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

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/* fortran/dlasdq.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 integer c__1 = 1;
/* > \brief \b DLASDQ computes the SVD of a real bidiagonal matrix with diagonal d and off-diagonal e. Used by
sbdsdc. */
/* =========== DOCUMENTATION =========== */
/* Online html documentation available at */
/* http://www.netlib.org/lapack/explore-html/ */
/* > \htmlonly */
/* > Download DLASDQ + dependencies */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlasdq.
f"> */
/* > [TGZ]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlasdq.
f"> */
/* > [ZIP]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlasdq.
f"> */
/* > [TXT]</a> */
/* > \endhtmlonly */
/* Definition: */
/* =========== */
/* SUBROUTINE DLASDQ( UPLO, SQRE, N, NCVT, NRU, NCC, D, E, VT, LDVT, */
/* U, LDU, C, LDC, WORK, INFO ) */
/* .. Scalar Arguments .. */
/* CHARACTER UPLO */
/* INTEGER INFO, LDC, LDU, LDVT, N, NCC, NCVT, NRU, SQRE */
/* .. */
/* .. Array Arguments .. */
/* DOUBLE PRECISION C( LDC, * ), D( * ), E( * ), U( LDU, * ), */
/* $ VT( LDVT, * ), WORK( * ) */
/* .. */
/* > \par Purpose: */
/* ============= */
/* > */
/* > \verbatim */
/* > */
/* > DLASDQ computes the singular value decomposition (SVD) of a real */
/* > (upper or lower) bidiagonal matrix with diagonal D and offdiagonal */
/* > E, accumulating the transformations if desired. Letting B denote */
/* > the input bidiagonal matrix, the algorithm computes orthogonal */
/* > matrices Q and P such that B = Q * S * P**T (P**T denotes the transpose */
/* > of P). The singular values S are overwritten on D. */
/* > */
/* > The input matrix U is changed to U * Q if desired. */
/* > The input matrix VT is changed to P**T * VT if desired. */
/* > The input matrix C is changed to Q**T * C if desired. */
/* > */
/* > See "Computing Small Singular Values of Bidiagonal Matrices With */
/* > Guaranteed High Relative Accuracy," by J. Demmel and W. Kahan, */
/* > LAPACK Working Note #3, for a detailed description of the algorithm. */
/* > \endverbatim */
/* Arguments: */
/* ========== */
/* > \param[in] UPLO */
/* > \verbatim */
/* > UPLO is CHARACTER*1 */
/* > On entry, UPLO specifies whether the input bidiagonal matrix */
/* > is upper or lower bidiagonal, and whether it is square are */
/* > not. */
/* > UPLO = 'U' or 'u' B is upper bidiagonal. */
/* > UPLO = 'L' or 'l' B is lower bidiagonal. */
/* > \endverbatim */
/* > */
/* > \param[in] SQRE */
/* > \verbatim */
/* > SQRE is INTEGER */
/* > = 0: then the input matrix is N-by-N. */
/* > = 1: then the input matrix is N-by-(N+1) if UPLU = 'U' and */
/* > (N+1)-by-N if UPLU = 'L'. */
/* > */
/* > The bidiagonal matrix has */
/* > N = NL + NR + 1 rows and */
/* > M = N + SQRE >= N columns. */
/* > \endverbatim */
/* > */
/* > \param[in] N */
/* > \verbatim */
/* > N is INTEGER */
/* > On entry, N specifies the number of rows and columns */
/* > in the matrix. N must be at least 0. */
/* > \endverbatim */
/* > */
/* > \param[in] NCVT */
/* > \verbatim */
/* > NCVT is INTEGER */
/* > On entry, NCVT specifies the number of columns of */
