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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 ZTPT05( UPLO, TRANS, DIAG, N, NRHS, AP, 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 DIAG, TRANS, UPLO 00010 INTEGER LDB, LDX, LDXACT, N, NRHS 00011 * .. 00012 * .. Array Arguments .. 00013 DOUBLE PRECISION BERR( * ), FERR( * ), RESLTS( * ) 00014 COMPLEX*16 AP( * ), B( LDB, * ), X( LDX, * ), 00015 $ XACT( LDXACT, * ) 00016 * .. 00017 * 00018 * Purpose 00019 * ======= 00020 * 00021 * ZTPT05 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 * triangular matrix in packed storage format. 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 matrix A is upper or lower triangular. 00039 * = 'U': Upper triangular 00040 * = 'L': Lower triangular 00041 * 00042 * TRANS (input) CHARACTER*1 00043 * Specifies the form of the system of equations. 00044 * = 'N': A * X = B (No transpose) 00045 * = 'T': A'* X = B (Transpose) 00046 * = 'C': A'* X = B (Conjugate transpose = Transpose) 00047 * 00048 * DIAG (input) CHARACTER*1 00049 * Specifies whether or not the matrix A is unit triangular. 00050 * = 'N': Non-unit triangular 00051 * = 'U': Unit triangular 00052 * 00053 * N (input) INTEGER 00054 * The number of rows of the matrices X, B, and XACT, and the 00055 * order of the matrix A. N >= 0. 00056 * 00057 * NRHS (input) INTEGER 00058 * The number of columns of the matrices X, B, and XACT. 00059 * NRHS >= 0. 00060 * 00061 * AP (input) COMPLEX*16 array, dimension (N*(N+1)/2) 00062 * The upper or lower triangular matrix A, packed columnwise in 00063 * a linear array. The j-th column of A is stored in the array 00064 * AP as follows: 00065 * if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; 00066 * if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. 00067 * If DIAG = 'U', the diagonal elements of A are not referenced 00068 * and are assumed to be 1. 00069 * 00070 * B (input) COMPLEX*16 array, dimension (LDB,NRHS) 00071 * The right hand side vectors for the system of linear 00072 * equations. 00073 * 00074 * LDB (input) INTEGER 00075 * The leading dimension of the array B. LDB >= max(1,N). 00076 * 00077 * X (input) COMPLEX*16 array, dimension (LDX,NRHS) 00078 * The computed solution vectors. Each vector is stored as a 00079 * column of the matrix X. 00080 * 00081 * LDX (input) INTEGER 00082 * The leading dimension of the array X. LDX >= max(1,N). 00083 * 00084 * XACT (input) COMPLEX*16 array, dimension (LDX,NRHS) 00085 * The exact solution vectors. Each vector is stored as a 00086 * column of the matrix XACT. 00087 * 00088 * LDXACT (input) INTEGER 00089 * The leading dimension of the array XACT. LDXACT >= max(1,N). 00090 * 00091 * FERR (input) DOUBLE PRECISION array, dimension (NRHS) 00092 * The estimated forward error bounds for each solution vector 00093 * X. If XTRUE is the true solution, FERR bounds the magnitude 00094 * of the largest entry in (X - XTRUE) divided by the magnitude 00095 * of the largest entry in X. 00096 * 00097 * BERR (input) DOUBLE PRECISION array, dimension (NRHS) 00098 * The componentwise relative backward error of each solution 00099 * vector (i.e., the smallest relative change in any entry of A 00100 * or B that makes X an exact solution). 00101 * 00102 * RESLTS (output) DOUBLE PRECISION array, dimension (2) 00103 * The maximum over the NRHS solution vectors of the ratios: 00104 * RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR ) 00105 * RESLTS(2) = BERR / ( (n+1)*EPS + (*) ) 00106 * 00107 * ===================================================================== 00108 * 00109 * .. Parameters .. 