1*> \brief \b SGET03 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 SGET03( N, A, LDA, AINV, LDAINV, WORK, LDWORK, RWORK, 12* RCOND, RESID ) 13* 14* .. Scalar Arguments .. 15* INTEGER LDA, LDAINV, LDWORK, N 16* REAL RCOND, RESID 17* .. 18* .. Array Arguments .. 19* REAL A( LDA, * ), AINV( LDAINV, * ), RWORK( * ), 20* $ WORK( LDWORK, * ) 21* .. 22* 23* 24*> \par Purpose: 25* ============= 26*> 27*> \verbatim 28*> 29*> SGET03 computes the residual for a general matrix times its inverse: 30*> norm( I - AINV*A ) / ( N * norm(A) * norm(AINV) * EPS ), 31*> where EPS is the machine epsilon. 32*> \endverbatim 33* 34* Arguments: 35* ========== 36* 37*> \param[in] N 38*> \verbatim 39*> N is INTEGER 40*> The number of rows and columns of the matrix A. N >= 0. 41*> \endverbatim 42*> 43*> \param[in] A 44*> \verbatim 45*> A is REAL array, dimension (LDA,N) 46*> The original N x N matrix A. 47*> \endverbatim 48*> 49*> \param[in] LDA 50*> \verbatim 51*> LDA is INTEGER 52*> The leading dimension of the array A. LDA >= max(1,N). 53*> \endverbatim 54*> 55*> \param[in] AINV 56*> \verbatim 57*> AINV is REAL array, dimension (LDAINV,N) 58*> The inverse of the matrix A. 59*> \endverbatim 60*> 61*> \param[in] LDAINV 62*> \verbatim 63*> LDAINV is INTEGER 64*> The leading dimension of the array AINV. LDAINV >= max(1,N). 65*> \endverbatim 66*> 67*> \param[out] WORK 68*> \verbatim 69*> WORK is REAL array, dimension (LDWORK,N) 70*> \endverbatim 71*> 72*> \param[in] LDWORK 73*> \verbatim 74*> LDWORK is INTEGER 75*> The leading dimension of the array WORK. LDWORK >= max(1,N). 76*> \endverbatim 77*> 78*> \param[out] RWORK 79*> \verbatim 80*> RWORK is REAL array, dimension (N) 81*> \endverbatim 82*> 83*> \param[out] RCOND 84*> \verbatim 85*> RCOND is REAL 86*> The reciprocal of the condition number of A, computed as 87*> ( 1/norm(A) ) / norm(AINV). 88*> \endverbatim 89*> 90*> \param[out] RESID 91*> \verbatim 92*> RESID is REAL 93*> norm(I - AINV*A) / ( N * norm(A) * norm(AINV) * EPS ) 94*> \endverbatim 95* 96* Authors: 97* ======== 98* 99*> \author Univ. of Tennessee 100*> \author Univ. of California Berkeley 101*> \author Univ. of Colorado Denver 102*> \author NAG Ltd. 103* 104*> \date November 2011 105* 106*> \ingroup single_lin 107* 108* ===================================================================== 109 SUBROUTINE SGET03( N, A, LDA, AINV, LDAINV, WORK, LDWORK, RWORK, 110 $ RCOND, RESID ) 111* 112* -- LAPACK test routine (version 3.4.0) -- 113* -- LAPACK is a software package provided by Univ. of Tennessee, -- 114* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 115* November 2011 116* 117* .. Scalar Arguments .. 118 INTEGER LDA, LDAINV, LDWORK, N 119 REAL RCOND, RESID 120* .. 121* .. Array Arguments .. 122 REAL A( LDA, * ), AINV( LDAINV, * ), RWORK( * ), 123 $ WORK( LDWORK, * ) 124* .. 125* 126* ===================================================================== 127* 128* .. Parameters .. 129 REAL ZERO, ONE 130 PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 ) 131* .. 132* .. Local Scalars .. 133 INTEGER I 134 REAL AINVNM, ANORM, EPS 135* .. 136* .. External Functions .. 137 REAL SLAMCH, SLANGE 138 EXTERNAL SLAMCH, SLANGE 139* .. 140* .. External Subroutines .. 141 EXTERNAL SGEMM 142* .. 143* .. Intrinsic Functions .. 144 INTRINSIC REAL 145* .. 146* .. Executable Statements .. 147* 148* Quick exit if N = 0. 149* 150 IF( N.LE.0 ) THEN 151 RCOND = ONE 152 RESID = ZERO 153 RETURN 154 END IF 155* 156* Exit with RESID = 1/EPS if ANORM = 0 or AINVNM = 0. 157* 158 EPS = SLAMCH( 'Epsilon' ) 159 ANORM = SLANGE( '1', N, N, A, LDA, RWORK ) 160 AINVNM = SLANGE( '1', N, N, AINV, LDAINV, RWORK ) 161 IF( ANORM.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN 162 RCOND = ZERO 163 RESID = ONE / EPS 164 RETURN 165 END IF 166 RCOND = ( ONE / ANORM ) / AINVNM 167* 168* Compute I - A * AINV 169* 170 CALL SGEMM( 'No transpose', 'No transpose', N, N, N, -ONE, 171 $ AINV, LDAINV, A, LDA, ZERO, WORK, LDWORK ) 172 DO 10 I = 1, N 173 WORK( I, I ) = ONE + WORK( I, I ) 174 10 CONTINUE 175* 176* Compute norm(I - AINV*A) / (N * norm(A) * norm(AINV) * EPS) 177* 178 RESID = SLANGE( '1', N, N, WORK, LDWORK, RWORK ) 179* 180 RESID = ( ( RESID*RCOND ) / EPS ) / REAL( N ) 181* 182 RETURN 183* 184* End of SGET03 185* 186 END 187