--- /dev/null
+#include "clapack.h"
+
+/* Table of constant values */
+
+static integer c__1 = 1;
+static integer c__2 = 2;
+static integer c__0 = 0;
+
+/* Subroutine */ int slasq1_(integer *n, real *d__, real *e, real *work,
+ integer *info)
+{
+ /* System generated locals */
+ integer i__1, i__2;
+ real r__1, r__2, r__3;
+
+ /* Builtin functions */
+ double sqrt(doublereal);
+
+ /* Local variables */
+ integer i__;
+ real eps;
+ extern /* Subroutine */ int slas2_(real *, real *, real *, real *, real *)
+ ;
+ real scale;
+ integer iinfo;
+ real sigmn, sigmx;
+ extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *,
+ integer *), slasq2_(integer *, real *, integer *);
+ extern doublereal slamch_(char *);
+ real safmin;
+ extern /* Subroutine */ int xerbla_(char *, integer *), slascl_(
+ char *, integer *, integer *, real *, real *, integer *, integer *
+, real *, integer *, integer *), slasrt_(char *, integer *
+, real *, integer *);
+
+
+/* -- LAPACK routine (version 3.1) -- */
+/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
+/* November 2006 */
+
+/* .. Scalar Arguments .. */
+/* .. */
+/* .. Array Arguments .. */
+/* .. */
+
+/* Purpose */
+/* ======= */
+
+/* SLASQ1 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 */
+
+/* "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. */
+
+/* Arguments */
+/* ========= */
+
+/* N (input) INTEGER */
+/* The number of rows and columns in the matrix. N >= 0. */
+
+/* D (input/output) REAL 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. */
+
+/* E (input/output) REAL 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. */
+
+/* WORK (workspace) REAL array, dimension (4*N) */
+
+/* INFO (output) 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 30*N */
+/* iterations (in inner while loop) */
+/* = 3, termination criterion of outer while loop not met */
+/* (program created more than N unreduced blocks) */
+
+/* ===================================================================== */
+
+/* .. Parameters .. */
+/* .. */
+/* .. Local Scalars .. */
+/* .. */
+/* .. External Subroutines .. */
+/* .. */
+/* .. External Functions .. */
+/* .. */
+/* .. Intrinsic Functions .. */
+/* .. */
+/* .. Executable Statements .. */
+
+ /* Parameter adjustments */
+ --work;
+ --e;
+ --d__;
+
+ /* Function Body */
+ *info = 0;
+ if (*n < 0) {
+ *info = -2;
+ i__1 = -(*info);
+ xerbla_("SLASQ1", &i__1);
+ return 0;
+ } else if (*n == 0) {
+ return 0;
+ } else if (*n == 1) {
+ d__[1] = dabs(d__[1]);
+ return 0;
+ } else if (*n == 2) {
+ slas2_(&d__[1], &e[1], &d__[2], &sigmn, &sigmx);
+ d__[1] = sigmx;
+ d__[2] = sigmn;
+ return 0;
+ }
+
+/* Estimate the largest singular value. */
+
+ sigmx = 0.f;
+ i__1 = *n - 1;
+ for (i__ = 1; i__ <= i__1; ++i__) {
+ d__[i__] = (r__1 = d__[i__], dabs(r__1));
+/* Computing MAX */
+ r__2 = sigmx, r__3 = (r__1 = e[i__], dabs(r__1));
+ sigmx = dmax(r__2,r__3);
+/* L10: */
+ }
+ d__[*n] = (r__1 = d__[*n], dabs(r__1));
+
+/* Early return if SIGMX is zero (matrix is already diagonal). */
+
+ if (sigmx == 0.f) {
+ slasrt_("D", n, &d__[1], &iinfo);
+ return 0;
+ }
+
+ i__1 = *n;
+ for (i__ = 1; i__ <= i__1; ++i__) {
+/* Computing MAX */
+ r__1 = sigmx, r__2 = d__[i__];
+ sigmx = dmax(r__1,r__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 = slamch_("Precision");
+ safmin = slamch_("Safe minimum");
+ scale = sqrt(eps / safmin);
+ scopy_(n, &d__[1], &c__1, &work[1], &c__2);
+ i__1 = *n - 1;
+ scopy_(&i__1, &e[1], &c__1, &work[2], &c__2);
+ i__1 = (*n << 1) - 1;
+ i__2 = (*n << 1) - 1;
+ slascl_("G", &c__0, &c__0, &sigmx, &scale, &i__1, &c__1, &work[1], &i__2,
+ &iinfo);
+
+/* Compute the q's and e's. */
+
+ i__1 = (*n << 1) - 1;
+ for (i__ = 1; i__ <= i__1; ++i__) {
+/* Computing 2nd power */
+ r__1 = work[i__];
+ work[i__] = r__1 * r__1;
+/* L30: */
+ }
+ work[*n * 2] = 0.f;
+
+ slasq2_(n, &work[1], info);
+
+ if (*info == 0) {
+ i__1 = *n;
+ for (i__ = 1; i__ <= i__1; ++i__) {
+ d__[i__] = sqrt(work[i__]);
+/* L40: */
+ }
+ slascl_("G", &c__0, &c__0, &scale, &sigmx, n, &c__1, &d__[1], n, &
+ iinfo);
+ }
+
+ return 0;
+
+/* End of SLASQ1 */
+
+} /* slasq1_ */
projects / opencv / blobdiff