--- /dev/null
+#include "clapack.h"
+
+/* Table of constant values */
+
+static doublereal c_b5 = -1.;
+static integer c__1 = 1;
+static doublereal c_b11 = 1.;
+static doublereal c_b13 = 0.;
+static integer c__0 = 0;
+
+/* Subroutine */ int dlals0_(integer *icompq, integer *nl, integer *nr,
+ integer *sqre, integer *nrhs, doublereal *b, integer *ldb, doublereal
+ *bx, integer *ldbx, 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 *info)
+{
+ /* System generated locals */
+ integer givcol_dim1, givcol_offset, b_dim1, b_offset, bx_dim1, bx_offset,
+ difr_dim1, difr_offset, givnum_dim1, givnum_offset, poles_dim1,
+ poles_offset, i__1, i__2;
+ doublereal d__1;
+
+ /* Local variables */
+ integer i__, j, m, n;
+ doublereal dj;
+ integer nlp1;
+ doublereal temp;
+ extern /* Subroutine */ int drot_(integer *, doublereal *, integer *,
+ doublereal *, integer *, doublereal *, doublereal *);
+ extern doublereal dnrm2_(integer *, doublereal *, integer *);
+ extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *,
+ integer *);
+ doublereal diflj, difrj, dsigj;
+ extern /* Subroutine */ int dgemv_(char *, integer *, integer *,
+ doublereal *, doublereal *, integer *, doublereal *, integer *,
+ doublereal *, doublereal *, integer *), dcopy_(integer *,
+ doublereal *, integer *, doublereal *, integer *);
+ extern doublereal dlamc3_(doublereal *, doublereal *);
+ extern /* Subroutine */ int dlascl_(char *, integer *, integer *,
+ doublereal *, doublereal *, integer *, integer *, doublereal *,
+ integer *, integer *), dlacpy_(char *, integer *, integer
+ *, doublereal *, integer *, doublereal *, integer *),
+ xerbla_(char *, integer *);
+ doublereal dsigjp;
+
+
+/* -- LAPACK routine (version 3.1) -- */
+/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
+/* November 2006 */
+
+/* .. Scalar Arguments .. */
+/* .. */
+/* .. Array Arguments .. */
+/* .. */
+
+/* Purpose */
+/* ======= */
+
+/* DLALS0 applies back the multiplying factors of either the left or the */
+/* right singular vector matrix of a diagonal matrix appended by a row */
+/* to the right hand side matrix B in solving the least squares problem */
+/* using the divide-and-conquer SVD approach. */
+
+/* For the left singular vector matrix, three types of orthogonal */
+/* matrices are involved: */
+
+/* (1L) Givens rotations: the number of such rotations is GIVPTR; the */
+/* pairs of columns/rows they were applied to are stored in GIVCOL; */
+/* and the C- and S-values of these rotations are stored in GIVNUM. */
+
+/* (2L) Permutation. The (NL+1)-st row of B is to be moved to the first */
+/* row, and for J=2:N, PERM(J)-th row of B is to be moved to the */
+/* J-th row. */
+
+/* (3L) The left singular vector matrix of the remaining matrix. */
+
+/* For the right singular vector matrix, four types of orthogonal */
+/* matrices are involved: */
+
+/* (1R) The right singular vector matrix of the remaining matrix. */
+
+/* (2R) If SQRE = 1, one extra Givens rotation to generate the right */
+/* null space. */
+
+/* (3R) The inverse transformation of (2L). */
+
+/* (4R) The inverse transformation of (1L). */
+
+/* Arguments */
+/* ========= */
