/* Ref: Weiss, Algorithm 11 CGS
* INPUT
* n : dimension of the problem
* b [n] : r-h-s vector
* atimes (int n, static double *x, double *b, void *param) :
* calc matrix-vector product A.x = b.
* atimes_param : parameters for atimes().
* it : struct iter. following entries are used
* it->max = kend : max of iteration
* it->eps = eps : criteria for |r^2|/|b^2|
* OUTPUT
* returned value : 0 == success, otherwise (-1) == failed
* x [n] : solution
* it->niter : # of iteration
* it->res2 : |r^2| / |b^2|
*/
int
cgs (int n, const double *b, double *x,
void (*atimes) (int, const double *, double *, void *),
void *atimes_param,
struct iter *it)
{
#ifndef HAVE_CBLAS_H
# ifdef HAVE_BLAS_H
/* use Fortran BLAS routines */
int i_1 = 1;
double d_m1 = -1.0;
double d_2 = 2.0;
# endif // !HAVE_BLAS_H
#endif // !HAVE_CBLAS_H
int ret = -1;
double eps2 = it->eps * it->eps;
int itmax = it->max;
double *r = (double *)malloc (sizeof (double) * n);
double *r0 = (double *)malloc (sizeof (double) * n);
double *p = (double *)malloc (sizeof (double) * n);
double *u = (double *)malloc (sizeof (double) * n);
double *ap = (double *)malloc (sizeof (double) * n);
double *q = (double *)malloc (sizeof (double) * n);
double *t = (double *)malloc (sizeof (double) * n);
CHECK_MALLOC (r, "cgs");
CHECK_MALLOC (r0, "cgs");
CHECK_MALLOC (p, "cgs");
CHECK_MALLOC (u, "cgs");
CHECK_MALLOC (ap, "cgs");
CHECK_MALLOC (q, "cgs");
CHECK_MALLOC (t, "cgs");
double r0ap;
double rho, rho1;
double delta;
double beta;
double res2 = 0.0;
#ifdef HAVE_CBLAS_H
/**
* ATLAS version
*/
double b2 = cblas_ddot (n, b, 1, b, 1); // (b,b)
eps2 *= b2;
// initial residue
atimes (n, x, r, atimes_param); // r = A.x
cblas_daxpy (n, -1.0, b, 1, r, 1); // r = A.x - b
cblas_dcopy (n, r, 1, r0, 1); // r0* = r
cblas_dcopy (n, r, 1, p, 1); // p = r
cblas_dcopy (n, r, 1, u, 1); // u = r
rho = cblas_ddot (n, r0, 1, r, 1); // rho = (r0*, r)
int i;
for (i = 0; i < itmax; i ++)
{
atimes (n, p, ap, atimes_param); // ap = A.p
r0ap = cblas_ddot (n, r0, 1, ap, 1); // r0ap = (r0*, A.p)
delta = - rho / r0ap;
cblas_dcopy (n, u, 1, q, 1); // q = u
cblas_dscal (n, 2.0, q, 1); // q = 2 u
cblas_daxpy (n, delta, ap, 1, q, 1); // q = 2 u + delta A.p
atimes (n, q, t, atimes_param); // t = A.q
cblas_daxpy (n, delta, t, 1, r, 1); // r = r + delta t
cblas_daxpy (n, delta, q, 1, x, 1); // x = x + delta q
res2 = cblas_ddot (n, r, 1, r, 1);
if (it->debug == 2)
{
fprintf (it->out, "libiter-cgs %d %e\n", i, res2 / b2);
}
if (res2 <= eps2)
{
ret = 0; // success
break;
}
rho1 = cblas_ddot (n, r0, 1, r, 1); // rho = (r0*, r)
beta = rho1 / rho;
rho = rho1;
// here t is not used so that this is used for working area.
