diff --git a/annotated.html b/annotated.html index 4b31a1c7a..a6b318d20 100644 --- a/annotated.html +++ b/annotated.html @@ -161,67 +161,69 @@ $(document).ready(function(){initNavTree('annotated.html',''); initResizable();  CLRUCacheLRU cache class  ►Npostfix_expression  CStackCreates an array to be used as stack for storing values - ▼NprobabilityFor std::vector - needed in testing - ►Nwindowed_median - CWindowedMedianA class to calculate the median of a leading sliding window at the back of a stream of integer values - ▼Nquadratic_probingAn implementation of hash table using quadratic probing algorithm - CEntry - ▼Nrange_queriesAlgorithms and Data Structures that support range queries and updates - ►Nheavy_light_decomposition - CHLDThe Heavy-Light Decomposition class - CSGSegment Tree, to store heavy chains - CTreeA Basic Tree, which supports binary lifting - ►CperSegTreeRange query here is range sum, but the code can be modified to make different queries like range max or min - CNode - ▼NsearchFor std::vector - ►Nsublist_search - CNodeA Node structure representing a single link Node in a linked list - ▼NstatisticsStatistical algorithms - Cstats_computer1 - Cstats_computer2 - ▼NstdSTL namespace - Cis_arithmetic< uint128_t > - Cis_arithmetic< uint256_t > - Cis_integral< uint128_t > - Cis_integral< uint256_t > - Cis_unsigned< uint128_t > - Cis_unsigned< uint256_t > - ▼Cbinary_search_treeThe Binary Search Tree class - Cbst_nodeA struct to represent a node in the Binary Search Tree - CBtree - Ccll - Ccompare - CComplexClass Complex to represent complex numbers as a field - CCycleCheck - Cdouble_linked_list - CEdge - CFenwickTree - CGraph - Chash_chainChain class with a given modulus - CItem - Clarge_number - Clinkedlist - Clist - CMinHeap - CMinHeapNode - Cmst - Cnode - CNode - CPoint - Cquery - Cqueue - CQueue - CRBtree - CSegmentIntersection - CSolution - Cstack - Cstack_linkedList - CTestCasesClass encapsulating the necessary test cases - Ctower - ▼CTrie - CTrieNode - Cuint128_tClass for 128-bit unsigned integer - Cuint256_tClass for 256-bit unsigned integer + ▼NprobabilityProbability algorithms + ►Ngeometric_dist + Cgeometric_distributionA class to model the geometric distribution + ►Nwindowed_median + CWindowedMedianA class to calculate the median of a leading sliding window at the back of a stream of integer values + ▼Nquadratic_probingAn implementation of hash table using quadratic probing algorithm + CEntry + ▼Nrange_queriesAlgorithms and Data Structures that support range queries and updates + ►Nheavy_light_decomposition + CHLDThe Heavy-Light Decomposition class + CSGSegment Tree, to store heavy chains + CTreeA Basic Tree, which supports binary lifting + ►CperSegTreeRange query here is range sum, but the code can be modified to make different queries like range max or min + CNode + ▼NsearchFor std::vector + ►Nsublist_search + CNodeA Node structure representing a single link Node in a linked list + ▼NstatisticsStatistical algorithms + Cstats_computer1 + Cstats_computer2 + ▼NstdSTL namespace + Cis_arithmetic< uint128_t > + Cis_arithmetic< uint256_t > + Cis_integral< uint128_t > + Cis_integral< uint256_t > + Cis_unsigned< uint128_t > + Cis_unsigned< uint256_t > + ▼Cbinary_search_treeThe Binary Search Tree class + Cbst_nodeA struct to represent a node in the Binary Search Tree + CBtree + Ccll + Ccompare + CComplexClass Complex to represent complex numbers as a field + CCycleCheck + Cdouble_linked_list + CEdge + CFenwickTree + CGraph + Chash_chainChain class with a given modulus + CItem + Clarge_number + Clinkedlist + Clist + CMinHeap + CMinHeapNode + Cmst + CNode + Cnode + CPoint + Cquery + Cqueue + CQueue + CRBtree + CSegmentIntersection + CSolution + Cstack + Cstack_linkedList + CTestCasesClass encapsulating the necessary test cases + Ctower + ▼CTrie + CTrieNode + Cuint128_tClass for 128-bit unsigned integer + Cuint256_tClass for 256-bit unsigned integer diff --git a/annotated_dup.js b/annotated_dup.js index e85d2d94f..e60b4a262 100644 --- a/annotated_dup.js +++ b/annotated_dup.js @@ -92,6 +92,9 @@ var annotated_dup = ] ] ] ], [ "probability", "d4/ded/namespaceprobability.html", [ + [ "geometric_dist", null, [ + [ "geometric_distribution", "da/d19/classprobability_1_1geometric__dist_1_1geometric__distribution.html", "da/d19/classprobability_1_1geometric__dist_1_1geometric__distribution" ] + ] ], [ "windowed_median", null, [ [ "WindowedMedian", "df/d34/classprobability_1_1windowed__median_1_1_windowed_median.html", "df/d34/classprobability_1_1windowed__median_1_1_windowed_median" ] ] ] @@ -142,8 +145,8 @@ var annotated_dup = [ "MinHeap", "d2/d05/class_min_heap.html", "d2/d05/class_min_heap" ], [ "MinHeapNode", "d5/d29/struct_min_heap_node.html", null ], [ "mst", "d1/d77/structmst.html", null ], - [ "node", "d5/da1/structnode.html", "d5/da1/structnode" ], [ "Node", "db/d8b/struct_node.html", null ], + [ "node", "d5/da1/structnode.html", "d5/da1/structnode" ], [ "Point", "d8/dc8/struct_point.html", "d8/dc8/struct_point" ], [ "query", "dd/d1b/structquery.html", null ], [ "queue", "db/da9/classqueue.html", "db/da9/classqueue" ], diff --git a/classes.html b/classes.html index 20382c50e..0f934e78a 100644 --- a/classes.html +++ b/classes.html @@ -115,7 +115,7 @@ $(document).ready(function(){initNavTree('classes.html',''); initResizable(); })
FenwickTree
G
-
Graph
Graph (graph)
Graph (graph::is_graph_bipartite)
+
geometric_distribution (probability::geometric_dist)
Graph
Graph (graph)
Graph (graph::is_graph_bipartite)
H
hash_chain
HillCipher (ciphers)
HKGraph (graph)
HLD (range_queries::heavy_light_decomposition)
@@ -130,7 +130,7 @@ $(document).ready(function(){initNavTree('classes.html',''); initResizable(); })
MinHeap
MinHeapNode
mst
N
-
NCRModuloP (math::ncr_modulo_p)
NeuralNetwork (machine_learning::neural_network)
Node (data_structures::linked_list)
Node (data_structures)
Node (data_structures::tree_234)
Trie::Node (data_structures::trie_using_hashmap)
node
Node
Node (operations_on_datastructures::inorder_traversal_of_bst)
Node (others::iterative_tree_traversals)
perSegTree::Node (range_queries)
Node (search::sublist_search)
+
NCRModuloP (math::ncr_modulo_p)
NeuralNetwork (machine_learning::neural_network)
Node (data_structures::linked_list)
Node (data_structures)
Node (data_structures::tree_234)
Trie::Node (data_structures::trie_using_hashmap)
Node
node
Node (operations_on_datastructures::inorder_traversal_of_bst)
Node (others::iterative_tree_traversals)
perSegTree::Node (range_queries)
Node (search::sublist_search)
P
perSegTree (range_queries)
Point (ciphers::elliptic_curve_key_exchange)
Point (geometry::jarvis)
Point
diff --git a/d1/ded/windowed__median_8cpp.html b/d1/ded/windowed__median_8cpp.html index 422e2cf5d..4ea2272f9 100644 --- a/d1/ded/windowed__median_8cpp.html +++ b/d1/ded/windowed__median_8cpp.html @@ -123,7 +123,7 @@ Classes

