1*> \brief \b CPPT03
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 CPPT03( UPLO, N, A, AINV, WORK, LDWORK, RWORK, RCOND,
12*                          RESID )
13*
14*       .. Scalar Arguments ..
15*       CHARACTER          UPLO
16*       INTEGER            LDWORK, N
17*       REAL               RCOND, RESID
18*       ..
19*       .. Array Arguments ..
20*       REAL               RWORK( * )
21*       COMPLEX            A( * ), AINV( * ), WORK( LDWORK, * )
22*       ..
23*
24*
25*> \par Purpose:
26*  =============
27*>
28*> \verbatim
29*>
30*> CPPT03 computes the residual for a Hermitian packed matrix times its
31*> inverse:
32*>    norm( I - A*AINV ) / ( N * norm(A) * norm(AINV) * EPS ),
33*> where EPS is the machine epsilon.
34*> \endverbatim
35*
36*  Arguments:
37*  ==========
38*
39*> \param[in] UPLO
40*> \verbatim
41*>          UPLO is CHARACTER*1
42*>          Specifies whether the upper or lower triangular part of the
43*>          Hermitian matrix A is stored:
44*>          = 'U':  Upper triangular
45*>          = 'L':  Lower triangular
46*> \endverbatim
47*>
48*> \param[in] N
49*> \verbatim
50*>          N is INTEGER
51*>          The number of rows and columns of the matrix A.  N >= 0.
52*> \endverbatim
53*>
54*> \param[in] A
55*> \verbatim
56*>          A is COMPLEX array, dimension (N*(N+1)/2)
57*>          The original Hermitian matrix A, stored as a packed
58*>          triangular matrix.
59*> \endverbatim
60*>
61*> \param[in] AINV
62*> \verbatim
63*>          AINV is COMPLEX array, dimension (N*(N+1)/2)
64*>          The (Hermitian) inverse of the matrix A, stored as a packed
65*>          triangular matrix.
66*> \endverbatim
67*>
68*> \param[out] WORK
69*> \verbatim
70*>          WORK is COMPLEX array, dimension (LDWORK,N)
71*> \endverbatim
72*>
73*> \param[in] LDWORK
74*> \verbatim
75*>          LDWORK is INTEGER
76*>          The leading dimension of the array WORK.  LDWORK >= max(1,N).
77*> \endverbatim
78*>
79*> \param[out] RWORK
80*> \verbatim
81*>          RWORK is REAL array, dimension (N)
82*> \endverbatim
83*>
84*> \param[out] RCOND
85*> \verbatim
86*>          RCOND is REAL
87*>          The reciprocal of the condition number of A, computed as
88*>          ( 1/norm(A) ) / norm(AINV).
89*> \endverbatim
90*>
91*> \param[out] RESID
92*> \verbatim
93*>          RESID is REAL
94*>          norm(I - A*AINV) / ( N * norm(A) * norm(AINV) * EPS )
95*> \endverbatim
96*
97*  Authors:
98*  ========
99*
100*> \author Univ. of Tennessee
101*> \author Univ. of California Berkeley
102*> \author Univ. of Colorado Denver
103*> \author NAG Ltd.
104*
105*> \date December 2016
106*
107*> \ingroup complex_lin
108*
109*  =====================================================================
110      SUBROUTINE CPPT03( UPLO, N, A, AINV, WORK, LDWORK, RWORK, RCOND,
111     $                   RESID )
112*
113*  -- LAPACK test routine (version 3.7.0) --
114*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
115*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
116*     December 2016
117*
118*     .. Scalar Arguments ..
119      CHARACTER          UPLO
120      INTEGER            LDWORK, N
121      REAL               RCOND, RESID
122*     ..
123*     .. Array Arguments ..
124      REAL               RWORK( * )
125      COMPLEX            A( * ), AINV( * ), WORK( LDWORK, * )
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, J, JJ
139      REAL               AINVNM, ANORM, EPS
140*     ..
141*     .. External Functions ..
142      LOGICAL            LSAME
143      REAL               CLANGE, CLANHP, SLAMCH
144      EXTERNAL           LSAME, CLANGE, CLANHP, SLAMCH
145*     ..
146*     .. Intrinsic Functions ..
