clalsa - compute the SVD of the coefficient matrix in compact form. Used by cgelsd
SUBROUTINE CLALSA(ICOMPQ, SMLSIZ, N, NRHS, B, LDB, BX, LDBX, U, LDU, VT, K, DIFL, DIFR, Z, POLES, GIVPTR, GIVCOL, LDGCOL, PERM, GIVNUM, C, S, RWORK, IWORK, INFO) INTEGER ICOMPQ, INFO, LDB, LDBX, LDGCOL, LDU, N, NRHS, SMLSIZ INTEGER GIVCOL(LDGCOL,*), GIVPTR(*), IWORK(*), K(*), PERM(LDGCOL,*) REAL C(*), DIFL(LDU,*), DIFR(LDU,*), GIVNUM(LDU,*), POLES(LDU,*), RWORK(*), S(*), U(LDU,*), VT(LDU,*), Z(LDU,*) COMPLEX B(LDB,*), BX(LDBX,*) SUBROUTINE CLALSA_64(ICOMPQ, SMLSIZ, N, NRHS, B, LDB, BX, LDBX, U, LDU, VT, K, DIFL, DIFR, Z, POLES, GIVPTR, GIVCOL, LDGCOL, PERM, GIVNUM, C, S, RWORK, IWORK, INFO) INTEGER*8 ICOMPQ, INFO, LDB, LDBX, LDGCOL, LDU, N, NRHS, SMLSIZ INTEGER*8 GIVCOL(LDGCOL,*), GIVPTR(*), IWORK(*), K(*), PERM(LDGCOL,*) REAL C(*), DIFL(LDU,*), DIFR(LDU,*), GIVNUM(LDU,*), POLES(LDU,*), RWORK(*), S(*), U(LDU,*), VT(LDU,*), Z(LDU,*) COMPLEX B(LDB,*), BX(LDBX,*) F95 INTERFACE SUBROUTINE LALSA( ICOMPQ, SMLSIZ, N, NRHS, B, LDB, BX, LDBX, U, LDU, VT, K, DIFL, DIFR, Z, POLES, GIVPTR, GIVCOL, LDGCOL, PERM, GIVNUM, C, S, RWORK, IWORK, INFO ) REAL, DIMENSION(:,:) :: U, VT, DIFL, DIFR, Z, POLES, GIVNUM INTEGER :: ICOMPQ, SMLSIZ, N, NRHS, LDB, LDBX, LDU, LDGCOL, INFO INTEGER, DIMENSION(:) :: K, GIVPTR, IWORK REAL, DIMENSION(:) :: C, S, RWORK COMPLEX, DIMENSION(:,:) :: B, BX INTEGER, DIMENSION(:,:) :: GIVCOL, PERM SUBROUTINE LALSA_64(ICOMPQ, SMLSIZ, N, NRHS, B, LDB, BX, LDBX, U, LDU, VT, K, DIFL, DIFR, Z, POLES, GIVPTR, GIVCOL, LDGCOL, PERM, GIVNUM, C, S, RWORK, IWORK, INFO) REAL, DIMENSION(:,:) :: U, VT, DIFL, DIFR, Z, POLES, GIVNUM INTEGER(8) :: ICOMPQ, SMLSIZ, N, NRHS, LDB, LDBX, LDU, LDGCOL, INFO INTEGER(8), DIMENSION(:) :: K, GIVPTR, IWORK REAL, DIMENSION(:) :: C, S, RWORK COMPLEX, DIMENSION(:,:) :: B, BX INTEGER(8), DIMENSION(:,:) :: GIVCOL, PERM C INTERFACE #include <sunperf.h> void clalsa (int icompq, int smlsiz, int n, int nrhs, floatcomplex *b, int ldb, floatcomplex *bx, int ldbx, float *u, int ldu, float *vt, int *k, float *difl, float *difr, float *z, float *poles, int *givptr, int *givcol, int ldgcol, int *perm, float *givnum, float *c, float *s, int *info); void clalsa_64 (long icompq, long smlsiz, long n, long nrhs, floatcom- plex *b, long ldb, floatcomplex *bx, long ldbx, float *u, long ldu, float *vt, long *k, float *difl, float *difr, float *z, float *poles, long *givptr, long *givcol, long ldgcol, long *perm, float *givnum, float *c, float *s, long *info);
Oracle Solaris Studio Performance Library clalsa(3P)
NAME
clalsa - compute the SVD of the coefficient matrix in compact form.
