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opencv/3rdparty/lapack/dlalsa.c

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#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_ */
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