--- /dev/null
+#include "clapack.h"
+
+/* Table of constant values */
+
+static doublereal c_b7 = 1.;
+static doublereal c_b8 = 0.;
+static integer c__2 = 2;
+
+/* Subroutine */ int dlalsa_(integer *icompq, integer *smlsiz, integer *n,
+ integer *nrhs, doublereal *b, integer *ldb, doublereal *bx, integer *
+ ldbx, doublereal *u, integer *ldu, doublereal *vt, integer *k,
+ doublereal *difl, doublereal *difr, doublereal *z__, doublereal *
+ poles, integer *givptr, integer *givcol, integer *ldgcol, integer *
+ perm, doublereal *givnum, doublereal *c__, doublereal *s, doublereal *
+ work, integer *iwork, integer *info)
+{
+ /* System generated locals */
+ integer givcol_dim1, givcol_offset, perm_dim1, perm_offset, b_dim1,
+ b_offset, bx_dim1, bx_offset, difl_dim1, difl_offset, difr_dim1,
+ difr_offset, givnum_dim1, givnum_offset, poles_dim1, poles_offset,
+ u_dim1, u_offset, vt_dim1, vt_offset, z_dim1, z_offset, i__1,
+ i__2;
+
+ /* Builtin functions */
+ integer pow_ii(integer *, integer *);
+
+ /* Local variables */
+ integer i__, j, i1, ic, lf, nd, ll, nl, nr, im1, nlf, nrf, lvl, ndb1,
+ nlp1, lvl2, nrp1, nlvl, sqre;
+ extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *,
+ integer *, doublereal *, doublereal *, integer *, doublereal *,
+ integer *, doublereal *, doublereal *, integer *);
+ integer inode, ndiml, ndimr;
+ extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *,
+ doublereal *, integer *), dlals0_(integer *, integer *, integer *,
+ integer *, integer *, doublereal *, integer *, doublereal *,
+ integer *, integer *, integer *, integer *, integer *, doublereal
+ *, integer *, doublereal *, doublereal *, doublereal *,
+ doublereal *, integer *, doublereal *, doublereal *, doublereal *,
+ integer *), dlasdt_(integer *, integer *, integer *, integer *,
+ integer *, integer *, integer *), xerbla_(char *, integer *);
+
+
+/* -- LAPACK routine (version 3.1) -- */
+/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
+/* November 2006 */
+
+/* .. Scalar Arguments .. */
+/* .. */
+/* .. Array Arguments .. */
+/* .. */
+
+/* Purpose */
+/* ======= */
+
+/* DLALSA is an itermediate step in solving the least squares problem */
+/* by computing the SVD of the coefficient matrix in compact form (The */
+/* singular vectors are computed as products of simple orthorgonal */
+/* matrices.). */
+
+/* If ICOMPQ = 0, DLALSA applies the inverse of the left singular vector */
+/* matrix of an upper bidiagonal matrix to the right hand side; and if */
+/* ICOMPQ = 1, DLALSA applies the right singular vector matrix to the */
+/* right hand side. The singular vector matrices were generated in */
+/* compact form by DLALSA. */
+
+/* Arguments */
+/* ========= */
+
+
+/* ICOMPQ (input) INTEGER */
+/* Specifies whether the left or the right singular vector */
+/* matrix is involved. */
+/* = 0: Left singular vector matrix */
+/* = 1: Right singular vector matrix */
+
+/* SMLSIZ (input) INTEGER */
+/* The maximum size of the subproblems at the bottom of the */
+/* computation tree. */
+
+/* N (input) INTEGER */
+/* The row and column dimensions of the upper bidiagonal matrix. */