00110 DOUBLE PRECISION ZERO, ONE 00111 PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) 00112 * .. 00113 * .. Local Scalars .. 00114 LOGICAL NOTRAN, UNIT, UPPER 00115 INTEGER I, IFU, IMAX, J, JC, K 00116 DOUBLE PRECISION AXBI, DIFF, EPS, ERRBND, OVFL, TMP, UNFL, XNORM 00117 COMPLEX*16 ZDUM 00118 * .. 00119 * .. External Functions .. 00120 LOGICAL LSAME 00121 INTEGER IZAMAX 00122 DOUBLE PRECISION DLAMCH 00123 EXTERNAL LSAME, IZAMAX, DLAMCH 00124 * .. 00125 * .. Intrinsic Functions .. 00126 INTRINSIC ABS, DBLE, DIMAG, MAX, MIN 00127 * .. 00128 * .. Statement Functions .. 00129 DOUBLE PRECISION CABS1 00130 * .. 00131 * .. Statement Function definitions .. 00132 CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) ) 00133 * .. 00134 * .. Executable Statements .. 00135 * 00136 * Quick exit if N = 0 or NRHS = 0. 00137 * 00138 IF( N.LE.0 .OR. NRHS.LE.0 ) THEN 00139 RESLTS( 1 ) = ZERO 00140 RESLTS( 2 ) = ZERO 00141 RETURN 00142 END IF 00143 * 00144 EPS = DLAMCH( 'Epsilon' ) 00145 UNFL = DLAMCH( 'Safe minimum' ) 00146 OVFL = ONE / UNFL 00147 UPPER = LSAME( UPLO, 'U' ) 00148 NOTRAN = LSAME( TRANS, 'N' ) 00149 UNIT = LSAME( DIAG, 'U' ) 00150 * 00151 * Test 1: Compute the maximum of 00152 * norm(X - XACT) / ( norm(X) * FERR ) 00153 * over all the vectors X and XACT using the infinity-norm. 00154 * 00155 ERRBND = ZERO 00156 DO 30 J = 1, NRHS 00157 IMAX = IZAMAX( N, X( 1, J ), 1 ) 00158 XNORM = MAX( CABS1( X( IMAX, J ) ), UNFL ) 00159 DIFF = ZERO 00160 DO 10 I = 1, N 00161 DIFF = MAX( DIFF, CABS1( X( I, J )-XACT( I, J ) ) ) 00162 10 CONTINUE 00163 * 00164 IF( XNORM.GT.ONE ) THEN 00165 GO TO 20 00166 ELSE IF( DIFF.LE.OVFL*XNORM ) THEN 00167 GO TO 20 00168 ELSE 00169 ERRBND = ONE / EPS 00170 GO TO 30 00171 END IF 00172 * 00173 20 CONTINUE 00174 IF( DIFF / XNORM.LE.FERR( J ) ) THEN 00175 ERRBND = MAX( ERRBND, ( DIFF / XNORM ) / FERR( J ) ) 00176 ELSE 00177 ERRBND = ONE / EPS 00178 END IF 00179 30 CONTINUE 00180 RESLTS( 1 ) = ERRBND 00181 * 00182 * Test 2: Compute the maximum of BERR / ( (n+1)*EPS + (*) ), where 00183 * (*) = (n+1)*UNFL / (min_i (abs(A)*abs(X) +abs(b))_i ) 00184 * 00185 IFU = 0 00186 IF( UNIT ) 00187 $ IFU = 1 00188 DO 90 K = 1, NRHS 00189 DO 80 I = 1, N 00190 TMP = CABS1( B( I, K ) ) 00191 IF( UPPER ) THEN 00192 JC = ( ( I-1 )*I ) / 2 00193 IF( .NOT.NOTRAN ) THEN 00194 DO 40 J = 1, I - IFU 00195 TMP = TMP + CABS1( AP( JC+J ) )*CABS1( X( J, K ) ) 00196 40 CONTINUE 00197 IF( UNIT ) 00198 $ TMP = TMP + CABS1( X( I, K ) ) 00199 ELSE 00200 JC = JC + I 00201 IF( UNIT ) THEN 00202 TMP = TMP + CABS1( X( I, K ) ) 00203 JC = JC + I 00204 END IF 00205 DO 50 J = I + IFU, N 00206 TMP = TMP + CABS1( AP( JC ) )*CABS1( X( J, K ) ) 00207 JC = JC + J 00208 50 CONTINUE 00209 END IF 00210 ELSE 00211 IF( NOTRAN ) THEN 00212 JC = I 00213 DO 60 J = 1, I - IFU 00214 TMP = TMP + CABS1( AP( JC ) )*CABS1( X( J, K ) ) 00215 JC = JC + N - J 00216 60 CONTINUE 00217 IF( UNIT ) 00218 $ TMP = TMP + CABS1( X( I, K ) ) 00219 ELSE 00220 JC = ( I-1 )*( N-I ) + ( I*( I+1 ) ) / 2 00221 IF( UNIT ) 00222 $ TMP = TMP + CABS1( X( I, K ) ) 00223 DO 70 J = I + IFU, N 00224 TMP = TMP + CABS1( AP( JC+J-I ) )* 00225 $ CABS1( X( J, K ) ) 00226 70 CONTINUE 00227 END IF 00228 END IF 00229 IF( I.EQ.1 ) THEN 00230 AXBI = TMP 00231 ELSE 00232 AXBI = MIN( AXBI, TMP ) 00233 END IF 00234 80 CONTINUE 00235 TMP = BERR( K ) / ( ( N+1 )*EPS+( N+1 )*UNFL / 00236 $ MAX( AXBI, ( N+1 )*UNFL ) ) 00237 IF( K.EQ.1 ) THEN 00238 RESLTS( 2 ) = TMP 00239 ELSE 00240 RESLTS( 2 ) = MAX( RESLTS( 2 ), TMP ) 00241 END IF 00242 90 CONTINUE 00243 * 00244 RETURN 00245 * 00246 * End of ZTPT05 00247 * 00248 END
1.7.3 
