LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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## ◆ zpot03()

 subroutine zpot03 ( character uplo, integer n, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( ldainv, * ) ainv, integer ldainv, complex*16, dimension( ldwork, * ) work, integer ldwork, double precision, dimension( * ) rwork, double precision rcond, double precision resid )

ZPOT03

Purpose:
``` ZPOT03 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*16 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*16 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*16 array, dimension (LDWORK,N)` [in] LDWORK ``` LDWORK is INTEGER The leading dimension of the array WORK. LDWORK >= max(1,N).``` [out] RWORK ` RWORK is DOUBLE PRECISION array, dimension (N)` [out] RCOND ``` RCOND is DOUBLE PRECISION The reciprocal of the condition number of A, computed as ( 1/norm(A) ) / norm(AINV).``` [out] RESID ``` RESID is DOUBLE PRECISION norm(I - A*AINV) / ( N * norm(A) * norm(AINV) * EPS )```

Definition at line 124 of file zpot03.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 DOUBLE PRECISION RCOND, RESID
135* ..
136* .. Array Arguments ..
137 DOUBLE PRECISION RWORK( * )
138 COMPLEX*16 A( LDA, * ), AINV( LDAINV, * ),
139 \$ WORK( LDWORK, * )
140* ..
141*
142* =====================================================================
143*
144* .. Parameters ..
145 DOUBLE PRECISION ZERO, ONE
146 parameter( zero = 0.0d+0, one = 1.0d+0 )
147 COMPLEX*16 CZERO, CONE
148 parameter( czero = ( 0.0d+0, 0.0d+0 ),
149 \$ cone = ( 1.0d+0, 0.0d+0 ) )
150* ..
151* .. Local Scalars ..
152 INTEGER I, J
153 DOUBLE PRECISION AINVNM, ANORM, EPS
154* ..
155* .. External Functions ..
156 LOGICAL LSAME
157 DOUBLE PRECISION DLAMCH, ZLANGE, ZLANHE
158 EXTERNAL lsame, dlamch, zlange, zlanhe
159* ..
160* .. External Subroutines ..
161 EXTERNAL zhemm
162* ..
163* .. Intrinsic Functions ..
164 INTRINSIC dble, dconjg
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 = dlamch( 'Epsilon' )
179 anorm = zlanhe( '1', uplo, n, a, lda, rwork )
180 ainvnm = zlanhe( '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 ZHEMM 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 ) = dconjg( 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 ) = dconjg( ainv( i, j ) )
201 30 CONTINUE
202 40 CONTINUE
203 END IF
204 CALL zhemm( '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 = zlange( '1', n, n, work, ldwork, rwork )
216*
217 resid = ( ( resid*rcond ) / eps ) / dble( n )
218*
219 RETURN
220*
221* End of ZPOT03
222*
subroutine zhemm(side, uplo, m, n, alpha, a, lda, b, ldb, beta, c, ldc)
ZHEMM
Definition zhemm.f:191
double precision function dlamch(cmach)
DLAMCH
Definition dlamch.f:69
double precision function zlange(norm, m, n, a, lda, work)
ZLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition zlange.f:115
double precision function zlanhe(norm, uplo, n, a, lda, work)
ZLANHE returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition zlanhe.f:124
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
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