LAPACK

NAME¶

lasd0 - lasd0: D&C step: top level solver

SYNOPSIS¶

Functions¶

subroutine dlasd0 (n, sqre, d, e, u, ldu, vt, ldvt, smlsiz, iwork, work, info)
DLASD0 computes the singular values of a real upper bidiagonal n-by-m matrix B with diagonal d and off-diagonal e. Used by sbdsdc. subroutine slasd0 (n, sqre, d, e, u, ldu, vt, ldvt, smlsiz, iwork, work, info)
SLASD0 computes the singular values of a real upper bidiagonal n-by-m matrix B with diagonal d and off-diagonal e. Used by sbdsdc.

Detailed Description¶

Function Documentation¶

subroutine dlasd0 (integer n, integer sqre, double precision, dimension( * ) d, double precision, dimension( * ) e, double precision, dimension( ldu, * ) u, integer ldu, double precision, dimension( ldvt, * ) vt, integer ldvt, integer smlsiz, integer, dimension( * ) iwork, double precision, dimension( * ) work, integer info)¶

DLASD0 computes the singular values of a real upper bidiagonal n-by-m matrix B with diagonal d and off-diagonal e. Used by sbdsdc.

Purpose:

!>
!> Using a divide and conquer approach, DLASD0 computes the singular
!> value decomposition (SVD) of a real upper bidiagonal N-by-M
!> matrix B with diagonal D and offdiagonal E, where M = N + SQRE.
!> The algorithm computes orthogonal matrices U and VT such that
!> B = U * S * VT. The singular values S are overwritten on D.
!>
!> A related subroutine, DLASDA, computes only the singular values,
!> and optionally, the singular vectors in compact form.
!>

Parameters

!>          N is INTEGER
!>         On entry, the row dimension of the upper bidiagonal matrix.
!>         This is also the dimension of the main diagonal array D.
!>

SQRE

!>          SQRE is INTEGER
!>         Specifies the column dimension of the bidiagonal matrix.
!>         = 0: The bidiagonal matrix has column dimension M = N;
!>         = 1: The bidiagonal matrix has column dimension M = N+1;
!>

!>          D is DOUBLE PRECISION array, dimension (N)
!>         On entry D contains the main diagonal of the bidiagonal
!>         matrix.
!>         On exit D, if INFO = 0, contains its singular values.
!>

!>          E is DOUBLE PRECISION array, dimension (M-1)
!>         Contains the subdiagonal entries of the bidiagonal matrix.
!>         On exit, E has been destroyed.
!>

!>          U is DOUBLE PRECISION array, dimension (LDU, N)
!>         On exit, U contains the left singular vectors, 
!>          if U passed in as (N, N) Identity.
!>

LDU

!>          LDU is INTEGER
!>         On entry, leading dimension of U.
!>

!>          VT is DOUBLE PRECISION array, dimension (LDVT, M)
!>         On exit, VT**T contains the right singular vectors,
!>          if VT passed in as (M, M) Identity.
!>

LDVT

!>          LDVT is INTEGER
!>         On entry, leading dimension of VT.
!>

SMLSIZ

!>          SMLSIZ is INTEGER
!>         On entry, maximum size of the subproblems at the
!>         bottom of the computation tree.
!>

IWORK

!>          IWORK is INTEGER array, dimension (8*N)
!>

WORK

!>          WORK is DOUBLE PRECISION array, dimension (3*M**2+2*M)
!>

INFO

!>          INFO is INTEGER
!>          = 0:  successful exit.
!>          < 0:  if INFO = -i, the i-th argument had an illegal value.
!>          > 0:  if INFO = 1, a singular value did not converge
!>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Contributors:

Ming Gu and Huan Ren, Computer Science Division, University of California at Berkeley, USA

subroutine slasd0 (integer n, integer sqre, real, dimension( * ) d, real, dimension( * ) e, real, dimension( ldu, * ) u, integer ldu, real, dimension( ldvt, * ) vt, integer ldvt, integer smlsiz, integer, dimension( * ) iwork, real, dimension( * ) work, integer info)¶

SLASD0 computes the singular values of a real upper bidiagonal n-by-m matrix B with diagonal d and off-diagonal e. Used by sbdsdc.