+
+/* ICOMPQ (input) INTEGER */
+/* Specifies whether singular vectors are to be computed in */
+/* factored form: */
+/* = 0: Left singular vector matrix. */
+/* = 1: Right singular vector matrix. */
+
+/* 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. */
+
+/* NRHS (input) INTEGER */
+/* The number of columns of B and BX. NRHS must be at least 1. */
+
+/* B (input/output) DOUBLE PRECISION array, dimension ( LDB, NRHS ) */
+/* On input, B contains the right hand sides of the least */
+/* squares problem in rows 1 through M. On output, B contains */
+/* the solution X in rows 1 through N. */
+
+/* LDB (input) INTEGER */
+/* The leading dimension of B. LDB must be at least */
+/* max(1,MAX( M, N ) ). */
+
+/* BX (workspace) DOUBLE PRECISION array, dimension ( LDBX, NRHS ) */
+
+/* LDBX (input) INTEGER */
+/* The leading dimension of BX. */
+
+/* PERM (input) INTEGER array, dimension ( N ) */
+/* The permutations (from deflation and sorting) applied */
+/* to the two blocks. */
+
+/* GIVPTR (input) INTEGER */
+/* The number of Givens rotations which took place in this */
+/* subproblem. */
+
+/* GIVCOL (input) INTEGER array, dimension ( LDGCOL, 2 ) */
+/* Each pair of numbers indicates a pair of rows/columns */
+/* involved in a Givens rotation. */
+
+/* LDGCOL (input) INTEGER */
+/* The leading dimension of GIVCOL, must be at least N. */
+
+/* GIVNUM (input) DOUBLE PRECISION array, dimension ( LDGNUM, 2 ) */
+/* Each number indicates the C or S value used in the */
+/* corresponding Givens rotation. */
+
+/* LDGNUM (input) INTEGER */
+/* The leading dimension of arrays DIFR, POLES and */
+/* GIVNUM, must be at least K. */
+
+/* POLES (input) DOUBLE PRECISION array, dimension ( LDGNUM, 2 ) */
+/* On entry, POLES(1:K, 1) contains the new singular */
+/* values obtained from solving the secular equation, and */
+/* POLES(1:K, 2) is an array containing the poles in the secular */
+/* equation. */
+
+/* DIFL (input) DOUBLE PRECISION array, dimension ( K ). */
+/* On entry, DIFL(I) is the distance between I-th updated */
+/* (undeflated) singular value and the I-th (undeflated) old */
+/* singular value. */
+
+/* DIFR (input) DOUBLE PRECISION array, dimension ( LDGNUM, 2 ). */
+/* On entry, DIFR(I, 1) contains the distances between I-th */
+/* updated (undeflated) singular value and the I+1-th */
+/* (undeflated) old singular value. And DIFR(I, 2) is the */
+/* normalizing factor for the I-th right singular vector. */
+
+/* Z (input) DOUBLE PRECISION array, dimension ( K ) */
+/* Contain the components of the deflation-adjusted updating row */
+/* vector. */
+
+/* K (input) INTEGER */
+/* Contains the dimension of the non-deflated matrix, */
+/* This is the order of the related secular equation. 1 <= K <=N. */
+
+/* C (input) 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 (input) 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 ( K ) */
+
+/* INFO (output) INTEGER */
+/* = 0: successful exit. */
+/* < 0: if INFO = -i, the i-th argument had an illegal value. */
+
+/* Further Details */
+/* =============== */
+
+/* Based on contributions by */
+/* Ming Gu and Ren-Cang Li, Computer Science Division, University of */