Namespaces

namespace  probability - for std::vector - needed in testing
+ Probability algorithms.
  namespace  windowed_median  Functions for the Windowed Median algorithm implementation.
diff --git a/d2/d84/classprobability_1_1geometric__dist_1_1geometric__distribution-members.html b/d2/d84/classprobability_1_1geometric__dist_1_1geometric__distribution-members.html new file mode 100644 index 000000000..0cb00d8dd --- /dev/null +++ b/d2/d84/classprobability_1_1geometric__dist_1_1geometric__distribution-members.html @@ -0,0 +1,118 @@ + + + + + + + +Algorithms_in_C++: Member List + + + + + + + + + + + + + + + +
+
+ + + + + + +
+
Algorithms_in_C++ 1.0.0 +
+
Set of algorithms implemented in C++.
+
+
+ + + + + + + +
+
+ +
+
+
+ +
+ +
+
+ + +
+ +
+ +
+
probability::geometric_dist::geometric_distribution Member List
+
+
+ +

This is the complete list of members for probability::geometric_dist::geometric_distribution, including all inherited members.

+ + + + + + + + + + + +
cumulative_distribution(const uint32_t &k) constprobability::geometric_dist::geometric_distributioninline
draw_sample() constprobability::geometric_dist::geometric_distributioninline
expected_value() constprobability::geometric_dist::geometric_distributioninline
geometric_distribution(const float &p)probability::geometric_dist::geometric_distributioninlineexplicit
inverse_cumulative_distribution(const float &cdf) constprobability::geometric_dist::geometric_distributioninline
pprobability::geometric_dist::geometric_distributionprivate
probability_density(const uint32_t &k) constprobability::geometric_dist::geometric_distributioninline
range_tries(const uint32_t &min_tries=1, const uint32_t &max_tries=std::numeric_limits< uint32_t >::max()) constprobability::geometric_dist::geometric_distributioninline
standard_deviation() constprobability::geometric_dist::geometric_distributioninline
variance() constprobability::geometric_dist::geometric_distributioninline
+
+ + + + diff --git a/d4/ded/namespaceprobability.html b/d4/ded/namespaceprobability.html index 7dcea5883..3e339e8a2 100644 --- a/d4/ded/namespaceprobability.html +++ b/d4/ded/namespaceprobability.html @@ -94,10 +94,12 @@ $(document).ready(function(){initNavTree('d4/ded/namespaceprobability.html','../
-

for std::vector - needed in testing +

Probability algorithms. More...

Detailed Description

-

for std::vector - needed in testing

+

Probability algorithms.

+

for std::vector - needed in testing

+

for assert for math functions for fixed size data types for time to initialize rng for std::cout for std::numeric_limits for random numbers for std::vector

for assert for std::rand - needed in testing for std::time - needed in testing for std::list - used to manage sliding window for std::multiset - used to manage multi-value sorted sliding window values

