clals0 - apply back multiplying factors in solving the least squares problem using divide and conquer SVD approach. Used by cgelsd
SUBROUTINE CLALS0(ICOMPQ, NL, NR, SQRE, NRHS, B, LDB, BX, LDBX, PERM, GIVPTR, GIVCOL, LDGCOL, GIVNUM, LDGNUM, POLES, DIFL, DIFR, Z, K, C, S, RWORK, INFO) INTEGER GIVPTR, ICOMPQ, INFO, K, LDB, LDBX, LDGCOL, LDGNUM, NL, NR, NRHS, SQRE REAL C, S INTEGER GIVCOL(LDGCOL,*), PERM(*) REAL DIFL(*), DIFR(LDGNUM,*), GIVNUM(LDGNUM,*), POLES(LDGNUM,*), RWORK(*), Z(*) COMPLEX B(LDB,*), BX(LDBX,*) SUBROUTINE CLALS0_64(ICOMPQ, NL, NR, SQRE, NRHS, B, LDB, BX, LDBX, PERM, GIVPTR, GIVCOL, LDGCOL, GIVNUM, LDGNUM, POLES, DIFL, DIFR, Z, K, C, S, RWORK, INFO) INTEGER*8 GIVPTR, ICOMPQ, INFO, K, LDB, LDBX, LDGCOL, LDGNUM, NL, NR, NRHS, SQRE REAL C, S INTEGER*8 GIVCOL(LDGCOL,*), PERM(*) REAL DIFL(*), DIFR(LDGNUM,*), GIVNUM(LDGNUM,*), POLES(LDGNUM,*), RWORK(*), Z(*) COMPLEX B(LDB,*), BX(LDBX,*) F95 INTERFACE SUBROUTINE LALS0(ICOMPQ, NL, NR, SQRE, NRHS, B, LDB, BX, LDBX, PERM, GIVPTR, GIVCOL, LDGCOL, GIVNUM, LDGNUM, POLES, DIFL, DIFR, Z, K, C, S, RWORK, INFO) REAL, DIMENSION(:,:) :: GIVNUM, POLES, DIFR INTEGER :: ICOMPQ, NL, NR, SQRE, NRHS, LDB, LDBX, GIVPTR, LDGCOL, LDGNUM, K, INFO INTEGER, DIMENSION(:) :: PERM REAL, DIMENSION(:) :: DIFL, Z, RWORK COMPLEX, DIMENSION(:,:) :: B, BX INTEGER, DIMENSION(:,:) :: GIVCOL REAL :: C, S SUBROUTINE LALS0_64(ICOMPQ, NL, NR, SQRE, NRHS, B, LDB, BX, LDBX, PERM, GIVPTR, GIVCOL, LDGCOL, GIVNUM, LDGNUM, POLES, DIFL, DIFR, Z, K, C, S, RWORK, INFO) REAL, DIMENSION(:,:) :: GIVNUM, POLES, DIFR INTEGER(8) :: ICOMPQ, NL, NR, SQRE, NRHS, LDB, LDBX, GIVPTR, LDGCOL, LDGNUM, K, INFO INTEGER(8), DIMENSION(:) :: PERM REAL, DIMENSION(:) :: DIFL, Z, RWORK COMPLEX, DIMENSION(:,:) :: B, BX INTEGER(8), DIMENSION(:,:) :: GIVCOL REAL :: C, S C INTERFACE #include <sunperf.h> void clals0 (int icompq, int nl, int nr, int sqre, int nrhs, floatcom- plex *b, int ldb, floatcomplex *bx, int ldbx, int *perm, int givptr, int *givcol, int ldgcol, float *givnum, int ldgnum, float *poles, float *difl, float *difr, float *z, int k, float c, float s, int *info); void clals0_64 (long icompq, long nl, long nr, long sqre, long nrhs, floatcomplex *b, long ldb, floatcomplex *bx, long ldbx, long *perm, long givptr, long *givcol, long ldgcol, float *givnum, long ldgnum, float *poles, float *difl, float *difr, float *z, long k, float c, float s, long *info);
Oracle Solaris Studio Performance Library clals0(3P)
NAME
clals0 - apply back multiplying factors in solving the least squares
problem using divide and conquer SVD approach. Used by cgelsd
SYNOPSIS
SUBROUTINE CLALS0(ICOMPQ, NL, NR, SQRE, NRHS, B, LDB, BX, LDBX, PERM,
GIVPTR, GIVCOL, LDGCOL, GIVNUM, LDGNUM, POLES, DIFL, DIFR, Z,
K, C, S, RWORK, INFO)
INTEGER GIVPTR, ICOMPQ, INFO, K, LDB, LDBX, LDGCOL, LDGNUM, NL, NR,
NRHS, SQRE
REAL C, S
INTEGER GIVCOL(LDGCOL,*), PERM(*)
REAL DIFL(*), DIFR(LDGNUM,*), GIVNUM(LDGNUM,*), POLES(LDGNUM,*),
RWORK(*), Z(*)
COMPLEX B(LDB,*), BX(LDBX,*)
SUBROUTINE CLALS0_64(ICOMPQ, NL, NR, SQRE, NRHS, B, LDB, BX, LDBX,
PERM, GIVPTR, GIVCOL, LDGCOL, GIVNUM, LDGNUM, POLES, DIFL,
DIFR, Z, K, C, S, RWORK, INFO)
INTEGER*8 GIVPTR, ICOMPQ, INFO, K, LDB, LDBX, LDGCOL, LDGNUM, NL, NR,
NRHS, SQRE
REAL C, S
INTEGER*8 GIVCOL(LDGCOL,*), PERM(*)
REAL DIFL(*), DIFR(LDGNUM,*), GIVNUM(LDGNUM,*), POLES(LDGNUM,*),
RWORK(*), Z(*)
COMPLEX B(LDB,*), BX(LDBX,*)
F95 INTERFACE
SUBROUTINE LALS0(ICOMPQ, NL, NR, SQRE, NRHS, B, LDB, BX, LDBX, PERM,
GIVPTR, GIVCOL, LDGCOL, GIVNUM, LDGNUM, POLES, DIFL, DIFR, Z,
K, C, S, RWORK, INFO)
REAL, DIMENSION(:,:) :: GIVNUM, POLES, DIFR
INTEGER :: ICOMPQ, NL, NR, SQRE, NRHS, LDB, LDBX, GIVPTR, LDGCOL,
LDGNUM, K, INFO
INTEGER, DIMENSION(:) :: PERM
