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c5a87f75d6cfbcca5a4b6e2e2f44865c55bf6a89
lammps/lib/linalg/dlatrd.cpp
Axel Kohlmeyer c5a87f75d6 convert linalg library from Fortran to C++
2022-12-28 13:18:38 -05:00

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/* fortran/dlatrd.f -- translated by f2c (version 20200916).
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
*/
#ifdef __cplusplus
extern "C" {
#endif
#include "lmp_f2c.h"
/* Table of constant values */
static doublereal c_b5 = -1.;
static doublereal c_b6 = 1.;
static integer c__1 = 1;
static doublereal c_b16 = 0.;
/* > \brief \b DLATRD reduces the first nb rows and columns of a symmetric/Hermitian matrix A to real tridiago
nal form by an orthogonal similarity transformation. */
/* =========== DOCUMENTATION =========== */
/* Online html documentation available at */
/* http://www.netlib.org/lapack/explore-html/ */
/* > \htmlonly */
/* > Download DLATRD + dependencies */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlatrd.
f"> */
/* > [TGZ]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlatrd.
f"> */
/* > [ZIP]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlatrd.
f"> */
/* > [TXT]</a> */
/* > \endhtmlonly */
/* Definition: */
/* =========== */
/* SUBROUTINE DLATRD( UPLO, N, NB, A, LDA, E, TAU, W, LDW ) */
/* .. Scalar Arguments .. */
/* CHARACTER UPLO */
/* INTEGER LDA, LDW, N, NB */
/* .. */
/* .. Array Arguments .. */
/* DOUBLE PRECISION A( LDA, * ), E( * ), TAU( * ), W( LDW, * ) */
/* .. */
/* > \par Purpose: */
/* ============= */
/* > */
/* > \verbatim */
/* > */
/* > DLATRD reduces NB rows and columns of a real symmetric matrix A to */
/* > symmetric tridiagonal form by an orthogonal similarity */
/* > transformation Q**T * A * Q, and returns the matrices V and W which are */
/* > needed to apply the transformation to the unreduced part of A. */
/* > */
/* > If UPLO = 'U', DLATRD reduces the last NB rows and columns of a */
/* > matrix, of which the upper triangle is supplied; */
/* > if UPLO = 'L', DLATRD reduces the first NB rows and columns of a */
/* > matrix, of which the lower triangle is supplied. */
/* > */
/* > This is an auxiliary routine called by DSYTRD. */
/* > \endverbatim */
/* Arguments: */
/* ========== */
/* > \param[in] UPLO */
/* > \verbatim */
/* > UPLO is CHARACTER*1 */
/* > Specifies whether the upper or lower triangular part of the */
/* > symmetric matrix A is stored: */
/* > = 'U': Upper triangular */
/* > = 'L': Lower triangular */
/* > \endverbatim */
/* > */
/* > \param[in] N */
/* > \verbatim */
/* > N is INTEGER */
/* > The order of the matrix A. */
/* > \endverbatim */
/* > */
/* > \param[in] NB */
/* > \verbatim */
/* > NB is INTEGER */
/* > The number of rows and columns to be reduced. */
/* > \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 last NB columns have been reduced to */
/* > tridiagonal form, with the diagonal elements overwriting */
/* > the diagonal elements of A; the elements above the diagonal */
