::::|| VU ||:::: MTH 603 Assignment 2 .. helping material

/******************************************************************************/
/* Perform Gauss-Jordan elimination with row-pivoting to obtain the solution to
* the system of linear equations
* A X = B
*
* Arguments:
* lhs - left-hand side of the equation, matrix A
* rhs - right-hand side of the equation, matrix B
* nrows - number of rows in the arrays lhs and rhs
* ncolsrhs- number of columns in the array rhs
*
* The function uses Gauss-Jordan elimination with pivoting. The solution X to
* the linear system winds up stored in the array rhs; create a copy to pass to
* the function if you wish to retain the original RHS array.
*
* Passing the identity matrix as the rhs argument results in the inverse of
* matrix A, if it exists.
*
* No library or header dependencies, but requires the function swaprows, which
* is included here.
*/

// swaprows - exchanges the contents of row0 and row1 in a 2d array
void swaprows(double** arr, long row0, long row1) {
double* temp;
temp=arr[row0];
arr[row0]=arr[row1];
arr[row1]=temp;
}

// gjelim
void gjelim(double** lhs, double** rhs, long nrows, long ncolsrhs) {

// augment lhs array with rhs array and store in arr2
double** arr2=new double*[nrows];
for (long row=0; row<nrows; ++row)
arr2[row]=new double[nrows+ncolsrhs];

for (long row=0; row<nrows; ++row) {
for (long col=0; col<nrows; ++col) {
arr2[row][col]=lhs[row][col];
}
for (long col=nrows; col<nrows+ncolsrhs; ++col) {
arr2[row][col]=rhs[row][col-nrows];
}
}

// perform forward elimination to get arr2 in row-echelon form
for (long dindex=0; dindex<nrows; ++dindex) {
// run along diagonal, swapping rows to move zeros in working position
// (along the diagonal) downwards
if ( (dindex==(nrows-1)) && (arr2[dindex][dindex]==0)) {
return; // no solution
} else if (arr2[dindex][dindex]==0) {
swaprows(arr2, dindex, dindex+1);
}
// divide working row by value of working position to get a 1 on the
// diagonal
if (arr2[dindex][dindex] == 0.0) {
return;
} else {
double tempval=arr2[dindex][dindex];
for (long col=0; col<nrows+ncolsrhs; ++col) {
arr2[dindex][col]/=tempval;
}
}

// eliminate value below working position by subtracting a multiple of
// the current row
for (long row=dindex+1; row<nrows; ++row) {
double wval=arr2[row][dindex];
for (long col=0; col<nrows+ncolsrhs; ++col) {
arr2[row][col]-=wval*arr2[dindex][col];
}
}
}

// backward substitution steps
for (long dindex=nrows-1; dindex>=0; --dindex) {
// eliminate value above working position by subtracting a multiple of
// the current row
for (long row=dindex-1; row>=0; --row) {
double wval=arr2[row][dindex];
for (long col=0; col<nrows+ncolsrhs; ++col) {
arr2[row][col]-=wval*arr2[dindex][col];
}
}
}

// assign result to replace rhs
for (long row=0; row<nrows; ++row) {
for (long col=0; col<ncolsrhs; ++col) {
rhs[row][col]=arr2[row][col+nrows];
}
}

for (long row=0; row<nrows; ++row)
delete[] arr2[row];
delete[] arr2;
}

MTH 603 Assignment 2 .. helping material


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http://www.vuforum.net/topic/299-mth-603-assignments/page__gopid__446#entry446
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