--- /dev/null
+#include "clapack.h"
+
+/* Table of constant values */
+
+static integer c__0 = 0;
+static doublereal c_b7 = 1.;
+static integer c__1 = 1;
+static integer c_n1 = -1;
+
+/* Subroutine */ int dlasd6_(integer *icompq, integer *nl, integer *nr,
+ integer *sqre, doublereal *d__, doublereal *vf, doublereal *vl,
+ doublereal *alpha, doublereal *beta, integer *idxq, integer *perm,
+ integer *givptr, integer *givcol, integer *ldgcol, doublereal *givnum,
+ integer *ldgnum, doublereal *poles, doublereal *difl, doublereal *
+ difr, doublereal *z__, integer *k, doublereal *c__, doublereal *s,
+ doublereal *work, integer *iwork, integer *info)
+{
+ /* System generated locals */
+ integer givcol_dim1, givcol_offset, givnum_dim1, givnum_offset,
+ poles_dim1, poles_offset, i__1;
+ doublereal d__1, d__2;
+
+ /* Local variables */
+ integer i__, m, n, n1, n2, iw, idx, idxc, idxp, ivfw, ivlw;
+ extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *,
+ doublereal *, integer *), dlasd7_(integer *, integer *, integer *,
+ integer *, integer *, doublereal *, doublereal *, doublereal *,
+ doublereal *, doublereal *, doublereal *, doublereal *,
+ doublereal *, doublereal *, doublereal *, integer *, integer *,
+ integer *, integer *, integer *, integer *, integer *, doublereal
+ *, integer *, doublereal *, doublereal *, integer *), dlasd8_(
+ integer *, integer *, doublereal *, doublereal *, doublereal *,
+ doublereal *, doublereal *, doublereal *, integer *, doublereal *,
+ doublereal *, integer *), dlascl_(char *, integer *, integer *,
+ doublereal *, doublereal *, integer *, integer *, doublereal *,
+ integer *, integer *), dlamrg_(integer *, integer *,
+ doublereal *, integer *, integer *, integer *);
+ integer isigma;
+ extern /* Subroutine */ int xerbla_(char *, integer *);
+ doublereal orgnrm;
+
+
+/* -- LAPACK auxiliary routine (version 3.1) -- */
+/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
+/* November 2006 */
+
+/* .. Scalar Arguments .. */
+/* .. */
+/* .. Array Arguments .. */
+/* .. */
+
+/* Purpose */
+/* ======= */
+
+/* DLASD6 computes the SVD of an updated upper bidiagonal matrix B */
+/* obtained by merging two smaller ones by appending a row. This */
+/* routine is used only for the problem which requires all singular */
+/* values and optionally singular vector matrices in factored form. */
+/* B is an N-by-M matrix with N = NL + NR + 1 and M = N + SQRE. */
+/* A related subroutine, DLASD1, handles the case in which all singular */
+/* values and singular vectors of the bidiagonal matrix are desired. */
+
+/* DLASD6 computes the SVD as follows: */
+
+/* ( D1(in) 0 0 0 ) */
+/* B = U(in) * ( Z1' a Z2' b ) * VT(in) */
+/* ( 0 0 D2(in) 0 ) */
+
+/* = U(out) * ( D(out) 0) * VT(out) */
+
+/* where Z' = (Z1' a Z2' b) = u' VT', and u is a vector of dimension M */
+/* with ALPHA and BETA in the NL+1 and NL+2 th entries and zeros */
+/* elsewhere; and the entry b is empty if SQRE = 0. */
+
+/* The singular values of B can be computed using D1, D2, the first */
+/* components of all the right singular vectors of the lower block, and */
+/* the last components of all the right singular vectors of the upper */
+/* block. These components are stored and updated in VF and VL, */
+/* respectively, in DLASD6. Hence U and VT are not explicitly */
+/* referenced. */
+
+/* The singular values are stored in D. The algorithm consists of two */
+/* stages: */
+
+/* The first stage consists of deflating the size of the problem */
+/* when there are multiple singular values or if there is a zero */
+/* in the Z vector. For each such occurence the dimension of the */
+/* secular equation problem is reduced by one. This stage is */
+/* performed by the routine DLASD7. */
+
+/* The second stage consists of calculating the updated */
+/* singular values. This is done by finding the roots of the */
+/* secular equation via the routine DLASD4 (as called by DLASD8). */
+/* This routine also updates VF and VL and computes the distances */
+/* between the updated singular values and the old singular */
+/* values. */
+
