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/* laso/dlabcm.f -- translated by f2c (version 20050501).
You must link the resulting object file with libf2c:
on Microsoft Windows system, link with libf2c.lib;
on Linux or Unix systems, link with .../path/to/libf2c.a -lm
or, if you install libf2c.a in a standard place, with -lf2c -lm
-- in that order, at the end of the command line, as in
cc *.o -lf2c -lm
Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
http://www.netlib.org/f2c/libf2c.zip
*/
#ifdef __cplusplus
extern "C" {
#endif
#include "v3p_netlib.h"
/* Table of constant values */
static integer c__1 = 1;
/* *********************************************************************** */
/*< >*/
/* Subroutine */ int dlabcm_(integer *n, integer *nband, integer *nl, integer
*nr, doublereal *a, doublereal *eigval, integer *lde, doublereal *
eigvec, doublereal *atol, doublereal *artol, doublereal *bound,
doublereal *atemp, doublereal *d__, doublereal *vtemp)
{
/* System generated locals */
integer a_dim1, a_offset, eigvec_dim1, eigvec_offset, i__1, i__2, i__3;
doublereal d__1, d__2;
/* Local variables */
integer i__, j, l, m;
doublereal rq, gap;
logical flag__;
doublereal errb;
extern doublereal ddot_(integer *, doublereal *, integer *, doublereal *,
integer *);
integer nval, numl;
extern doublereal dnrm2_(integer *, doublereal *, integer *);
extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *,
integer *);
doublereal sigma, resid;
extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *,
doublereal *, integer *), daxpy_(integer *, doublereal *,
doublereal *, integer *, doublereal *, integer *);
doublereal vnorm;
extern /* Subroutine */ int dlabfc_(integer *, integer *, doublereal *,
doublereal *, integer *, integer *, doublereal *, integer *,
integer *, doublereal *, doublereal *, doublereal *), dlabax_(
integer *, integer *, doublereal *, doublereal *, doublereal *),
dlaran_(integer *, doublereal *);
integer numvec;
/* THIS SUBROUTINE ORGANIZES THE CALCULATION OF THE EIGENVALUES */
/* FOR THE BNDEIG PACKAGE. EIGENVALUES ARE COMPUTED BY */
/* A MODIFIED RAYLEIGH QUOTIENT ITERATION. THE EIGENVALUE COUNT */
/* OBTAINED BY EACH FACTORIZATION IS USED TO OCCASIONALLY OVERRIDE */
/* THE COMPUTED RAYLEIGH QUOTIENT WITH A DIFFERENT SHIFT TO */
/* INSURE CONVERGENCE TO THE DESIRED EIGENVALUES. */
/* FORMAL PARAMETERS. */
/*< INTEGER N, NBAND, NL, NR, LDE >*/
/*< >*/
