TESTING/EIG/dbdt03.f(3)

NAME
TESTING/EIG/dbdt03.f

SYNOPSIS

  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

              N is INTEGER
              The order of the matrix B.

    KD

              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

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

    E

              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

              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

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

    VT

              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.

Author

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