464 lines
15 KiB
C++
464 lines
15 KiB
C++
/* fortran/zhetrd.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 integer c_n1 = -1;
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static integer c__3 = 3;
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static integer c__2 = 2;
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static doublereal c_b23 = 1.;
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/* > \brief \b ZHETRD */
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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 ZHETRD + dependencies */
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/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zhetrd.
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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/zhetrd.
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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/zhetrd.
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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 ZHETRD( UPLO, N, A, LDA, D, E, TAU, WORK, LWORK, INFO ) */
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/* .. Scalar Arguments .. */
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/* CHARACTER UPLO */
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/* INTEGER INFO, LDA, LWORK, N */
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/* .. */
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/* .. Array Arguments .. */
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/* DOUBLE PRECISION D( * ), E( * ) */
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/* COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) */
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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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/* > ZHETRD reduces a complex Hermitian matrix A to real symmetric */
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/* > tridiagonal form T by a unitary similarity transformation: */
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/* > Q**H * 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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/* > = 'U': Upper triangle of A is stored; */
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/* > = 'L': Lower triangle of A is stored. */
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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 COMPLEX*16 array, dimension (LDA,N) */
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/* > On entry, the Hermitian 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 unitary */
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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 unitary 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 COMPLEX*16 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] WORK */
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/* > \verbatim */
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/* > WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) */
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/* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] LWORK */
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/* > \verbatim */
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/* > LWORK is INTEGER */
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/* > The dimension of the array WORK. LWORK >= 1. */
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/* > For optimum performance LWORK >= N*NB, where NB is the */
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/* > optimal blocksize. */
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/* > */
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/* > If LWORK = -1, then a workspace query is assumed; the routine */
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/* > only calculates the optimal size of the WORK array, returns */
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/* > this value as the first entry of the WORK array, and no error */
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/* > message related to LWORK is issued by XERBLA. */
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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 complex16HEcomputational */
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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**H */
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/* > */
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/* > where tau is a complex scalar, and v is a complex 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**H */
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/* > */
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/* > where tau is a complex scalar, and v is a complex 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 zhetrd_(char *uplo, integer *n, doublecomplex *a,
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integer *lda, doublereal *d__, doublereal *e, doublecomplex *tau,
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doublecomplex *work, integer *lwork, integer *info, 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, i__4, i__5;
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doublecomplex z__1;
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/* Local variables */
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integer i__, j, nb, kk, nx, iws;
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extern logical lsame_(char *, char *, ftnlen, ftnlen);
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integer nbmin, iinfo;
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logical upper;
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extern /* Subroutine */ int zhetd2_(char *, integer *, doublecomplex *,
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integer *, doublereal *, doublereal *, doublecomplex *, integer *,
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ftnlen), zher2k_(char *, char *, integer *, integer *,
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doublecomplex *, doublecomplex *, integer *, doublecomplex *,
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integer *, doublereal *, doublecomplex *, integer *, ftnlen,
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ftnlen), xerbla_(char *, integer *, ftnlen);
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extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
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integer *, integer *, ftnlen, ftnlen);
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extern /* Subroutine */ int zlatrd_(char *, integer *, integer *,
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doublecomplex *, integer *, doublereal *, doublecomplex *,
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doublecomplex *, integer *, ftnlen);
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integer ldwork, lwkopt;
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logical lquery;
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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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/* .. Intrinsic Functions .. */
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/* .. */
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/* .. External 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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--work;
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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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lquery = *lwork == -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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} else if (*lwork < 1 && ! lquery) {
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*info = -9;
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}
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if (*info == 0) {
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/* Determine the block size. */
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nb = ilaenv_(&c__1, (char *)"ZHETRD", uplo, n, &c_n1, &c_n1, &c_n1, (ftnlen)6,
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(ftnlen)1);
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lwkopt = *n * nb;
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work[1].r = (doublereal) lwkopt, work[1].i = 0.;
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}
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if (*info != 0) {
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i__1 = -(*info);
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xerbla_((char *)"ZHETRD", &i__1, (ftnlen)6);
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return 0;
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} else if (lquery) {
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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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work[1].r = 1., work[1].i = 0.;
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return 0;
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}
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nx = *n;
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iws = 1;
