*> \brief \b SORT03 * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE SORT03( RC, MU, MV, N, K, U, LDU, V, LDV, WORK, LWORK, * RESULT, INFO ) * * .. Scalar Arguments .. * CHARACTER*( * ) RC * INTEGER INFO, K, LDU, LDV, LWORK, MU, MV, N * REAL RESULT * .. * .. Array Arguments .. * REAL U( LDU, * ), V( LDV, * ), WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> SORT03 compares two orthogonal matrices U and V to see if their *> corresponding rows or columns span the same spaces. The rows are *> checked if RC = 'R', and the columns are checked if RC = 'C'. *> *> RESULT is the maximum of *> *> | V*V' - I | / ( MV ulp ), if RC = 'R', or *> *> | V'*V - I | / ( MV ulp ), if RC = 'C', *> *> and the maximum over rows (or columns) 1 to K of *> *> | U(i) - S*V(i) |/ ( N ulp ) *> *> where S is +-1 (chosen to minimize the expression), U(i) is the i-th *> row (column) of U, and V(i) is the i-th row (column) of V. *> \endverbatim * * Arguments: * ========== * *> \param[in] RC *> \verbatim *> RC is CHARACTER*1 *> If RC = 'R' the rows of U and V are to be compared. *> If RC = 'C' the columns of U and V are to be compared. *> \endverbatim *> *> \param[in] MU *> \verbatim *> MU is INTEGER *> The number of rows of U if RC = 'R', and the number of *> columns if RC = 'C'. If MU = 0 SORT03 does nothing. *> MU must be at least zero. *> \endverbatim *> *> \param[in] MV *> \verbatim *> MV is INTEGER *> The number of rows of V if RC = 'R', and the number of *> columns if RC = 'C'. If MV = 0 SORT03 does nothing. *> MV must be at least zero. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> If RC = 'R', the number of columns in the matrices U and V, *> and if RC = 'C', the number of rows in U and V. If N = 0 *> SORT03 does nothing. N must be at least zero. *> \endverbatim *> *> \param[in] K *> \verbatim *> K is INTEGER *> The number of rows or columns of U and V to compare. *> 0 <= K <= max(MU,MV). *> \endverbatim *> *> \param[in] U *> \verbatim *> U is REAL array, dimension (LDU,N) *> The first matrix to compare. If RC = 'R', U is MU by N, and *> if RC = 'C', U is N by MU. *> \endverbatim *> *> \param[in] LDU *> \verbatim *> LDU is INTEGER *> The leading dimension of U. If RC = 'R', LDU >= max(1,MU), *> and if RC = 'C', LDU >= max(1,N). *> \endverbatim *> *> \param[in] V *> \verbatim *> V is REAL array, dimension (LDV,N) *> The second matrix to compare. If RC = 'R', V is MV by N, and *> if RC = 'C', V is N by MV. *> \endverbatim *> *> \param[in] LDV *> \verbatim *> LDV is INTEGER *> The leading dimension of V. If RC = 'R', LDV >= max(1,MV), *> and if RC = 'C', LDV >= max(1,N). *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is REAL array, dimension (LWORK) *> \endverbatim *> *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER *> The length of the array WORK. For best performance, LWORK *> should be at least N*N if RC = 'C' or M*M if RC = 'R', but *> the tests will be done even if LWORK is 0. *> \endverbatim *> *> \param[out] RESULT *> \verbatim *> RESULT is REAL *> The value computed by the test described above. RESULT is *> limited to 1/ulp to avoid overflow. *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> 0 indicates a successful exit *> -k indicates the k-th parameter had an illegal value *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \ingroup single_eig * * ===================================================================== SUBROUTINE SORT03( RC, MU, MV, N, K, U, LDU, V, LDV, WORK, LWORK, $ RESULT, INFO ) * * -- LAPACK test routine -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * * .. Scalar Arguments .. CHARACTER*( * ) RC INTEGER INFO, K, LDU, LDV, LWORK, MU, MV, N REAL RESULT * .. * .. Array Arguments .. REAL U( LDU, * ), V( LDV, * ), WORK( * ) * .. * * ===================================================================== * * .. Parameters .. REAL ZERO, ONE PARAMETER ( ZERO = 0.0E0, ONE = 1.0E0 ) * .. * .. Local Scalars .. INTEGER I, IRC, J, LMX REAL RES1, RES2, S, ULP * .. * .. External Functions .. LOGICAL LSAME INTEGER ISAMAX REAL SLAMCH EXTERNAL LSAME, ISAMAX, SLAMCH * .. * .. Intrinsic Functions .. INTRINSIC ABS, MAX, MIN, REAL, SIGN * .. * .. External Subroutines .. EXTERNAL SORT01, XERBLA * .. * .. Executable Statements .. * * Check inputs * INFO = 0 IF( LSAME( RC, 'R' ) ) THEN IRC = 0 ELSE IF( LSAME( RC, 'C' ) ) THEN IRC = 1 ELSE IRC = -1 END IF IF( IRC.EQ.-1 ) THEN INFO = -1 ELSE IF( MU.LT.0 ) THEN INFO = -2 ELSE IF( MV.LT.0 ) THEN INFO = -3 ELSE IF( N.LT.0 ) THEN INFO = -4 ELSE IF( K.LT.0 .OR. K.GT.MAX( MU, MV ) ) THEN INFO = -5 ELSE IF( ( IRC.EQ.0 .AND. LDU.LT.MAX( 1, MU ) ) .OR. $ ( IRC.EQ.1 .AND. LDU.LT.MAX( 1, N ) ) ) THEN INFO = -7 ELSE IF( ( IRC.EQ.0 .AND. LDV.LT.MAX( 1, MV ) ) .OR. $ ( IRC.EQ.1 .AND. LDV.LT.MAX( 1, N ) ) ) THEN INFO = -9 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'SORT03', -INFO ) RETURN END IF * * Initialize result * RESULT = ZERO IF( MU.EQ.0 .OR. MV.EQ.0 .OR. N.EQ.0 ) $ RETURN * * Machine constants * ULP = SLAMCH( 'Precision' ) * IF( IRC.EQ.0 ) THEN * * Compare rows * RES1 = ZERO DO 20 I = 1, K LMX = ISAMAX( N, U( I, 1 ), LDU ) S = SIGN( ONE, U( I, LMX ) )*SIGN( ONE, V( I, LMX ) ) DO 10 J = 1, N RES1 = MAX( RES1, ABS( U( I, J )-S*V( I, J ) ) ) 10 CONTINUE 20 CONTINUE RES1 = RES1 / ( REAL( N )*ULP ) * * Compute orthogonality of rows of V. * CALL SORT01( 'Rows', MV, N, V, LDV, WORK, LWORK, RES2 ) * ELSE * * Compare columns * RES1 = ZERO DO 40 I = 1, K LMX = ISAMAX( N, U( 1, I ), 1 ) S = SIGN( ONE, U( LMX, I ) )*SIGN( ONE, V( LMX, I ) ) DO 30 J = 1, N RES1 = MAX( RES1, ABS( U( J, I )-S*V( J, I ) ) ) 30 CONTINUE 40 CONTINUE RES1 = RES1 / ( REAL( N )*ULP ) * * Compute orthogonality of columns of V. * CALL SORT01( 'Columns', N, MV, V, LDV, WORK, LWORK, RES2 ) END IF * RESULT = MIN( MAX( RES1, RES2 ), ONE / ULP ) RETURN * * End of SORT03 * END