LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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zhet01.f
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1*> \brief \b ZHET01
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 ZHET01( UPLO, N, A, LDA, AFAC, LDAFAC, IPIV, C, LDC,
12* RWORK, RESID )
13*
14* .. Scalar Arguments ..
15* CHARACTER UPLO
16* INTEGER LDA, LDAFAC, LDC, N
17* DOUBLE PRECISION RESID
18* ..
19* .. Array Arguments ..
20* INTEGER IPIV( * )
21* DOUBLE PRECISION RWORK( * )
22* COMPLEX*16 A( LDA, * ), AFAC( LDAFAC, * ), C( LDC, * )
23* ..
24*
25*
26*> \par Purpose:
27* =============
28*>
29*> \verbatim
30*>
31*> ZHET01 reconstructs a Hermitian indefinite matrix A from its
32*> block L*D*L' or U*D*U' factorization and computes the residual
33*> norm( C - A ) / ( N * norm(A) * EPS ),
34*> where C is the reconstructed matrix, EPS is the machine epsilon,
35*> L' is the conjugate transpose of L, and U' is the conjugate transpose
36*> of U.
37*> \endverbatim
38*
39* Arguments:
40* ==========
41*
42*> \param[in] UPLO
43*> \verbatim
44*> UPLO is CHARACTER*1
45*> Specifies whether the upper or lower triangular part of the
46*> Hermitian matrix A is stored:
47*> = 'U': Upper triangular
48*> = 'L': Lower triangular
49*> \endverbatim
50*>
51*> \param[in] N
52*> \verbatim
53*> N is INTEGER
54*> The number of rows and columns of the matrix A. N >= 0.
55*> \endverbatim
56*>
57*> \param[in] A
58*> \verbatim
59*> A is COMPLEX*16 array, dimension (LDA,N)
60*> The original Hermitian matrix A.
61*> \endverbatim
62*>
63*> \param[in] LDA
64*> \verbatim
65*> LDA is INTEGER
66*> The leading dimension of the array A. LDA >= max(1,N)
67*> \endverbatim
68*>
69*> \param[in] AFAC
70*> \verbatim
71*> AFAC is COMPLEX*16 array, dimension (LDAFAC,N)
72*> The factored form of the matrix A. AFAC contains the block
73*> diagonal matrix D and the multipliers used to obtain the
74*> factor L or U from the block L*D*L' or U*D*U' factorization
75*> as computed by ZHETRF.
76*> \endverbatim
77*>
78*> \param[in] LDAFAC
79*> \verbatim
80*> LDAFAC is INTEGER
81*> The leading dimension of the array AFAC. LDAFAC >= max(1,N).
82*> \endverbatim
83*>
84*> \param[in] IPIV
85*> \verbatim
86*> IPIV is INTEGER array, dimension (N)
87*> The pivot indices from ZHETRF.
88*> \endverbatim
89*>
90*> \param[out] C
91*> \verbatim
92*> C is COMPLEX*16 array, dimension (LDC,N)
93*> \endverbatim
94*>
95*> \param[in] LDC
96*> \verbatim
97*> LDC is INTEGER
98*> The leading dimension of the array C. LDC >= max(1,N).
99*> \endverbatim
100*>
101*> \param[out] RWORK
102*> \verbatim
103*> RWORK is DOUBLE PRECISION array, dimension (N)
104*> \endverbatim
105*>
106*> \param[out] RESID
107*> \verbatim
108*> RESID is DOUBLE PRECISION
109*> If UPLO = 'L', norm(L*D*L' - A) / ( N * norm(A) * EPS )
110*> If UPLO = 'U', norm(U*D*U' - A) / ( N * norm(A) * EPS )
111*> \endverbatim
112*
113* Authors:
114* ========
115*
116*> \author Univ. of Tennessee
117*> \author Univ. of California Berkeley
118*> \author Univ. of Colorado Denver
119*> \author NAG Ltd.
