|
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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 |
SUBROUTINE CTBT02( UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, X,
$ LDX, B, LDB, WORK, RWORK, 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 REAL RESID * .. * .. Array Arguments .. REAL RWORK( * ) COMPLEX AB( LDAB, * ), B( LDB, * ), WORK( * ), $ X( LDX, * ) * .. * * Purpose * ======= * * CTBT02 computes the residual for the computed solution to a * triangular system of linear equations A*x = b, A**T *x = b, or * A**H *x = b when A is a triangular band matrix. Here A**T denotes * the transpose of A, A**H denotes the conjugate 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, A**T, or A**H, 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**T *x = b (Transpose) * = 'C': A**H *x = b (Conjugate 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) COMPLEX array, dimension (LDA,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 >= max(1,KD+1). * * X (input) COMPLEX 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) COMPLEX 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) COMPLEX array, dimension (N) * * RWORK (workspace) REAL array, dimension (N) * * RESID (output) REAL * The maximum over the number of right hand sides of * norm(op(A)*x - b) / ( norm(op(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 .. LOGICAL LSAME REAL CLANTB, SCASUM, SLAMCH EXTERNAL LSAME, CLANTB, SCASUM, SLAMCH * .. * .. External Subroutines .. EXTERNAL CAXPY, CCOPY, CTBMV * .. * .. Intrinsic Functions .. INTRINSIC CMPLX, 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 = CLANTB( '1', UPLO, DIAG, N, KD, AB, LDAB, RWORK ) ELSE ANORM = CLANTB( 'I', UPLO, DIAG, N, KD, AB, LDAB, RWORK ) END IF * * Exit with RESID = 1/EPS if ANORM = 0. * EPS = SLAMCH( '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 CCOPY( N, X( 1, J ), 1, WORK, 1 ) CALL CTBMV( UPLO, TRANS, DIAG, N, KD, AB, LDAB, WORK, 1 ) CALL CAXPY( N, CMPLX( -ONE ), B( 1, J ), 1, WORK, 1 ) BNORM = SCASUM( N, WORK, 1 ) XNORM = SCASUM( 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 CTBT02 * END |