TESTING/EIG/cbdt03.f(3)

NAME
TESTING/EIG/cbdt03.f

SYNOPSIS

  Functions/Subroutines
subroutine cbdt03 (uplo, n, kd, d, e, u, ldu, s, vt, ldvt, work, resid)
CBDT03

Function/Subroutine Documentation

  subroutine cbdt03 (character uplo, integer n, integer kd, real, dimension( * ) d, real, dimension( * ) e, complex, dimension( ldu, * ) u, integer ldu, real, dimension( * ) s, complex, dimension( ldvt, * ) vt, integer ldvt, complex, dimension( * ) work, real resid)

CBDT03

Purpose:

    !>
    !> CBDT03 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 COMPLEX 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 COMPLEX 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 COMPLEX 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 cbdt03.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.