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/* ../SRC/dneigh.f -- translated by f2c (version 20061008).
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
*/
#include "f2c.h"
/* Common Block Declarations */
struct {
integer logfil, ndigit, mgetv0, msaupd, msaup2, msaitr, mseigt, msapps,
msgets, mseupd, mnaupd, mnaup2, mnaitr, mneigh, mnapps, mngets,
mneupd, mcaupd, mcaup2, mcaitr, mceigh, mcapps, mcgets, mceupd;
} debug_;
#define debug_1 debug_
struct {
integer nopx, nbx, nrorth, nitref, nrstrt;
real tsaupd, tsaup2, tsaitr, tseigt, tsgets, tsapps, tsconv, tnaupd,
tnaup2, tnaitr, tneigh, tngets, tnapps, tnconv, tcaupd, tcaup2,
tcaitr, tceigh, tcgets, tcapps, tcconv, tmvopx, tmvbx, tgetv0,
titref, trvec;
} timing_;
#define timing_1 timing_
/* Table of constant values */
static logical c_true = TRUE_;
static integer c__1 = 1;
static doublereal c_b18 = 1.;
static doublereal c_b20 = 0.;
/* ----------------------------------------------------------------------- */
/* \BeginDoc */
/* \Name: dneigh */
/* \Description: */
/* Compute the eigenvalues of the current upper Hessenberg matrix */
/* and the corresponding Ritz estimates given the current residual norm. */
/* \Usage: */
/* call dneigh */
/* ( RNORM, N, H, LDH, RITZR, RITZI, BOUNDS, Q, LDQ, WORKL, IERR ) */
/* \Arguments */
/* RNORM Double precision scalar. (INPUT) */
/* Residual norm corresponding to the current upper Hessenberg */
/* matrix H. */
/* N Integer. (INPUT) */
/* Size of the matrix H. */
/* H Double precision N by N array. (INPUT) */
/* H contains the current upper Hessenberg matrix. */
/* LDH Integer. (INPUT) */
/* Leading dimension of H exactly as declared in the calling */
/* program. */
/* RITZR, Double precision arrays of length N. (OUTPUT) */
/* RITZI On output, RITZR(1:N) (resp. RITZI(1:N)) contains the real */
/* (respectively imaginary) parts of the eigenvalues of H. */
/* BOUNDS Double precision array of length N. (OUTPUT) */
/* On output, BOUNDS contains the Ritz estimates associated with */
/* the eigenvalues RITZR and RITZI. This is equal to RNORM */
/* times the last components of the eigenvectors corresponding */
/* to the eigenvalues in RITZR and RITZI. */
/* Q Double precision N by N array. (WORKSPACE) */
/* Workspace needed to store the eigenvectors of H. */
/* LDQ Integer. (INPUT) */
/* Leading dimension of Q exactly as declared in the calling */
/* program. */
/* WORKL Double precision work array of length N**2 + 3*N. (WORKSPACE) */
/* Private (replicated) array on each PE or array allocated on */
/* the front end. This is needed to keep the full Schur form */
/* of H and also in the calculation of the eigenvectors of H. */
/* IERR Integer. (OUTPUT) */
/* Error exit flag from dlaqrb or dtrevc. */
/* \EndDoc */
/* ----------------------------------------------------------------------- */
/* \BeginLib */
/* \Local variables: */
/* xxxxxx real */
/* \Routines called: */
/* dlaqrb ARPACK routine to compute the real Schur form of an */
/* upper Hessenberg matrix and last row of the Schur vectors. */
/* second ARPACK utility routine for timing. */
/* dmout ARPACK utility routine that prints matrices */
/* dvout ARPACK utility routine that prints vectors. */
/* dlacpy LAPACK matrix copy routine. */
/* dlapy2 LAPACK routine to compute sqrt(x**2+y**2) carefully. */
/* dtrevc LAPACK routine to compute the eigenvectors of a matrix */
/* in upper quasi-triangular form */
/* dgemv Level 2 BLAS routine for matrix vector multiplication. */
/* dcopy Level 1 BLAS that copies one vector to another . */
/* dnrm2 Level 1 BLAS that computes the norm of a vector. */
/* dscal Level 1 BLAS that scales a vector. */
/* \Author */
/* Danny Sorensen Phuong Vu */
/* Richard Lehoucq CRPC / Rice University */
/* Dept. of Computational & Houston, Texas */
/* Applied Mathematics */
/* Rice University */
/* Houston, Texas */
/* \Revision history: */
/* xx/xx/92: Version ' 2.1' */
/* \SCCS Information: @(#) */
/* FILE: neigh.F SID: 2.3 DATE OF SID: 4/20/96 RELEASE: 2 */
/* \Remarks */
