LAPACK  3.6.0
LAPACK: Linear Algebra PACKage

§ sbdt04()

subroutine sbdt04 ( character  UPLO,
integer  N,
real, dimension( * )  D,
real, dimension( * )  E,
real, dimension( * )  S,
integer  NS,
real, dimension( ldu, * )  U,
integer  LDU,
real, dimension( ldvt, * )  VT,
integer  LDVT,
real, dimension( * )  WORK,
real  RESID 
)
Purpose:

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.

Parameters
[in]UPLO
          UPLO is CHARACTER*1
          Specifies whether the matrix B is upper or lower bidiagonal.
          = 'U':  Upper bidiagonal
          = 'L':  Lower bidiagonal
[in]N
          N is INTEGER
          The order of the matrix B.
[in]D
          D is REAL array, dimension (N)
          The n diagonal elements of the bidiagonal matrix B.
[in]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'.
[in]S
          S is REAL array, dimension (NS)
          The singular values from the (partial) SVD of B, sorted in 
          decreasing order.
[in]NS
          NS is INTEGER
          The number of singular values/vectors from the (partial) 
          SVD of B.
[in]U
          U is REAL array, dimension (LDU,NS)
          The n by ns orthogonal matrix U in S = U' * B * V.
[in]LDU
          LDU is INTEGER
          The leading dimension of the array U.  LDU >= max(1,N)
[in]VT
          VT is REAL array, dimension (LDVT,N)
          The n by ns orthogonal matrix V in S = U' * B * V.
[in]LDVT
          LDVT is INTEGER
          The leading dimension of the array VT.
[out]WORK
          WORK is REAL array, dimension (2*N)
[out]RESID
          RESID is REAL
          The test ratio:  norm(S - U' * B * V) / ( n * norm(B) * EPS )
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011