1*> \brief \b ZSPT01
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 ZSPT01( UPLO, N, A, AFAC, IPIV, C, LDC, RWORK, RESID )
12*
13*       .. Scalar Arguments ..
14*       CHARACTER          UPLO
15*       INTEGER            LDC, N
16*       DOUBLE PRECISION   RESID
17*       ..
18*       .. Array Arguments ..
19*       INTEGER            IPIV( * )
20*       DOUBLE PRECISION   RWORK( * )
21*       COMPLEX*16         A( * ), AFAC( * ), C( LDC, * )
22*       ..
23*
24*
25*> \par Purpose:
26*  =============
27*>
28*> \verbatim
29*>
30*> ZSPT01 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*16 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*16 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 ZSPTRF.
69*> \endverbatim
70*>
71*> \param[in] IPIV
72*> \verbatim
73*>          IPIV is INTEGER array, dimension (N)
74*>          The pivot indices from ZSPTRF.
75*> \endverbatim
76*>
77*> \param[out] C
78*> \verbatim
79*>          C is COMPLEX*16 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 DOUBLE PRECISION array, dimension (N)
91*> \endverbatim
92*>
93*> \param[out] RESID
94*> \verbatim
95*>          RESID is DOUBLE PRECISION
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*> \date December 2016
109*
110*> \ingroup complex16_lin
111*
112*  =====================================================================
113      SUBROUTINE ZSPT01( UPLO, N, A, AFAC, IPIV, C, LDC, RWORK, RESID )
114*
115*  -- LAPACK test routine (version 3.7.0) --
116*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
117*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
118*     December 2016
119*
120*     .. Scalar Arguments ..
121      CHARACTER          UPLO
122      INTEGER            LDC, N
123      DOUBLE PRECISION   RESID
124*     ..
125*     .. Array Arguments ..
126      INTEGER            IPIV( * )
127      DOUBLE PRECISION   RWORK( * )
128      COMPLEX*16         A( * ), AFAC( * ), C( LDC, * )
129*     ..
130*
131*  =====================================================================
132*
133*     .. Parameters ..
134      DOUBLE PRECISION   ZERO, ONE
135      PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0 )
136      COMPLEX*16         CZERO, CONE
137      PARAMETER          ( CZERO = ( 0.0D+0, 0.0D+0 ),
138     $                   CONE = ( 1.0D+0, 0.0D+0 ) )
139*     ..
140*     .. Local Scalars ..
141      INTEGER            I, INFO, J, JC
142      DOUBLE PRECISION   ANORM, EPS
143*     ..
144*     .. External Functions ..
145      LOGICAL            LSAME
146      DOUBLE PRECISION   DLAMCH, ZLANSP, ZLANSY
147      EXTERNAL           LSAME, DLAMCH, ZLANSP, ZLANSY
148*     ..
149*     .. External Subroutines ..
150      EXTERNAL           ZLASET, ZLAVSP
151*     ..
152*     .. Intrinsic Functions ..
153      INTRINSIC          DBLE
154*     ..
155*     .. Executable Statements ..
156*
157*     Quick exit if N = 0.
158*
159      IF( N.LE.0 ) THEN
160         RESID = ZERO
161         RETURN
162      END IF
163*
164*     Determine EPS and the norm of A.
165*
166      EPS = DLAMCH( 'Epsilon' )
167      ANORM = ZLANSP( '1', UPLO, N, A, RWORK )
168*
169*     Initialize C to the identity matrix.
170*
171      CALL ZLASET( 'Full', N, N, CZERO, CONE, C, LDC )
172*
173*     Call ZLAVSP to form the product D * U' (or D * L' ).
174*
175      CALL ZLAVSP( UPLO, 'Transpose', 'Non-unit', N, N, AFAC, IPIV, C,
176     $             LDC, INFO )
177*
178*     Call ZLAVSP again to multiply by U ( or L ).
179*
180      CALL ZLAVSP( UPLO, 'No transpose', 'Unit', N, N, AFAC, IPIV, C,
181     $             LDC, INFO )
182*
183*     Compute the difference  C - A .
184*
185      IF( LSAME( UPLO, 'U' ) ) THEN
186         JC = 0
187         DO 20 J = 1, N
188            DO 10 I = 1, J
189               C( I, J ) = C( I, J ) - A( JC+I )
190   10       CONTINUE
191            JC = JC + J
192   20    CONTINUE
193      ELSE
194         JC = 1
195         DO 40 J = 1, N
196            DO 30 I = J, N
197               C( I, J ) = C( I, J ) - A( JC+I-J )
198   30       CONTINUE
199            JC = JC + N - J + 1
200   40    CONTINUE
201      END IF
202*
203*     Compute norm( C - A ) / ( N * norm(A) * EPS )
204*
205      RESID = ZLANSY( '1', UPLO, N, C, LDC, RWORK )
206*
207      IF( ANORM.LE.ZERO ) THEN
208         IF( RESID.NE.ZERO )
209     $      RESID = ONE / EPS
210      ELSE
211         RESID = ( ( RESID / DBLE( N ) ) / ANORM ) / EPS
212      END IF
213*
214      RETURN
215*
216*     End of ZSPT01
217*
218      END
219