LAPACK

NAME¶

bdsdc - bdsdc: bidiagonal SVD, divide and conquer

SYNOPSIS¶

Functions¶

subroutine dbdsdc (uplo, compq, n, d, e, u, ldu, vt, ldvt, q, iq, work, iwork, info)
DBDSDC subroutine sbdsdc (uplo, compq, n, d, e, u, ldu, vt, ldvt, q, iq, work, iwork, info)
SBDSDC

Detailed Description¶

Function Documentation¶

subroutine dbdsdc (character uplo, character compq, integer n, double precision, dimension( * ) d, double precision, dimension( * ) e, double precision, dimension( ldu, * ) u, integer ldu, double precision, dimension( ldvt, * ) vt, integer ldvt, double precision, dimension( * ) q, integer, dimension( * ) iq, double precision, dimension( * ) work, integer, dimension( * ) iwork, integer info)¶

DBDSDC

Purpose:



 DBDSDC computes the singular value decomposition (SVD) of a real


 N-by-N (upper or lower) bidiagonal matrix B:  B = U * S * VT,


 using a divide and conquer method, where S is a diagonal matrix


 with non-negative diagonal elements (the singular values of B), and


 U and VT are orthogonal matrices of left and right singular vectors,


 respectively. DBDSDC can be used to compute all singular values,


 and optionally, singular vectors or singular vectors in compact form.


 The code currently calls DLASDQ if singular values only are desired.


 However, it can be slightly modified to compute singular values


 using the divide and conquer method.

Parameters

UPLO



          UPLO is CHARACTER*1


          = 'U':  B is upper bidiagonal.


          = 'L':  B is lower bidiagonal.

COMPQ



          COMPQ is CHARACTER*1


          Specifies whether singular vectors are to be computed


          as follows:


          = 'N':  Compute singular values only;


          = 'P':  Compute singular values and compute singular


                  vectors in compact form;


          = 'I':  Compute singular values and singular vectors.



          N is INTEGER


          The order of the matrix B.  N >= 0.



          D is DOUBLE PRECISION array, dimension (N)


          On entry, the n diagonal elements of the bidiagonal matrix B.


          On exit, if INFO=0, the singular values of B.



          E is DOUBLE PRECISION array, dimension (N-1)


          On entry, the elements of E contain the offdiagonal


          elements of the bidiagonal matrix whose SVD is desired.


          On exit, E has been destroyed.



          U is DOUBLE PRECISION array, dimension (LDU,N)


          If  COMPQ = 'I', then:


             On exit, if INFO = 0, U contains the left singular vectors


             of the bidiagonal matrix.


          For other values of COMPQ, U is not referenced.

LDU



          LDU is INTEGER


          The leading dimension of the array U.  LDU >= 1.


          If singular vectors are desired, then LDU >= max( 1, N ).



          VT is DOUBLE PRECISION array, dimension (LDVT,N)


          If  COMPQ = 'I', then:


             On exit, if INFO = 0, VT**T contains the right singular


             vectors of the bidiagonal matrix.


          For other values of COMPQ, VT is not referenced.

LDVT



          LDVT is INTEGER


          The leading dimension of the array VT.  LDVT >= 1.


          If singular vectors are desired, then LDVT >= max( 1, N ).



          Q is DOUBLE PRECISION array, dimension (LDQ)


          If  COMPQ = 'P', then:


             On exit, if INFO = 0, Q and IQ contain the left


             and right singular vectors in a compact form,


             requiring O(N log N) space instead of 2*N**2.


             In particular, Q contains all the DOUBLE PRECISION data in


             LDQ >= N*(11 + 2*SMLSIZ + 8*INT(LOG_2(N/(SMLSIZ+1))))


             words of memory, where SMLSIZ is returned by ILAENV and


             is equal to the maximum size of the subproblems at the


             bottom of the computation tree (usually about 25).


          For other values of COMPQ, Q is not referenced.



          IQ is INTEGER array, dimension (LDIQ)


          If  COMPQ = 'P', then:


             On exit, if INFO = 0, Q and IQ contain the left


             and right singular vectors in a compact form,


             requiring O(N log N) space instead of 2*N**2.


             In particular, IQ contains all INTEGER data in


             LDIQ >= N*(3 + 3*INT(LOG_2(N/(SMLSIZ+1))))


             words of memory, where SMLSIZ is returned by ILAENV and


             is equal to the maximum size of the subproblems at the


             bottom of the computation tree (usually about 25).


          For other values of COMPQ, IQ is not referenced.

WORK



          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))


          If COMPQ = 'N' then LWORK >= (4 * N).


          If COMPQ = 'P' then LWORK >= (6 * N).


          If COMPQ = 'I' then LWORK >= (3 * N**2 + 4 * N).

IWORK



          IWORK is INTEGER array, dimension (8*N)

INFO



          INFO is INTEGER


          = 0:  successful exit.


          < 0:  if INFO = -i, the i-th argument had an illegal value.


          > 0:  The algorithm failed to compute a singular value.


                The update process of divide and conquer failed.

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 sbdsdc (character uplo, character compq, integer n, real, dimension( * ) d, real, dimension( * ) e, real, dimension( ldu, * ) u, integer ldu, real, dimension( ldvt, * ) vt, integer ldvt, real, dimension( * ) q, integer, dimension( * ) iq, real, dimension( * ) work, integer, dimension( * ) iwork, integer info)¶

SBDSDC