+/* DLASD6 is called from DLASDA. */
+
+/* Arguments */
+/* ========= */
+
+/* ICOMPQ (input) INTEGER */
+/* Specifies whether singular vectors are to be computed in */
+/* factored form: */
+/* = 0: Compute singular values only. */
+/* = 1: Compute singular vectors in factored form as well. */
+
+/* NL (input) INTEGER */
+/* The row dimension of the upper block. NL >= 1. */
+
+/* NR (input) INTEGER */
+/* The row dimension of the lower block. NR >= 1. */
+
+/* SQRE (input) INTEGER */
+/* = 0: the lower block is an NR-by-NR square matrix. */
+/* = 1: the lower block is an NR-by-(NR+1) rectangular matrix. */
+
+/* The bidiagonal matrix has row dimension N = NL + NR + 1, */
+/* and column dimension M = N + SQRE. */
+
+/* D (input/output) DOUBLE PRECISION array, dimension ( NL+NR+1 ). */
+/* On entry D(1:NL,1:NL) contains the singular values of the */
+/* upper block, and D(NL+2:N) contains the singular values */
+/* of the lower block. On exit D(1:N) contains the singular */
+/* values of the modified matrix. */
+
+/* VF (input/output) DOUBLE PRECISION array, dimension ( M ) */
+/* On entry, VF(1:NL+1) contains the first components of all */
+/* right singular vectors of the upper block; and VF(NL+2:M) */
+/* contains the first components of all right singular vectors */
+/* of the lower block. On exit, VF contains the first components */
+/* of all right singular vectors of the bidiagonal matrix. */
+
+/* VL (input/output) DOUBLE PRECISION array, dimension ( M ) */
+/* On entry, VL(1:NL+1) contains the last components of all */
+/* right singular vectors of the upper block; and VL(NL+2:M) */
+/* contains the last components of all right singular vectors of */
+/* the lower block. On exit, VL contains the last components of */
+/* all right singular vectors of the bidiagonal matrix. */
+
+/* ALPHA (input/output) DOUBLE PRECISION */
+/* Contains the diagonal element associated with the added row. */
+
+/* BETA (input/output) DOUBLE PRECISION */
+/* Contains the off-diagonal element associated with the added */
+/* row. */
+
+/* IDXQ (output) INTEGER array, dimension ( N ) */
+/* This contains the permutation which will reintegrate the */
+/* subproblem just solved back into sorted order, i.e. */
+/* D( IDXQ( I = 1, N ) ) will be in ascending order. */
+
+/* PERM (output) INTEGER array, dimension ( N ) */
+/* The permutations (from deflation and sorting) to be applied */
+/* to each block. Not referenced if ICOMPQ = 0. */
+
+/* GIVPTR (output) INTEGER */
+/* The number of Givens rotations which took place in this */
+/* subproblem. Not referenced if ICOMPQ = 0. */
+
+/* GIVCOL (output) INTEGER array, dimension ( LDGCOL, 2 ) */
+/* Each pair of numbers indicates a pair of columns to take place */
+/* in a Givens rotation. Not referenced if ICOMPQ = 0. */
+
+/* LDGCOL (input) INTEGER */
+/* leading dimension of GIVCOL, must be at least N. */
+
+/* GIVNUM (output) DOUBLE PRECISION array, dimension ( LDGNUM, 2 ) */
+/* Each number indicates the C or S value to be used in the */
+/* corresponding Givens rotation. Not referenced if ICOMPQ = 0. */
+
+/* LDGNUM (input) INTEGER */
+/* The leading dimension of GIVNUM and POLES, must be at least N. */
+
+/* POLES (output) DOUBLE PRECISION array, dimension ( LDGNUM, 2 ) */
+/* On exit, POLES(1,*) is an array containing the new singular */
+/* values obtained from solving the secular equation, and */
+/* POLES(2,*) is an array containing the poles in the secular */
+/* equation. Not referenced if ICOMPQ = 0. */
+
+/* DIFL (output) DOUBLE PRECISION array, dimension ( N ) */
+/* On exit, DIFL(I) is the distance between I-th updated */
+/* (undeflated) singular value and the I-th (undeflated) old */
+/* singular value. */
+
+/* DIFR (output) DOUBLE PRECISION array, */
+/* dimension ( LDGNUM, 2 ) if ICOMPQ = 1 and */
+/* dimension ( N ) if ICOMPQ = 0. */
+/* On exit, DIFR(I, 1) is the distance between I-th updated */
+/* (undeflated) singular value and the I+1-th (undeflated) old */
+/* singular value. */
+
+/* If ICOMPQ = 1, DIFR(1:K,2) is an array containing the */
+/* normalizing factors for the right singular vector matrix. */
