zunt01.f - Man Page

subroutine zunt01 (rowcol, m, n, u, ldu, work, lwork, rwork, resid)
ZUNT01

ZUNT01

Purpose:

 ZUNT01 checks that the matrix U is unitary by computing the ratio

    RESID = norm( I - U*U' ) / ( n * EPS ), if ROWCOL = 'R',
 or
    RESID = norm( I - U'*U ) / ( m * EPS ), if ROWCOL = 'C'.

 Alternatively, if there isn't sufficient workspace to form
 I - U*U' or I - U'*U, the ratio is computed as

    RESID = abs( I - U*U' ) / ( n * EPS ), if ROWCOL = 'R',
 or
    RESID = abs( I - U'*U ) / ( m * EPS ), if ROWCOL = 'C'.

 where EPS is the machine precision.  ROWCOL is used only if m = n;
 if m > n, ROWCOL is assumed to be 'C', and if m < n, ROWCOL is
 assumed to be 'R'.

Parameters

ROWCOL

          ROWCOL is CHARACTER
          Specifies whether the rows or columns of U should be checked
          for orthogonality.  Used only if M = N.
          = 'R':  Check for orthogonal rows of U
          = 'C':  Check for orthogonal columns of U

M

          M is INTEGER
          The number of rows of the matrix U.

N

          N is INTEGER
          The number of columns of the matrix U.

U

          U is COMPLEX*16 array, dimension (LDU,N)
          The unitary matrix U.  U is checked for orthogonal columns
          if m > n or if m = n and ROWCOL = 'C'.  U is checked for
          orthogonal rows if m < n or if m = n and ROWCOL = 'R'.

LDU

          LDU is INTEGER
          The leading dimension of the array U.  LDU >= max(1,M).

WORK

          WORK is COMPLEX*16 array, dimension (LWORK)

LWORK

          LWORK is INTEGER
          The length of the array WORK.  For best performance, LWORK
          should be at least N*N if ROWCOL = 'C' or M*M if
          ROWCOL = 'R', but the test will be done even if LWORK is 0.

RWORK

          RWORK is DOUBLE PRECISION array, dimension (min(M,N))
          Used only if LWORK is large enough to use the Level 3 BLAS
          code.

RESID

          RESID is DOUBLE PRECISION
          RESID = norm( I - U * U' ) / ( n * EPS ), if ROWCOL = 'R', or
          RESID = norm( I - U' * U ) / ( m * EPS ), if ROWCOL = 'C'.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 124 of file zunt01.f.