LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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cpot01.f
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1*> \brief \b CPOT01
2*
3* =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6* http://www.netlib.org/lapack/explore-html/
7*
8* Definition:
9* ===========
10*
11* SUBROUTINE CPOT01( UPLO, N, A, LDA, AFAC, LDAFAC, RWORK, RESID )
12*
13* .. Scalar Arguments ..
14* CHARACTER UPLO
15* INTEGER LDA, LDAFAC, N
16* REAL RESID
17* ..
18* .. Array Arguments ..
19* REAL RWORK( * )
20* COMPLEX A( LDA, * ), AFAC( LDAFAC, * )
21* ..
22*
23*
24*> \par Purpose:
25* =============
26*>
27*> \verbatim
28*>
29*> CPOT01 reconstructs a Hermitian positive definite matrix A from
30*> its L*L' or U'*U factorization and computes the residual
31*> norm( L*L' - A ) / ( N * norm(A) * EPS ) or
32*> norm( U'*U - A ) / ( N * norm(A) * EPS ),
33*> where EPS is the machine epsilon, L' is the conjugate transpose of L,
34*> and U' is the conjugate transpose of U.
35*> \endverbatim
36*
37* Arguments:
38* ==========
39*
40*> \param[in] UPLO
41*> \verbatim
42*> UPLO is CHARACTER*1
43*> Specifies whether the upper or lower triangular part of the
44*> Hermitian matrix A is stored:
45*> = 'U': Upper triangular
46*> = 'L': Lower triangular
47*> \endverbatim
48*>
49*> \param[in] N
50*> \verbatim
51*> N is INTEGER
52*> The number of rows and columns of the matrix A. N >= 0.
53*> \endverbatim
54*>
55*> \param[in] A
56*> \verbatim
57*> A is COMPLEX array, dimension (LDA,N)
58*> The original Hermitian matrix A.
59*> \endverbatim
60*>
61*> \param[in] LDA
62*> \verbatim
63*> LDA is INTEGER
64*> The leading dimension of the array A. LDA >= max(1,N)
65*> \endverbatim
66*>
67*> \param[in,out] AFAC
68*> \verbatim
69*> AFAC is COMPLEX array, dimension (LDAFAC,N)
70*> On entry, the factor L or U from the L * L**H or U**H * U
71*> factorization of A.
72*> Overwritten with the reconstructed matrix, and then with
73*> the difference L * L**H - A (or U**H * U - A).
74*> \endverbatim
75*>
76*> \param[in] LDAFAC
77*> \verbatim
78*> LDAFAC is INTEGER
79*> The leading dimension of the array AFAC. LDAFAC >= max(1,N).
80*> \endverbatim
81*>
82*> \param[out] RWORK
83*> \verbatim
84*> RWORK is REAL array, dimension (N)
85*> \endverbatim
86*>
87*> \param[out] RESID
88*> \verbatim
89*> RESID is REAL
90*> If UPLO = 'L', norm(L * L**H - A) / ( N * norm(A) * EPS )
91*> If UPLO = 'U', norm(U**H * U - A) / ( N * norm(A) * EPS )
92*> \endverbatim
93*
94* Authors:
95* ========
96*
97*> \author Univ. of Tennessee
98*> \author Univ. of California Berkeley
99*> \author Univ. of Colorado Denver
100*> \author NAG Ltd.
101*
102*> \ingroup complex_lin
103*
104* =====================================================================
105 SUBROUTINE cpot01( UPLO, N, A, LDA, AFAC, LDAFAC, RWORK, RESID )
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*
237 END
subroutine cpot01(uplo, n, a, lda, afac, ldafac, rwork, resid)
CPOT01
Definition cpot01.f:106
subroutine cher(uplo, n, alpha, x, incx, a, lda)
CHER
Definition cher.f:135
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