1*> \brief \b DPOT03
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 DPOT03( UPLO, N, A, LDA, AINV, LDAINV, WORK, LDWORK,
12*                          RWORK, RCOND, RESID )
13*
14*       .. Scalar Arguments ..
15*       CHARACTER          UPLO
16*       INTEGER            LDA, LDAINV, LDWORK, N
17*       DOUBLE PRECISION   RCOND, RESID
18*       ..
19*       .. Array Arguments ..
20*       DOUBLE PRECISION   A( LDA, * ), AINV( LDAINV, * ), RWORK( * ),
21*      $                   WORK( LDWORK, * )
22*       ..
23*
24*
25*> \par Purpose:
26*  =============
27*>
28*> \verbatim
29*>
30*> DPOT03 computes the residual for a symmetric 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 (LDA,N)
57*>          The original symmetric matrix A.
58*> \endverbatim
59*>
60*> \param[in] LDA
61*> \verbatim
62*>          LDA is INTEGER
63*>          The leading dimension of the array A.  LDA >= max(1,N)
64*> \endverbatim
65*>
66*> \param[in,out] AINV
67*> \verbatim
68*>          AINV is DOUBLE PRECISION array, dimension (LDAINV,N)
69*>          On entry, the inverse of the matrix A, stored as a symmetric
70*>          matrix in the same format as A.
71*>          In this version, AINV is expanded into a full matrix and
72*>          multiplied by A, so the opposing triangle of AINV will be
73*>          changed; i.e., if the upper triangular part of AINV is
74*>          stored, the lower triangular part will be used as work space.
75*> \endverbatim
76*>
77*> \param[in] LDAINV
78*> \verbatim
79*>          LDAINV is INTEGER
80*>          The leading dimension of the array AINV.  LDAINV >= max(1,N).
81*> \endverbatim
82*>
83*> \param[out] WORK
84*> \verbatim
85*>          WORK is DOUBLE PRECISION array, dimension (LDWORK,N)
86*> \endverbatim
87*>
88*> \param[in] LDWORK
89*> \verbatim
90*>          LDWORK is INTEGER
91*>          The leading dimension of the array WORK.  LDWORK >= max(1,N).
92*> \endverbatim
93*>
94*> \param[out] RWORK
95*> \verbatim
96*>          RWORK is DOUBLE PRECISION array, dimension (N)
97*> \endverbatim
98*>
99*> \param[out] RCOND
100*> \verbatim
101*>          RCOND is DOUBLE PRECISION
102*>          The reciprocal of the condition number of A, computed as
103*>          ( 1/norm(A) ) / norm(AINV).
104*> \endverbatim
105*>
106*> \param[out] RESID
107*> \verbatim
108*>          RESID is DOUBLE PRECISION
109*>          norm(I - A*AINV) / ( N * norm(A) * norm(AINV) * EPS )
110*> \endverbatim
111*
112*  Authors:
113*  ========
114*
115*> \author Univ. of Tennessee
116*> \author Univ. of California Berkeley
117*> \author Univ. of Colorado Denver
118*> \author NAG Ltd.
119*
120*> \ingroup double_lin
121*
122*  =====================================================================
123      SUBROUTINE DPOT03( UPLO, N, A, LDA, AINV, LDAINV, WORK, LDWORK,
124     $                   RWORK, RCOND, RESID )
125*
126*  -- LAPACK test routine --
127*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
128*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
129*
130*     .. Scalar Arguments ..
131      CHARACTER          UPLO
132      INTEGER            LDA, LDAINV, LDWORK, N
133      DOUBLE PRECISION   RCOND, RESID
134*     ..
135*     .. Array Arguments ..
136      DOUBLE PRECISION   A( LDA, * ), AINV( LDAINV, * ), RWORK( * ),
137     $                   WORK( LDWORK, * )
138*     ..
139*
140*  =====================================================================
141*
142*     .. Parameters ..
143      DOUBLE PRECISION   ZERO, ONE
144      PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0 )
145*     ..
146*     .. Local Scalars ..
147      INTEGER            I, J
148      DOUBLE PRECISION   AINVNM, ANORM, EPS
149*     ..
150*     .. External Functions ..
151      LOGICAL            LSAME
152      DOUBLE PRECISION   DLAMCH, DLANGE, DLANSY
153      EXTERNAL           LSAME, DLAMCH, DLANGE, DLANSY
154*     ..
155*     .. External Subroutines ..
156      EXTERNAL           DSYMM
157*     ..
158*     .. Intrinsic Functions ..
159      INTRINSIC          DBLE
160*     ..
161*     .. Executable Statements ..
162*
163*     Quick exit if N = 0.
164*
165      IF( N.LE.0 ) THEN
166         RCOND = ONE
167         RESID = ZERO
168         RETURN
169      END IF
170*
171*     Exit with RESID = 1/EPS if ANORM = 0 or AINVNM = 0.
172*
173      EPS = DLAMCH( 'Epsilon' )
174      ANORM = DLANSY( '1', UPLO, N, A, LDA, RWORK )
175      AINVNM = DLANSY( '1', UPLO, N, AINV, LDAINV, RWORK )
176      IF( ANORM.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN
177         RCOND = ZERO
178         RESID = ONE / EPS
179         RETURN
180      END IF
181      RCOND = ( ONE / ANORM ) / AINVNM
182*
183*     Expand AINV into a full matrix and call DSYMM to multiply
184*     AINV on the left by A.
185*
186      IF( LSAME( UPLO, 'U' ) ) THEN
187         DO 20 J = 1, N
188            DO 10 I = 1, J - 1
189               AINV( J, I ) = AINV( I, J )
190   10       CONTINUE
191   20    CONTINUE
192      ELSE
193         DO 40 J = 1, N
194            DO 30 I = J + 1, N
195               AINV( J, I ) = AINV( I, J )
196   30       CONTINUE
197   40    CONTINUE
198      END IF
199      CALL DSYMM( 'Left', UPLO, N, N, -ONE, A, LDA, AINV, LDAINV, ZERO,
200     $            WORK, LDWORK )
201*
202*     Add the identity matrix to WORK .
203*
204      DO 50 I = 1, N
205         WORK( I, I ) = WORK( I, I ) + ONE
206   50 CONTINUE
207*
208*     Compute norm(I - A*AINV) / (N * norm(A) * norm(AINV) * EPS)
209*
210      RESID = DLANGE( '1', N, N, WORK, LDWORK, RWORK )
211*
212      RESID = ( ( RESID*RCOND ) / EPS ) / DBLE( N )
213*
214      RETURN
215*
216*     End of DPOT03
217*
218      END
219