/* > the matrix VT. NCVT must be at least 0. */
/* > \endverbatim */
/* > */
/* > \param[in] NRU */
/* > \verbatim */
/* > NRU is INTEGER */
/* > On entry, NRU specifies the number of rows of */
/* > the matrix U. NRU must be at least 0. */
/* > \endverbatim */
/* > */
/* > \param[in] NCC */
/* > \verbatim */
/* > NCC is INTEGER */
/* > On entry, NCC specifies the number of columns of */
/* > the matrix C. NCC must be at least 0. */
/* > \endverbatim */
/* > */
/* > \param[in,out] D */
/* > \verbatim */
/* > D is DOUBLE PRECISION array, dimension (N) */
/* > On entry, D contains the diagonal entries of the */
/* > bidiagonal matrix whose SVD is desired. On normal exit, */
/* > D contains the singular values in ascending order. */
/* > \endverbatim */
/* > */
/* > \param[in,out] E */
/* > \verbatim */
/* > E is DOUBLE PRECISION array. */
/* > dimension is (N-1) if SQRE = 0 and N if SQRE = 1. */
/* > On entry, the entries of E contain the offdiagonal entries */
/* > of the bidiagonal matrix whose SVD is desired. On normal */
/* > exit, E will contain 0. If the algorithm does not converge, */
/* > D and E will contain the diagonal and superdiagonal entries */
/* > of a bidiagonal matrix orthogonally equivalent to the one */
/* > given as input. */
/* > \endverbatim */
/* > */
/* > \param[in,out] VT */
/* > \verbatim */
/* > VT is DOUBLE PRECISION array, dimension (LDVT, NCVT) */
/* > On entry, contains a matrix which on exit has been */
/* > premultiplied by P**T, dimension N-by-NCVT if SQRE = 0 */
/* > and (N+1)-by-NCVT if SQRE = 1 (not referenced if NCVT=0). */
/* > \endverbatim */
/* > */
/* > \param[in] LDVT */
/* > \verbatim */
/* > LDVT is INTEGER */
/* > On entry, LDVT specifies the leading dimension of VT as */
/* > declared in the calling (sub) program. LDVT must be at */
/* > least 1. If NCVT is nonzero LDVT must also be at least N. */
/* > \endverbatim */
/* > */
/* > \param[in,out] U */
/* > \verbatim */
/* > U is DOUBLE PRECISION array, dimension (LDU, N) */
/* > On entry, contains a matrix which on exit has been */
/* > postmultiplied by Q, dimension NRU-by-N if SQRE = 0 */
/* > and NRU-by-(N+1) if SQRE = 1 (not referenced if NRU=0). */
/* > \endverbatim */
/* > */
/* > \param[in] LDU */
/* > \verbatim */
/* > LDU is INTEGER */
/* > On entry, LDU specifies the leading dimension of U as */
/* > declared in the calling (sub) program. LDU must be at */
/* > least max( 1, NRU ) . */
/* > \endverbatim */
/* > */
/* > \param[in,out] C */
/* > \verbatim */
/* > C is DOUBLE PRECISION array, dimension (LDC, NCC) */
/* > On entry, contains an N-by-NCC matrix which on exit */
/* > has been premultiplied by Q**T dimension N-by-NCC if SQRE = 0 */
/* > and (N+1)-by-NCC if SQRE = 1 (not referenced if NCC=0). */
/* > \endverbatim */
/* > */
/* > \param[in] LDC */
/* > \verbatim */
/* > LDC is INTEGER */
/* > On entry, LDC specifies the leading dimension of C as */
/* > declared in the calling (sub) program. LDC must be at */
/* > least 1. If NCC is nonzero, LDC must also be at least N. */
/* > \endverbatim */
/* > */
/* > \param[out] WORK */
/* > \verbatim */
/* > WORK is DOUBLE PRECISION array, dimension (4*N) */
