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LAPACK 3.3.1
Linear Algebra PACKage
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LAPACK 3.3.1
Linear Algebra PACKage
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00001 SUBROUTINE DGTT05( TRANS, N, NRHS, DL, D, DU, B, LDB, X, LDX, 00002 $ XACT, LDXACT, FERR, BERR, RESLTS ) 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, LDXACT, N, NRHS 00011 * .. 00012 * .. Array Arguments .. 00013 DOUBLE PRECISION B( LDB, * ), BERR( * ), D( * ), DL( * ), 00014 $ DU( * ), FERR( * ), RESLTS( * ), X( LDX, * ), 00015 $ XACT( LDXACT, * ) 00016 * .. 00017 * 00018 * Purpose 00019 * ======= 00020 * 00021 * DGTT05 tests the error bounds from iterative refinement for the 00022 * computed solution to a system of equations A*X = B, where A is a 00023 * general tridiagonal matrix of order n and op(A) = A or A**T, 00024 * depending on TRANS. 00025 * 00026 * RESLTS(1) = test of the error bound 00027 * = norm(X - XACT) / ( norm(X) * FERR ) 00028 * 00029 * A large value is returned if this ratio is not less than one. 00030 * 00031 * RESLTS(2) = residual from the iterative refinement routine 00032 * = the maximum of BERR / ( NZ*EPS + (*) ), where 00033 * (*) = NZ*UNFL / (min_i (abs(op(A))*abs(X) +abs(b))_i ) 00034 * and NZ = max. number of nonzeros in any row of A, plus 1 00035 * 00036 * Arguments 00037 * ========= 00038 * 00039 * TRANS (input) CHARACTER*1 00040 * Specifies the form of the system of equations. 00041 * = 'N': A * X = B (No transpose) 00042 * = 'T': A**T * X = B (Transpose) 00043 * = 'C': A**H * X = B (Conjugate transpose = Transpose) 00044 * 00045 * N (input) INTEGER 00046 * The number of rows of the matrices X and XACT. N >= 0. 00047 * 00048 * NRHS (input) INTEGER 00049 * The number of columns of the matrices X and XACT. NRHS >= 0. 00050 * 00051 * DL (input) DOUBLE PRECISION array, dimension (N-1) 00052 * The (n-1) sub-diagonal elements of A. 00053 * 00054 * D (input) DOUBLE PRECISION array, dimension (N) 00055 * The diagonal elements of A. 00056 * 00057 * DU (input) DOUBLE PRECISION array, dimension (N-1) 00058 * The (n-1) super-diagonal elements of A. 00059 * 00060 * B (input) DOUBLE PRECISION array, dimension (LDB,NRHS) 00061 * The right hand side vectors for the system of linear 00062 * equations. 00063 * 00064 * LDB (input) INTEGER 00065 * The leading dimension of the array B. LDB >= max(1,N). 00066 * 00067 * X (input) DOUBLE PRECISION array, dimension (LDX,NRHS) 00068 * The computed solution vectors. Each vector is stored as a 00069 * column of the matrix X. 00070 * 00071 * LDX (input) INTEGER 00072 * The leading dimension of the array X. LDX >= max(1,N). 00073 * 00074 * XACT (input) DOUBLE PRECISION array, dimension (LDX,NRHS) 00075 * The exact solution vectors. Each vector is stored as a 00076 * column of the matrix XACT. 00077 * 00078 * LDXACT (input) INTEGER 00079 * The leading dimension of the array XACT. LDXACT >= max(1,N). 00080 * 00081 * FERR (input) DOUBLE PRECISION array, dimension (NRHS) 00082 * The estimated forward error bounds for each solution vector 00083 * X. If XTRUE is the true solution, FERR bounds the magnitude 00084 * of the largest entry in (X - XTRUE) divided by the magnitude 00085 * of the largest entry in X. 00086 * 00087 * BERR (input) DOUBLE PRECISION array, dimension (NRHS) 00088 * The componentwise relative backward error of each solution 00089 * vector (i.e., the smallest relative change in any entry of A 00090 * or B that makes X an exact solution). 