LAPACK
3.6.1
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.
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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. |
Definition at line 282 of file dlasd7.f.