120*
121*> \ingroup complex16_lin
122*
123* =====================================================================
124 SUBROUTINE zhet01( UPLO, N, A, LDA, AFAC, LDAFAC, IPIV, C, LDC,
125 \$ RWORK, RESID )
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, LDAFAC, LDC, N
134 DOUBLE PRECISION RESID
135* ..
136* .. Array Arguments ..
137 INTEGER IPIV( * )
138 DOUBLE PRECISION RWORK( * )
139 COMPLEX*16 A( LDA, * ), AFAC( LDAFAC, * ), C( LDC, * )
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, INFO, J
153 DOUBLE PRECISION ANORM, EPS
154* ..
155* .. External Functions ..
156 LOGICAL LSAME
157 DOUBLE PRECISION DLAMCH, ZLANHE
158 EXTERNAL lsame, dlamch, zlanhe
159* ..
160* .. External Subroutines ..
161 EXTERNAL zlaset, zlavhe
162* ..
163* .. Intrinsic Functions ..
164 INTRINSIC dble, dimag
165* ..
166* .. Executable Statements ..
167*
168* Quick exit if N = 0.
169*
170 IF( n.LE.0 ) THEN
171 resid = zero
172 RETURN
173 END IF
174*
175* Determine EPS and the norm of A.
176*
177 eps = dlamch( 'Epsilon' )
178 anorm = zlanhe( '1', uplo, n, a, lda, rwork )
179*
180* Check the imaginary parts of the diagonal elements and return with
181* an error code if any are nonzero.
182*
183 DO 10 j = 1, n
184 IF( dimag( afac( j, j ) ).NE.zero ) THEN
185 resid = one / eps
186 RETURN
187 END IF
188 10 CONTINUE
189*
190* Initialize C to the identity matrix.
191*
192 CALL zlaset( 'Full', n, n, czero, cone, c, ldc )
193*
194* Call ZLAVHE to form the product D * U' (or D * L' ).
195*
196 CALL zlavhe( uplo, 'Conjugate', 'Non-unit', n, n, afac, ldafac,
197 \$ ipiv, c, ldc, info )
198*
199* Call ZLAVHE again to multiply by U (or L ).
200*
201 CALL zlavhe( uplo, 'No transpose', 'Unit', n, n, afac, ldafac,
202 \$ ipiv, c, ldc, info )
203*
204* Compute the difference C - A .
205*
206 IF( lsame( uplo, 'U' ) ) THEN
207 DO 30 j = 1, n
208 DO 20 i = 1, j - 1
209 c( i, j ) = c( i, j ) - a( i, j )
210 20 CONTINUE
211 c( j, j ) = c( j, j ) - dble( a( j, j ) )
212 30 CONTINUE
213 ELSE
214 DO 50 j = 1, n
215 c( j, j ) = c( j, j ) - dble( a( j, j ) )
216 DO 40 i = j + 1, n
217 c( i, j ) = c( i, j ) - a( i, j )
218 40 CONTINUE
219 50 CONTINUE
220 END IF
221*
222* Compute norm( C - A ) / ( N * norm(A) * EPS )
223*
224 resid = zlanhe( '1', uplo, n, c, ldc, rwork )
225*
226 IF( anorm.LE.zero ) THEN
227 IF( resid.NE.zero )
228 \$ resid = one / eps
229 ELSE
230 resid = ( ( resid / dble( n ) ) / anorm ) / eps
231 END IF
232*
233 RETURN
234*
235* End of ZHET01
236*
237 END
subroutine zlaset(uplo, m, n, alpha, beta, a, lda)
ZLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
Definition zlaset.f:106
subroutine zhet01(uplo, n, a, lda, afac, ldafac, ipiv, c, ldc, rwork, resid)
ZHET01
Definition zhet01.f:126
subroutine zlavhe(uplo, trans, diag, n, nrhs, a, lda, ipiv, b, ldb, info)
ZLAVHE
Definition zlavhe.f:153