dbdt03.f3

Usage

Functions/Subroutines

subroutine dbdt03 (uplo, n, kd, d, e, u, ldu, s, vt, ldvt, work, resid)
DBDT03

Function/Subroutine Documentation

subroutine dbdt03 (character uplo, integer n, integer kd, double precision, dimension( * ) d, double precision, dimension( * ) e, double precision, dimension( ldu, * ) u, integer ldu, double precision, dimension( * ) s, double precision, dimension( ldvt, * ) vt, integer ldvt, double precision, dimension( * ) work, double precision resid)

DBDT03

Purpose:

!>
!> DBDT03 reconstructs a bidiagonal matrix B from its SVD:
!>    S = U' * B * V
!> where U and V are orthogonal matrices and S is diagonal.
!>
!> The test ratio to test the singular value decomposition is
!>    RESID = norm( B - U * S * VT ) / ( n * norm(B) * EPS )
!> where VT = V' and EPS is the machine precision.
!>

Parameters

UPLO

!>          UPLO is CHARACTER*1
!>          Specifies whether the matrix B is upper or lower bidiagonal.
!>          = 'U':  Upper bidiagonal
!>          = 'L':  Lower bidiagonal
!>

!>          N is INTEGER
!>          The order of the matrix B.
!>

!>          KD is INTEGER
!>          The bandwidth of the bidiagonal matrix B.  If KD = 1, the
!>          matrix B is bidiagonal, and if KD = 0, B is diagonal and E is
!>          not referenced.  If KD is greater than 1, it is assumed to be
!>          1, and if KD is less than 0, it is assumed to be 0.
!>

!>          D is DOUBLE PRECISION array, dimension (N)
!>          The n diagonal elements of the bidiagonal matrix B.
!>

!>          E is DOUBLE PRECISION array, dimension (N-1)
!>          The (n-1) superdiagonal elements of the bidiagonal matrix B
!>          if UPLO = 'U', or the (n-1) subdiagonal elements of B if
!>          UPLO = 'L'.
!>

!>          U is DOUBLE PRECISION array, dimension (LDU,N)
!>          The n by n orthogonal matrix U in the reduction B = U'*A*P.
!>

LDU

!>          LDU is INTEGER
!>          The leading dimension of the array U.  LDU >= max(1,N)
!>

!>          S is DOUBLE PRECISION array, dimension (N)
!>          The singular values from the SVD of B, sorted in decreasing
!>          order.
!>

!>          VT is DOUBLE PRECISION array, dimension (LDVT,N)
!>          The n by n orthogonal matrix V' in the reduction
!>          B = U * S * V'.
!>

LDVT

!>          LDVT is INTEGER
!>          The leading dimension of the array VT.
!>

WORK

!>          WORK is DOUBLE PRECISION array, dimension (2*N)
!>

RESID

!>          RESID is DOUBLE PRECISION
!>          The test ratio:  norm(B - U * S * V') / ( n * norm(A) * EPS )
!>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 133 of file dbdt03.f.