CFD/hypre
1
0
Fork 0
Code Issues Pull Requests Packages Projects Releases Wiki Activity
aa5ec210b6
hypre/lapack/dsterf.c
falgout 46488e8cbc Added HYPRE_Complex and HYPRE_Real types in place of double. 
Added an example code to test CG on a 4D HYPRE_SSTRUCT complex problem.
Added regression tests for bigint, maxdim, and complex.
Added a test to make sure double types are not added to the source.
See [Issue995] in the tracker for more details.
2013-10-11 19:48:06 +00:00

436 lines
9.1 KiB
C
Raw Blame History

#include "hypre_lapack.h"
#include "f2c.h"
/* Subroutine */ HYPRE_Int dsterf_(integer *n, doublereal *d__, doublereal *e,
integer *info)
{
/* -- LAPACK routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
June 30, 1999
Purpose
=======
DSTERF computes all eigenvalues of a symmetric tridiagonal matrix
using the Pal-Walker-Kahan variant of the QL or QR algorithm.
Arguments
=========
N (input) INTEGER
The order of the matrix. N >= 0.
D (input/output) DOUBLE PRECISION array, dimension (N)
On entry, the n diagonal elements of the tridiagonal matrix.
On exit, if INFO = 0, the eigenvalues in ascending order.
E (input/output) DOUBLE PRECISION array, dimension (N-1)
On entry, the (n-1) subdiagonal elements of the tridiagonal
matrix.
On exit, E has been destroyed.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: the algorithm failed to find all of the eigenvalues in
a total of 30*N iterations; if INFO = i, then i
elements of E have not converged to zero.
=====================================================================
Test the input parameters.
Parameter adjustments */
/* Table of constant values */
static integer c__0 = 0;
static integer c__1 = 1;
static doublereal c_b32 = 1.;
/* System generated locals */
integer i__1;
doublereal d__1, d__2, d__3;
/* Builtin functions */
HYPRE_Real sqrt(doublereal), d_sign(doublereal *, doublereal *);
/* Local variables */
static doublereal oldc;
static integer lend, jtot;
extern /* Subroutine */ HYPRE_Int dlae2_(doublereal *, doublereal *, doublereal
*, doublereal *, doublereal *);
static doublereal c__;
static integer i__, l, m;
static doublereal p, gamma, r__, s, alpha, sigma, anorm;
static integer l1;
extern doublereal dlapy2_(doublereal *, doublereal *);
static doublereal bb;
extern doublereal dlamch_(char *);
static integer iscale;
extern /* Subroutine */ HYPRE_Int dlascl_(char *, integer *, integer *,
doublereal *, doublereal *, integer *, integer *, doublereal *,
integer *, integer *);
static doublereal oldgam, safmin;
extern /* Subroutine */ HYPRE_Int xerbla_(char *, integer *);
static doublereal safmax;
extern doublereal dlanst_(char *, integer *, doublereal *, doublereal *);
extern /* Subroutine */ HYPRE_Int dlasrt_(char *, integer *, doublereal *,
integer *);
static integer lendsv;
static doublereal ssfmin;
static integer nmaxit;
static doublereal ssfmax, rt1, rt2, eps, rte;
static integer lsv;
static doublereal eps2;
--e;
--d__;
/* Function Body */
*info = 0;
/* Quick return if possible */
if (*n < 0) {
*info = -1;
i__1 = -(*info);
xerbla_("DSTERF", &i__1);
return 0;
}
if (*n <= 1) {
return 0;
}
/* Determine the unit roundoff for this environment. */
eps = dlamch_("E");
/* Computing 2nd power */
d__1 = eps;
eps2 = d__1 * d__1;
safmin = dlamch_("S");
safmax = 1. / safmin;
ssfmax = sqrt(safmax) / 3.;
ssfmin = sqrt(safmin) / eps2;
/* Compute the eigenvalues of the tridiagonal matrix. */
nmaxit = *n * 30;
sigma = 0.;
jtot = 0;
/* Determine where the matrix splits and choose QL or QR iteration
for each block, according to whether top or bottom diagonal
element is smaller. */
l1 = 1;
L10:
if (l1 > *n) {
goto L170;
}
if (l1 > 1) {
e[l1 - 1] = 0.;
}
i__1 = *n - 1;
for (m = l1; m <= i__1; ++m) {
if ((d__3 = e[m], abs(d__3)) <= sqrt((d__1 = d__[m], abs(d__1))) *
sqrt((d__2 = d__[m + 1], abs(d__2))) * eps) {
e[m] = 0.;
goto L30;
}
/* L20: */
}
m = *n;
L30:
l = l1;
lsv = l;
lend = m;
lendsv = lend;
l1 = m + 1;
if (lend == l) {
goto L10;
}
/* Scale submatrix in rows and columns L to LEND */
i__1 = lend - l + 1;
anorm = dlanst_("I", &i__1, &d__[l], &e[l]);
iscale = 0;
if (anorm > ssfmax) {
iscale = 1;
