sort01.f3

!>
!> 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'.
!> 

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 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'.
!> 

LDU

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

WORK

!>          WORK is REAL array, dimension (LWORK)
!> 

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.
!> 

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'.
!> 

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