | 18 +- search/functions_c.js | 102 ++-- search/functions_d.js | 174 +++--- search/functions_e.js | 102 ++-- search/functions_f.js | 116 ++-- search/groups_0.js | 2 +- search/groups_1.js | 4 +- search/groups_2.js | 2 +- search/namespaces_0.js | 2 +- search/namespaces_1.js | 2 +- search/namespaces_10.js | 17 +- search/namespaces_11.js | 16 +- search/namespaces_12.js | 2 +- search/namespaces_13.js | 3 +- search/namespaces_14.js | 3 +- search/namespaces_15.html | 36 ++ search/namespaces_15.js | 4 + search/namespaces_2.js | 8 +- search/namespaces_3.js | 6 +- search/namespaces_4.js | 3 +- search/namespaces_5.js | 4 +- search/namespaces_6.js | 3 +- search/namespaces_7.js | 2 +- search/namespaces_8.js | 3 +- search/namespaces_9.js | 5 +- search/namespaces_a.js | 8 +- search/namespaces_b.js | 9 +- search/namespaces_c.js | 6 +- search/namespaces_d.js | 4 +- search/namespaces_e.js | 5 +- search/namespaces_f.js | 4 +- search/pages_0.js | 4 +- search/pages_1.js | 2 +- search/pages_2.js | 2 +- search/pages_3.js | 2 +- search/pages_4.js | 4 +- search/related_0.js | 10 +- search/searchdata.js | 2 +- search/typedefs_0.js | 2 +- search/typedefs_1.js | 2 +- search/typedefs_2.js | 2 +- search/variables_0.js | 4 +- search/variables_1.js | 10 +- search/variables_10.js | 20 +- search/variables_11.js | 2 +- search/variables_12.js | 4 +- search/variables_13.js | 2 +- search/variables_14.js | 2 +- search/variables_15.js | 2 +- search/variables_2.js | 2 +- search/variables_3.js | 4 +- search/variables_4.js | 4 +- search/variables_5.js | 8 +- search/variables_6.js | 16 +- search/variables_7.js | 4 +- search/variables_8.js | 2 +- search/variables_9.js | 6 +- search/variables_a.js | 12 +- search/variables_b.js | 8 +- search/variables_c.js | 16 +- search/variables_d.js | 4 +- search/variables_e.js | 2 +- search/variables_f.js | 18 +- 208 files changed, 4970 insertions(+), 4621 deletions(-) create mode 100644 d1/de0/namespacenumerical__methods.html delete mode 100644 dd/d29/false__position_8cpp_a2003b5b2dcfff0769b957ab5c968b03d_cgraph.map delete mode 100644 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mode 100644 dd/d29/false__position_8cpp_ae66f6b31b5ad750f1fe042a706a4e3d4_cgraph.map delete mode 100644 dd/d29/false__position_8cpp_ae66f6b31b5ad750f1fe042a706a4e3d4_cgraph.md5 delete mode 100644 dd/d29/false__position_8cpp_ae66f6b31b5ad750f1fe042a706a4e3d4_cgraph.svg create mode 100644 df/dea/namespacefalse__position.html create mode 100644 search/namespaces_15.html create mode 100644 search/namespaces_15.js diff --git a/d1/dbe/lu__decomposition_8h_source.html b/d1/dbe/lu__decomposition_8h_source.html index 1384a59da..f4826afbd 100644 --- a/d1/dbe/lu__decomposition_8h_source.html +++ b/d1/dbe/lu__decomposition_8h_source.html @@ -207,7 +207,6 @@ $(document).ready(function(){initNavTree('d1/dbe/lu__decomposition_8h_source.htm
math::lcmSum
uint64_t lcmSum(const uint16_t &num)
Definition: lcm_sum.cpp:28
prime_numbers
std::vector< int > prime_numbers
Definition: prime_factorization.cpp:16
main
int main()
Definition: primes_up_to_billion.cpp:26
-
MAX_ITERATIONS
#define MAX_ITERATIONS
Maximum number of iterations to check.
Definition: false_position.cpp:24
statistics::stats_computer2::operator>>
friend std::istream & operator>>(std::istream &input, stats_computer2 &stat)
Definition: realtime_stats.cpp:97
mat_size
ll mat_size
Definition: matrix_exponentiation.cpp:45
EPSILON
#define EPSILON
solution accuracy limit
Definition: golden_search_extrema.cpp:17
@@ -216,7 +215,9 @@ $(document).ready(function(){initNavTree('d1/dbe/lu__decomposition_8h_source.htm
std::uniform_int_distribution
primes
std::vector< int > primes(int max)
Definition: prime_numbers.cpp:12
miller_rabin_primality_test
bool miller_rabin_primality_test(T num, T repeats)
Definition: miller_rabin.cpp:125
+
numerical_methods::false_position::regula_falsi
static float regula_falsi(float x1, float x2, float y1, float y2)
This function finds root of the equation in given interval i.e. (x1,x2).
Definition: false_position.cpp:54
std::clock_t
+
numerical_methods