+
+/* 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 in the calling subprogram. */
+/* LDB must be at least max(1,MAX( M, N ) ). */
+
+/* BX (output) DOUBLE PRECISION array, dimension ( LDBX, NRHS ) */
+/* On exit, the result of applying the left or right singular */
+/* vector matrix to B. */
+
+/* LDBX (input) INTEGER */
+/* The leading dimension of BX. */
+
+/* U (input) DOUBLE PRECISION array, dimension ( LDU, SMLSIZ ). */
+/* On entry, U contains the left singular vector matrices of all */
+/* subproblems at the bottom level. */
+
+/* LDU (input) INTEGER, LDU = > N. */
+/* The leading dimension of arrays U, VT, DIFL, DIFR, */
+/* POLES, GIVNUM, and Z. */
+
+/* VT (input) DOUBLE PRECISION array, dimension ( LDU, SMLSIZ+1 ). */
+/* On entry, VT' contains the right singular vector matrices of */
+/* all subproblems at the bottom level. */
+
+/* K (input) INTEGER array, dimension ( N ). */
+
+/* DIFL (input) DOUBLE PRECISION array, dimension ( LDU, NLVL ). */
+/* where NLVL = INT(log_2 (N/(SMLSIZ+1))) + 1. */
+
+/* DIFR (input) DOUBLE PRECISION array, dimension ( LDU, 2 * NLVL ). */
+/* On entry, DIFL(*, I) and DIFR(*, 2 * I -1) record */
+/* distances between singular values on the I-th level and */
+/* singular values on the (I -1)-th level, and DIFR(*, 2 * I) */
+/* record the normalizing factors of the right singular vectors */
+/* matrices of subproblems on I-th level. */
+
+/* Z (input) DOUBLE PRECISION array, dimension ( LDU, NLVL ). */
+/* On entry, Z(1, I) contains the components of the deflation- */
+/* adjusted updating row vector for subproblems on the I-th */
+/* level. */
+
+/* POLES (input) DOUBLE PRECISION array, dimension ( LDU, 2 * NLVL ). */
+/* On entry, POLES(*, 2 * I -1: 2 * I) contains the new and old */
+/* singular values involved in the secular equations on the I-th */
+/* level. */
+
+/* GIVPTR (input) INTEGER array, dimension ( N ). */
+/* On entry, GIVPTR( I ) records the number of Givens */
+/* rotations performed on the I-th problem on the computation */
+/* tree. */
+
+/* GIVCOL (input) INTEGER array, dimension ( LDGCOL, 2 * NLVL ). */
+/* On entry, for each I, GIVCOL(*, 2 * I - 1: 2 * I) records the */
+/* locations of Givens rotations performed on the I-th level on */
+/* the computation tree. */
+
+/* LDGCOL (input) INTEGER, LDGCOL = > N. */
+/* The leading dimension of arrays GIVCOL and PERM. */
+
+/* PERM (input) INTEGER array, dimension ( LDGCOL, NLVL ). */
+/* On entry, PERM(*, I) records permutations done on the I-th */
+/* level of the computation tree. */
+
+/* GIVNUM (input) DOUBLE PRECISION array, dimension ( LDU, 2 * NLVL ). */
+/* On entry, GIVNUM(*, 2 *I -1 : 2 * I) records the C- and S- */
+/* values of Givens rotations performed on the I-th level on the */
+/* computation tree. */
+
+/* C (input) DOUBLE PRECISION array, dimension ( N ). */
+/* On entry, if the I-th subproblem is not square, */
+/* C( I ) contains the C-value of a Givens rotation related to */
+/* the right null space of the I-th subproblem. */
+
+/* S (input) DOUBLE PRECISION array, dimension ( N ). */
+/* On entry, if the I-th subproblem is not square, */
