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LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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| subroutine dlasd7 | ( | integer | ICOMPQ, |
| integer | NL, | ||
| integer | NR, | ||
| integer | SQRE, | ||
| integer | K, | ||
| double precision, dimension( * ) | D, | ||
| double precision, dimension( * ) | Z, | ||
| double precision, dimension( * ) | ZW, | ||
| double precision, dimension( * ) | VF, | ||
| double precision, dimension( * ) | VFW, | ||
| double precision, dimension( * ) | VL, | ||
| double precision, dimension( * ) | VLW, | ||
| double precision | ALPHA, | ||
| double precision | BETA, | ||
| double precision, dimension( * ) | DSIGMA, | ||
| integer, dimension( * ) | IDX, | ||
| integer, dimension( * ) | IDXP, | ||
| integer, dimension( * ) | IDXQ, | ||
| integer, dimension( * ) | PERM, | ||
| integer | GIVPTR, | ||
| integer, dimension( ldgcol, * ) | GIVCOL, | ||
| integer | LDGCOL, | ||
| double precision, dimension( ldgnum, * ) | GIVNUM, | ||
| integer | LDGNUM, | ||
| double precision | C, | ||
| double precision | S, | ||
| integer | INFO | ||
| ) |
DLASD7 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 sbdsdc.
Download DLASD7 + dependencies [TGZ] [ZIP] [TXT]
DLASD7 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. DLASD7 is called from DLASD6.
| [in] | ICOMPQ | ICOMPQ is 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. |
| [in] | NL | NL is INTEGER
The row dimension of the upper block. NL >= 1. |
| [in] | NR | NR is INTEGER
The row dimension of the lower block. NR >= 1. |
| [in] | SQRE | SQRE is 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. |
| [out] | K | K is INTEGER
Contains the dimension of the non-deflated matrix, this is
the order of the related secular equation. 1 <= K <=N. |
| [in,out] | D | D is DOUBLE PRECISION array, dimension ( N )
On entry D contains the singular values of the two submatrices
to be combined. On exit D contains the trailing (N-K) updated
singular values (those which were deflated) sorted into
increasing order. |
| [out] | Z | Z is DOUBLE PRECISION array, dimension ( M )
On exit Z contains the updating row vector in the secular
equation. |
| [out] | ZW | ZW is DOUBLE PRECISION array, dimension ( M )
Workspace for Z. |
| [in,out] | VF | VF is DOUBLE PRECISION 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. On exit, VF contains the first components
of all right singular vectors of the bidiagonal matrix. |
| [out] | VFW | VFW is DOUBLE PRECISION array, dimension ( M )
Workspace for VF. |
| [in,out] | VL | VL is DOUBLE PRECISION 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. On exit, VL contains the last components
of all right singular vectors of the bidiagonal matrix. |
| [out] | VLW | VLW is DOUBLE PRECISION array, dimension ( M )
Workspace for VL. |
| [in] | ALPHA | ALPHA is DOUBLE PRECISION
Contains the diagonal element associated with the added row. |
| [in] | BETA | BETA is DOUBLE PRECISION
Contains the off-diagonal element associated with the added
row. |
| [out] | DSIGMA | DSIGMA is DOUBLE PRECISION array, dimension ( N )
Contains a copy of the diagonal elements (K-1 singular values
and one zero) in the secular equation. |
| [out] | IDX | IDX is INTEGER array, dimension ( N )
This will contain the permutation used to sort the contents of
D into ascending order. |
| [out] | IDXP | IDXP is INTEGER array, dimension ( N )
This will contain the permutation used to place deflated
values of D at the end of the array. On output IDXP(2:K)
points to the nondeflated D-values and IDXP(K+1:N)
points to the deflated singular values. |
| [in] | IDXQ | IDXQ is 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. |
| [out] | PERM | PERM is INTEGER array, dimension ( N )
The permutations (from deflation and sorting) to be applied
to each singular block. Not referenced if ICOMPQ = 0. |
| [out] | GIVPTR | GIVPTR is INTEGER
The number of Givens rotations which took place in this
subproblem. Not referenced if ICOMPQ = 0. |
| [out] | GIVCOL | GIVCOL is 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. |
| [in] | LDGCOL | LDGCOL is INTEGER
The leading dimension of GIVCOL, must be at least N. |
| [out] | GIVNUM | GIVNUM is DOUBLE PRECISION 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. |
| [in] | LDGNUM | LDGNUM is INTEGER
The leading dimension of GIVNUM, must be at least N. |
| [out] | C | C is DOUBLE PRECISION
C contains garbage if SQRE =0 and the C-value of a Givens
rotation related to the right null space if SQRE = 1. |
| [out] | S | S is DOUBLE PRECISION
S contains garbage if SQRE =0 and the S-value of a Givens
rotation related to the right null space if SQRE = 1. |
| [out] | INFO | INFO is INTEGER
= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an illegal value. |
1.9.4