/* None */
/* \EndLib */
/* ----------------------------------------------------------------------- */
/* Subroutine */ int dneigh_(doublereal *rnorm, integer *n, doublereal *h__,
integer *ldh, doublereal *ritzr, doublereal *ritzi, doublereal *
bounds, doublereal *q, integer *ldq, doublereal *workl, integer *ierr)
{
/* System generated locals */
integer h_dim1, h_offset, q_dim1, q_offset, i__1;
doublereal d__1, d__2;
/* Local variables */
static integer i__;
static real t0, t1;
static doublereal vl[1], temp;
extern doublereal dnrm2_(integer *, doublereal *, integer *);
extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *,
integer *);
static integer iconj;
extern /* Subroutine */ int dgemv_(char *, integer *, integer *,
doublereal *, doublereal *, integer *, doublereal *, integer *,
doublereal *, doublereal *, integer *, ftnlen), dmout_(integer *,
integer *, integer *, doublereal *, integer *, integer *, char *,
ftnlen), dvout_(integer *, integer *, doublereal *, integer *,
char *, ftnlen);
extern doublereal dlapy2_(doublereal *, doublereal *);
extern /* Subroutine */ int dlaqrb_(logical *, integer *, integer *,
integer *, doublereal *, integer *, doublereal *, doublereal *,
doublereal *, integer *), second_(real *);
static logical select[1];
static integer msglvl;
extern /* Subroutine */ int dlacpy_(char *, integer *, integer *,
doublereal *, integer *, doublereal *, integer *, ftnlen),
dtrevc_(char *, char *, logical *, integer *, doublereal *,
integer *, doublereal *, integer *, doublereal *, integer *,
integer *, integer *, doublereal *, integer *, ftnlen, ftnlen);
/* %----------------------------------------------------% */
/* | Include files for debugging and timing information | */
/* %----------------------------------------------------% */
/* \SCCS Information: @(#) */
/* FILE: debug.h SID: 2.3 DATE OF SID: 11/16/95 RELEASE: 2 */
/* %---------------------------------% */
/* | See debug.doc for documentation | */
/* %---------------------------------% */
/* %------------------% */
/* | Scalar Arguments | */
/* %------------------% */
/* %--------------------------------% */
/* | See stat.doc for documentation | */
/* %--------------------------------% */
/* \SCCS Information: @(#) */
/* FILE: stat.h SID: 2.2 DATE OF SID: 11/16/95 RELEASE: 2 */
/* %-----------------% */
/* | Array Arguments | */
/* %-----------------% */
/* %------------% */
/* | Parameters | */
/* %------------% */
/* %------------------------% */
/* | Local Scalars & Arrays | */
/* %------------------------% */
/* %----------------------% */
/* | External Subroutines | */
/* %----------------------% */
/* %--------------------% */
/* | External Functions | */
/* %--------------------% */
/* %---------------------% */
/* | Intrinsic Functions | */
/* %---------------------% */
/* %-----------------------% */
/* | Executable Statements | */
/* %-----------------------% */
/* %-------------------------------% */
/* | Initialize timing statistics | */
/* | & message level for debugging | */
/* %-------------------------------% */
/* Parameter adjustments */
--workl;
--bounds;
--ritzi;
--ritzr;
h_dim1 = *ldh;
h_offset = 1 + h_dim1;
h__ -= h_offset;
q_dim1 = *ldq;
q_offset = 1 + q_dim1;
q -= q_offset;
/* Function Body */
second_(&t0);
msglvl = debug_1.mneigh;
if (msglvl > 2) {
dmout_(&debug_1.logfil, n, n, &h__[h_offset], ldh, &debug_1.ndigit,
"_neigh: Entering upper Hessenberg matrix H ", (ftnlen)43);
}
/* %-----------------------------------------------------------% */
/* | 1. Compute the eigenvalues, the last components of the | */
/* | corresponding Schur vectors and the full Schur form T | */
/* | of the current upper Hessenberg matrix H. | */
/* | dlaqrb returns the full Schur form of H in WORKL(1:N**2) | */
/* | and the last components of the Schur vectors in BOUNDS. | */
/* %-----------------------------------------------------------% */
dlacpy_("All", n, n, &h__[h_offset], ldh, &workl[1], n, (ftnlen)3);
dlaqrb_(&c_true, n, &c__1, n, &workl[1], n, &ritzr[1], &ritzi[1], &bounds[