double *qu = t;
cblas_dcopy (n, q, 1, qu, 1); // qu = q
cblas_daxpy (n, -1.0, u, 1, qu, 1); // qu = q - u
cblas_dcopy (n, r, 1, u, 1); // u = r
cblas_daxpy (n, beta, qu, 1, u, 1); // u = r + beta (q - u)
cblas_daxpy (n, beta, p, 1, qu, 1); // qu = q - u + beta * p
cblas_dcopy (n, u, 1, p, 1); // p = u
cblas_daxpy (n, beta, qu, 1, p, 1); // p = u + beta (q - u + b * p)
}
#else // !HAVE_CBLAS_H
# ifdef HAVE_BLAS_H
/**
* BLAS version
*/
double b2 = ddot_ (&n, b, &i_1, b, &i_1); // (b,b)
eps2 *= b2;
// initial residue
atimes (n, x, r, atimes_param); // r = A.x
daxpy_ (&n, &d_m1, b, &i_1, r, &i_1); // r = A.x - b
dcopy_ (&n, r, &i_1, r0, &i_1); // r0* = r
dcopy_ (&n, r, &i_1, p, &i_1); // p = r
dcopy_ (&n, r, &i_1, u, &i_1); // u = r
rho = ddot_ (&n, r0, &i_1, r, &i_1); // rho = (r0*, r)
int i;
for (i = 0; i < itmax; i ++)
{
atimes (n, p, ap, atimes_param); // ap = A.p
r0ap = ddot_ (&n, r0, &i_1, ap, &i_1); // r0ap = (r0*, A.p)
delta = - rho / r0ap;
dcopy_ (&n, u, &i_1, q, &i_1); // q = u
dscal_ (&n, &d_2, q, &i_1); // q = 2 u
daxpy_ (&n, &delta, ap, &i_1, q, &i_1); // q = 2 u + delta A.p
atimes (n, q, t, atimes_param); // t = A.q
daxpy_ (&n, &delta, t, &i_1, r, &i_1); // r = r + delta t
daxpy_ (&n, &delta, q, &i_1, x, &i_1); // x = x + delta q
res2 = ddot_ (&n, r, &i_1, r, &i_1);
if (it->debug == 2)
{
fprintf (it->out, "libiter-cgs %d %e\n", i, res2 / b2);
}
if (res2 <= eps2)
{
ret = 0; // success
break;
}
rho1 = ddot_ (&n, r0, &i_1, r, &i_1); // rho = (r0*, r)
beta = rho1 / rho;
rho = rho1;
// here t is not used so that this is used for working area.
double *qu = t;
dcopy_ (&n, q, &i_1, qu, &i_1); // qu = q
daxpy_ (&n, &d_m1, u, &i_1, qu, &i_1); // qu = q - u
dcopy_ (&n, r, &i_1, u, &i_1); // u = r
daxpy_ (&n, &beta, qu, &i_1, u, &i_1); // u = r + beta (q - u)
daxpy_ (&n, &beta, p, &i_1, qu, &i_1); // qu = q - u + beta * p
dcopy_ (&n, u, &i_1, p, &i_1); // p = u
daxpy_ (&n, &beta, qu, &i_1, p, &i_1); // p = u + beta (q - u + b * p)
}
# else // !HAVE_BLAS_H
/**
* local BLAS version
*/
double b2 = my_ddot (n, b, 1, b, 1); // (b,b)
eps2 *= b2;
// initial residue
atimes (n, x, r, atimes_param); // r = A.x
my_daxpy (n, -1.0, b, 1, r, 1); // r = A.x - b
my_dcopy (n, r, 1, r0, 1); // r0* = r
my_dcopy (n, r, 1, p, 1); // p = r
my_dcopy (n, r, 1, u, 1); // u = r
rho = my_ddot (n, r0, 1, r, 1); // rho = (r0*, r)
int i;
for (i = 0; i < itmax; i ++)
{
atimes (n, p, ap, atimes_param); // ap = A.p
r0ap = my_ddot (n, r0, 1, ap, 1); // r0ap = (r0*, A.p)
delta = - rho / r0ap;
my_dcopy (n, u, 1, q, 1); // q = u
my_dscal (n, 2.0, q, 1); // q = 2 u
my_daxpy (n, delta, ap, 1, q, 1); // q = 2 u + delta A.p
atimes (n, q, t, atimes_param); // t = A.q
my_daxpy (n, delta, t, 1, r, 1); // r = r + delta t
my_daxpy (n, delta, q, 1, x, 1); // x = x + delta q
res2 = my_ddot (n, r, 1, r, 1);
if (it->debug == 2)
{
fprintf (it->out, "libiter-cgs %d %e\n", i, res2 / b2);
}
if (res2 <= eps2)
{
ret = 0; // success
break;
}
rho1 = my_ddot (n, r0, 1, r, 1); // rho = (r0*, r)
beta = rho1 / rho;
rho = rho1;
// here t is not used so that this is used for working area.
