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.