SUBROUTINE SQRT16( TRANS, M, N, NRHS, A, LDA, X, LDX, B, LDB, \$ RWORK, RESID ) * * -- LAPACK test routine (version 3.1) -- * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. * November 2006 * * .. Scalar Arguments .. CHARACTER TRANS INTEGER LDA, LDB, LDX, M, N, NRHS REAL RESID * .. * .. Array Arguments .. REAL A( LDA, * ), B( LDB, * ), RWORK( * ), \$ X( LDX, * ) * .. * * Purpose * ======= * * SQRT16 computes the residual for a solution of a system of linear * equations A*x = b or A'*x = b: * RESID = norm(B - A*X) / ( max(m,n) * norm(A) * norm(X) * EPS ), * where EPS is the machine epsilon. * * Arguments * ========= * * TRANS (input) CHARACTER*1 * Specifies the form of the system of equations: * = 'N': A *x = b * = 'T': A'*x = b, where A' is the transpose of A * = 'C': A'*x = b, where A' is the transpose of A * * M (input) INTEGER * The number of rows of the matrix A. M >= 0. * * N (input) INTEGER * The number of 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) REAL array, dimension (LDA,N) * The original M x N matrix A. * * LDA (input) INTEGER * The leading dimension of the array A. LDA >= max(1,M). * * X (input) REAL 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,M). * * B (input/output) REAL 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) REAL array, dimension (M) * * RESID (output) REAL * The maximum over the number of right hand sides of * norm(B - A*X) / ( max(m,n) * norm(A) * norm(X) * EPS ). * * ===================================================================== * * .. Parameters .. REAL ZERO, ONE PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 ) * .. * .. Local Scalars .. INTEGER J, N1, N2 REAL ANORM, BNORM, EPS, XNORM * .. * .. External Functions .. LOGICAL LSAME REAL SASUM, SLAMCH, SLANGE EXTERNAL LSAME, SASUM, SLAMCH, SLANGE * .. * .. External Subroutines .. EXTERNAL SGEMM * .. * .. Intrinsic Functions .. INTRINSIC MAX * .. * .. Executable Statements .. * * Quick exit if M = 0 or N = 0 or NRHS = 0 * IF( M.LE.0 .OR. N.LE.0 .OR. NRHS.EQ.0 ) THEN RESID = ZERO RETURN END IF * IF( LSAME( TRANS, 'T' ) .OR. LSAME( TRANS, 'C' ) ) THEN ANORM = SLANGE( 'I', M, N, A, LDA, RWORK ) N1 = N N2 = M ELSE ANORM = SLANGE( '1', M, N, A, LDA, RWORK ) N1 = M N2 = N END IF * EPS = SLAMCH( 'Epsilon' ) * * Compute B - A*X (or B - A'*X ) and store in B. * CALL SGEMM( TRANS, 'No transpose', N1, NRHS, N2, -ONE, A, LDA, X, \$ LDX, ONE, B, LDB ) * * Compute the maximum over the number of right hand sides of * norm(B - A*X) / ( max(m,n) * norm(A) * norm(X) * EPS ) . * RESID = ZERO DO 10 J = 1, NRHS BNORM = SASUM( N1, B( 1, J ), 1 ) XNORM = SASUM( N2, X( 1, J ), 1 ) IF( ANORM.EQ.ZERO .AND. BNORM.EQ.ZERO ) THEN RESID = ZERO ELSE IF( ANORM.LE.ZERO .OR. XNORM.LE.ZERO ) THEN RESID = ONE / EPS ELSE RESID = MAX( RESID, ( ( BNORM / ANORM ) / XNORM ) / \$ ( MAX( M, N )*EPS ) ) END IF 10 CONTINUE * RETURN * * End of SQRT16 * END