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/*************************************************************************
* Copyright (c) 2011 AT&T Intellectual Property
* All rights reserved. This program and the accompanying materials
* are made available under the terms of the Eclipse Public License v1.0
* which accompanies this distribution, and is available at
* https://www.eclipse.org/legal/epl-v10.html
*
* Contributors: Details at https://graphviz.org
*************************************************************************/
#include <neatogen/matrix_ops.h>
#include <neatogen/conjgrad.h>
#include <stdbool.h>
#include <stdlib.h>
#include <util/alloc.h>
/*************************
** C.G. method - SPARSE *
*************************/
int conjugate_gradient
(vtx_data * A, double *x, double *b, int n, double tol,
int max_iterations) {
/* Solves Ax=b using Conjugate-Gradients method */
/* 'x' and 'b' are orthogonalized against 1 */
int i, rv = 0;
double alpha, beta, r_r, r_r_new, p_Ap;
double *r = gv_calloc(n, sizeof(double));
double *p = gv_calloc(n, sizeof(double));
double *Ap = gv_calloc(n, sizeof(double));
double *Ax = gv_calloc(n, sizeof(double));
double *alphap = gv_calloc(n, sizeof(double));
double *orth_b = gv_calloc(n, sizeof(double));
copy_vector(n, b, orth_b);
orthog1(n, orth_b);
orthog1(n, x);
right_mult_with_vector(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(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 */
r_r_new = vectors_inner_product(n, r, r);
if (r_r == 0) {
agerrorf("conjugate_gradient: unexpected length 0 vector\n");
rv = 1;
goto cleanup0;
}
beta = r_r_new / r_r;
r_r = r_r_new;
vectors_scalar_mult(n, p, beta, p);
vectors_addition(n, r, p, p);
}
}
cleanup0 :
free(r);
free(p);
free(Ap);
free(Ax);
free(alphap);
free(orth_b);
return rv;
}
/****************************
** C.G. method - DENSE *
****************************/
int conjugate_gradient_f
(float **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, rv = 0;
double alpha, beta, r_r, r_r_new, p_Ap;
double *r = gv_calloc(n, sizeof(double));
double *p = gv_calloc(n, sizeof(double));
double *Ap = gv_calloc(n, sizeof(double));
double *Ax = gv_calloc(n, sizeof(double));
double *alphap = gv_calloc(n, sizeof(double));
double *orth_b = gv_calloc(n, sizeof(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 */
// Alternative 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;
agerrorf("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;
}
int
conjugate_gradient_mkernel(float *A, float *x, float *b, int n,
double tol, int max_iterations)
{
/* Solves Ax=b using Conjugate-Gradients method */
/* A is a packed symmetric matrix */
// matrix A is “packed” (only upper triangular portion exists, row-major)
int i, rv = 0;
double alpha, beta, r_r, r_r_new, p_Ap;
float *r = gv_calloc(n, sizeof(float));
float *p = gv_calloc(n, sizeof(float));
float *Ap = gv_calloc(n, sizeof(float));
float *Ax = gv_calloc(n, sizeof(float));
/* centering x and b */
orthog1f(n, x);
orthog1f(n, b);
right_mult_with_vector_ff(A, n, x, Ax);
/* centering Ax */
orthog1f(n, Ax);
vectors_subtractionf(n, b, Ax, r);
copy_vectorf(n, r, p);
r_r = vectors_inner_productf(n, r, r);
for (i = 0; i < max_iterations && max_absf(n, r) > tol; i++) {
orthog1f(n, p);
orthog1f(n, x);
orthog1f(n, r);
right_mult_with_vector_ff(A, n, p, Ap);
/* centering Ap */
orthog1f(n, Ap);
p_Ap = vectors_inner_productf(n, p, Ap);
if (p_Ap == 0)
break;
alpha = r_r / p_Ap;
/* derive new x: */
vectors_mult_additionf(n, x, (float) alpha, p);
/* compute values for next iteration: */
if (i < max_iterations - 1) { /* not last iteration */
vectors_mult_additionf(n, r, (float) -alpha, Ap);
r_r_new = vectors_inner_productf(n, r, r);
if (r_r == 0) {
rv = 1;
agerrorf("conjugate_gradient: unexpected length 0 vector\n");
goto cleanup2;
}
beta = r_r_new / r_r;
r_r = r_r_new;
for (size_t j = 0; j < (size_t)n; ++j) {
p[j] = (float)beta * p[j] + r[j];
}
}
}
cleanup2 :
free(r);
free(p);
free(Ap);
free(Ax);
return rv;
}
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