Visible to Intel only — GUID: GUID-020CC0E2-37E2-48D1-86C3-67B98FBC8BCA
Visible to Intel only — GUID: GUID-020CC0E2-37E2-48D1-86C3-67B98FBC8BCA
?lasd7
Merges the two sets of singular values together into a single sorted set. Then it tries to deflate the size of the problem. Used by ?bdsdc.
Syntax
call slasd7( icompq, nl, nr, sqre, k, d, z, zw, vf, vfw, vl, vlw, alpha, beta, dsigma, idx, idxp, idxq, perm, givptr, givcol, ldgcol, givnum, ldgnum, c, s, info )
call dlasd7( icompq, nl, nr, sqre, k, d, z, zw, vf, vfw, vl, vlw, alpha, beta, dsigma, idx, idxp, idxq, perm, givptr, givcol, ldgcol, givnum, ldgnum, c, s, info )
Include Files
- mkl.fi
Description
The routine ?lasd7 merges the two sets of singular values together into a single sorted set. Then it tries to deflate the size of the problem. There are two ways in which deflation can occur: when two or more singular values are close together or if there is a tiny entry in the Z vector. For each such occurrence the order of the related secular equation problem is reduced by one. ?lasd7 is called from ?lasd6.
Input Parameters
- icompq
-
INTEGER. Specifies whether singular vectors are to be computed in compact form, as follows:
= 0: Compute singular values only.
= 1: Compute singular vectors of upper bidiagonal matrix in compact form.
- nl
-
INTEGER. The row dimension of the upper block.
nl≥ 1.
- nr
-
INTEGER. The row dimension of the lower block.
nr≥ 1.
- sqre
-
INTEGER.
= 0: the lower block is an nr-by-nr square matrix.
= 1: the lower block is an nr-by-(nr+1) rectangular matrix. The bidiagonal matrix has n = nl + nr + 1 rows and m = n + sqre≥n columns.
- d
-
REAL for slasd7.
DOUBLE PRECISION for dlasd7.
Array, DIMENSION (n). On entry d contains the singular values of the two submatrices to be combined.
- zw
-
REAL for slasd7.
DOUBLE PRECISION for dlasd7.
Array, DIMENSION ( m ).
Workspace for z.
- vf
-
REAL for slasd7.
DOUBLE PRECISION for dlasd7.
Array, DIMENSION ( m ). On entry, vf(1:nl+1) contains the first components of all right singular vectors of the upper block; and vf(nl+2:m) contains the first components of all right singular vectors of the lower block.
- vfw
-
REAL for slasd7.
DOUBLE PRECISION for dlasd7.
Array, DIMENSION ( m ).
Workspace for vf.
- vl
-
REAL for slasd7.
DOUBLE PRECISION for dlasd7.
Array, DIMENSION ( m ).
On entry, vl(1:nl+1) contains the last components of all right singular vectors of the upper block; and vl(nl+2:m) contains the last components of all right singular vectors of the lower block.
- VLW
-
REAL for slasd7.
DOUBLE PRECISION for dlasd7.
Array, DIMENSION ( m ).
Workspace for VL.
- alpha
-
REAL for slasd7
DOUBLE PRECISION for dlasd7.
Contains the diagonal element associated with the added row.
- beta
-
REAL for slasd7.
DOUBLE PRECISION for dlasd7.
Contains the off-diagonal element associated with the added row.
- idx
-
INTEGER.
Workspace array, DIMENSION (n). This will contain the permutation used to sort the contents of d into ascending order.
- idxp
-
INTEGER.
Workspace array, DIMENSION (n). This will contain the permutation used to place deflated values of d at the end of the array.
- idxq
-
INTEGER.
Array, DIMENSION (n).
This contains the permutation which separately sorts the two sub-problems in d into ascending order. Note that entries in the first half of this permutation must first be moved one position backward; and entries in the second half must first have nl+1 added to their values.
- ldgcol
-
INTEGER.The leading dimension of the output array givcol, must be at least n.
- ldgnum
-
INTEGER. The leading dimension of the output array givnum, must be at least n.
Output Parameters
- k
-
INTEGER. Contains the dimension of the non-deflated matrix, this is the order of the related secular equation.
1 ≤ k ≤ n.
- d
-
On exit, d contains the trailing (n-k) updated singular values (those which were deflated) sorted into increasing order.
- z
-
REAL for slasd7.
DOUBLE PRECISION for dlasd7.
Array, DIMENSION (m).
On exit, Z contains the updating row vector in the secular equation.
- vf
-
On exit, vf contains the first components of all right singular vectors of the bidiagonal matrix.
- vl
-
On exit, vl contains the last components of all right singular vectors of the bidiagonal matrix.
- dsigma
-
REAL for slasd7.
DOUBLE PRECISION for dlasd7.
Array, DIMENSION (n). Contains a copy of the diagonal elements (k-1 singular values and one zero) in the secular equation.
- idxp
-
On output, idxp(2: k) points to the nondeflated d-values and idxp( k+1:n) points to the deflated singular values.
- perm
-
INTEGER.
Array, DIMENSION (n).
The permutations (from deflation and sorting) to be applied to each singular block. Not referenced if icompq = 0.
- givptr
-
INTEGER.
The number of Givens rotations which took place in this subproblem. Not referenced if icompq = 0.
- givcol
-
INTEGER.
Array, DIMENSION ( ldgcol, 2 ). Each pair of numbers indicates a pair of columns to take place in a Givens rotation. Not referenced if icompq = 0.
- givnum
-
REAL for slasd7.
DOUBLE PRECISION for dlasd7.
Array, DIMENSION ( ldgnum, 2 ). Each number indicates the C or S value to be used in the corresponding Givens rotation. Not referenced if icompq = 0.
- c
-
REAL for slasd7.
DOUBLE PRECISION for dlasd7.
If sqre =0, then c contains garbage, and if sqre = 1, then c contains C-value of a Givens rotation related to the right null space.
- S
-
REAL for slasd7.
DOUBLE PRECISION for dlasd7.
If sqre =0, then s contains garbage, and if sqre = 1, then s contains S-value of a Givens rotation related to the right null space.
- info
-
INTEGER.
= 0: successful exit.
< 0: if info = -i, the i-th argument had an illegal value.