sort01()

subroutine sort01	(	character	ROWCOL,
		integer	M,
		integer	N,
		real, dimension( ldu, * )	U,
		integer	LDU,
		real, dimension( * )	WORK,
		integer	LWORK,
		real	RESID
	)

SORT01

Purpose:

 SORT01 checks that the matrix U is orthogonal 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

[in]	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
[in]	M	M is INTEGER The number of rows of the matrix U.
[in]	N	N is INTEGER The number of columns of the matrix U.
[in]	U	U is REAL array, dimension (LDU,N) The orthogonal 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'.
[in]	LDU	LDU is INTEGER The leading dimension of the array U. LDU >= max(1,M).
[out]	WORK	WORK is REAL array, dimension (LWORK)
[in]	LWORK	LWORK is INTEGER The length of the array WORK. For best performance, LWORK should be at least N*(N+1) if ROWCOL = 'C' or M*(M+1) if ROWCOL = 'R', but the test will be done even if LWORK is 0.
[out]	RESID	RESID is REAL 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.