390 lines
12 KiB
C++
390 lines
12 KiB
C++
/* fortran/dsytd2.f -- translated by f2c (version 20200916).
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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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#ifdef __cplusplus
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extern "C" {
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#endif
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#include "lmp_f2c.h"
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/* Table of constant values */
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static integer c__1 = 1;
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static doublereal c_b8 = 0.;
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static doublereal c_b14 = -1.;
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/* > \brief \b DSYTD2 reduces a symmetric matrix to real symmetric tridiagonal form by an orthogonal similarit
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y transformation (unblocked algorithm). */
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/* =========== DOCUMENTATION =========== */
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/* Online html documentation available at */
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/* http://www.netlib.org/lapack/explore-html/ */
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/* > \htmlonly */
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/* > Download DSYTD2 + dependencies */
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/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dsytd2.
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f"> */
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/* > [TGZ]</a> */
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/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dsytd2.
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f"> */
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/* > [ZIP]</a> */
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/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dsytd2.
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f"> */
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/* > [TXT]</a> */
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/* > \endhtmlonly */
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/* Definition: */
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/* =========== */
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/* SUBROUTINE DSYTD2( UPLO, N, A, LDA, D, E, TAU, INFO ) */
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/* .. Scalar Arguments .. */
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/* CHARACTER UPLO */
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/* INTEGER INFO, LDA, N */
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/* .. */
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/* .. Array Arguments .. */
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/* DOUBLE PRECISION A( LDA, * ), D( * ), E( * ), TAU( * ) */
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/* .. */
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/* > \par Purpose: */
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/* ============= */
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/* > */
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/* > \verbatim */
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/* > */
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/* > DSYTD2 reduces a real symmetric matrix A to symmetric tridiagonal */
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/* > form T by an orthogonal similarity transformation: Q**T * A * Q = T. */
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/* > \endverbatim */
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/* Arguments: */
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/* ========== */
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/* > \param[in] UPLO */
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/* > \verbatim */
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/* > UPLO is CHARACTER*1 */
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/* > Specifies whether the upper or lower triangular part of the */
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/* > symmetric matrix A is stored: */
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/* > = 'U': Upper triangular */
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/* > = 'L': Lower triangular */
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/* > \endverbatim */
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/* > */
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/* > \param[in] N */
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/* > \verbatim */
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/* > N is INTEGER */
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/* > The order of the matrix A. N >= 0. */
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/* > \endverbatim */
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/* > */
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/* > \param[in,out] A */
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/* > \verbatim */
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/* > A is DOUBLE PRECISION array, dimension (LDA,N) */
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/* > On entry, the symmetric matrix A. If UPLO = 'U', the leading */
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/* > n-by-n upper triangular part of A contains the upper */
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/* > triangular part of the matrix A, and the strictly lower */
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/* > triangular part of A is not referenced. If UPLO = 'L', the */
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/* > leading n-by-n lower triangular part of A contains the lower */
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/* > triangular part of the matrix A, and the strictly upper */
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/* > triangular part of A is not referenced. */
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/* > On exit, if UPLO = 'U', the diagonal and first superdiagonal */
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/* > of A are overwritten by the corresponding elements of the */
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/* > tridiagonal matrix T, and the elements above the first */
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/* > superdiagonal, with the array TAU, represent the orthogonal */
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/* > matrix Q as a product of elementary reflectors; if UPLO */
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/* > = 'L', the diagonal and first subdiagonal of A are over- */
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/* > written by the corresponding elements of the tridiagonal */
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/* > matrix T, and the elements below the first subdiagonal, with */
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/* > the array TAU, represent the orthogonal matrix Q as a product */
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/* > of elementary reflectors. See Further Details. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] LDA */
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/* > \verbatim */
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/* > LDA is INTEGER */
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/* > The leading dimension of the array A. LDA >= max(1,N). */
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/* > \endverbatim */
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/* > */
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/* > \param[out] D */
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/* > \verbatim */
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/* > D is DOUBLE PRECISION array, dimension (N) */
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/* > The diagonal elements of the tridiagonal matrix T: */
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/* > D(i) = A(i,i). */
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/* > \endverbatim */
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/* > */
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/* > \param[out] E */
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/* > \verbatim */
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/* > E is DOUBLE PRECISION array, dimension (N-1) */
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/* > The off-diagonal elements of the tridiagonal matrix T: */
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/* > E(i) = A(i,i+1) if UPLO = 'U', E(i) = A(i+1,i) if UPLO = 'L'. */
