table of contents
other versions
- jessie 3.5.0-4
- jessie-backports 3.7.0-1~bpo8+1
- stretch 3.7.0-2
dlals0.f(3) | LAPACK | dlals0.f(3) |
NAME¶
dlals0.f -SYNOPSIS¶
Functions/Subroutines¶
subroutine dlals0 (ICOMPQ, NL, NR, SQRE, NRHS, B, LDB, BX, LDBX, PERM, GIVPTR, GIVCOL, LDGCOL, GIVNUM, LDGNUM, POLES, DIFL, DIFR, Z, K, C, S, WORK, INFO)
Function/Subroutine Documentation¶
subroutine dlals0 (integerICOMPQ, integerNL, integerNR, integerSQRE, integerNRHS, double precision, dimension( ldb, * )B, integerLDB, double precision, dimension( ldbx, * )BX, integerLDBX, integer, dimension( * )PERM, integerGIVPTR, integer, dimension( ldgcol, * )GIVCOL, integerLDGCOL, double precision, dimension( ldgnum, * )GIVNUM, integerLDGNUM, double precision, dimension( ldgnum, * )POLES, double precision, dimension( * )DIFL, double precision, dimension( ldgnum, * )DIFR, double precision, dimension( * )Z, integerK, double precisionC, double precisionS, double precision, dimension( * )WORK, integerINFO)¶
DLALS0 applies back multiplying factors in solving the least squares problem using divide and conquer SVD approach. Used by sgelsd. Purpose:DLALS0 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).
ICOMPQ
Author:
ICOMPQ is INTEGER Specifies whether singular vectors are to be computed in factored form: = 0: Left singular vector matrix. = 1: Right singular vector matrix.NL
NL is INTEGER The row dimension of the upper block. NL >= 1.NR
NR is INTEGER The row dimension of the lower block. NR >= 1.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.NRHS
NRHS is INTEGER The number of columns of B and BX. NRHS must be at least 1.B
B is DOUBLE PRECISION 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.LDB
LDB is INTEGER The leading dimension of B. LDB must be at least max(1,MAX( M, N ) ).BX
BX is DOUBLE PRECISION array, dimension ( LDBX, NRHS )LDBX
LDBX is INTEGER The leading dimension of BX.PERM
PERM is INTEGER array, dimension ( N ) The permutations (from deflation and sorting) applied to the two blocks.GIVPTR
GIVPTR is INTEGER The number of Givens rotations which took place in this subproblem.GIVCOL
GIVCOL is INTEGER array, dimension ( LDGCOL, 2 ) Each pair of numbers indicates a pair of rows/columns involved in a Givens rotation.LDGCOL
LDGCOL is INTEGER The leading dimension of GIVCOL, must be at least N.GIVNUM
GIVNUM is DOUBLE PRECISION array, dimension ( LDGNUM, 2 ) Each number indicates the C or S value used in the corresponding Givens rotation.LDGNUM
LDGNUM is INTEGER The leading dimension of arrays DIFR, POLES and GIVNUM, must be at least K.POLES
POLES is DOUBLE PRECISION 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.DIFL
DIFL is DOUBLE PRECISION 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.DIFR
DIFR is DOUBLE PRECISION 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.Z
Z is DOUBLE PRECISION array, dimension ( K ) Contain the components of the deflation-adjusted updating row vector.K
K is INTEGER Contains the dimension of the non-deflated matrix, This is the order of the related secular equation. 1 <= K <=N.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.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.WORK
WORK is DOUBLE PRECISION array, dimension ( K )INFO
INFO is INTEGER = 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value.
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
September 2012
Contributors:
Ming Gu and Ren-Cang Li, Computer Science Division,
University of California at Berkeley, USA
Osni Marques, LBNL/NERSC, USA
Definition at line 267 of file dlals0.f.
Osni Marques, LBNL/NERSC, USA
Author¶
Generated automatically by Doxygen for LAPACK from the source code.Wed Oct 15 2014 | Version 3.4.2 |