dlalsa - compute the SVD of the coefficient matrix in compact form. Used by dgelsd
SUBROUTINE DLALSA(ICOMPQ, SMLSIZ, N, NRHS, B, LDB, BX, LDBX, U, LDU, VT, K, DIFL, DIFR, Z, POLES, GIVPTR, GIVCOL, LDGCOL, PERM, GIVNUM, C, S, WORK, IWORK, INFO) INTEGER ICOMPQ, INFO, LDB, LDBX, LDGCOL, LDU, N, NRHS, SMLSIZ INTEGER GIVCOL(LDGCOL,*), GIVPTR(*), IWORK(*), K(*), PERM(LDGCOL,*) DOUBLE PRECISION B(LDB,*), BX(LDBX,*), C(*), DIFL(LDU,*), DIFR(LDU,*), GIVNUM(LDU,*), POLES(LDU,*), S(*), U(LDU,*), VT(LDU,*), WORK(*), Z(LDU,*) SUBROUTINE DLALSA_64(ICOMPQ, SMLSIZ, N, NRHS, B, LDB, BX, LDBX, U, LDU, VT, K, DIFL, DIFR, Z, POLES, GIVPTR, GIVCOL, LDGCOL, PERM, GIVNUM, C, S, WORK, IWORK, INFO) INTEGER*8 ICOMPQ, INFO, LDB, LDBX, LDGCOL, LDU, N, NRHS, SMLSIZ INTEGER*8 GIVCOL(LDGCOL,*), GIVPTR(*), IWORK(*), K(*), PERM(LDGCOL,*) DOUBLE PRECISION B(LDB,*), BX(LDBX,*), C(*), DIFL(LDU,*), DIFR(LDU,*), GIVNUM(LDU,*), POLES(LDU,*), S(*), U(LDU,*), VT(LDU,*), WORK(*), Z(LDU,*) 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, WORK, IWORK, INFO) REAL(8), DIMENSION(:,:) :: B, BX, U, VT, DIFL, DIFR, Z, POLES, GIVNUM INTEGER :: ICOMPQ, SMLSIZ, N, NRHS, LDB, LDBX, LDU, LDGCOL, INFO INTEGER, DIMENSION(:) :: K, GIVPTR, IWORK REAL(8), DIMENSION(:) :: C, S, WORK 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, WORK, IWORK, INFO) REAL(8), DIMENSION(:,:) :: B, BX, 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(8), DIMENSION(:) :: C, S, WORK INTEGER(8), DIMENSION(:,:) :: GIVCOL, PERM C INTERFACE #include <sunperf.h> void dlalsa (int icompq, int smlsiz, int n, int nrhs, double *b, int ldb, double *bx, int ldbx, double *u, int ldu, double *vt, int *k, double *difl, double *difr, double *z, double *poles, int *givptr, int *givcol, int ldgcol, int *perm, double *givnum, double *c, double *s, int *info); void dlalsa_64 (long icompq, long smlsiz, long n, long nrhs, double *b, long ldb, double *bx, long ldbx, double *u, long ldu, double *vt, long *k, double *difl, double *difr, double *z, double *poles, long *givptr, long *givcol, long ldgcol, long *perm, double *givnum, double *c, double *s, long *info);
Oracle Solaris Studio Performance Library dlalsa(3P) NAME dlalsa - compute the SVD of the coefficient matrix in compact form. Used by dgelsd SYNOPSIS SUBROUTINE DLALSA(ICOMPQ, SMLSIZ, N, NRHS, B, LDB, BX, LDBX, U, LDU, VT, K, DIFL, DIFR, Z, POLES, GIVPTR, GIVCOL, LDGCOL, PERM, GIVNUM, C, S, WORK, IWORK, INFO) INTEGER ICOMPQ, INFO, LDB, LDBX, LDGCOL, LDU, N, NRHS, SMLSIZ INTEGER GIVCOL(LDGCOL,*), GIVPTR(*), IWORK(*), K(*), PERM(LDGCOL,*) DOUBLE PRECISION B(LDB,*), BX(LDBX,*), C(*), DIFL(LDU,*), DIFR(LDU,*), GIVNUM(LDU,*), POLES(LDU,*), S(*), U(LDU,*), VT(LDU,*), WORK(*), Z(LDU,*) SUBROUTINE DLALSA_64(ICOMPQ, SMLSIZ, N, NRHS, B, LDB, BX, LDBX, U, LDU, VT, K, DIFL, DIFR, Z, POLES, GIVPTR, GIVCOL, LDGCOL, PERM, GIVNUM, C, S, WORK, IWORK, INFO) INTEGER*8 ICOMPQ, INFO, LDB, LDBX, LDGCOL, LDU, N, NRHS, SMLSIZ INTEGER*8 GIVCOL(LDGCOL,*), GIVPTR(*), IWORK(*), K(*), PERM(LDGCOL,*) DOUBLE PRECISION B(LDB,*), BX(LDBX,*), C(*), DIFL(LDU,*), DIFR(LDU,*), GIVNUM(LDU,*), POLES(LDU,*), S(*), U(LDU,*), VT(LDU,*), WORK(*), Z(LDU,*) 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, WORK, IWORK, INFO) REAL(8), DIMENSION(:,:) :: B, BX, U, VT, DIFL, DIFR, Z, POLES, GIVNUM INTEGER :: ICOMPQ, SMLSIZ, N, NRHS, LDB, LDBX, LDU, LDGCOL, INFO INTEGER, DIMENSION(:) :: K, GIVPTR, IWORK REAL(8), DIMENSION(:) :: C, S, WORK 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, WORK, IWORK, INFO) REAL(8), DIMENSION(:,:) :: B, BX, 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(8), DIMENSION(:) :: C, S, WORK INTEGER(8), DIMENSION(:,:) :: GIVCOL, PERM C INTERFACE #include <sunperf.h> void dlalsa (int icompq, int smlsiz, int n, int nrhs, double *b, int ldb, double *bx, int ldbx, double *u, int ldu, double *vt, int *k, double *difl, double *difr, double *z, double *poles, int *givptr, int *givcol, int ldgcol, int *perm, double *givnum, double *c, double *s, int *info); void dlalsa_64 (long icompq, long smlsiz, long n, long nrhs, double *b, long ldb, double *bx, long ldbx, double *u, long ldu, double *vt, long *k, double *difl, double *difr, double *z, double *poles, long *givptr, long *givcol, long ldgcol, long *perm, double *givnum, double *c, double *s, long *info); PURPOSE dlalsa 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, DLALSA applies the inverse of the left singular vector matrix of an upper bidiagonal matrix to the right hand side; and if ICOMPQ = 1, DLALSA applies the right singular vector matrix to the right hand side. The singular vector matrices were generated in compact form by DLALSA. 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 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 (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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (LDU, SMLSIZ+1) On entry, VT**T 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 DOUBLE PRECISION array, dimension (LDU, NLVL) where NLVL = INT(log_2 (N/(SMLSIZ+1))) + 1. DIFR (input) DIFR is DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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. WORK (output) WORK is DOUBLE PRECISION array The dimension must be at least N. 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 dlalsa(3P)