for io operations
test_3
static void test_3()
Definition: heavy_light_decomposition.cpp:592
std::pair
main
int main()
Definition: brent_method_extrema.cpp:204
@@ -230,6 +231,7 @@ $(document).ready(function(){initNavTree('d1/dbe/lu__decomposition_8h_source.htm
test_2
static void test_2()
Definition: heavy_light_decomposition.cpp:549
ans
ll ans(ll n)
Definition: matrix_exponentiation.cpp:91
main
int main()
Definition: sieve_of_eratosthenes.cpp:65
+
numerical_methods::false_position::eq
static float eq(float x)
This function gives the value of f(x) for given x.
Definition: false_position.cpp:44
test
static void test()
Definition: lcm_sum.cpp:65
sieve
std::vector< bool > sieve(uint32_t N)
Definition: sieve_of_eratosthenes.cpp:26
complex_str
const char * complex_str(const std::complex< double > &x)
Definition: durand_kerner_roots.cpp:76
@@ -259,6 +261,7 @@ $(document).ready(function(){initNavTree('d1/dbe/lu__decomposition_8h_source.htm
std::isnan
T isnan(T... args)
statistics
Statistical algorithms.
test2
void test2()
Definition: sum_of_digits.cpp:49
+
false_position
Functions for False Position method.
EPSILON
constexpr double EPSILON
system accuracy limit
Definition: newton_raphson_method.cpp:20
std::snprintf
T snprintf(T... args)
std::random_device
@@ -266,7 +269,7 @@ $(document).ready(function(){initNavTree('d1/dbe/lu__decomposition_8h_source.htm
std::numeric_limits::infinity
T infinity(T... args)
std::cout
std::ofstream
STL class.
-
main
int main()
Definition: false_position.cpp:39
+
main
int main()
Main function.
Definition: false_position.cpp:106
std::isinf
T isinf(T... args)
main
int main()
Main function.
Definition: lcm_sum.cpp:96
statistics::stats_computer2::variance
double variance() const
Definition: realtime_stats.cpp:89
@@ -286,7 +289,6 @@ $(document).ready(function(){initNavTree('d1/dbe/lu__decomposition_8h_source.htm
math::magic_number
bool magic_number(const uint64_t &n)
Definition: magic_number.cpp:32
tests
static void tests()
Test function.
Definition: magic_number.cpp:51
main
int main(int argc, char **argv)
Definition: realtime_stats.cpp:158
-
sgn
int sgn(T val)
Definition: false_position.cpp:34
print
void print(uint32_t N, const std::vector< bool > &is_prime)
Definition: sieve_of_eratosthenes.cpp:44
std::rand
T rand(T... args)
std::swap
T swap(T... args)
@@ -327,7 +329,6 @@ $(document).ready(function(){initNavTree('d1/dbe/lu__decomposition_8h_source.htm
test1
void test1()
Definition: sum_of_digits.cpp:40
std::complex
STL class.
std::complex::imag
T imag(T... args)
-
eq
static double eq(double i)
Definition: false_position.cpp:28
test1
void test1()
Test function to find root for the function in the interval Expected result = 2.
Definition: brent_method_extrema.cpp:143
add
std::string add(std::string a, std::string b)
Definition: string_fibonacci.cpp:24
std::make_pair
T make_pair(T... args)
@@ -345,6 +346,7 @@ $(document).ready(function(){initNavTree('d1/dbe/lu__decomposition_8h_source.htm
Sieve
void Sieve(int64_t n)
Definition: primes_up_to_billion.cpp:13
std::cin
operator<<
std::ostream & operator<<(std::ostream &out, matrix< T > const &v)
Definition: lu_decompose.cpp:18
+
numerical_methods::false_position::printRoot
void printRoot(float root, const int16_t &count)
This function prints roots of the equation.
Definition: false_position.cpp:84
statistics::stats_computer2::mean
double mean() const
Definition: realtime_stats.cpp:86
isPrime
bool isPrime(int64_t m)
Definition: modular_inverse_fermat_little_theorem.cpp:68
std::ofstream::is_open
T is_open(T... args)
diff --git a/d1/de0/namespacenumerical__methods.html b/d1/de0/namespacenumerical__methods.html new file mode 100644 index 000000000..0d5d04c80 --- /dev/null +++ b/d1/de0/namespacenumerical__methods.html @@ -0,0 +1,114 @@ + + + + + + + +Algorithms_in_C++: numerical_methods Namespace Reference + + + + + + + + + + + + + + + +
+
+ + + + + + +
+
Algorithms_in_C++ +  1.0.0 +
+
Set of algorithms implemented in C++.
+
+
+ + + + + + + +
+
+ +
+
+
+ +
+ +
+
+ + +
+ +
+ +
+
+
numerical_methods Namespace Reference
+
+
+ +