/* > with the array TAU, represent the orthogonal matrix Q as a */
/* > product of elementary reflectors; */
/* > if UPLO = 'L', the first NB columns have been reduced to */
/* > tridiagonal form, with the diagonal elements overwriting */
/* > the diagonal elements of A; the elements below the diagonal */
/* > 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 >= (1,N). */
/* > \endverbatim */
/* > */
/* > \param[out] E */
/* > \verbatim */
/* > E is DOUBLE PRECISION array, dimension (N-1) */
/* > If UPLO = 'U', E(n-nb:n-1) contains the superdiagonal */
/* > elements of the last NB columns of the reduced matrix; */
/* > if UPLO = 'L', E(1:nb) contains the subdiagonal elements of */
/* > the first NB columns of the reduced matrix. */
/* > \endverbatim */
/* > */
/* > \param[out] TAU */
/* > \verbatim */
/* > TAU is DOUBLE PRECISION array, dimension (N-1) */
/* > The scalar factors of the elementary reflectors, stored in */
/* > TAU(n-nb:n-1) if UPLO = 'U', and in TAU(1:nb) if UPLO = 'L'. */
/* > See Further Details. */
/* > \endverbatim */
/* > */
/* > \param[out] W */
/* > \verbatim */
/* > W is DOUBLE PRECISION array, dimension (LDW,NB) */
/* > The n-by-nb matrix W required to update the unreduced part */
/* > of A. */
/* > \endverbatim */
/* > */
/* > \param[in] LDW */
/* > \verbatim */
/* > LDW is INTEGER */
/* > The leading dimension of the array W. LDW >= max(1,N). */
/* > \endverbatim */
/* Authors: */
/* ======== */
/* > \author Univ. of Tennessee */
/* > \author Univ. of California Berkeley */
/* > \author Univ. of Colorado Denver */
/* > \author NAG Ltd. */
/* > \ingroup doubleOTHERauxiliary */
/* > \par Further Details: */
/* ===================== */
/* > */
/* > \verbatim */
/* > */
/* > If UPLO = 'U', the matrix Q is represented as a product of elementary */
/* > reflectors */
/* > */
/* > Q = H(n) H(n-1) . . . H(n-nb+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:n) = 0 and v(i-1) = 1; v(1:i-1) is stored on exit in A(1:i-1,i), */
/* > and tau in TAU(i-1). */
/* > */
/* > If UPLO = 'L', the matrix Q is represented as a product of elementary */
/* > reflectors */
/* > */
/* > Q = H(1) H(2) . . . H(nb). */
/* > */
/* > 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+1:n) is stored on exit in A(i+1:n,i), */
/* > and tau in TAU(i). */
/* > */
/* > The elements of the vectors v together form the n-by-nb matrix V */
/* > which is needed, with W, to apply the transformation to the unreduced */
/* > part of the matrix, using a symmetric rank-2k update of the form: */
/* > A := A - V*W**T - W*V**T. */
/* > */
/* > The contents of A on exit are illustrated by the following examples */
/* > with n = 5 and nb = 2: */
/* > */
/* > if UPLO = 'U': if UPLO = 'L': */
/* > */
/* > ( a a a v4 v5 ) ( d ) */
/* > ( a a v4 v5 ) ( 1 d ) */
/* > ( a 1 v5 ) ( v1 1 a ) */
/* > ( d 1 ) ( v1 v2 a a ) */
/* > ( d ) ( v1 v2 a a a ) */
/* > */
/* > where d denotes a diagonal element of the reduced matrix, a denotes */
