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references/igraph-1.0.1/vendor/lapack/dsytrd.c
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/* -- translated by f2c (version 20240504).
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"
/* Table of constant values */
static integer c__1 = 1;
static integer c_n1 = -1;
static integer c__3 = 3;
static integer c__2 = 2;
static doublereal c_b22 = -1.;
static doublereal c_b23 = 1.;
/* > \brief \b DSYTRD
=========== DOCUMENTATION ===========
Online html documentation available at
http://www.netlib.org/lapack/explore-html/
> \htmlonly
> Download DSYTRD + dependencies
> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dsytrd.
f">
> [TGZ]</a>
> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dsytrd.
f">
> [ZIP]</a>
> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dsytrd.
f">
> [TXT]</a>
> \endhtmlonly
Definition:
===========
SUBROUTINE DSYTRD( UPLO, N, A, LDA, D, E, TAU, WORK, LWORK, INFO )
CHARACTER UPLO
INTEGER INFO, LDA, LWORK, N
DOUBLE PRECISION A( LDA, * ), D( * ), E( * ), TAU( * ),
$ WORK( * )
> \par Purpose:
=============
>
> \verbatim
>
> DSYTRD reduces a real symmetric matrix A to real symmetric
> tridiagonal form T by an orthogonal similarity transformation:
> Q**T * A * Q = T.
> \endverbatim
Arguments:
==========
> \param[in] UPLO
> \verbatim
> UPLO is CHARACTER*1
> = 'U': Upper triangle of A is stored;
> = 'L': Lower triangle of A is stored.
> \endverbatim
>
> \param[in] N
> \verbatim
> N is INTEGER
> The order of the matrix A. N >= 0.
> \endverbatim
>
> \param[in,out] A
> \verbatim
> A is DOUBLE PRECISION array, dimension (LDA,N)
> On entry, the symmetric matrix A. If UPLO = 'U', the leading
> N-by-N upper triangular part of A contains the upper
> triangular part of the matrix A, and the strictly lower
> triangular part of A is not referenced. If UPLO = 'L', the
> leading N-by-N lower triangular part of A contains the lower
> triangular part of the matrix A, and the strictly upper
> triangular part of A is not referenced.
> On exit, if UPLO = 'U', the diagonal and first superdiagonal
> of A are overwritten by the corresponding elements of the
> tridiagonal matrix T, and the elements above the first
> superdiagonal, with the array TAU, represent the orthogonal
> matrix Q as a product of elementary reflectors; if UPLO
> = 'L', the diagonal and first subdiagonal of A are over-
> written by the corresponding elements of the tridiagonal
> matrix T, and the elements below the first subdiagonal, with
> the array TAU, represent the orthogonal matrix Q as a product
> of elementary reflectors. See Further Details.
> \endverbatim
>
> \param[in] LDA
> \verbatim
> LDA is INTEGER
> The leading dimension of the array A. LDA >= max(1,N).
> \endverbatim
>
> \param[out] D
> \verbatim
> D is DOUBLE PRECISION array, dimension (N)
> The diagonal elements of the tridiagonal matrix T:
> D(i) = A(i,i).
> \endverbatim
>
> \param[out] E
> \verbatim
> E is DOUBLE PRECISION array, dimension (N-1)
> The off-diagonal elements of the tridiagonal matrix T:
> E(i) = A(i,i+1) if UPLO = 'U', E(i) = A(i+1,i) if UPLO = 'L'.
> \endverbatim
>
> \param[out] TAU
> \verbatim
> TAU is DOUBLE PRECISION array, dimension (N-1)
> The scalar factors of the elementary reflectors (see Further
> Details).
> \endverbatim
>
> \param[out] WORK
> \verbatim
> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
> \endverbatim
>
> \param[in] LWORK
> \verbatim
> LWORK is INTEGER
> The dimension of the array WORK. LWORK >= 1.
> For optimum performance LWORK >= N*NB, where NB is the
> optimal blocksize.
>
> If LWORK = -1, then a workspace query is assumed; the routine
> only calculates the optimal size of the WORK array, returns
> this value as the first entry of the WORK array, and no error
> message related to LWORK is issued by XERBLA.