+/* S( I ) contains the S-value of a Givens rotation related to */
+/* the right null space of the I-th subproblem. */
+
+/* WORK (workspace) DOUBLE PRECISION array. */
+/* The dimension must be at least N. */
+
+/* IWORK (workspace) INTEGER array. */
+/* The dimension must be at least 3 * N */
+
+/* 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 .. */
+/* .. */
+/* .. 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;
+ givnum_dim1 = *ldu;
+ givnum_offset = 1 + givnum_dim1;
+ givnum -= givnum_offset;
+ poles_dim1 = *ldu;
+ poles_offset = 1 + poles_dim1;
+ poles -= poles_offset;
+ z_dim1 = *ldu;
+ z_offset = 1 + z_dim1;
+ z__ -= z_offset;
+ difr_dim1 = *ldu;
+ difr_offset = 1 + difr_dim1;
+ difr -= difr_offset;
+ difl_dim1 = *ldu;
+ difl_offset = 1 + difl_dim1;
+ difl -= difl_offset;
+ vt_dim1 = *ldu;
+ vt_offset = 1 + vt_dim1;
+ vt -= vt_offset;
+ u_dim1 = *ldu;
+ u_offset = 1 + u_dim1;
+ u -= u_offset;
+ --k;
+ --givptr;
+ perm_dim1 = *ldgcol;
+ perm_offset = 1 + perm_dim1;
+ perm -= perm_offset;
+ givcol_dim1 = *ldgcol;
+ givcol_offset = 1 + givcol_dim1;
+ givcol -= givcol_offset;
+ --c__;
+ --s;
+ --work;
+ --iwork;
+
+ /* Function Body */
+ *info = 0;
+
+ if (*icompq < 0 || *icompq > 1) {
+ *info = -1;
+ } else if (*smlsiz < 3) {
+ *info = -2;
+ } else if (*n < *smlsiz) {
+ *info = -3;
+ } else if (*nrhs < 1) {
+ *info = -4;
+ } else if (*ldb < *n) {
+ *info = -6;
+ } else if (*ldbx < *n) {
+ *info = -8;
+ } else if (*ldu < *n) {
+ *info = -10;
+ } else if (*ldgcol < *n) {
+ *info = -19;
+ }
+ if (*info != 0) {
+ i__1 = -(*info);
+ xerbla_("DLALSA", &i__1);
+ return 0;
+ }
+
+/* Book-keeping and setting up the computation tree. */
+
+ inode = 1;
+ ndiml = inode + *n;
+ ndimr = ndiml + *n;
+
+ dlasdt_(n, &nlvl, &nd, &iwork[inode], &iwork[ndiml], &iwork[ndimr],
+ smlsiz);
+
+/* The following code applies back the left singular vector factors. */
+/* For applying back the right singular vector factors, go to 50. */
+
+ if (*icompq == 1) {
+ goto L50;
+ }
+
+/* The nodes on the bottom level of the tree were solved */
+/* by DLASDQ. The corresponding left and right singular vector */
+/* matrices are in explicit form. First apply back the left */
+/* singular vector matrices. */
+
+ ndb1 = (nd + 1) / 2;
+ i__1 = nd;
+ for (i__ = ndb1; i__ <= i__1; ++i__) {
+
+/* IC : center row of each node */
+/* NL : number of rows of left subproblem */
+/* NR : number of rows of right subproblem */
+/* NLF: starting row of the left subproblem */
+/* NRF: starting row of the right subproblem */
+
+ i1 = i__ - 1;
+ ic = iwork[inode + i1];
+ nl = iwork[ndiml + i1];
+ nr = iwork[ndimr + i1];
+ nlf = ic - nl;
+ nrf = ic + 1;
+ dgemm_("T", "N", &nl, nrhs, &nl, &c_b7, &u[nlf + u_dim1], ldu, &b[nlf
+ + b_dim1], ldb, &c_b8, &bx[nlf + bx_dim1], ldbx);
+ dgemm_("T", "N", &nr, nrhs, &nr, &c_b7, &u[nrf + u_dim1], ldu, &b[nrf
+ + b_dim1], ldb, &c_b8, &bx[nrf + bx_dim1], ldbx);
+/* L10: */
+ }
+
+/* Next copy the rows of B that correspond to unchanged rows */
+/* in the bidiagonal matrix to BX. */
+
+ i__1 = nd;
+ for (i__ = 1; i__ <= i__1; ++i__) {
+ ic = iwork[inode + i__ - 1];
