int dlalsa_(int *icompq, int *smlsiz, int *n,
int *nrhs, double *b, int *ldb, double *bx, int *
ldbx, double *u, int *ldu, double *vt, int *k,
double *difl, double *difr, double *z__, double *
poles, int *givptr, int *givcol, int *ldgcol, int *
perm, double *givnum, double *c__, double *s, double *
work, int *iwork, int *info)
{
/* System generated locals */
int 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 */
int pow_ii(int *, int *);
/* Local variables */
int i__, j, i1, ic, lf, nd, ll, nl, nr, im1, nlf, nrf, lvl, ndb1,
nlp1, lvl2, nrp1, nlvl, sqre;
extern int dgemm_(char *, char *, int *, int *,
int *, double *, double *, int *, double *,
int *, double *, double *, int *);
int inode, ndiml, ndimr;
extern int dcopy_(int *, double *, int *,
double *, int *), dlals0_(int *, int *, int *,
int *, int *, double *, int *, double *,
int *, int *, int *, int *, int *, double
*, int *, double *, double *, double *,
double *, int *, double *, double *, double *,
int *), dlasdt_(int *, int *, int *, int *,
int *, int *, int *), xerbla_(char *, int *);
/* -- LAPACK routine (version 3.2) -- */
/* 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_ */
/* 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 computational routine (version 3.4.2) -- */
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
/* September 2012 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* ===================================================================== */
/* .. 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 */
}
/* 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)
{
/* -- LAPACK routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
June 30, 1999
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) 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
=====================================================================
Test the input parameters.
Parameter adjustments */
/* Table of constant values */
static doublereal c_b7 = 1.;
static doublereal c_b8 = 0.;
static integer c__2 = 2;
/* 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 */
static integer nlvl, sqre, i__, j;
extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *,
integer *, doublereal *, doublereal *, integer *, doublereal *,
integer *, doublereal *, doublereal *, integer *);
static integer inode, ndiml, ndimr;
extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *,
doublereal *, integer *);
static integer i1;
extern /* Subroutine */ int 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 *);
static integer ic, lf, nd, ll, nl, nr;
extern /* Subroutine */ int dlasdt_(integer *, integer *, integer *,
integer *, integer *, integer *, integer *), xerbla_(char *,
integer *);
static integer im1, nlf, nrf, lvl, ndb1, nlp1, lvl2, nrp1;
#define difl_ref(a_1,a_2) difl[(a_2)*difl_dim1 + a_1]
#define difr_ref(a_1,a_2) difr[(a_2)*difr_dim1 + a_1]
#define perm_ref(a_1,a_2) perm[(a_2)*perm_dim1 + a_1]
#define b_ref(a_1,a_2) b[(a_2)*b_dim1 + a_1]
#define u_ref(a_1,a_2) u[(a_2)*u_dim1 + a_1]
#define z___ref(a_1,a_2) z__[(a_2)*z_dim1 + a_1]
#define poles_ref(a_1,a_2) poles[(a_2)*poles_dim1 + a_1]
#define bx_ref(a_1,a_2) bx[(a_2)*bx_dim1 + a_1]
#define vt_ref(a_1,a_2) vt[(a_2)*vt_dim1 + a_1]
#define givcol_ref(a_1,a_2) givcol[(a_2)*givcol_dim1 + a_1]
#define givnum_ref(a_1,a_2) givnum[(a_2)*givnum_dim1 + a_1]
b_dim1 = *ldb;
b_offset = 1 + b_dim1 * 1;
b -= b_offset;
bx_dim1 = *ldbx;
bx_offset = 1 + bx_dim1 * 1;
bx -= bx_offset;
givnum_dim1 = *ldu;
givnum_offset = 1 + givnum_dim1 * 1;
givnum -= givnum_offset;
poles_dim1 = *ldu;
poles_offset = 1 + poles_dim1 * 1;
poles -= poles_offset;
z_dim1 = *ldu;
z_offset = 1 + z_dim1 * 1;
z__ -= z_offset;
difr_dim1 = *ldu;
difr_offset = 1 + difr_dim1 * 1;
difr -= difr_offset;
difl_dim1 = *ldu;
difl_offset = 1 + difl_dim1 * 1;
difl -= difl_offset;
vt_dim1 = *ldu;
vt_offset = 1 + vt_dim1 * 1;
vt -= vt_offset;
u_dim1 = *ldu;
u_offset = 1 + u_dim1 * 1;
u -= u_offset;
--k;
--givptr;
perm_dim1 = *ldgcol;
perm_offset = 1 + perm_dim1 * 1;
perm -= perm_offset;
givcol_dim1 = *ldgcol;
givcol_offset = 1 + givcol_dim1 * 1;
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_ref(nlf, 1), ldu, &b_ref(
nlf, 1), ldb, &c_b8, &bx_ref(nlf, 1), ldbx);
dgemm_("T", "N", &nr, nrhs, &nr, &c_b7, &u_ref(nrf, 1), ldu, &b_ref(
nrf, 1), ldb, &c_b8, &bx_ref(nrf, 1), 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_ref(ic, 1), ldb, &bx_ref(ic, 1), 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_ref(nlf, 1), ldbx, &
b_ref(nlf, 1), ldb, &perm_ref(nlf, lvl), &givptr[j], &
givcol_ref(nlf, lvl2), ldgcol, &givnum_ref(nlf, lvl2),
ldu, &poles_ref(nlf, lvl2), &difl_ref(nlf, lvl), &
difr_ref(nlf, lvl2), &z___ref(nlf, lvl), &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_ref(nlf, 1), ldb, &
bx_ref(nlf, 1), ldbx, &perm_ref(nlf, lvl), &givptr[j], &
givcol_ref(nlf, lvl2), ldgcol, &givnum_ref(nlf, lvl2),
ldu, &poles_ref(nlf, lvl2), &difl_ref(nlf, lvl), &
difr_ref(nlf, lvl2), &z___ref(nlf, lvl), &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_ref(nlf, 1), ldu, &
b_ref(nlf, 1), ldb, &c_b8, &bx_ref(nlf, 1), ldbx);
dgemm_("T", "N", &nrp1, nrhs, &nrp1, &c_b7, &vt_ref(nrf, 1), ldu, &
b_ref(nrf, 1), ldb, &c_b8, &bx_ref(nrf, 1), ldbx);
/* L80: */
}
L90:
return 0;
/* End of DLALSA */
} /* dlalsa_ */
