ZLALSA is an intermediate 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 orthogonal
 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.

ICOMPQ

          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

          SMLSIZ is INTEGER
         The maximum size of the subproblems at the bottom of the
         computation tree.

N

          N is INTEGER
         The row and column dimensions of the upper bidiagonal matrix.

NRHS

          NRHS is INTEGER
         The number of columns of B and BX. NRHS must be at least 1.

B

          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

          LDB is INTEGER
         The leading dimension of B in the calling subprogram.
         LDB must be at least max(1,MAX( M, N ) ).

BX

          BX is COMPLEX*16 array, dimension ( LDBX, NRHS )
         On exit, the result of applying the left or right singular
         vector matrix to B.

LDBX

          LDBX is INTEGER
         The leading dimension of BX.

U

          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

          LDU is INTEGER, LDU = > N.
         The leading dimension of arrays U, VT, DIFL, DIFR,
         POLES, GIVNUM, and Z.

VT

          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

          K is INTEGER array, dimension ( N ).

DIFL

          DIFL is DOUBLE PRECISION array, dimension ( LDU, NLVL ).
         where NLVL = INT(log_2 (N/(SMLSIZ+1))) + 1.

DIFR

          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

          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

          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

          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

          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

          LDGCOL is INTEGER, LDGCOL = > N.
         The leading dimension of arrays GIVCOL and PERM.

PERM

          PERM is INTEGER array, dimension ( LDGCOL, NLVL ).
         On entry, PERM(*, I) records permutations done on the I-th
         level of the computation tree.

GIVNUM

          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

          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

          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

          RWORK is DOUBLE PRECISION array, dimension at least
         MAX( (SMLSZ+1)*NRHS*3, N*(1+NRHS) + 2*NRHS ).

IWORK

          IWORK is INTEGER array, dimension (3*N)

INFO

          INFO is INTEGER
          = 0:  successful exit.
          < 0:  if INFO = -i, the i-th argument had an illegal value.

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Ming Gu and Ren-Cang Li, Computer Science Division, University of California at Berkeley, USA
Osni Marques, LBNL/NERSC, USA