181 lines
5.3 KiB
FortranFixed
181 lines
5.3 KiB
FortranFixed
SUBROUTINE CUNT01( ROWCOL, M, N, U, LDU, WORK, LWORK, RWORK,
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$ RESID )
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*
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* -- LAPACK test routine (version 3.1) --
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* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
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* November 2006
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*
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* .. Scalar Arguments ..
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CHARACTER ROWCOL
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INTEGER LDU, LWORK, M, N
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REAL RESID
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* ..
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* .. Array Arguments ..
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REAL RWORK( * )
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COMPLEX U( LDU, * ), WORK( * )
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* ..
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*
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* Purpose
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* =======
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*
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* CUNT01 checks that the matrix U is unitary by computing the ratio
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*
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* RESID = norm( I - U*U' ) / ( n * EPS ), if ROWCOL = 'R',
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* or
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* RESID = norm( I - U'*U ) / ( m * EPS ), if ROWCOL = 'C'.
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*
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* Alternatively, if there isn't sufficient workspace to form
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* I - U*U' or I - U'*U, the ratio is computed as
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*
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* RESID = abs( I - U*U' ) / ( n * EPS ), if ROWCOL = 'R',
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* or
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* RESID = abs( I - U'*U ) / ( m * EPS ), if ROWCOL = 'C'.
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*
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* where EPS is the machine precision. ROWCOL is used only if m = n;
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* if m > n, ROWCOL is assumed to be 'C', and if m < n, ROWCOL is
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* assumed to be 'R'.
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*
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* Arguments
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* =========
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*
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* ROWCOL (input) CHARACTER
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* Specifies whether the rows or columns of U should be checked
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* for orthogonality. Used only if M = N.
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* = 'R': Check for orthogonal rows of U
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* = 'C': Check for orthogonal columns of U
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*
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* M (input) INTEGER
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* The number of rows of the matrix U.
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*
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* N (input) INTEGER
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* The number of columns of the matrix U.
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*
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* U (input) COMPLEX array, dimension (LDU,N)
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* The unitary matrix U. U is checked for orthogonal columns
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* if m > n or if m = n and ROWCOL = 'C'. U is checked for
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* orthogonal rows if m < n or if m = n and ROWCOL = 'R'.
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*
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* LDU (input) INTEGER
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* The leading dimension of the array U. LDU >= max(1,M).
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*
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* WORK (workspace) COMPLEX array, dimension (LWORK)
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*
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* LWORK (input) INTEGER
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* The length of the array WORK. For best performance, LWORK
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* should be at least N*N if ROWCOL = 'C' or M*M if
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* ROWCOL = 'R', but the test will be done even if LWORK is 0.
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*
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* RWORK (workspace) REAL array, dimension (min(M,N))
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* Used only if LWORK is large enough to use the Level 3 BLAS
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* code.
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*
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* RESID (output) REAL
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* RESID = norm( I - U * U' ) / ( n * EPS ), if ROWCOL = 'R', or
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* RESID = norm( I - U' * U ) / ( m * EPS ), if ROWCOL = 'C'.
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*
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* =====================================================================
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*
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* .. Parameters ..
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REAL ZERO, ONE
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PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 )
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* ..
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* .. Local Scalars ..
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CHARACTER TRANSU
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INTEGER I, J, K, LDWORK, MNMIN
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REAL EPS
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COMPLEX TMP, ZDUM
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* ..
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* .. External Functions ..
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LOGICAL LSAME
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REAL CLANSY, SLAMCH
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COMPLEX CDOTC
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EXTERNAL LSAME, CLANSY, SLAMCH, CDOTC
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* ..
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* .. External Subroutines ..
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EXTERNAL CHERK, CLASET
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC ABS, AIMAG, CMPLX, MAX, MIN, REAL
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* ..
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* .. Statement Functions ..
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REAL CABS1
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* ..
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* .. Statement Function definitions ..
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CABS1( ZDUM ) = ABS( REAL( ZDUM ) ) + ABS( AIMAG( ZDUM ) )
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* ..
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* .. Executable Statements ..
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*
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RESID = ZERO
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*
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* Quick return if possible
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*
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IF( M.LE.0 .OR. N.LE.0 )
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$ RETURN
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*
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EPS = SLAMCH( 'Precision' )
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IF( M.LT.N .OR. ( M.EQ.N .AND. LSAME( ROWCOL, 'R' ) ) ) THEN
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TRANSU = 'N'
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K = N
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ELSE
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TRANSU = 'C'
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K = M
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END IF
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MNMIN = MIN( M, N )
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*
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IF( ( MNMIN+1 )*MNMIN.LE.LWORK ) THEN
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LDWORK = MNMIN
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ELSE
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LDWORK = 0
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END IF
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IF( LDWORK.GT.0 ) THEN
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*
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* Compute I - U*U' or I - U'*U.
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*
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CALL CLASET( 'Upper', MNMIN, MNMIN, CMPLX( ZERO ),
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$ CMPLX( ONE ), WORK, LDWORK )
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CALL CHERK( 'Upper', TRANSU, MNMIN, K, -ONE, U, LDU, ONE, WORK,
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$ LDWORK )
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*
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* Compute norm( I - U*U' ) / ( K * EPS ) .
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*
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RESID = CLANSY( '1', 'Upper', MNMIN, WORK, LDWORK, RWORK )
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RESID = ( RESID / REAL( K ) ) / EPS
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ELSE IF( TRANSU.EQ.'C' ) THEN
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*
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* Find the maximum element in abs( I - U'*U ) / ( m * EPS )
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*
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DO 20 J = 1, N
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DO 10 I = 1, J
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IF( I.NE.J ) THEN
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TMP = ZERO
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ELSE
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TMP = ONE
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END IF
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TMP = TMP - CDOTC( M, U( 1, I ), 1, U( 1, J ), 1 )
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RESID = MAX( RESID, CABS1( TMP ) )
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10 CONTINUE
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20 CONTINUE
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RESID = ( RESID / REAL( M ) ) / EPS
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ELSE
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*
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* Find the maximum element in abs( I - U*U' ) / ( n * EPS )
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*
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DO 40 J = 1, M
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DO 30 I = 1, J
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IF( I.NE.J ) THEN
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TMP = ZERO
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ELSE
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TMP = ONE
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END IF
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TMP = TMP - CDOTC( N, U( J, 1 ), LDU, U( I, 1 ), LDU )
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RESID = MAX( RESID, CABS1( TMP ) )
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30 CONTINUE
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40 CONTINUE
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RESID = ( RESID / REAL( N ) ) / EPS
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END IF
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RETURN
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*
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* End of CUNT01
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*
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END
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