c++ - 用于计算矩阵指数的意外输出
问题描述
已编辑
我正在尝试计算矩阵的指数或矩阵的 e。使用一些预期的结果，例如对于 1 + I 的简单复数。我已经实现了一些更改以除以 n 阶乘。仍然有一个类似的问题，即经过一些迭代后，值会像疯了一样爆炸。
输出 这个程序将计算
> Blockquotee the exp of a matrix A
Calculating power of matrix
(1,1)(1,1)(1,1)
(1,1)(1,1)(1,1)
(1,1)(1,1)(1,1)
Performing scalar division
(1,1)(1,1)(1,1)
(1,1)(1,1)(1,1)
(1,1)(1,1)(1,1)
Performing Summation
(1,1)(1,1)(1,1)
(1,1)(1,1)(1,1)
(1,1)(1,1)(1,1)
1
Calculating power of matrix
(0,6)(0,6)(0,6)
(0,6)(0,6)(0,6)
(0,6)(0,6)(0,6)
Performing scalar division
(0,6)(0,6)(0,6)
(0,6)(0,6)(0,6)
(0,6)(0,6)(0,6)
Performing Summation
(1,7)(1,7)(1,7)
(1,7)(1,7)(1,7)
(1,7)(1,7)(1,7)
2
Calculating power of matrix
(-18,18)(-18,18)(-18,18)
(-18,18)(-18,18)(-18,18)
(-18,18)(-18,18)(-18,18)
Performing scalar division
(-18,18)(-18,18)(-18,18)
(-18,18)(-18,18)(-18,18)
(-18,18)(-18,18)(-18,18)
Performing Summation
(-17,25)(-17,25)(-17,25)
(-17,25)(-17,25)(-17,25)
(-17,25)(-17,25)(-17,25)
3
Calculating power of matrix
(-108,0)(-108,0)(-108,0)
(-108,0)(-108,0)(-108,0)
(-108,0)(-108,0)(-108,0)
Performing scalar division
(-108,0)(-108,0)(-108,0)
(-108,0)(-108,0)(-108,0)
(-108,0)(-108,0)(-108,0)
Performing Summation
(-125,25)(-125,25)(-125,25)
(-125,25)(-125,25)(-125,25)
(-125,25)(-125,25)(-125,25)
4
Calculating power of matrix
(-324,-324)(-324,-324)(-324,-324)
(-324,-324)(-324,-324)(-324,-324)
(-324,-324)(-324,-324)(-324,-324)
Performing scalar division
(-324,-324)(-324,-324)(-324,-324)
(-324,-324)(-324,-324)(-324,-324)
(-324,-324)(-324,-324)(-324,-324)
Performing Summation
(-449,-299)(-449,-299)(-449,-299)
(-449,-299)(-449,-299)(-449,-299) (-449,-299)(-449,-299)(-449,-299) 5
Calculating power of matrix
(0,-1944)(0,-1944)(0,-1944)
(0,-1944)(0,-1944)(0,-1944)
(0,-1944)(0,-1944)(0,-1944)
Performing scalar division
(0,-1944)(0,-1944)(0,-1944)
(0,-1944)(0,-1944)(0,-1944)
(0,-1944)(0,-1944)(0,-1944)
Performing Summation
(-449,-2243)(-449,-2243)(-449,-2243)
(-449,-2243)(-449,-2243)(-449,-2243)
(-449,-2243)(-449,-2243)(-449,-2243)
6
Calculating power of matrix
(5832,-5832)(5832,-5832)(5832,-5832)
(5832,-5832)(5832,-5832)(5832,-5832)
(5832,-5832)(5832,-5832)(5832,-5832)
Performing scalar division
(5832,-5832)(5832,-5832)(5832,-5832)
(5832,-5832)(5832,-5832)(5832,-5832)
(5832,-5832)(5832,-5832)(5832,-5832)
Performing Summation
(5383,-8075)(5383,-8075)(5383,-8075)
(5383,-8075)(5383,-8075)(5383,-8075)
(5383,-8075)(5383,-8075)(5383,-8075)
7
Calculating power of matrix
(34992,0)(34992,0)(34992,0)
(34992,0)(34992,0)(34992,0)
(34992,0)(34992,0)(34992,0)
Performing scalar division
(34992,0)(34992,0)(34992,0)
(34992,0)(34992,0)(34992,0)
(34992,0)(34992,0)(34992,0)
Performing Summation
(40375,-8075)(40375,-8075)(40375,-8075)
(40375,-8075)(40375,-8075)(40375,-8075)
(40375,-8075)(40375,-8075)(40375,-8075)
8
Calculating power of matrix
(104976,104976)(104976,104976)(104976,104976)
(104976,104976)(104976,104976)(104976,104976)
(104976,104976)(104976,104976)(104976,104976)
Performing scalar division
(104976,104976)(104976,104976)(104976,104976)
(104976,104976)(104976,104976)(104976,104976)
(104976,104976)(104976,104976)(104976,104976)
Performing Summation
(145351,96901)(145351,96901)(145351,96901)
(145351,96901)(145351,96901)(145351,96901)
(145351,96901)(145351,96901)(145351,96901)
9
#pragma once
#include <iostream>
#include <complex>
#include <cmath>
#include <cassert>