Used by cgelsd
SYNOPSIS
SUBROUTINE CLALSA(ICOMPQ, SMLSIZ, N, NRHS, B, LDB, BX, LDBX, U, LDU,
VT, K, DIFL, DIFR, Z, POLES, GIVPTR, GIVCOL, LDGCOL, PERM,
GIVNUM, C, S, RWORK, IWORK, INFO)
INTEGER ICOMPQ, INFO, LDB, LDBX, LDGCOL, LDU, N, NRHS, SMLSIZ
INTEGER GIVCOL(LDGCOL,*), GIVPTR(*), IWORK(*), K(*), PERM(LDGCOL,*)
REAL C(*), DIFL(LDU,*), DIFR(LDU,*), GIVNUM(LDU,*), POLES(LDU,*),
RWORK(*), S(*), U(LDU,*), VT(LDU,*), Z(LDU,*)
COMPLEX B(LDB,*), BX(LDBX,*)
SUBROUTINE CLALSA_64(ICOMPQ, SMLSIZ, N, NRHS, B, LDB, BX, LDBX, U, LDU,
VT, K, DIFL, DIFR, Z, POLES, GIVPTR, GIVCOL, LDGCOL, PERM,
GIVNUM, C, S, RWORK, IWORK, INFO)
INTEGER*8 ICOMPQ, INFO, LDB, LDBX, LDGCOL, LDU, N, NRHS, SMLSIZ
INTEGER*8 GIVCOL(LDGCOL,*), GIVPTR(*), IWORK(*), K(*), PERM(LDGCOL,*)
REAL C(*), DIFL(LDU,*), DIFR(LDU,*), GIVNUM(LDU,*), POLES(LDU,*),
RWORK(*), S(*), U(LDU,*), VT(LDU,*), Z(LDU,*)
COMPLEX B(LDB,*), BX(LDBX,*)
F95 INTERFACE
SUBROUTINE LALSA( ICOMPQ, SMLSIZ, N, NRHS, B, LDB, BX, LDBX, U, LDU,
VT, K, DIFL, DIFR, Z, POLES, GIVPTR, GIVCOL, LDGCOL, PERM,
GIVNUM, C, S, RWORK, IWORK, INFO )
REAL, DIMENSION(:,:) :: U, VT, DIFL, DIFR, Z, POLES, GIVNUM
INTEGER :: ICOMPQ, SMLSIZ, N, NRHS, LDB, LDBX, LDU, LDGCOL, INFO
INTEGER, DIMENSION(:) :: K, GIVPTR, IWORK
REAL, DIMENSION(:) :: C, S, RWORK
COMPLEX, DIMENSION(:,:) :: B, BX
INTEGER, DIMENSION(:,:) :: GIVCOL, PERM
SUBROUTINE LALSA_64(ICOMPQ, SMLSIZ, N, NRHS, B, LDB, BX, LDBX, U, LDU,
VT, K, DIFL, DIFR, Z, POLES, GIVPTR, GIVCOL, LDGCOL, PERM,
GIVNUM, C, S, RWORK, IWORK, INFO)
REAL, DIMENSION(:,:) :: U, VT, DIFL, DIFR, Z, POLES, GIVNUM
INTEGER(8) :: ICOMPQ, SMLSIZ, N, NRHS, LDB, LDBX, LDU, LDGCOL, INFO
INTEGER(8), DIMENSION(:) :: K, GIVPTR, IWORK
REAL, DIMENSION(:) :: C, S, RWORK
COMPLEX, DIMENSION(:,:) :: B, BX
INTEGER(8), DIMENSION(:,:) :: GIVCOL, PERM
C INTERFACE
#include <sunperf.h>
void clalsa (int icompq, int smlsiz, int n, int nrhs, floatcomplex *b,
int ldb, floatcomplex *bx, int ldbx, float *u, int ldu, float
*vt, int *k, float *difl, float *difr, float *z, float
*poles, int *givptr, int *givcol, int ldgcol, int *perm,
float *givnum, float *c, float *s, int *info);
void clalsa_64 (long icompq, long smlsiz, long n, long nrhs, floatcom-
plex *b, long ldb, floatcomplex *bx, long ldbx, float *u,
long ldu, float *vt, long *k, float *difl, float *difr, float
*z, float *poles, long *givptr, long *givcol, long ldgcol,
long *perm, float *givnum, float *c, float *s, long *info);
PURPOSE
clalsa is an itermediate step in solving the least squares problem by
computing the SVD of the coefficient matrix in compact form (The singu-
lar vectors are computed as products of simple orthorgonal matrices.).
