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TheAlgorithms/C++: numerical_methods/composite_simpson_rule.cpp Source File

Go to the documentation of this file. 67double

evaluate_by_simpson(std::int32_t N,

double h

,

double

a,

68 const

std::function<

double

(

double

)>& func) {

69

std::map<std::int32_t, double>

75 for

(std::int32_t i = 0; i <= N; i++) {

78

std::pair<std::int32_t, double>(i, temp));

84 double

evaluate_integral = 0;

85 for

(std::int32_t i = 0; i <= N; i++) {

86 if

(i == 0 || i == N) {

87

evaluate_integral += data_table.at(i);

88

}

else if

(i % 2 == 1) {

89

evaluate_integral += 4 * data_table.at(i);

91

evaluate_integral += 2 * data_table.at(i);

96

evaluate_integral *=

h

/ 3;

100

assert(!std::isnan(evaluate_integral) &&

101 "The definite integral can't be evaluated. Check the validity of " 104 return

evaluate_integral;

113double f

(

double

x) {

return

std::sqrt(x) + std::log(x); }

115double g

(

double

x) {

return

std::exp(-x) * (4 - std::pow(x, 2)); }

117double k

(

double

x) {

return

std::sqrt(2 * std::pow(x, 3) + 3); }

119double l

(

double

x) {

return

x + std::log(2 * x + 1); }

132static void test

(std::int32_t N,

double h

,

double

a,

double

b,

133 bool

used_argv_parameters) {

135 double

result_f = numerical_methods::simpson_method::evaluate_by_simpson(

137

assert((used_argv_parameters || (result_f >= 4.09 && result_f <= 4.10)) &&

138 "The result of f(x) is wrong"

);

139

std::cout <<

"The result of integral f(x) on interval ["

<< a <<

", "

<< b

140

<<

"] is equal to: "

<< result_f << std::endl;

142 double

result_g = numerical_methods::simpson_method::evaluate_by_simpson(

144

assert((used_argv_parameters || (result_g >= 0.27 && result_g <= 0.28)) &&

145 "The result of g(x) is wrong"

);

146

std::cout <<

"The result of integral g(x) on interval ["

<< a <<

", "

<< b

147

<<

"] is equal to: "

<< result_g << std::endl;

149 double

result_k = numerical_methods::simpson_method::evaluate_by_simpson(

151

assert((used_argv_parameters || (result_k >= 9.06 && result_k <= 9.07)) &&

152 "The result of k(x) is wrong"

);

153

std::cout <<

"The result of integral k(x) on interval ["

<< a <<

", "

<< b

154

<<

"] is equal to: "

<< result_k << std::endl;

156 double

result_l = numerical_methods::simpson_method::evaluate_by_simpson(

158

assert((used_argv_parameters || (result_l >= 7.16 && result_l <= 7.17)) &&

159 "The result of l(x) is wrong"

);

160

std::cout <<

"The result of integral l(x) on interval ["

<< a <<

", "

<< b

161

<<

"] is equal to: "

<< result_l << std::endl;

170int main

(

int

argc,

char

** argv) {

177 bool

used_argv_parameters =

184

N = std::atoi(argv[1]);

185

a = std::atof(argv[2]);

186

b = std::atof(argv[3]);

188

assert(a < b &&

"a has to be less than b"

);

189

assert(N > 0 &&

"N has to be > 0"

);

190 if

(N < 16 || a != 1 || b != 3) {

191

used_argv_parameters =

true

;

193

std::cout <<

"You selected N="

<< N <<

", a="

<< a <<

", b="

<< b

196

std::cout <<

"Default N="

<< N <<

", a="

<< a <<

", b="

<< b

203 test

(N,

h

, a, b, used_argv_parameters);

double k(double x)

Another test function.

double g(double x)

Another test function.

double f(double x)

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

double l(double x)

Another test function.

static void test()

Self-test implementations.

int main()

Main function.

Contains the Simpson's method implementation.

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