Probability algorithms

diff --git a/d4/ded/namespaceprobability.js b/d4/ded/namespaceprobability.js index 10ff6cf7d..9b71132cb 100644 --- a/d4/ded/namespaceprobability.js +++ b/d4/ded/namespaceprobability.js @@ -1,5 +1,9 @@ var namespaceprobability = [ + [ "geometric_dist", null, [ + [ "geometric_distribution", "da/d19/classprobability_1_1geometric__dist_1_1geometric__distribution.html", "da/d19/classprobability_1_1geometric__dist_1_1geometric__distribution" ], + [ "generate_uniform", "de/d72/geometric__dist_8cpp.html#a82964ca6180507deb5fafc71050012ba", null ] + ] ], [ "windowed_median", null, [ [ "WindowedMedian", "df/d34/classprobability_1_1windowed__median_1_1_windowed_median.html", "df/d34/classprobability_1_1windowed__median_1_1_windowed_median" ] ] ] diff --git a/d5/d88/md__d_i_r_e_c_t_o_r_y.html b/d5/d88/md__d_i_r_e_c_t_o_r_y.html index a4939c32b..7763d624e 100644 --- a/d5/d88/md__d_i_r_e_c_t_o_r_y.html +++ b/d5/d88/md__d_i_r_e_c_t_o_r_y.html @@ -396,6 +396,7 @@ Probability
  • Addition Rule
  • Bayes Theorem
  • Binomial Dist
    • +
  • Geometric Dist
  • Poisson Dist
  • Windowed Median
    • diff --git a/d6/db0/binomial__dist_8cpp.html b/d6/db0/binomial__dist_8cpp.html index c59d52a9b..6864f5825 100644 --- a/d6/db0/binomial__dist_8cpp.html +++ b/d6/db0/binomial__dist_8cpp.html @@ -216,7 +216,7 @@ Functions
    80 return probability;
    81}
    nCr
    double nCr(double n, double r)
    Definition: binomial_dist.cpp:47
    -
    probability
    for std::vector - needed in testing
    +
    probability
    Probability algorithms.
    std::pow
    T pow(T... args)
    std::upper_bound
    T upper_bound(T... args)
    diff --git a/d9/d24/poisson__dist_8cpp.html b/d9/d24/poisson__dist_8cpp.html index f291f1936..e3786d13b 100644 --- a/d9/d24/poisson__dist_8cpp.html +++ b/d9/d24/poisson__dist_8cpp.html @@ -274,7 +274,7 @@ Here is the call graph for this function:
    58 }
    59 return probability;
    60}
    -
    probability
    for std::vector - needed in testing
    +
    probability
    Probability algorithms.
    Here is the call graph for this function:
    diff --git a/da/d19/classprobability_1_1geometric__dist_1_1geometric__distribution.html b/da/d19/classprobability_1_1geometric__dist_1_1geometric__distribution.html new file mode 100644 index 000000000..e6b60ac1e --- /dev/null +++ b/da/d19/classprobability_1_1geometric__dist_1_1geometric__distribution.html @@ -0,0 +1,528 @@ + + + + + + + +Algorithms_in_C++: probability::geometric_dist::geometric_distribution Class Reference + + + + + + + + + + + + + + + +
    +
    + + + + + + +
    +
    Algorithms_in_C++ 1.0.0 +
    +
    Set of algorithms implemented in C++.
    +
    +
    + + + + + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    + +
    + +
    +
    +Public Member Functions | +Private Attributes | +List of all members
    +
    probability::geometric_dist::geometric_distribution Class Reference
    +
    +
    + +

    A class to model the geometric distribution. + More...

    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

    +Public Member Functions

     geometric_distribution (const float &p)
     Constructor for the geometric distribution. More...
     
    float expected_value () const
     The expected value of a geometrically distributed random variable X. More...
     
    float variance () const
     The variance of a geometrically distributed random variable X. More...
     
    float standard_deviation () const
     The standard deviation of a geometrically distributed random variable X. More...
     
    float probability_density (const uint32_t &k) const
     The probability density function. More...
     
    float cumulative_distribution (const uint32_t &k) const
     The cumulative distribution function. More...
     
    float inverse_cumulative_distribution (const float &cdf) const
     The inverse cumulative distribution function. More...
     
    uint32_t draw_sample () const
     Generates a (discrete) sample according to the geometrical distribution. More...
     
    float range_tries (const uint32_t &min_tries=1, const uint32_t &max_tries=std::numeric_limits< uint32_t >::max()) const
     This function computes the probability to have success in a given range of tries. More...
     
    + + + + +

    +Private Attributes

    +float p
     The succes probability p.
     
    +

    Detailed Description

    +

    A class to model the geometric distribution.

    +

    Constructor & Destructor Documentation

    + +

    ◆ geometric_distribution()

    + +
    +
    + + + + + +
    + + + + + + + + +
    probability::geometric_dist::geometric_distribution::geometric_distribution (const float & p)
    +     		+inlineexplicit
    +
    + +

    Constructor for the geometric distribution.

    +
    Parameters
    + + +
    pThe success probability
    +
    +
    +
    59: p(p) {}
    +
    probability::geometric_dist::geometric_distribution::p
    float p
    The succes probability p.
    Definition: geometric_dist.cpp:52
    +
    +
    +
    +

    Member Function Documentation

    + +

    ◆ cumulative_distribution()

    + +
    +
    + + + + + +
    + + + + + + + + +
    float probability::geometric_dist::geometric_distribution::cumulative_distribution (const uint32_t & k) const
    +     		+inline
    +
    + +

    The cumulative distribution function.

    +

    The sum of all probabilities up to (and including) k trials. Basically CDF(k) = P(x <= k)

    Parameters
    + + +
    kThe number of trials in [1,\infty)
    +
    +
    +
    Returns
    The probability to have success within k trials
    +
    102 {
    +
    103 return 1.0f - std::pow((1.0f - p), static_cast<float>(k));
    +
    104 }
    +
    std::pow
    T pow(T... args)
    +
    +Here is the call graph for this function:
    +
    +
    +
    +
    + +
    +
    + +

    ◆ draw_sample()

    + +
    +
    + + + + + +
    + + + + + + + +
    uint32_t probability::geometric_dist::geometric_distribution::draw_sample () const
    +     		+inline
    +
    + +

    Generates a (discrete) sample according to the geometrical distribution.

    +
    Returns
    A geometrically distributed number in [1,\infty)
    +
    121 {
    +
    122 float uniform_sample = generate_uniform();
    +
    123 return static_cast<uint32_t>(inverse_cumulative_distribution(uniform_sample)) + 1;
    +
    124 }
    +
    probability::geometric_dist::geometric_distribution::inverse_cumulative_distribution
    float inverse_cumulative_distribution(const float &cdf) const
    The inverse cumulative distribution function.
    Definition: geometric_dist.cpp:113
    +
    probability::geometric_dist::generate_uniform
    float generate_uniform()
    Returns a random number between [0,1].
    Definition: geometric_dist.cpp:42
    +
    +Here is the call graph for this function:
    +
    +
    +
    +
    + +
    +
    + +

    ◆ expected_value()

    + +
    +
    + + + + + +
    + + + + + + + +
    float probability::geometric_dist::geometric_distribution::expected_value () const
    +     		+inline
    +
    + +

    The expected value of a geometrically distributed random variable X.

