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#include <stdio.h>
#include <iostream>
#include <algorithm>
#define N 10
double matrix_det ( double **in_matrix, int n )
{
int i, j, k;
double **matrix;
double det = 1;
matrix = new double *[n];
for (i=0;i<n;i++)
matrix[i] = new double[n];
for (i=0;i<n;i++) {
for (j=0;j<n;j++)
matrix[i][j] = in_matrix[i][j];
}
for (k=0;k<n;k++) {
if (matrix[k][k] == 0 ) {
bool ok = false;
for (j=k;j<n;j++) {
if (matrix[j][k] != 0 )
ok = true;
}
if ( !ok )
return 0;
for (i=k;i<n;i++)
std::swap ( matrix[i][j], matrix[i][k] );
det = -det;
}
det *= matrix[k][k];
if (k+1<n) {
for (i=k+1;i<n;i++) {
for (j=k+1;j<n;j++)
matrix[i][j] = matrix[i][j] - matrix[i][k] *
matrix[k][j] / matrix[k][k];
}
}
}
for (i=0;i<n;i++)
delete [] matrix[i];
delete [] matrix;
return det;
}
int main(void)
{
int i, j;
double **arr, **arr1, **arr2, **arr3, **arr4, **arr5, **arr6, **arr7, **arr8, **arr9, **arr10;
double f[N], c[11], d[N], e[N];
arr = new double *[N];
arr1 = new double *[N];
arr2 = new double *[N];
arr3 = new double *[N];
arr4 = new double *[N];
arr5 = new double *[N];
arr6 = new double *[N];
arr7 = new double *[N];
arr8 = new double *[N];
arr9 = new double *[N];
arr10 = new double *[N];
for (i=0;i<N;i++)
{
arr[i] = new double[N];
arr1[i] = new double[N];
arr2[i] = new double[N];
arr3[i] = new double[N];
arr4[i] = new double[N];
arr5[i] = new double[N];
arr6[i] = new double[N];
arr7[i] = new double[N];
arr8[i] = new double[N];
arr9[i] = new double[N];
arr10[i] = new double[N];
}
for (i=0;i<N;i++)
{ for(j=0;j<N;j++)
{
arr[i][j] = (2*i*j)/((i+j)*((i+j)*(i+j)-1)) - 32/((i+j+1)*(i+j+2)*(i+j+3));
arr1[i][j] = arr[i][j];
arr2[i][j] = arr[i][j];
arr3[i][j] = arr[i][j];
arr4[i][j] = arr[i][j];
arr5[i][j] = arr[i][j];
arr6[i][j] = arr[i][j];
arr7[i][j] = arr[i][j];
arr8[i][j] = arr[i][j];
arr9[i][j] = arr[i][j];
arr10[i][j] = arr[i][j];
}
}
for (i=0;i<N;i++)
{
f[i] = -1/((3+i)*(4+i));
}
for (i=0;i<N;i++)
{ arr1[i][0] = f[i];
}
for (i=0;i<N;i++)
{ arr2[i][1] = f[i];
}
for (i=0;i<N;i++)
{ arr3[i][2] = f[i];
}
for (i=0;i<N;i++)
{ arr4[i][3] = f[i];
}
for (i=0;i<N;i++)
{ arr5[i][4] = f[i];
}
for (i=0;i<N;i++)
{ arr6[i][5] = f[i];
}
for (i=0;i<N;i++)
{ arr7[i][6] = f[i];
}
for (i=0;i<N;i++)
{ arr8[i][7] = f[i];
}
for (i=0;i<N;i++)
{ arr9[i][8] = f[i];
}
for (i=0;i<N;i++)
{ arr10[i][9] = f[i];
}
c[0] = matrix_det(arr,N);
c[1] = matrix_det(arr1,N);
c[2] = matrix_det(arr2,N);
c[3] = matrix_det(arr3,N);
c[4] = matrix_det(arr4,N);
c[5] = matrix_det(arr5,N);
c[6] = matrix_det(arr6,N);
c[7] = matrix_det(arr7,N);
c[8] = matrix_det(arr8,N);
c[9] = matrix_det(arr9,N);
c[10] = matrix_det(arr10,N);
for (i=0;i<N;i++)
{
int g = i+1;
d[i] = c[g] / c[i];
}
e[0] = d[0];
for (i=1;i<N;i++)
{
int h = i-1;
e[i] = d[i] - d[h];
}
printf("The ten parameter Rayleigh-Ritz solution is given by: \n");
printf("u = %fx + %fx^2 + %fx^3 + %fx^4 + %fx^5 + %fx^6 + %fx^7 + %fx^8 + %fx^9 + %fx^10", e[0], e[1], e[2], e[3], e[4], e[5], e[6], e[7], e[8], e[9]);
return 0;
}
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