+/* California at Berkeley, USA */
+/* Osni Marques, LBNL/NERSC, USA */
+
+/* ===================================================================== */
+
+/* .. Parameters .. */
+/* .. */
+/* .. Local Scalars .. */
+/* .. */
+/* .. External Subroutines .. */
+/* .. */
+/* .. External Functions .. */
+/* .. */
+/* .. Intrinsic Functions .. */
+/* .. */
+/* .. Executable Statements .. */
+
+/* Test the input parameters. */
+
+ /* Parameter adjustments */
+ b_dim1 = *ldb;
+ b_offset = 1 + b_dim1;
+ b -= b_offset;
+ bx_dim1 = *ldbx;
+ bx_offset = 1 + bx_dim1;
+ bx -= bx_offset;
+ --perm;
+ givcol_dim1 = *ldgcol;
+ givcol_offset = 1 + givcol_dim1;
+ givcol -= givcol_offset;
+ difr_dim1 = *ldgnum;
+ difr_offset = 1 + difr_dim1;
+ difr -= difr_offset;
+ poles_dim1 = *ldgnum;
+ poles_offset = 1 + poles_dim1;
+ poles -= poles_offset;
+ givnum_dim1 = *ldgnum;
+ givnum_offset = 1 + givnum_dim1;
+ givnum -= givnum_offset;
+ --difl;
+ --z__;
+ --work;
+
+ /* Function Body */
+ *info = 0;
+
+ 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;
+ }
+
+ n = *nl + *nr + 1;
+
+ if (*nrhs < 1) {
+ *info = -5;
+ } else if (*ldb < n) {
+ *info = -7;
+ } else if (*ldbx < n) {
+ *info = -9;
+ } else if (*givptr < 0) {
+ *info = -11;
+ } else if (*ldgcol < n) {
+ *info = -13;
+ } else if (*ldgnum < n) {
+ *info = -15;
+ } else if (*k < 1) {
+ *info = -20;
+ }
+ if (*info != 0) {
+ i__1 = -(*info);
+ xerbla_("DLALS0", &i__1);
+ return 0;
+ }
+
+ m = n + *sqre;
+ nlp1 = *nl + 1;
+
+ if (*icompq == 0) {
+
+/* Apply back orthogonal transformations from the left. */
+
+/* Step (1L): apply back the Givens rotations performed. */
+
+ i__1 = *givptr;
+ for (i__ = 1; i__ <= i__1; ++i__) {
+ drot_(nrhs, &b[givcol[i__ + (givcol_dim1 << 1)] + b_dim1], ldb, &
+ b[givcol[i__ + givcol_dim1] + b_dim1], ldb, &givnum[i__ +
+ (givnum_dim1 << 1)], &givnum[i__ + givnum_dim1]);
+/* L10: */
+ }
+
+/* Step (2L): permute rows of B. */
+
+ dcopy_(nrhs, &b[nlp1 + b_dim1], ldb, &bx[bx_dim1 + 1], ldbx);
+ i__1 = n;
+ for (i__ = 2; i__ <= i__1; ++i__) {
+ dcopy_(nrhs, &b[perm[i__] + b_dim1], ldb, &bx[i__ + bx_dim1],
+ ldbx);
+/* L20: */
+ }
+
+/* Step (3L): apply the inverse of the left singular vector */
+/* matrix to BX. */
+
+ if (*k == 1) {
+ dcopy_(nrhs, &bx[bx_offset], ldbx, &b[b_offset], ldb);
+ if (z__[1] < 0.) {
+ dscal_(nrhs, &c_b5, &b[b_offset], ldb);
+ }
+ } else {
+ i__1 = *k;
+ for (j = 1; j <= i__1; ++j) {
+ diflj = difl[j];
+ dj = poles[j + poles_dim1];
+ dsigj = -poles[j + (poles_dim1 << 1)];
+ if (j < *k) {
+ difrj = -difr[j + difr_dim1];
+ dsigjp = -poles[j + 1 + (poles_dim1 << 1)];
+ }
+ if (z__[j] == 0. || poles[j + (poles_dim1 << 1)] == 0.) {
+ work[j] = 0.;
+ } else {
+ work[j] = -poles[j + (poles_dim1 << 1)] * z__[j] / diflj /
+ (poles[j + (poles_dim1 << 1)] + dj);
+ }
+ i__2 = j - 1;
+ for (i__ = 1; i__ <= i__2; ++i__) {
+ if (z__[i__] == 0. || poles[i__ + (poles_dim1 << 1)] ==
+ 0.) {
+ work[i__] = 0.;
+ } else {
+ work[i__] = poles[i__ + (poles_dim1 << 1)] * z__[i__]
+ / (dlamc3_(&poles[i__ + (poles_dim1 << 1)], &
+ dsigj) - diflj) / (poles[i__ + (poles_dim1 <<
+ 1)] + dj);
+ }
