Abdelrahman Said
384 lines
12 KiB
C
384 lines
12 KiB
C
/* -- translated by f2c (version 20240504).
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You must link the resulting object file with libf2c:
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on Microsoft Windows system, link with libf2c.lib;
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on Linux or Unix systems, link with .../path/to/libf2c.a -lm
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or, if you install libf2c.a in a standard place, with -lf2c -lm
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-- in that order, at the end of the command line, as in
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cc *.o -lf2c -lm
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Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
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http://www.netlib.org/f2c/libf2c.zip
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*/
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#include "f2c.h"
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/* Table of constant values */
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static logical c_true = TRUE_;
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static integer c__1 = 1;
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static doublereal c_b23 = 1.;
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static doublereal c_b25 = 0.;
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/* -----------------------------------------------------------------------
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\BeginDoc
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\Name: dneigh
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\Description:
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Compute the eigenvalues of the current upper Hessenberg matrix
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and the corresponding Ritz estimates given the current residual norm.
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\Usage:
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call dneigh
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( RNORM, N, H, LDH, RITZR, RITZI, BOUNDS, Q, LDQ, WORKL, IERR )
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\Arguments
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RNORM Double precision scalar. (INPUT)
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Residual norm corresponding to the current upper Hessenberg
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matrix H.
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N Integer. (INPUT)
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Size of the matrix H.
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H Double precision N by N array. (INPUT)
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H contains the current upper Hessenberg matrix.
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LDH Integer. (INPUT)
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Leading dimension of H exactly as declared in the calling
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program.
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RITZR, Double precision arrays of length N. (OUTPUT)
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RITZI On output, RITZR(1:N) (resp. RITZI(1:N)) contains the real
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(respectively imaginary) parts of the eigenvalues of H.
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BOUNDS Double precision array of length N. (OUTPUT)
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On output, BOUNDS contains the Ritz estimates associated with
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the eigenvalues RITZR and RITZI. This is equal to RNORM
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times the last components of the eigenvectors corresponding
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to the eigenvalues in RITZR and RITZI.
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Q Double precision N by N array. (WORKSPACE)
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Workspace needed to store the eigenvectors of H.
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LDQ Integer. (INPUT)
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Leading dimension of Q exactly as declared in the calling
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program.
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WORKL Double precision work array of length N**2 + 3*N. (WORKSPACE)
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Private (replicated) array on each PE or array allocated on
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the front end. This is needed to keep the full Schur form
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of H and also in the calculation of the eigenvectors of H.
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IERR Integer. (OUTPUT)
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Error exit flag from dlahqr or dtrevc.
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\EndDoc
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-----------------------------------------------------------------------
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\BeginLib
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\Local variables:
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xxxxxx real
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\Routines called:
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dlahqr LAPACK routine to compute the real Schur form of an
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upper Hessenberg matrix and last row of the Schur vectors.
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arscnd ARPACK utility routine for timing.
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dmout ARPACK utility routine that prints matrices
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dvout ARPACK utility routine that prints vectors.
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dlacpy LAPACK matrix copy routine.
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dlapy2 LAPACK routine to compute sqrt(x**2+y**2) carefully.
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dtrevc LAPACK routine to compute the eigenvectors of a matrix
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in upper quasi-triangular form
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dgemv Level 2 BLAS routine for matrix vector multiplication.
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dcopy Level 1 BLAS that copies one vector to another .
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dnrm2 Level 1 BLAS that computes the norm of a vector.
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dscal Level 1 BLAS that scales a vector.
