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#include "clapack.h"
/* Table of constant values */
static integer c__0 = 0;
static doublereal c_b11 = 0.;
static doublereal c_b12 = 1.;
static integer c__1 = 1;
static integer c__2 = 2;
/* Subroutine */ int dlasda_(integer *icompq, integer *smlsiz, integer *n,
integer *sqre, doublereal *d__, doublereal *e, 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, 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, m, i1, ic, lf, nd, ll, nl, vf, nr, vl, im1, ncc, nlf, nrf,
vfi, iwk, vli, lvl, nru, ndb1, nlp1, lvl2, nrp1;
doublereal beta;
integer idxq, nlvl;
doublereal alpha;
integer inode, ndiml, ndimr, idxqi, itemp;
extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *,
doublereal *, integer *);
integer sqrei;
extern /* Subroutine */ int dlasd6_(integer *, integer *, integer *,
integer *, doublereal *, doublereal *, doublereal *, doublereal *,
doublereal *, integer *, integer *, integer *, integer *,
integer *, doublereal *, integer *, doublereal *, doublereal *,
doublereal *, doublereal *, integer *, doublereal *, doublereal *,
doublereal *, integer *, integer *);
integer nwork1, nwork2;
extern /* Subroutine */ int dlasdq_(char *, integer *, integer *, integer
*, integer *, integer *, doublereal *, doublereal *, doublereal *,
integer *, doublereal *, integer *, doublereal *, integer *,
doublereal *, integer *), dlasdt_(integer *, integer *,
integer *, integer *, integer *, integer *, integer *), dlaset_(
char *, integer *, integer *, doublereal *, doublereal *,
doublereal *, integer *), xerbla_(char *, integer *);
integer smlszp;
/* -- LAPACK auxiliary routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* Using a divide and conquer approach, DLASDA computes the singular */
/* value decomposition (SVD) of a real upper bidiagonal N-by-M matrix */
/* B with diagonal D and offdiagonal E, where M = N + SQRE. The */
/* algorithm computes the singular values in the SVD B = U * S * VT. */
/* The orthogonal matrices U and VT are optionally computed in */
/* compact form. */
/* A related subroutine, DLASD0, computes the singular values and */
/* the singular vectors in explicit form. */
/* Arguments */
/* ========= */
/* ICOMPQ (input) INTEGER */
/* Specifies whether singular vectors are to be computed */
/* in compact form, as follows */
/* = 0: Compute singular values only. */
/* = 1: Compute singular vectors of upper bidiagonal */
/* matrix in compact form. */
/* SMLSIZ (input) INTEGER */
/* The maximum size of the subproblems at the bottom of the */
/* computation tree. */
/* N (input) INTEGER */
/* The row dimension of the upper bidiagonal matrix. This is */
/* also the dimension of the main diagonal array D. */
/* SQRE (input) INTEGER */
/* Specifies the column dimension of the bidiagonal matrix. */
/* = 0: The bidiagonal matrix has column dimension M = N; */
/* = 1: The bidiagonal matrix has column dimension M = N + 1. */
/* D (input/output) DOUBLE PRECISION array, dimension ( N ) */
/* On entry D contains the main diagonal of the bidiagonal */
/* matrix. On exit D, if INFO = 0, contains its singular values. */
/* E (input) DOUBLE PRECISION array, dimension ( M-1 ) */
/* Contains the subdiagonal entries of the bidiagonal matrix. */
/* On exit, E has been destroyed. */
/* U (output) DOUBLE PRECISION array, */
/* dimension ( LDU, SMLSIZ ) if ICOMPQ = 1, and not referenced */
/* if ICOMPQ = 0. If ICOMPQ = 1, on exit, 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 (output) DOUBLE PRECISION array, */
/* dimension ( LDU, SMLSIZ+1 ) if ICOMPQ = 1, and not referenced */
/* if ICOMPQ = 0. If ICOMPQ = 1, on exit, VT' contains the right */
/* singular vector matrices of all subproblems at the bottom */
/* level. */
/* K (output) INTEGER array, */
/* dimension ( N ) if ICOMPQ = 1 and dimension 1 if ICOMPQ = 0. */
