void conjugate_gradient
(double **A, double *x, double *b, int n, double tol,
int max_iterations, bool ortho1) {
/* Solves Ax=b using Conjugate-Gradients method */
/* 'x' and 'b' are orthogonalized against 1 if 'ortho1=true' */
int i;
double alpha, beta, r_r, r_r_new, p_Ap;
double r[n];
double p[n];
double Ap[n];
double Ax[n];
double alphap[n];
double orth_b[n];
copy_vector(n, b, orth_b);
if (ortho1) {
orthog1(n, orth_b);
orthog1(n, x);
}
right_mult_with_vector_d(A, n, n, x, Ax);
vectors_subtraction(n, orth_b, Ax, r);
copy_vector(n, r, p);
r_r = vectors_inner_product(n, r, r);
for (i = 0; i < max_iterations && max_abs(n, r) > tol; i++) {
right_mult_with_vector_d(A, n, n, p, Ap);
p_Ap = vectors_inner_product(n, p, Ap);
if (p_Ap == 0) break;
alpha = r_r / p_Ap;
/* derive new x: */
vectors_scalar_mult(n, p, alpha, alphap);
vectors_addition(n, x, alphap, x);
/* compute values for next iteration: */
if (i < max_iterations - 1) { /* not last iteration */
vectors_scalar_mult(n, Ap, alpha, Ap);
vectors_subtraction(n, r, Ap, r); /* fast computation of r, the residual */
/* Alternaive accurate, but slow, computation of the residual - r */
/* right_mult_with_vector(A, n, x, Ax); */
/* vectors_subtraction(n,b,Ax,r); */
r_r_new = vectors_inner_product(n, r, r);
if (r_r == 0) exit(1);
beta = r_r_new / r_r;
r_r = r_r_new;
vectors_scalar_mult(n, p, beta, p);
vectors_addition(n, r, p, p);
}
}
}
int conjugate_gradient_f
(float **A, double *x, double *b, int n, double tol,
int max_iterations, boolean ortho1) {
/* Solves Ax=b using Conjugate-Gradients method */
/* 'x' and 'b' are orthogonalized against 1 if 'ortho1=true' */
int i, rv = 0;
double alpha, beta, r_r, r_r_new, p_Ap;
double *r = N_GNEW(n, double);
double *p = N_GNEW(n, double);
double *Ap = N_GNEW(n, double);
double *Ax = N_GNEW(n, double);
double *alphap = N_GNEW(n, double);
double *orth_b = N_GNEW(n, double);
copy_vector(n, b, orth_b);
if (ortho1) {
orthog1(n, orth_b);
orthog1(n, x);
}
right_mult_with_vector_f(A, n, x, Ax);
vectors_subtraction(n, orth_b, Ax, r);
copy_vector(n, r, p);
r_r = vectors_inner_product(n, r, r);
for (i = 0; i < max_iterations && max_abs(n, r) > tol; i++) {
right_mult_with_vector_f(A, n, p, Ap);
p_Ap = vectors_inner_product(n, p, Ap);
if (p_Ap == 0)
break; /*exit(1); */
alpha = r_r / p_Ap;
/* derive new x: */
vectors_scalar_mult(n, p, alpha, alphap);
vectors_addition(n, x, alphap, x);
/* compute values for next iteration: */
if (i < max_iterations - 1) { /* not last iteration */
vectors_scalar_mult(n, Ap, alpha, Ap);
vectors_subtraction(n, r, Ap, r); /* fast computation of r, the residual */
/* Alternaive accurate, but slow, computation of the residual - r */
/* right_mult_with_vector(A, n, x, Ax); */
/* vectors_subtraction(n,b,Ax,r); */
r_r_new = vectors_inner_product(n, r, r);
if (r_r == 0) {
rv = 1;
agerr (AGERR, "conjugate_gradient: unexpected length 0 vector\n");
goto cleanup1;
}
beta = r_r_new / r_r;
r_r = r_r_new;
vectors_scalar_mult(n, p, beta, p);
vectors_addition(n, r, p, p);
}
}
cleanup1:
free(r);
free(p);
free(Ap);
free(Ax);
free(alphap);
free(orth_b);
return rv;
}