double *qu = t;
my_dcopy (n, q, 1, qu, 1); // qu = q
my_daxpy (n, -1.0, u, 1, qu, 1); // qu = q - u
my_dcopy (n, r, 1, u, 1); // u = r
my_daxpy (n, beta, qu, 1, u, 1); // u = r + beta (q - u)
my_daxpy (n, beta, p, 1, qu, 1); // qu = q - u + beta * p
my_dcopy (n, u, 1, p, 1); // p = u
my_daxpy (n, beta, qu, 1, p, 1); // p = u + beta (q - u + b * p)
}
# endif // !HAVE_BLAS_H
#endif // !HAVE_CBLAS_H
free (r);
free (r0);
free (p);
free (u);
free (ap);
free (q);
free (t);
if (it->debug == 1)
{
fprintf (it->out, "libiter-cgs it= %d res^2= %e\n", i, res2);
}
it->niter = i;
it->res2 = res2 / b2;
return (ret);
}
/* Ref: Weiss, Algorithm 12 BiCGSTAB
* INPUT
* n : dimension of the problem
* b [n] : r-h-s vector
* atimes (int n, static double *x, double *b, void *param) :
* calc matrix-vector product A.x = b.
* atimes_param : parameters for atimes().
* it : struct iter. following entries are used
* it->max = kend : max of iteration
* it->eps = eps : criteria for |r^2|/|b^2|
* OUTPUT
* returned value : 0 == success, otherwise (-1) == failed
* x [n] : solution
* it->niter : # of iteration
* it->res2 : |r^2| / |b^2|
*/
int
bicgstab (int n, const double *b, double *x,
void (*atimes) (int, const double *, double *, void *),
void *atimes_param,
struct iter *it)
{
#ifndef HAVE_CBLAS_H
# ifdef HAVE_BLAS_H
/* use Fortran BLAS routines */
int i_1 = 1;
double d_1 = 1.0;
double d_m1 = -1.0;
# endif // !HAVE_BLAS_H
#endif // !HAVE_CBLAS_H
int ret = -1;
double eps2 = it->eps * it->eps;
int itmax = it->max;
double *r = (double *)malloc (sizeof (double) * n);
double *rs = (double *)malloc (sizeof (double) * n);
double *p = (double *)malloc (sizeof (double) * n);
double *ap = (double *)malloc (sizeof (double) * n);
double *s = (double *)malloc (sizeof (double) * n);
double *t = (double *)malloc (sizeof (double) * n);
CHECK_MALLOC (r, "bicgstab");
CHECK_MALLOC (rs, "bicgstab");
CHECK_MALLOC (p, "bicgstab");
CHECK_MALLOC (ap, "bicgstab");
CHECK_MALLOC (s, "bicgstab");
CHECK_MALLOC (t, "bicgstab");
double rsap; // (r*, A.p)
double st;
double t2;
double rho, rho1;
double delta;
double gamma;
double beta;
double res2 = 0.0;
#ifdef HAVE_CBLAS_H
/**
* ATLAS version
*/
double b2 = cblas_ddot (n, b, 1, b, 1); // (b,b)
eps2 *= b2;
atimes (n, x, r, atimes_param); // r = A.x ...
cblas_daxpy (n, -1.0, b, 1, r, 1); // - b
cblas_dcopy (n, r, 1, rs, 1); // r* = r
cblas_dcopy (n, r, 1, p, 1); // p = r
rho = cblas_ddot (n, rs, 1, r, 1); // rho = (r*, r)
int i;
for (i = 0; i < itmax; i ++)
{
atimes (n, p, ap, atimes_param); // ap = A.p
rsap = cblas_ddot (n, rs, 1, ap, 1); // rsap = (r*, A.p)
delta = - rho / rsap;
cblas_dcopy (n, r, 1, s, 1); // s = r ...
