我必须设计一种算法作为前向消除的扩展,在矩阵上进行Gauss Jordan Eliminations。我的程序正在执行并创建数字的对角线,但它们并非都是1。它也不会访问第一行和第一列以将它们更改为0。最后一栏,答案应该是,不会改变。我能做些什么来接近解决方案?
#include <cmath>
using namespace std;
double BetterForwardElimination(double A[8][9])
{
//Implements Gaussian elimination with partial pivoting
//Input: Matrix A[1..n,1..n] and column-vector b[1..n]
//Output: An equivalent upper-triangular matrix in place ofAand the
//corresponding right-hand side values in place of the (n+1)st column
//size of array
int n = 8;
//int n = sizeof(A)/sizeof(A[0]);
for (int i = 1; i<n; i++)
{
int pivotrow = i;
for (int j=i+1; j<n; j++)
{
if (A[j][i] > A[pivotrow][i])
{
pivotrow = j;
}
}
for (int k=i; k<n-1; k++)
{
swap(A[i][k], A[pivotrow][k]);
}
for (int j=i+1; j<n; j++)
{
//int temp = A[j][i]/A[i][i];
for (int k = i; k<n; k++)
{
A[j][k] = A[j][k] - A[i][k]*(A[j][i]/A[i][i]);
}
A[i][j] = 0;
}
}
return A[n][n];
}
我的输出是这样的:
1 1 1 1 1 1 1 1 0
1 2 0 0 0 0 0 0 0
1 0 3 0 0 0 0 0 0
1 0 0 4 0 0 0 0 0
11 0 0 0 5 0 0 0 20
1 0 0 0 0 1 0 0 34
1 0 0 0 0 0 1 0 -51
1 0 0 0 0 0 0 -1 -6
预期输出应为:
1 0 0 0 0 0 0 0 2
0 1 0 0 0 0 0 0 3
0 0 1 0 0 0 0 0 5
0 0 0 1 0 0 0 0 7
0 0 0 0 1 0 0 0 -7
0 0 0 0 0 1 0 0 -5
0 0 0 0 0 0 1 0 -3
0 0 0 0 0 0 0 1 -2
答案 0 :(得分:1)
根据算法,A[j][i] > A[pivotrow][i]
应为|A[j][i]| > |A[pivotrow][i
] |,两者都是绝对值。你的掉期功能在哪里?我不认为C ++有自己的swap(int[][] a, int[][]b)
。
答案 1 :(得分:1)
我刚刚创建了一个QMatrix类。它使用内置向量&gt;容器。
您可以按如下方式使用它:
#include "QMatrix.h"
#include <iostream>
int main(){
QMatrix<double> A(3,3,true);
QMatrix<double> Result = A.inverse()*A; //should give the idendity matrix
std::cout<<A.inverse()<<std::endl;
std::cout<<Result<<std::endl; // for checking
return 0;
}
如果您想了解它是如何工作的,则反函数实现如下:
该课程包含以下字段:
template<class T> class QMatrix{
public:
int rows, cols;
std::vector<std::vector<T> > A;
inverse()函数:
template<class T>
QMatrix<T> QMatrix<T>:: inverse(){
Identity<T> Id(rows); //the Identity Matrix as a subclass of QMatrix.
QMatrix<T> Result = *this; // making a copy and transforming it to the Identity matrix
T epsilon = 0.000001;
for(int i=0;i<rows;++i){
//check if Result(i,i)==0, if true, switch the row with another
for(int j=i;j<rows;++j){
if(std::abs(Result(j,j))<epsilon) { //uses Overloading()(int int) to extract element from Result Matrix
Result.replace_rows(i,j+1); //switches rows i with j+1
}
else break;
}
// main part, making a triangular matrix
Id(i)=Id(i)*(1.0/Result(i,i));
Result(i)=Result(i)*(1.0/Result(i,i)); // Using overloading ()(int) to get a row form the matrix
for(int j=i+1;j<rows;++j){
T temp = Result(j,i);
Result(j) = Result(j) - Result(i)*temp;
Id(j) = Id(j) - Id(i)*temp; //doing the same operations to the identity matrix
Result(j,i)=0; //not necessary, but looks nicer than 10^-15
}
}
// solving a triangular matrix
for(int i=rows-1;i>0;--i){
for(int j=i-1;j>=0;--j){
T temp = Result(j,i);
Id(j) = Id(j) - temp*Id(i);
Result(j)=Result(j)-temp*Result(i);
}
}
return Id;
}
它工作得很好......但是应该有办法在不影响灵活性的情况下提高速度。