+
+/* See DLASD8 for details on DIFL and DIFR. */
+
+/* Z (output) DOUBLE PRECISION array, dimension ( M ) */
+/* The first elements of this array contain the components */
+/* of the deflation-adjusted updating row vector. */
+
+/* K (output) INTEGER */
+/* Contains the dimension of the non-deflated matrix, */
+/* This is the order of the related secular equation. 1 <= K <=N. */
+
+/* C (output) DOUBLE PRECISION */
+/* C contains garbage if SQRE =0 and the C-value of a Givens */
+/* rotation related to the right null space if SQRE = 1. */
+
+/* S (output) DOUBLE PRECISION */
+/* S contains garbage if SQRE =0 and the S-value of a Givens */
+/* rotation related to the right null space if SQRE = 1. */
+
+/* WORK (workspace) DOUBLE PRECISION array, dimension ( 4 * M ) */
+
+/* IWORK (workspace) INTEGER array, dimension ( 3 * N ) */
+
+/* INFO (output) INTEGER */
+/* = 0: successful exit. */
+/* < 0: if INFO = -i, the i-th argument had an illegal value. */
+/* > 0: if INFO = 1, an singular value did not converge */
+
+/* Further Details */
+/* =============== */
+
+/* Based on contributions by */
+/* Ming Gu and Huan Ren, Computer Science Division, University of */
+/* California at Berkeley, USA */
+
+/* ===================================================================== */
+
+/* .. Parameters .. */
+/* .. */
+/* .. Local Scalars .. */
+/* .. */
+/* .. External Subroutines .. */
+/* .. */
+/* .. Intrinsic Functions .. */
+/* .. */
+/* .. Executable Statements .. */
+
+/* Test the input parameters. */
+
+ /* Parameter adjustments */
+ --d__;
+ --vf;
+ --vl;
+ --idxq;
+ --perm;
+ givcol_dim1 = *ldgcol;
+ givcol_offset = 1 + givcol_dim1;
+ givcol -= givcol_offset;
+ poles_dim1 = *ldgnum;
+ poles_offset = 1 + poles_dim1;
+ poles -= poles_offset;
+ givnum_dim1 = *ldgnum;
+ givnum_offset = 1 + givnum_dim1;
+ givnum -= givnum_offset;
+ --difl;
+ --difr;
+ --z__;
+ --work;
+ --iwork;
+
+ /* Function Body */
+ *info = 0;
+ n = *nl + *nr + 1;
+ m = n + *sqre;
+
+ if (*icompq < 0 || *icompq > 1) {
+ *info = -1;
+ } else if (*nl < 1) {
+ *info = -2;
+ } else if (*nr < 1) {
+ *info = -3;
+ } else if (*sqre < 0 || *sqre > 1) {
+ *info = -4;
+ } else if (*ldgcol < n) {
+ *info = -14;
+ } else if (*ldgnum < n) {
+ *info = -16;
+ }
+ if (*info != 0) {
+ i__1 = -(*info);
+ xerbla_("DLASD6", &i__1);
+ return 0;
+ }
+
+/* The following values are for bookkeeping purposes only. They are */
+/* integer pointers which indicate the portion of the workspace */
+/* used by a particular array in DLASD7 and DLASD8. */
+
+ isigma = 1;
+ iw = isigma + n;
+ ivfw = iw + m;
+ ivlw = ivfw + m;
+
+ idx = 1;
+ idxc = idx + n;
+ idxp = idxc + n;
+
+/* Scale. */
+
+/* Computing MAX */
+ d__1 = abs(*alpha), d__2 = abs(*beta);
+ orgnrm = max(d__1,d__2);
+ d__[*nl + 1] = 0.;
+ i__1 = n;
+ for (i__ = 1; i__ <= i__1; ++i__) {
+ if ((d__1 = d__[i__], abs(d__1)) > orgnrm) {
+ orgnrm = (d__1 = d__[i__], abs(d__1));
+ }
+/* L10: */
+ }
+ dlascl_("G", &c__0, &c__0, &orgnrm, &c_b7, &n, &c__1, &d__[1], &n, info);
+ *alpha /= orgnrm;
+ *beta /= orgnrm;
+
+/* Sort and Deflate singular values. */
+
+ dlasd7_(icompq, nl, nr, sqre, k, &d__[1], &z__[1], &work[iw], &vf[1], &
+ work[ivfw], &vl[1], &work[ivlw], alpha, beta, &work[isigma], &
+ iwork[idx], &iwork[idxp], &idxq[1], &perm[1], givptr, &givcol[
+ givcol_offset], ldgcol, &givnum[givnum_offset], ldgnum, c__, s,
+ info);
+
+/* Solve Secular Equation, compute DIFL, DIFR, and update VF, VL. */
+
+ dlasd8_(icompq, k, &d__[1], &z__[1], &vf[1], &vl[1], &difl[1], &difr[1],
+ ldgnum, &work[isigma], &work[iw], info);
+
+/* Save the poles if ICOMPQ = 1. */
+
+ if (*icompq == 1) {
+ dcopy_(k, &d__[1], &c__1, &poles[poles_dim1 + 1], &c__1);
+ dcopy_(k, &work[isigma], &c__1, &poles[(poles_dim1 << 1) + 1], &c__1);
+ }
+
+/* Unscale. */
+
+ dlascl_("G", &c__0, &c__0, &c_b7, &orgnrm, &n, &c__1, &d__[1], &n, info);
+
+/* Prepare the IDXQ sorting permutation. */
+
+ n1 = *k;
+ n2 = n - *k;
+ dlamrg_(&n1, &n2, &d__[1], &c__1, &c_n1, &idxq[1]);
+
+ return 0;
+
+/* End of DLASD6 */
+
+} /* dlasd6_ */
projects / opencv / blobdiff