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SUBROUTINE ZGET04( N, NRHS, X, LDX, XACT, LDXACT, RCOND, 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 LDX, LDXACT, N, NRHS
DOUBLE PRECISION RCOND, RESID
* ..
* .. Array Arguments ..
COMPLEX*16 X( LDX, * ), XACT( LDXACT, * )
* ..
*
* Purpose
* =======
*
* ZGET04 computes the difference between a computed solution and the
* true solution to a system of linear equations.
*
* RESID = ( norm(X-XACT) * RCOND ) / ( norm(XACT) * EPS ),
* where RCOND is the reciprocal of the condition number and EPS is the
* machine epsilon.
*
* Arguments
* =========
*
* N (input) INTEGER
* The number of rows of the matrices X and XACT. N >= 0.
*
* NRHS (input) INTEGER
* The number of columns of the matrices X and XACT. NRHS >= 0.
*
* X (input) COMPLEX*16 array, dimension (LDX,NRHS)
* The computed solution vectors. Each vector is stored as a
* column of the matrix X.
*
* LDX (input) INTEGER
* The leading dimension of the array X. LDX >= max(1,N).
*
* XACT (input) COMPLEX*16 array, dimension (LDX,NRHS)
* The exact solution vectors. Each vector is stored as a
* column of the matrix XACT.
*
* LDXACT (input) INTEGER
* The leading dimension of the array XACT. LDXACT >= max(1,N).
*
* RCOND (input) DOUBLE PRECISION
* The reciprocal of the condition number of the coefficient
* matrix in the system of equations.
*
* RESID (output) DOUBLE PRECISION
* The maximum over the NRHS solution vectors of
* ( norm(X-XACT) * RCOND ) / ( norm(XACT) * EPS )
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ZERO
PARAMETER ( ZERO = 0.0D+0 )
* ..
* .. Local Scalars ..
INTEGER I, IX, J
DOUBLE PRECISION DIFFNM, EPS, XNORM
COMPLEX*16 ZDUM
* ..
* .. External Functions ..
INTEGER IZAMAX
DOUBLE PRECISION DLAMCH
EXTERNAL IZAMAX, DLAMCH
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, DBLE, DIMAG, MAX
* ..
* .. Statement Functions ..
DOUBLE PRECISION CABS1
* ..
* .. Statement Function definitions ..
CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) )
* ..
* .. Executable Statements ..
*
* Quick exit if N = 0 or NRHS = 0.
*
IF( N.LE.0 .OR. NRHS.LE.0 ) THEN
RESID = ZERO
RETURN
END IF
*
* Exit with RESID = 1/EPS if RCOND is invalid.
*
EPS = DLAMCH( 'Epsilon' )
IF( RCOND.LT.ZERO ) THEN
RESID = 1.0D0 / EPS
RETURN
END IF
*
* Compute the maximum of
* norm(X - XACT) / ( norm(XACT) * EPS )
* over all the vectors X and XACT .
*
RESID = ZERO
DO 20 J = 1, NRHS
IX = IZAMAX( N, XACT( 1, J ), 1 )
XNORM = CABS1( XACT( IX, J ) )
DIFFNM = ZERO
DO 10 I = 1, N
DIFFNM = MAX( DIFFNM, CABS1( X( I, J )-XACT( I, J ) ) )
10 CONTINUE
IF( XNORM.LE.ZERO ) THEN
IF( DIFFNM.GT.ZERO )
$ RESID = 1.0D0 / EPS
ELSE
RESID = MAX( RESID, ( DIFFNM / XNORM )*RCOND )
END IF
20 CONTINUE
IF( RESID*EPS.LT.1.0D0 )
$ RESID = RESID / EPS
*
RETURN
*
* End of ZGET04
*
END
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