 LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ 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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