SUBROUTINE ZPBT02( UPLO, N, KD, 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 UPLO INTEGER KD, LDA, LDB, LDX, N, NRHS DOUBLE PRECISION RESID * .. * .. Array Arguments .. DOUBLE PRECISION RWORK( * ) COMPLEX*16 A( LDA, * ), B( LDB, * ), X( LDX, * ) * .. * * Purpose * ======= * * ZPBT02 computes the residual for a solution of a Hermitian banded * system of equations A*x = b: * RESID = norm( B - A*X ) / ( norm(A) * norm(X) * EPS) * where EPS is the machine precision. * * Arguments * ========= * * UPLO (input) CHARACTER*1 * Specifies whether the upper or lower triangular part of the * Hermitian 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. * * KD (input) INTEGER * The number of super-diagonals of the matrix A if UPLO = 'U', * or the number of sub-diagonals if UPLO = 'L'. KD >= 0. * * A (input) COMPLEX*16 array, dimension (LDA,N) * The original Hermitian band matrix A. If UPLO = 'U', the * upper triangular part of A is stored as a band matrix; if * UPLO = 'L', the lower triangular part of A is stored. The * columns of the appropriate triangle are stored in the columns * of A and the diagonals of the triangle are stored in the rows * of A. See ZPBTRF for further details. * * LDA (input) INTEGER. * The leading dimension of the array A. LDA >= max(1,KD+1). * * X (input) COMPLEX*16 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/output) COMPLEX*16 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. 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 PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) COMPLEX*16 CONE PARAMETER ( CONE = ( 1.0D+0, 0.0D+0 ) ) * .. * .. Local Scalars .. INTEGER J DOUBLE PRECISION ANORM, BNORM, EPS, XNORM * .. * .. External Functions .. DOUBLE PRECISION DLAMCH, DZASUM, ZLANHB EXTERNAL DLAMCH, DZASUM, ZLANHB * .. * .. External Subroutines .. EXTERNAL ZHBMV * .. * .. 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 * * Exit with RESID = 1/EPS if ANORM = 0. * EPS = DLAMCH( 'Epsilon' ) ANORM = ZLANHB( '1', UPLO, N, KD, A, LDA, RWORK ) IF( ANORM.LE.ZERO ) THEN RESID = ONE / EPS RETURN END IF * * Compute B - A*X * DO 10 J = 1, NRHS CALL ZHBMV( UPLO, N, KD, -CONE, A, LDA, X( 1, J ), 1, CONE, \$ B( 1, J ), 1 ) 10 CONTINUE * * Compute the maximum over the number of right hand sides of * norm( B - A*X ) / ( norm(A) * norm(X) * EPS ) * RESID = ZERO DO 20 J = 1, NRHS BNORM = DZASUM( N, B( 1, J ), 1 ) XNORM = DZASUM( N, X( 1, J ), 1 ) IF( XNORM.LE.ZERO ) THEN RESID = ONE / EPS ELSE RESID = MAX( RESID, ( ( BNORM / ANORM ) / XNORM ) / EPS ) END IF 20 CONTINUE * RETURN * * End of ZPBT02 * END