    +
    Returns
    E[X] = 1/p
    +
    65 {
    +
    66 return 1.0f/ p;
    +
    67 }
    +
    +
    +
    + +

    ◆ inverse_cumulative_distribution()

    + +
    +
    + + + + + +
    + + + + + + + + +
    float probability::geometric_dist::geometric_distribution::inverse_cumulative_distribution (const float & cdf) const
    +     		+inline
    +
    + +

    The inverse cumulative distribution function.

    +

    This functions answers the question: Up to how many trials are needed to have success with a probability of cdf? The exact floating point value is reported.

    Parameters
    + + +
    cdfThe probability in [0,1]
    +
    +
    +
    Returns
    The number of (exact) trials.
    +
    113 {
    +
    114 return std::log(1.0f - cdf) / std::log(1.0f - p);
    +
    115 }
    +
    std::log
    T log(T... args)
    +
    +Here is the call graph for this function:
    +
    +
    +
    +
    + +
    +
    + +

    ◆ probability_density()

    + +
    +
    + + + + + +
    + + + + + + + + +
    float probability::geometric_dist::geometric_distribution::probability_density (const uint32_t & k) const
    +     		+inline
    +
    + +

    The probability density function.

    +

    As we use the first definition of the geometric series (1), we are doing k - 1 failed trials and the k-th trial is a success.

    Parameters
    + + +
    kThe number of trials to observe the first success in [1,\infty)
    +
    +
    +
    Returns
    A number between [0,1] according to p * (1-p)^{k-1}
    +
    92 {
    +
    93 return std::pow((1.0f - p), static_cast<float>(k - 1)) * p;
    +
    94 }
    +
    +Here is the call graph for this function:
    +
    +
    +
    +
    + +
    +
    + +

    ◆ range_tries()

    + +
    +
    + + + + + +
    + + + + + + + + + + + + + + + + + + +
    float probability::geometric_dist::geometric_distribution::range_tries (const uint32_t & min_tries = 1,
    const uint32_t & max_tries = std::numeric_limits<uint32_t>::max() 
    ) const
    +     		+inline
    +
    + +

    This function computes the probability to have success in a given range of tries.

    +

    Computes P(min_tries <= x <= max_tries). Can be used to calculate P(x >= min_tries) by not passing a second argument. Can be used to calculate P(x <= max_tries) by passing 1 as the first argument

    Parameters
    + + + +
    min_triesThe minimum number of tries in [1,\infty) (inclusive)
    max_triesThe maximum number of tries in [min_tries, \infty) (inclusive)
    +
    +
    +
    Returns
    The probability of having success within a range of tries [min_tries, max_tries]
    +
    135 {
    +
    136 float cdf_lower = cumulative_distribution(min_tries - 1);
    +
    137 float cdf_upper = max_tries == std::numeric_limits<uint32_t>::max() ? 1.0f : cumulative_distribution(max_tries);
    +
    138 return cdf_upper - cdf_lower;
    +
    139 }
    +
    probability::geometric_dist::geometric_distribution::cumulative_distribution
    float cumulative_distribution(const uint32_t &k) const
    The cumulative distribution function.
    Definition: geometric_dist.cpp:102
    +
    std::numeric_limits::max
    T max(T... args)
    +
    +Here is the call graph for this function:
    +
    +
    +
    +
    + +
    +
    + +

    ◆ standard_deviation()

    + +
    +
    + + + + + +
    + + + + + + + +
    float probability::geometric_dist::geometric_distribution::standard_deviation () const
    +     		+inline
    +
    + +

    The standard deviation of a geometrically distributed random variable X.

    +
    Returns
    \sigma = \sqrt{V[X]}
    +
    81 {
    +
    82 return std::sqrt(variance());
    +
    83 }
    +
    probability::geometric_dist::geometric_distribution::variance
    float variance() const
    The variance of a geometrically distributed random variable X.
    Definition: geometric_dist.cpp:73
    +
    std::sqrt
    T sqrt(T... args)
    +
    +Here is the call graph for this function:
    +
    +
    +
    +
    + +
    +
    + +

    ◆ variance()

    + +
    +
    + + + + + +
    + + + + + + + +
    float probability::geometric_dist::geometric_distribution::variance () const
    +     		+inline
    +
    + +

    The variance of a geometrically distributed random variable X.