1], ierr);
if (*ierr != 0) {
goto L9000;
}
if (msglvl > 1) {
dvout_(&debug_1.logfil, n, &bounds[1], &debug_1.ndigit, "_neigh: las"
"t row of the Schur matrix for H", (ftnlen)42);
}
/* %-----------------------------------------------------------% */
/* | 2. Compute the eigenvectors of the full Schur form T and | */
/* | apply the last components of the Schur vectors to get | */
/* | the last components of the corresponding eigenvectors. | */
/* | Remember that if the i-th and (i+1)-st eigenvalues are | */
/* | complex conjugate pairs, then the real & imaginary part | */
/* | of the eigenvector components are split across adjacent | */
/* | columns of Q. | */
/* %-----------------------------------------------------------% */
dtrevc_("R", "A", select, n, &workl[1], n, vl, n, &q[q_offset], ldq, n, n,
&workl[*n * *n + 1], ierr, (ftnlen)1, (ftnlen)1);
if (*ierr != 0) {
goto L9000;
}
/* %------------------------------------------------% */
/* | Scale the returning eigenvectors so that their | */
/* | euclidean norms are all one. LAPACK subroutine | */
/* | dtrevc returns each eigenvector normalized so | */
/* | that the element of largest magnitude has | */
/* | magnitude 1; here the magnitude of a complex | */
/* | number (x,y) is taken to be |x| + |y|. | */
/* %------------------------------------------------% */
iconj = 0;
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
if ((d__1 = ritzi[i__], abs(d__1)) <= 0.) {
/* %----------------------% */
/* | Real eigenvalue case | */
/* %----------------------% */
temp = dnrm2_(n, &q[i__ * q_dim1 + 1], &c__1);
d__1 = 1. / temp;
dscal_(n, &d__1, &q[i__ * q_dim1 + 1], &c__1);
} else {
/* %-------------------------------------------% */
/* | Complex conjugate pair case. Note that | */
/* | since the real and imaginary part of | */
/* | the eigenvector are stored in consecutive | */
/* | columns, we further normalize by the | */
/* | square root of two. | */
/* %-------------------------------------------% */
if (iconj == 0) {
d__1 = dnrm2_(n, &q[i__ * q_dim1 + 1], &c__1);
d__2 = dnrm2_(n, &q[(i__ + 1) * q_dim1 + 1], &c__1);
temp = dlapy2_(&d__1, &d__2);
d__1 = 1. / temp;
dscal_(n, &d__1, &q[i__ * q_dim1 + 1], &c__1);
d__1 = 1. / temp;
dscal_(n, &d__1, &q[(i__ + 1) * q_dim1 + 1], &c__1);
iconj = 1;
} else {
iconj = 0;
}
}
/* L10: */
}
dgemv_("T", n, n, &c_b18, &q[q_offset], ldq, &bounds[1], &c__1, &c_b20, &
workl[1], &c__1, (ftnlen)1);
if (msglvl > 1) {
dvout_(&debug_1.logfil, n, &workl[1], &debug_1.ndigit, "_neigh: Last"
" row of the eigenvector matrix for H", (ftnlen)48);
}
/* %----------------------------% */
/* | Compute the Ritz estimates | */
/* %----------------------------% */
iconj = 0;
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
if ((d__1 = ritzi[i__], abs(d__1)) <= 0.) {
/* %----------------------% */
/* | Real eigenvalue case | */
/* %----------------------% */
bounds[i__] = *rnorm * (d__1 = workl[i__], abs(d__1));
} else {
/* %-------------------------------------------% */
/* | Complex conjugate pair case. Note that | */
/* | since the real and imaginary part of | */
/* | the eigenvector are stored in consecutive | */
/* | columns, we need to take the magnitude | */
/* | of the last components of the two vectors | */
/* %-------------------------------------------% */
if (iconj == 0) {
bounds[i__] = *rnorm * dlapy2_(&workl[i__], &workl[i__ + 1]);
bounds[i__ + 1] = bounds[i__];
iconj = 1;
} else {
iconj = 0;
}
}
/* L20: */
}
if (msglvl > 2) {
dvout_(&debug_1.logfil, n, &ritzr[1], &debug_1.ndigit, "_neigh: Real"
" part of the eigenvalues of H", (ftnlen)41);
dvout_(&debug_1.logfil, n, &ritzi[1], &debug_1.ndigit, "_neigh: Imag"
"inary part of the eigenvalues of H", (ftnlen)46);
dvout_(&debug_1.logfil, n, &bounds[1], &debug_1.ndigit, "_neigh: Rit"
"z estimates for the eigenvalues of H", (ftnlen)47);
}
second_(&t1);
timing_1.tneigh += t1 - t0;
L9000:
return 0;
/* %---------------% */
/* | End of dneigh | */
/* %---------------% */
} /* dneigh_ */
|
