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.

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 )

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