217 lines
6.2 KiB
C
217 lines
6.2 KiB
C
/* slasq1.f -- translated by f2c (version 20061008).
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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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#include "clapack.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__2 = 2;
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static integer c__0 = 0;
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/* Subroutine */ int slasq1_(integer *n, real *d__, real *e, real *work,
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integer *info)
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{
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/* System generated locals */
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integer i__1, i__2;
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real r__1, r__2, r__3;
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/* Builtin functions */
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double sqrt(doublereal);
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/* Local variables */
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integer i__;
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real eps;
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extern /* Subroutine */ int slas2_(real *, real *, real *, real *, real *)
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;
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real scale;
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integer iinfo;
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real sigmn, sigmx;
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extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *,
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integer *), slasq2_(integer *, real *, integer *);
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extern doublereal slamch_(char *);
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real safmin;
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extern /* Subroutine */ int xerbla_(char *, integer *), slascl_(
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char *, integer *, integer *, real *, real *, integer *, integer *
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, real *, integer *, integer *), slasrt_(char *, integer *
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, real *, integer *);
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/* -- LAPACK routine (version 3.2) -- */
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/* -- Contributed by Osni Marques of the Lawrence Berkeley National -- */
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/* -- Laboratory and Beresford Parlett of the Univ. of California at -- */
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/* -- Berkeley -- */
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/* -- November 2008 -- */
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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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/* Purpose */
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/* ======= */
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/* SLASQ1 computes the singular values of a real N-by-N bidiagonal */
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/* matrix with diagonal D and off-diagonal E. The singular values */
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/* are computed to high relative accuracy, in the absence of */
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/* denormalization, underflow and overflow. The algorithm was first */
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/* presented in */
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/* "Accurate singular values and differential qd algorithms" by K. V. */
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/* Fernando and B. N. Parlett, Numer. Math., Vol-67, No. 2, pp. 191-230, */
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/* 1994, */
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/* and the present implementation is described in "An implementation of */
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/* the dqds Algorithm (Positive Case)", LAPACK Working Note. */
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/* Arguments */
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/* ========= */
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/* N (input) INTEGER */
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/* The number of rows and columns in the matrix. N >= 0. */
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/* D (input/output) REAL array, dimension (N) */
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/* On entry, D contains the diagonal elements of the */
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/* bidiagonal matrix whose SVD is desired. On normal exit, */
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/* D contains the singular values in decreasing order. */
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/* E (input/output) REAL array, dimension (N) */
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/* On entry, elements E(1:N-1) contain the off-diagonal elements */
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/* of the bidiagonal matrix whose SVD is desired. */
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/* On exit, E is overwritten. */
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/* WORK (workspace) REAL array, dimension (4*N) */
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/* INFO (output) 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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/* > 0: the algorithm failed */
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/* = 1, a split was marked by a positive value in E */
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/* = 2, current block of Z not diagonalized after 30*N */
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/* iterations (in inner while loop) */
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/* = 3, termination criterion of outer while loop not met */
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/* (program created more than N unreduced blocks) */
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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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/* .. External Functions .. */
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/* .. */
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/* .. Intrinsic Functions .. */
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/* .. */
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/* .. Executable Statements .. */
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/* Parameter adjustments */
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--work;
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--e;
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--d__;
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/* Function Body */
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*info = 0;
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if (*n < 0) {
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*info = -2;
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i__1 = -(*info);
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xerbla_("SLASQ1", &i__1);
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return 0;
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} else if (*n == 0) {
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return 0;
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} else if (*n == 1) {
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d__[1] = dabs(d__[1]);
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return 0;
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} else if (*n == 2) {
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slas2_(&d__[1], &e[1], &d__[2], &sigmn, &sigmx);
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d__[1] = sigmx;
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d__[2] = sigmn;
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return 0;
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}
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/* Estimate the largest singular value. */
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sigmx = 0.f;
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i__1 = *n - 1;
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for (i__ = 1; i__ <= i__1; ++i__) {
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d__[i__] = (r__1 = d__[i__], dabs(r__1));
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/* Computing MAX */
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r__2 = sigmx, r__3 = (r__1 = e[i__], dabs(r__1));
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sigmx = dmax(r__2,r__3);
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/* L10: */
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}
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d__[*n] = (r__1 = d__[*n], dabs(r__1));
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/* Early return if SIGMX is zero (matrix is already diagonal). */
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if (sigmx == 0.f) {
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slasrt_("D", n, &d__[1], &iinfo);
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return 0;
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}
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i__1 = *n;
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for (i__ = 1; i__ <= i__1; ++i__) {
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/* Computing MAX */
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r__1 = sigmx, r__2 = d__[i__];
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sigmx = dmax(r__1,r__2);
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/* L20: */
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}
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/* Copy D and E into WORK (in the Z format) and scale (squaring the */
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/* input data makes scaling by a power of the radix pointless). */
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eps = slamch_("Precision");
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safmin = slamch_("Safe minimum");
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scale = sqrt(eps / safmin);
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scopy_(n, &d__[1], &c__1, &work[1], &c__2);
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i__1 = *n - 1;
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scopy_(&i__1, &e[1], &c__1, &work[2], &c__2);
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i__1 = (*n << 1) - 1;
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i__2 = (*n << 1) - 1;
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slascl_("G", &c__0, &c__0, &sigmx, &scale, &i__1, &c__1, &work[1], &i__2,
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&iinfo);
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/* Compute the q's and e's. */
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i__1 = (*n << 1) - 1;
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for (i__ = 1; i__ <= i__1; ++i__) {
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/* Computing 2nd power */
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r__1 = work[i__];
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work[i__] = r__1 * r__1;
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/* L30: */
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}
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work[*n * 2] = 0.f;
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slasq2_(n, &work[1], info);
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if (*info == 0) {
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i__1 = *n;
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for (i__ = 1; i__ <= i__1; ++i__) {
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d__[i__] = sqrt(work[i__]);
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/* L40: */
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}
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slascl_("G", &c__0, &c__0, &scale, &sigmx, n, &c__1, &d__[1], n, &
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iinfo);
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}
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return 0;
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/* End of SLASQ1 */
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} /* slasq1_ */
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