1*> \brief \b CSPT03
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 CSPT03( UPLO, N, A, AINV, WORK, LDW, RWORK, RCOND,
12*                          RESID )
13*
14*       .. Scalar Arguments ..
15*       CHARACTER          UPLO
16*       INTEGER            LDW, N
17*       REAL               RCOND, RESID
18*       ..
19*       .. Array Arguments ..
20*       REAL               RWORK( * )
21*       COMPLEX            A( * ), AINV( * ), WORK( LDW, * )
22*       ..
23*
24*
25*> \par Purpose:
26*  =============
27*>
28*> \verbatim
29*>
30*> CSPT03 computes the residual for a complex symmetric packed matrix
31*> times its 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*>          complex symmetric 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 complex symmetric 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 (symmetric) 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 (LDW,N)
71*> \endverbatim
72*>
73*> \param[in] LDW
74*> \verbatim
75*>          LDW is INTEGER
76*>          The leading dimension of the array WORK.  LDW >= 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 November 2011
106*
107*> \ingroup complex_lin
108*
109*  =====================================================================
110      SUBROUTINE CSPT03( UPLO, N, A, AINV, WORK, LDW, RWORK, RCOND,
111     $                   RESID )
112*
113*  -- LAPACK test routine (version 3.4.0) --
114*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
115*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
116*     November 2011
117*
118*     .. Scalar Arguments ..
119      CHARACTER          UPLO
120      INTEGER            LDW, N
121      REAL               RCOND, RESID
122*     ..
123*     .. Array Arguments ..
124      REAL               RWORK( * )
125      COMPLEX            A( * ), AINV( * ), WORK( LDW, * )
126*     ..
127*
128*  =====================================================================
129*
130*     .. Parameters ..
131      REAL               ZERO, ONE
132      PARAMETER          ( ZERO = 0.0E+0, ONE = 1.0E+0 )
133*     ..
134*     .. Local Scalars ..
135      INTEGER            I, ICOL, J, JCOL, K, KCOL, NALL
136      REAL               AINVNM, ANORM, EPS
137      COMPLEX            T
138*     ..
139*     .. External Functions ..
140      LOGICAL            LSAME
141      REAL               CLANGE, CLANSP, SLAMCH
142      COMPLEX            CDOTU
143      EXTERNAL           LSAME, CLANGE, CLANSP, SLAMCH, CDOTU
144*     ..
145*     .. Intrinsic Functions ..
146      INTRINSIC          REAL
147*     ..
148*     .. Executable Statements ..
149*
150*     Quick exit if N = 0.
151*
152      IF( N.LE.0 ) THEN
153         RCOND = ONE
154         RESID = ZERO
155         RETURN
156      END IF
157*
158*     Exit with RESID = 1/EPS if ANORM = 0 or AINVNM = 0.
159*
160      EPS = SLAMCH( 'Epsilon' )
161      ANORM = CLANSP( '1', UPLO, N, A, RWORK )
162      AINVNM = CLANSP( '1', UPLO, N, AINV, RWORK )
163      IF( ANORM.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN
164         RCOND = ZERO
165         RESID = ONE / EPS
166         RETURN
167      END IF
168      RCOND = ( ONE/ANORM ) / AINVNM
169*
170*     Case where both A and AINV are upper triangular:
171*     Each element of - A * AINV is computed by taking the dot product
172*     of a row of A with a column of AINV.