+ dcopy_(nrhs, &b[ic + b_dim1], ldb, &bx[ic + bx_dim1], ldbx);
+/* L20: */
+ }
+
+/* Finally go through the left singular vector matrices of all */
+/* the other subproblems bottom-up on the tree. */
+
+ j = pow_ii(&c__2, &nlvl);
+ sqre = 0;
+
+ for (lvl = nlvl; lvl >= 1; --lvl) {
+ lvl2 = (lvl << 1) - 1;
+
+/* find the first node LF and last node LL on */
+/* the current level LVL */
+
+ if (lvl == 1) {
+ lf = 1;
+ ll = 1;
+ } else {
+ i__1 = lvl - 1;
+ lf = pow_ii(&c__2, &i__1);
+ ll = (lf << 1) - 1;
+ }
+ i__1 = ll;
+ for (i__ = lf; i__ <= i__1; ++i__) {
+ im1 = i__ - 1;
+ ic = iwork[inode + im1];
+ nl = iwork[ndiml + im1];
+ nr = iwork[ndimr + im1];
+ nlf = ic - nl;
+ nrf = ic + 1;
+ --j;
+ dlals0_(icompq, &nl, &nr, &sqre, nrhs, &bx[nlf + bx_dim1], ldbx, &
+ b[nlf + b_dim1], ldb, &perm[nlf + lvl * perm_dim1], &
+ givptr[j], &givcol[nlf + lvl2 * givcol_dim1], ldgcol, &
+ givnum[nlf + lvl2 * givnum_dim1], ldu, &poles[nlf + lvl2 *
+ poles_dim1], &difl[nlf + lvl * difl_dim1], &difr[nlf +
+ lvl2 * difr_dim1], &z__[nlf + lvl * z_dim1], &k[j], &c__[
+ j], &s[j], &work[1], info);
+/* L30: */
+ }
+/* L40: */
+ }
+ goto L90;
+
+/* ICOMPQ = 1: applying back the right singular vector factors. */
+
+L50:
+
+/* First now go through the right singular vector matrices of all */
+/* the tree nodes top-down. */
+
+ j = 0;
+ i__1 = nlvl;
+ for (lvl = 1; lvl <= i__1; ++lvl) {
+ lvl2 = (lvl << 1) - 1;
+
+/* Find the first node LF and last node LL on */
+/* the current level LVL. */
+
+ if (lvl == 1) {
+ lf = 1;
+ ll = 1;
+ } else {
+ i__2 = lvl - 1;
+ lf = pow_ii(&c__2, &i__2);
+ ll = (lf << 1) - 1;
+ }
+ i__2 = lf;
+ for (i__ = ll; i__ >= i__2; --i__) {
+ im1 = i__ - 1;
+ ic = iwork[inode + im1];
+ nl = iwork[ndiml + im1];
+ nr = iwork[ndimr + im1];
+ nlf = ic - nl;
+ nrf = ic + 1;
+ if (i__ == ll) {
+ sqre = 0;
+ } else {
+ sqre = 1;
+ }
+ ++j;
+ dlals0_(icompq, &nl, &nr, &sqre, nrhs, &b[nlf + b_dim1], ldb, &bx[
+ nlf + bx_dim1], ldbx, &perm[nlf + lvl * perm_dim1], &
+ givptr[j], &givcol[nlf + lvl2 * givcol_dim1], ldgcol, &
+ givnum[nlf + lvl2 * givnum_dim1], ldu, &poles[nlf + lvl2 *
+ poles_dim1], &difl[nlf + lvl * difl_dim1], &difr[nlf +
+ lvl2 * difr_dim1], &z__[nlf + lvl * z_dim1], &k[j], &c__[
+ j], &s[j], &work[1], info);
+/* L60: */
+ }
+/* L70: */
+ }
+
+/* The nodes on the bottom level of the tree were solved */
+/* by DLASDQ. The corresponding right singular vector */
+/* matrices are in explicit form. Apply them back. */
+
+ ndb1 = (nd + 1) / 2;
+ i__1 = nd;
+ for (i__ = ndb1; i__ <= i__1; ++i__) {
+ i1 = i__ - 1;
+ ic = iwork[inode + i1];
+ nl = iwork[ndiml + i1];
+ nr = iwork[ndimr + i1];
+ nlp1 = nl + 1;
+ if (i__ == nd) {
+ nrp1 = nr;
+ } else {
+ nrp1 = nr + 1;
+ }
+ nlf = ic - nl;
+ nrf = ic + 1;
+ dgemm_("T", "N", &nlp1, nrhs, &nlp1, &c_b7, &vt[nlf + vt_dim1], ldu, &
+ b[nlf + b_dim1], ldb, &c_b8, &bx[nlf + bx_dim1], ldbx);
+ dgemm_("T", "N", &nrp1, nrhs, &nrp1, &c_b7, &vt[nrf + vt_dim1], ldu, &
+ b[nrf + b_dim1], ldb, &c_b8, &bx[nrf + bx_dim1], ldbx);
+/* L80: */
+ }
+
+L90:
+
+ return 0;
+
+/* End of DLALSA */
+
+} /* dlalsa_ */
projects / opencv / blobdiff