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cg.c
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Sun, Apr 28, 07:34

cg.c
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#include "cg.h"
const double TOLERANCE = 1.0e-10;
/*
cgsolver solves the linear equation A*x = b where A is
of size m x n
Code based on MATLAB code (from wikipedia ;-) ):
function x = conjgrad(A, b, x)
r = b - A * x;
p = r;
rsold = r' * r;
for i = 1:length(b)
Ap = A * p;
alpha = rsold / (p' * Ap);
x = x + alpha * p;
r = r - alpha * Ap;
rsnew = r' * r;
if sqrt(rsnew) < 1e-10
break;
end
p = r + (rsnew / rsold) * p;
rsold = rsnew;
end
end
*/
void cgsolver( double *A, double *b, double *x, int m, int n ){
double * r;
double * rt;
double * p;
double * pt;
double rsold;
double rsnew;
double * Ap;
double * tmp;
double alpha;
int incx = 1;
int incy = 1;
int lda = m;
double al = 1.;
double be = 0.;
int k = 0;
r = (double*) malloc(n* sizeof(double));
rt = (double*) malloc(n* sizeof(double));
p = (double*) malloc(n* sizeof(double));
pt = (double*) malloc(n* sizeof(double));
Ap = (double*) malloc(n* sizeof(double));
tmp = (double*) malloc(n* sizeof(double));
// r = b - A * x;
cblas_dgemv (CblasColMajor, CblasNoTrans, m, n, al , A, lda, x, incx, be, Ap, incy);
cblas_dcopy(n,b,1,tmp,1);
cblas_daxpy(n, -1. , Ap,1, tmp, 1 );
cblas_dcopy(n,tmp,1,r,1);
// p = r;
cblas_dcopy (n, r, incx, p, incy);
cblas_dcopy(n,r,1,rt,1);
cblas_dcopy(n,p,1,pt,1);
// rsold = r' * r;
rsold = cblas_ddot (n,r,incx,rt,incy);
// for i = 1:length(b)
while ( k < n ){
printf("[k=%d] ",k+1);
printf("\tresidual = %f\n",sqrt(rsold));
// Ap = A * p;
cblas_dgemv (CblasColMajor, CblasNoTrans, m, n, al, A, lda, p, incx, be, Ap, incy);
// alpha = rsold / (p' * Ap);
alpha = rsold / fmax( cblas_ddot(n, pt, incx, Ap, incy ), NEARZERO );
// x = x + alpha * p;
cblas_daxpy(n, alpha, p, 1, x, 1);
// r = r - alpha * Ap;
cblas_daxpy(n, -alpha, Ap, 1, r, 1);
// rsnew = r' * r;
rsnew = cblas_ddot (n,r,incx,r,incy);
// if sqrt(rsnew) < 1e-10
// break;
if ( sqrt(rsnew) < TOLERANCE ) break; // Convergence test
// p = r + (rsnew / rsold) * p;
cblas_dcopy(n,r,1,tmp,1);
cblas_daxpy(n, (double)(rsnew/rsold), p, 1, tmp, 1);
cblas_dcopy(n,tmp,1,p,1);
cblas_dcopy(n,p,1,pt,1);
// rsold = rsnew;
rsold = rsnew;
k++;
}
free(r);
free(rt);
free(p);
free(pt);
free(Ap);
free(tmp);
}
double * init_source_term(int n, double h){
double * f;
int i;
f = (double*) malloc(n*sizeof(double*));
for(i = 0; i < n; i++) {
f[i] = (double)i * -2. * M_PI * M_PI * sin(10.*M_PI*i*h) * sin(10.*M_PI*i*h);
}
return f;
}

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