LAPACK 3.11.0
LAPACK: Linear Algebra PACKage

◆ sbdt03()

subroutine sbdt03 ( character  UPLO,
integer  N,
integer  KD,
real, dimension( * )  D,
real, dimension( * )  E,
real, dimension( ldu, * )  U,
integer  LDU,
real, dimension( * )  S,
real, dimension( ldvt, * )  VT,
integer  LDVT,
real, dimension( * )  WORK,
real  RESID 
)

SBDT03

Purpose:
 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.
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]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.
[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]U
          U is REAL array, dimension (LDU,N)
          The n by n orthogonal matrix U in the reduction B = U'*A*P.
[in]LDU
          LDU is INTEGER
          The leading dimension of the array U.  LDU >= max(1,N)
[in]S
          S is REAL array, dimension (N)
          The singular values from the SVD of B, sorted in decreasing
          order.
[in]VT
          VT is REAL array, dimension (LDVT,N)
          The n by n orthogonal matrix V' in the reduction
          B = U * S * 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(B - U * S * V') / ( n * norm(A) * EPS )
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.