d1r10.cpp

数值计算c++源代码,包括各种算法。很有用的。

#include "iostream.h"
#include "math.h"

void chobsb(double a[], int n, double d[], double b[])
{
	int i,j;
	double sum;
    for (i = 1; i<=n; i++)
	{
        sum = b[i];
        for (j = 1; j<=i - 1; j++)
		{
            sum = sum - a[(i-1)*n+j] * b[j];
        }
        b[i] = sum;
    }
    for (i = n; i>=1; i--)
	{
        if (d[i] == 0.0)
		{
            cout<<"  singular matrix";
            return;
		}
        else
		{
            sum = b[i] / d[i];
        }
        for (j = i + 1; j<=n; j++)
		{
            sum = sum - a[(j-1)*n+i] * b[j];
        }
        b[i] = sum;
    }
}

void chodcm(double a[], int n, double d[], double t[])
{
	int i,j,k;
	double sum;
    for (i = 1; i<=n; i++)
	{
        sum = a[(i-1)*n+i];
        for (j = 1; j<=i - 1; j++)
		{
            t[j] = a[(j-1)*n+i];
            for (k = 1; k<=j - 1; k++)
			{
                t[j] = t[j] - t[k] * a[(j-1)*n+k];
            }
            if (d[j] == 0.0)
			{
                if (t[j] != 0.0)
				{
                    cout<<"no cholesky decomposition"<<endl;
				}
                else
				{
                    a[(i-1)*n+j] = 1.0;
                }
			}
            else
			{
                a[(i-1)*n+j] = t[j] / d[j];
            }
            sum = sum - t[j] * a[(i-1)*n+j];
        }
        d[i] = sum;
    }
}

void main()
{
    //program d1r10
    //driver program for routine chobsb,chodcm
    int i,j,l,n = 5;
    double a[6][6], b[6], c[26], d[6], t[6], x[6];
    //输入已知的方程组的系数矩阵
    a[1][1]=1.4; a[1][2]=2.1; a[1][3]=2.1; a[1][4]=7.4; a[1][5]=9.6;
    a[2][1]=1.6; a[2][2]=1.5; a[2][3]=1.1; a[2][4]=0.7; a[2][5]=5.0;
    a[3][1]=3.8; a[3][2]=8.0; a[3][3]=9.6; a[3][4]=5.4; a[3][5]=8.8;
    a[4][1]=4.6; a[4][2]=8.2; a[4][3]=8.4; a[4][4]=0.4; a[4][5]=8.0;
    a[5][1]=2.6; a[5][2]=2.9; a[5][3]=0.1; a[5][4]=9.9; a[5][5]=7.7;
    //输入已知的方程组的右端向量b
    b[1] = 4.0;
    b[2] = 9.3;
    b[3] = 8.4;
    b[4] = 0.4;
    b[5] = 4.1;
    cout<<endl;
    cout<<"已知的方程组的右端向量"<<endl;
	cout.setf(ios::fixed|ios::right);
	cout.precision(5);    cout<<b[1]<<endl;
	cout.width(12);       cout<<b[2]<<endl;
	cout.width(12);       cout<<b[3]<<endl;
	cout.width(12);       cout<<b[4]<<endl;
	cout.width(12);       cout<<b[5]<<endl;
    for (i = 1; i<=n; i++)
	{
        for (j = 1; j<=n; j++)
		{
           c[(i-1)*n+j] = a[i][j];
        }
    }
    chodcm(c, n, d, t);
    for (i = 1; i<=n; i++)
	{
        x[i] = b[i];
    }
    chobsb(c, n, d, x);
    cout<<endl;
    cout<<"计算出的方程组的解"<<endl;
	cout.width(12);    cout<<x[1]<<endl;
	cout.width(12);    cout<<x[2]<<endl;
	cout.width(12);    cout<<x[3]<<endl;
	cout.width(12);    cout<<x[4]<<endl;
	cout.width(12);    cout<<x[5]<<endl;
    //将计算出的解x乘以系数矩阵，以验证计算结果正确
    for (l = 1; j<=n; j++)
	{
        b[l] = 0.0;
        for (j = 1; j<=l; j++)
		{
            b[l] = b[l] + a[j][l] * x[j];
        }
        for (j = l + 1; j<=n; j++)
		{
            b[l] = b[l] + a[l][j] * x[j];
        }
    }
    cout<<endl;
    cout<<"计算出的解乘以系数矩阵的结果"<<endl;
	cout.width(12);    cout<<b[1]<<endl;
	cout.width(12);    cout<<b[2]<<endl;
	cout.width(12);    cout<<b[3]<<endl;
	cout.width(12);    cout<<b[4]<<endl;
	cout.width(12);    cout<<b[5]<<endl;
}