"atomic bomb" commit. Reorganized OpenCV directory structure
This commit is contained in:
Vadim Pisarevsky
436
3rdparty/lapack/sstein.c
vendored
Normal file
436
3rdparty/lapack/sstein.c
vendored
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@@ -0,0 +1,436 @@
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#include "clapack.h"
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/* Table of constant values */
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static integer c__2 = 2;
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static integer c__1 = 1;
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static integer c_n1 = -1;
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/* Subroutine */ int sstein_(integer *n, real *d__, real *e, integer *m, real
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*w, integer *iblock, integer *isplit, real *z__, integer *ldz, real *
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work, integer *iwork, integer *ifail, integer *info)
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{
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/* System generated locals */
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integer z_dim1, z_offset, i__1, i__2, i__3;
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real r__1, r__2, r__3, r__4, r__5;
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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__, j, b1, j1, bn;
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real xj, scl, eps, ctr, sep, nrm, tol;
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integer its;
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real xjm, eps1;
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integer jblk, nblk, jmax;
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extern doublereal sdot_(integer *, real *, integer *, real *, integer *),
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snrm2_(integer *, real *, integer *);
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integer iseed[4], gpind, iinfo;
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extern /* Subroutine */ int sscal_(integer *, real *, real *, integer *);
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extern doublereal sasum_(integer *, real *, integer *);
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extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *,
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integer *);
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real ortol;
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extern /* Subroutine */ int saxpy_(integer *, real *, real *, integer *,
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real *, integer *);
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integer indrv1, indrv2, indrv3, indrv4, indrv5;
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extern doublereal slamch_(char *);
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extern /* Subroutine */ int xerbla_(char *, integer *), slagtf_(
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integer *, real *, real *, real *, real *, real *, real *,
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integer *, integer *);
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integer nrmchk;
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extern integer isamax_(integer *, real *, integer *);
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extern /* Subroutine */ int slagts_(integer *, integer *, real *, real *,
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real *, real *, integer *, real *, real *, integer *);
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integer blksiz;
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real onenrm, pertol;
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extern /* Subroutine */ int slarnv_(integer *, integer *, integer *, real
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*);
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real stpcrt;
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/* -- LAPACK routine (version 3.1) -- */
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/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
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/* November 2006 */
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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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/* SSTEIN computes the eigenvectors of a real symmetric tridiagonal */
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/* matrix T corresponding to specified eigenvalues, using inverse */
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/* iteration. */
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/* The maximum number of iterations allowed for each eigenvector is */
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/* specified by an internal parameter MAXITS (currently set to 5). */
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/* Arguments */
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/* ========= */
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/* N (input) INTEGER */
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/* The order of the matrix. N >= 0. */
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/* D (input) REAL array, dimension (N) */
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/* The n diagonal elements of the tridiagonal matrix T. */
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/* E (input) REAL array, dimension (N-1) */
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/* The (n-1) subdiagonal elements of the tridiagonal matrix */
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/* T, in elements 1 to N-1. */
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/* M (input) INTEGER */
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/* The number of eigenvectors to be found. 0 <= M <= N. */
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/* W (input) REAL array, dimension (N) */
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/* The first M elements of W contain the eigenvalues for */
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/* which eigenvectors are to be computed. The eigenvalues */
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/* should be grouped by split-off block and ordered from */
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/* smallest to largest within the block. ( The output array */
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/* W from SSTEBZ with ORDER = 'B' is expected here. ) */
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/* IBLOCK (input) INTEGER array, dimension (N) */
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/* The submatrix indices associated with the corresponding */
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/* eigenvalues in W; IBLOCK(i)=1 if eigenvalue W(i) belongs to */
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/* the first submatrix from the top, =2 if W(i) belongs to */
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/* the second submatrix, etc. ( The output array IBLOCK */
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/* from SSTEBZ is expected here. ) */
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/* ISPLIT (input) INTEGER array, dimension (N) */
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/* The splitting points, at which T breaks up into submatrices. */
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/* The first submatrix consists of rows/columns 1 to */
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/* ISPLIT( 1 ), the second of rows/columns ISPLIT( 1 )+1 */
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/* through ISPLIT( 2 ), etc. */
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/* ( The output array ISPLIT from SSTEBZ is expected here. ) */
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/* Z (output) REAL array, dimension (LDZ, M) */
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/* The computed eigenvectors. The eigenvector associated */
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/* with the eigenvalue W(i) is stored in the i-th column of */
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/* Z. Any vector which fails to converge is set to its current */
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/* iterate after MAXITS iterations. */
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/* LDZ (input) INTEGER */
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/* The leading dimension of the array Z. LDZ >= max(1,N). */
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/* WORK (workspace) REAL array, dimension (5*N) */
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/* IWORK (workspace) INTEGER array, dimension (N) */
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/* IFAIL (output) INTEGER array, dimension (M) */
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/* On normal exit, all elements of IFAIL are zero. */
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/* If one or more eigenvectors fail to converge after */
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/* MAXITS iterations, then their indices are stored in */