/* > Workspace. Only referenced if one of NCVT, NRU, or NCC is */
/* > nonzero, and if N is at least 2. */
/* > \endverbatim */
/* > */
/* > \param[out] INFO */
/* > \verbatim */
/* > INFO is INTEGER */
/* > On exit, a value of 0 indicates a successful exit. */
/* > If INFO < 0, argument number -INFO is illegal. */
/* > If INFO > 0, the algorithm did not converge, and INFO */
/* > specifies how many superdiagonals did not converge. */
/* > \endverbatim */
/* Authors: */
/* ======== */
/* > \author Univ. of Tennessee */
/* > \author Univ. of California Berkeley */
/* > \author Univ. of Colorado Denver */
/* > \author NAG Ltd. */
/* > \ingroup OTHERauxiliary */
/* > \par Contributors: */
/* ================== */
/* > */
/* > Ming Gu and Huan Ren, Computer Science Division, University of */
/* > California at Berkeley, USA */
/* > */
/* ===================================================================== */
/* Subroutine */ int dlasdq_(char *uplo, integer *sqre, integer *n, integer *
ncvt, integer *nru, integer *ncc, doublereal *d__, doublereal *e,
doublereal *vt, integer *ldvt, doublereal *u, integer *ldu,
doublereal *c__, integer *ldc, doublereal *work, integer *info,
ftnlen uplo_len)
{
/* System generated locals */
integer c_dim1, c_offset, u_dim1, u_offset, vt_dim1, vt_offset, i__1,
i__2;
/* Local variables */
integer i__, j;
doublereal r__, cs, sn;
integer np1, isub;
doublereal smin;
integer sqre1;
extern logical lsame_(char *, char *, ftnlen, ftnlen);
extern /* Subroutine */ int dlasr_(char *, char *, char *, integer *,
integer *, doublereal *, doublereal *, doublereal *, integer *,
ftnlen, ftnlen, ftnlen), dswap_(integer *, doublereal *, integer *
, doublereal *, integer *);
integer iuplo;
extern /* Subroutine */ int dlartg_(doublereal *, doublereal *,
doublereal *, doublereal *, doublereal *), xerbla_(char *,
integer *, ftnlen), dbdsqr_(char *, integer *, integer *, integer
*, integer *, doublereal *, doublereal *, doublereal *, integer *,
doublereal *, integer *, doublereal *, integer *, doublereal *,
integer *, ftnlen);
logical rotate;
/* -- 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 .. */
/* Test the input parameters. */
/* Parameter adjustments */
--d__;
--e;
vt_dim1 = *ldvt;
vt_offset = 1 + vt_dim1;
vt -= vt_offset;
u_dim1 = *ldu;
u_offset = 1 + u_dim1;
u -= u_offset;
c_dim1 = *ldc;
c_offset = 1 + c_dim1;
c__ -= c_offset;
--work;
/* Function Body */
*info = 0;
iuplo = 0;
if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) {
iuplo = 1;
}
if (lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) {
iuplo = 2;
}
if (iuplo == 0) {
*info = -1;
} else if (*sqre < 0 || *sqre > 1) {
*info = -2;
} else if (*n < 0) {
*info = -3;
} else if (*ncvt < 0) {
*info = -4;
} else if (*nru < 0) {
*info = -5;
} else if (*ncc < 0) {
*info = -6;
} else if (*ncvt == 0 && *ldvt < 1 || *ncvt > 0 && *ldvt < max(1,*n)) {
*info = -10;
} else if (*ldu < max(1,*nru)) {
*info = -12;
} else if (*ncc == 0 && *ldc < 1 || *ncc > 0 && *ldc < max(1,*n)) {
*info = -14;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_((char *)"DLASDQ", &i__1, (ftnlen)6);
return 0;
}
if (*n == 0) {
return 0;
}
/* ROTATE is true if any singular vectors desired, false otherwise */