/* > an element of the original matrix that is unchanged, and vi denotes */
/* > an element of the vector defining H(i). */
/* > \endverbatim */
/* > */
/* ===================================================================== */
/* Subroutine */ int dlatrd_(char *uplo, integer *n, integer *nb, doublereal *
a, integer *lda, doublereal *e, doublereal *tau, doublereal *w,
integer *ldw, ftnlen uplo_len)
{
/* System generated locals */
integer a_dim1, a_offset, w_dim1, w_offset, i__1, i__2, i__3;
/* Local variables */
integer i__, iw;
extern doublereal ddot_(integer *, doublereal *, integer *, doublereal *,
integer *);
doublereal alpha;
extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *,
integer *);
extern logical lsame_(char *, char *, ftnlen, ftnlen);
extern /* Subroutine */ int dgemv_(char *, integer *, integer *,
doublereal *, doublereal *, integer *, doublereal *, integer *,
doublereal *, doublereal *, integer *, ftnlen), daxpy_(integer *,
doublereal *, doublereal *, integer *, doublereal *, integer *),
dsymv_(char *, integer *, doublereal *, doublereal *, integer *,
doublereal *, integer *, doublereal *, doublereal *, integer *,
ftnlen), dlarfg_(integer *, doublereal *, doublereal *, integer *,
doublereal *);
/* -- LAPACK auxiliary routine -- */
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Quick return if possible */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--e;
--tau;
w_dim1 = *ldw;
w_offset = 1 + w_dim1;
w -= w_offset;
/* Function Body */
if (*n <= 0) {
return 0;
}
if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) {
/* Reduce last NB columns of upper triangle */
i__1 = *n - *nb + 1;
for (i__ = *n; i__ >= i__1; --i__) {
iw = i__ - *n + *nb;
if (i__ < *n) {
/* Update A(1:i,i) */
i__2 = *n - i__;
dgemv_((char *)"No transpose", &i__, &i__2, &c_b5, &a[(i__ + 1) *
a_dim1 + 1], lda, &w[i__ + (iw + 1) * w_dim1], ldw, &
c_b6, &a[i__ * a_dim1 + 1], &c__1, (ftnlen)12);
i__2 = *n - i__;
dgemv_((char *)"No transpose", &i__, &i__2, &c_b5, &w[(iw + 1) *
w_dim1 + 1], ldw, &a[i__ + (i__ + 1) * a_dim1], lda, &
c_b6, &a[i__ * a_dim1 + 1], &c__1, (ftnlen)12);
}
if (i__ > 1) {
/* Generate elementary reflector H(i) to annihilate */
/* A(1:i-2,i) */
i__2 = i__ - 1;
dlarfg_(&i__2, &a[i__ - 1 + i__ * a_dim1], &a[i__ * a_dim1 +
1], &c__1, &tau[i__ - 1]);
e[i__ - 1] = a[i__ - 1 + i__ * a_dim1];
a[i__ - 1 + i__ * a_dim1] = 1.;
/* Compute W(1:i-1,i) */
i__2 = i__ - 1;
dsymv_((char *)"Upper", &i__2, &c_b6, &a[a_offset], lda, &a[i__ *
a_dim1 + 1], &c__1, &c_b16, &w[iw * w_dim1 + 1], &
c__1, (ftnlen)5);
if (i__ < *n) {
i__2 = i__ - 1;
i__3 = *n - i__;
dgemv_((char *)"Transpose", &i__2, &i__3, &c_b6, &w[(iw + 1) *
w_dim1 + 1], ldw, &a[i__ * a_dim1 + 1], &c__1, &
c_b16, &w[i__ + 1 + iw * w_dim1], &c__1, (ftnlen)
9);
i__2 = i__ - 1;
i__3 = *n - i__;
dgemv_((char *)"No transpose", &i__2, &i__3, &c_b5, &a[(i__ + 1) *
a_dim1 + 1], lda, &w[i__ + 1 + iw * w_dim1], &
c__1, &c_b6, &w[iw * w_dim1 + 1], &c__1, (ftnlen)