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/* > \endverbatim */
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/* > */
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/* > \param[out] TAU */
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/* > \verbatim */
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/* > TAU is DOUBLE PRECISION array, dimension (N-1) */
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/* > The scalar factors of the elementary reflectors (see Further */
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/* > Details). */
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/* > \endverbatim */
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/* > */
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/* > \param[out] INFO */
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/* > \verbatim */
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/* > INFO is INTEGER */
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/* > = 0: successful exit */
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/* > < 0: if INFO = -i, the i-th argument had an illegal value. */
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/* > \endverbatim */
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/* Authors: */
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/* ======== */
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/* > \author Univ. of Tennessee */
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/* > \author Univ. of California Berkeley */
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/* > \author Univ. of Colorado Denver */
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/* > \author NAG Ltd. */
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/* > \ingroup doubleSYcomputational */
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/* > \par Further Details: */
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/* ===================== */
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/* > */
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/* > \verbatim */
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/* > */
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/* > If UPLO = 'U', the matrix Q is represented as a product of elementary */
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/* > reflectors */
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/* > */
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/* > Q = H(n-1) . . . H(2) H(1). */
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/* > */
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/* > Each H(i) has the form */
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/* > */
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/* > H(i) = I - tau * v * v**T */
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/* > */
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/* > where tau is a real scalar, and v is a real vector with */
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/* > v(i+1:n) = 0 and v(i) = 1; v(1:i-1) is stored on exit in */
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/* > A(1:i-1,i+1), and tau in TAU(i). */
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/* > */
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/* > If UPLO = 'L', the matrix Q is represented as a product of elementary */
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/* > reflectors */
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/* > */
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/* > Q = H(1) H(2) . . . H(n-1). */
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/* > */
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/* > Each H(i) has the form */
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/* > */
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/* > H(i) = I - tau * v * v**T */
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/* > */
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/* > where tau is a real scalar, and v is a real vector with */
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/* > v(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in A(i+2:n,i), */
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/* > and tau in TAU(i). */
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/* > */
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/* > The contents of A on exit are illustrated by the following examples */
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/* > with n = 5: */
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/* > */
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/* > if UPLO = 'U': if UPLO = 'L': */
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/* > */
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/* > ( d e v2 v3 v4 ) ( d ) */
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/* > ( d e v3 v4 ) ( e d ) */
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/* > ( d e v4 ) ( v1 e d ) */
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/* > ( d e ) ( v1 v2 e d ) */
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/* > ( d ) ( v1 v2 v3 e d ) */
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/* > */
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/* > where d and e denote diagonal and off-diagonal elements of T, and vi */
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/* > denotes an element of the vector defining H(i). */
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/* > \endverbatim */
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/* > */
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/* ===================================================================== */
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/* Subroutine */ int dsytd2_(char *uplo, integer *n, doublereal *a, integer *
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lda, doublereal *d__, doublereal *e, doublereal *tau, integer *info,
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ftnlen uplo_len)
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{
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/* System generated locals */
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integer a_dim1, a_offset, i__1, i__2, i__3;
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/* Local variables */
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integer i__;
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extern doublereal ddot_(integer *, doublereal *, integer *, doublereal *,
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integer *);
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doublereal taui;
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extern /* Subroutine */ int dsyr2_(char *, integer *, doublereal *,
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doublereal *, integer *, doublereal *, integer *, doublereal *,
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integer *, ftnlen);
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doublereal alpha;
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extern logical lsame_(char *, char *, ftnlen, ftnlen);
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extern /* Subroutine */ int daxpy_(integer *, doublereal *, doublereal *,
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integer *, doublereal *, integer *);
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logical upper;
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extern /* Subroutine */ int dsymv_(char *, integer *, doublereal *,
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doublereal *, integer *, doublereal *, integer *, doublereal *,
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doublereal *, integer *, ftnlen), dlarfg_(integer *, doublereal *,
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doublereal *, integer *, doublereal *), xerbla_(char *, integer *
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, ftnlen);
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/* -- LAPACK computational routine -- */
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/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
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/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
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/* .. Scalar Arguments .. */
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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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/* .. Local Scalars .. */
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/* .. */
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/* .. External Subroutines .. */
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/* .. */
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/* .. External Functions .. */