cblas_daxpy (n, delta, ap, 1, s, 1); // + delta A.p
atimes (n, s, t, atimes_param); // t = A.s
st = cblas_ddot (n, s, 1, t, 1); // st = (s, t)
t2 = cblas_ddot (n, t, 1, t, 1); // t2 = (t, t)
gamma = - st / t2;
cblas_dcopy (n, s, 1, r, 1); // r = s ...
cblas_daxpy (n, gamma, t, 1, r, 1); // + gamma t
cblas_daxpy (n, delta, p, 1, x, 1); // x = x + delta p...
cblas_daxpy (n, gamma, s, 1, x, 1); // + gamma s
res2 = cblas_ddot (n, r, 1, r, 1);
if (it->debug == 2)
{
fprintf (it->out,
"libiter-bicgstab(cblas) %d %e\n",
i, res2 / b2);
}
if (res2 <= eps2)
{
ret = 0; // success
break;
}
rho1 = cblas_ddot (n, rs, 1, r, 1); // rho = (r*, r)
beta = rho1 / rho * delta / gamma;
rho = rho1;
cblas_daxpy (n, gamma, ap, 1, p, 1); // p = p + gamma A.p
cblas_dscal (n, beta, p, 1); // p = beta (p + gamma A.p)
cblas_daxpy (n, 1.0, r, 1, p, 1); // p = r + beta(p + gamma A.p)
}
#else // !HAVE_CBLAS_H
# ifdef HAVE_BLAS_H
/**
* BLAS version
*/
double b2 = ddot_ (&n, b, &i_1, b, &i_1); // (b,b)
eps2 *= b2;
atimes (n, x, r, atimes_param); // r = A.x ...
daxpy_ (&n, &d_m1, b, &i_1, r, &i_1); // - b
dcopy_ (&n, r, &i_1, rs, &i_1); // r* = r
dcopy_ (&n, r, &i_1, p, &i_1); // p = r
rho = ddot_ (&n, rs, &i_1, r, &i_1); // rho = (r*, r)
int i;
for (i = 0; i < itmax; i ++)
{
atimes (n, p, ap, atimes_param); // ap = A.p
rsap = ddot_ (&n, rs, &i_1, ap, &i_1); // rsap = (r*, A.p)
delta = - rho / rsap;
dcopy_ (&n, r, &i_1, s, &i_1); // s = r ...
daxpy_ (&n, &delta, ap, &i_1, s, &i_1); // + delta A.p
atimes (n, s, t, atimes_param); // t = A.s
st = ddot_ (&n, s, &i_1, t, &i_1); // st = (s, t)
t2 = ddot_ (&n, t, &i_1, t, &i_1); // t2 = (t, t)
gamma = - st / t2;
dcopy_ (&n, s, &i_1, r, &i_1); // r = s ...
daxpy_ (&n, &gamma, t, &i_1, r, &i_1); // + gamma t
daxpy_ (&n, &delta, p, &i_1, x, &i_1); // x = x + delta p...
daxpy_ (&n, &gamma, s, &i_1, x, &i_1); // + gamma s
res2 = ddot_ (&n, r, &i_1, r, &i_1);
if (it->debug == 2)
{
fprintf (it->out,
"libiter-bicgstab(blas) %d %e\n",
i, res2 / b2);
}
if (res2 <= eps2)
{
ret = 0; // success
break;
}
if (res2 > 1.0e20)
{
// already too big residual
break;
}
rho1 = ddot_ (&n, rs, &i_1, r, &i_1); // rho = (r*, r)
beta = rho1 / rho * delta / gamma;
rho = rho1;
daxpy_ (&n, &gamma, ap, &i_1, p, &i_1); // p = p + gamma A.p
dscal_ (&n, &beta, p, &i_1); // p = beta (p + gamma A.p)
daxpy_ (&n, &d_1, r, &i_1, p, &i_1); // p = r + beta(p + gamma A.p)
}
# else // !HAVE_BLAS_H
/**
* local BLAS version
*/
double b2 = my_ddot (n, b, 1, b, 1); // (b,b)
eps2 *= b2;
atimes (n, x, r, atimes_param); // r = A.x ...
