/* dlals0.f -- translated by f2c (version 20061008).
You must link the resulting object file with libf2c:
on Microsoft Windows system, link with libf2c.lib;
on Linux or Unix systems, link with .../path/to/libf2c.a -lm
or, if you install libf2c.a in a standard place, with -lf2c -lm
-- in that order, at the end of the command line, as in
cc *.o -lf2c -lm
Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
http://www.netlib.org/f2c/libf2c.zip
*/
#include "f2c.h"
#include "blaswrap.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 3.2) -- */
/* 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_ */