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/* array IFAIL. */
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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: if INFO = i, then i eigenvectors failed to converge */
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/* in MAXITS iterations. Their indices are stored in */
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/* array IFAIL. */
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/* Internal Parameters */
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/* =================== */
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/* MAXITS INTEGER, default = 5 */
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/* The maximum number of iterations performed. */
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/* EXTRA INTEGER, default = 2 */
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/* The number of iterations performed after norm growth */
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/* criterion is satisfied, should be at least 1. */
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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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/* .. Local Arrays .. */
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/* .. */
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/* .. External Functions .. */
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/* .. */
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/* .. External Subroutines .. */
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/* .. */
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/* .. Intrinsic Functions .. */
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/* .. */
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/* .. Executable Statements .. */
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/* Test the input parameters. */
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/* Parameter adjustments */
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--d__;
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--e;
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--w;
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--iblock;
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--isplit;
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z_dim1 = *ldz;
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z_offset = 1 + z_dim1;
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z__ -= z_offset;
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--work;
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--iwork;
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--ifail;
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/* Function Body */
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*info = 0;
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i__1 = *m;
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for (i__ = 1; i__ <= i__1; ++i__) {
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ifail[i__] = 0;
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/* L10: */
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}
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if (*n < 0) {
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*info = -1;
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} else if (*m < 0 || *m > *n) {
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*info = -4;
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} else if (*ldz < max(1,*n)) {
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*info = -9;
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} else {
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i__1 = *m;
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for (j = 2; j <= i__1; ++j) {
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if (iblock[j] < iblock[j - 1]) {
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*info = -6;
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goto L30;
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}
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if (iblock[j] == iblock[j - 1] && w[j] < w[j - 1]) {
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*info = -5;
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goto L30;
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}
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/* L20: */
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}
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L30:
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;
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}
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if (*info != 0) {
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i__1 = -(*info);
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xerbla_("SSTEIN", &i__1);
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return 0;
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}
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/* Quick return if possible */
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if (*n == 0 || *m == 0) {
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return 0;
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} else if (*n == 1) {
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z__[z_dim1 + 1] = 1.f;
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return 0;
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}
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/* Get machine constants. */
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eps = slamch_("Precision");
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/* Initialize seed for random number generator SLARNV. */
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for (i__ = 1; i__ <= 4; ++i__) {
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iseed[i__ - 1] = 1;
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/* L40: */
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}
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/* Initialize pointers. */
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indrv1 = 0;
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indrv2 = indrv1 + *n;
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indrv3 = indrv2 + *n;
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indrv4 = indrv3 + *n;
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indrv5 = indrv4 + *n;
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/* Compute eigenvectors of matrix blocks. */
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j1 = 1;
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i__1 = iblock[*m];
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for (nblk = 1; nblk <= i__1; ++nblk) {
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/* Find starting and ending indices of block nblk. */
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if (nblk == 1) {
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b1 = 1;
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} else {
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b1 = isplit[nblk - 1] + 1;
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}
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bn = isplit[nblk];
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blksiz = bn - b1 + 1;
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if (blksiz == 1) {
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goto L60;
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}
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gpind = b1;
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/* Compute reorthogonalization criterion and stopping criterion. */
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onenrm = (r__1 = d__[b1], dabs(r__1)) + (r__2 = e[b1], dabs(r__2));
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/* Computing MAX */
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r__3 = onenrm, r__4 = (r__1 = d__[bn], dabs(r__1)) + (r__2 = e[bn - 1]
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, dabs(r__2));
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onenrm = dmax(r__3,r__4);
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i__2 = bn - 1;
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for (i__ = b1 + 1; i__ <= i__2; ++i__) {
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/* Computing MAX */
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r__4 = onenrm, r__5 = (r__1 = d__[i__], dabs(r__1)) + (r__2 = e[
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i__ - 1], dabs(r__2)) + (r__3 = e[i__], dabs(r__3));
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onenrm = dmax(r__4,r__5);
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/* L50: */
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}
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ortol = onenrm * .001f;
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stpcrt = sqrt(.1f / blksiz);
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/* Loop through eigenvalues of block nblk. */
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L60:
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jblk = 0;
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i__2 = *m;
