00001 SUBROUTINE CGTT02( TRANS, N, NRHS, DL, D, DU, X, LDX, B, LDB, 00002 $ RWORK, RESID ) 00003 * 00004 * -- LAPACK test routine (version 3.1) -- 00005 * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. 00006 * November 2006 00007 * 00008 * .. Scalar Arguments .. 00009 CHARACTER TRANS 00010 INTEGER LDB, LDX, N, NRHS 00011 REAL RESID 00012 * .. 00013 * .. Array Arguments .. 00014 REAL RWORK( * ) 00015 COMPLEX B( LDB, * ), D( * ), DL( * ), DU( * ), 00016 $ X( LDX, * ) 00017 * .. 00018 * 00019 * Purpose 00020 * ======= 00021 * 00022 * CGTT02 computes the residual for the solution to a tridiagonal 00023 * system of equations: 00024 * RESID = norm(B - op(A)*X) / (norm(A) * norm(X) * EPS), 00025 * where EPS is the machine epsilon. 00026 * 00027 * Arguments 00028 * ========= 00029 * 00030 * TRANS (input) CHARACTER 00031 * Specifies the form of the residual. 00032 * = 'N': B - A * X (No transpose) 00033 * = 'T': B - A**T * X (Transpose) 00034 * = 'C': B - A**H * X (Conjugate transpose) 00035 * 00036 * N (input) INTEGTER 00037 * The order of the matrix A. N >= 0. 00038 * 00039 * NRHS (input) INTEGER 00040 * The number of right hand sides, i.e., the number of columns 00041 * of the matrices B and X. NRHS >= 0. 00042 * 00043 * DL (input) COMPLEX array, dimension (N-1) 00044 * The (n-1) sub-diagonal elements of A. 00045 * 00046 * D (input) COMPLEX array, dimension (N) 00047 * The diagonal elements of A. 00048 * 00049 * DU (input) COMPLEX array, dimension (N-1) 00050 * The (n-1) super-diagonal elements of A. 00051 * 00052 * X (input) COMPLEX array, dimension (LDX,NRHS) 00053 * The computed solution vectors X. 00054 * 00055 * LDX (input) INTEGER 00056 * The leading dimension of the array X. LDX >= max(1,N). 00057 * 00058 * B (input/output) COMPLEX array, dimension (LDB,NRHS) 00059 * On entry, the right hand side vectors for the system of 00060 * linear equations. 00061 * On exit, B is overwritten with the difference B - op(A)*X. 00062 * 00063 * LDB (input) INTEGER 00064 * The leading dimension of the array B. LDB >= max(1,N). 00065 * 00066 * RWORK (workspace) REAL array, dimension (N) 00067 * 00068 * RESID (output) REAL 00069 * norm(B - op(A)*X) / (norm(A) * norm(X) * EPS) 00070 * 00071 * ===================================================================== 00072 * 00073 * .. Parameters .. 00074 REAL ONE, ZERO 00075 PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 ) 00076 * .. 00077 * .. Local Scalars .. 00078 INTEGER J 00079 REAL ANORM, BNORM, EPS, XNORM 00080 * .. 00081 * .. External Functions .. 00082 LOGICAL LSAME 00083 REAL CLANGT, SCASUM, SLAMCH 00084 EXTERNAL LSAME, CLANGT, SCASUM, SLAMCH 00085 * .. 00086 * .. External Subroutines .. 00087 EXTERNAL CLAGTM 00088 * .. 00089 * .. Intrinsic Functions .. 00090 INTRINSIC MAX 00091 * .. 00092 * .. Executable Statements .. 00093 * 00094 * Quick exit if N = 0 or NRHS = 0 00095 * 00096 RESID = ZERO 00097 IF( N.LE.0 .OR. NRHS.EQ.0 ) 00098 $ RETURN 00099 * 00100 * Compute the maximum over the number of right hand sides of 00101 * norm(B - op(A)*X) / ( norm(A) * norm(X) * EPS ). 00102 * 00103 IF( LSAME( TRANS, 'N' ) ) THEN 00104 ANORM = CLANGT( '1', N, DL, D, DU ) 00105 ELSE 00106 ANORM = CLANGT( 'I', N, DL, D, DU ) 00107 END IF 00108 * 00109 * Exit with RESID = 1/EPS if ANORM = 0. 00110 * 00111 EPS = SLAMCH( 'Epsilon' ) 00112 IF( ANORM.LE.ZERO ) THEN 00113 RESID = ONE / EPS 00114 RETURN 00115 END IF 00116 * 00117 * Compute B - op(A)*X. 00118 * 00119 CALL CLAGTM( TRANS, N, NRHS, -ONE, DL, D, DU, X, LDX, ONE, B, 00120 $ LDB ) 00121 * 00122 DO 10 J = 1, NRHS 00123 BNORM = SCASUM( N, B( 1, J ), 1 ) 00124 XNORM = SCASUM( N, X( 1, J ), 1 ) 00125 IF( XNORM.LE.ZERO ) THEN 00126 RESID = ONE / EPS 00127 ELSE 00128 RESID = MAX( RESID, ( ( BNORM / ANORM ) / XNORM ) / EPS ) 00129 END IF 00130 10 CONTINUE 00131 * 00132 RETURN 00133 * 00134 * End of CGTT02 00135 * 00136 END
1.7.2