zbdt03.f - Man Page

subroutine zbdt03 (uplo, n, kd, d, e, u, ldu, s, vt, ldvt, work, resid)
ZBDT03

ZBDT03

Purpose:

 ZBDT03 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

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 DOUBLE PRECISION array, dimension (N)
          The n diagonal elements of the bidiagonal matrix B.

E

          E is DOUBLE PRECISION 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 COMPLEX*16 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 DOUBLE PRECISION array, dimension (N)
          The singular values from the SVD of B, sorted in decreasing
          order.

VT

          VT is COMPLEX*16 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 COMPLEX*16 array, dimension (2*N)

RESID

          RESID is DOUBLE PRECISION
          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.

Definition at line 133 of file zbdt03.f.