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for (j = j1; j <= i__2; ++j) {
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if (iblock[j] != nblk) {
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j1 = j;
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goto L160;
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}
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++jblk;
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xj = w[j];
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/* Skip all the work if the block size is one. */
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if (blksiz == 1) {
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work[indrv1 + 1] = 1.f;
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goto L120;
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}
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/* If eigenvalues j and j-1 are too close, add a relatively */
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/* small perturbation. */
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if (jblk > 1) {
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eps1 = (r__1 = eps * xj, dabs(r__1));
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pertol = eps1 * 10.f;
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sep = xj - xjm;
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if (sep < pertol) {
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xj = xjm + pertol;
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}
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}
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its = 0;
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nrmchk = 0;
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/* Get random starting vector. */
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slarnv_(&c__2, iseed, &blksiz, &work[indrv1 + 1]);
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/* Copy the matrix T so it won't be destroyed in factorization. */
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scopy_(&blksiz, &d__[b1], &c__1, &work[indrv4 + 1], &c__1);
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i__3 = blksiz - 1;
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scopy_(&i__3, &e[b1], &c__1, &work[indrv2 + 2], &c__1);
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i__3 = blksiz - 1;
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scopy_(&i__3, &e[b1], &c__1, &work[indrv3 + 1], &c__1);
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/* Compute LU factors with partial pivoting ( PT = LU ) */
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tol = 0.f;
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slagtf_(&blksiz, &work[indrv4 + 1], &xj, &work[indrv2 + 2], &work[
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indrv3 + 1], &tol, &work[indrv5 + 1], &iwork[1], &iinfo);
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/* Update iteration count. */
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L70:
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++its;
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if (its > 5) {
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goto L100;
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}
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/* Normalize and scale the righthand side vector Pb. */
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/* Computing MAX */
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r__2 = eps, r__3 = (r__1 = work[indrv4 + blksiz], dabs(r__1));
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scl = blksiz * onenrm * dmax(r__2,r__3) / sasum_(&blksiz, &work[
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indrv1 + 1], &c__1);
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sscal_(&blksiz, &scl, &work[indrv1 + 1], &c__1);
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/* Solve the system LU = Pb. */
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slagts_(&c_n1, &blksiz, &work[indrv4 + 1], &work[indrv2 + 2], &
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work[indrv3 + 1], &work[indrv5 + 1], &iwork[1], &work[
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indrv1 + 1], &tol, &iinfo);
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/* Reorthogonalize by modified Gram-Schmidt if eigenvalues are */
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/* close enough. */
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if (jblk == 1) {
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goto L90;
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}
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if ((r__1 = xj - xjm, dabs(r__1)) > ortol) {
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gpind = j;
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}
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if (gpind != j) {
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i__3 = j - 1;
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for (i__ = gpind; i__ <= i__3; ++i__) {
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ctr = -sdot_(&blksiz, &work[indrv1 + 1], &c__1, &z__[b1 +
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i__ * z_dim1], &c__1);
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saxpy_(&blksiz, &ctr, &z__[b1 + i__ * z_dim1], &c__1, &
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work[indrv1 + 1], &c__1);
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/* L80: */
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}
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}
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/* Check the infinity norm of the iterate. */
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L90:
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jmax = isamax_(&blksiz, &work[indrv1 + 1], &c__1);
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nrm = (r__1 = work[indrv1 + jmax], dabs(r__1));
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/* Continue for additional iterations after norm reaches */
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/* stopping criterion. */
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if (nrm < stpcrt) {
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goto L70;
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}
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++nrmchk;
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if (nrmchk < 3) {
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goto L70;
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}
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goto L110;
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/* If stopping criterion was not satisfied, update info and */
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/* store eigenvector number in array ifail. */
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L100:
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++(*info);
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ifail[*info] = j;
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/* Accept iterate as jth eigenvector. */
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L110:
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scl = 1.f / snrm2_(&blksiz, &work[indrv1 + 1], &c__1);
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jmax = isamax_(&blksiz, &work[indrv1 + 1], &c__1);
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if (work[indrv1 + jmax] < 0.f) {
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scl = -scl;
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}
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sscal_(&blksiz, &scl, &work[indrv1 + 1], &c__1);
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L120:
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i__3 = *n;
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for (i__ = 1; i__ <= i__3; ++i__) {
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z__[i__ + j * z_dim1] = 0.f;
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/* L130: */
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}
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i__3 = blksiz;
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for (i__ = 1; i__ <= i__3; ++i__) {
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z__[b1 + i__ - 1 + j * z_dim1] = work[indrv1 + i__];
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/* L140: */
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}
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/* Save the shift to check eigenvalue spacing at next */
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/* iteration. */
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xjm = xj;
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/* L150: */
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}
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L160:
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;
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}
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return 0;
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/* End of SSTEIN */
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} /* sstein_ */
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