SUBROUTINE SGET04( N, NRHS, X, LDX, XACT, LDXACT, RCOND, RESID ) * * -- LAPACK test routine (version 3.1) -- * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. * November 2006 * * .. Scalar Arguments .. INTEGER LDX, LDXACT, N, NRHS REAL RCOND, RESID * .. * .. Array Arguments .. REAL X( LDX, * ), XACT( LDXACT, * ) * .. * * Purpose * ======= * * SGET04 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) REAL 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) REAL 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) REAL * The reciprocal of the condition number of the coefficient * matrix in the system of equations. * * RESID (output) REAL * The maximum over the NRHS solution vectors of * ( norm(X-XACT) * RCOND ) / ( norm(XACT) * EPS ) * * ===================================================================== * * .. Parameters .. REAL ZERO PARAMETER ( ZERO = 0.0E+0 ) * .. * .. Local Scalars .. INTEGER I, IX, J REAL DIFFNM, EPS, XNORM * .. * .. External Functions .. INTEGER ISAMAX REAL SLAMCH EXTERNAL ISAMAX, SLAMCH * .. * .. Intrinsic Functions .. INTRINSIC ABS, MAX * .. * .. 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 = SLAMCH( 'Epsilon' ) IF( RCOND.LT.ZERO ) THEN RESID = 1.0 / 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 = ISAMAX( N, XACT( 1, J ), 1 ) XNORM = ABS( XACT( IX, J ) ) DIFFNM = ZERO DO 10 I = 1, N DIFFNM = MAX( DIFFNM, ABS( X( I, J )-XACT( I, J ) ) ) 10 CONTINUE IF( XNORM.LE.ZERO ) THEN IF( DIFFNM.GT.ZERO ) \$ RESID = 1.0 / EPS ELSE RESID = MAX( RESID, ( DIFFNM / XNORM )*RCOND ) END IF 20 CONTINUE IF( RESID*EPS.LT.1.0 ) \$ RESID = RESID / EPS * RETURN * * End of SGET04 * END