LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ cpot03()

 subroutine cpot03 ( character UPLO, 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 )

CPOT03

Purpose:
``` CPOT03 computes the residual for a Hermitian matrix times its
inverse:
norm( I - A*AINV ) / ( N * norm(A) * norm(AINV) * EPS ),
where EPS is the machine epsilon.```
Parameters
 [in] UPLO ``` UPLO is CHARACTER*1 Specifies whether the upper or lower triangular part of the Hermitian matrix A is stored: = 'U': Upper triangular = 'L': Lower triangular``` [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 Hermitian matrix A.``` [in] LDA ``` LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N)``` [in,out] AINV ``` AINV is COMPLEX array, dimension (LDAINV,N) On entry, the inverse of the matrix A, stored as a Hermitian matrix in the same format as A. In this version, AINV is expanded into a full matrix and multiplied by A, so the opposing triangle of AINV will be changed; i.e., if the upper triangular part of AINV is stored, the lower triangular part will be used as work space.``` [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 - A*AINV) / ( N * norm(A) * norm(AINV) * EPS )```

Definition at line 124 of file cpot03.f.

126*
127* -- LAPACK test routine --
128* -- LAPACK is a software package provided by Univ. of Tennessee, --
129* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
130*
131* .. Scalar Arguments ..
132 CHARACTER UPLO
133 INTEGER LDA, LDAINV, LDWORK, N
134 REAL RCOND, RESID
135* ..
136* .. Array Arguments ..
137 REAL RWORK( * )
138 COMPLEX A( LDA, * ), AINV( LDAINV, * ),
139 \$ WORK( LDWORK, * )
140* ..
141*
142* =====================================================================
143*
144* .. Parameters ..
145 REAL ZERO, ONE
146 parameter( zero = 0.0e+0, one = 1.0e+0 )
147 COMPLEX CZERO, CONE
148 parameter( czero = ( 0.0e+0, 0.0e+0 ),
149 \$ cone = ( 1.0e+0, 0.0e+0 ) )
150* ..
151* .. Local Scalars ..
152 INTEGER I, J
153 REAL AINVNM, ANORM, EPS
154* ..
155* .. External Functions ..
156 LOGICAL LSAME
157 REAL CLANGE, CLANHE, SLAMCH
158 EXTERNAL lsame, clange, clanhe, slamch
159* ..
160* .. External Subroutines ..
161 EXTERNAL chemm
162* ..
163* .. Intrinsic Functions ..
164 INTRINSIC conjg, real
165* ..
166* .. Executable Statements ..
167*
168* Quick exit if N = 0.
169*
170 IF( n.LE.0 ) THEN
171 rcond = one
172 resid = zero
173 RETURN
174 END IF
175*
176* Exit with RESID = 1/EPS if ANORM = 0 or AINVNM = 0.
177*
178 eps = slamch( 'Epsilon' )
179 anorm = clanhe( '1', uplo, n, a, lda, rwork )
180 ainvnm = clanhe( '1', uplo, n, ainv, ldainv, rwork )
181 IF( anorm.LE.zero .OR. ainvnm.LE.zero ) THEN
182 rcond = zero
183 resid = one / eps
184 RETURN
185 END IF
186 rcond = ( one/anorm ) / ainvnm
187*
188* Expand AINV into a full matrix and call CHEMM to multiply
189* AINV on the left by A.
190*
191 IF( lsame( uplo, 'U' ) ) THEN
192 DO 20 j = 1, n
193 DO 10 i = 1, j - 1
194 ainv( j, i ) = conjg( ainv( i, j ) )
195 10 CONTINUE
196 20 CONTINUE
197 ELSE
198 DO 40 j = 1, n
199 DO 30 i = j + 1, n
200 ainv( j, i ) = conjg( ainv( i, j ) )
201 30 CONTINUE
202 40 CONTINUE
203 END IF
204 CALL chemm( 'Left', uplo, n, n, -cone, a, lda, ainv, ldainv,
205 \$ czero, work, ldwork )
206*
207* Add the identity matrix to WORK .
208*
209 DO 50 i = 1, n
210 work( i, i ) = work( i, i ) + cone
211 50 CONTINUE
212*
213* Compute norm(I - A*AINV) / (N * norm(A) * norm(AINV) * EPS)
214*
215 resid = clange( '1', n, n, work, ldwork, rwork )
216*
217 resid = ( ( resid*rcond )/eps ) / real( n )
218*
219 RETURN
220*
221* End of CPOT03
222*
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine chemm(SIDE, UPLO, M, N, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
CHEMM
Definition: chemm.f:191
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 clanhe(NORM, UPLO, N, A, LDA, WORK)
CLANHE returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: clanhe.f:124
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
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