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if (nb > 1 && nb < *n) {
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/* Determine when to cross over from blocked to unblocked code */
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/* (last block is always handled by unblocked code). */
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/* Computing MAX */
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i__1 = nb, i__2 = ilaenv_(&c__3, (char *)"ZHETRD", uplo, n, &c_n1, &c_n1, &
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c_n1, (ftnlen)6, (ftnlen)1);
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nx = max(i__1,i__2);
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if (nx < *n) {
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/* Determine if workspace is large enough for blocked code. */
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ldwork = *n;
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iws = ldwork * nb;
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if (*lwork < iws) {
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/* Not enough workspace to use optimal NB: determine the */
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/* minimum value of NB, and reduce NB or force use of */
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/* unblocked code by setting NX = N. */
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/* Computing MAX */
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i__1 = *lwork / ldwork;
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nb = max(i__1,1);
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nbmin = ilaenv_(&c__2, (char *)"ZHETRD", uplo, n, &c_n1, &c_n1, &c_n1,
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(ftnlen)6, (ftnlen)1);
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if (nb < nbmin) {
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nx = *n;
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}
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}
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} else {
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nx = *n;
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}
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} else {
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nb = 1;
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}
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if (upper) {
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/* Reduce the upper triangle of A. */
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/* Columns 1:kk are handled by the unblocked method. */
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kk = *n - (*n - nx + nb - 1) / nb * nb;
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i__1 = kk + 1;
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i__2 = -nb;
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for (i__ = *n - nb + 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ +=
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i__2) {
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/* Reduce columns i:i+nb-1 to tridiagonal form and form the */
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/* matrix W which is needed to update the unreduced part of */
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/* the matrix */
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i__3 = i__ + nb - 1;
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zlatrd_(uplo, &i__3, &nb, &a[a_offset], lda, &e[1], &tau[1], &
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work[1], &ldwork, (ftnlen)1);
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/* Update the unreduced submatrix A(1:i-1,1:i-1), using an */
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/* update of the form: A := A - V*W**H - W*V**H */
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i__3 = i__ - 1;
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z__1.r = -1., z__1.i = -0.;
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zher2k_(uplo, (char *)"No transpose", &i__3, &nb, &z__1, &a[i__ * a_dim1
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+ 1], lda, &work[1], &ldwork, &c_b23, &a[a_offset], lda, (
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ftnlen)1, (ftnlen)12);
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/* Copy superdiagonal elements back into A, and diagonal */
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/* elements into D */
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i__3 = i__ + nb - 1;
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for (j = i__; j <= i__3; ++j) {
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i__4 = j - 1 + j * a_dim1;
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i__5 = j - 1;
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a[i__4].r = e[i__5], a[i__4].i = 0.;
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i__4 = j + j * a_dim1;
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d__[j] = a[i__4].r;
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/* L10: */
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}
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/* L20: */
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}
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/* Use unblocked code to reduce the last or only block */
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zhetd2_(uplo, &kk, &a[a_offset], lda, &d__[1], &e[1], &tau[1], &iinfo,
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(ftnlen)1);
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} else {
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/* Reduce the lower triangle of A */
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i__2 = *n - nx;
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i__1 = nb;
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for (i__ = 1; i__1 < 0 ? i__ >= i__2 : i__ <= i__2; i__ += i__1) {
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/* Reduce columns i:i+nb-1 to tridiagonal form and form the */
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/* matrix W which is needed to update the unreduced part of */
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/* the matrix */
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i__3 = *n - i__ + 1;
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zlatrd_(uplo, &i__3, &nb, &a[i__ + i__ * a_dim1], lda, &e[i__], &
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tau[i__], &work[1], &ldwork, (ftnlen)1);
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/* Update the unreduced submatrix A(i+nb:n,i+nb:n), using */
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/* an update of the form: A := A - V*W**H - W*V**H */
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i__3 = *n - i__ - nb + 1;
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z__1.r = -1., z__1.i = -0.;
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zher2k_(uplo, (char *)"No transpose", &i__3, &nb, &z__1, &a[i__ + nb +
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i__ * a_dim1], lda, &work[nb + 1], &ldwork, &c_b23, &a[
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i__ + nb + (i__ + nb) * a_dim1], lda, (ftnlen)1, (ftnlen)
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12);
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/* Copy subdiagonal elements back into A, and diagonal */
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/* elements into D */
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i__3 = i__ + nb - 1;
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for (j = i__; j <= i__3; ++j) {
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i__4 = j + 1 + j * a_dim1;
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i__5 = j;
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a[i__4].r = e[i__5], a[i__4].i = 0.;
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i__4 = j + j * a_dim1;
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d__[j] = a[i__4].r;
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/* L30: */
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}
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/* L40: */
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}
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/* Use unblocked code to reduce the last or only block */
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i__1 = *n - i__ + 1;
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zhetd2_(uplo, &i__1, &a[i__ + i__ * a_dim1], lda, &d__[i__], &e[i__],
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&tau[i__], &iinfo, (ftnlen)1);
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}
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work[1].r = (doublereal) lwkopt, work[1].i = 0.;
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return 0;
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/* End of ZHETRD */
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} /* zhetrd_ */
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#ifdef __cplusplus
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}
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#endif
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