|
1
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 |
SUBROUTINE SPBT02( 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 REAL RESID * .. * .. Array Arguments .. REAL A( LDA, * ), B( LDB, * ), RWORK( * ), $ X( LDX, * ) * .. * * Purpose * ======= * * SPBT02 computes the residual for a solution of a symmetric 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 * 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. * * 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) REAL array, dimension (LDA,N) * The original symmetric 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 SPBTRF for further details. * * LDA (input) INTEGER. * The leading dimension of the array A. LDA >= max(1,KD+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. LDX >= max(1,N). * * 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. LDB >= max(1,N). * * RWORK (workspace) REAL array, dimension (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 J REAL ANORM, BNORM, EPS, XNORM * .. * .. External Functions .. REAL SASUM, SLAMCH, SLANSB EXTERNAL SASUM, SLAMCH, SLANSB * .. * .. External Subroutines .. EXTERNAL SSBMV * .. * .. 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 = SLAMCH( 'Epsilon' ) ANORM = SLANSB( '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 SSBMV( UPLO, N, KD, -ONE, A, LDA, X( 1, J ), 1, ONE, $ 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 = SASUM( N, B( 1, J ), 1 ) XNORM = SASUM( 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 SPBT02 * END |