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SUBROUTINE DORT03( RC, MU, MV, N, K, U, LDU, V, LDV, WORK, LWORK,
$ RESULT, INFO ) * * -- LAPACK test routine (version 3.1) -- * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. * November 2006 * * .. Scalar Arguments .. CHARACTER*( * ) RC INTEGER INFO, K, LDU, LDV, LWORK, MU, MV, N DOUBLE PRECISION RESULT * .. * .. Array Arguments .. DOUBLE PRECISION U( LDU, * ), V( LDV, * ), WORK( * ) * .. * * Purpose * ======= * * DORT03 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. * * Arguments * ========== * * RC (input) 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. * * MU (input) INTEGER * The number of rows of U if RC = 'R', and the number of * columns if RC = 'C'. If MU = 0 DORT03 does nothing. * MU must be at least zero. * * MV (input) INTEGER * The number of rows of V if RC = 'R', and the number of * columns if RC = 'C'. If MV = 0 DORT03 does nothing. * MV must be at least zero. * * N (input) 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 * DORT03 does nothing. N must be at least zero. * * K (input) INTEGER * The number of rows or columns of U and V to compare. * 0 <= K <= max(MU,MV). * * U (input) DOUBLE PRECISION 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. * * LDU (input) INTEGER * The leading dimension of U. If RC = 'R', LDU >= max(1,MU), * and if RC = 'C', LDU >= max(1,N). * * V (input) DOUBLE PRECISION 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. * * LDV (input) INTEGER * The leading dimension of V. If RC = 'R', LDV >= max(1,MV), * and if RC = 'C', LDV >= max(1,N). * * WORK (workspace) DOUBLE PRECISION array, dimension (LWORK) * * LWORK (input) 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. * * RESULT (output) DOUBLE PRECISION * The value computed by the test described above. RESULT is * limited to 1/ulp to avoid overflow. * * INFO (output) INTEGER * 0 indicates a successful exit * -k indicates the k-th parameter had an illegal value * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, ONE PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 ) * .. * .. Local Scalars .. INTEGER I, IRC, J, LMX DOUBLE PRECISION RES1, RES2, S, ULP * .. * .. External Functions .. LOGICAL LSAME INTEGER IDAMAX DOUBLE PRECISION DLAMCH EXTERNAL LSAME, IDAMAX, DLAMCH * .. * .. Intrinsic Functions .. INTRINSIC ABS, DBLE, MAX, MIN, SIGN * .. * .. External Subroutines .. EXTERNAL DORT01, 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( 'DORT03', -INFO ) RETURN END IF * * Initialize result * RESULT = ZERO IF( MU.EQ.0 .OR. MV.EQ.0 .OR. N.EQ.0 ) $ RETURN * * Machine constants * ULP = DLAMCH( 'Precision' ) * IF( IRC.EQ.0 ) THEN * * Compare rows * RES1 = ZERO DO 20 I = 1, K LMX = IDAMAX( 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 / ( DBLE( N )*ULP ) * * Compute orthogonality of rows of V. * CALL DORT01( 'Rows', MV, N, V, LDV, WORK, LWORK, RES2 ) * ELSE * * Compare columns * RES1 = ZERO DO 40 I = 1, K LMX = IDAMAX( 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 / ( DBLE( N )*ULP ) * * Compute orthogonality of columns of V. * CALL DORT01( 'Columns', N, MV, V, LDV, WORK, LWORK, RES2 ) END IF * RESULT = MIN( MAX( RES1, RES2 ), ONE / ULP ) RETURN * * End of DORT03 * END |