ZLALSA(3) LAPACK routine of NEC Numeric Library Collection ZLALSA(3)
NAME
ZLALSA
SYNOPSIS
SUBROUTINE ZLALSA (ICOMPQ, SMLSIZ, N, NRHS, B, LDB, BX, LDBX, U, LDU,
VT, K, DIFL, DIFR, Z, POLES, GIVPTR, GIVCOL, LDGCOL, PERM, GIVNUM,
C, S, RWORK, IWORK, INFO)
PURPOSE
ZLALSA 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, ZLALSA applies the inverse of the left singular vector
matrix of an upper bidiagonal matrix to the right hand side; and if
ICOMPQ = 1, ZLALSA applies the right singular vector matrix to the
right hand side. The singular vector matrices were generated in
compact form by ZLALSA.
ARGUMENTS
ICOMPQ (input)
ICOMPQ is 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)
SMLSIZ is INTEGER
The maximum size of the subproblems at the bottom of the
computation tree.
N (input)
N is INTEGER
The row and column dimensions of the upper bidiagonal matrix.
NRHS (input)
NRHS is INTEGER
The number of columns of B and BX. NRHS must be at least 1.
B (input/output)
B is COMPLEX*16 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)
LDB is INTEGER
The leading dimension of B in the calling subprogram.
LDB must be at least max(1,MAX( M, N ) ).
BX (output)
BX is COMPLEX*16 array, dimension ( LDBX, NRHS )
On exit, the result of applying the left or right singular
vector matrix to B.
LDBX (input)
LDBX is INTEGER
The leading dimension of BX.
U (input)
U is DOUBLE PRECISION array, dimension ( LDU, SMLSIZ ).
On entry, U contains the left singular vector matrices of all
subproblems at the bottom level.
LDU (input)
LDU is INTEGER, LDU = > N.
The leading dimension of arrays U, VT, DIFL, DIFR,
POLES, GIVNUM, and Z.
VT (input)
VT is DOUBLE PRECISION array, dimension ( LDU, SMLSIZ+1 ).
On entry, VT**H contains the right singular vector matrices of
all subproblems at the bottom level.
K (input)
K is INTEGER array, dimension ( N ).
DIFL (input)
DIFL is DOUBLE PRECISION array, dimension ( LDU, NLVL ).
where NLVL = INT(log_2 (N/(SMLSIZ+1))) + 1.
DIFR (input)
DIFR is 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)
Z is 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)
POLES is 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)
GIVPTR is 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)
GIVCOL is 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)
LDGCOL is INTEGER, LDGCOL = > N.
The leading dimension of arrays GIVCOL and PERM.
PERM (input)
PERM is INTEGER array, dimension ( LDGCOL, NLVL ).
On entry, PERM(*, I) records permutations done on the I-th
level of the computation tree.
GIVNUM (input)
GIVNUM is 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)
C is 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)
S is 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.
RWORK (output)
RWORK is DOUBLE PRECISION array, dimension at least
MAX( (SMLSZ+1)*NRHS*3, N*(1+NRHS) + 2*NRHS ).
IWORK (output)
IWORK is INTEGER array.
The dimension must be at least 3 * N
INFO (output)
INFO is INTEGER
= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an illegal value.
LAPACK routine 31 October 2017 ZLALSA(3)