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convert linalg library from Fortran to C++

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Axel Kohlmeyer
2022-12-28 13:18:38 -05:00
parent 7cceabe5bd
commit c5a87f75d6
410 changed files with 80736 additions and 30 deletions
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lib/linalg/dlasq1.cpp Normal file
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/* fortran/dlasq1.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;
static integer c__2 = 2;
static integer c__0 = 0;
/* > \brief \b DLASQ1 computes the singular values of a real square bidiagonal matrix. Used by sbdsqr. */
/* =========== DOCUMENTATION =========== */
/* Online html documentation available at */
/* http://www.netlib.org/lapack/explore-html/ */
/* > \htmlonly */
/* > Download DLASQ1 + dependencies */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlasq1.
f"> */
/* > [TGZ]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlasq1.
f"> */
/* > [ZIP]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlasq1.
f"> */
/* > [TXT]</a> */
/* > \endhtmlonly */
/* Definition: */
/* =========== */
/* SUBROUTINE DLASQ1( N, D, E, WORK, INFO ) */
/* .. Scalar Arguments .. */
/* INTEGER INFO, N */
/* .. */
/* .. Array Arguments .. */
/* DOUBLE PRECISION D( * ), E( * ), WORK( * ) */
/* .. */
/* > \par Purpose: */
/* ============= */
/* > */
/* > \verbatim */
/* > */
/* > DLASQ1 computes the singular values of a real N-by-N bidiagonal */
/* > matrix with diagonal D and off-diagonal E. The singular values */
/* > are computed to high relative accuracy, in the absence of */
/* > denormalization, underflow and overflow. The algorithm was first */
/* > presented in */
/* > */
/* > (char *)"Accurate singular values and differential qd algorithms" by K. V. */
/* > Fernando and B. N. Parlett, Numer. Math., Vol-67, No. 2, pp. 191-230, */
/* > 1994, */
/* > */
/* > and the present implementation is described in "An implementation of */
/* > the dqds Algorithm (Positive Case)", LAPACK Working Note. */
/* > \endverbatim */
/* Arguments: */
/* ========== */
/* > \param[in] N */
/* > \verbatim */
/* > N is INTEGER */
/* > The number of rows and columns in the matrix. N >= 0. */
/* > \endverbatim */
/* > */
/* > \param[in,out] D */
/* > \verbatim */
/* > D is DOUBLE PRECISION array, dimension (N) */
/* > On entry, D contains the diagonal elements of the */
/* > bidiagonal matrix whose SVD is desired. On normal exit, */
/* > D contains the singular values in decreasing order. */
/* > \endverbatim */
/* > */
/* > \param[in,out] E */
/* > \verbatim */
/* > E is DOUBLE PRECISION array, dimension (N) */
/* > On entry, elements E(1:N-1) contain the off-diagonal elements */
/* > of the bidiagonal matrix whose SVD is desired. */
/* > On exit, E is overwritten. */
/* > \endverbatim */
/* > */
/* > \param[out] WORK */
/* > \verbatim */
/* > WORK is DOUBLE PRECISION array, dimension (4*N) */
/* > \endverbatim */
/* > */
/* > \param[out] INFO */
/* > \verbatim */
/* > INFO is INTEGER */
/* > = 0: successful exit */
/* > < 0: if INFO = -i, the i-th argument had an illegal value */
/* > > 0: the algorithm failed */
/* > = 1, a split was marked by a positive value in E */
/* > = 2, current block of Z not diagonalized after 100*N */
/* > iterations (in inner while loop) On exit D and E */
/* > represent a matrix with the same singular values */
/* > which the calling subroutine could use to finish the */
/* > computation, or even feed back into DLASQ1 */
/* > = 3, termination criterion of outer while loop not met */
/* > (program created more than N unreduced blocks) */
/* > \endverbatim */
/* Authors: */
/* ======== */
/* > \author Univ. of Tennessee */
