// performs backwards substitution on the linear system U*x = b, returning x as a new Mat;
// leaves U and b untouched
Mat BackSub(Mat &U, Mat &b) {
// check that matrix sizes match
if (U.Rows() != b.Rows() || U.Rows() != U.Cols() || b.Cols() != 1) {
fprintf(stderr,"BackSub error, illegal matrix/vector dimensions\n");
fprintf(stderr," Mat is %li x %li, rhs is %li x %li\n",
U.Rows(), U.Cols(), b.Rows(), b.Cols());
Mat *x = new Mat(0,0);
return *x;
}
// create new Mat for output
Mat *x = new Mat(U.Rows(),1);
// call existing BackSub routine for computations
if (BackSub(U, *x, b) != 0)
fprintf(stderr,"BackSub Warning: error in BackSub call\n");
// return result
return *x;
}
int main(int argc, char *argv[]) {
printf("WG size of kernel 1 = %d, WG size of kernel 2= %d X %d\n", BLOCK_SIZE_0, BLOCK_SIZE_1_X, BLOCK_SIZE_1_Y);
float *a=NULL, *b=NULL, *finalVec=NULL;
float *m=NULL;
int size = -1;
FILE *fp;
// args
char filename[200];
int quiet=1,timing=0,platform=-1,device=-1;
// parse command line
if (parseCommandline(argc, argv, filename,
&quiet, &timing, &platform, &device, &size)) {
printUsage();
return 0;
}
context = cl_init_context(platform,device,quiet);
if(size < 1)
{
fp = fopen(filename, "r");
fscanf(fp, "%d", &size);
a = (float *) malloc(size * size * sizeof(float));
InitMat(fp,size, a, size, size);
b = (float *) malloc(size * sizeof(float));
InitAry(fp, b, size);
fclose(fp);
}
else
{
printf("create input internally before create, size = %d \n", size);
a = (float *) malloc(size * size * sizeof(float));
create_matrix(a, size);
b = (float *) malloc(size * sizeof(float));
for (int i =0; i< size; i++)
b[i]=1.0;
}
if (!quiet) {
printf("The input matrix a is:\n");
PrintMat(a, size, size, size);
printf("The input array b is:\n");
PrintAry(b, size);
}
// create the solution matrix
m = (float *) malloc(size * size * sizeof(float));
// create a new vector to hold the final answer
finalVec = (float *) malloc(size * sizeof(float));
InitPerRun(size,m);
//begin timing
// printf("The result of array b is before run: \n");
// PrintAry(b, size);
// run kernels
ForwardSub(context,a,b,m,size,timing);
// printf("The result of array b is after run: \n");
// PrintAry(b, size);
DIVIDEND_CL_WRAP(clFinish)(command_queue);
//end timing
if (!quiet) {
printf("The result of matrix m is: \n");
PrintMat(m, size, size, size);
printf("The result of matrix a is: \n");
PrintMat(a, size, size, size);
printf("The result of array b is: \n");
PrintAry(b, size);
BackSub(a,b,finalVec,size);
printf("The final solution is: \n");
PrintAry(finalVec,size);
}
free(m);
free(a);
free(b);
free(finalVec);
cl_cleanup();
//OpenClGaussianElimination(context,timing);
return 0;
}
// solves a linear system A*x = b, filling in the input Mat x
int Solve(Mat &A, Mat &x, Mat &b) {
// create temporary variables
long int i, j, k, p, n;
double tmp, Amax;
// check that matrix sizes match
if (A.Rows() != b.Rows() || A.Rows() != A.Cols() ||
b.Cols() != 1 || x.Rows() != A.Rows() || x.Cols() != 1) {
fprintf(stderr,"Solve error, illegal matrix/vector dimensions\n");
fprintf(stderr," Mat is %li x %li, sol is %li x %li, rhs is %li x %li\n",
A.Rows(), A.Cols(), x.Rows(), x.Cols(), b.Rows(), b.Cols());
return 1;
}
// determine maximum absolute entry in A (for singularity check later)
Amax = A.MaxNorm();
// perform Gaussian elimination to convert A,b to an upper-triangular system
n = A.Rows();
for (k=0; k<n-1; k++) { // loop over diagonals
// find the pivot row p
p=k;
for (i=k; i<n; i++)
if (fabs(A(i,k)) > fabs(A(p,k)))
p=i;
// swap rows in A
for (j=k; j<n; j++) {
tmp = A(p,j);
A(p,j) = A(k,j);
A(k,j) = tmp;
}
// swap rows in b
tmp = b(p);
b(p) = b(k);
b(k) = tmp;
// check for singular matrix
if (fabs(A(k,k)) < 1.e-13*Amax) {
fprintf(stderr,"Solve error: numerically singular matrix!\n");
return 1;
}
// perform elimination on remaining submatrix of A using row k
for (j=k+1; j<n; j++)
for (i=k+1; i<n; i++)
A(i,j) = A(i,j) - A(i,k)/A(k,k)*A(k,j);
// perform elimination on remainder of b using row k
for (i=k+1; i<n; i++) b(i) -= A(i,k)/A(k,k)*b(k);
}
// check for singularity at end (only need to check final diagonal entry)
if (fabs(A(n-1,n-1)) < 1.e-13*Amax) {
fprintf(stderr,"Solve error: numerically singular matrix!\n");
return 1;
}
// perform Backwards Substitution on result
if (BackSub(A, x, b) != 0) {
fprintf(stderr,"Solve error in BackSub call\n");
return 1;
}
// return success
return 0;
}