    +
    Returns
    V[X] = (1 - p) / p^2
    +
    73 {
    +
    74 return (1.0f - p) / (p * p);
    +
    75 }
    +
    +
    +
    +
    The documentation for this class was generated from the following file: +
    +
    + + + + diff --git a/da/d19/classprobability_1_1geometric__dist_1_1geometric__distribution.js b/da/d19/classprobability_1_1geometric__dist_1_1geometric__distribution.js new file mode 100644 index 000000000..d400d28e6 --- /dev/null +++ b/da/d19/classprobability_1_1geometric__dist_1_1geometric__distribution.js @@ -0,0 +1,13 @@ +var classprobability_1_1geometric__dist_1_1geometric__distribution = +[ + [ "geometric_distribution", "da/d19/classprobability_1_1geometric__dist_1_1geometric__distribution.html#aa12088ba133dd0910103db0eb0ef2797", null ], + [ "cumulative_distribution", "da/d19/classprobability_1_1geometric__dist_1_1geometric__distribution.html#a08328dc7d62188427111f176b56a105a", null ], + [ "draw_sample", "da/d19/classprobability_1_1geometric__dist_1_1geometric__distribution.html#a8aae1cebcf42ed2332f1c7217c401aa3", null ], + [ "expected_value", "da/d19/classprobability_1_1geometric__dist_1_1geometric__distribution.html#a41051365f8ac7700f2ed5880a6760413", null ], + [ "inverse_cumulative_distribution", "da/d19/classprobability_1_1geometric__dist_1_1geometric__distribution.html#aaf762e88c66918d7afda4234f28a7ddf", null ], + [ "probability_density", "da/d19/classprobability_1_1geometric__dist_1_1geometric__distribution.html#aee973db9f0435e0cb4cc70f8eb3447a1", null ], + [ "range_tries", "da/d19/classprobability_1_1geometric__dist_1_1geometric__distribution.html#a4620163a196709484225774d87de6d69", null ], + [ "standard_deviation", "da/d19/classprobability_1_1geometric__dist_1_1geometric__distribution.html#a0a10c512e13dd3a052e1c6d7f4d6f0f2", null ], + [ "variance", "da/d19/classprobability_1_1geometric__dist_1_1geometric__distribution.html#aea8b0d649f0dc9a6f8baf3341a0b4960", null ], + [ "p", "da/d19/classprobability_1_1geometric__dist_1_1geometric__distribution.html#ad5ed23a251dbe55ad1ed06bf1a465ad3", null ] +]; \ No newline at end of file diff --git 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+::inverse_cumulative_distribution + + + + + +Node2 + + +std::log + + + + + +Node1->Node2 + + + + + diff --git a/da/d19/classprobability_1_1geometric__dist_1_1geometric__distribution_aee973db9f0435e0cb4cc70f8eb3447a1_cgraph.map b/da/d19/classprobability_1_1geometric__dist_1_1geometric__distribution_aee973db9f0435e0cb4cc70f8eb3447a1_cgraph.map new file mode 100644 index 000000000..bf973a1d3 --- /dev/null +++ b/da/d19/classprobability_1_1geometric__dist_1_1geometric__distribution_aee973db9f0435e0cb4cc70f8eb3447a1_cgraph.map @@ -0,0 +1,4 @@ + + + + diff --git a/da/d19/classprobability_1_1geometric__dist_1_1geometric__distribution_aee973db9f0435e0cb4cc70f8eb3447a1_cgraph.md5 b/da/d19/classprobability_1_1geometric__dist_1_1geometric__distribution_aee973db9f0435e0cb4cc70f8eb3447a1_cgraph.md5 new file mode 100644 index 000000000..99adbe6d6 --- /dev/null +++ b/da/d19/classprobability_1_1geometric__dist_1_1geometric__distribution_aee973db9f0435e0cb4cc70f8eb3447a1_cgraph.md5 @@ -0,0 +1 @@ +6552b600c577bdff25fef46e0bceeab6 \ No newline at end of file diff --git a/da/d19/classprobability_1_1geometric__dist_1_1geometric__distribution_aee973db9f0435e0cb4cc70f8eb3447a1_cgraph.svg b/da/d19/classprobability_1_1geometric__dist_1_1geometric__distribution_aee973db9f0435e0cb4cc70f8eb3447a1_cgraph.svg new file mode 100644 index 000000000..297780641 --- /dev/null +++ b/da/d19/classprobability_1_1geometric__dist_1_1geometric__distribution_aee973db9f0435e0cb4cc70f8eb3447a1_cgraph.svg @@ -0,0 +1,39 @@ + + + + + + +probability::geometric_dist::geometric_distribution::probability_density + + + +Node1 + + +probability::geometric +_dist::geometric_distribution +::probability_density + + + + + +Node2 + + +std::pow + + + + + +Node1->Node2 + + + + + diff --git a/dd/d8a/namespacegeometric__dist.html b/dd/d8a/namespacegeometric__dist.html new file mode 100644 index 000000000..a7a9f3464 --- /dev/null +++ b/dd/d8a/namespacegeometric__dist.html @@ -0,0 +1,111 @@ + + + + + + + +Algorithms_in_C++: geometric_dist Namespace Reference + + + + + + + + + + + + + + + +
    +
    + + + + + + +
    +
    Algorithms_in_C++ 1.0.0 +
    +
    Set of algorithms implemented in C++.
    +
    +
    + + + + + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    + +
    + +
    +
    geometric_dist Namespace Reference
    +
    +
    + +

    Functions for the Geometric Distribution algorithm implementation. +More...

    +

    Detailed Description

    +

    Functions for the Geometric Distribution algorithm implementation.

    +
    +
    + + + + diff --git a/de/d72/geometric__dist_8cpp.html b/de/d72/geometric__dist_8cpp.html new file mode 100644 index 000000000..8d6a092a7 --- /dev/null +++ b/de/d72/geometric__dist_8cpp.html @@ -0,0 +1,376 @@ + + + + + + + +Algorithms_in_C++: probability/geometric_dist.cpp File Reference + + + + + + + + + + + + + + + +
    +
    + + + + + + +
    +
    Algorithms_in_C++ 1.0.0 +
    +
    Set of algorithms implemented in C++.
    +
    +
    + + + + + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    + +
    + +
    +
    +Classes | +Namespaces | +Functions
    +
    geometric_dist.cpp File Reference
    +
    +
    + +

    Geometric Distribution +More...

    +
    #include <cassert>
    +#include <cmath>
    +#include <cstdint>
    +#include <ctime>
    +#include <iostream>
    +#include <limits>
    +#include <random>
    +#include <vector>
    +
    +Include dependency graph for geometric_dist.cpp:
    +
    +
    +
    +
    +
    + + + + +

    +Classes

    class  probability::geometric_dist::geometric_distribution
     A class to model the geometric distribution. More...
     
    + + + + + + + +

    +Namespaces

    namespace  probability
     Probability algorithms.
     
    namespace  geometric_dist
     Functions for the Geometric Distribution algorithm implementation.
     
    + + + + + + + + + + + + + +

    +Functions

    float probability::geometric_dist::generate_uniform ()
     Returns a random number between [0,1]. More...
     
    void sample_test (const probability::geometric_dist::geometric_distribution &dist)
     Tests the sampling method of the geometric distribution. More...
     
    static void test ()
     Self-test implementations. More...
     
    int main ()
     Main function. More...
     
