Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

ID 766686
Date 3/31/2023
Public

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?lalsa

Computes the SVD of the coefficient matrix in compact form. Used by ?gelsd.

Syntax

call slalsa( icompq, smlsiz, n, nrhs, b, ldb, bx, ldbx, u, ldu, vt, k, difl, difr, z, poles, givptr, givcol, ldgcol, perm, givnum, c, s, work, iwork, info )

call dlalsa( icompq, smlsiz, n, nrhs, b, ldb, bx, ldbx, u, ldu, vt, k, difl, difr, z, poles, givptr, givcol, ldgcol, perm, givnum, c, s, work, iwork, info )

call clalsa( 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 )

call 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 )

Include Files
  • mkl.fi
Description

The routine 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, ?lalsa applies the inverse of the left singular vector matrix of an upper bidiagonal matrix to the right hand side; and if icompq = 1, the routine applies the right singular vector matrix to the right hand side. The singular vector matrices were generated in the compact form by ?lalsa.

Input Parameters
icompq

INTEGER. Specifies whether the left or the right singular vector matrix is involved. If icompq = 0: left singular vector matrix is used

If icompq = 1: right singular vector matrix is used.

smlsiz

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

n

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

nrhs

INTEGER. The number of columns of b and bx. Must be at least 1.

b

REAL for slalsa

DOUBLE PRECISION for dlalsa

COMPLEX for clalsa

DOUBLE COMPLEX for zlalsa

Array, DIMENSION (ldb, nrhs). Contains the right hand sides of the least squares problem in rows 1 through m.

ldb

INTEGER. The leading dimension of b in the calling subprogram. Must be at least max(1,max( m, n )).

ldbx

INTEGER. The leading dimension of the output array bx.

u

REAL for slalsa/clalsa

DOUBLE PRECISION for dlalsa/zlalsa

Array, DIMENSION (ldu, smlsiz). On entry, u contains the left singular vector matrices of all subproblems at the bottom level.

ldu

INTEGER, ldun. The leading dimension of arrays u, vt, difl, difr, poles, givnum, and z.

vt

REAL for slalsa/clalsa

DOUBLE PRECISION for dlalsa/zlalsa

Array, DIMENSION(ldu, smlsiz +1). On entry, vt T (for real flavors) or vt H (for complex flavors) contains the right singular vector matrices of all subproblems at the bottom level.

k

INTEGER array, DIMENSION ( n ).

difl

REAL for slalsa/clalsa

DOUBLE PRECISION for dlalsa/zlalsa

Array, DIMENSION (ldu, nlvl), where nlvl = int(log2(n /(smlsiz+1))) + 1.

difr

REAL for slalsa/clalsa

DOUBLE PRECISION for dlalsa/zlalsa

Array, DIMENSION(ldu, 2*nlvl). On entry, difl(*, i) and difr(*, 2i -1) record distances between singular values on the i-th level and singular values on the (i -1)-th level, and difr(*, 2i) record the normalizing factors of the right singular vectors matrices of subproblems on i-th level.

z

REAL for slalsa/clalsa

DOUBLE PRECISION for dlalsa/zlalsa

Array, DIMENSION (ldu, nlvl . On entry, z(1, i) contains the components of the deflation- adjusted updating the row vector for subproblems on the i-th level.

poles

REAL for slalsa/clalsa

DOUBLE PRECISION for dlalsa/zlalsa

Array, DIMENSION (ldu, 2*nlvl).

On entry, poles(*, 2i-1: 2i) contains the new and old singular values involved in the secular equations on the i-th level.

givptr

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

INTEGER. Array, DIMENSION ( ldgcol, 2*nlvl ). On entry, for each i, givcol(*, 2i-1: 2i) records the locations of Givens rotations performed on the i-th level on the computation tree.

ldgcol

INTEGER, ldgcoln. The leading dimension of arrays givcol and perm.

perm

INTEGER. Array, DIMENSION ( ldgcol, nlvl ). On entry, perm(*, i) records permutations done on the i-th level of the computation tree.

givnum

REAL for slalsa/clalsa

DOUBLE PRECISION for dlalsa/zlalsa

Array, DIMENSION (ldu, 2*nlvl). On entry, givnum(*, 2i-1 : 2i) records the c and s values of Givens rotations performed on the i-th level on the computation tree.

c

REAL for slalsa/clalsa

DOUBLE PRECISION for dlalsa/zlalsa

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

REAL for slalsa/clalsa

DOUBLE PRECISION for dlalsa/zlalsa

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

REAL for slalsa

DOUBLE PRECISION for dlalsa

Workspace array, DIMENSION at least (n). Used with real flavors only.

rwork

REAL for clalsa

DOUBLE PRECISION for zlalsa

Workspace array, DIMENSION at least max(n, (smlsz+1)*nrhs*3). Used with complex flavors only.

iwork

INTEGER.

Workspace array, DIMENSION at least (3n).

Output Parameters
b

On exit, contains the solution X in rows 1 through n.

bx

REAL for slalsa

DOUBLE PRECISION for dlalsa

COMPLEX for clalsa

DOUBLE COMPLEX for zlalsa

Array, DIMENSION (ldbx, nrhs). On exit, the result of applying the left or right singular vector matrix to b.

info

INTEGER. If info = 0: successful exit

If info = -i < 0, the i-th argument had an illegal value.