for io operations +More...

+

Detailed Description

+

for io operations

+

for math operations

+

Numerical methods

+
+
+ + + + diff --git a/da/df2/durand__kerner__roots_8cpp.html b/da/df2/durand__kerner__roots_8cpp.html index cee77c07e..913740094 100644 --- a/da/df2/durand__kerner__roots_8cpp.html +++ b/da/df2/durand__kerner__roots_8cpp.html @@ -146,7 +146,7 @@ int main (int argc, ch

Compute all possible approximate roots of any given polynomial using Durand Kerner algorithm

Author
Krishna Vedala

Test the algorithm online: https://gist.github.com/kvedala/27f1b0b6502af935f6917673ec43bcd7

-

Try the highly unstable Wilkinson's polynomial:

./numerical_methods/durand_kerner_roots 1 -210 20615 -1256850 53327946
+

Try the highly unstable Wilkinson's polynomial:

./numerical_methods/durand_kerner_roots 1 -210 20615 -1256850 53327946
-1672280820 40171771630 -756111184500 11310276995381 -135585182899530
1307535010540395 -10142299865511450 63030812099294896 -311333643161390640
1206647803780373360 -3599979517947607200 8037811822645051776
@@ -552,6 +552,7 @@ Here is the call graph for this function:
check_termination
bool check_termination(long double delta)
Definition: durand_kerner_roots.cpp:91
+
numerical_methods
for io operations
std::pair
complex_str
const char * complex_str(const std::complex< double > &x)
Definition: durand_kerner_roots.cpp:76
durand_kerner_algo
std::pair< uint32_t, double > durand_kerner_algo(const std::valarray< double > &coeffs, std::valarray< std::complex< double >> *roots, bool write_log=false)
Definition: durand_kerner_roots.cpp:109
diff --git a/dc/de2/false__position_8cpp__incl.map b/dc/de2/false__position_8cpp__incl.map index 5ae67bde1..45c168f57 100644 --- a/dc/de2/false__position_8cpp__incl.map +++ b/dc/de2/false__position_8cpp__incl.map @@ -1,7 +1,5 @@ - - - - - + + + diff --git a/dc/de2/false__position_8cpp__incl.md5 b/dc/de2/false__position_8cpp__incl.md5 index b1e8b238f..02f74003b 100644 --- a/dc/de2/false__position_8cpp__incl.md5 +++ b/dc/de2/false__position_8cpp__incl.md5 @@ -1 +1 @@ -af7e510fea5907e77434a402cd0066d5 \ No newline at end of file +39d01b65c27902f09e5b364fbbe0afed \ No newline at end of file diff --git a/dc/de2/false__position_8cpp__incl.svg b/dc/de2/false__position_8cpp__incl.svg index 53e4beaf3..35d4ff8f9 100644 --- a/dc/de2/false__position_8cpp__incl.svg +++ b/dc/de2/false__position_8cpp__incl.svg @@ -4,18 +4,18 @@ - + numerical_methods/false_position.cpp - + Node1 - -numerical_methods/false -_position.cpp + +numerical_methods/false +_position.cpp @@ -23,61 +23,31 @@ Node2 - -cmath + +cmath Node1->Node2 - - + + Node3 - -cstdlib + +iostream Node1->Node3 - - - - - -Node4 - - -iostream - - - - - -Node1->Node4 - - - - - -Node5 - - -limits - - - - - -Node1->Node5 - - + + diff --git a/dd/d29/false__position_8cpp.html b/dd/d29/false__position_8cpp.html index 876cb1d24..b1309e8af 100644 --- a/dd/d29/false__position_8cpp.html +++ b/dd/d29/false__position_8cpp.html @@ -91,7 +91,7 @@ $(document).ready(function(){initNavTree('dd/d29/false__position_8cpp.html','../
-Macros | +Namespaces | Functions
false_position.cpp File Reference
@@ -101,46 +101,52 @@ $(document).ready(function(){initNavTree('dd/d29/false__position_8cpp.html','../

Solve the equation \(f(x)=0\) using false position method, also known as the Secant method. More...

