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use long double for errors and tolerance checks

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This commit is contained in:
Krishna Vedala
2020-06-04 15:20:31 -04:00
parent b7d05eab9e
commit 42f78bbe19
1 changed files with 28 additions and 16 deletions
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44
numerical_methods/durand_kerner_roots.cpp
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@@ -104,7 +104,7 @@ bool check_termination(long double delta) {
std::pair<uint32_t, double> durand_kerner_algo(
const std::valarray<double> &coeffs,
std::valarray<std::complex<double>> *roots, bool write_log = false) {
double tol_condition = 1;
long double tol_condition = 1;
uint32_t iter = 0;
int i, n;
std::ofstream log_file;
@@ -153,11 +153,11 @@ std::pair<uint32_t, double> durand_kerner_algo(
if (i != n)
denominator *= (*roots)[n] - (*roots)[i];
delta = numerator / denominator;
std::complex<long double> delta = numerator / denominator;
if (std::isnan(std::abs(delta)) || std::isinf(std::abs(delta))) {
std::cerr << "\n\nOverflow/underrun error - got value = "
<< std::abs(delta);
<< std::abs(delta) << "\n";
// return std::pair<uint32_t, double>(iter, tol_condition);
break_loop = true;
}
@@ -188,7 +188,7 @@ std::pair<uint32_t, double> durand_kerner_algo(
log_file << tol_condition;
}
return std::pair<uint32_t, double>(iter, tol_condition);
return std::pair<uint32_t, long double>(iter, tol_condition);
}
/**
@@ -197,15 +197,19 @@ std::pair<uint32_t, double> durand_kerner_algo(
*/
void test1() {
const std::valarray<double> coeffs = {1, 0, 4}; // x^2 - 2 = 0
std::valarray<std::complex<double>> roots = {
std::complex<double>(-100., 100.),
std::complex<double>(100., -100.) // initial approximate roots
};
std::valarray<std::complex<double>> roots(2);
std::valarray<std::complex<double>> expected = {
std::complex<double>(0., 2.),
std::complex<double>(0., -2.) // known expected roots
};
/* initialize root approximations with random values */
for (int n = 0; n < roots.size(); n++) {
roots[n] = std::complex<double>(std::rand() % 100, std::rand() % 100);
roots[n] -= 50.f;
roots[n] /= 25.f;
}
auto result = durand_kerner_algo(coeffs, &roots, false);
for (int i = 0; i < roots.size(); i++) {
@@ -229,17 +233,24 @@ void test1() {
void test2() {
const std::valarray<double> coeffs = {// 0.015625 x^3 - 1 = 0
1. / 64., 0., 0., -1.};
std::valarray<std::complex<double>> roots = {
std::complex<double>(-100., 100.), std::complex<double>(-101., 101.),
std::complex<double>(2., -2.) // initial approximate roots
};
std::valarray<std::complex<double>> expected = {
std::valarray<std::complex<double>> roots(3);
const std::valarray<std::complex<double>> expected = {
std::complex<double>(4., 0.), std::complex<double>(-2., 3.46410162),
std::complex<double>(-2., -3.46410162) // known expected roots
};
/* initialize root approximations with random values */
for (int n = 0; n < roots.size(); n++) {
roots[n] = std::complex<double>(std::rand() % 100, std::rand() % 100);
roots[n] -= 50.f;
roots[n] /= 25.f;
}
auto result = durand_kerner_algo(coeffs, &roots, false);
for (int n = 0; n < roots.size(); n++)
std::cout << "\t" << complex_str(roots[n]) << "\n";
for (int i = 0; i < roots.size(); i++) {
// check if approximations are have < 0.1% error with one of the
// expected roots
@@ -248,6 +259,7 @@ void test2() {
err1 |= std::abs(std::abs(roots[i] - expected[j])) < 1e-3;
assert(err1);
}
std::cout << "Test 2 passed! - " << result.first << " iterations, "
<< result.second << " accuracy"
<< "\n";
@@ -263,6 +275,9 @@ void test2() {
* will find roots of the polynomial \f$1\cdot x^2 + 0\cdot x^1 + (-4)=0\f$
**/
int main(int argc, char **argv) {
/* initialize random seed: */
std::srand(std::time(nullptr));
if (argc < 2) {
test1(); // run tests when no input is provided
test2(); // and skip tests when input polynomial is provided
@@ -275,9 +290,6 @@ int main(int argc, char **argv) {
int n, degree = argc - 1; // detected polynomial degree
std::valarray<double> coeffs(degree); // create coefficiencts array
/* initialize random seed: */
std::srand(std::time(nullptr));
// number of roots = degree - 1
std::valarray<std::complex<double>> s0(degree - 1);