    +

    Detailed Description

    +

    Geometric Distribution

    +

    The geometric distribution models the experiment of doing Bernoulli trials until a sucess was observed. There are two formulations of the geometric distribution: 1) The probability distribution of the number X of Bernoulli trials needed to get one success, supported on the set { 1, 2, 3, ... } 2) The probability distribution of the number Y = X − 1 of failures before the first success, supported on the set { 0, 1, 2, 3, ... } Here, the first one is implemented.

    +

    Common variables used: p - The success probability k - The number of tries

    +
    Author
    Domenic Zingsheim
    +

    Function Documentation

    + +

    ◆ generate_uniform()

    + +
    +
    + + + + + + + +
    float probability::geometric_dist::generate_uniform ()
    +
    + +

    Returns a random number between [0,1].

    +
    Returns
    A uniformly distributed random number between 0 (included) and 1 (included)
    +
    42 {
    +
    43 return static_cast<float>(rand()) / static_cast<float>(RAND_MAX);
    +
    44}
    +
    std::rand
    T rand(T... args)
    +
    +Here is the call graph for this function:
    +
    +
    +
    +
    + +
    +
    + +

    ◆ main()

    + +
    +
    + + + + + + + + +
    int main (void )
    +
    + +

    Main function.

    +
    Returns
    0 on exit
    +
    232 {
    +
    233 srand(time(nullptr));
    +
    234 test(); // run self-test implementations
    +
    235 return 0;
    +
    236}
    +
    test
    static void test()
    Self-test implementations.
    Definition: geometric_dist.cpp:179
    +
    std::srand
    T srand(T... args)
    +
    std::time
    T time(T... args)
    +
    +Here is the call graph for this function:
    +
    +
    +
    +
    + +
    +
    + +

    ◆ sample_test()

    + +
    +
    + + + + + + + + +
    void sample_test (const probability::geometric_dist::geometric_distribution & dist)
    +
    + +

    Tests the sampling method of the geometric distribution.

    +

    Draws 1000000 random samples and estimates mean and variance These should be close to the expected value and variance of the given distribution to pass.

    Parameters
    + + +
    distThe distribution to test
    +
    +
    +
    150 {
    +
    151 uint32_t n_tries = 1000000;
    +
    152 std::vector<float> tries;
    +
    153 tries.resize(n_tries);
    +
    154
    +
    155 float mean = 0.0f;
    +
    156 for (uint32_t i = 0; i < n_tries; ++i) {
    +
    157 tries[i] = static_cast<float>(dist.draw_sample());
    +
    158 mean += tries[i];
    +
    159 }
    +
    160
    +
    161 mean /= static_cast<float>(n_tries);
    +
    162
    +
    163 float var = 0.0f;
    +
    164 for (uint32_t i = 0; i < n_tries; ++i) {
    +
    165 var += (tries[i] - mean) * (tries[i] - mean);
    +
    166 }
    +
    167
    +
    168 //Unbiased estimate of variance
    +
    169 var /= static_cast<float>(n_tries - 1);
    +
    170
    +
    171 std::cout << "This value should be near " << dist.expected_value() << ": " << mean << std::endl;
    +
    172 std::cout << "This value should be near " << dist.variance() << ": " << var << std::endl;
    +
    173}
    + +
    probability::geometric_dist::geometric_distribution::expected_value
    float expected_value() const
    The expected value of a geometrically distributed random variable X.
    Definition: geometric_dist.cpp:65
    +
    probability::geometric_dist::geometric_distribution::draw_sample
    uint32_t draw_sample() const
    Generates a (discrete) sample according to the geometrical distribution.
    Definition: geometric_dist.cpp:121
    +
    probability::geometric_dist::geometric_distribution::variance
    float variance() const
    The variance of a geometrically distributed random variable X.
    Definition: geometric_dist.cpp:73
    +
    std::endl
    T endl(T... args)
    +
    std::vector::resize
    T resize(T... args)
    + +
    +Here is the call graph for this function:
    +
    +
    +
    +
    + +
    +
    + +

    ◆ test()

    + +
    +
    + + + + + +
    + + + + + + + +
    static void test ()
    +     		+static
    +
    + +

    Self-test implementations.

