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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 slasd2 | ( | integer | NL, |
| integer | NR, | ||
| integer | SQRE, | ||
| integer | K, | ||
| real, dimension( * ) | D, | ||
| real, dimension( * ) | Z, | ||
| real | ALPHA, | ||
| real | BETA, | ||
| real, dimension( ldu, * ) | U, | ||
| integer | LDU, | ||
| real, dimension( ldvt, * ) | VT, | ||
| integer | LDVT, | ||
| real, dimension( * ) | DSIGMA, | ||
| real, dimension( ldu2, * ) | U2, | ||
| integer | LDU2, | ||
| real, dimension( ldvt2, * ) | VT2, | ||
| integer | LDVT2, | ||
| integer, dimension( * ) | IDXP, | ||
| integer, dimension( * ) | IDX, | ||
| integer, dimension( * ) | IDXC, | ||
| integer, dimension( * ) | IDXQ, | ||
| integer, dimension( * ) | COLTYP, | ||
| integer | INFO | ||
| ) |
SLASD2 merges the two sets of singular values together into a single sorted set. Used by sbdsdc.
Download SLASD2 + dependencies [TGZ] [ZIP] [TXT]
SLASD2 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. SLASD2 is called from SLASD1.
| [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 REAL 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 REAL array, dimension (N)
On exit Z contains the updating row vector in the secular
equation. |
| [in] | ALPHA | ALPHA is REAL
Contains the diagonal element associated with the added row. |
| [in] | BETA | BETA is REAL
Contains the off-diagonal element associated with the added
row. |
| [in,out] | U | U is REAL array, dimension (LDU,N)
On entry U contains the left singular vectors of two
submatrices in the two square blocks with corners at (1,1),
(NL, NL), and (NL+2, NL+2), (N,N).
On exit U contains the trailing (N-K) updated left singular
vectors (those which were deflated) in its last N-K columns. |
| [in] | LDU | LDU is INTEGER
The leading dimension of the array U. LDU >= N. |
| [in,out] | VT | VT is REAL array, dimension (LDVT,M)
On entry VT**T contains the right singular vectors of two
submatrices in the two square blocks with corners at (1,1),
(NL+1, NL+1), and (NL+2, NL+2), (M,M).
On exit VT**T contains the trailing (N-K) updated right singular
vectors (those which were deflated) in its last N-K columns.
In case SQRE =1, the last row of VT spans the right null
space. |
| [in] | LDVT | LDVT is INTEGER
The leading dimension of the array VT. LDVT >= M. |
| [out] | DSIGMA | DSIGMA is REAL array, dimension (N)
Contains a copy of the diagonal elements (K-1 singular values
and one zero) in the secular equation. |
| [out] | U2 | U2 is REAL array, dimension (LDU2,N)
Contains a copy of the first K-1 left singular vectors which
will be used by SLASD3 in a matrix multiply (SGEMM) to solve
for the new left singular vectors. U2 is arranged into four
blocks. The first block contains a column with 1 at NL+1 and
zero everywhere else; the second block contains non-zero
entries only at and above NL; the third contains non-zero
entries only below NL+1; and the fourth is dense. |
| [in] | LDU2 | LDU2 is INTEGER
The leading dimension of the array U2. LDU2 >= N. |
| [out] | VT2 | VT2 is REAL array, dimension (LDVT2,N)
VT2**T contains a copy of the first K right singular vectors
which will be used by SLASD3 in a matrix multiply (SGEMM) to
solve for the new right singular vectors. VT2 is arranged into
three blocks. The first block contains a row that corresponds
to the special 0 diagonal element in SIGMA; the second block
contains non-zeros only at and before NL +1; the third block
contains non-zeros only at and after NL +2. |
| [in] | LDVT2 | LDVT2 is INTEGER
The leading dimension of the array VT2. LDVT2 >= M. |
| [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. |
| [out] | IDX | IDX is INTEGER array, dimension (N)
This will contain the permutation used to sort the contents of
D into ascending order. |
| [out] | IDXC | IDXC is INTEGER array, dimension (N)
This will contain the permutation used to arrange the columns
of the deflated U matrix into three groups: the first group
contains non-zero entries only at and above NL, the second
contains non-zero entries only below NL+2, and the third is
dense. |
| [in,out] | 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 hlaf 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] | COLTYP | COLTYP is INTEGER array, dimension (N)
As workspace, this will contain a label which will indicate
which of the following types a column in the U2 matrix or a
row in the VT2 matrix is:
1 : non-zero in the upper half only
2 : non-zero in the lower half only
3 : dense
4 : deflated
On exit, it is an array of dimension 4, with COLTYP(I) being
the dimension of the I-th type columns. |
| [out] | INFO | INFO is INTEGER
= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an illegal value. |
1.9.4