> \endverbatim
>
> \param[out] INFO
> \verbatim
> INFO is INTEGER
> = 0: successful exit
> < 0: if INFO = -i, the i-th argument had an illegal value
> \endverbatim
Authors:
========
> \author Univ. of Tennessee
> \author Univ. of California Berkeley
> \author Univ. of Colorado Denver
> \author NAG Ltd.
> \date November 2011
> \ingroup doubleSYcomputational
> \par Further Details:
=====================
>
> \verbatim
>
> If UPLO = 'U', the matrix Q is represented as a product of elementary
> reflectors
>
> Q = H(n-1) . . . H(2) H(1).
>
> Each H(i) has the form
>
> H(i) = I - tau * v * v**T
>
> where tau is a real scalar, and v is a real vector with
> v(i+1:n) = 0 and v(i) = 1; v(1:i-1) is stored on exit in
> A(1:i-1,i+1), and tau in TAU(i).
>
> If UPLO = 'L', the matrix Q is represented as a product of elementary
> reflectors
>
> Q = H(1) H(2) . . . H(n-1).
>
> Each H(i) has the form
>
> H(i) = I - tau * v * v**T
>
> where tau is a real scalar, and v is a real vector with
> v(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in A(i+2:n,i),
> and tau in TAU(i).
>
> The contents of A on exit are illustrated by the following examples
> with n = 5:
>
> if UPLO = 'U': if UPLO = 'L':
>
> ( d e v2 v3 v4 ) ( d )
> ( d e v3 v4 ) ( e d )
> ( d e v4 ) ( v1 e d )
> ( d e ) ( v1 v2 e d )
> ( d ) ( v1 v2 v3 e d )
>
> where d and e denote diagonal and off-diagonal elements of T, and vi
> denotes an element of the vector defining H(i).
> \endverbatim
>
=====================================================================
Subroutine */ int igraphdsytrd_(char *uplo, integer *n, doublereal *a, integer *
lda, doublereal *d__, doublereal *e, doublereal *tau, doublereal *
work, integer *lwork, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3;
/* Local variables */
integer i__, j, nb, kk, nx, iws;
extern logical igraphlsame_(char *, char *);
integer nbmin, iinfo;
logical upper;
extern /* Subroutine */ int igraphdsytd2_(char *, integer *, doublereal *,
integer *, doublereal *, doublereal *, doublereal *, integer *), igraphdsyr2k_(char *, char *, integer *, integer *, doublereal
*, doublereal *, integer *, doublereal *, integer *, doublereal *,
doublereal *, integer *), igraphdlatrd_(char *,
integer *, integer *, doublereal *, integer *, doublereal *,
doublereal *, doublereal *, integer *), igraphxerbla_(char *,
integer *, ftnlen);
extern integer igraphilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
integer ldwork, lwkopt;
logical lquery;
/* -- LAPACK computational routine (version 3.4.0) --
-- LAPACK is a software package provided by Univ. of Tennessee, --
-- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
November 2011
=====================================================================
Test the input parameters
Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--d__;
--e;
--tau;
--work;
/* Function Body */
*info = 0;
upper = igraphlsame_(uplo, "U");
lquery = *lwork == -1;
if (! upper && ! igraphlsame_(uplo, "L")) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*lda < max(1,*n)) {
*info = -4;
} else if (*lwork < 1 && ! lquery) {
*info = -9;
}
if (*info == 0) {
/* Determine the block size. */
nb = igraphilaenv_(&c__1, "DSYTRD", uplo, n, &c_n1, &c_n1, &c_n1, (ftnlen)6,
(ftnlen)1);
lwkopt = *n * nb;
work[1] = (doublereal) lwkopt;
}
if (*info != 0) {
i__1 = -(*info);
igraphxerbla_("DSYTRD", &i__1, (ftnlen)6);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
if (*n == 0) {
work[1] = 1.;
return 0;
}
nx = *n;
iws = 1;
if (nb > 1 && nb < *n) {
/* Determine when to cross over from blocked to unblocked code
(last block is always handled by unblocked code).
