1*> \brief \b DPPT03
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 DPPT03( UPLO, N, A, AINV, WORK, LDWORK, RWORK, RCOND,
12*                          RESID )
13*
14*       .. Scalar Arguments ..
15*       CHARACTER          UPLO
16*       INTEGER            LDWORK, N
17*       DOUBLE PRECISION   RCOND, RESID
18*       ..
19*       .. Array Arguments ..
20*       DOUBLE PRECISION   A( * ), AINV( * ), RWORK( * ),
21*      $                   WORK( LDWORK, * )
22*       ..
23*
24*
25*> \par Purpose:
26*  =============
27*>
28*> \verbatim
29*>
30*> DPPT03 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (N)
82*> \endverbatim
83*>
84*> \param[out] RCOND
85*> \verbatim
86*>          RCOND is DOUBLE PRECISION
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 DOUBLE PRECISION
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 double_lin
108*
109*  =====================================================================
110      SUBROUTINE DPPT03( 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      DOUBLE PRECISION   RCOND, RESID
122*     ..
123*     .. Array Arguments ..
124      DOUBLE PRECISION   A( * ), AINV( * ), RWORK( * ),
125     $                   WORK( LDWORK, * )
126*     ..
127*
128*  =====================================================================
129*
130*     .. Parameters ..
131      DOUBLE PRECISION   ZERO, ONE
132      PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0 )
133*     ..
134*     .. Local Scalars ..
135      INTEGER            I, J, JJ
136      DOUBLE PRECISION   AINVNM, ANORM, EPS
137*     ..
138*     .. External Functions ..
139      LOGICAL            LSAME
140      DOUBLE PRECISION   DLAMCH, DLANGE, DLANSP
141      EXTERNAL           LSAME, DLAMCH, DLANGE, DLANSP
142*     ..
143*     .. Intrinsic Functions ..
144      INTRINSIC          DBLE
145*     ..
146*     .. External Subroutines ..
147      EXTERNAL           DCOPY, DSPMV
148*     ..
149*     .. Executable Statements ..
150*
151*     Quick exit if N = 0.
152*
153      IF( N.LE.0 ) THEN
154         RCOND = ONE
155         RESID = ZERO
156         RETURN
157      END IF
158*
159*     Exit with RESID = 1/EPS if ANORM = 0 or AINVNM = 0.
160*
161      EPS = DLAMCH( 'Epsilon' )
162      ANORM = DLANSP( '1', UPLO, N, A, RWORK )
163      AINVNM = DLANSP( '1', UPLO, N, AINV, RWORK )
164      IF( ANORM.LE.ZERO .OR. AINVNM.EQ.ZERO ) THEN
165         RCOND = ZERO
166         RESID = ONE / EPS
167         RETURN
168      END IF
169      RCOND = ( ONE / ANORM ) / AINVNM
170*
171*     UPLO = 'U':
172*     Copy the leading N-1 x N-1 submatrix of AINV to WORK(1:N,2:N) and
173*     expand it to a full matrix, then multiply by A one column at a
174*     time, moving the result one column to the left.
175*
176      IF( LSAME( UPLO, 'U' ) ) THEN
177*
178*        Copy AINV
179*
180         JJ = 1
181         DO 10 J = 1, N - 1
182            CALL DCOPY( J, AINV( JJ ), 1, WORK( 1, J+1 ), 1 )
183            CALL DCOPY( J-1, AINV( JJ ), 1, WORK( J, 2 ), LDWORK )
184            JJ = JJ + J
185   10    CONTINUE
186         JJ = ( ( N-1 )*N ) / 2 + 1
187         CALL DCOPY( N-1, AINV( JJ ), 1, WORK( N, 2 ), LDWORK )
188*
189*        Multiply by A
190*
191         DO 20 J = 1, N - 1
192            CALL DSPMV( 'Upper', N, -ONE, A, WORK( 1, J+1 ), 1, ZERO,
193     $                  WORK( 1, J ), 1 )
194   20    CONTINUE
195         CALL DSPMV( 'Upper', N, -ONE, A, AINV( JJ ), 1, ZERO,
196     $               WORK( 1, N ), 1 )
197*
198*     UPLO = 'L':
199*     Copy the trailing N-1 x N-1 submatrix of AINV to WORK(1:N,1:N-1)
200*     and multiply by A, moving each column to the right.
201*
202      ELSE
203*
204*        Copy AINV
205*
206         CALL DCOPY( N-1, AINV( 2 ), 1, WORK( 1, 1 ), LDWORK )
207         JJ = N + 1
208         DO 30 J = 2, N
209            CALL DCOPY( N-J+1, AINV( JJ ), 1, WORK( J, J-1 ), 1 )
210            CALL DCOPY( N-J, AINV( JJ+1 ), 1, WORK( J, J ), LDWORK )
211            JJ = JJ + N - J + 1
212   30    CONTINUE
213*
214*        Multiply by A
215*
216         DO 40 J = N, 2, -1
217            CALL DSPMV( 'Lower', N, -ONE, A, WORK( 1, J-1 ), 1, ZERO,
218     $                  WORK( 1, J ), 1 )
219   40    CONTINUE
220         CALL DSPMV( 'Lower', N, -ONE, A, AINV( 1 ), 1, ZERO,
221     $               WORK( 1, 1 ), 1 )
222*
223      END IF
224*
225*     Add the identity matrix to WORK .
226*
227      DO 50 I = 1, N
228         WORK( I, I ) = WORK( I, I ) + ONE
229   50 CONTINUE
230*
231*     Compute norm(I - A*AINV) / (N * norm(A) * norm(AINV) * EPS)
232*
233      RESID = DLANGE( '1', N, N, WORK, LDWORK, RWORK )
234*
235      RESID = ( ( RESID*RCOND ) / EPS ) / DBLE( N )
236*
237      RETURN
238*
239*     End of DPPT03
240*
241      END
242