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 )

Univ. of Tennessee

Univ. of California Berkeley

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