LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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cspt01.f
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1*> \brief \b CSPT01
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 CSPT01( UPLO, N, A, AFAC, IPIV, C, LDC, RWORK, RESID )
12*
13* .. Scalar Arguments ..
14* CHARACTER UPLO
15* INTEGER LDC, N
16* REAL RESID
17* ..
18* .. Array Arguments ..
19* INTEGER IPIV( * )
20* REAL RWORK( * )
21* COMPLEX A( * ), AFAC( * ), C( LDC, * )
22* ..
23*
24*
25*> \par Purpose:
26* =============
27*>
28*> \verbatim
29*>
30*> CSPT01 reconstructs a symmetric indefinite packed matrix A from its
31*> diagonal pivoting factorization A = U*D*U' or A = L*D*L' and computes
32*> the residual
33*> norm( C - A ) / ( N * norm(A) * EPS ),
34*> where C is the reconstructed matrix and EPS is the machine epsilon.
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 order of the matrix A. N >= 0.
53*> \endverbatim
54*>
55*> \param[in] A
56*> \verbatim
57*> A is COMPLEX array, dimension (N*(N+1)/2)
58*> The original symmetric matrix A, stored as a packed
59*> triangular matrix.
60*> \endverbatim
61*>
62*> \param[in] AFAC
63*> \verbatim
64*> AFAC is COMPLEX array, dimension (N*(N+1)/2)
65*> The factored form of the matrix A, stored as a packed
66*> triangular matrix. AFAC contains the block diagonal matrix D
67*> and the multipliers used to obtain the factor L or U from the
68*> L*D*L' or U*D*U' factorization as computed by CSPTRF.
69*> \endverbatim
70*>
71*> \param[in] IPIV
72*> \verbatim
73*> IPIV is INTEGER array, dimension (N)
74*> The pivot indices from CSPTRF.
75*> \endverbatim
76*>
77*> \param[out] C
78*> \verbatim
79*> C is COMPLEX array, dimension (LDC,N)
80*> \endverbatim
81*>
82*> \param[in] LDC
83*> \verbatim
84*> LDC is INTEGER
85*> The leading dimension of the array C. LDC >= max(1,N).
86*> \endverbatim
87*>
88*> \param[out] RWORK
89*> \verbatim
90*> RWORK is REAL array, dimension (N)
91*> \endverbatim
92*>
93*> \param[out] RESID
94*> \verbatim
95*> RESID is REAL
96*> If UPLO = 'L', norm(L*D*L' - A) / ( N * norm(A) * EPS )
97*> If UPLO = 'U', norm(U*D*U' - A) / ( N * norm(A) * EPS )
98*> \endverbatim
99*
100* Authors:
101* ========
102*
103*> \author Univ. of Tennessee
104*> \author Univ. of California Berkeley
105*> \author Univ. of Colorado Denver
106*> \author NAG Ltd.
107*
108*> \ingroup complex_lin
109*
110* =====================================================================
111 SUBROUTINE cspt01( UPLO, N, A, AFAC, IPIV, C, LDC, RWORK, RESID )
112*
113* -- LAPACK test routine --
114* -- LAPACK is a software package provided by Univ. of Tennessee, --
115* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
116*
117* .. Scalar Arguments ..
118 CHARACTER UPLO
119 INTEGER LDC, N
120 REAL RESID
121* ..
122* .. Array Arguments ..
123 INTEGER IPIV( * )
124 REAL RWORK( * )
125 COMPLEX A( * ), AFAC( * ), C( LDC, * )
126* ..
127*
128* =====================================================================
129*
130* .. Parameters ..
131 REAL ZERO, ONE
132 parameter( zero = 0.0e+0, one = 1.0e+0 )
133 COMPLEX CZERO, CONE
134 parameter( czero = ( 0.0e+0, 0.0e+0 ),
135 \$ cone = ( 1.0e+0, 0.0e+0 ) )
136* ..
137* .. Local Scalars ..
138 INTEGER I, INFO, J, JC
139 REAL ANORM, EPS
140* ..
141* .. External Functions ..
142 LOGICAL LSAME
143 REAL CLANSP, CLANSY, SLAMCH
144 EXTERNAL lsame, clansp, clansy, slamch
145* ..
146* .. External Subroutines ..
147 EXTERNAL clavsp, claset
148* ..
149* .. Intrinsic Functions ..
150 INTRINSIC real
151* ..
152* .. Executable Statements ..
153*
154* Quick exit if N = 0.
155*
156 IF( n.LE.0 ) THEN
157 resid = zero
158 RETURN
159 END IF
160*
161* Determine EPS and the norm of A.
162*
163 eps = slamch( 'Epsilon' )
164 anorm = clansp( '1', uplo, n, a, rwork )
165*
166* Initialize C to the identity matrix.
167*
168 CALL claset( 'Full', n, n, czero, cone, c, ldc )
169*
170* Call CLAVSP to form the product D * U' (or D * L' ).
171*
172 CALL clavsp( uplo, 'Transpose', 'Non-unit', n, n, afac, ipiv, c,
173 \$ ldc, info )
174*
175* Call CLAVSP again to multiply by U ( or L ).
176*
177 CALL clavsp( uplo, 'No transpose', 'Unit', n, n, afac, ipiv, c,
178 \$ ldc, info )
179*
180* Compute the difference C - A .
181*
182 IF( lsame( uplo, 'U' ) ) THEN
183 jc = 0
184 DO 20 j = 1, n
185 DO 10 i = 1, j
186 c( i, j ) = c( i, j ) - a( jc+i )
187 10 CONTINUE
188 jc = jc + j
189 20 CONTINUE
190 ELSE
191 jc = 1
192 DO 40 j = 1, n
193 DO 30 i = j, n
194 c( i, j ) = c( i, j ) - a( jc+i-j )
195 30 CONTINUE
196 jc = jc + n - j + 1
197 40 CONTINUE
198 END IF
199*
200* Compute norm( C - A ) / ( N * norm(A) * EPS )
201*
202 resid = clansy( '1', uplo, n, c, ldc, rwork )
203*
204 IF( anorm.LE.zero ) THEN
205 IF( resid.NE.zero )
206 \$ resid = one / eps
207 ELSE
208 resid = ( ( resid/real( n ) )/anorm ) / eps
209 END IF
210*
211 RETURN
212*
213* End of CSPT01
214*
215 END
subroutine clavsp(uplo, trans, diag, n, nrhs, a, ipiv, b, ldb, info)
CLAVSP
Definition clavsp.f:131
subroutine cspt01(uplo, n, a, afac, ipiv, c, ldc, rwork, resid)
CSPT01
Definition cspt01.f:112
subroutine claset(uplo, m, n, alpha, beta, a, lda)
CLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
Definition claset.f:106