    +
    Returns
    void
    +
    179 {
    +
    180 probability::geometric_dist::geometric_distribution dist(0.3);
    +
    181
    +
    182 const float threshold = 1e-3f;
    +
    183
    +
    184 std::cout << "Starting tests for p = 0.3..." << std::endl;
    +
    185 assert(std::abs(dist.expected_value() - 3.33333333f) < threshold);
    +
    186 assert(std::abs(dist.variance() - 7.77777777f) < threshold);
    +
    187 assert(std::abs(dist.standard_deviation() - 2.788866755) < threshold);
    +
    188 assert(std::abs(dist.probability_density(5) - 0.07203) < threshold);
    +
    189 assert(std::abs(dist.cumulative_distribution(6) - 0.882351) < threshold);
    +
    190 assert(std::abs(dist.inverse_cumulative_distribution(dist.cumulative_distribution(8)) - 8) < threshold);
    +
    191 assert(std::abs(dist.range_tries() - 1.0f) < threshold);
    +
    192 assert(std::abs(dist.range_tries(3) - 0.49f) < threshold);
    +
    193 assert(std::abs(dist.range_tries(5, 11) - 0.2203267f) < threshold);
    +
    194 std::cout << "All tests passed" << std::endl;
    +
    195 sample_test(dist);
    +
    196
    +
    197 dist = probability::geometric_dist::geometric_distribution(0.5f);
    +
    198
    +
    199 std::cout << "Starting tests for p = 0.5..." << std::endl;
    +
    200 assert(std::abs(dist.expected_value() - 2.0f) < threshold);
    +
    201 assert(std::abs(dist.variance() - 2.0f) < threshold);
    +
    202 assert(std::abs(dist.standard_deviation() - 1.4142135f) < threshold);
    +
    203 assert(std::abs(dist.probability_density(5) - 0.03125) < threshold);
    +
    204 assert(std::abs(dist.cumulative_distribution(6) - 0.984375) < threshold);
    +
    205 assert(std::abs(dist.inverse_cumulative_distribution(dist.cumulative_distribution(8)) - 8) < threshold);
    +
    206 assert(std::abs(dist.range_tries() - 1.0f) < threshold);
    +
    207 assert(std::abs(dist.range_tries(3) - 0.25f) < threshold);
    +
    208 assert(std::abs(dist.range_tries(5, 11) - 0.062011f) < threshold);
    +
    209 std::cout << "All tests passed" << std::endl;
    +
    210 sample_test(dist);
    +
    211
    +
    212 dist = probability::geometric_dist::geometric_distribution(0.8f);
    +
    213
    +
    214 std::cout << "Starting tests for p = 0.8..." << std::endl;
    +
    215 assert(std::abs(dist.expected_value() - 1.25f) < threshold);
    +
    216 assert(std::abs(dist.variance() - 0.3125f) < threshold);
    +
    217 assert(std::abs(dist.standard_deviation() - 0.559016f) < threshold);
    +
    218 assert(std::abs(dist.probability_density(5) - 0.00128) < threshold);
    +
    219 assert(std::abs(dist.cumulative_distribution(6) - 0.999936) < threshold);
    +
    220 assert(std::abs(dist.inverse_cumulative_distribution(dist.cumulative_distribution(8)) - 8) < threshold);
    +
    221 assert(std::abs(dist.range_tries() - 1.0f) < threshold);
    +
    222 assert(std::abs(dist.range_tries(3) - 0.04f) < threshold);
    +
    223 assert(std::abs(dist.range_tries(5, 11) - 0.00159997f) < threshold);
    +
    224 std::cout << "All tests have successfully passed!" << std::endl;
    +
    225 sample_test(dist);
    +
    226}
    +
    probability::geometric_dist::geometric_distribution
    A class to model the geometric distribution.
    Definition: geometric_dist.cpp:50
    +
    sample_test
    void sample_test(const probability::geometric_dist::geometric_distribution &dist)
    Tests the sampling method of the geometric distribution.
    Definition: geometric_dist.cpp:150
    +
    +Here is the call graph for this function:
    +
    +
    +
    +
    + +
    +
    +
    +
    + + + + diff --git a/de/d72/geometric__dist_8cpp.js b/de/d72/geometric__dist_8cpp.js new file mode 100644 index 000000000..8aaf92bd8 --- /dev/null +++ b/de/d72/geometric__dist_8cpp.js @@ -0,0 +1,8 @@ +var geometric__dist_8cpp = +[ + [ "probability::geometric_dist::geometric_distribution", "da/d19/classprobability_1_1geometric__dist_1_1geometric__distribution.html", "da/d19/classprobability_1_1geometric__dist_1_1geometric__distribution" ], + [ "generate_uniform", "de/d72/geometric__dist_8cpp.html#a82964ca6180507deb5fafc71050012ba", null ], + [ "main", "de/d72/geometric__dist_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4", null ], + [ "sample_test", "de/d72/geometric__dist_8cpp.html#a70fd1cc5c3a2813f28683dc75dcd65b6", null ], + [ "test", "de/d72/geometric__dist_8cpp.html#aa8dca7b867074164d5f45b0f3851269d", null ] +]; \ No newline at end of file diff --git a/de/d72/geometric__dist_8cpp_a70fd1cc5c3a2813f28683dc75dcd65b6_cgraph.map 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b/dir_82e494173a87936756866de2fa774307.html @@ -105,6 +105,9 @@ Files file  binomial_dist.cpp  Binomial distribution example
      +file  geometric_dist.cpp + Geometric Distribution
    +  file  poisson_dist.cpp  Poisson statistics
      diff --git a/dir_82e494173a87936756866de2fa774307.js b/dir_82e494173a87936756866de2fa774307.js index e45f93992..06b892b5f 100644 --- a/dir_82e494173a87936756866de2fa774307.js +++ b/dir_82e494173a87936756866de2fa774307.js @@ -3,6 +3,7 @@ var dir_82e494173a87936756866de2fa774307 = [ "addition_rule.cpp", "d6/d4a/addition__rule_8cpp.html", "d6/d4a/addition__rule_8cpp" ], [ "bayes_theorem.cpp", "d5/d67/bayes__theorem_8cpp.html", "d5/d67/bayes__theorem_8cpp" ], [ "binomial_dist.cpp", "d6/db0/binomial__dist_8cpp.html", "d6/db0/binomial__dist_8cpp" ], + [ "geometric_dist.cpp", "de/d72/geometric__dist_8cpp.html", "de/d72/geometric__dist_8cpp" ], [ "poisson_dist.cpp", "d9/d24/poisson__dist_8cpp.html", "d9/d24/poisson__dist_8cpp" ], [ "windowed_median.cpp", "d1/ded/windowed__median_8cpp.html", "d1/ded/windowed__median_8cpp" ] ]; \ No newline at end of file diff --git a/files.html b/files.html index 848a45111..70d7de1e7 100644 --- a/files.html +++ b/files.html @@ -290,8 +290,9 @@ solve-a-rat-in-a-maze-c-java-pytho/"  addition_rule.cppAddition rule of probabilities  bayes_theorem.cppBayes' theorem  binomial_dist.cppBinomial distribution example - poisson_dist.cppPoisson statistics - windowed_median.cppAn implementation of a median calculation of a sliding window along a data stream + geometric_dist.cppGeometric Distribution + poisson_dist.cppPoisson statistics + windowed_median.cppAn implementation of a median calculation of a sliding window along a data stream  ► range_queries  fenwick_tree.cppFenwick tree  heavy_light_decomposition.cppHeavy Light Decomposition implementation diff --git a/functions_c.html b/functions_c.html index 2e2d5f8a2..8c816d1f0 100644 --- a/functions_c.html +++ b/functions_c.html @@ -110,6 +110,7 @@ $(document).ready(function(){initNavTree('functions_c.html',''); initResizable()