173*
174      IF( LSAME( UPLO, 'U' ) ) THEN
175         DO 70 I = 1, N
176            ICOL = ( ( I-1 )*I ) / 2 + 1
177*
178*           Code when J <= I
179*
180            DO 30 J = 1, I
181               JCOL = ( ( J-1 )*J ) / 2 + 1
182               T = CDOTU( J, A( ICOL ), 1, AINV( JCOL ), 1 )
183               JCOL = JCOL + 2*J - 1
184               KCOL = ICOL - 1
185               DO 10 K = J + 1, I
186                  T = T + A( KCOL+K )*AINV( JCOL )
187                  JCOL = JCOL + K
188   10          CONTINUE
189               KCOL = KCOL + 2*I
190               DO 20 K = I + 1, N
191                  T = T + A( KCOL )*AINV( JCOL )
192                  KCOL = KCOL + K
193                  JCOL = JCOL + K
194   20          CONTINUE
195               WORK( I, J ) = -T
196   30       CONTINUE
197*
198*           Code when J > I
199*
200            DO 60 J = I + 1, N
201               JCOL = ( ( J-1 )*J ) / 2 + 1
202               T = CDOTU( I, A( ICOL ), 1, AINV( JCOL ), 1 )
203               JCOL = JCOL - 1
204               KCOL = ICOL + 2*I - 1
205               DO 40 K = I + 1, J
206                  T = T + A( KCOL )*AINV( JCOL+K )
207                  KCOL = KCOL + K
208   40          CONTINUE
209               JCOL = JCOL + 2*J
210               DO 50 K = J + 1, N
211                  T = T + A( KCOL )*AINV( JCOL )
212                  KCOL = KCOL + K
213                  JCOL = JCOL + K
214   50          CONTINUE
215               WORK( I, J ) = -T
216   60       CONTINUE
217   70    CONTINUE
218      ELSE
219*
220*        Case where both A and AINV are lower triangular
221*
222         NALL = ( N*( N+1 ) ) / 2
223         DO 140 I = 1, N
224*
225*           Code when J <= I
226*
227            ICOL = NALL - ( ( N-I+1 )*( N-I+2 ) ) / 2 + 1
228            DO 100 J = 1, I
229               JCOL = NALL - ( ( N-J )*( N-J+1 ) ) / 2 - ( N-I )
230               T = CDOTU( N-I+1, A( ICOL ), 1, AINV( JCOL ), 1 )
231               KCOL = I
232               JCOL = J
233               DO 80 K = 1, J - 1
234                  T = T + A( KCOL )*AINV( JCOL )
235                  JCOL = JCOL + N - K
236                  KCOL = KCOL + N - K
237   80          CONTINUE
238               JCOL = JCOL - J
239               DO 90 K = J, I - 1
240                  T = T + A( KCOL )*AINV( JCOL+K )
241                  KCOL = KCOL + N - K
242   90          CONTINUE
243               WORK( I, J ) = -T
244  100       CONTINUE
245*
246*           Code when J > I
247*
248            ICOL = NALL - ( ( N-I )*( N-I+1 ) ) / 2
249            DO 130 J = I + 1, N
250               JCOL = NALL - ( ( N-J+1 )*( N-J+2 ) ) / 2 + 1
251               T = CDOTU( N-J+1, A( ICOL-N+J ), 1, AINV( JCOL ), 1 )
252               KCOL = I
253               JCOL = J
254               DO 110 K = 1, I - 1
255                  T = T + A( KCOL )*AINV( JCOL )
256                  JCOL = JCOL + N - K
257                  KCOL = KCOL + N - K
258  110          CONTINUE
259               KCOL = KCOL - I
260               DO 120 K = I, J - 1
261                  T = T + A( KCOL+K )*AINV( JCOL )
262                  JCOL = JCOL + N - K
263  120          CONTINUE
264               WORK( I, J ) = -T
265  130       CONTINUE
266  140    CONTINUE
267      END IF
268*
269*     Add the identity matrix to WORK .
270*
271      DO 150 I = 1, N
272         WORK( I, I ) = WORK( I, I ) + ONE
273  150 CONTINUE
274*
275*     Compute norm(I - A*AINV) / (N * norm(A) * norm(AINV) * EPS)
276*
277      RESID = CLANGE( '1', N, N, WORK, LDW, RWORK )
278*
279      RESID = ( ( RESID*RCOND )/EPS ) / REAL( N )
280*
281      RETURN
282*
283*     End of CSPT03
284*
285      END
286