/* If ICOMPQ = 1, on exit, K(I) is the dimension of the I-th */
/* secular equation on the computation tree. */
/* DIFL (output) DOUBLE PRECISION array, dimension ( LDU, NLVL ), */
/* where NLVL = floor(log_2 (N/SMLSIZ))). */
/* DIFR (output) DOUBLE PRECISION array, */
/* dimension ( LDU, 2 * NLVL ) if ICOMPQ = 1 and */
/* dimension ( N ) if ICOMPQ = 0. */
/* If ICOMPQ = 1, on exit, DIFL(1:N, I) and DIFR(1:N, 2 * I - 1) */
/* record distances between singular values on the I-th */
/* level and singular values on the (I -1)-th level, and */
/* DIFR(1:N, 2 * I ) contains the normalizing factors for */
/* the right singular vector matrix. See DLASD8 for details. */
/* Z (output) DOUBLE PRECISION array, */
/* dimension ( LDU, NLVL ) if ICOMPQ = 1 and */
/* dimension ( N ) if ICOMPQ = 0. */
/* The first K elements of Z(1, I) contain the components of */
/* the deflation-adjusted updating row vector for subproblems */
/* on the I-th level. */
/* POLES (output) DOUBLE PRECISION array, */
/* dimension ( LDU, 2 * NLVL ) if ICOMPQ = 1, and not referenced */
/* if ICOMPQ = 0. If ICOMPQ = 1, on exit, POLES(1, 2*I - 1) and */
/* POLES(1, 2*I) contain the new and old singular values */
/* involved in the secular equations on the I-th level. */
/* GIVPTR (output) INTEGER array, */
/* dimension ( N ) if ICOMPQ = 1, and not referenced if */
/* ICOMPQ = 0. If ICOMPQ = 1, on exit, GIVPTR( I ) records */
/* the number of Givens rotations performed on the I-th */
/* problem on the computation tree. */
/* GIVCOL (output) INTEGER array, */
/* dimension ( LDGCOL, 2 * NLVL ) if ICOMPQ = 1, and not */
/* referenced if ICOMPQ = 0. If ICOMPQ = 1, on exit, for each I, */
/* GIVCOL(1, 2 *I - 1) and GIVCOL(1, 2 *I) record 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 (output) INTEGER array, */
/* dimension ( LDGCOL, NLVL ) if ICOMPQ = 1, and not referenced */
/* if ICOMPQ = 0. If ICOMPQ = 1, on exit, PERM(1, I) records */
/* permutations done on the I-th level of the computation tree. */
/* GIVNUM (output) DOUBLE PRECISION array, */
/* dimension ( LDU, 2 * NLVL ) if ICOMPQ = 1, and not */
/* referenced if ICOMPQ = 0. If ICOMPQ = 1, on exit, for each I, */
/* GIVNUM(1, 2 *I - 1) and GIVNUM(1, 2 *I) record the C- and S- */
/* values of Givens rotations performed on the I-th level on */
/* the computation tree. */
/* C (output) DOUBLE PRECISION array, */
/* dimension ( N ) if ICOMPQ = 1, and dimension 1 if ICOMPQ = 0. */
/* If ICOMPQ = 1 and the I-th subproblem is not square, on exit, */
/* C( I ) contains the C-value of a Givens rotation related to */
/* the right null space of the I-th subproblem. */
/* S (output) DOUBLE PRECISION array, dimension ( N ) if */
/* ICOMPQ = 1, and dimension 1 if ICOMPQ = 0. If ICOMPQ = 1 */
/* and the I-th subproblem is not square, on exit, 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, dimension */
/* (6 * N + (SMLSIZ + 1)*(SMLSIZ + 1)). */
/* IWORK (workspace) INTEGER array. */
/* Dimension must be at least (7 * N). */
/* INFO (output) INTEGER */
/* = 0: successful exit. */
/* < 0: if INFO = -i, the i-th argument had an illegal value. */
/* > 0: if INFO = 1, an singular value did not converge */
/* Further Details */
/* =============== */
/* Based on contributions by */
/* Ming Gu and Huan Ren, Computer Science Division, University of */
/* California at Berkeley, USA */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input parameters. */
/* Parameter adjustments */
--d__;
--e;
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 < 0) {
*info = -3;
} else if (*sqre < 0 || *sqre > 1) {
*info = -4;
} else if (*ldu < *n + *sqre) {
*info = -8;
} else if (*ldgcol < *n) {
*info = -17;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("DLASDA", &i__1);
return 0;
}
m = *n + *sqre;
/* If the input matrix is too small, call DLASDQ to find the SVD. */
if (*n <= *smlsiz) {
