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SUBROUTINE SORT03( RC, MU, MV, N, K, U, LDU, V, LDV, WORK, LWORK,
$ RESULT, INFO )
*
* -- LAPACK test routine (version 3.0) --
* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
* Courant Institute, Argonne National Lab, and Rice University
* February 29, 1992
*
* .. Scalar Arguments ..
CHARACTER*( * ) RC
INTEGER INFO, K, LDU, LDV, LWORK, MU, MV, N
REAL RESULT
* ..
* .. Array Arguments ..
REAL U( LDU, * ), V( LDV, * ), WORK( * )
* ..
*
* Purpose
* =======
*
* 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.
*
* 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 SORT03 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 SORT03 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
* SORT03 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) 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.
*
* 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) 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.
*
* 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) REAL 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) REAL
* 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 ..
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
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