TESTING/EIG/sbdt04.f(3)

NAME
TESTING/EIG/sbdt04.f

SYNOPSIS

  Functions/Subroutines
subroutine sbdt04 (uplo, n, d, e, s, ns, u, ldu, vt, ldvt, work, resid)
SBDT04

Function/Subroutine Documentation

  subroutine sbdt04 (character uplo, integer n, real, dimension( * ) d, real, dimension( * ) e, real, dimension( * ) s, integer ns, real, dimension( ldu, * ) u, integer ldu, real, dimension( ldvt, * ) vt, integer ldvt, real, dimension( * ) work, real resid)

SBDT04

Purpose:

    !>
    !> SBDT04 reconstructs a bidiagonal matrix B from its (partial) 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( S - U' * B * V ) / ( 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.
    !>

    D

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

    E

    !>          E is REAL 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'.
    !>

    S

    !>          S is REAL array, dimension (NS)
    !>          The singular values from the (partial) SVD of B, sorted in
    !>          decreasing order.
    !>

    NS

    !>          NS is INTEGER
    !>          The number of singular values/vectors from the (partial)
    !>          SVD of B.
    !>

    U

    !>          U is REAL array, dimension (LDU,NS)
    !>          The n by ns orthogonal matrix U in S = U' * B * V.
    !>

    LDU

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

    VT

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

    LDVT

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

    WORK

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

    RESID

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

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 129 of file sbdt04.f.

Author

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