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/* .. */
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/* .. Intrinsic Functions .. */
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/* .. */
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/* .. Executable Statements .. */
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/* Test the input parameters */
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/* Parameter adjustments */
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a_dim1 = *lda;
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a_offset = 1 + a_dim1;
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a -= a_offset;
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--d__;
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--e;
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--tau;
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/* Function Body */
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*info = 0;
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upper = lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1);
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if (! upper && ! lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) {
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*info = -1;
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} else if (*n < 0) {
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*info = -2;
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} else if (*lda < max(1,*n)) {
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*info = -4;
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}
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if (*info != 0) {
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i__1 = -(*info);
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xerbla_((char *)"DSYTD2", &i__1, (ftnlen)6);
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return 0;
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}
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/* Quick return if possible */
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if (*n <= 0) {
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return 0;
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}
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if (upper) {
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/* Reduce the upper triangle of A */
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for (i__ = *n - 1; i__ >= 1; --i__) {
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/* Generate elementary reflector H(i) = I - tau * v * v**T */
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/* to annihilate A(1:i-1,i+1) */
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dlarfg_(&i__, &a[i__ + (i__ + 1) * a_dim1], &a[(i__ + 1) * a_dim1
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+ 1], &c__1, &taui);
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e[i__] = a[i__ + (i__ + 1) * a_dim1];
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if (taui != 0.) {
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/* Apply H(i) from both sides to A(1:i,1:i) */
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a[i__ + (i__ + 1) * a_dim1] = 1.;
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/* Compute x := tau * A * v storing x in TAU(1:i) */
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dsymv_(uplo, &i__, &taui, &a[a_offset], lda, &a[(i__ + 1) *
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a_dim1 + 1], &c__1, &c_b8, &tau[1], &c__1, (ftnlen)1);
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/* Compute w := x - 1/2 * tau * (x**T * v) * v */
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alpha = taui * -.5 * ddot_(&i__, &tau[1], &c__1, &a[(i__ + 1)
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* a_dim1 + 1], &c__1);
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daxpy_(&i__, &alpha, &a[(i__ + 1) * a_dim1 + 1], &c__1, &tau[
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1], &c__1);
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/* Apply the transformation as a rank-2 update: */
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/* A := A - v * w**T - w * v**T */
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dsyr2_(uplo, &i__, &c_b14, &a[(i__ + 1) * a_dim1 + 1], &c__1,
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&tau[1], &c__1, &a[a_offset], lda, (ftnlen)1);
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a[i__ + (i__ + 1) * a_dim1] = e[i__];
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}
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d__[i__ + 1] = a[i__ + 1 + (i__ + 1) * a_dim1];
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tau[i__] = taui;
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/* L10: */
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}
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d__[1] = a[a_dim1 + 1];
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} else {
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/* Reduce the lower triangle of A */
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i__1 = *n - 1;
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for (i__ = 1; i__ <= i__1; ++i__) {
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/* Generate elementary reflector H(i) = I - tau * v * v**T */
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/* to annihilate A(i+2:n,i) */
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i__2 = *n - i__;
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/* Computing MIN */
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i__3 = i__ + 2;
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dlarfg_(&i__2, &a[i__ + 1 + i__ * a_dim1], &a[min(i__3,*n) + i__ *
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a_dim1], &c__1, &taui);
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e[i__] = a[i__ + 1 + i__ * a_dim1];
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if (taui != 0.) {
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/* Apply H(i) from both sides to A(i+1:n,i+1:n) */
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a[i__ + 1 + i__ * a_dim1] = 1.;
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/* Compute x := tau * A * v storing y in TAU(i:n-1) */
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i__2 = *n - i__;
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dsymv_(uplo, &i__2, &taui, &a[i__ + 1 + (i__ + 1) * a_dim1],
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lda, &a[i__ + 1 + i__ * a_dim1], &c__1, &c_b8, &tau[
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i__], &c__1, (ftnlen)1);
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/* Compute w := x - 1/2 * tau * (x**T * v) * v */
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i__2 = *n - i__;
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alpha = taui * -.5 * ddot_(&i__2, &tau[i__], &c__1, &a[i__ +
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1 + i__ * a_dim1], &c__1);
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i__2 = *n - i__;
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daxpy_(&i__2, &alpha, &a[i__ + 1 + i__ * a_dim1], &c__1, &tau[
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i__], &c__1);
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/* Apply the transformation as a rank-2 update: */
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/* A := A - v * w**T - w * v**T */
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i__2 = *n - i__;
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dsyr2_(uplo, &i__2, &c_b14, &a[i__ + 1 + i__ * a_dim1], &c__1,
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&tau[i__], &c__1, &a[i__ + 1 + (i__ + 1) * a_dim1],
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lda, (ftnlen)1);
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a[i__ + 1 + i__ * a_dim1] = e[i__];
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}
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d__[i__] = a[i__ + i__ * a_dim1];
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tau[i__] = taui;
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/* L20: */
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}
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d__[*n] = a[*n + *n * a_dim1];
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}
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return 0;
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/* End of DSYTD2 */
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} /* dsytd2_ */
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#ifdef __cplusplus
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}
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#endif
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