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SUBROUTINE SGBT02( TRANS, M, N, KL, KU, NRHS, A, LDA, X, LDX, B,
$ LDB, RESID ) * * -- LAPACK test routine (version 3.1) -- * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. * November 2006 * * .. Scalar Arguments .. CHARACTER TRANS INTEGER KL, KU, LDA, LDB, LDX, M, N, NRHS REAL RESID * .. * .. Array Arguments .. REAL A( LDA, * ), B( LDB, * ), X( LDX, * ) * .. * * Purpose * ======= * * SGBT02 computes the residual for a solution of a banded system of * equations A*x = b or A'*x = b: * RESID = norm( B - A*X ) / ( norm(A) * norm(X) * EPS). * where EPS is the machine precision. * * 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. * * KL (input) INTEGER * The number of subdiagonals within the band of A. KL >= 0. * * KU (input) INTEGER * The number of superdiagonals within the band of A. KU >= 0. * * NRHS (input) INTEGER * The number of columns of B. NRHS >= 0. * * A (input) REAL array, dimension (LDA,N) * The original matrix A in band storage, stored in rows 1 to * KL+KU+1. * * LDA (input) INTEGER * The leading dimension of the array A. LDA >= max(1,KL+KU+1). * * 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). * * RESID (output) REAL * The maximum over the number of right hand sides of * norm(B - A*X) / ( norm(A) * norm(X) * EPS ). * * ===================================================================== * * .. Parameters .. REAL ZERO, ONE PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 ) * .. * .. Local Scalars .. INTEGER I1, I2, J, KD, N1 REAL ANORM, BNORM, EPS, XNORM * .. * .. External Functions .. LOGICAL LSAME REAL SASUM, SLAMCH EXTERNAL LSAME, SASUM, SLAMCH * .. * .. External Subroutines .. EXTERNAL SGBMV * .. * .. Intrinsic Functions .. INTRINSIC MAX, MIN * .. * .. Executable Statements .. * * Quick return if N = 0 pr NRHS = 0 * IF( M.LE.0 .OR. N.LE.0 .OR. NRHS.LE.0 ) THEN RESID = ZERO RETURN END IF * * Exit with RESID = 1/EPS if ANORM = 0. * EPS = SLAMCH( 'Epsilon' ) KD = KU + 1 ANORM = ZERO DO 10 J = 1, N I1 = MAX( KD+1-J, 1 ) I2 = MIN( KD+M-J, KL+KD ) ANORM = MAX( ANORM, SASUM( I2-I1+1, A( I1, J ), 1 ) ) 10 CONTINUE IF( ANORM.LE.ZERO ) THEN RESID = ONE / EPS RETURN END IF * IF( LSAME( TRANS, 'T' ) .OR. LSAME( TRANS, 'C' ) ) THEN N1 = N ELSE N1 = M END IF * * Compute B - A*X (or B - A'*X ) * DO 20 J = 1, NRHS CALL SGBMV( TRANS, M, N, KL, KU, -ONE, A, LDA, X( 1, J ), 1, $ ONE, B( 1, J ), 1 ) 20 CONTINUE * * Compute the maximum over the number of right hand sides of * norm(B - A*X) / ( norm(A) * norm(X) * EPS ). * RESID = ZERO DO 30 J = 1, NRHS BNORM = SASUM( N1, B( 1, J ), 1 ) XNORM = SASUM( N1, X( 1, J ), 1 ) IF( XNORM.LE.ZERO ) THEN RESID = ONE / EPS ELSE RESID = MAX( RESID, ( ( BNORM / ANORM ) / XNORM ) / EPS ) END IF 30 CONTINUE * RETURN * * End of SGBT02 * END |