/* LOCAL VARIABLES */
/*< LOGICAL FLAG >*/
/*< INTEGER I, J, L, M, NUML, NUMVEC, NVAL >*/
/*< DOUBLE PRECISION ERRB, GAP, RESID, RQ, SIGMA, VNORM >*/
/* FUNCTIONS CALLED */
/*< INTEGER MIN0 >*/
/*< DOUBLE PRECISION DMAX1, DMIN1, DDOT, DNRM2 >*/
/* SUBROUTINES CALLED */
/* DLABAX, DLABFC, DLARAN, DAXPY, DCOPY, DSCAL */
/* REPLACE ZERO VECTORS BY RANDOM */
/*< NVAL = NR - NL + 1 >*/
/* Parameter adjustments */
a_dim1 = *nband;
a_offset = 1 + a_dim1;
a -= a_offset;
--eigval;
eigvec_dim1 = *lde;
eigvec_offset = 1 + eigvec_dim1;
eigvec -= eigvec_offset;
bound -= 3;
--atemp;
--d__;
--vtemp;
/* Function Body */
nval = *nr - *nl + 1;
/*< FLAG = .FALSE. >*/
flag__ = FALSE_;
/*< DO 5 I = 1, NVAL >*/
i__1 = nval;
for (i__ = 1; i__ <= i__1; ++i__) {
/*< >*/
if (ddot_(n, &eigvec[i__ * eigvec_dim1 + 1], &c__1, &eigvec[i__ *
eigvec_dim1 + 1], &c__1) == 0.) {
dlaran_(n, &eigvec[i__ * eigvec_dim1 + 1]);
}
/*< 5 CONTINUE >*/
/* L5: */
}
/* LOOP OVER EIGENVALUES */
/*< SIGMA = BOUND(2,NVAL+1) >*/
sigma = bound[((nval + 1) << 1) + 2];
/*< DO 400 J = 1, NVAL >*/
i__1 = nval;
for (j = 1; j <= i__1; ++j) {
/*< NUML = J >*/
numl = j;
/* PREPARE TO COMPUTE FIRST RAYLEIGH QUOTIENT */
/*< 10 CALL DLABAX(N, NBAND, A, EIGVEC(1,J), VTEMP) >*/
L10:
dlabax_(n, nband, &a[a_offset], &eigvec[j * eigvec_dim1 + 1], &vtemp[
1]);
/*< VNORM = DNRM2(N, VTEMP, 1) >*/
vnorm = dnrm2_(n, &vtemp[1], &c__1);
/*< IF(VNORM .EQ. 0.0D0) GO TO 20 >*/
if (vnorm == 0.) {
goto L20;
}
/*< CALL DSCAL(N, 1.0D0/VNORM, VTEMP, 1) >*/
d__1 = 1. / vnorm;
dscal_(n, &d__1, &vtemp[1], &c__1);
/*< CALL DSCAL(N, 1.0D0/VNORM, EIGVEC(1,J), 1) >*/
d__1 = 1. / vnorm;
dscal_(n, &d__1, &eigvec[j * eigvec_dim1 + 1], &c__1);
/*< CALL DAXPY(N, -SIGMA, EIGVEC(1,J), 1, VTEMP, 1) >*/
d__1 = -sigma;
daxpy_(n, &d__1, &eigvec[j * eigvec_dim1 + 1], &c__1, &vtemp[1], &
c__1);
/* LOOP OVER SHIFTS */
/* COMPUTE RAYLEIGH QUOTIENT, RESIDUAL NORM, AND CURRENT TOLERANCE */
/*< 20 VNORM = DNRM2(N, EIGVEC(1,J), 1) >*/
L20:
vnorm = dnrm2_(n, &eigvec[j * eigvec_dim1 + 1], &c__1);
/*< IF(VNORM .NE. 0.0D0) GO TO 30 >*/
if (vnorm != 0.) {
goto L30;
}
/*< CALL DLARAN(N, EIGVEC(1,J)) >*/
dlaran_(n, &eigvec[j * eigvec_dim1 + 1]);
/*< GO TO 10 >*/
goto L10;
/*< >*/
L30:
rq = sigma + ddot_(n, &eigvec[j * eigvec_dim1 + 1], &c__1, &vtemp[1],
&c__1) / vnorm / vnorm;
/*< CALL DAXPY(N, SIGMA-RQ, EIGVEC(1,J), 1, VTEMP, 1) >*/
d__1 = sigma - rq;
daxpy_(n, &d__1, &eigvec[j * eigvec_dim1 + 1], &c__1, &vtemp[1], &