#include <cmath>
-#include <cstdlib>
#include <iostream>
-#include <limits>
Include dependency graph for false_position.cpp:
-
+
- - - - - - + + + + + + +

-Macros

-#define EPSILON    1e-6
 
-#define MAX_ITERATIONS   50000
 Maximum number of iterations to check.
 

+Namespaces

 numerical_methods
 for io operations
 
 false_position
 Functions for False Position method.
 
- - - - - + + + + + + + + + +

Functions

static double eq (double i)
 
template<typename T >
int sgn (T val)
 
static float numerical_methods::false_position::eq (float x)
 This function gives the value of f(x) for given x. More...
 
static float numerical_methods::false_position::regula_falsi (float x1, float x2, float y1, float y2)
 This function finds root of the equation in given interval i.e. (x1,x2). More...
 
void numerical_methods::false_position::printRoot (float root, const int16_t &count)
 This function prints roots of the equation. More...
 
int main ()
 Main function. More...
 

Detailed Description

Solve the equation \(f(x)=0\) using false position method, also known as the Secant method.

-

Given two points \(a\) and \(b\) such that \(f(a)<0\) and \(f(b)>0\), then the \((i+1)^\text{th}\) approximation is given by:

+

First, multiple intervals are selected with the interval gap provided. Separate recursive function called for every root. Roots are printed Separatelt.

+

For an interval [a,b] \(a\) and \(b\) such that \(f(a)<0\) and \(f(b)>0\), then the \((i+1)^\text{th}\) approximation is given by:

\[ x_{i+1} = \frac{a_i\cdot f(b_i) - b_i\cdot f(a_i)}{f(b_i) - f(a_i)} \]

For the next iteration, the interval is selected as: \([a,x]\) if \(x>0\) or \([x,b]\) if \(x<0\). The Process is continued till a close enough approximation is achieved.

-
See also
newton_raphson_method.cpp, bisection_method.cpp
+
See also
newton_raphson_method.cpp, bisection_method.cpp
+
Author
Unknown author
+
+Samruddha Patil

Function Documentation

- -

◆ eq()

+ +

◆ eq()

@@ -149,10 +155,10 @@ Functions - + - - + +
static double eq static float numerical_methods::false_position::eq (double i)float x)
@@ -162,14 +168,22 @@ Functions
-

define \(f(x)\) to find root for

-
28  {
-
29  return (std::pow(i, 3) - (4 * i) - 9); // origial equation
-
30 }
+ +

This function gives the value of f(x) for given x.

+
Parameters
+ + +
xvalue for which we have to find value of f(x).
+
+
+
Returns
value of f(x) for given x.
+
44  {
+
45  return (x*x-x); // original equation
+
46 }
Here is the call graph for this function:
-
+
@@ -190,85 +204,188 @@ Here is the call graph for this function:
-

main function

-
39  {
-
40  double a = -1, b = 1, x, z, m, n, c;
-
41  int i;
-
42 
-
43  // loop to find initial intervals a, b
-
44  for (int i = 0; i < MAX_ITERATIONS; i++) {
-
45  z = eq(a);
-
46  x = eq(b);
-
47  if (sgn(z) == sgn(x)) { // same signs, increase interval
-
48  b++;
-
49  a--;
-
50  } else { // if opposite signs, we got our interval
-
51  break;
-
52  }
-
53  }
-
54 
-
55  std::cout << "\nFirst initial: " << a;
-
56  std::cout << "\nSecond initial: " << b;
-
57 
-
58  for (i = 0; i < MAX_ITERATIONS; i++) {
-
59  m = eq(a);
-
60  n = eq(b);
-
61 
-
62  c = ((a * n) - (b * m)) / (n - m);
-
63 
-
64  a = c;
-
65  z = eq(c);
-
66 
-
67  if (std::abs(z) < EPSILON) { // stoping criteria
-
68  break;
-
69  }
-
70  }
-
71 
-
72  std::cout << "\n\nRoot: " << c << "\t\tSteps: " << i << std::endl;
-
73  return 0;
-
74 }
-
-Here is the call graph for this function:
-
-
-
-
+

Main function.

