
NAMEzlalsa.f SYNOPSISFunctions/Subroutinessubroutine zlalsa (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) Function/Subroutine Documentationsubroutine zlalsa (integerICOMPQ, integerSMLSIZ, integerN, integerNRHS, complex*16, dimension( ldb, * )B, integerLDB, complex*16, dimension( ldbx, * )BX, integerLDBX, double precision, dimension( ldu, * )U, integerLDU, double precision, dimension( ldu, * )VT, integer, dimension( * )K, double precision, dimension( ldu, * )DIFL, double precision, dimension( ldu, * )DIFR, double precision, dimension( ldu, * )Z, double precision, dimension( ldu, * )POLES, integer, dimension( * )GIVPTR, integer, dimension( ldgcol, * )GIVCOL, integerLDGCOL, integer, dimension( ldgcol, * )PERM, double precision, dimension( ldu, * )GIVNUM, double precision, dimension( * )C, double precision, dimension( * )S, double precision, dimension( * )RWORK, integer, dimension( * )IWORK, integerINFO)ZLALSA computes the SVD of the coefficient matrix in compact form. Used by sgelsd. Purpose:ZLALSA is an itermediate step in solving the least squares problem by computing the SVD of the coefficient matrix in compact form (The singular vectors are computed as products of simple orthorgonal matrices.). If ICOMPQ = 0, ZLALSA applies the inverse of the left singular vector matrix of an upper bidiagonal matrix to the right hand side; and if ICOMPQ = 1, ZLALSA applies the right singular vector matrix to the right hand side. The singular vector matrices were generated in compact form by ZLALSA. ICOMPQ
Author:
ICOMPQ is INTEGER Specifies whether the left or the right singular vector matrix is involved. = 0: Left singular vector matrix = 1: Right singular vector matrixSMLSIZ SMLSIZ is INTEGER The maximum size of the subproblems at the bottom of the computation tree.N N is INTEGER The row and column dimensions of the upper bidiagonal matrix.NRHS NRHS is INTEGER The number of columns of B and BX. NRHS must be at least 1.B B is COMPLEX*16 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 in the calling subprogram. LDB must be at least max(1,MAX( M, N ) ).BX BX is COMPLEX*16 array, dimension ( LDBX, NRHS ) On exit, the result of applying the left or right singular vector matrix to B.LDBX LDBX is INTEGER The leading dimension of BX.U 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 LDU is INTEGER, LDU = > N. The leading dimension of arrays U, VT, DIFL, DIFR, POLES, GIVNUM, and Z.VT VT is DOUBLE PRECISION array, dimension ( LDU, SMLSIZ+1 ). On entry, VT**H contains the right singular vector matrices of all subproblems at the bottom level.K K is INTEGER array, dimension ( N ).DIFL DIFL is DOUBLE PRECISION array, dimension ( LDU, NLVL ). where NLVL = INT(log_2 (N/(SMLSIZ+1))) + 1.DIFR 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 Ith level and singular values on the (I 1)th level, and DIFR(*, 2 * I) record the normalizing factors of the right singular vectors matrices of subproblems on Ith level.Z 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 Ith level.POLES POLES is DOUBLE PRECISION array, dimension ( LDU, 2 * NLVL ). On entry, POLES(*, 2 * I 1: 2 * I) contains the new and old singular values involved in the secular equations on the Ith level.GIVPTR GIVPTR is INTEGER array, dimension ( N ). On entry, GIVPTR( I ) records the number of Givens rotations performed on the Ith problem on the computation tree.GIVCOL 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 Ith level on the computation tree.LDGCOL LDGCOL is INTEGER, LDGCOL = > N. The leading dimension of arrays GIVCOL and PERM.PERM PERM is INTEGER array, dimension ( LDGCOL, NLVL ). On entry, PERM(*, I) records permutations done on the Ith level of the computation tree.GIVNUM 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 Ith level on the computation tree.C C is DOUBLE PRECISION array, dimension ( N ). On entry, if the Ith subproblem is not square, C( I ) contains the Cvalue of a Givens rotation related to the right null space of the Ith subproblem.S S is DOUBLE PRECISION array, dimension ( N ). On entry, if the Ith subproblem is not square, S( I ) contains the Svalue of a Givens rotation related to the right null space of the Ith subproblem.RWORK RWORK is DOUBLE PRECISION array, dimension at least MAX( (SMLSZ+1)*NRHS*3, N*(1+NRHS) + 2*NRHS ).IWORK IWORK is INTEGER array. The dimension must be at least 3 * NINFO INFO is INTEGER = 0: successful exit. < 0: if INFO = i, the ith 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 RenCang Li, Computer Science Division,
University of California at Berkeley, USA
Definition at line 266 of file zlalsa.f.
Osni Marques, LBNL/NERSC, USA AuthorGenerated automatically by Doxygen for LAPACK from the source code.
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