1*> \brief \b SPPT03
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 SPPT03( 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               A( * ), AINV( * ), RWORK( * ),
21*      $                   WORK( LDWORK, * )
22*       ..
23*
24*
25*> \par Purpose:
26*  =============
27*>
28*> \verbatim
29*>
30*> SPPT03 computes the residual for a symmetric 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*>          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 REAL array, dimension (N*(N+1)/2)
57*>          The original symmetric matrix A, stored as a packed
58*>          triangular matrix.
59*> \endverbatim
60*>
61*> \param[in] AINV
62*> \verbatim
63*>          AINV is REAL 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 REAL 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*> \ingroup single_lin
106*
107*  =====================================================================
108      SUBROUTINE SPPT03( UPLO, N, A, AINV, WORK, LDWORK, RWORK, RCOND,
109     $                   RESID )
110*
111*  -- LAPACK test routine --
112*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
113*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
114*
115*     .. Scalar Arguments ..
116      CHARACTER          UPLO
117      INTEGER            LDWORK, N
118      REAL               RCOND, RESID
119*     ..
120*     .. Array Arguments ..
121      REAL               A( * ), AINV( * ), RWORK( * ),
122     $                   WORK( LDWORK, * )
123*     ..
124*
125*  =====================================================================
126*
127*     .. Parameters ..
128      REAL               ZERO, ONE
129      PARAMETER          ( ZERO = 0.0E+0, ONE = 1.0E+0 )
130*     ..
131*     .. Local Scalars ..
132      INTEGER            I, J, JJ
133      REAL               AINVNM, ANORM, EPS
134*     ..
135*     .. External Functions ..
136      LOGICAL            LSAME
137      REAL               SLAMCH, SLANGE, SLANSP
138      EXTERNAL           LSAME, SLAMCH, SLANGE, SLANSP
139*     ..
140*     .. Intrinsic Functions ..
141      INTRINSIC          REAL
142*     ..
143*     .. External Subroutines ..
144      EXTERNAL           SCOPY, SSPMV
145*     ..
146*     .. Executable Statements ..
147*
148*     Quick exit if N = 0.
149*
150      IF( N.LE.0 ) THEN
151         RCOND = ONE
152         RESID = ZERO
153         RETURN
154      END IF
155*
156*     Exit with RESID = 1/EPS if ANORM = 0 or AINVNM = 0.
157*
158      EPS = SLAMCH( 'Epsilon' )
159      ANORM = SLANSP( '1', UPLO, N, A, RWORK )
160      AINVNM = SLANSP( '1', UPLO, N, AINV, RWORK )
161      IF( ANORM.LE.ZERO .OR. AINVNM.EQ.ZERO ) THEN
162         RCOND = ZERO
163         RESID = ONE / EPS
164         RETURN
165      END IF
166      RCOND = ( ONE / ANORM ) / AINVNM
167*
168*     UPLO = 'U':
169*     Copy the leading N-1 x N-1 submatrix of AINV to WORK(1:N,2:N) and
170*     expand it to a full matrix, then multiply by A one column at a
171*     time, moving the result one column to the left.
172*
173      IF( LSAME( UPLO, 'U' ) ) THEN
174*
175*        Copy AINV
176*
177         JJ = 1
178         DO 10 J = 1, N - 1
179            CALL SCOPY( J, AINV( JJ ), 1, WORK( 1, J+1 ), 1 )
180            CALL SCOPY( J-1, AINV( JJ ), 1, WORK( J, 2 ), LDWORK )
181            JJ = JJ + J
182   10    CONTINUE
183         JJ = ( ( N-1 )*N ) / 2 + 1
184         CALL SCOPY( N-1, AINV( JJ ), 1, WORK( N, 2 ), LDWORK )
185*
186*        Multiply by A
187*
188         DO 20 J = 1, N - 1
189            CALL SSPMV( 'Upper', N, -ONE, A, WORK( 1, J+1 ), 1, ZERO,
190     $                  WORK( 1, J ), 1 )
191   20    CONTINUE
192         CALL SSPMV( 'Upper', N, -ONE, A, AINV( JJ ), 1, ZERO,
193     $               WORK( 1, N ), 1 )
194*
195*     UPLO = 'L':
196*     Copy the trailing N-1 x N-1 submatrix of AINV to WORK(1:N,1:N-1)
197*     and multiply by A, moving each column to the right.
198*
199      ELSE
200*
201*        Copy AINV
202*
203         CALL SCOPY( N-1, AINV( 2 ), 1, WORK( 1, 1 ), LDWORK )
204         JJ = N + 1
205         DO 30 J = 2, N
206            CALL SCOPY( N-J+1, AINV( JJ ), 1, WORK( J, J-1 ), 1 )
207            CALL SCOPY( N-J, AINV( JJ+1 ), 1, WORK( J, J ), LDWORK )
208            JJ = JJ + N - J + 1
209   30    CONTINUE
210*
211*        Multiply by A
212*
213         DO 40 J = N, 2, -1
214            CALL SSPMV( 'Lower', N, -ONE, A, WORK( 1, J-1 ), 1, ZERO,
215     $                  WORK( 1, J ), 1 )
216   40    CONTINUE
217         CALL SSPMV( 'Lower', N, -ONE, A, AINV( 1 ), 1, ZERO,
218     $               WORK( 1, 1 ), 1 )
219*
220      END IF
221*
222*     Add the identity matrix to WORK .
223*
224      DO 50 I = 1, N
225         WORK( I, I ) = WORK( I, I ) + ONE
226   50 CONTINUE
227*
228*     Compute norm(I - A*AINV) / (N * norm(A) * norm(AINV) * EPS)
229*
230      RESID = SLANGE( '1', N, N, WORK, LDWORK, RWORK )
231*
232      RESID = ( ( RESID*RCOND ) / EPS ) / REAL( N )
233*
234      RETURN
235*
236*     End of SPPT03
237*
238      END
239