+
Returns
0 on exit
+
106  {
+
107  float a=0, b=0,i=0,root=0;
+
108  int16_t count=0;
+
109  float range = 100000; //Range in which we have to find the root. (-range,range)
+
110  float gap = 0.5; // interval gap. lesser the gap more the accuracy
+
111  a = numerical_methods::false_position::eq((-1)*range);
+
112  i=((-1)*range + gap);
+
113  //while loop for selecting proper interval in provided range and with provided interval gap.
+
114  while(i<=range){
+
115  b = numerical_methods::false_position::eq(i);
+
116  if(b==0){
+
117  count++;
+
118  numerical_methods::false_position::printRoot(i,count);
+
119  }
+
120  if(a*b<0){
+
121  root = numerical_methods::false_position::regula_falsi(i-gap,i,a,b);
+
122  count++;
+
123  numerical_methods::false_position::printRoot(root,count);
+
124  }
+
125  a=b;
+
126  i+=gap;
+
127  }
+
128  return 0;
+
129 }
+
- -

◆ sgn()

+ +

◆ printRoot()

-
-template<typename T >
- + - - + + + + + + + + + + + +
int sgn void numerical_methods::false_position::printRoot (T val)float root,
const int16_t & count 
)
-

get the sign of any given number

-
34  {
-
35  return (T(0) < val) - (val < T(0));
-
36 }
-
+ +

This function prints roots of the equation.

+
Parameters
+ + + +
rootwhich we have to print.
countwhich is count of the root in an interval [-range,range].
+
+
+
84  {
+
85  if(count==1){
+
86  std::cout << "Your 1st root is : " << root << std::endl;
+
87  }
+
88  else if(count==2){
+
89  std::cout << "Your 2nd root is : " << root << std::endl;
+
90  }
+
91  else if(count==3){
+
92  std::cout << "Your 3rd root is : " << root << std::endl;
+
93  }
+
94  else{
+
95  std::cout << "Your "<<count<<"th root is : " << root << std::endl;
+
96  }
+
97 }
+
+Here is the call graph for this function:
+
+
+
+
+ +
+
+ +

◆ regula_falsi()

+ +
+
+ + + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
static float numerical_methods::false_position::regula_falsi (float x1,
float x2,
float y1,
float y2 
)
+ 		+static
+
+ +

This function finds root of the equation in given interval i.e. (x1,x2).

+
Parameters
+ + + +
x1,x2values for an interval in which root is present.
y1,y2values of function at x1, x2 espectively.
+
+
+
Returns
root of the equation in the given interval.
+
54  {
+
55  float diff = x1-x2;
+
56  if(diff<0){
+
57  diff= (-1)*diff;
+
58  }
+
59  if(diff<0.00001){
+
60  if (y1<0) {
+
61  y1=-y1;
+
62  }
+
63  if (y2<0) {
+
64  y2=-y2;
+
65  }
+
66  if (y1<y2) {
+
67  return x1;
+
68  }
+
69  else {
+
70  return x2;
+
71  }
+
72  }
+
73  float x3=0,y3=0;
+
74  x3 = x1 - (x1-x2)*(y1)/(y1-y2);
+
75  y3 = eq(x3);
+
76  return regula_falsi(x2,x3,y2,y3);
+
77 }
+
+Here is the call graph for this function:
+
+
+
+
+
-
MAX_ITERATIONS
#define MAX_ITERATIONS
Maximum number of iterations to check.
Definition: false_position.cpp:24
-
EPSILON
constexpr double EPSILON
system accuracy limit
Definition: newton_raphson_method.cpp:20
+
numerical_methods::false_position::regula_falsi
static float regula_falsi(float x1, float x2, float y1, float y2)
This function finds root of the equation in given interval i.e. (x1,x2).
Definition: false_position.cpp:54
+
numerical_methods::false_position::eq
static float eq(float x)
This function gives the value of f(x) for given x.
Definition: false_position.cpp:44
std::cout
-
sgn
int sgn(T val)
Definition: false_position.cpp:34
std::endl
T endl(T... args)
-
eq
static double eq(double i)
Definition: false_position.cpp:28
-
std::pow
T pow(T... args)
+
numerical_methods::false_position::printRoot
void printRoot(float root, const int16_t &count)
This function prints roots of the equation.
Definition: false_position.cpp:84
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