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SUBROUTINE DBDT02( M, N, B, LDB, C, LDC, U, LDU, WORK, RESID )
*
* -- 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 ..
INTEGER LDB, LDC, LDU, M, N
DOUBLE PRECISION RESID
* ..
* .. Array Arguments ..
DOUBLE PRECISION B( LDB, * ), C( LDC, * ), U( LDU, * ),
$ WORK( * )
* ..
*
* Purpose
* =======
*
* DBDT02 tests the change of basis C = U' * B by computing the residual
*
* RESID = norm( B - U * C ) / ( max(m,n) * norm(B) * EPS ),
*
* where B and C are M by N matrices, U is an M by M orthogonal matrix,
* and EPS is the machine precision.
*
* Arguments
* =========
*
* M (input) INTEGER
* The number of rows of the matrices B and C and the order of
* the matrix Q.
*
* N (input) INTEGER
* The number of columns of the matrices B and C.
*
* B (input) DOUBLE PRECISION array, dimension (LDB,N)
* The m by n matrix B.
*
* LDB (input) INTEGER
* The leading dimension of the array B. LDB >= max(1,M).
*
* C (input) DOUBLE PRECISION array, dimension (LDC,N)
* The m by n matrix C, assumed to contain U' * B.
*
* LDC (input) INTEGER
* The leading dimension of the array C. LDC >= max(1,M).
*
* U (input) DOUBLE PRECISION array, dimension (LDU,M)
* The m by m orthogonal matrix U.
*
* LDU (input) INTEGER
* The leading dimension of the array U. LDU >= max(1,M).
*
* WORK (workspace) DOUBLE PRECISION array, dimension (M)
*
* RESID (output) DOUBLE PRECISION
* RESID = norm( B - U * C ) / ( max(m,n) * norm(B) * EPS ),
*
* ======================================================================
*
* .. Parameters ..
DOUBLE PRECISION ZERO, ONE
PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
* ..
* .. Local Scalars ..
INTEGER J
DOUBLE PRECISION BNORM, EPS, REALMN
* ..
* .. External Functions ..
DOUBLE PRECISION DASUM, DLAMCH, DLANGE
EXTERNAL DASUM, DLAMCH, DLANGE
* ..
* .. External Subroutines ..
EXTERNAL DCOPY, DGEMV
* ..
* .. Intrinsic Functions ..
INTRINSIC DBLE, MAX, MIN
* ..
* .. Executable Statements ..
*
* Quick return if possible
*
RESID = ZERO
IF( M.LE.0 .OR. N.LE.0 )
$ RETURN
REALMN = DBLE( MAX( M, N ) )
EPS = DLAMCH( 'Precision' )
*
* Compute norm( B - U * C )
*
DO 10 J = 1, N
CALL DCOPY( M, B( 1, J ), 1, WORK, 1 )
CALL DGEMV( 'No transpose', M, M, -ONE, U, LDU, C( 1, J ), 1,
$ ONE, WORK, 1 )
RESID = MAX( RESID, DASUM( M, WORK, 1 ) )
10 CONTINUE
*
* Compute norm of B.
*
BNORM = DLANGE( '1', M, N, B, LDB, WORK )
*
IF( BNORM.LE.ZERO ) THEN
IF( RESID.NE.ZERO )
$ RESID = ONE / EPS
ELSE
IF( BNORM.GE.RESID ) THEN
RESID = ( RESID / BNORM ) / ( REALMN*EPS )
ELSE
IF( BNORM.LT.ONE ) THEN
RESID = ( MIN( RESID, REALMN*BNORM ) / BNORM ) /
$ ( REALMN*EPS )
ELSE
RESID = MIN( RESID / BNORM, REALMN ) / ( REALMN*EPS )
END IF
END IF
END IF
RETURN
*
* End of DBDT02
*
END
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