my_daxpy (n, -1.0, b, 1, r, 1); // - b
my_dcopy (n, r, 1, rs, 1); // r* = r
my_dcopy (n, r, 1, p, 1); // p = r
rho = my_ddot (n, rs, 1, r, 1); // rho = (r*, r)
int i;
for (i = 0; i < itmax; i ++)
{
atimes (n, p, ap, atimes_param); // ap = A.p
rsap = my_ddot (n, rs, 1, ap, 1); // rsap = (r*, A.p)
delta = - rho / rsap;
my_dcopy (n, r, 1, s, 1); // s = r ...
my_daxpy (n, delta, ap, 1, s, 1); // + delta A.p
atimes (n, s, t, atimes_param); // t = A.s
st = my_ddot (n, s, 1, t, 1); // st = (s, t)
t2 = my_ddot (n, t, 1, t, 1); // t2 = (t, t)
gamma = - st / t2;
my_dcopy (n, s, 1, r, 1); // r = s ...
my_daxpy (n, gamma, t, 1, r, 1); // + gamma t
my_daxpy (n, delta, p, 1, x, 1); // x = x + delta p...
my_daxpy (n, gamma, s, 1, x, 1); // + gamma s
res2 = my_ddot (n, r, 1, r, 1);
if (it->debug == 2)
{
fprintf (it->out,
"libiter-bicgstab(myblas) %d %e\n",
i, res2 / b2);
}
if (res2 <= eps2)
{
ret = 0; // success
break;
}
rho1 = my_ddot (n, rs, 1, r, 1); // rho = (r*, r)
beta = rho1 / rho * delta / gamma;
rho = rho1;
my_daxpy (n, gamma, ap, 1, p, 1); // p = p + gamma A.p
my_dscal (n, beta, p, 1); // p = beta (p + gamma A.p)
my_daxpy (n, 1.0, r, 1, p, 1); // p = r + beta(p + gamma A.p)
}
# endif // !HAVE_BLAS_H
#endif // !HAVE_CBLAS_H
free (r);
free (rs);
free (p);
free (ap);
free (s);
free (t);
if (it->debug == 1)
{
fprintf (it->out, "libiter-bicgstab %d %e\n", i, res2 / b2);
}
it->niter = i;
it->res2 = res2 / b2;
return (ret);
}
/* Classical CG method -- Weiss' Algorithm 2
* INPUT
* n : dimension of the problem
* b [n] : r-h-s vector
* atimes (int n, static double *x, double *b, void *param) :
* calc matrix-vector product A.x = b.
* atimes_param : parameters for atimes().
* it : struct iter. following entries are used
* it->max = kend : max of iteration
* it->eps = eps : criteria for |r^2|/|b^2|
* OUTPUT
* returned value : 0 == success, otherwise (-1) == failed
* x [n] : solution
* it->niter : # of iteration
* it->res2 : |r^2| / |b^2|
*/
int
cg (int n, const double *b, double *x,
void (*atimes) (int, const double *, double *, void *),
void *atimes_param,
struct iter *it)
{
#ifndef HAVE_CBLAS_H
# ifdef HAVE_BLAS_H
/* use Fortran BLAS routines */
int i_1 = 1;
double d_1 = 1.0;
double d_m1 = -1.0;
# endif // !HAVE_BLAS_H
#endif // !HAVE_CBLAS_H
int ret = -1;
double eps2 = it->eps * it->eps;
int itmax = it->max;
double *p = (double *)malloc (sizeof (double) * n);
double *r = (double *)malloc (sizeof (double) * n);
double *ap = (double *)malloc (sizeof (double) * n);
CHECK_MALLOC (p, "cg");
CHECK_MALLOC (r, "cg");
CHECK_MALLOC (ap, "cg");
double r2;
double res2 = 0.0;
double pap;
double gamma;
double beta;
int i;
#ifdef HAVE_CBLAS_H
/**
* ATLAS version
*/
double b2 = cblas_ddot (n, b, 1, b, 1); // (b,b)
eps2 *= b2;
atimes (n, x, r, atimes_param); // r = A.x
