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LAPACK 3.3.0
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LAPACK 3.3.0
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00001 SUBROUTINE ZPOT05( UPLO, N, NRHS, A, LDA, B, LDB, X, LDX, XACT, 00002 $ 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 UPLO 00010 INTEGER LDA, LDB, LDX, LDXACT, N, NRHS 00011 * .. 00012 * .. Array Arguments .. 00013 DOUBLE PRECISION BERR( * ), FERR( * ), RESLTS( * ) 00014 COMPLEX*16 A( LDA, * ), B( LDB, * ), X( LDX, * ), 00015 $ XACT( LDXACT, * ) 00016 * .. 00017 * 00018 * Purpose 00019 * ======= 00020 * 00021 * ZPOT05 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 * Hermitian n by n matrix. 00024 * 00025 * RESLTS(1) = test of the error bound 00026 * = norm(X - XACT) / ( norm(X) * FERR ) 00027 * 00028 * A large value is returned if this ratio is not less than one. 00029 * 00030 * RESLTS(2) = residual from the iterative refinement routine 00031 * = the maximum of BERR / ( (n+1)*EPS + (*) ), where 00032 * (*) = (n+1)*UNFL / (min_i (abs(A)*abs(X) +abs(b))_i ) 00033 * 00034 * Arguments 00035 * ========= 00036 * 00037 * UPLO (input) CHARACTER*1 00038 * Specifies whether the upper or lower triangular part of the 00039 * Hermitian matrix A is stored. 00040 * = 'U': Upper triangular 00041 * = 'L': Lower triangular 00042 * 00043 * N (input) INTEGER 00044 * The number of rows of the matrices X, B, and XACT, and the 00045 * order of the matrix A. N >= 0. 00046 * 00047 * NRHS (input) INTEGER 00048 * The number of columns of the matrices X, B, and XACT. 00049 * NRHS >= 0. 00050 * 00051 * A (input) COMPLEX*16 array, dimension (LDA,N) 00052 * The Hermitian matrix A. If UPLO = 'U', the leading n by n 00053 * upper triangular part of A contains the upper triangular part 00054 * of the matrix A, and the strictly lower triangular part of A 00055 * is not referenced. If UPLO = 'L', the leading n by n lower 00056 * triangular part of A contains the lower triangular part of 00057 * the matrix A, and the strictly upper triangular part of A is 00058 * not referenced. 00059 * 00060 * LDA (input) INTEGER 00061 * The leading dimension of the array A. LDA >= max(1,N). 00062 * 00063 * B (input) COMPLEX*16 array, dimension (LDB,NRHS) 00064 * The right hand side vectors for the system of linear 00065 * equations. 00066 * 00067 * LDB (input) INTEGER 00068 * The leading dimension of the array B. LDB >= max(1,N). 00069 * 00070 * X (input) COMPLEX*16 array, dimension (LDX,NRHS) 00071 * The computed solution vectors. Each vector is stored as a 00072 * column of the matrix X. 00073 * 00074 * LDX (input) INTEGER 00075 * The leading dimension of the array X. LDX >= max(1,N). 00076 * 00077 * XACT (input) COMPLEX*16 array, dimension (LDX,NRHS) 00078 * The exact solution vectors. Each vector is stored as a 00079 * column of the matrix XACT. 00080 * 00081 * LDXACT (input) INTEGER 00082 * The leading dimension of the array XACT. LDXACT >= max(1,N). 00083 * 00084 * FERR (input) DOUBLE PRECISION array, dimension (NRHS) 00085 * The estimated forward error bounds for each solution vector 00086 * X. If XTRUE is the true solution, FERR bounds the magnitude 00087 * of the largest entry in (X - XTRUE) divided by the magnitude 00088 * of the largest entry in X. 00089 * 00090 * BERR (input) DOUBLE PRECISION array, dimension (NRHS) 00091 * The componentwise relative backward error of each solution 00092 * vector (i.e., the smallest relative change in any entry of A 00093 * or B that makes X an exact solution). 