1*> \brief \b SPOT02 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 SPOT02( UPLO, N, NRHS, A, LDA, X, LDX, B, LDB, RWORK, 12* RESID ) 13* 14* .. Scalar Arguments .. 15* CHARACTER UPLO 16* INTEGER LDA, LDB, LDX, N, NRHS 17* REAL RESID 18* .. 19* .. Array Arguments .. 20* REAL A( LDA, * ), B( LDB, * ), RWORK( * ), 21* $ X( LDX, * ) 22* .. 23* 24* 25*> \par Purpose: 26* ============= 27*> 28*> \verbatim 29*> 30*> SPOT02 computes the residual for the solution of a symmetric system 31*> of linear equations A*x = b: 32*> 33*> RESID = norm(B - A*X) / ( norm(A) * norm(X) * EPS ), 34*> 35*> where EPS is the machine epsilon. 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 REAL array, dimension (LDA,N) 66*> The original symmetric matrix A. 67*> \endverbatim 68*> 69*> \param[in] LDA 70*> \verbatim 71*> LDA is INTEGER 72*> The leading dimension of the array A. LDA >= max(1,N) 73*> \endverbatim 74*> 75*> \param[in] X 76*> \verbatim 77*> X is REAL array, dimension (LDX,NRHS) 78*> The computed solution vectors for the system of linear 79*> equations. 80*> \endverbatim 81*> 82*> \param[in] LDX 83*> \verbatim 84*> LDX is INTEGER 85*> The leading dimension of the array X. LDX >= max(1,N). 86*> \endverbatim 87*> 88*> \param[in,out] B 89*> \verbatim 90*> B is REAL array, dimension (LDB,NRHS) 91*> On entry, the right hand side vectors for the system of 92*> linear equations. 93*> On exit, B is overwritten with the difference B - A*X. 94*> \endverbatim 95*> 96*> \param[in] LDB 97*> \verbatim 98*> LDB is INTEGER 99*> The leading dimension of the array B. LDB >= max(1,N). 100*> \endverbatim 101*> 102*> \param[out] RWORK 103*> \verbatim 104*> RWORK is REAL array, dimension (N) 105*> \endverbatim 106*> 107*> \param[out] RESID 108*> \verbatim 109*> RESID is REAL 110*> The maximum over the number of right hand sides of 111*> norm(B - A*X) / ( norm(A) * norm(X) * EPS ). 112*> \endverbatim 113* 114* Authors: 115* ======== 116* 117*> \author Univ. of Tennessee 118*> \author Univ. of California Berkeley 119*> \author Univ. of Colorado Denver 120*> \author NAG Ltd. 121* 122*> \date November 2011 123* 124*> \ingroup single_lin 125* 126* ===================================================================== 127 SUBROUTINE SPOT02( UPLO, N, NRHS, A, LDA, X, LDX, B, LDB, RWORK, 128 $ RESID ) 129* 130* -- LAPACK test routine (version 3.4.0) -- 131* -- LAPACK is a software package provided by Univ. of Tennessee, -- 132* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 133* November 2011 134* 135* .. Scalar Arguments .. 136 CHARACTER UPLO 137 INTEGER LDA, LDB, LDX, N, NRHS 138 REAL RESID 139* .. 140* .. Array Arguments .. 141 REAL A( LDA, * ), B( LDB, * ), RWORK( * ), 142 $ X( LDX, * ) 143* .. 144* 145* ===================================================================== 146* 147* .. Parameters .. 148 REAL ZERO, ONE 149 PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 ) 150* .. 151* .. Local Scalars .. 152 INTEGER J 153 REAL ANORM, BNORM, EPS, XNORM 154* .. 155* .. External Functions .. 156 REAL SASUM, SLAMCH, SLANSY 157 EXTERNAL SASUM, SLAMCH, SLANSY 158* .. 159* .. External Subroutines .. 160 EXTERNAL SSYMM 161* .. 162* .. Intrinsic Functions .. 163 INTRINSIC MAX 164* .. 165* .. Executable Statements .. 166* 167* Quick exit if N = 0 or NRHS = 0. 168* 169 IF( N.LE.0 .OR. NRHS.LE.0 ) THEN 170 RESID = ZERO 171 RETURN 172 END IF 173* 174* Exit with RESID = 1/EPS if ANORM = 0. 175* 176 EPS = SLAMCH( 'Epsilon' ) 177 ANORM = SLANSY( '1', UPLO, N, A, LDA, RWORK ) 178 IF( ANORM.LE.ZERO ) THEN 179 RESID = ONE / EPS 180 RETURN 181 END IF 182* 183* Compute B - A*X 184* 185 CALL SSYMM( 'Left', UPLO, N, NRHS, -ONE, A, LDA, X, LDX, ONE, B, 186 $ LDB ) 187* 188* Compute the maximum over the number of right hand sides of 189* norm( B - A*X ) / ( norm(A) * norm(X) * EPS ) . 190* 191 RESID = ZERO 192 DO 10 J = 1, NRHS 193 BNORM = SASUM( N, B( 1, J ), 1 ) 194 XNORM = SASUM( N, X( 1, J ), 1 ) 195 IF( XNORM.LE.ZERO ) THEN 196 RESID = ONE / EPS 197 ELSE 198 RESID = MAX( RESID, ( ( BNORM / ANORM ) / XNORM ) / EPS ) 199 END IF 200 10 CONTINUE 201* 202 RETURN 203* 204* End of SPOT02 205* 206 END 207