  • Convexhull() : geometry::jarvis::Convexhull
  • count : data_structures::tree_234::Node
  • createNewNode() : others::iterative_tree_traversals::BinaryTree
    • +
  • cumulative_distribution() : probability::geometric_dist::geometric_distribution
    • diff --git a/functions_d.html b/functions_d.html index a43c9a5aa..5e1d02d71 100644 --- a/functions_d.html +++ b/functions_d.html @@ -119,6 +119,7 @@ $(document).ready(function(){initNavTree('functions_d.html',''); initResizable()
  • displayList() : data_structures::SkipList
  • dist : graph::HKGraph
  • divide() : uint128_t, uint256_t
    • +
  • draw_sample() : probability::geometric_dist::geometric_distribution
    • diff --git a/functions_e.html b/functions_e.html index 1032bd44b..09fcc9e29 100644 --- a/functions_e.html +++ b/functions_e.html @@ -104,6 +104,7 @@ $(document).ready(function(){initNavTree('functions_e.html',''); initResizable()
  • eta : machine_learning::adaline
  • evaluate() : machine_learning::neural_network::NeuralNetwork
  • evaluate_from_csv() : machine_learning::neural_network::NeuralNetwork
    • +
  • expected_value() : probability::geometric_dist::geometric_distribution
  • extractMin() : MinHeap
    • diff --git a/functions_func_c.html b/functions_func_c.html index e4f522681..8a110f374 100644 --- a/functions_func_c.html +++ b/functions_func_c.html @@ -106,6 +106,7 @@ $(document).ready(function(){initNavTree('functions_func_c.html',''); initResiza
  • Contains() : data_structures::tree_234::Node
  • Convexhull() : geometry::jarvis::Convexhull
  • createNewNode() : others::iterative_tree_traversals::BinaryTree
    • +
  • cumulative_distribution() : probability::geometric_dist::geometric_distribution
    • diff --git a/functions_func_d.html b/functions_func_d.html index eff74487f..75ef471b5 100644 --- a/functions_func_d.html +++ b/functions_func_d.html @@ -116,6 +116,7 @@ $(document).ready(function(){initNavTree('functions_func_d.html',''); initResiza
  • display() : data_structures::linked_list::list, data_structures::queue_using_array::Queue_Array, hash_chain, others::lru_cache::LRUCache, queue< Kind >, stack< Type >
  • displayList() : data_structures::SkipList
  • divide() : uint128_t, uint256_t
    • +
  • draw_sample() : probability::geometric_dist::geometric_distribution
    • diff --git a/functions_func_e.html b/functions_func_e.html index b89a528b0..0c8c18470 100644 --- a/functions_func_e.html +++ b/functions_func_e.html @@ -103,6 +103,7 @@ $(document).ready(function(){initNavTree('functions_func_e.html',''); initResiza
  • eraseFromSorted() : probability::windowed_median::WindowedMedian
  • evaluate() : machine_learning::neural_network::NeuralNetwork
  • evaluate_from_csv() : machine_learning::neural_network::NeuralNetwork
    • +
  • expected_value() : probability::geometric_dist::geometric_distribution
  • extractMin() : MinHeap
    • diff --git a/functions_func_g.html b/functions_func_g.html index 06fbc7337..7af36a993 100644 --- a/functions_func_g.html +++ b/functions_func_g.html @@ -99,6 +99,7 @@ $(document).ready(function(){initNavTree('functions_func_g.html',''); initResiza
  • generate_encryption_key() : ciphers::HillCipher
  • generate_keys() : ciphers::HillCipher
  • generate_possible_moves() : machine_learning::aystar_search::EightPuzzle< N >
    • +
  • geometric_distribution() : probability::geometric_dist::geometric_distribution
  • get() : machine_learning::aystar_search::EightPuzzle< N >
  • get_all_words() : data_structures::trie_using_hashmap::Trie
  • get_char_idx() : ciphers::HillCipher
    • diff --git a/functions_func_i.html b/functions_func_i.html index dcb9e398f..f6c10499c 100644 --- a/functions_func_i.html +++ b/functions_func_i.html @@ -110,6 +110,7 @@ $(document).ready(function(){initNavTree('functions_func_i.html',''); initResiza
  • InsertPostMerge() : data_structures::tree_234::Tree234
  • InsertPreSplit() : data_structures::tree_234::Tree234
  • insertToSorted() : probability::windowed_median::WindowedMedian
    • +
  • inverse_cumulative_distribution() : probability::geometric_dist::geometric_distribution
  • Is2Node() : data_structures::tree_234::Node
  • Is34Node() : data_structures::tree_234::Node
  • is_bipartite() : graph::is_graph_bipartite::Graph
    • diff --git a/functions_func_p.html b/functions_func_p.html index f373d9fa2..03847d40c 100644 --- a/functions_func_p.html +++ b/functions_func_p.html @@ -103,6 +103,7 @@ $(document).ready(function(){initNavTree('functions_func_p.html',''); initResiza
  • preOrderIterative() : others::iterative_tree_traversals::BinaryTree
  • Print() : data_structures::tree_234::Tree234
  • PrintNode() : data_structures::tree_234::Tree234
    • +
  • probability_density() : probability::geometric_dist::geometric_distribution
  • push() : stack< Type >
  • push_back() : data_structures::linked_list::list
  • push_front() : data_structures::linked_list::list
    • diff --git a/functions_func_r.html b/functions_func_r.html index a1ce5160c..c9673951c 100644 --- a/functions_func_r.html +++ b/functions_func_r.html @@ -95,6 +95,7 @@ $(document).ready(function(){initNavTree('functions_func_r.html',''); initResiza

    - r -