00094 * 00095 * RESLTS (output) DOUBLE PRECISION array, dimension (2) 00096 * The maximum over the NRHS solution vectors of the ratios: 00097 * RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR ) 00098 * RESLTS(2) = BERR / ( (n+1)*EPS + (*) ) 00099 * 00100 * ===================================================================== 00101 * 00102 * .. Parameters .. 00103 DOUBLE PRECISION ZERO, ONE 00104 PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) 00105 * .. 00106 * .. Local Scalars .. 00107 LOGICAL UPPER 00108 INTEGER I, IMAX, J, K 00109 DOUBLE PRECISION AXBI, DIFF, EPS, ERRBND, OVFL, TMP, UNFL, XNORM 00110 COMPLEX*16 ZDUM 00111 * .. 00112 * .. External Functions .. 00113 LOGICAL LSAME 00114 INTEGER IZAMAX 00115 DOUBLE PRECISION DLAMCH 00116 EXTERNAL LSAME, IZAMAX, DLAMCH 00117 * .. 00118 * .. Intrinsic Functions .. 00119 INTRINSIC ABS, DBLE, DIMAG, MAX, MIN 00120 * .. 00121 * .. Statement Functions .. 00122 DOUBLE PRECISION CABS1 00123 * .. 00124 * .. Statement Function definitions .. 00125 CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) ) 00126 * .. 00127 * .. Executable Statements .. 00128 * 00129 * Quick exit if N = 0 or NRHS = 0. 00130 * 00131 IF( N.LE.0 .OR. NRHS.LE.0 ) THEN 00132 RESLTS( 1 ) = ZERO 00133 RESLTS( 2 ) = ZERO 00134 RETURN 00135 END IF 00136 * 00137 EPS = DLAMCH( 'Epsilon' ) 00138 UNFL = DLAMCH( 'Safe minimum' ) 00139 OVFL = ONE / UNFL 00140 UPPER = LSAME( UPLO, 'U' ) 00141 * 00142 * Test 1: Compute the maximum of 00143 * norm(X - XACT) / ( norm(X) * FERR ) 00144 * over all the vectors X and XACT using the infinity-norm. 00145 * 00146 ERRBND = ZERO 00147 DO 30 J = 1, NRHS 00148 IMAX = IZAMAX( N, X( 1, J ), 1 ) 00149 XNORM = MAX( CABS1( X( IMAX, J ) ), UNFL ) 00150 DIFF = ZERO 00151 DO 10 I = 1, N 00152 DIFF = MAX( DIFF, CABS1( X( I, J )-XACT( I, J ) ) ) 00153 10 CONTINUE 00154 * 00155 IF( XNORM.GT.ONE ) THEN 00156 GO TO 20 00157 ELSE IF( DIFF.LE.OVFL*XNORM ) THEN 00158 GO TO 20 00159 ELSE 00160 ERRBND = ONE / EPS 00161 GO TO 30 00162 END IF 00163 * 00164 20 CONTINUE 00165 IF( DIFF / XNORM.LE.FERR( J ) ) THEN 00166 ERRBND = MAX( ERRBND, ( DIFF / XNORM ) / FERR( J ) ) 00167 ELSE 00168 ERRBND = ONE / EPS 00169 END IF 00170 30 CONTINUE 00171 RESLTS( 1 ) = ERRBND 00172 * 00173 * Test 2: Compute the maximum of BERR / ( (n+1)*EPS + (*) ), where 00174 * (*) = (n+1)*UNFL / (min_i (abs(A)*abs(X) +abs(b))_i ) 00175 * 00176 DO 90 K = 1, NRHS 00177 DO 80 I = 1, N 00178 TMP = CABS1( B( I, K ) ) 00179 IF( UPPER ) THEN 00180 DO 40 J = 1, I - 1 00181 TMP = TMP + CABS1( A( J, I ) )*CABS1( X( J, K ) ) 00182 40 CONTINUE 00183 TMP = TMP + ABS( DBLE( A( I, I ) ) )*CABS1( X( I, K ) ) 00184 DO 50 J = I + 1, N 00185 TMP = TMP + CABS1( A( I, J ) )*CABS1( X( J, K ) ) 00186 50 CONTINUE 00187 ELSE 00188 DO 60 J = 1, I - 1 00189 TMP = TMP + CABS1( A( I, J ) )*CABS1( X( J, K ) ) 00190 60 CONTINUE 00191 TMP = TMP + ABS( DBLE( A( I, I ) ) )*CABS1( X( I, K ) ) 00192 DO 70 J = I + 1, N 00193 TMP = TMP + CABS1( A( J, I ) )*CABS1( X( J, K ) ) 00194 70 CONTINUE 00195 END IF 00196 IF( I.EQ.1 ) THEN 00197 AXBI = TMP 00198 ELSE 00199 AXBI = MIN( AXBI, TMP ) 00200 END IF 00201 80 CONTINUE 00202 TMP = BERR( K ) / ( ( N+1 )*EPS+( N+1 )*UNFL / 00203 $ MAX( AXBI, ( N+1 )*UNFL ) ) 00204 IF( K.EQ.1 ) THEN 00205 RESLTS( 2 ) = TMP 00206 ELSE 00207 RESLTS( 2 ) = MAX( RESLTS( 2 ), TMP ) 00208 END IF 00209 90 CONTINUE 00210 * 00211 RETURN 00212 * 00213 * End of ZPOT05 00214 * 00215 END
1.7.3 