+/* L30: */
+ }
+ i__2 = *k;
+ for (i__ = j + 1; i__ <= i__2; ++i__) {
+ if (z__[i__] == 0. || poles[i__ + (poles_dim1 << 1)] ==
+ 0.) {
+ work[i__] = 0.;
+ } else {
+ work[i__] = poles[i__ + (poles_dim1 << 1)] * z__[i__]
+ / (dlamc3_(&poles[i__ + (poles_dim1 << 1)], &
+ dsigjp) + difrj) / (poles[i__ + (poles_dim1 <<
+ 1)] + dj);
+ }
+/* L40: */
+ }
+ work[1] = -1.;
+ temp = dnrm2_(k, &work[1], &c__1);
+ dgemv_("T", k, nrhs, &c_b11, &bx[bx_offset], ldbx, &work[1], &
+ c__1, &c_b13, &b[j + b_dim1], ldb);
+ dlascl_("G", &c__0, &c__0, &temp, &c_b11, &c__1, nrhs, &b[j +
+ b_dim1], ldb, info);
+/* L50: */
+ }
+ }
+
+/* Move the deflated rows of BX to B also. */
+
+ if (*k < max(m,n)) {
+ i__1 = n - *k;
+ dlacpy_("A", &i__1, nrhs, &bx[*k + 1 + bx_dim1], ldbx, &b[*k + 1
+ + b_dim1], ldb);
+ }
+ } else {
+
+/* Apply back the right orthogonal transformations. */
+
+/* Step (1R): apply back the new right singular vector matrix */
+/* to B. */
+
+ if (*k == 1) {
+ dcopy_(nrhs, &b[b_offset], ldb, &bx[bx_offset], ldbx);
+ } else {
+ i__1 = *k;
+ for (j = 1; j <= i__1; ++j) {
+ dsigj = poles[j + (poles_dim1 << 1)];
+ if (z__[j] == 0.) {
+ work[j] = 0.;
+ } else {
+ work[j] = -z__[j] / difl[j] / (dsigj + poles[j +
+ poles_dim1]) / difr[j + (difr_dim1 << 1)];
+ }
+ i__2 = j - 1;
+ for (i__ = 1; i__ <= i__2; ++i__) {
+ if (z__[j] == 0.) {
+ work[i__] = 0.;
+ } else {
+ d__1 = -poles[i__ + 1 + (poles_dim1 << 1)];
+ work[i__] = z__[j] / (dlamc3_(&dsigj, &d__1) - difr[
+ i__ + difr_dim1]) / (dsigj + poles[i__ +
+ poles_dim1]) / difr[i__ + (difr_dim1 << 1)];
+ }
+/* L60: */
+ }
+ i__2 = *k;
+ for (i__ = j + 1; i__ <= i__2; ++i__) {
+ if (z__[j] == 0.) {
+ work[i__] = 0.;
+ } else {
+ d__1 = -poles[i__ + (poles_dim1 << 1)];
+ work[i__] = z__[j] / (dlamc3_(&dsigj, &d__1) - difl[
+ i__]) / (dsigj + poles[i__ + poles_dim1]) /
+ difr[i__ + (difr_dim1 << 1)];
+ }
+/* L70: */
+ }
+ dgemv_("T", k, nrhs, &c_b11, &b[b_offset], ldb, &work[1], &
+ c__1, &c_b13, &bx[j + bx_dim1], ldbx);
+/* L80: */
+ }
+ }
+
+/* Step (2R): if SQRE = 1, apply back the rotation that is */
+/* related to the right null space of the subproblem. */
+
+ if (*sqre == 1) {
+ dcopy_(nrhs, &b[m + b_dim1], ldb, &bx[m + bx_dim1], ldbx);
+ drot_(nrhs, &bx[bx_dim1 + 1], ldbx, &bx[m + bx_dim1], ldbx, c__,
+ s);
+ }
+ if (*k < max(m,n)) {
+ i__1 = n - *k;
+ dlacpy_("A", &i__1, nrhs, &b[*k + 1 + b_dim1], ldb, &bx[*k + 1 +
+ bx_dim1], ldbx);
+ }
+
+/* Step (3R): permute rows of B. */
+
+ dcopy_(nrhs, &bx[bx_dim1 + 1], ldbx, &b[nlp1 + b_dim1], ldb);
+ if (*sqre == 1) {
+ dcopy_(nrhs, &bx[m + bx_dim1], ldbx, &b[m + b_dim1], ldb);
+ }
+ i__1 = n;
+ for (i__ = 2; i__ <= i__1; ++i__) {
+ dcopy_(nrhs, &bx[i__ + bx_dim1], ldbx, &b[perm[i__] + b_dim1],
+ ldb);
+/* L90: */
+ }
+
+/* Step (4R): apply back the Givens rotations performed. */
+
+ for (i__ = *givptr; i__ >= 1; --i__) {
+ d__1 = -givnum[i__ + givnum_dim1];
+ drot_(nrhs, &b[givcol[i__ + (givcol_dim1 << 1)] + b_dim1], ldb, &
+ b[givcol[i__ + givcol_dim1] + b_dim1], ldb, &givnum[i__ +
+ (givnum_dim1 << 1)], &d__1);
+/* L100: */
+ }
+ }
+
+ return 0;
+
+/* End of DLALS0 */
+
+} /* dlals0_ */
projects / opencv / blobdiff