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.

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 )

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