 LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ cget03()

 subroutine cget03 ( integer N, complex, dimension( lda, * ) A, integer LDA, complex, dimension( ldainv, * ) AINV, integer LDAINV, complex, dimension( ldwork, * ) WORK, integer LDWORK, real, dimension( * ) RWORK, real RCOND, real RESID )

CGET03

Purpose:
``` CGET03 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 COMPLEX 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 COMPLEX 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 COMPLEX 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 108 of file cget03.f.

110*
111* -- LAPACK test routine --
112* -- LAPACK is a software package provided by Univ. of Tennessee, --
113* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
114*
115* .. Scalar Arguments ..
116 INTEGER LDA, LDAINV, LDWORK, N
117 REAL RCOND, RESID
118* ..
119* .. Array Arguments ..
120 REAL RWORK( * )
121 COMPLEX A( LDA, * ), AINV( LDAINV, * ),
122 \$ WORK( LDWORK, * )
123* ..
124*
125* =====================================================================
126*
127* .. Parameters ..
128 REAL ZERO, ONE
129 parameter( zero = 0.0e+0, one = 1.0e+0 )
130 COMPLEX CZERO, CONE
131 parameter( czero = ( 0.0e+0, 0.0e+0 ),
132 \$ cone = ( 1.0e+0, 0.0e+0 ) )
133* ..
134* .. Local Scalars ..
135 INTEGER I
136 REAL AINVNM, ANORM, EPS
137* ..
138* .. External Functions ..
139 REAL CLANGE, SLAMCH
140 EXTERNAL clange, slamch
141* ..
142* .. External Subroutines ..
143 EXTERNAL cgemm
144* ..
145* .. Intrinsic Functions ..
146 INTRINSIC real
147* ..
148* .. Executable Statements ..
149*
150* Quick exit if N = 0.
151*
152 IF( n.LE.0 ) THEN
153 rcond = one
154 resid = zero
155 RETURN
156 END IF
157*
158* Exit with RESID = 1/EPS if ANORM = 0 or AINVNM = 0.
159*
160 eps = slamch( 'Epsilon' )
161 anorm = clange( '1', n, n, a, lda, rwork )
162 ainvnm = clange( '1', n, n, ainv, ldainv, rwork )
163 IF( anorm.LE.zero .OR. ainvnm.LE.zero ) THEN
164 rcond = zero
165 resid = one / eps
166 RETURN
167 END IF
168 rcond = ( one/anorm ) / ainvnm
169*
170* Compute I - A * AINV
171*
172 CALL cgemm( 'No transpose', 'No transpose', n, n, n, -cone,
173 \$ ainv, ldainv, a, lda, czero, work, ldwork )
174 DO 10 i = 1, n
175 work( i, i ) = cone + work( i, i )
176 10 CONTINUE
177*
178* Compute norm(I - AINV*A) / (N * norm(A) * norm(AINV) * EPS)
179*
180 resid = clange( '1', n, n, work, ldwork, rwork )
181*
182 resid = ( ( resid*rcond )/eps ) / real( n )
183*
184 RETURN
185*
186* End of CGET03
187*
subroutine cgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
CGEMM
Definition: cgemm.f:187
real function clange(NORM, M, N, A, LDA, WORK)
CLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition: clange.f:115
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
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