TESTING/EIG/sbdt03.f(3)

NAME
TESTING/EIG/sbdt03.f

SYNOPSIS

  Functions/Subroutines
subroutine sbdt03 (uplo, n, kd, d, e, u, ldu, s, vt, ldvt, work, resid)
SBDT03

Function/Subroutine Documentation

  subroutine sbdt03 (character uplo, integer n, integer kd, real, dimension( * ) d, real, dimension( * ) e, real, dimension( ldu, * ) u, integer ldu, real, dimension( * ) s, real, dimension( ldvt, * ) vt, integer ldvt, real, dimension( * ) work, real resid)

SBDT03

Purpose:

    !>
    !> SBDT03 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 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'.
    !>

    U

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

    VT

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

    RESID

    !>          RESID is REAL
    !>          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 sbdt03.f.

Author

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