c__1);
/*< RESID = DMAX1(ATOL, DNRM2(N, VTEMP, 1)/VNORM) >*/
/* Computing MAX */
d__1 = *atol, d__2 = dnrm2_(n, &vtemp[1], &c__1) / vnorm;
resid = max(d__1,d__2);
/*< CALL DSCAL(N, 1.0/VNORM, EIGVEC(1,J), 1) >*/
d__1 = (float)1. / vnorm;
dscal_(n, &d__1, &eigvec[j * eigvec_dim1 + 1], &c__1);
/* ACCEPT EIGENVALUE IF THE INTERVAL IS SMALL ENOUGH */
/*< IF(BOUND(2,J+1) - BOUND(1,J+1) .LT. 3.0D0*ATOL) GO TO 300 >*/
if (bound[((j + 1) << 1) + 2] - bound[((j + 1) << 1) + 1] < *atol * 3.) {
goto L300;
}
/* COMPUTE MINIMAL ERROR BOUND */
/*< ERRB = RESID >*/
errb = resid;
/*< GAP = DMIN1(BOUND(1,J+2) - RQ, RQ - BOUND(2,J)) >*/
/* Computing MIN */
d__1 = bound[((j + 2) << 1) + 1] - rq, d__2 = rq - bound[(j << 1) + 2];
gap = min(d__1,d__2);
/*< IF(GAP .GT. RESID) ERRB = DMAX1(ATOL, RESID*RESID/GAP) >*/
if (gap > resid) {
/* Computing MAX */
d__1 = *atol, d__2 = resid * resid / gap;
errb = max(d__1,d__2);
}
/* TENTATIVE NEW SHIFT */
/*< SIGMA = 0.5D0*(BOUND(1,J+1) + BOUND(2,J+1)) >*/
sigma = (bound[((j + 1) << 1) + 1] + bound[((j + 1) << 1) + 2]) * .5;
/* CHECK FOR TERMINALTION */
/*< IF(RESID .GT. 2.0D0*ATOL) GO TO 40 >*/
if (resid > *atol * 2.) {
goto L40;
}
/*< >*/
if (rq - errb > bound[(j << 1) + 2] && rq + errb < bound[((j + 2) << 1)
+ 1]) {
goto L310;
}
/* RQ IS TO THE LEFT OF THE INTERVAL */
/*< 40 IF(RQ .GE. BOUND(1,J+1)) GO TO 50 >*/
L40:
if (rq >= bound[((j + 1) << 1) + 1]) {
goto L50;
}
/*< IF(RQ - ERRB .GT. BOUND(2,J)) GO TO 100 >*/
if (rq - errb > bound[(j << 1) + 2]) {
goto L100;
}
/*< IF(RQ + ERRB .LT. BOUND(1,J+1)) CALL DLARAN(N,EIGVEC(1,J)) >*/
if (rq + errb < bound[((j + 1) << 1) + 1]) {
dlaran_(n, &eigvec[j * eigvec_dim1 + 1]);
}
/*< GO TO 200 >*/
goto L200;
/* RQ IS TO THE RIGHT OF THE INTERVAL */
/*< 50 IF(RQ .LE. BOUND(2,J+1)) GO TO 100 >*/
L50:
if (rq <= bound[((j + 1) << 1) + 2]) {
goto L100;
}
/*< IF(RQ + ERRB .LT. BOUND(1,J+2)) GO TO 100 >*/
if (rq + errb < bound[((j + 2) << 1) + 1]) {
goto L100;
}
/* SAVE THE REJECTED VECTOR IF INDICATED */
/*< IF(RQ - ERRB .LE. BOUND(2,J+1)) GO TO 200 >*/
if (rq - errb <= bound[((j + 1) << 1) + 2]) {
goto L200;
}
/*< DO 60 I = J, NVAL >*/
i__2 = nval;
for (i__ = j; i__ <= i__2; ++i__) {
/*< IF(BOUND(2,I+1) .GT. RQ) GO TO 70 >*/
if (bound[((i__ + 1) << 1) + 2] > rq) {
goto L70;
}
/*< 60 CONTINUE >*/
/* L60: */
}
/*< GO TO 80 >*/
goto L80;
/*< 70 CALL DCOPY(N, EIGVEC(1,J), 1, EIGVEC(1,I), 1) >*/
L70:
