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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 clals0 | ( | integer | ICOMPQ, |
| integer | NL, | ||
| integer | NR, | ||
| integer | SQRE, | ||
| integer | NRHS, | ||
| complex, dimension( ldb, * ) | B, | ||
| integer | LDB, | ||
| complex, dimension( ldbx, * ) | BX, | ||
| integer | LDBX, | ||
| integer, dimension( * ) | PERM, | ||
| integer | GIVPTR, | ||
| integer, dimension( ldgcol, * ) | GIVCOL, | ||
| integer | LDGCOL, | ||
| real, dimension( ldgnum, * ) | GIVNUM, | ||
| integer | LDGNUM, | ||
| real, dimension( ldgnum, * ) | POLES, | ||
| real, dimension( * ) | DIFL, | ||
| real, dimension( ldgnum, * ) | DIFR, | ||
| real, dimension( * ) | Z, | ||
| integer | K, | ||
| real | C, | ||
| real | S, | ||
| real, dimension( * ) | RWORK, | ||
| integer | INFO | ||
| ) |
CLALS0 applies back multiplying factors in solving the least squares problem using divide and conquer SVD approach. Used by sgelsd.
Download CLALS0 + dependencies [TGZ] [ZIP] [TXT]
CLALS0 applies back the multiplying factors of either the left or the
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). | [in] | ICOMPQ | ICOMPQ is INTEGER
Specifies whether singular vectors are to be computed in
factored form:
= 0: Left singular vector matrix.
= 1: Right singular vector matrix. |
| [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 row dimension N = NL + NR + 1,
and column dimension M = N + SQRE. |
| [in] | NRHS | NRHS is INTEGER
The number of columns of B and BX. NRHS must be at least 1. |
| [in,out] | B | B is COMPLEX array, dimension ( LDB, NRHS )
On input, B contains the right hand sides of the least
squares problem in rows 1 through M. On output, B contains
the solution X in rows 1 through N. |
| [in] | LDB | LDB is INTEGER
The leading dimension of B. LDB must be at least
max(1,MAX( M, N ) ). |
| [out] | BX | BX is COMPLEX array, dimension ( LDBX, NRHS ) |
| [in] | LDBX | LDBX is INTEGER
The leading dimension of BX. |
| [in] | PERM | PERM is INTEGER array, dimension ( N )
The permutations (from deflation and sorting) applied
to the two blocks. |
| [in] | GIVPTR | GIVPTR is INTEGER
The number of Givens rotations which took place in this
subproblem. |
| [in] | GIVCOL | GIVCOL is INTEGER array, dimension ( LDGCOL, 2 )
Each pair of numbers indicates a pair of rows/columns
involved in a Givens rotation. |
| [in] | LDGCOL | LDGCOL is INTEGER
The leading dimension of GIVCOL, must be at least N. |
| [in] | GIVNUM | GIVNUM is REAL array, dimension ( LDGNUM, 2 )
Each number indicates the C or S value used in the
corresponding Givens rotation. |
| [in] | LDGNUM | LDGNUM is INTEGER
The leading dimension of arrays DIFR, POLES and
GIVNUM, must be at least K. |
| [in] | POLES | POLES is REAL 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. |
| [in] | DIFL | DIFL is REAL 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. |
| [in] | DIFR | DIFR is REAL 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. |
| [in] | Z | Z is REAL array, dimension ( K )
Contain the components of the deflation-adjusted updating row
vector. |
| [in] | 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] | C | C is REAL
C contains garbage if SQRE =0 and the C-value of a Givens
rotation related to the right null space if SQRE = 1. |
| [in] | S | S is REAL
S contains garbage if SQRE =0 and the S-value of a Givens
rotation related to the right null space if SQRE = 1. |
| [out] | RWORK | RWORK is REAL array, dimension
( K*(1+NRHS) + 2*NRHS ) |
| [out] | INFO | INFO is INTEGER
= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an illegal value. |
Definition at line 267 of file clals0.f.
1.9.5