382 lines
13 KiB
C++
382 lines
13 KiB
C++
/* fortran/dsygs2.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 doublereal c_b6 = -1.;
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static integer c__1 = 1;
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static doublereal c_b27 = 1.;
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/* > \brief \b DSYGS2 reduces a symmetric definite generalized eigenproblem to standard form, using the factor
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ization results obtained from spotrf (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 DSYGS2 + dependencies */
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/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dsygs2.
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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/dsygs2.
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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/dsygs2.
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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 DSYGS2( ITYPE, UPLO, N, A, LDA, B, LDB, INFO ) */
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/* .. Scalar Arguments .. */
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/* CHARACTER UPLO */
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/* INTEGER INFO, ITYPE, LDA, LDB, N */
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/* .. */
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/* .. Array Arguments .. */
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/* DOUBLE PRECISION A( LDA, * ), B( LDB, * ) */
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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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/* > DSYGS2 reduces a real symmetric-definite generalized eigenproblem */
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/* > to standard form. */
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/* > */
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/* > If ITYPE = 1, the problem is A*x = lambda*B*x, */
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/* > and A is overwritten by inv(U**T)*A*inv(U) or inv(L)*A*inv(L**T) */
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/* > */
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/* > If ITYPE = 2 or 3, the problem is A*B*x = lambda*x or */
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/* > B*A*x = lambda*x, and A is overwritten by U*A*U**T or L**T *A*L. */
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/* > */
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/* > B must have been previously factorized as U**T *U or L*L**T by DPOTRF. */
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/* > \endverbatim */
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/* Arguments: */
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/* ========== */
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/* > \param[in] ITYPE */
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/* > \verbatim */
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/* > ITYPE is INTEGER */
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/* > = 1: compute inv(U**T)*A*inv(U) or inv(L)*A*inv(L**T); */
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/* > = 2 or 3: compute U*A*U**T or L**T *A*L. */
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/* > \endverbatim */
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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, and how B has been factorized. */
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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 matrices A and B. 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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/* > */
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/* > On exit, if INFO = 0, the transformed matrix, stored in the */
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/* > same format as A. */
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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[in] B */
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/* > \verbatim */
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/* > B is DOUBLE PRECISION array, dimension (LDB,N) */
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/* > The triangular factor from the Cholesky factorization of B, */
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/* > as returned by DPOTRF. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] LDB */
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/* > \verbatim */
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/* > LDB is INTEGER */
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/* > The leading dimension of the array B. LDB >= max(1,N). */
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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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/* ===================================================================== */
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/* Subroutine */ int dsygs2_(integer *itype, char *uplo, integer *n,
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doublereal *a, integer *lda, doublereal *b, integer *ldb, integer *
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info, ftnlen uplo_len)
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{
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/* System generated locals */
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integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2;
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doublereal d__1;
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/* Local variables */
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integer k;
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doublereal ct, akk, bkk;
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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), dscal_(integer *, doublereal *, doublereal *,
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integer *);
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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 dtrmv_(char *, char *, char *, integer *,
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doublereal *, integer *, doublereal *, integer *, ftnlen, ftnlen,
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ftnlen), dtrsv_(char *, char *, char *, integer *, doublereal *,
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integer *, doublereal *, integer *, ftnlen, ftnlen, ftnlen),
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xerbla_(char *, integer *, 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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/* .. 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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b_dim1 = *ldb;
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b_offset = 1 + b_dim1;
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b -= b_offset;
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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 (*itype < 1 || *itype > 3) {
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*info = -1;
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} else if (! upper && ! lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) {
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*info = -2;
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} else if (*n < 0) {
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*info = -3;
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} else if (*lda < max(1,*n)) {
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*info = -5;
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} else if (*ldb < max(1,*n)) {
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*info = -7;
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}
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if (*info != 0) {
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i__1 = -(*info);
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xerbla_((char *)"DSYGS2", &i__1, (ftnlen)6);
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return 0;
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}
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if (*itype == 1) {
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if (upper) {
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/* Compute inv(U**T)*A*inv(U) */
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i__1 = *n;
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for (k = 1; k <= i__1; ++k) {
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/* Update the upper triangle of A(k:n,k:n) */
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akk = a[k + k * a_dim1];
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bkk = b[k + k * b_dim1];
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/* Computing 2nd power */
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d__1 = bkk;
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akk /= d__1 * d__1;
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a[k + k * a_dim1] = akk;
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if (k < *n) {
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i__2 = *n - k;