i__1 = lend - l + 1;
dlascl_("G", &c__0, &c__0, &anorm, &ssfmax, &i__1, &c__1, &d__[l], n,
info);
i__1 = lend - l;
dlascl_("G", &c__0, &c__0, &anorm, &ssfmax, &i__1, &c__1, &e[l], n,
info);
} else if (anorm < ssfmin) {
iscale = 2;
i__1 = lend - l + 1;
dlascl_("G", &c__0, &c__0, &anorm, &ssfmin, &i__1, &c__1, &d__[l], n,
info);
i__1 = lend - l;
dlascl_("G", &c__0, &c__0, &anorm, &ssfmin, &i__1, &c__1, &e[l], n,
info);
}
i__1 = lend - 1;
for (i__ = l; i__ <= i__1; ++i__) {
/* Computing 2nd power */
d__1 = e[i__];
e[i__] = d__1 * d__1;
/* L40: */
}
/* Choose between QL and QR iteration */
if ((d__1 = d__[lend], abs(d__1)) < (d__2 = d__[l], abs(d__2))) {
lend = lsv;
l = lendsv;
}
if (lend >= l) {
/* QL Iteration
Look for small subdiagonal element. */
L50:
if (l != lend) {
i__1 = lend - 1;
for (m = l; m <= i__1; ++m) {
if ((d__2 = e[m], abs(d__2)) <= eps2 * (d__1 = d__[m] * d__[m
+ 1], abs(d__1))) {
goto L70;
}
/* L60: */
}
}
m = lend;
L70:
if (m < lend) {
e[m] = 0.;
}
p = d__[l];
if (m == l) {
goto L90;
}
/* If remaining matrix is 2 by 2, use DLAE2 to compute its
eigenvalues. */
if (m == l + 1) {
rte = sqrt(e[l]);
dlae2_(&d__[l], &rte, &d__[l + 1], &rt1, &rt2);
d__[l] = rt1;
d__[l + 1] = rt2;
e[l] = 0.;
l += 2;
if (l <= lend) {
goto L50;
}
goto L150;
}
if (jtot == nmaxit) {
goto L150;
}
++jtot;
/* Form shift. */
rte = sqrt(e[l]);
sigma = (d__[l + 1] - p) / (rte * 2.);
r__ = dlapy2_(&sigma, &c_b32);
sigma = p - rte / (sigma + d_sign(&r__, &sigma));
c__ = 1.;
s = 0.;
gamma = d__[m] - sigma;
p = gamma * gamma;
/* Inner loop */
i__1 = l;
for (i__ = m - 1; i__ >= i__1; --i__) {
bb = e[i__];
r__ = p + bb;
if (i__ != m - 1) {
e[i__ + 1] = s * r__;
}
oldc = c__;
c__ = p / r__;
s = bb / r__;
oldgam = gamma;
alpha = d__[i__];
gamma = c__ * (alpha - sigma) - s * oldgam;
d__[i__ + 1] = oldgam + (alpha - gamma);
if (c__ != 0.) {
p = gamma * gamma / c__;
} else {
p = oldc * bb;
}
/* L80: */
}
e[l] = s * p;
d__[l] = sigma + gamma;
goto L50;
/* Eigenvalue found. */
L90:
d__[l] = p;
++l;
if (l <= lend) {
goto L50;
}
goto L150;
} else {
/* QR Iteration
Look for small superdiagonal element. */
L100:
i__1 = lend + 1;
for (m = l; m >= i__1; --m) {
if ((d__2 = e[m - 1], abs(d__2)) <= eps2 * (d__1 = d__[m] * d__[m
- 1], abs(d__1))) {
goto L120;
}
/* L110: */
}
m = lend;
L120:
if (m > lend) {
e[m - 1] = 0.;
}
p = d__[l];
if (m == l) {
goto L140;
}
/* If remaining matrix is 2 by 2, use DLAE2 to compute its
eigenvalues. */
if (m == l - 1) {
rte = sqrt(e[l - 1]);
dlae2_(&d__[l], &rte, &d__[l - 1], &rt1, &rt2);
d__[l] = rt1;
d__[l - 1] = rt2;
e[l - 1] = 0.;
l += -2;
if (l >= lend) {
goto L100;
}
goto L150;
}
if (jtot == nmaxit) {
goto L150;
}
++jtot;
/* Form shift. */
rte = sqrt(e[l - 1]);
sigma = (d__[l - 1] - p) / (rte * 2.);
r__ = dlapy2_(&sigma, &c_b32);
sigma = p - rte / (sigma + d_sign(&r__, &sigma));
c__ = 1.;
s = 0.;
gamma = d__[m] - sigma;
p = gamma * gamma;
/* Inner loop */
i__1 = l - 1;
for (i__ = m; i__ <= i__1; ++i__) {
bb = e[i__];
r__ = p + bb;
if (i__ != m) {
e[i__ - 1] = s * r__;
}
oldc = c__;
c__ = p / r__;
s = bb / r__;
oldgam = gamma;
alpha = d__[i__ + 1];
gamma = c__ * (alpha - sigma) - s * oldgam;
d__[i__] = oldgam + (alpha - gamma);
if (c__ != 0.) {
p = gamma * gamma / c__;
} else {
p = oldc * bb;
}
/* L130: */
}
e[l - 1] = s * p;
d__[l] = sigma + gamma;
goto L100;
/* Eigenvalue found. */
L140:
d__[l] = p;
--l;
if (l >= lend) {
goto L100;
}
goto L150;
}
/* Undo scaling if necessary */
L150:
if (iscale == 1) {
i__1 = lendsv - lsv + 1;
dlascl_("G", &c__0, &c__0, &ssfmax, &anorm, &i__1, &c__1, &d__[lsv],
n, info);
}
if (iscale == 2) {
i__1 = lendsv - lsv + 1;
dlascl_("G", &c__0, &c__0, &ssfmin, &anorm, &i__1, &c__1, &d__[lsv],
n, info);
}
/* Check for no convergence to an eigenvalue after a total
of N*MAXIT iterations. */
if (jtot < nmaxit) {
goto L10;
}
i__1 = *n - 1;
for (i__ = 1; i__ <= i__1; ++i__) {
if (e[i__] != 0.) {
++(*info);
}
/* L160: */
}
goto L180;
/* Sort eigenvalues in increasing order. */
L170:
dlasrt_("I", n, &d__[1], info);
L180:
return 0;
/* End of DSTERF */
} /* dsterf_ */
Reference in New Issue View Git Blame Copy Permalink