dcopy_(n, &eigvec[j * eigvec_dim1 + 1], &c__1, &eigvec[i__ *
eigvec_dim1 + 1], &c__1);
/*< 80 CALL DLARAN(N, EIGVEC(1,J)) >*/
L80:
dlaran_(n, &eigvec[j * eigvec_dim1 + 1]);
/*< GO TO 200 >*/
goto L200;
/* PERTURB RQ TOWARD THE MIDDLE */
/*< 100 IF(SIGMA .LT. RQ) SIGMA = DMAX1(SIGMA, RQ-ERRB) >*/
L100:
if (sigma < rq) {
/* Computing MAX */
d__1 = sigma, d__2 = rq - errb;
sigma = max(d__1,d__2);
}
/*< IF(SIGMA .GT. RQ) SIGMA = DMIN1(SIGMA, RQ+ERRB) >*/
if (sigma > rq) {
/* Computing MIN */
d__1 = sigma, d__2 = rq + errb;
sigma = min(d__1,d__2);
}
/* FACTOR AND SOLVE */
/*< 200 DO 210 I = J, NVAL >*/
L200:
i__2 = nval;
for (i__ = j; i__ <= i__2; ++i__) {
/*< IF(SIGMA .LT. BOUND(1,I+1)) GO TO 220 >*/
if (sigma < bound[((i__ + 1) << 1) + 1]) {
goto L220;
}
/*< 210 CONTINUE >*/
/* L210: */
}
/*< I = NVAL + 1 >*/
i__ = nval + 1;
/*< 220 NUMVEC = I - J >*/
L220:
numvec = i__ - j;
/*< NUMVEC = MIN0(NUMVEC, NBAND + 2) >*/
/* Computing MIN */
i__2 = numvec, i__3 = *nband + 2;
numvec = min(i__2,i__3);
/*< IF(RESID .LT. ARTOL) NUMVEC = MIN0(1,NUMVEC) >*/
if (resid < *artol) {
numvec = min(1,numvec);
}
/*< CALL DCOPY(N, EIGVEC(1,J), 1, VTEMP, 1) >*/
dcopy_(n, &eigvec[j * eigvec_dim1 + 1], &c__1, &vtemp[1], &c__1);
/*< >*/
i__2 = (*nband << 1) - 1;
dlabfc_(n, nband, &a[a_offset], &sigma, &numvec, lde, &eigvec[j *
eigvec_dim1 + 1], &numl, &i__2, &atemp[1], &d__[1], atol);
/* PARTIALLY SCALE EXTRA VECTORS TO PREVENT UNDERFLOW OR OVERFLOW */
/*< IF(NUMVEC .EQ. 1) GO TO 227 >*/
if (numvec == 1) {
goto L227;
}
/*< L = NUMVEC - 1 >*/
l = numvec - 1;
/*< DO 225 I = 1,L >*/
i__2 = l;
for (i__ = 1; i__ <= i__2; ++i__) {
/*< M = J + I >*/
m = j + i__;
/*< CALL DSCAL(N, 1.0D0/VNORM, EIGVEC(1,M), 1) >*/
d__1 = 1. / vnorm;
dscal_(n, &d__1, &eigvec[m * eigvec_dim1 + 1], &c__1);
/*< 225 CONTINUE >*/
/* L225: */
}
/* UPDATE INTERVALS */
/*< 227 NUML = NUML - NL + 1 >*/
L227:
numl = numl - *nl + 1;
/*< IF(NUML .GE. 0) BOUND(2,1) = DMIN1(BOUND(2,1), SIGMA) >*/
if (numl >= 0) {
bound[4] = min(bound[4],sigma);
}
/*< DO 230 I = J, NVAL >*/
i__2 = nval;
for (i__ = j; i__ <= i__2; ++i__) {
/*< IF(SIGMA .LT. BOUND(1,I+1)) GO TO 20 >*/
if (sigma < bound[((i__ + 1) << 1) + 1]) {
goto L20;
}
/*< IF(NUML .LT. I) BOUND(1,I+1) = SIGMA >*/
if (numl < i__) {
bound[((i__ + 1) << 1) + 1] = sigma;
}
/*< IF(NUML .GE. I) BOUND(2,I+1) = SIGMA >*/
if (numl >= i__) {
bound[((i__ + 1) << 1) + 2] = sigma;
}
/*< 230 CONTINUE >*/
/* L230: */
}
