LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ cpot01()

 subroutine cpot01 ( character UPLO, integer N, complex, dimension( lda, * ) A, integer LDA, complex, dimension( ldafac, * ) AFAC, integer LDAFAC, real, dimension( * ) RWORK, real RESID )

CPOT01

Purpose:
``` CPOT01 reconstructs a Hermitian positive definite matrix  A  from
its L*L' or U'*U factorization and computes the residual
norm( L*L' - A ) / ( N * norm(A) * EPS ) or
norm( U'*U - A ) / ( N * norm(A) * EPS ),
where EPS is the machine epsilon, L' is the conjugate transpose of L,
and U' is the conjugate transpose of U.```
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] AFAC ``` AFAC is COMPLEX array, dimension (LDAFAC,N) On entry, the factor L or U from the L * L**H or U**H * U factorization of A. Overwritten with the reconstructed matrix, and then with the difference L * L**H - A (or U**H * U - A).``` [in] LDAFAC ``` LDAFAC is INTEGER The leading dimension of the array AFAC. LDAFAC >= max(1,N).``` [out] RWORK ` RWORK is REAL array, dimension (N)` [out] RESID ``` RESID is REAL If UPLO = 'L', norm(L * L**H - A) / ( N * norm(A) * EPS ) If UPLO = 'U', norm(U**H * U - A) / ( N * norm(A) * EPS )```

Definition at line 105 of file cpot01.f.

106*
107* -- LAPACK test routine --
108* -- LAPACK is a software package provided by Univ. of Tennessee, --
109* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
110*
111* .. Scalar Arguments ..
112 CHARACTER UPLO
113 INTEGER LDA, LDAFAC, N
114 REAL RESID
115* ..
116* .. Array Arguments ..
117 REAL RWORK( * )
118 COMPLEX A( LDA, * ), AFAC( LDAFAC, * )
119* ..
120*
121* =====================================================================
122*
123* .. Parameters ..
124 REAL ZERO, ONE
125 parameter( zero = 0.0e+0, one = 1.0e+0 )
126* ..
127* .. Local Scalars ..
128 INTEGER I, J, K
129 REAL ANORM, EPS, TR
130 COMPLEX TC
131* ..
132* .. External Functions ..
133 LOGICAL LSAME
134 REAL CLANHE, SLAMCH
135 COMPLEX CDOTC
136 EXTERNAL lsame, clanhe, slamch, cdotc
137* ..
138* .. External Subroutines ..
139 EXTERNAL cher, cscal, ctrmv
140* ..
141* .. Intrinsic Functions ..
142 INTRINSIC aimag, real
143* ..
144* .. Executable Statements ..
145*
146* Quick exit if N = 0.
147*
148 IF( n.LE.0 ) THEN
149 resid = zero
150 RETURN
151 END IF
152*
153* Exit with RESID = 1/EPS if ANORM = 0.
154*
155 eps = slamch( 'Epsilon' )
156 anorm = clanhe( '1', uplo, n, a, lda, rwork )
157 IF( anorm.LE.zero ) THEN
158 resid = one / eps
159 RETURN
160 END IF
161*
162* Check the imaginary parts of the diagonal elements and return with
163* an error code if any are nonzero.
164*
165 DO 10 j = 1, n
166 IF( aimag( afac( j, j ) ).NE.zero ) THEN
167 resid = one / eps
168 RETURN
169 END IF
170 10 CONTINUE
171*
172* Compute the product U**H * U, overwriting U.
173*
174 IF( lsame( uplo, 'U' ) ) THEN
175 DO 20 k = n, 1, -1
176*
177* Compute the (K,K) element of the result.
178*
179 tr = real( cdotc( k, afac( 1, k ), 1, afac( 1, k ), 1 ) )
180 afac( k, k ) = tr
181*
182* Compute the rest of column K.
183*
184 CALL ctrmv( 'Upper', 'Conjugate', 'Non-unit', k-1, afac,
185 \$ ldafac, afac( 1, k ), 1 )
186*
187 20 CONTINUE
188*
189* Compute the product L * L**H, overwriting L.
190*
191 ELSE
192 DO 30 k = n, 1, -1
193*
194* Add a multiple of column K of the factor L to each of
195* columns K+1 through N.
196*
197 IF( k+1.LE.n )
198 \$ CALL cher( 'Lower', n-k, one, afac( k+1, k ), 1,
199 \$ afac( k+1, k+1 ), ldafac )
200*
201* Scale column K by the diagonal element.
202*
203 tc = afac( k, k )
204 CALL cscal( n-k+1, tc, afac( k, k ), 1 )
205*
206 30 CONTINUE
207 END IF
208*
209* Compute the difference L * L**H - A (or U**H * U - A).
210*
211 IF( lsame( uplo, 'U' ) ) THEN
212 DO 50 j = 1, n
213 DO 40 i = 1, j - 1
214 afac( i, j ) = afac( i, j ) - a( i, j )
215 40 CONTINUE
216 afac( j, j ) = afac( j, j ) - real( a( j, j ) )
217 50 CONTINUE
218 ELSE
219 DO 70 j = 1, n
220 afac( j, j ) = afac( j, j ) - real( a( j, j ) )
221 DO 60 i = j + 1, n
222 afac( i, j ) = afac( i, j ) - a( i, j )
223 60 CONTINUE
224 70 CONTINUE
225 END IF
226*
227* Compute norm(L*U - A) / ( N * norm(A) * EPS )
228*
229 resid = clanhe( '1', uplo, n, afac, ldafac, rwork )
230*
231 resid = ( ( resid / real( n ) ) / anorm ) / eps
232*
233 RETURN
234*
235* End of CPOT01
236*
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
complex function cdotc(N, CX, INCX, CY, INCY)
CDOTC
Definition: cdotc.f:83
subroutine cscal(N, CA, CX, INCX)
CSCAL
Definition: cscal.f:78
subroutine ctrmv(UPLO, TRANS, DIAG, N, A, LDA, X, INCX)
CTRMV
Definition: ctrmv.f:147
subroutine cher(UPLO, N, ALPHA, X, INCX, A, LDA)
CHER
Definition: cher.f:135
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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