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ヤコビ法
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// | |
// Jacobi.cpp | |
// ヤコビ法(行列の固有値計算) | |
// Created by knuu on 2014/06/23. | |
// | |
// | |
#include <iostream> | |
#include <iomanip> // std::setpricision | |
#include <Eigen/Dense> // 行列計算のライブラリ | |
#include <algorithm> | |
#include <cmath> | |
#define M_PRE 10 // 小数点以下の桁数 | |
#define SIZE_A 3 // 行列のサイズ | |
#define EPS 0.00000000001 // 誤差 | |
#define square(x) (x) * (x) | |
void yacobi(Eigen::Matrix<double, Eigen::Dynamic, Eigen::Dynamic> A) | |
{ | |
std::cout<<std::fixed<<std::setprecision(M_PRE); // 小数点以下の桁数設定 | |
Eigen::Matrix<double, Eigen::Dynamic, Eigen::Dynamic> P_n; | |
P_n = Eigen::MatrixXd::Identity(A.cols(), A.rows()); | |
int count = 1; // 計算回数をカウント | |
while (true) { | |
double a_km[2] = {0, 1}; // 非対角要素の絶対値最大の位置a_km = {k, m} | |
// 非対角要素の絶対値最大の位置を見つける | |
double a_m; | |
for (int i = 0; i < A.cols(); i++) { | |
for (int j = 0; j < A.rows(); j++) { | |
if (i == j) continue; | |
a_m = A(a_km[0], a_km[1]); | |
double a_ij = A(i, j); // std::abs(A(i,j))が0になってしまう? | |
if (std::abs(a_m) < std::abs(a_ij)) { | |
a_km[0] = i, a_km[1] = j; | |
} | |
} | |
} | |
// 非対角要素の大きさ判定 | |
a_m = A(a_km[0], a_km[1]); | |
if (std::abs(a_m) < EPS) { | |
break; | |
} | |
// sinphi, cosphiを求める | |
double s = (A(a_km[0], a_km[0]) - A(a_km[1], a_km[1]))/ 2.0; | |
double r = std::sqrt(s * s + a_m * a_m); | |
double sigphi; | |
s >= 0 ? sigphi = 1.0 : sigphi = -1.0; | |
double cosphi = std::sqrt(0.5 * (1 + sigphi * s / r)); | |
double sinphi = sigphi * a_m / (2.0 * r * cosphi); | |
// 求めたcosphiとsinphiについて行列Pを求める | |
Eigen::Matrix<double, Eigen::Dynamic, Eigen::Dynamic> P; | |
P = Eigen::MatrixXd::Identity(A.cols(), A.rows()); | |
P(a_km[0], a_km[0]) = cosphi, P(a_km[1], a_km[1]) = cosphi; | |
P(a_km[0], a_km[1]) = -sinphi, P(a_km[1], a_km[0]) = sinphi; | |
// A=(P^T)APを計算 | |
P_n = P_n * P; | |
Eigen::Matrix<double, Eigen::Dynamic, Eigen::Dynamic> Pt = P.transpose(); | |
A = Pt * A * P; | |
// 対角化途中の行列を表示 | |
/* | |
std::cout<<"対角化途中("<<c<<"回目)の行列A_i = "<<std::endl; | |
std::cout<<A<<std::endl; | |
std::cout<<"対角化途中("<<count<<"回目)の対角化行列P_i = "<<std::endl; | |
std::cout<<P<<std::endl; | |
*/ | |
// カウントを増やす | |
count++; | |
} | |
// 対角化された行列を表示 | |
std::cout<<"計算回数: "<<count<<std::endl; | |
std::cout<<"対角化された行列A_n = "<<std::endl; | |
std::cout<<A<<std::endl; | |
// 固有ベクトルを表示 | |
for (int i = 0; i < A.rows(); i++) { | |
std::cout<<i+1<<"番目の固有ベクトル = \t"<<std::endl; | |
std::cout<<P_n.col(i)<<std::endl; | |
} | |
} | |
int main() | |
{ | |
Eigen::Matrix<double, SIZE_A, SIZE_A> A; | |
A << 3,0.01,0.1, 0.01,2,0.01, 0.1,0.01,1; | |
yacobi(A); | |
} |
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