Computing MAX */
i__1 = nb, i__2 = igraphilaenv_(&c__3, "DSYTRD", uplo, n, &c_n1, &c_n1, &
c_n1, (ftnlen)6, (ftnlen)1);
nx = max(i__1,i__2);
if (nx < *n) {
/* Determine if workspace is large enough for blocked code. */
ldwork = *n;
iws = ldwork * nb;
if (*lwork < iws) {
/* Not enough workspace to use optimal NB: determine the
minimum value of NB, and reduce NB or force use of
unblocked code by setting NX = N.
Computing MAX */
i__1 = *lwork / ldwork;
nb = max(i__1,1);
nbmin = igraphilaenv_(&c__2, "DSYTRD", uplo, n, &c_n1, &c_n1, &c_n1,
(ftnlen)6, (ftnlen)1);
if (nb < nbmin) {
nx = *n;
}
}
} else {
nx = *n;
}
} else {
nb = 1;
}
if (upper) {
/* Reduce the upper triangle of A.
Columns 1:kk are handled by the unblocked method. */
kk = *n - (*n - nx + nb - 1) / nb * nb;
i__1 = kk + 1;
i__2 = -nb;
for (i__ = *n - nb + 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ +=
i__2) {
/* Reduce columns i:i+nb-1 to tridiagonal form and form the
matrix W which is needed to update the unreduced part of
the matrix */
i__3 = i__ + nb - 1;
igraphdlatrd_(uplo, &i__3, &nb, &a[a_offset], lda, &e[1], &tau[1], &
work[1], &ldwork);
/* Update the unreduced submatrix A(1:i-1,1:i-1), using an
update of the form: A := A - V*W**T - W*V**T */
i__3 = i__ - 1;
igraphdsyr2k_(uplo, "No transpose", &i__3, &nb, &c_b22, &a[i__ * a_dim1
+ 1], lda, &work[1], &ldwork, &c_b23, &a[a_offset], lda);
/* Copy superdiagonal elements back into A, and diagonal
elements into D */
i__3 = i__ + nb - 1;
for (j = i__; j <= i__3; ++j) {
a[j - 1 + j * a_dim1] = e[j - 1];
d__[j] = a[j + j * a_dim1];
/* L10: */
}
/* L20: */
}
/* Use unblocked code to reduce the last or only block */
igraphdsytd2_(uplo, &kk, &a[a_offset], lda, &d__[1], &e[1], &tau[1], &iinfo);
} else {
/* Reduce the lower triangle of A */
i__2 = *n - nx;
i__1 = nb;
for (i__ = 1; i__1 < 0 ? i__ >= i__2 : i__ <= i__2; i__ += i__1) {
/* Reduce columns i:i+nb-1 to tridiagonal form and form the
matrix W which is needed to update the unreduced part of
the matrix */
i__3 = *n - i__ + 1;
igraphdlatrd_(uplo, &i__3, &nb, &a[i__ + i__ * a_dim1], lda, &e[i__], &
tau[i__], &work[1], &ldwork);
/* Update the unreduced submatrix A(i+ib:n,i+ib:n), using
an update of the form: A := A - V*W**T - W*V**T */
i__3 = *n - i__ - nb + 1;
igraphdsyr2k_(uplo, "No transpose", &i__3, &nb, &c_b22, &a[i__ + nb +
i__ * a_dim1], lda, &work[nb + 1], &ldwork, &c_b23, &a[
i__ + nb + (i__ + nb) * a_dim1], lda);
/* Copy subdiagonal elements back into A, and diagonal
elements into D */
i__3 = i__ + nb - 1;
for (j = i__; j <= i__3; ++j) {
a[j + 1 + j * a_dim1] = e[j];
d__[j] = a[j + j * a_dim1];
/* L30: */
}
/* L40: */
}
/* Use unblocked code to reduce the last or only block */
i__1 = *n - i__ + 1;
igraphdsytd2_(uplo, &i__1, &a[i__ + i__ * a_dim1], lda, &d__[i__], &e[i__],
&tau[i__], &iinfo);
}
work[1] = (doublereal) lwkopt;
return 0;
/* End of DSYTRD */
} /* igraphdsytrd_ */