cblas_daxpy (n, -1.0, b, 1, r, 1); // r = A.x - b
cblas_dcopy (n, r, 1, p, 1); // p = r
for (i = 0; i < itmax; i ++)
{
r2 = cblas_ddot (n, r, 1, r, 1); // r2 = (r, r)
atimes (n, p, ap, atimes_param); // ap = A.p
pap = cblas_ddot (n, p, 1, ap, 1); // pap = (p, A.p)
gamma = - r2 / pap; // gamma = - (r, r) / (p, A.p)
cblas_daxpy (n, gamma, p, 1, x, 1); // x += gamma p
cblas_daxpy (n, gamma, ap, 1, r, 1); // r += gamma Ap
// new norm of r
res2 = cblas_ddot (n, r, 1, r, 1); // (r, r)
if (it->debug == 2)
{
fprintf (it->out, "libiter-cg %d %e\n", i, res2 / b2);
}
if (res2 <= eps2)
{
ret = 0; // success
break;
}
beta = res2 / r2; // beta = (r, r) / (r0, r0)
cblas_dscal (n, beta, p, 1); // p *= beta
cblas_daxpy (n, 1.0, r, 1, p, 1); // p = r + beta p
r2 = res2;
}
#else // !HAVE_CBLAS_H
# ifdef HAVE_BLAS_H
/**
* BLAS version
*/
double b2 = ddot_ (&n, b, &i_1, b, &i_1); // (b,b)
eps2 *= b2;
atimes (n, x, r, atimes_param); // r = A.x
daxpy_ (&n, &d_m1, b, &i_1, r, &i_1); // r = A.x - b
dcopy_ (&n, r, &i_1, p, &i_1); // p = r
for (i = 0; i < itmax; i ++)
{
r2 = ddot_ (&n, r, &i_1, r, &i_1); // r2 = (r, r)
atimes (n, p, ap, atimes_param); // ap = A.p
pap = ddot_ (&n, p, &i_1, ap, &i_1); // pap = (p, A.p)
gamma = - r2 / pap; // gamma = - (r, r) / (p, A.p)
daxpy_ (&n, &gamma, p, &i_1, x, &i_1); // x += gamma p
daxpy_ (&n, &gamma, ap, &i_1, r, &i_1); // r += gamma Ap
// new norm of r
res2 = ddot_ (&n, r, &i_1, r, &i_1); // (r, r)
if (it->debug == 2)
{
fprintf (it->out, "libiter-cg %d %e\n", i, res2 / b2);
}
if (res2 <= eps2)
{
ret = 0; // success
break;
}
beta = res2 / r2; // beta = (r, r) / (r0, r0)
dscal_ (&n, &beta, p, &i_1); // p *= beta
daxpy_ (&n, &d_1, r, &i_1, p, &i_1); // p = r + beta p
r2 = res2;
}
# else // !HAVE_BLAS_H
/**
* local BLAS version
*/
double b2 = my_ddot (n, b, 1, b, 1); // (b,b)
eps2 *= b2;
atimes (n, x, r, atimes_param); // r = A.x
my_daxpy (n, -1.0, b, 1, r, 1); // r = A.x - b
my_dcopy (n, r, 1, p, 1); // p = r
for (i = 0; i < itmax; i ++)
{
r2 = my_ddot (n, r, 1, r, 1); // r2 = (r, r)
atimes (n, p, ap, atimes_param); // ap = A.p
pap = my_ddot (n, p, 1, ap, 1); // pap = (p, A.p)
gamma = - r2 / pap; // gamma = - (r, r) / (p, A.p)
my_daxpy (n, gamma, p, 1, x, 1); // x += gamma p
my_daxpy (n, gamma, ap, 1, r, 1); // r += gamma Ap
// new norm of r
res2 = my_ddot (n, r, 1, r, 1); // (r, r)
if (it->debug == 2)
{
fprintf (it->out, "libiter-cg %d %e\n", i, res2 / b2);
}
if (res2 <= eps2)
{
ret = 0; // success
break;
}
beta = res2 / r2; // beta = (r, r) / (r0, r0)
my_dscal (n, beta, p, 1); // p *= beta
my_daxpy (n, 1.0, r, 1, p, 1); // p = r + beta p
r2 = res2;
}
# endif // !HAVE_BLAS_H
#endif // !HAVE_CBLAS_H
free (p);
free (r);
free (ap);
if (it->debug == 1)
{
fprintf (it->out, "libiter-cg it= %d res^2= %e\n", i, res2 / b2);
}
it->niter = i;
it->res2 = res2 / b2;
return (ret);
}
