void init_mat(void)
{
matrix_begin();
matrix_t* A = matrix_matrix(2, 2);
ELEMENT(A, 0, 0) = 1.0; ELEMENT(A, 0, 0) = 3.0;
ELEMENT(A, 0, 0) = 2.0; ELEMENT(A, 0, 0) = 4.0;
sq_init_matrix(A);
matrix_end();
}
void gmres(double *A, double *D, double *x, double *b, int N, int max_restart, int max_iter, double tol)
{
int i, j, k, l, m, N2;
double resid, *normb, *beta, *temp_nrm, temp, *r, *q, *Aq, *qA, *Dq, *w, *cs, *sn, *s, *y, *Q, *H, *res;
normb = (double *) malloc(1*sizeof(double));
beta = (double *) malloc(1*sizeof(double));
temp_nrm = (double *) malloc(1*sizeof(double));
Q = (double *) malloc(N*N*(max_iter+1)*sizeof(double));
H = (double *) malloc((N+1)*max_iter*sizeof(double));
r = (double *) malloc(N*N*sizeof(double));
q = (double *) malloc(N*N*sizeof(double));
Aq = (double *) malloc(N*N*sizeof(double));
qA = (double *) malloc(N*N*sizeof(double));
Dq = (double *) malloc(N*N*sizeof(double));
w = (double *) malloc(N*N*sizeof(double));
cs = (double *) malloc((max_iter+1)*sizeof(double));
sn = (double *) malloc((max_iter+1)*sizeof(double));
s = (double *) malloc((max_iter+1)*sizeof(double));
y = (double *) malloc((max_iter+1)*sizeof(double));
res = (double *) malloc(max_iter*sizeof(double));
N2 = N*N;
norm(b, normb, N2);
for (k=0; k<N2; k++) r[k] = b[k];
norm(r, beta, N2);
if ((resid = *beta / *normb) <= tol)
{
tol = resid;
max_iter = 0;
}
for (m=0; m<max_restart; m++)
{
for (i=0; i<N2; i++) Q[i] = r[i] / *beta;
for (i=0; i<max_iter; i++) s[i+1] = 0.0;
s[0] = *beta;
for (i = 0; i<max_iter; i++)
{
q_subQ(q, Q, N2, i);
matrix_matrix(A, q, Aq, N);
matrix_matrix(q, A, qA, N);
matrix_matrix(D, q, Dq, N);
for (k=0; k<N2; k++) w[k] = Aq[k] + qA[k] + Dq[k];
for (k=0; k<=i; k++)
{
q_subQ(q, Q, N2, k);
H[max_iter*k+i] = inner_product(q, w, N2);
w_shift(w, q, H[max_iter*k+i], N2);
}
/* for (k=0; k<=i; k++)
{
H[max_iter*k+i] = 0.0;
for (j=0; j<N2; j++) H[max_iter*k+i] += Q[N2*k+j]*w[j];
}
for (k=0; k<=i; k++)
{
for (j=0; j<N2; j++) w[j] = w[j] - H[max_iter*k+i]*Q[N2*k+j];
}
*/
norm(w, temp_nrm, N2);
H[max_iter*(i+1)+i] = *temp_nrm;
subQ_v(Q, w, N2, i+1, H[max_iter*(i+1)+i]);
for (k = 0; k < i; k++)
{
//ApplyPlaneRotation(H(k,i), H(k+1,i), cs(k), sn(k))
temp = cs[k]*H[max_iter*k+i] + sn[k]*H[max_iter*(k+1)+i];
H[max_iter*(k+1)+i] = -1.0*sn[k]*H[max_iter*k+i] + cs[k]*H[max_iter*(k+1)+i];
H[max_iter*k+i] = temp;
}
GeneratePlaneRotation(H[max_iter*i+i], H[max_iter*(i+1)+i], cs, sn, i);
//ApplyPlaneRotation(H(i,i), H(i+1,i), cs(i), sn(i))
H[max_iter*i+i] = cs[i]*H[max_iter*i+i] + sn[i]*H[max_iter*(i+1)+i];
H[max_iter*(i+1)+i] = 0.0;
//ApplyPlaneRotation(s(i), s(i+1), cs(i), sn(i));
temp = cs[i]*s[i];
s[i+1] = -1.0*sn[i]*s[i];
s[i] = temp;
resid = fabs(s[i+1] / *beta);
res[i] = resid;
if (resid < tol)
{
// backsolve(H, s, y, N, max_iter, i);
for (k=0; k<max_iter+1; k++) y[k] = s[k];
cblas_dtrsv(CblasRowMajor, CblasUpper, CblasNoTrans, CblasNonUnit, i, H, max_iter, y, 1);
for(j=0; j<N; j++)
{
for (l=0; l<N; l++)
{
for(k=0; k<=i; k++)
{
x[N*j+l] += Q[N2*k+N*j+l]*y[k];
}
}
}
break;
}
}//end inside for
if (resid < tol)
{
printf(" resid = %e \n", resid);
printf(" Converges at %d cycle %d step. \n", m, i+1);
break;
}
// Caution : i = i + 1.
i = i - 1;
backsolve(H, s, y, N, max_iter, i);
for(j=0; j<N; j++)
{
for (l=0; l<N; l++)
{
for(k=0; k<=i; k++)
{
x[N*j+l] += Q[N2*k+N*j+l]*y[k];
}
}
}
matrix_matrix(A, x, Aq, N);
matrix_matrix(x, A, qA, N);
matrix_matrix(D, x, Dq, N);
for (j=0; j<N2; j++) r[j] = b[j] - (Aq[j] + qA[j] + Dq[j]);
norm(r, beta, N2);
s[i+1] = *beta;
resid = s[i+1] / *normb;
if ( resid < tol)
{
printf(" resid = %e \n", resid);
printf(" Converges at %d cycle %d step. \n", m, i);
break;
}
}//end outside for
}