using namespace std;
class ComplexMatrix
{
private:
complex<long double>** Arr;
int mi = 3;
int mj = 3;
public:
ComplexMatrix();
//~ComplexMatrix();
ComplexMatrix(int i, int j);
ComplexMatrix(const ComplexMatrix&);
void Initialise(complex<long double>);
void DisplayMatrix();
void DeleteMatrix();
void EnterComplexMatrix(int, int);
ComplexMatrix matrixPower(ComplexMatrix&, int);
ComplexMatrix ScalarDivision_Fac(ComplexMatrix& , complex<long
double>);
ComplexMatrix MatrixAddition(ComplexMatrix&, ComplexMatrix&);
ComplexMatrix matrixSq(ComplexMatrix&);
ComplexMatrix Multiply(ComplexMatrix, ComplexMatrix);
ComplexMatrix matrixe_A(ComplexMatrix&, int);
ComplexMatrix operator*(const ComplexMatrix&);
ComplexMatrix operator=(const ComplexMatrix&);
friend ComplexMatrix operator+(const ComplexMatrix&, const ComplexMatrix&);
};
//Constructor to initialise a default 3 x 3 complex matrix with 0s for real and imaginary values
ComplexMatrix::ComplexMatrix()
{
Arr = new complex<long double> * [mi];
for (int x = 0; x < mi; x++)
{
Arr[x] = new complex<long double> [mj];
}
for (int x1 = 0; x1 < mi; x1++)
{
for (int y1 = 0; y1 < mj; y1++)
{
Arr[x1][y1] = (0.0, 0.0);
}
}
}
//Constructor to initialise a user defined complex matrix of a particular size with 0s for real
and imaginary values
ComplexMatrix::ComplexMatrix(int i, int j)
{
mi = i;
mj = j;
Arr = new complex<long double> * [i];
for (int x = 0; x < i; x++)
{
Arr[x] = new complex<long double>[j];
}
for (int x1 = 0; x1 < i; x1++)
{
for (int y1 = 0; y1 < j; y1++)
{
Arr[x1][y1] = (0.0, 0.0);
}
}
}
//Copy Constructor
ComplexMatrix::ComplexMatrix(const ComplexMatrix& CM)
//lets only have ARR mean one thing to make it easier to read, understand,
and to avoid this->
clutter.
{
Arr = new complex<long double> * [mi];
for (int x = 0; x < mi; x++)
{
Arr[x] = new complex<long double>[mj];
}
for (int x1 = 0; x1 < mi; x1++)
{
for (int y1 = 0; y1 < mj; y1++)
{
Arr[x1][y1] = CM.Arr[x1][y1];
}
}
}
/*
ComplexMatrix::~ComplexMatrix()
{
for (int x = 0; x < mi; x++)
{
delete[] Arr[x];
}
delete[] Arr;
}
*/
//Initialise matrix elements to a particular value
void ComplexMatrix::Initialise(complex<long double> x)
{
for (int i = 0; i < mi; i++)
{
for (int j = 0; j < mj; j++)
{
Arr[i][j] = x;
}
}
}
//Display the matrix member function
void ComplexMatrix::DisplayMatrix()
{
for (int x = 0; x < mi; x++)
{
for (int y = 0; y < mj; y++)
{
cout << Arr[x][y];
}
cout << endl;
}
}
//Delete the memory allocated by the matrix member function
void ComplexMatrix::DeleteMatrix()
{
for (int x = 0; x < mi; x++)
{
delete[] Arr[x];
}
delete[] Arr;
}
//Enter complex matrix elements member function
void ComplexMatrix::EnterComplexMatrix(int i, int j)
{
double real, img;
complex < long double> temp = (0.0, 0.0);
cout << "Your matrix will have " << i * j << " elements" << endl;
//Prompt for user input and assign values for real and imaginary values
for (int x = 0; x < i; x++)
{
for (int y = 0; y < j; y++)
{
cout << "Enter the details for the real part of element" << "[" <<
x << "]" << "[" << y
<< "]" << endl;
cin >> real;
cout << "Enter the details for the real part of element" << "[" <<
x << "]" << "[" << y
<< "]" << endl;
cin >> img;
temp = (real, img);
Arr[x][y] = temp;
}
}
}
ComplexMatrix ComplexMatrix::Multiply(ComplexMatrix x, ComplexMatrix y)
{
ComplexMatrix z(3, 3);
for (int x1 = 0; x1 < 3; ++x1)