/*< >*/
if (numl < nval + 1) {
/* Computing MAX */
d__1 = sigma, d__2 = bound[((nval + 2) << 1) + 1];
bound[((nval + 2) << 1) + 1] = max(d__1,d__2);
}
/*< GO TO 20 >*/
goto L20;
/* ACCEPT AN EIGENPAIR */
/*< 300 CALL DLARAN(N, EIGVEC(1,J)) >*/
L300:
dlaran_(n, &eigvec[j * eigvec_dim1 + 1]);
/*< FLAG = .TRUE. >*/
flag__ = TRUE_;
/*< GO TO 310 >*/
goto L310;
/*< 305 FLAG = .FALSE. >*/
L305:
flag__ = FALSE_;
/*< RQ = 0.5D0*(BOUND(1,J+1) + BOUND(2,J+1)) >*/
rq = (bound[((j + 1) << 1) + 1] + bound[((j + 1) << 1) + 2]) * .5;
/*< >*/
i__2 = (*nband << 1) - 1;
dlabfc_(n, nband, &a[a_offset], &rq, &numvec, lde, &eigvec[j *
eigvec_dim1 + 1], &numl, &i__2, &atemp[1], &d__[1], atol);
/*< VNORM = DNRM2(N, EIGVEC(1,J), 1) >*/
vnorm = dnrm2_(n, &eigvec[j * eigvec_dim1 + 1], &c__1);
/*< IF(VNORM .NE. 0.0) CALL DSCAL(N, 1.0D0/VNORM, EIGVEC(1,J), 1) >*/
if (vnorm != (float)0.) {
d__1 = 1. / vnorm;
dscal_(n, &d__1, &eigvec[j * eigvec_dim1 + 1], &c__1);
}
/* ORTHOGONALIZE THE NEW EIGENVECTOR AGAINST THE OLD ONES */
/*< 310 EIGVAL(J) = RQ >*/
L310:
eigval[j] = rq;
/*< IF(J .EQ. 1) GO TO 330 >*/
if (j == 1) {
goto L330;
}
/*< M = J - 1 >*/
m = j - 1;
/*< DO 320 I = 1, M >*/
i__2 = m;
for (i__ = 1; i__ <= i__2; ++i__) {
/*< >*/
d__1 = -ddot_(n, &eigvec[i__ * eigvec_dim1 + 1], &c__1, &eigvec[j
* eigvec_dim1 + 1], &c__1);
daxpy_(n, &d__1, &eigvec[i__ * eigvec_dim1 + 1], &c__1, &eigvec[j
* eigvec_dim1 + 1], &c__1);
/*< 320 CONTINUE >*/
/* L320: */
}
/*< 330 VNORM = DNRM2(N, EIGVEC(1,J), 1) >*/
L330:
vnorm = dnrm2_(n, &eigvec[j * eigvec_dim1 + 1], &c__1);
/*< IF(VNORM .EQ. 0.0D0) GO TO 305 >*/
if (vnorm == 0.) {
goto L305;
}
/*< CALL DSCAL(N, 1.0D0/VNORM, EIGVEC(1,J), 1) >*/
d__1 = 1. / vnorm;
dscal_(n, &d__1, &eigvec[j * eigvec_dim1 + 1], &c__1);
/* ORTHOGONALIZE LATER VECTORS AGAINST THE CONVERGED ONE */
/*< IF(FLAG) GO TO 305 >*/
if (flag__) {
goto L305;
}
/*< IF(J .EQ. NVAL) RETURN >*/
if (j == nval) {
return 0;
}
/*< M = J + 1 >*/
m = j + 1;
/*< DO 340 I = M, NVAL >*/
i__2 = nval;
for (i__ = m; i__ <= i__2; ++i__) {
/*< >*/
d__1 = -ddot_(n, &eigvec[j * eigvec_dim1 + 1], &c__1, &eigvec[i__
* eigvec_dim1 + 1], &c__1);
daxpy_(n, &d__1, &eigvec[j * eigvec_dim1 + 1], &c__1, &eigvec[i__
* eigvec_dim1 + 1], &c__1);
/*< 340 CONTINUE >*/
/* L340: */
}
/*< 400 CONTINUE >*/
/* L400: */
}
/*< RETURN >*/
return 0;
/*< 500 CONTINUE >*/
/* L500: */
/*< END >*/
return 0;
} /* dlabcm_ */
#ifdef __cplusplus
}
#endif
|