rotate = *ncvt > 0 || *nru > 0 || *ncc > 0;
np1 = *n + 1;
sqre1 = *sqre;
/* If matrix non-square upper bidiagonal, rotate to be lower */
/* bidiagonal. The rotations are on the right. */
if (iuplo == 1 && sqre1 == 1) {
i__1 = *n - 1;
for (i__ = 1; i__ <= i__1; ++i__) {
dlartg_(&d__[i__], &e[i__], &cs, &sn, &r__);
d__[i__] = r__;
e[i__] = sn * d__[i__ + 1];
d__[i__ + 1] = cs * d__[i__ + 1];
if (rotate) {
work[i__] = cs;
work[*n + i__] = sn;
}
/* L10: */
}
dlartg_(&d__[*n], &e[*n], &cs, &sn, &r__);
d__[*n] = r__;
e[*n] = 0.;
if (rotate) {
work[*n] = cs;
work[*n + *n] = sn;
}
iuplo = 2;
sqre1 = 0;
/* Update singular vectors if desired. */
if (*ncvt > 0) {
dlasr_((char *)"L", (char *)"V", (char *)"F", &np1, ncvt, &work[1], &work[np1], &vt[
vt_offset], ldvt, (ftnlen)1, (ftnlen)1, (ftnlen)1);
}
}
/* If matrix lower bidiagonal, rotate to be upper bidiagonal */
/* by applying Givens rotations on the left. */
if (iuplo == 2) {
i__1 = *n - 1;
for (i__ = 1; i__ <= i__1; ++i__) {
dlartg_(&d__[i__], &e[i__], &cs, &sn, &r__);
d__[i__] = r__;
e[i__] = sn * d__[i__ + 1];
d__[i__ + 1] = cs * d__[i__ + 1];
if (rotate) {
work[i__] = cs;
work[*n + i__] = sn;
}
/* L20: */
}
/* If matrix (N+1)-by-N lower bidiagonal, one additional */
/* rotation is needed. */
if (sqre1 == 1) {
dlartg_(&d__[*n], &e[*n], &cs, &sn, &r__);
d__[*n] = r__;
if (rotate) {
work[*n] = cs;
work[*n + *n] = sn;
}
}
/* Update singular vectors if desired. */
if (*nru > 0) {
if (sqre1 == 0) {
dlasr_((char *)"R", (char *)"V", (char *)"F", nru, n, &work[1], &work[np1], &u[
u_offset], ldu, (ftnlen)1, (ftnlen)1, (ftnlen)1);
} else {
dlasr_((char *)"R", (char *)"V", (char *)"F", nru, &np1, &work[1], &work[np1], &u[
u_offset], ldu, (ftnlen)1, (ftnlen)1, (ftnlen)1);
}
}
if (*ncc > 0) {
if (sqre1 == 0) {
dlasr_((char *)"L", (char *)"V", (char *)"F", n, ncc, &work[1], &work[np1], &c__[
c_offset], ldc, (ftnlen)1, (ftnlen)1, (ftnlen)1);
} else {
dlasr_((char *)"L", (char *)"V", (char *)"F", &np1, ncc, &work[1], &work[np1], &c__[
c_offset], ldc, (ftnlen)1, (ftnlen)1, (ftnlen)1);
}
}
}
/* Call DBDSQR to compute the SVD of the reduced real */
/* N-by-N upper bidiagonal matrix. */
dbdsqr_((char *)"U", n, ncvt, nru, ncc, &d__[1], &e[1], &vt[vt_offset], ldvt, &u[
u_offset], ldu, &c__[c_offset], ldc, &work[1], info, (ftnlen)1);
/* Sort the singular values into ascending order (insertion sort on */
/* singular values, but only one transposition per singular vector) */
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
/* Scan for smallest D(I). */
isub = i__;
smin = d__[i__];
i__2 = *n;
for (j = i__ + 1; j <= i__2; ++j) {
if (d__[j] < smin) {
isub = j;
smin = d__[j];
}
/* L30: */
}
if (isub != i__) {
/* Swap singular values and vectors. */
d__[isub] = d__[i__];
d__[i__] = smin;
if (*ncvt > 0) {
dswap_(ncvt, &vt[isub + vt_dim1], ldvt, &vt[i__ + vt_dim1],
ldvt);
}
if (*nru > 0) {
dswap_(nru, &u[isub * u_dim1 + 1], &c__1, &u[i__ * u_dim1 + 1]
, &c__1);
}
if (*ncc > 0) {
dswap_(ncc, &c__[isub + c_dim1], ldc, &c__[i__ + c_dim1], ldc)
;
}
}
/* L40: */
}
return 0;
/* End of DLASDQ */
} /* dlasdq_ */
#ifdef __cplusplus
}
#endif
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