Developer Reference for Intel® oneAPI Math Kernel Library for Fortran
?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
slalsa dlalsa clalsa zlalsa
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 , ldu≥n . 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:code:`T` (for real flavors) or vt:code:`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(log_{2}(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 (*, 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
-
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 (*, 2 i -1: 2 i ) 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 (*, 2 i -1: 2 i ) records the locations of Givens rotations performed on the i -th level on the computation tree.
- ldgcol
-
INTEGER , ldgcol≥n . 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 (*, 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
-
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 (3 n ).
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.