/* > \author Univ. of California Berkeley */
/* > \author Univ. of Colorado Denver */
/* > \author NAG Ltd. */
/* > \ingroup auxOTHERcomputational */
/* ===================================================================== */
/* Subroutine */ int dlasq1_(integer *n, doublereal *d__, doublereal *e,
doublereal *work, integer *info)
{
/* System generated locals */
integer i__1, i__2;
doublereal d__1, d__2, d__3;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
integer i__;
doublereal eps;
extern /* Subroutine */ int dlas2_(doublereal *, doublereal *, doublereal
*, doublereal *, doublereal *);
doublereal scale;
integer iinfo;
doublereal sigmn;
extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *,
doublereal *, integer *);
doublereal sigmx;
extern /* Subroutine */ int dlasq2_(integer *, doublereal *, integer *);
extern doublereal dlamch_(char *, ftnlen);
extern /* Subroutine */ int dlascl_(char *, integer *, integer *,
doublereal *, doublereal *, integer *, integer *, doublereal *,
integer *, integer *, ftnlen);
doublereal safmin;
extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen), dlasrt_(
char *, integer *, doublereal *, integer *, ftnlen);
/* -- LAPACK computational 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 .. */
/* Parameter adjustments */
--work;
--e;
--d__;
/* Function Body */
*info = 0;
if (*n < 0) {
*info = -1;
i__1 = -(*info);
xerbla_((char *)"DLASQ1", &i__1, (ftnlen)6);
return 0;
} else if (*n == 0) {
return 0;
} else if (*n == 1) {
d__[1] = abs(d__[1]);
return 0;
} else if (*n == 2) {
dlas2_(&d__[1], &e[1], &d__[2], &sigmn, &sigmx);
d__[1] = sigmx;
d__[2] = sigmn;
return 0;
}
/* Estimate the largest singular value. */
sigmx = 0.;
i__1 = *n - 1;
for (i__ = 1; i__ <= i__1; ++i__) {
d__[i__] = (d__1 = d__[i__], abs(d__1));
/* Computing MAX */
d__2 = sigmx, d__3 = (d__1 = e[i__], abs(d__1));
sigmx = max(d__2,d__3);
/* L10: */
}
d__[*n] = (d__1 = d__[*n], abs(d__1));
/* Early return if SIGMX is zero (matrix is already diagonal). */
if (sigmx == 0.) {
dlasrt_((char *)"D", n, &d__[1], &iinfo, (ftnlen)1);
return 0;
}
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
/* Computing MAX */
d__1 = sigmx, d__2 = d__[i__];
sigmx = max(d__1,d__2);
/* L20: */
}
/* Copy D and E into WORK (in the Z format) and scale (squaring the */
/* input data makes scaling by a power of the radix pointless). */
eps = dlamch_((char *)"Precision", (ftnlen)9);
safmin = dlamch_((char *)"Safe minimum", (ftnlen)12);
scale = sqrt(eps / safmin);
dcopy_(n, &d__[1], &c__1, &work[1], &c__2);
i__1 = *n - 1;
dcopy_(&i__1, &e[1], &c__1, &work[2], &c__2);
i__1 = (*n << 1) - 1;
i__2 = (*n << 1) - 1;
dlascl_((char *)"G", &c__0, &c__0, &sigmx, &scale, &i__1, &c__1, &work[1], &i__2,
&iinfo, (ftnlen)1);
/* Compute the q's and e's. */
i__1 = (*n << 1) - 1;
for (i__ = 1; i__ <= i__1; ++i__) {
/* Computing 2nd power */
d__1 = work[i__];
work[i__] = d__1 * d__1;
/* L30: */
}
work[*n * 2] = 0.;
dlasq2_(n, &work[1], info);
if (*info == 0) {
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
d__[i__] = sqrt(work[i__]);
/* L40: */
}
dlascl_((char *)"G", &c__0, &c__0, &scale, &sigmx, n, &c__1, &d__[1], n, &
iinfo, (ftnlen)1);
} else if (*info == 2) {
/* Maximum number of iterations exceeded. Move data from WORK */
/* into D and E so the calling subroutine can try to finish */
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
d__[i__] = sqrt(work[(i__ << 1) - 1]);
e[i__] = sqrt(work[i__ * 2]);
}
dlascl_((char *)"G", &c__0, &c__0, &scale, &sigmx, n, &c__1, &d__[1], n, &
iinfo, (ftnlen)1);
dlascl_((char *)"G", &c__0, &c__0, &scale, &sigmx, n, &c__1, &e[1], n, &iinfo,
(ftnlen)1);
}
return 0;
/* End of DLASQ1 */
} /* dlasq1_ */
#ifdef __cplusplus
}
#endif