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Showing content from https://TheAlgorithms.github.io/C-Plus-Plus/db/d40/integral__approximation2_8cpp_source.html below:

TheAlgorithms/C++: math/integral_approximation2.cpp Source File

Go to the documentation of this file. 24#define _USE_MATH_DEFINES 46using

Function = std::function<double(

66 const

uint32_t& num_samples,

67 const

uint32_t& discard = 100000) {

68

std::vector<double> samples;

69

samples.reserve(num_samples);

71 double

x_t = start_point;

73

std::default_random_engine generator;

74

std::uniform_real_distribution<double> uniform(0.0, 1.0);

75

std::normal_distribution<double> normal(0.0, 1.0);

76

generator.seed(time(

nullptr

));

78 for

(uint32_t t = 0; t < num_samples + discard; ++t) {

81 double

x_dash = normal(generator) + x_t;

82 double

acceptance_probability = std::min(pdf(x_dash) / pdf(x_t), 1.0);

83 double

u = uniform(generator);

86 if

(u <= acceptance_probability) {

91

samples.push_back(x_t);

114 const

uint32_t& num_samples = 1000000) {

115 double

integral = 0.0;

116

std::vector<double> samples =

119 for

(

double

sample : samples) {

120

integral += function(sample) / pdf(sample);

123 return

integral /

static_cast<double>

(samples.size());

134

std::cout <<

"Disclaimer: Because this is a randomized algorithm," 137

"it may happen that singular samples deviate from the true result." 142

math::monte_carlo::Function f;

143

math::monte_carlo::Function pdf;

145 double

lower_bound = 0, upper_bound = 0;

148

f = [&](

double

& x) {

return

-x * x + 4.0; };

152

pdf = [&](

double

& x) {

153 if

(x >= lower_bound && x <= -1.0) {

156 if

(x <= upper_bound && x >= 1.0) {

159 if

(x > -1.0 && x < 1.0) {

166

(upper_bound - lower_bound) / 2.0, f, pdf);

168

std::cout <<

"This number should be close to 10.666666: "

<< integral

172

f = [&](

double

& x) {

return

std::exp(x); };

176

pdf = [&](

double

& x) {

177 if

(x >= lower_bound && x <= 0.2) {

180 if

(x > 0.2 && x <= 0.4) {

183 if

(x > 0.4 && x < upper_bound) {

190

(upper_bound - lower_bound) / 2.0, f, pdf);

192

std::cout <<

"This number should be close to 1.7182818: "

<< integral

199

f = [&](

double

& x) {

return

std::sin(M_PI * x) / (M_PI * x); };

201

pdf = [&](

double

& x) {

202 return

1.0 / std::sqrt(2.0 * M_PI) * std::exp(-x * x / 2.0);

207

std::cout <<

"This number should be close to 1.0: "

<< integral

std::vector< double > generate_samples(const double &start_point, const Function &pdf, const uint32_t &num_samples, const uint32_t &discard=100000)

short-hand for std::functions used in this implementation

static void test()

Self-test implementations.

int main()

Main function.

double integral_monte_carlo(const double &start_point, const Function &function, const Function &pdf, const uint32_t &num_samples=1000000)

Compute an approximation of an integral using Monte Carlo integration.

Functions for the Monte Carlo Integration implementation.

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