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SUBROUTINE DPOT06( UPLO, N, NRHS, A, LDA, X, LDX, B, LDB,
$ RWORK, RESID ) * * -- LAPACK test routine (version 3.1.2) -- * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. * April 2007 * * .. Scalar Arguments .. CHARACTER UPLO INTEGER LDA, LDB, LDX, N, NRHS DOUBLE PRECISION RESID * .. * .. Array Arguments .. DOUBLE PRECISION A( LDA, * ), B( LDB, * ), RWORK( * ), $ X( LDX, * ) * .. * * Purpose * ======= * * DPOT06 computes the residual for a solution of a system of linear * equations A*x = b : * RESID = norm(B - A*X,inf) / ( norm(A,inf) * norm(X,inf) * EPS ), * where EPS is the machine epsilon. * * Arguments * ========= * * UPLO (input) CHARACTER*1 * Specifies whether the upper or lower triangular part of the * symmetric matrix A is stored: * = 'U': Upper triangular * = 'L': Lower triangular * * N (input) INTEGER * The number of rows and columns of the matrix A. N >= 0. * * NRHS (input) INTEGER * The number of columns of B, the matrix of right hand sides. * NRHS >= 0. * * A (input) DOUBLE PRECISION array, dimension (LDA,N) * The original M x N matrix A. * * LDA (input) INTEGER * The leading dimension of the array A. LDA >= max(1,N). * * X (input) DOUBLE PRECISION array, dimension (LDX,NRHS) * The computed solution vectors for the system of linear * equations. * * LDX (input) INTEGER * The leading dimension of the array X. If TRANS = 'N', * LDX >= max(1,N); if TRANS = 'T' or 'C', LDX >= max(1,N). * * B (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS) * On entry, the right hand side vectors for the system of * linear equations. * On exit, B is overwritten with the difference B - A*X. * * LDB (input) INTEGER * The leading dimension of the array B. IF TRANS = 'N', * LDB >= max(1,M); if TRANS = 'T' or 'C', LDB >= max(1,N). * * RWORK (workspace) DOUBLE PRECISION array, dimension (N) * * RESID (output) DOUBLE PRECISION * The maximum over the number of right hand sides of * norm(B - A*X) / ( norm(A) * norm(X) * EPS ). * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, ONE, NEGONE PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) PARAMETER ( NEGONE = -1.0D+0 ) * .. * .. Local Scalars .. INTEGER IFAIL, J DOUBLE PRECISION ANORM, BNORM, EPS, XNORM * .. * .. External Functions .. LOGICAL LSAME INTEGER IDAMAX DOUBLE PRECISION DLAMCH, DLANSY EXTERNAL LSAME, IDAMAX, DLAMCH, DLANSY * .. * .. External Subroutines .. EXTERNAL DSYMM * .. * .. Intrinsic Functions .. INTRINSIC MAX, ABS * .. * .. Executable Statements .. * * Quick exit if N = 0 or NRHS = 0 * IF( N.LE.0 .OR. NRHS.EQ.0 ) THEN RESID = ZERO RETURN END IF * * Exit with RESID = 1/EPS if ANORM = 0. * EPS = DLAMCH( 'Epsilon' ) ANORM = DLANSY( 'I', UPLO, N, A, LDA, RWORK ) IF( ANORM.LE.ZERO ) THEN RESID = ONE / EPS RETURN END IF * * Compute B - A*X and store in B. IFAIL=0 * CALL DSYMM( 'Left', UPLO, N, NRHS, NEGONE, A, LDA, X, $ LDX, ONE, B, LDB ) * * Compute the maximum over the number of right hand sides of * norm(B - A*X) / ( norm(A) * norm(X) * EPS ) . * RESID = ZERO DO 10 J = 1, NRHS BNORM = ABS(B(IDAMAX( N, B( 1, J ), 1 ),J)) XNORM = ABS(X(IDAMAX( N, X( 1, J ), 1 ),J)) IF( XNORM.LE.ZERO ) THEN RESID = ONE / EPS ELSE RESID = MAX( RESID, ( ( BNORM / ANORM ) / XNORM ) / EPS ) END IF 10 CONTINUE * RETURN * * End of DPOT06 * END |