{
for (int y1 = 0; y1 < 3; ++y1)
{
for (int z1 = 0; z1 < 3; ++z1)
{
Arr[x1][y1] += x.Arr[x1][z1] * y.Arr[z1][y1];
}
}
}
return z;
}
ComplexMatrix ComplexMatrix::ScalarDivision_Fac(ComplexMatrix& x,
complex<long double> n)
{
ComplexMatrix newCompArr(3, 3);
complex <long double> fac = 0.0;
int n1 = static_cast <int>(n.real());
n1 = static_cast <int>(n1);
complex <long double> i1;
for (int i = 1; i < n1; i++)
{
i1 = i;
fac = fac * i1;
}
for (int x1 = 0; x1 < mi; x1++)
{
for (int y1 = 0; y1 < mj; y1++)
{
newCompArr.Arr[x1][y1] = x.Arr[x1][y1] / fac;
}
}
return newCompArr;
}
ComplexMatrix ComplexMatrix::matrixSq(ComplexMatrix& x)
{
ComplexMatrix result(mi, mj);
result = x * x;
return result;
}
ComplexMatrix ComplexMatrix::matrixPower(ComplexMatrix& a, int n)
{
ComplexMatrix result(mi, mj);
ComplexMatrix temp(mi, mj);
temp = a;
if (n % 2 == 0)
{
for (int i = 1; i < n / 2; i++)
{
result = temp * a;
temp = result;
}
result = temp;
result = result.matrixSq(result);
}
else
{
for (int j = 0; j < (n - 1) ; j++)
{
result = temp * a;
temp = result;
}
result = temp;
}
return result;
}
ComplexMatrix ComplexMatrix::matrixe_A(ComplexMatrix& A, int n)
{
ComplexMatrix expA(mi, mj);
ComplexMatrix sum(mi, mj);
sum.Initialise({ 0.0, 0.0 });
ComplexMatrix A_n(mi, mj);
ComplexMatrix A_n_div_n(mi, mj);
ComplexMatrix temp(mi, mj);
ComplexMatrix zero(mi, mj);
zero.Initialise({ 0.0, 0.0 });
complex <long double> j;
for (int i = 1; i < n; i++)
{
cout << "Calculating power of matrix" << endl;
A_n = A.matrixPower(A, i);
A_n.DisplayMatrix();
A_n_div_n = A_n;
cout << "Performing scalar division" << endl;
A_n_div_n.ScalarDivision(A_n_div_n, i);
A_n_div_n.DisplayMatrix();
cout << endl;
temp = zero;
temp = A_n_div_n;
cout << "Performing Summation" << endl;
sum = sum + temp;
sum.DisplayMatrix();
cout << i << endl;
cout << endl;
temp = zero;
A_n = A.matrixPower(A, i);
}
return sum;
}
ComplexMatrix ComplexMatrix::operator*(const ComplexMatrix& CompArr)
{
ComplexMatrix newCompArr(3, 3);
for (int x1 = 0; x1 < 3; ++x1)
{
for (int y1 = 0; y1 < 3; ++y1)
{
newCompArr.Arr[x1][y1] = {0.0, 0.0};
for (int z1 = 0; z1 < 3; ++z1)
{
newCompArr.Arr[x1][y1] += Arr[x1][z1] * CompArr.Arr[z1][y1];
}
}
}
return newCompArr;
}
ComplexMatrix ComplexMatrix::operator=(const ComplexMatrix& CM)
{
mi = 3;
mj = 3;
//ComplexMatrix Arr(3, 3);
for (int x1 = 0; x1 < mi; x1++)
{
for (int y1 = 0; y1 < mj; y1++)
{
Arr[x1][y1] = CM.Arr[x1][y1];
}
}
//return Arr;
return *this;
}
ComplexMatrix operator+(const ComplexMatrix &x, const ComplexMatrix &y)
{
int mi = 3;
int mj = 3;
ComplexMatrix newCompArr(3, 3);
for (int x1 = 0; x1 < mi; x1++)
{
for (int y1 = 0; y1 < mj; y1++)
{
newCompArr.Arr[x1][y1] = { (x.Arr[x1][y1].real() + y.Arr[x1][y1].real()) ,
(x.Arr[x1][y1].imag() + y.Arr[x1][y1].imag()) };
}
}
return newCompArr;
}
#include <iostream>
#include "Header.h"
#include <complex>
#include <cmath>
using namespace std;
int main()
{
std::cout << "This program will calculate the exp of a matrix A\n";
complex<long double> x = {1, 1};
complex<long double> y = {2, 2};
complex<long double> z = { 0.0, 0.0 };
ComplexMatrix z1(3, 3);
ComplexMatrix z2(3, 3);
ComplexMatrix z3(3, 3);
z2.Initialise(x);
z3 = z2.matrixe_A(z2, 10);
//z3.DisplayMatrix();
z1.DeleteMatrix();
z2.DeleteMatrix();
}
解决方案
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