|
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 |
SUBROUTINE STPT02( UPLO, TRANS, DIAG, N, NRHS, AP, 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 LDB, LDX, N, NRHS REAL RESID * .. * .. Array Arguments .. REAL AP( * ), B( LDB, * ), WORK( * ), X( LDX, * ) * .. * * Purpose * ======= * * STPT02 computes the residual for the computed solution to a * triangular system of linear equations A*x = b or A'*x = b when * the triangular matrix A is stored in packed format. 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. * * NRHS (input) INTEGER * The number of right hand sides, i.e., the number of columns * of the matrices X and B. NRHS >= 0. * * AP (input) REAL array, dimension (N*(N+1)/2) * The upper or lower triangular matrix A, packed columnwise in * a linear array. The j-th column of A is stored in the array * AP as follows: * if UPLO = 'U', AP((j-1)*j/2 + i) = A(i,j) for 1<=i<=j; * if UPLO = 'L', * AP((j-1)*(n-j) + j*(j+1)/2 + i-j) = A(i,j) for j<=i<=n. * * 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) REAL 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) 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 SASUM, SLAMCH, SLANTP EXTERNAL LSAME, SASUM, SLAMCH, SLANTP * .. * .. External Subroutines .. EXTERNAL SAXPY, SCOPY, STPMV * .. * .. 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 = SLANTP( '1', UPLO, DIAG, N, AP, WORK ) ELSE ANORM = SLANTP( 'I', UPLO, DIAG, N, AP, WORK ) 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 SCOPY( N, X( 1, J ), 1, WORK, 1 ) CALL STPMV( UPLO, TRANS, DIAG, N, AP, WORK, 1 ) CALL SAXPY( N, -ONE, B( 1, J ), 1, WORK, 1 ) BNORM = SASUM( N, WORK, 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 10 CONTINUE * RETURN * * End of STPT02 * END |