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d__1 = 1. / bkk;
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dscal_(&i__2, &d__1, &a[k + (k + 1) * a_dim1], lda);
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ct = akk * -.5;
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i__2 = *n - k;
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daxpy_(&i__2, &ct, &b[k + (k + 1) * b_dim1], ldb, &a[k + (
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k + 1) * a_dim1], lda);
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i__2 = *n - k;
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dsyr2_(uplo, &i__2, &c_b6, &a[k + (k + 1) * a_dim1], lda,
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&b[k + (k + 1) * b_dim1], ldb, &a[k + 1 + (k + 1)
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* a_dim1], lda, (ftnlen)1);
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i__2 = *n - k;
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daxpy_(&i__2, &ct, &b[k + (k + 1) * b_dim1], ldb, &a[k + (
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k + 1) * a_dim1], lda);
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i__2 = *n - k;
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dtrsv_(uplo, (char *)"Transpose", (char *)"Non-unit", &i__2, &b[k + 1 + (
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k + 1) * b_dim1], ldb, &a[k + (k + 1) * a_dim1],
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lda, (ftnlen)1, (ftnlen)9, (ftnlen)8);
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}
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/* L10: */
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}
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} else {
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/* Compute inv(L)*A*inv(L**T) */
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i__1 = *n;
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for (k = 1; k <= i__1; ++k) {
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/* Update the lower triangle of A(k:n,k:n) */
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akk = a[k + k * a_dim1];
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bkk = b[k + k * b_dim1];
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/* Computing 2nd power */
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d__1 = bkk;
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akk /= d__1 * d__1;
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a[k + k * a_dim1] = akk;
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if (k < *n) {
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i__2 = *n - k;
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d__1 = 1. / bkk;
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dscal_(&i__2, &d__1, &a[k + 1 + k * a_dim1], &c__1);
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ct = akk * -.5;
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i__2 = *n - k;
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daxpy_(&i__2, &ct, &b[k + 1 + k * b_dim1], &c__1, &a[k +
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1 + k * a_dim1], &c__1);
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i__2 = *n - k;
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dsyr2_(uplo, &i__2, &c_b6, &a[k + 1 + k * a_dim1], &c__1,
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&b[k + 1 + k * b_dim1], &c__1, &a[k + 1 + (k + 1)
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* a_dim1], lda, (ftnlen)1);
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i__2 = *n - k;
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daxpy_(&i__2, &ct, &b[k + 1 + k * b_dim1], &c__1, &a[k +
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1 + k * a_dim1], &c__1);
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i__2 = *n - k;
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dtrsv_(uplo, (char *)"No transpose", (char *)"Non-unit", &i__2, &b[k + 1
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+ (k + 1) * b_dim1], ldb, &a[k + 1 + k * a_dim1],
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&c__1, (ftnlen)1, (ftnlen)12, (ftnlen)8);
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}
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/* L20: */
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}
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}
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} else {
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if (upper) {
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/* Compute U*A*U**T */
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i__1 = *n;
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for (k = 1; k <= i__1; ++k) {
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/* Update the upper triangle of A(1:k,1:k) */
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akk = a[k + k * a_dim1];
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bkk = b[k + k * b_dim1];
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i__2 = k - 1;
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dtrmv_(uplo, (char *)"No transpose", (char *)"Non-unit", &i__2, &b[b_offset],
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ldb, &a[k * a_dim1 + 1], &c__1, (ftnlen)1, (ftnlen)12,
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(ftnlen)8);
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ct = akk * .5;
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i__2 = k - 1;
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daxpy_(&i__2, &ct, &b[k * b_dim1 + 1], &c__1, &a[k * a_dim1 +
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1], &c__1);
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i__2 = k - 1;
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dsyr2_(uplo, &i__2, &c_b27, &a[k * a_dim1 + 1], &c__1, &b[k *
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b_dim1 + 1], &c__1, &a[a_offset], lda, (ftnlen)1);
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i__2 = k - 1;
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daxpy_(&i__2, &ct, &b[k * b_dim1 + 1], &c__1, &a[k * a_dim1 +
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1], &c__1);
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i__2 = k - 1;
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dscal_(&i__2, &bkk, &a[k * a_dim1 + 1], &c__1);
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/* Computing 2nd power */
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d__1 = bkk;
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a[k + k * a_dim1] = akk * (d__1 * d__1);
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/* L30: */
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}
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} else {
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/* Compute L**T *A*L */
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i__1 = *n;
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for (k = 1; k <= i__1; ++k) {
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/* Update the lower triangle of A(1:k,1:k) */
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akk = a[k + k * a_dim1];
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bkk = b[k + k * b_dim1];
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i__2 = k - 1;
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dtrmv_(uplo, (char *)"Transpose", (char *)"Non-unit", &i__2, &b[b_offset],
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ldb, &a[k + a_dim1], lda, (ftnlen)1, (ftnlen)9, (
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ftnlen)8);
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ct = akk * .5;
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i__2 = k - 1;
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daxpy_(&i__2, &ct, &b[k + b_dim1], ldb, &a[k + a_dim1], lda);
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i__2 = k - 1;
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dsyr2_(uplo, &i__2, &c_b27, &a[k + a_dim1], lda, &b[k +
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b_dim1], ldb, &a[a_offset], lda, (ftnlen)1);
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i__2 = k - 1;
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daxpy_(&i__2, &ct, &b[k + b_dim1], ldb, &a[k + a_dim1], lda);
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i__2 = k - 1;
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dscal_(&i__2, &bkk, &a[k + a_dim1], lda);
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/* Computing 2nd power */
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d__1 = bkk;
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a[k + k * a_dim1] = akk * (d__1 * d__1);
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/* L40: */
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}
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}
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}
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return 0;
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/* End of DSYGS2 */
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} /* dsygs2_ */
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#ifdef __cplusplus
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}
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#endif
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