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Showing content from https://TheAlgorithms.github.io/C-Plus-Plus/db/d40/integral__approximation2_8cpp.html below:

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

Self-test implementations.

133 {

134 std::cout << "Disclaimer: Because this is a randomized algorithm,"

135 << std::endl;

136 std::cout

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

138 << std::endl

139 << std::endl;

140 ;

141

math::monte_carlo::Function

;

143 math::monte_carlo::Function pdf;

144 double integral = 0;

145 double lower_bound = 0, upper_bound = 0;

146

147

= [&](

& x) {

-x * x + 4.0; };

149

150 lower_bound = -2.0;

151 upper_bound = 2.0;

152 pdf = [&](double& x) {

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

154 return 0.1;

155 }

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

157 return 0.1;

158 }

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

160 return 0.4;

161 }

162 return 0.0;

163 };

164

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

167

168 std::cout << "This number should be close to 10.666666: " << integral

169 << std::endl;

170

171

= [&](

& x) {

std::exp(x); };

173

174 lower_bound = 0.0;

175 upper_bound = 1.0;

176 pdf = [&](double& x) {

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

178 return 0.1;

179 }

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

181 return 0.4;

182 }

183 if (x > 0.4 && x < upper_bound) {

184 return 1.5;

185 }

186 return 0.0;

187 };

188

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

191

192 std::cout << "This number should be close to 1.7182818: " << integral

193 << std::endl;

194

195

196

197

198

= [&](

& x) {

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

200

201 pdf = [&](double& x) {

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

203 };

204

206

207 std::cout << "This number should be close to 1.0: " << integral

208 << std::endl;

209}

double f(double x)

A function f(x) that will be used to test the method.

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.

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