 LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ sget03()

 subroutine sget03 ( integer N, real, dimension( lda, * ) A, integer LDA, real, dimension( ldainv, * ) AINV, integer LDAINV, real, dimension( ldwork, * ) WORK, integer LDWORK, real, dimension( * ) RWORK, real RCOND, real RESID )

SGET03

Purpose:
``` SGET03 computes the residual for a general matrix times its inverse:
norm( I - AINV*A ) / ( N * norm(A) * norm(AINV) * EPS ),
where EPS is the machine epsilon.```
Parameters
 [in] N ``` N is INTEGER The number of rows and columns of the matrix A. N >= 0.``` [in] A ``` A is REAL array, dimension (LDA,N) The original N x N matrix A.``` [in] LDA ``` LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).``` [in] AINV ``` AINV is REAL array, dimension (LDAINV,N) The inverse of the matrix A.``` [in] LDAINV ``` LDAINV is INTEGER The leading dimension of the array AINV. LDAINV >= max(1,N).``` [out] WORK ` WORK is REAL array, dimension (LDWORK,N)` [in] LDWORK ``` LDWORK is INTEGER The leading dimension of the array WORK. LDWORK >= max(1,N).``` [out] RWORK ` RWORK is REAL array, dimension (N)` [out] RCOND ``` RCOND is REAL The reciprocal of the condition number of A, computed as ( 1/norm(A) ) / norm(AINV).``` [out] RESID ``` RESID is REAL norm(I - AINV*A) / ( N * norm(A) * norm(AINV) * EPS )```

Definition at line 107 of file sget03.f.

109*
110* -- LAPACK test routine --
111* -- LAPACK is a software package provided by Univ. of Tennessee, --
112* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
113*
114* .. Scalar Arguments ..
115 INTEGER LDA, LDAINV, LDWORK, N
116 REAL RCOND, RESID
117* ..
118* .. Array Arguments ..
119 REAL A( LDA, * ), AINV( LDAINV, * ), RWORK( * ),
120 \$ WORK( LDWORK, * )
121* ..
122*
123* =====================================================================
124*
125* .. Parameters ..
126 REAL ZERO, ONE
127 parameter( zero = 0.0e+0, one = 1.0e+0 )
128* ..
129* .. Local Scalars ..
130 INTEGER I
131 REAL AINVNM, ANORM, EPS
132* ..
133* .. External Functions ..
134 REAL SLAMCH, SLANGE
135 EXTERNAL slamch, slange
136* ..
137* .. External Subroutines ..
138 EXTERNAL sgemm
139* ..
140* .. Intrinsic Functions ..
141 INTRINSIC real
142* ..
143* .. Executable Statements ..
144*
145* Quick exit if N = 0.
146*
147 IF( n.LE.0 ) THEN
148 rcond = one
149 resid = zero
150 RETURN
151 END IF
152*
153* Exit with RESID = 1/EPS if ANORM = 0 or AINVNM = 0.
154*
155 eps = slamch( 'Epsilon' )
156 anorm = slange( '1', n, n, a, lda, rwork )
157 ainvnm = slange( '1', n, n, ainv, ldainv, rwork )
158 IF( anorm.LE.zero .OR. ainvnm.LE.zero ) THEN
159 rcond = zero
160 resid = one / eps
161 RETURN
162 END IF
163 rcond = ( one / anorm ) / ainvnm
164*
165* Compute I - A * AINV
166*
167 CALL sgemm( 'No transpose', 'No transpose', n, n, n, -one,
168 \$ ainv, ldainv, a, lda, zero, work, ldwork )
169 DO 10 i = 1, n
170 work( i, i ) = one + work( i, i )
171 10 CONTINUE
172*
173* Compute norm(I - AINV*A) / (N * norm(A) * norm(AINV) * EPS)
174*
175 resid = slange( '1', n, n, work, ldwork, rwork )
176*
177 resid = ( ( resid*rcond ) / eps ) / real( n )
178*
179 RETURN
180*
181* End of SGET03
182*
real function slange(NORM, M, N, A, LDA, WORK)
SLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition: slange.f:114
subroutine sgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
SGEMM
Definition: sgemm.f:187
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
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