Visible to Intel only — GUID: GUID-DE862267-9099-4791-80EA-E4D02088916F
Visible to Intel only — GUID: GUID-DE862267-9099-4791-80EA-E4D02088916F
?lals0
Applies back multiplying factors in solving the least squares problem using divide and conquer SVD approach. Used by ?gelsd.
Syntax
call slals0( icompq, nl, nr, sqre, nrhs, b, ldb, bx, ldbx, perm, givptr, givcol, ldgcol, givnum, ldgnum, poles, difl, difr, z, k, c, s, work, info )
call dlals0( icompq, nl, nr, sqre, nrhs, b, ldb, bx, ldbx, perm, givptr, givcol, ldgcol, givnum, ldgnum, poles, difl, difr, z, k, c, s, work, info )
call clals0( icompq, nl, nr, sqre, nrhs, b, ldb, bx, ldbx, perm, givptr, givcol, ldgcol, givnum, ldgnum, poles, difl, difr, z, k, c, s, rwork, info )
call zlals0( icompq, nl, nr, sqre, nrhs, b, ldb, bx, ldbx, perm, givptr, givcol, ldgcol, givnum, ldgnum, poles, difl, difr, z, k, c, s, rwork, info )
Include Files
- mkl.fi
Description
The routine applies back the multiplying factors of either the left or right singular vector matrix of a diagonal matrix appended by a row to the right hand side matrix B in solving the least squares problem using the divide-and-conquer SVD approach.
For the left singular vector matrix, three types of orthogonal matrices are involved:
(1L) Givens rotations: the number of such rotations is givptr;the pairs of columns/rows they were applied to are stored in givcol;and the c- and s-values of these rotations are stored in givnum.
(2L) Permutation. The (nl+1)-st row of B is to be moved to the first row, and for j=2:n, perm(j)-th row of B is to be moved to the j-th row.
(3L) The left singular vector matrix of the remaining matrix.
For the right singular vector matrix, four types of orthogonal matrices are involved:
(1R) The right singular vector matrix of the remaining matrix.
(2R) If sqre = 1, one extra Givens rotation to generate the right null space.
(3R) The inverse transformation of (2L).
(4R) The inverse transformation of (1L).
Input Parameters
- icompq
-
INTEGER. Specifies whether singular vectors are to be computed in factored form:
If icompq = 0: Left singular vector matrix.
If icompq = 1: Right singular vector matrix.
- nl
-
INTEGER. The row dimension of the upper block.
nl≥ 1.
- nr
-
INTEGER. The row dimension of the lower block.
nr≥ 1.
- sqre
-
INTEGER.
If sqre = 0: the lower block is an nr-by-nr square matrix.
If sqre = 1: the lower block is an nr-by-(nr+1) rectangular matrix. The bidiagonal matrix has row dimension n = nl + nr + 1, and column dimension m = n + sqre.
- nrhs
-
INTEGER. The number of columns of B and bx.
Must be at least 1.
- b
-
REAL for slals0
DOUBLE PRECISION for dlals0
COMPLEX for clals0
DOUBLE COMPLEX for zlals0.
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.
Must be at least max(1,max( m, n )).
- bx
-
REAL for slals0
DOUBLE PRECISION for dlals0
COMPLEX for clals0
DOUBLE COMPLEX for zlals0.
Workspace array, DIMENSION ( ldbx, nrhs ).
- ldbx
-
INTEGER. The leading dimension of bx.
- perm
-
INTEGER. Array, DIMENSION (n).
The permutations (from deflation and sorting) applied to the two blocks.
- givptr
-
INTEGER. The number of Givens rotations which took place in this subproblem.
- givcol
-
INTEGER. Array, DIMENSION ( ldgcol, 2 ). Each pair of numbers indicates a pair of rows/columns involved in a Givens rotation.
- ldgcol
-
INTEGER. The leading dimension of givcol, must be at least n.
- givnum
-
REAL for slals0/clals0
DOUBLE PRECISION for dlals0/zlals0
Array, DIMENSION ( ldgnum, 2 ). Each number indicates the c or s value used in the corresponding Givens rotation.
- ldgnum
-
INTEGER. The leading dimension of arrays difr, poles and givnum, must be at least k.
- poles
-
REAL for slals0/clals0
DOUBLE PRECISION for dlals0/zlals0
Array, DIMENSION ( ldgnum, 2 ). On entry, poles(1:k, 1) contains the new singular values obtained from solving the secular equation, and poles(1:k, 2) is an array containing the poles in the secular equation.
- difl
-
REAL for slals0/clals0
DOUBLE PRECISION for dlals0/zlals0
Array, DIMENSION ( k ). On entry, difl(i) is the distance between i-th updated (undeflated) singular value and the i-th (undeflated) old singular value.
- difr
-
REAL for slals0/clals0
DOUBLE PRECISION for dlals0/zlals0
Array, DIMENSION ( ldgnum, 2 ). On entry, difr(i, 1) contains the distances between i-th updated (undeflated) singular value and the i+1-th (undeflated) old singular value. And difr(i, 2) is the normalizing factor for the i-th right singular vector.
- z
-
REAL for slals0/clals0
DOUBLE PRECISION for dlals0/zlals0
Array, DIMENSION ( k ). Contains the components of the deflation-adjusted updating row vector.
- K
-
INTEGER. Contains the dimension of the non-deflated matrix. This is the order of the related secular equation. 1 ≤ k ≤ n.
- c
-
REAL for slals0/clals0
DOUBLE PRECISION for dlals0/zlals0
Contains garbage if sqre =0 and the c value of a Givens rotation related to the right null space if sqre = 1.
- s
-
REAL for slals0/clals0
DOUBLE PRECISION for dlals0/zlals0
Contains garbage if sqre =0 and the s value of a Givens rotation related to the right null space if sqre = 1.
- work
-
REAL for slals0
DOUBLE PRECISION for dlals0
Workspace array, DIMENSION ( k ). Used with real flavors only.
- rwork
-
REAL for clals0
DOUBLE PRECISION for zlals0
Workspace array, DIMENSION (k*(1+nrhs) + 2*nrhs). Used with complex flavors only.
Output Parameters
- b
-
On exit, contains the solution X in rows 1 through n.
- info
-
INTEGER.
If info = 0: successful exit.
If info = -i < 0, the i-th argument had an illegal value.