1*> \brief \b DPPT02 2* 3* =========== DOCUMENTATION =========== 4* 5* Online html documentation available at 6* http://www.netlib.org/lapack/explore-html/ 7* 8* Definition: 9* =========== 10* 11* SUBROUTINE DPPT02( UPLO, N, NRHS, A, X, LDX, B, LDB, RWORK, 12* RESID ) 13* 14* .. Scalar Arguments .. 15* CHARACTER UPLO 16* INTEGER LDB, LDX, N, NRHS 17* DOUBLE PRECISION RESID 18* .. 19* .. Array Arguments .. 20* DOUBLE PRECISION A( * ), B( LDB, * ), RWORK( * ), X( LDX, * ) 21* .. 22* 23* 24*> \par Purpose: 25* ============= 26*> 27*> \verbatim 28*> 29*> DPPT02 computes the residual in the solution of a symmetric system 30*> of linear equations A*x = b when packed storage is used for the 31*> coefficient matrix. The ratio computed is 32*> 33*> RESID = norm(B - A*X) / ( norm(A) * norm(X) * EPS), 34*> 35*> where EPS is the machine precision. 36*> \endverbatim 37* 38* Arguments: 39* ========== 40* 41*> \param[in] UPLO 42*> \verbatim 43*> UPLO is CHARACTER*1 44*> Specifies whether the upper or lower triangular part of the 45*> symmetric matrix A is stored: 46*> = 'U': Upper triangular 47*> = 'L': Lower triangular 48*> \endverbatim 49*> 50*> \param[in] N 51*> \verbatim 52*> N is INTEGER 53*> The number of rows and columns of the matrix A. N >= 0. 54*> \endverbatim 55*> 56*> \param[in] NRHS 57*> \verbatim 58*> NRHS is INTEGER 59*> The number of columns of B, the matrix of right hand sides. 60*> NRHS >= 0. 61*> \endverbatim 62*> 63*> \param[in] A 64*> \verbatim 65*> A is DOUBLE PRECISION array, dimension (N*(N+1)/2) 66*> The original symmetric matrix A, stored as a packed 67*> triangular matrix. 68*> \endverbatim 69*> 70*> \param[in] X 71*> \verbatim 72*> X is DOUBLE PRECISION array, dimension (LDX,NRHS) 73*> The computed solution vectors for the system of linear 74*> equations. 75*> \endverbatim 76*> 77*> \param[in] LDX 78*> \verbatim 79*> LDX is INTEGER 80*> The leading dimension of the array X. LDX >= max(1,N). 81*> \endverbatim 82*> 83*> \param[in,out] B 84*> \verbatim 85*> B is DOUBLE PRECISION array, dimension (LDB,NRHS) 86*> On entry, the right hand side vectors for the system of 87*> linear equations. 88*> On exit, B is overwritten with the difference B - A*X. 89*> \endverbatim 90*> 91*> \param[in] LDB 92*> \verbatim 93*> LDB is INTEGER 94*> The leading dimension of the array B. LDB >= max(1,N). 95*> \endverbatim 96*> 97*> \param[out] RWORK 98*> \verbatim 99*> RWORK is DOUBLE PRECISION array, dimension (N) 100*> \endverbatim 101*> 102*> \param[out] RESID 103*> \verbatim 104*> RESID is DOUBLE PRECISION 105*> The maximum over the number of right hand sides of 106*> norm(B - A*X) / ( norm(A) * norm(X) * EPS ). 107*> \endverbatim 108* 109* Authors: 110* ======== 111* 112*> \author Univ. of Tennessee 113*> \author Univ. of California Berkeley 114*> \author Univ. of Colorado Denver 115*> \author NAG Ltd. 116* 117*> \date November 2011 118* 119*> \ingroup double_lin 120* 121* ===================================================================== 122 SUBROUTINE DPPT02( UPLO, N, NRHS, A, X, LDX, B, LDB, RWORK, 123 $ RESID ) 124* 125* -- LAPACK test routine (version 3.4.0) -- 126* -- LAPACK is a software package provided by Univ. of Tennessee, -- 127* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 128* November 2011 129* 130* .. Scalar Arguments .. 131 CHARACTER UPLO 132 INTEGER LDB, LDX, N, NRHS 133 DOUBLE PRECISION RESID 134* .. 135* .. Array Arguments .. 136 DOUBLE PRECISION A( * ), B( LDB, * ), RWORK( * ), X( LDX, * ) 137* .. 138* 139* ===================================================================== 140* 141* .. Parameters .. 142 DOUBLE PRECISION ZERO, ONE 143 PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) 144* .. 145* .. Local Scalars .. 146 INTEGER J 147 DOUBLE PRECISION ANORM, BNORM, EPS, XNORM 148* .. 149* .. External Functions .. 150 DOUBLE PRECISION DASUM, DLAMCH, DLANSP 151 EXTERNAL DASUM, DLAMCH, DLANSP 152* .. 153* .. External Subroutines .. 154 EXTERNAL DSPMV 155* .. 156* .. Intrinsic Functions .. 157 INTRINSIC MAX 158* .. 159* .. Executable Statements .. 160* 161* Quick exit if N = 0 or NRHS = 0. 162* 163 IF( N.LE.0 .OR. NRHS.LE.0 ) THEN 164 RESID = ZERO 165 RETURN 166 END IF 167* 168* Exit with RESID = 1/EPS if ANORM = 0. 169* 170 EPS = DLAMCH( 'Epsilon' ) 171 ANORM = DLANSP( '1', UPLO, N, A, RWORK ) 172 IF( ANORM.LE.ZERO ) THEN 173 RESID = ONE / EPS 174 RETURN 175 END IF 176* 177* Compute B - A*X for the matrix of right hand sides B. 178* 179 DO 10 J = 1, NRHS 180 CALL DSPMV( UPLO, N, -ONE, A, X( 1, J ), 1, ONE, B( 1, J ), 1 ) 181 10 CONTINUE 182* 183* Compute the maximum over the number of right hand sides of 184* norm( B - A*X ) / ( norm(A) * norm(X) * EPS ) . 185* 186 RESID = ZERO 187 DO 20 J = 1, NRHS 188 BNORM = DASUM( N, B( 1, J ), 1 ) 189 XNORM = DASUM( N, X( 1, J ), 1 ) 190 IF( XNORM.LE.ZERO ) THEN 191 RESID = ONE / EPS 192 ELSE 193 RESID = MAX( RESID, ( ( BNORM / ANORM ) / XNORM ) / EPS ) 194 END IF 195 20 CONTINUE 196* 197 RETURN 198* 199* End of DPPT02 200* 201 END 202