12);
i__2 = i__ - 1;
i__3 = *n - i__;
dgemv_((char *)"Transpose", &i__2, &i__3, &c_b6, &a[(i__ + 1) *
a_dim1 + 1], lda, &a[i__ * a_dim1 + 1], &c__1, &
c_b16, &w[i__ + 1 + iw * w_dim1], &c__1, (ftnlen)
9);
i__2 = i__ - 1;
i__3 = *n - i__;
dgemv_((char *)"No transpose", &i__2, &i__3, &c_b5, &w[(iw + 1) *
w_dim1 + 1], ldw, &w[i__ + 1 + iw * w_dim1], &
c__1, &c_b6, &w[iw * w_dim1 + 1], &c__1, (ftnlen)
12);
}
i__2 = i__ - 1;
dscal_(&i__2, &tau[i__ - 1], &w[iw * w_dim1 + 1], &c__1);
i__2 = i__ - 1;
alpha = tau[i__ - 1] * -.5 * ddot_(&i__2, &w[iw * w_dim1 + 1],
&c__1, &a[i__ * a_dim1 + 1], &c__1);
i__2 = i__ - 1;
daxpy_(&i__2, &alpha, &a[i__ * a_dim1 + 1], &c__1, &w[iw *
w_dim1 + 1], &c__1);
}
/* L10: */
}
} else {
/* Reduce first NB columns of lower triangle */
i__1 = *nb;
for (i__ = 1; i__ <= i__1; ++i__) {
/* Update A(i:n,i) */
i__2 = *n - i__ + 1;
i__3 = i__ - 1;
dgemv_((char *)"No transpose", &i__2, &i__3, &c_b5, &a[i__ + a_dim1], lda,
&w[i__ + w_dim1], ldw, &c_b6, &a[i__ + i__ * a_dim1], &
c__1, (ftnlen)12);
i__2 = *n - i__ + 1;
i__3 = i__ - 1;
dgemv_((char *)"No transpose", &i__2, &i__3, &c_b5, &w[i__ + w_dim1], ldw,
&a[i__ + a_dim1], lda, &c_b6, &a[i__ + i__ * a_dim1], &
c__1, (ftnlen)12);
if (i__ < *n) {
/* Generate elementary reflector H(i) to annihilate */
/* A(i+2:n,i) */
i__2 = *n - i__;
/* Computing MIN */
i__3 = i__ + 2;
dlarfg_(&i__2, &a[i__ + 1 + i__ * a_dim1], &a[min(i__3,*n) +
i__ * a_dim1], &c__1, &tau[i__]);
e[i__] = a[i__ + 1 + i__ * a_dim1];
a[i__ + 1 + i__ * a_dim1] = 1.;
/* Compute W(i+1:n,i) */
i__2 = *n - i__;
dsymv_((char *)"Lower", &i__2, &c_b6, &a[i__ + 1 + (i__ + 1) * a_dim1]
, lda, &a[i__ + 1 + i__ * a_dim1], &c__1, &c_b16, &w[
i__ + 1 + i__ * w_dim1], &c__1, (ftnlen)5);
i__2 = *n - i__;
i__3 = i__ - 1;
dgemv_((char *)"Transpose", &i__2, &i__3, &c_b6, &w[i__ + 1 + w_dim1],
ldw, &a[i__ + 1 + i__ * a_dim1], &c__1, &c_b16, &w[
i__ * w_dim1 + 1], &c__1, (ftnlen)9);
i__2 = *n - i__;
i__3 = i__ - 1;
dgemv_((char *)"No transpose", &i__2, &i__3, &c_b5, &a[i__ + 1 +
a_dim1], lda, &w[i__ * w_dim1 + 1], &c__1, &c_b6, &w[
i__ + 1 + i__ * w_dim1], &c__1, (ftnlen)12);
i__2 = *n - i__;
i__3 = i__ - 1;
dgemv_((char *)"Transpose", &i__2, &i__3, &c_b6, &a[i__ + 1 + a_dim1],
lda, &a[i__ + 1 + i__ * a_dim1], &c__1, &c_b16, &w[
i__ * w_dim1 + 1], &c__1, (ftnlen)9);
i__2 = *n - i__;
i__3 = i__ - 1;
dgemv_((char *)"No transpose", &i__2, &i__3, &c_b5, &w[i__ + 1 +
w_dim1], ldw, &w[i__ * w_dim1 + 1], &c__1, &c_b6, &w[
i__ + 1 + i__ * w_dim1], &c__1, (ftnlen)12);
i__2 = *n - i__;
dscal_(&i__2, &tau[i__], &w[i__ + 1 + i__ * w_dim1], &c__1);
i__2 = *n - i__;
alpha = tau[i__] * -.5 * ddot_(&i__2, &w[i__ + 1 + i__ *
w_dim1], &c__1, &a[i__ + 1 + i__ * a_dim1], &c__1);
i__2 = *n - i__;
daxpy_(&i__2, &alpha, &a[i__ + 1 + i__ * a_dim1], &c__1, &w[
i__ + 1 + i__ * w_dim1], &c__1);
}
/* L20: */
}
}
return 0;
/* End of DLATRD */
} /* dlatrd_ */
#ifdef __cplusplus
}
#endif
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