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\Author
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Danny Sorensen Phuong Vu
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Richard Lehoucq CRPC / Rice University
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Dept. of Computational & Houston, Texas
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Applied Mathematics
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Rice University
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Houston, Texas
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\Revision history:
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xx/xx/92: Version ' 2.1'
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\SCCS Information: @(#)
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FILE: neigh.F SID: 2.3 DATE OF SID: 4/20/96 RELEASE: 2
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\Remarks
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None
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\EndLib
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-----------------------------------------------------------------------
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Subroutine */ int igraphdneigh_(doublereal *rnorm, integer *n, doublereal *h__,
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integer *ldh, doublereal *ritzr, doublereal *ritzi, doublereal *
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bounds, doublereal *q, integer *ldq, doublereal *workl, integer *ierr)
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{
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/* System generated locals */
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integer h_dim1, h_offset, q_dim1, q_offset, i__1;
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doublereal d__1, d__2;
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/* Local variables */
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integer i__, j;
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real t0, t1;
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doublereal vl[1], temp;
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extern doublereal igraphdnrm2_(integer *, doublereal *, integer *);
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extern /* Subroutine */ int igraphdscal_(integer *, doublereal *, doublereal *,
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integer *);
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integer iconj;
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extern /* Subroutine */ int igraphdgemv_(char *, integer *, integer *,
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doublereal *, doublereal *, integer *, doublereal *, integer *,
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doublereal *, doublereal *, integer *), igraphdmout_(integer *,
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integer *, integer *, doublereal *, integer *, integer *, char *,
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ftnlen), igraphdvout_(integer *, integer *, doublereal *, integer *,
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char *, ftnlen);
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extern doublereal igraphdlapy2_(doublereal *, doublereal *);
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integer mneigh=0;
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extern /* Subroutine */ int igrapharscnd_(real *), igraphdlahqr_(logical *, logical *,
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integer *, integer *, integer *, doublereal *, integer *,
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doublereal *, doublereal *, integer *, integer *, doublereal *,
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integer *, integer *), igraphdlacpy_(char *, integer *, integer *,
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doublereal *, integer *, doublereal *, integer *);
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integer logfil=6, ndigit=-3;
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logical select[1];
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real tneigh=0;
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extern /* Subroutine */ int igraphdtrevc_(char *, char *, logical *, integer *,
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doublereal *, integer *, doublereal *, integer *, doublereal *,
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integer *, integer *, integer *, doublereal *, integer *);
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integer msglvl;
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/* %----------------------------------------------------%
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| Include files for debugging and timing information |
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%----------------------------------------------------%
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%------------------%
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| Scalar Arguments |
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%------------------%
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%-----------------%
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| Array Arguments |
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%-----------------%
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%------------%
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| Parameters |
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%------------%
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%------------------------%
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| Local Scalars & Arrays |
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%------------------------%
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%----------------------%
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| External Subroutines |
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%----------------------%
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%--------------------%
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| External Functions |
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%--------------------%
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%---------------------%
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| Intrinsic Functions |
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%---------------------%
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%-----------------------%
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| Executable Statements |
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%-----------------------%
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%-------------------------------%
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| Initialize timing statistics |
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| & message level for debugging |
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%-------------------------------%
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Parameter adjustments */
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--workl;
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--bounds;
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--ritzi;
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--ritzr;
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h_dim1 = *ldh;
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h_offset = 1 + h_dim1;
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h__ -= h_offset;
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q_dim1 = *ldq;
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q_offset = 1 + q_dim1;
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q -= q_offset;
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/* Function Body */
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igrapharscnd_(&t0);
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msglvl = mneigh;
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if (msglvl > 2) {
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igraphdmout_(&logfil, n, n, &h__[h_offset], ldh, &ndigit, "_neigh: Enterin"
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"g upper Hessenberg matrix H ", (ftnlen)43);
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}
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/* %-----------------------------------------------------------%
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| 1. Compute the eigenvalues, the last components of the |
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| corresponding Schur vectors and the full Schur form T |
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| of the current upper Hessenberg matrix H. |
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| dlahqr returns the full Schur form of H in WORKL(1:N**2) |
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| and the last components of the Schur vectors in BOUNDS. |
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%-----------------------------------------------------------% */
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igraphdlacpy_("All", n, n, &h__[h_offset], ldh, &workl[1], n);
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i__1 = *n - 1;
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for (j = 1; j <= i__1; ++j) {
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bounds[j] = 0.;
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/* L5: */
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}
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bounds[*n] = 1.;
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igraphdlahqr_(&c_true, &c_true, n, &c__1, n, &workl[1], n, &ritzr[1], &ritzi[1],
