SUBROUTINE DTBT02( UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, X, \$ LDX, B, LDB, WORK, RESID ) * * -- LAPACK test routine (version 3.1) -- * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. * November 2006 * * .. Scalar Arguments .. CHARACTER DIAG, TRANS, UPLO INTEGER KD, LDAB, LDB, LDX, N, NRHS DOUBLE PRECISION RESID * .. * .. Array Arguments .. DOUBLE PRECISION AB( LDAB, * ), B( LDB, * ), WORK( * ), \$ X( LDX, * ) * .. * * Purpose * ======= * * DTBT02 computes the residual for the computed solution to a * triangular system of linear equations A*x = b or A' *x = b when * A is a triangular band matrix. Here A' is the transpose of A and * x and b are N by NRHS matrices. The test ratio is the maximum over * the number of right hand sides of * norm(b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ), * where op(A) denotes A or A' and EPS is the machine epsilon. * * Arguments * ========= * * UPLO (input) CHARACTER*1 * Specifies whether the matrix A is upper or lower triangular. * = 'U': Upper triangular * = 'L': Lower triangular * * TRANS (input) CHARACTER*1 * Specifies the operation applied to A. * = 'N': A *x = b (No transpose) * = 'T': A'*x = b (Transpose) * = 'C': A'*x = b (Conjugate transpose = Transpose) * * DIAG (input) CHARACTER*1 * Specifies whether or not the matrix A is unit triangular. * = 'N': Non-unit triangular * = 'U': Unit triangular * * N (input) INTEGER * The order of the matrix A. N >= 0. * * KD (input) INTEGER * The number of superdiagonals or subdiagonals of the * triangular band matrix A. KD >= 0. * * NRHS (input) INTEGER * The number of right hand sides, i.e., the number of columns * of the matrices X and B. NRHS >= 0. * * AB (input) DOUBLE PRECISION array, dimension (LDAB,N) * The upper or lower triangular band matrix A, stored in the * first kd+1 rows of the array. The j-th column of A is stored * in the j-th column of the array AB as follows: * if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; * if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). * * LDAB (input) INTEGER * The leading dimension of the array AB. LDAB >= KD+1. * * 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. LDX >= max(1,N). * * B (input) DOUBLE PRECISION array, dimension (LDB,NRHS) * The right hand side vectors for the system of linear * equations. * * LDB (input) INTEGER * The leading dimension of the array B. LDB >= max(1,N). * * WORK (workspace) DOUBLE PRECISION array, dimension (N) * * RESID (output) DOUBLE PRECISION * The maximum over the number of right hand sides of * norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ). * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, ONE PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) * .. * .. Local Scalars .. INTEGER J DOUBLE PRECISION ANORM, BNORM, EPS, XNORM * .. * .. External Functions .. LOGICAL LSAME DOUBLE PRECISION DASUM, DLAMCH, DLANTB EXTERNAL LSAME, DASUM, DLAMCH, DLANTB * .. * .. External Subroutines .. EXTERNAL DAXPY, DCOPY, DTBMV * .. * .. Intrinsic Functions .. INTRINSIC 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 * * Compute the 1-norm of A or A'. * IF( LSAME( TRANS, 'N' ) ) THEN ANORM = DLANTB( '1', UPLO, DIAG, N, KD, AB, LDAB, WORK ) ELSE ANORM = DLANTB( 'I', UPLO, DIAG, N, KD, AB, LDAB, WORK ) END IF * * Exit with RESID = 1/EPS if ANORM = 0. * EPS = DLAMCH( 'Epsilon' ) IF( ANORM.LE.ZERO ) THEN RESID = ONE / EPS RETURN END IF * * Compute the maximum over the number of right hand sides of * norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ). * RESID = ZERO DO 10 J = 1, NRHS CALL DCOPY( N, X( 1, J ), 1, WORK, 1 ) CALL DTBMV( UPLO, TRANS, DIAG, N, KD, AB, LDAB, WORK, 1 ) CALL DAXPY( N, -ONE, B( 1, J ), 1, WORK, 1 ) BNORM = DASUM( N, WORK, 1 ) XNORM = DASUM( N, X( 1, J ), 1 ) IF( XNORM.LE.ZERO ) THEN RESID = ONE / EPS ELSE RESID = MAX( RESID, ( ( BNORM / ANORM ) / XNORM ) / EPS ) END IF 10 CONTINUE * RETURN * * End of DTBT02 * END