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*> \brief \b DORT03
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE DORT03( 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
* DOUBLE PRECISION RESULT
* ..
* .. Array Arguments ..
* DOUBLE PRECISION U( LDU, * ), V( LDV, * ), WORK( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> 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.
*> \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 DORT03 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 DORT03 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
*> DORT03 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 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.
*> \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 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.
*> \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 DOUBLE PRECISION 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 DOUBLE PRECISION
*> 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.
*
*> \date November 2011
*
*> \ingroup double_eig
*
* =====================================================================
SUBROUTINE DORT03( RC, MU, MV, N, K, U, LDU, V, LDV, WORK, LWORK,
$ RESULT, INFO )
*
* -- LAPACK test routine (version 3.4.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* November 2011
*
* .. 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( * )
* ..
*
* =====================================================================
*
* .. 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
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