00091 * 00092 * RESLTS (output) DOUBLE PRECISION array, dimension (2) 00093 * The maximum over the NRHS solution vectors of the ratios: 00094 * RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR ) 00095 * RESLTS(2) = BERR / ( NZ*EPS + (*) ) 00096 * 00097 * ===================================================================== 00098 * 00099 * .. Parameters .. 00100 DOUBLE PRECISION ZERO, ONE 00101 PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) 00102 * .. 00103 * .. Local Scalars .. 00104 LOGICAL NOTRAN 00105 INTEGER I, IMAX, J, K, NZ 00106 DOUBLE PRECISION AXBI, DIFF, EPS, ERRBND, OVFL, TMP, UNFL, XNORM 00107 * .. 00108 * .. External Functions .. 00109 LOGICAL LSAME 00110 INTEGER IDAMAX 00111 DOUBLE PRECISION DLAMCH 00112 EXTERNAL LSAME, IDAMAX, DLAMCH 00113 * .. 00114 * .. Intrinsic Functions .. 00115 INTRINSIC ABS, MAX, MIN 00116 * .. 00117 * .. Executable Statements .. 00118 * 00119 * Quick exit if N = 0 or NRHS = 0. 00120 * 00121 IF( N.LE.0 .OR. NRHS.LE.0 ) THEN 00122 RESLTS( 1 ) = ZERO 00123 RESLTS( 2 ) = ZERO 00124 RETURN 00125 END IF 00126 * 00127 EPS = DLAMCH( 'Epsilon' ) 00128 UNFL = DLAMCH( 'Safe minimum' ) 00129 OVFL = ONE / UNFL 00130 NOTRAN = LSAME( TRANS, 'N' ) 00131 NZ = 4 00132 * 00133 * Test 1: Compute the maximum of 00134 * norm(X - XACT) / ( norm(X) * FERR ) 00135 * over all the vectors X and XACT using the infinity-norm. 00136 * 00137 ERRBND = ZERO 00138 DO 30 J = 1, NRHS 00139 IMAX = IDAMAX( N, X( 1, J ), 1 ) 00140 XNORM = MAX( ABS( X( IMAX, J ) ), UNFL ) 00141 DIFF = ZERO 00142 DO 10 I = 1, N 00143 DIFF = MAX( DIFF, ABS( X( I, J )-XACT( I, J ) ) ) 00144 10 CONTINUE 00145 * 00146 IF( XNORM.GT.ONE ) THEN 00147 GO TO 20 00148 ELSE IF( DIFF.LE.OVFL*XNORM ) THEN 00149 GO TO 20 00150 ELSE 00151 ERRBND = ONE / EPS 00152 GO TO 30 00153 END IF 00154 * 00155 20 CONTINUE 00156 IF( DIFF / XNORM.LE.FERR( J ) ) THEN 00157 ERRBND = MAX( ERRBND, ( DIFF / XNORM ) / FERR( J ) ) 00158 ELSE 00159 ERRBND = ONE / EPS 00160 END IF 00161 30 CONTINUE 00162 RESLTS( 1 ) = ERRBND 00163 * 00164 * Test 2: Compute the maximum of BERR / ( NZ*EPS + (*) ), where 00165 * (*) = NZ*UNFL / (min_i (abs(op(A))*abs(X) +abs(b))_i ) 00166 * 00167 DO 60 K = 1, NRHS 00168 IF( NOTRAN ) THEN 00169 IF( N.EQ.1 ) THEN 00170 AXBI = ABS( B( 1, K ) ) + ABS( D( 1 )*X( 1, K ) ) 00171 ELSE 00172 AXBI = ABS( B( 1, K ) ) + ABS( D( 1 )*X( 1, K ) ) + 00173 $ ABS( DU( 1 )*X( 2, K ) ) 00174 DO 40 I = 2, N - 1 00175 TMP = ABS( B( I, K ) ) + ABS( DL( I-1 )*X( I-1, K ) ) 00176 $ + ABS( D( I )*X( I, K ) ) + 00177 $ ABS( DU( I )*X( I+1, K ) ) 00178 AXBI = MIN( AXBI, TMP ) 00179 40 CONTINUE 00180 TMP = ABS( B( N, K ) ) + ABS( DL( N-1 )*X( N-1, K ) ) + 00181 $ ABS( D( N )*X( N, K ) ) 00182 AXBI = MIN( AXBI, TMP ) 00183 END IF 00184 ELSE 00185 IF( N.EQ.1 ) THEN 00186 AXBI = ABS( B( 1, K ) ) + ABS( D( 1 )*X( 1, K ) ) 00187 ELSE 00188 AXBI = ABS( B( 1, K ) ) + ABS( D( 1 )*X( 1, K ) ) + 00189 $ ABS( DL( 1 )*X( 2, K ) ) 00190 DO 50 I = 2, N - 1 00191 TMP = ABS( B( I, K ) ) + ABS( DU( I-1 )*X( I-1, K ) ) 00192 $ + ABS( D( I )*X( I, K ) ) + 00193 $ ABS( DL( I )*X( I+1, K ) ) 00194 AXBI = MIN( AXBI, TMP ) 00195 50 CONTINUE 00196 TMP = ABS( B( N, K ) ) + ABS( DU( N-1 )*X( N-1, K ) ) + 00197 $ ABS( D( N )*X( N, K ) ) 00198 AXBI = MIN( AXBI, TMP ) 00199 END IF 00200 END IF 00201 TMP = BERR( K ) / ( NZ*EPS+NZ*UNFL / MAX( AXBI, NZ*UNFL ) ) 00202 IF( K.EQ.1 ) THEN 00203 RESLTS( 2 ) = TMP 00204 ELSE 00205 RESLTS( 2 ) = MAX( RESLTS( 2 ), TMP ) 00206 END IF 00207 60 CONTINUE 00208 * 00209 RETURN 00210 * 00211 * End of DGTT05 00212 * 00213 END
1.7.3 