if (*icompq == 0) {
dlasdq_("U", sqre, n, &c__0, &c__0, &c__0, &d__[1], &e[1], &vt[
vt_offset], ldu, &u[u_offset], ldu, &u[u_offset], ldu, &
work[1], info);
} else {
dlasdq_("U", sqre, n, &m, n, &c__0, &d__[1], &e[1], &vt[vt_offset]
, ldu, &u[u_offset], ldu, &u[u_offset], ldu, &work[1],
info);
}
return 0;
}
/* Book-keeping and set up the computation tree. */
inode = 1;
ndiml = inode + *n;
ndimr = ndiml + *n;
idxq = ndimr + *n;
iwk = idxq + *n;
ncc = 0;
nru = 0;
smlszp = *smlsiz + 1;
vf = 1;
vl = vf + m;
nwork1 = vl + m;
nwork2 = nwork1 + smlszp * smlszp;
dlasdt_(n, &nlvl, &nd, &iwork[inode], &iwork[ndiml], &iwork[ndimr],
smlsiz);
/* for the nodes on bottom level of the tree, solve */
/* their subproblems by DLASDQ. */
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];
nlp1 = nl + 1;
nr = iwork[ndimr + i1];
nlf = ic - nl;
nrf = ic + 1;
idxqi = idxq + nlf - 2;
vfi = vf + nlf - 1;
vli = vl + nlf - 1;
sqrei = 1;
if (*icompq == 0) {
dlaset_("A", &nlp1, &nlp1, &c_b11, &c_b12, &work[nwork1], &smlszp);
dlasdq_("U", &sqrei, &nl, &nlp1, &nru, &ncc, &d__[nlf], &e[nlf], &
work[nwork1], &smlszp, &work[nwork2], &nl, &work[nwork2],
&nl, &work[nwork2], info);
itemp = nwork1 + nl * smlszp;
dcopy_(&nlp1, &work[nwork1], &c__1, &work[vfi], &c__1);
dcopy_(&nlp1, &work[itemp], &c__1, &work[vli], &c__1);
} else {
dlaset_("A", &nl, &nl, &c_b11, &c_b12, &u[nlf + u_dim1], ldu);
dlaset_("A", &nlp1, &nlp1, &c_b11, &c_b12, &vt[nlf + vt_dim1],
ldu);
dlasdq_("U", &sqrei, &nl, &nlp1, &nl, &ncc, &d__[nlf], &e[nlf], &
vt[nlf + vt_dim1], ldu, &u[nlf + u_dim1], ldu, &u[nlf +
u_dim1], ldu, &work[nwork1], info);
dcopy_(&nlp1, &vt[nlf + vt_dim1], &c__1, &work[vfi], &c__1);
dcopy_(&nlp1, &vt[nlf + nlp1 * vt_dim1], &c__1, &work[vli], &c__1)
;
}
if (*info != 0) {
return 0;
}
i__2 = nl;
for (j = 1; j <= i__2; ++j) {
iwork[idxqi + j] = j;
/* L10: */
}
if (i__ == nd && *sqre == 0) {
sqrei = 0;
} else {
sqrei = 1;
}
idxqi += nlp1;
vfi += nlp1;
vli += nlp1;
nrp1 = nr + sqrei;
if (*icompq == 0) {
dlaset_("A", &nrp1, &nrp1, &c_b11, &c_b12, &work[nwork1], &smlszp);
dlasdq_("U", &sqrei, &nr, &nrp1, &nru, &ncc, &d__[nrf], &e[nrf], &
work[nwork1], &smlszp, &work[nwork2], &nr, &work[nwork2],
&nr, &work[nwork2], info);
itemp = nwork1 + (nrp1 - 1) * smlszp;
dcopy_(&nrp1, &work[nwork1], &c__1, &work[vfi], &c__1);
dcopy_(&nrp1, &work[itemp], &c__1, &work[vli], &c__1);
} else {
dlaset_("A", &nr, &nr, &c_b11, &c_b12, &u[nrf + u_dim1], ldu);
dlaset_("A", &nrp1, &nrp1, &c_b11, &c_b12, &vt[nrf + vt_dim1],
ldu);
dlasdq_("U", &sqrei, &nr, &nrp1, &nr, &ncc, &d__[nrf], &e[nrf], &
vt[nrf + vt_dim1], ldu, &u[nrf + u_dim1], ldu, &u[nrf +
u_dim1], ldu, &work[nwork1], info);
dcopy_(&nrp1, &vt[nrf + vt_dim1], &c__1, &work[vfi], &c__1);
dcopy_(&nrp1, &vt[nrf + nrp1 * vt_dim1], &c__1, &work[vli], &c__1)
;
}
if (*info != 0) {
return 0;
}
i__2 = nr;
for (j = 1; j <= i__2; ++j) {
iwork[idxqi + j] = j;
/* L20: */
}
/* L30: */
}
/* Now conquer each subproblem bottom-up. */
j = pow_ii(&c__2, &nlvl);
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;
if (i__ == ll) {
sqrei = *sqre;
} else {
sqrei = 1;
}
vfi = vf + nlf - 1;
vli = vl + nlf - 1;
idxqi = idxq + nlf - 1;
alpha = d__[ic];
beta = e[ic];
if (*icompq == 0) {
dlasd6_(icompq, &nl, &nr, &sqrei, &d__[nlf], &work[vfi], &
work[vli], &alpha, &beta, &iwork[idxqi], &perm[
perm_offset], &givptr[1], &givcol[givcol_offset],
ldgcol, &givnum[givnum_offset], ldu, &poles[
poles_offset], &difl[difl_offset], &difr[difr_offset],
&z__[z_offset], &k[1], &c__[1], &s[1], &work[nwork1],
&iwork[iwk], info);
} else {
--j;
dlasd6_(icompq, &nl, &nr, &sqrei, &d__[nlf], &work[vfi], &
work[vli], &alpha, &beta, &iwork[idxqi], &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[nwork1], &iwork[iwk], info);
}
if (*info != 0) {
return 0;
}
/* L40: */
}
/* L50: */
}
return 0;
/* End of DLASDA */
} /* dlasda_ */