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&c__1, &c__1, &bounds[1], &c__1, ierr);
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if (*ierr != 0) {
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goto L9000;
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}
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if (msglvl > 1) {
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igraphdvout_(&logfil, n, &bounds[1], &ndigit, "_neigh: last row of the Sch"
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"ur matrix for H", (ftnlen)42);
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}
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/* %-----------------------------------------------------------%
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| 2. Compute the eigenvectors of the full Schur form T and |
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| apply the last components of the Schur vectors to get |
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| the last components of the corresponding eigenvectors. |
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| Remember that if the i-th and (i+1)-st eigenvalues are |
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| complex conjugate pairs, then the real & imaginary part |
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| of the eigenvector components are split across adjacent |
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| columns of Q. |
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%-----------------------------------------------------------% */
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igraphdtrevc_("R", "A", select, n, &workl[1], n, vl, n, &q[q_offset], ldq, n, n,
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&workl[*n * *n + 1], ierr);
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if (*ierr != 0) {
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goto L9000;
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}
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/* %------------------------------------------------%
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| Scale the returning eigenvectors so that their |
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| euclidean norms are all one. LAPACK subroutine |
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| dtrevc returns each eigenvector normalized so |
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| that the element of largest magnitude has |
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| magnitude 1; here the magnitude of a complex |
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| number (x,y) is taken to be |x| + |y|. |
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%------------------------------------------------% */
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iconj = 0;
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i__1 = *n;
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for (i__ = 1; i__ <= i__1; ++i__) {
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if ((d__1 = ritzi[i__], abs(d__1)) <= 0.) {
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/* %----------------------%
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| Real eigenvalue case |
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%----------------------% */
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temp = igraphdnrm2_(n, &q[i__ * q_dim1 + 1], &c__1);
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d__1 = 1. / temp;
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igraphdscal_(n, &d__1, &q[i__ * q_dim1 + 1], &c__1);
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} else {
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/* %-------------------------------------------%
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| Complex conjugate pair case. Note that |
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| since the real and imaginary part of |
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| the eigenvector are stored in consecutive |
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| columns, we further normalize by the |
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| square root of two. |
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%-------------------------------------------% */
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if (iconj == 0) {
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d__1 = igraphdnrm2_(n, &q[i__ * q_dim1 + 1], &c__1);
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d__2 = igraphdnrm2_(n, &q[(i__ + 1) * q_dim1 + 1], &c__1);
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temp = igraphdlapy2_(&d__1, &d__2);
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d__1 = 1. / temp;
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igraphdscal_(n, &d__1, &q[i__ * q_dim1 + 1], &c__1);
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d__1 = 1. / temp;
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igraphdscal_(n, &d__1, &q[(i__ + 1) * q_dim1 + 1], &c__1);
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iconj = 1;
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} else {
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iconj = 0;
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}
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}
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/* L10: */
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}
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igraphdgemv_("T", n, n, &c_b23, &q[q_offset], ldq, &bounds[1], &c__1, &c_b25, &
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workl[1], &c__1);
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if (msglvl > 1) {
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igraphdvout_(&logfil, n, &workl[1], &ndigit, "_neigh: Last row of the eige"
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"nvector matrix for H", (ftnlen)48);
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}
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/* %----------------------------%
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| Compute the Ritz estimates |
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%----------------------------% */
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iconj = 0;
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i__1 = *n;
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for (i__ = 1; i__ <= i__1; ++i__) {
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if ((d__1 = ritzi[i__], abs(d__1)) <= 0.) {
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/* %----------------------%
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| Real eigenvalue case |
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%----------------------% */
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bounds[i__] = *rnorm * (d__1 = workl[i__], abs(d__1));
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} else {
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/* %-------------------------------------------%
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| Complex conjugate pair case. Note that |
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| since the real and imaginary part of |
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| the eigenvector are stored in consecutive |
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| columns, we need to take the magnitude |
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| of the last components of the two vectors |
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%-------------------------------------------% */
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if (iconj == 0) {
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bounds[i__] = *rnorm * igraphdlapy2_(&workl[i__], &workl[i__ + 1]);
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bounds[i__ + 1] = bounds[i__];
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iconj = 1;
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} else {
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iconj = 0;
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}
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}
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/* L20: */
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}
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if (msglvl > 2) {
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igraphdvout_(&logfil, n, &ritzr[1], &ndigit, "_neigh: Real part of the eig"
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"envalues of H", (ftnlen)41);
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igraphdvout_(&logfil, n, &ritzi[1], &ndigit, "_neigh: Imaginary part of th"
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"e eigenvalues of H", (ftnlen)46);
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igraphdvout_(&logfil, n, &bounds[1], &ndigit, "_neigh: Ritz estimates for "
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"the eigenvalues of H", (ftnlen)47);
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}
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igrapharscnd_(&t1);
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tneigh += t1 - t0;
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L9000:
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return 0;
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/* %---------------%
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| End of dneigh |
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%---------------% */
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} /* igraphdneigh_ */
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