If ICOMPQ = 0, CLALSA applies the inverse of the left singular vector
matrix of an upper bidiagonal matrix to the right hand side; and if
ICOMPQ = 1, CLALSA applies the right singular vector matrix to the
right hand side. The singular vector matrices were generated in compact
form by CLALSA.
ARGUMENTS
ICOMPQ (input)
ICOMPQ is INTEGER
Specifies whether the left or the right singular vector
matrix is involved.
= 0: Left singular vector matrix,
= 1: Right singular vector matrix.
SMLSIZ (input)
SMLSIZ is INTEGER
The maximum size of the subproblems at the bottom of the com-
putation tree.
N (input)
N is INTEGER
The row and column dimensions of the upper bidiagonal matrix.
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 in the calling subprogram. LDB
must be at least max(1,MAX(M, N)).
BX (output)
BX is COMPLEX array, dimension (LDBX, NRHS)
On exit, the result of applying the left or right singular
vector matrix to B.
LDBX (input)
LDBX is INTEGER
The leading dimension of BX.
U (input)
U is REAL array, dimension (LDU, SMLSIZ)
On entry, U contains the left singular vector matrices of all
subproblems at the bottom level.
LDU (input)
LDU is INTEGER, LDU = > N.
The leading dimension of arrays U, VT, DIFL, DIFR, POLES,
GIVNUM, and Z.
VT (input)
VT is REAL array, dimension (LDU, SMLSIZ+1)
On entry, VT**H contains the right singular vector matrices
of all subproblems at the bottom level.
K (input)
K is INTEGER array, dimension (N)
DIFL (input)
DIFL is REAL array, dimension (LDU, NLVL)
where NLVL = INT(log_2 (N/(SMLSIZ+1)))+1.
DIFR (input)
DIFR is REAL array, dimension (LDU, 2*NLVL)
On entry, DIFL(*, I) and DIFR(*, 2*I-1) record distances
between singular values on the I-th level and singular values
on the (I -1)-th level, and DIFR(*, 2*I) record the normaliz-
ing factors of the right singular vectors matrices of sub-
problems on I-th level.
Z (input)
Z is REAL array, dimension (LDU, NLVL)
On entry, Z(1, I) contains the components of the deflation-
adjusted updating row vector for subproblems on the I-th
level.
POLES (input)
POLES is REAL array, dimension (LDU, 2*NLVL)
On entry, POLES(*, 2*I-1 : 2*I) contains the new and old sin-
gular values involved in the secular equations on the I-th
level.
GIVPTR (input)
GIVPTR is INTEGER array, dimension (N)
On entry, GIVPTR(I) records the number of Givens rotations
performed on the I-th problem on the computation tree.
GIVCOL (input)
GIVCOL is INTEGER array, dimension (LDGCOL, 2*NLVL)
On entry, for each I, GIVCOL(*, 2*I-1 : 2*I) records the
locations of Givens rotations performed on the I-th level on
the computation tree.
LDGCOL (input)
LDGCOL is INTEGER, LDGCOL = > N.
The leading dimension of arrays GIVCOL and PERM.
PERM (input)
PERM is INTEGER array, dimension (LDGCOL, NLVL)
On entry, PERM(*, I) records permutations done on the I-th
level of the computation tree.
GIVNUM (input)
GIVNUM is REAL array, dimension (LDU, 2*NLVL)
On entry, GIVNUM(*, 2*I-1 : 2*I) records the C- and S- values
of Givens rotations performed on the I-th level on the compu-
tation tree.
C (input)
C is REAL array, dimension (N)
On entry, if the I-th subproblem is not square, C(I) contains
the C-value of a Givens rotation related to the right null
space of the I-th subproblem.
S (input)
S is REAL array, dimension (N)
On entry, if the I-th subproblem is not square, S(I) contains
the S-value of a Givens rotation related to the right null
space of the I-th subproblem.
RWORK (output)
RWORK is REAL array, dimension at least
MAX((SMLSZ+1)*NRHS*3, N*(1+NRHS)+2*NRHS)
IWORK (output)
IWORK is INTEGER array
The dimension must be at least 3*N.
INFO (output)
INFO is INTEGER
= 0: successful exit,
< 0: if INFO = -i, the i-th argument had an illegal value.
7 Nov 2015 clalsa(3P)