147      INTRINSIC          CONJG, REAL
148*     ..
149*     .. External Subroutines ..
150      EXTERNAL           CCOPY, CHPMV
151*     ..
152*     .. Executable Statements ..
153*
154*     Quick exit if N = 0.
155*
156      IF( N.LE.0 ) THEN
157         RCOND = ONE
158         RESID = ZERO
159         RETURN
160      END IF
161*
162*     Exit with RESID = 1/EPS if ANORM = 0 or AINVNM = 0.
163*
164      EPS = SLAMCH( 'Epsilon' )
165      ANORM = CLANHP( '1', UPLO, N, A, RWORK )
166      AINVNM = CLANHP( '1', UPLO, N, AINV, RWORK )
167      IF( ANORM.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN
168         RCOND = ZERO
169         RESID = ONE / EPS
170         RETURN
171      END IF
172      RCOND = ( ONE/ANORM ) / AINVNM
173*
174*     UPLO = 'U':
175*     Copy the leading N-1 x N-1 submatrix of AINV to WORK(1:N,2:N) and
176*     expand it to a full matrix, then multiply by A one column at a
177*     time, moving the result one column to the left.
178*
179      IF( LSAME( UPLO, 'U' ) ) THEN
180*
181*        Copy AINV
182*
183         JJ = 1
184         DO 20 J = 1, N - 1
185            CALL CCOPY( J, AINV( JJ ), 1, WORK( 1, J+1 ), 1 )
186            DO 10 I = 1, J - 1
187               WORK( J, I+1 ) = CONJG( AINV( JJ+I-1 ) )
188   10       CONTINUE
189            JJ = JJ + J
190   20    CONTINUE
191         JJ = ( ( N-1 )*N ) / 2 + 1
192         DO 30 I = 1, N - 1
193            WORK( N, I+1 ) = CONJG( AINV( JJ+I-1 ) )
194   30    CONTINUE
195*
196*        Multiply by A
197*
198         DO 40 J = 1, N - 1
199            CALL CHPMV( 'Upper', N, -CONE, A, WORK( 1, J+1 ), 1, CZERO,
200     $                  WORK( 1, J ), 1 )
201   40    CONTINUE
202         CALL CHPMV( 'Upper', N, -CONE, A, AINV( JJ ), 1, CZERO,
203     $               WORK( 1, N ), 1 )
204*
205*     UPLO = 'L':
206*     Copy the trailing N-1 x N-1 submatrix of AINV to WORK(1:N,1:N-1)
207*     and multiply by A, moving each column to the right.
208*
209      ELSE
210*
211*        Copy AINV
212*
213         DO 50 I = 1, N - 1
214            WORK( 1, I ) = CONJG( AINV( I+1 ) )
215   50    CONTINUE
216         JJ = N + 1
217         DO 70 J = 2, N
218            CALL CCOPY( N-J+1, AINV( JJ ), 1, WORK( J, J-1 ), 1 )
219            DO 60 I = 1, N - J
220               WORK( J, J+I-1 ) = CONJG( AINV( JJ+I ) )
221   60       CONTINUE
222            JJ = JJ + N - J + 1
223   70    CONTINUE
224*
225*        Multiply by A
226*
227         DO 80 J = N, 2, -1
228            CALL CHPMV( 'Lower', N, -CONE, A, WORK( 1, J-1 ), 1, CZERO,
229     $                  WORK( 1, J ), 1 )
230   80    CONTINUE
231         CALL CHPMV( 'Lower', N, -CONE, A, AINV( 1 ), 1, CZERO,
232     $               WORK( 1, 1 ), 1 )
233*
234      END IF
235*
236*     Add the identity matrix to WORK .
237*
238      DO 90 I = 1, N
239         WORK( I, I ) = WORK( I, I ) + CONE
240   90 CONTINUE
241*
242*     Compute norm(I - A*AINV) / (N * norm(A) * norm(AINV) * EPS)
243*
244      RESID = CLANGE( '1', N, N, WORK, LDWORK, RWORK )
245*
246      RESID = ( ( RESID*RCOND )/EPS ) / REAL( N )
247*
248      RETURN
249*
250*     End of CPPT03
251*
252      END
253