REAL, DIMENSION(:) :: DIFL, Z, RWORK
COMPLEX, DIMENSION(:,:) :: B, BX
INTEGER, DIMENSION(:,:) :: GIVCOL
REAL :: C, S
SUBROUTINE LALS0_64(ICOMPQ, NL, NR, SQRE, NRHS, B, LDB, BX, LDBX, PERM,
GIVPTR, GIVCOL, LDGCOL, GIVNUM, LDGNUM, POLES, DIFL, DIFR, Z,
K, C, S, RWORK, INFO)
REAL, DIMENSION(:,:) :: GIVNUM, POLES, DIFR
INTEGER(8) :: ICOMPQ, NL, NR, SQRE, NRHS, LDB, LDBX, GIVPTR, LDGCOL,
LDGNUM, K, INFO
INTEGER(8), DIMENSION(:) :: PERM
REAL, DIMENSION(:) :: DIFL, Z, RWORK
COMPLEX, DIMENSION(:,:) :: B, BX
INTEGER(8), DIMENSION(:,:) :: GIVCOL
REAL :: C, S
C INTERFACE
#include <sunperf.h>
void clals0 (int icompq, int nl, int nr, int sqre, int nrhs, floatcom-
plex *b, int ldb, floatcomplex *bx, int ldbx, int *perm, int
givptr, int *givcol, int ldgcol, float *givnum, int ldgnum,
float *poles, float *difl, float *difr, float *z, int k,
float c, float s, int *info);
void clals0_64 (long icompq, long nl, long nr, long sqre, long nrhs,
floatcomplex *b, long ldb, floatcomplex *bx, long ldbx, long
*perm, long givptr, long *givcol, long ldgcol, float *givnum,
long ldgnum, float *poles, float *difl, float *difr, float
*z, long k, float c, float s, long *info);
PURPOSE
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).
ARGUMENTS
ICOMPQ (input)
ICOMPQ is INTEGER
Specifies whether singular vectors are to be computed in the
factored form:
= 0: Left singular vector matrix.
= 1: Right singular vector matrix.
NL (input)
NL is INTEGER
The row dimension of the upper block. NL >= 1.
NR (input)
NR is INTEGER
The row dimension of the lower block. NR >= 1.
SQRE (input)
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 (input)
NRHS is INTEGER
The number of columns of B and BX. NRHS must be at least 1.
B (input/output)
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.
LDB (input)
LDB is INTEGER
The leading dimension of B. LDB must be at least
max(1,MAX(M,N)).
BX (output)
BX is COMPLEX array, dimension (LDBX, NRHS)
LDBX (input)
LDBX is INTEGER
The leading dimension of BX.
PERM (input)
PERM is INTEGER array, dimension (N)
The permutations (from deflation and sorting) applied to the
two blocks.
GIVPTR (input)
GIVPTR is INTEGER
The number of Givens rotations which took place in this sub-
problem.
GIVCOL (input)
GIVCOL is INTEGER array, dimension (LDGCOL, 2)
Each pair of numbers indicates a pair of rows/columns
involved in a Givens rotation.
LDGCOL (input)
LDGCOL is INTEGER
The leading dimension of GIVCOL, must be at least N.
GIVNUM (input)
GIVNUM is REAL array, dimension (LDGNUM, 2)
Each number indicates the C or S value used in the corre-
sponding Givens rotation.
LDGNUM (input)
LDGNUM is INTEGER
The leading dimension of arrays DIFR, POLES and GIVNUM, must
be at least K.
POLES (input)
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.
DIFL (input)
DIFL is REAL array, dimension (K)
On entry, DIFL(I) is the distance between I-th updated (unde-
flated) singular value and the I-th (undeflated) old singular
value.
DIFR (input)
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 (unde-
flated) old singular value. And DIFR(I, 2) is the normalizing
factor for the I-th right singular vector.
Z (input)
Z is REAL array, dimension (K)
Contain the components of the deflation-adjusted updating row
vector.
K (input)
K is INTEGER
Contains the dimension of the non-deflated matrix. This is
the order of the related secular equation. 1 <= K <=N.
C (input)
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.
S (input)
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.
RWORK (output)
RWORK is REAL array, dimension (K*(1+NRHS)+2*NRHS)
INFO (output)
INFO is INTEGER
= 0: successful exit,
< 0: if INFO = -i, the i-th argument had an illegal value.
7 Nov 2015 clals0(3P)