1*> \brief \b DSYTRI2
2*
3*  =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6*            http://www.netlib.org/lapack/explore-html/
7*
8*> \htmlonly
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15*> [TXT]</a>
16*> \endhtmlonly
17*
18*  Definition:
19*  ===========
20*
21*       SUBROUTINE DSYTRI2( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
22*
23*       .. Scalar Arguments ..
24*       CHARACTER          UPLO
25*       INTEGER            INFO, LDA, LWORK, N
26*       ..
27*       .. Array Arguments ..
28*       INTEGER            IPIV( * )
29*       DOUBLE PRECISION   A( LDA, * ), WORK( * )
30*       ..
31*
32*
33*> \par Purpose:
34*  =============
35*>
36*> \verbatim
37*>
38*> DSYTRI2 computes the inverse of a DOUBLE PRECISION symmetric indefinite matrix
39*> A using the factorization A = U*D*U**T or A = L*D*L**T computed by
40*> DSYTRF. DSYTRI2 sets the LEADING DIMENSION of the workspace
41*> before calling DSYTRI2X that actually computes the inverse.
42*> \endverbatim
43*
44*  Arguments:
45*  ==========
46*
47*> \param[in] UPLO
48*> \verbatim
49*>          UPLO is CHARACTER*1
50*>          Specifies whether the details of the factorization are stored
51*>          as an upper or lower triangular matrix.
52*>          = 'U':  Upper triangular, form is A = U*D*U**T;
53*>          = 'L':  Lower triangular, form is A = L*D*L**T.
54*> \endverbatim
55*>
56*> \param[in] N
57*> \verbatim
58*>          N is INTEGER
59*>          The order of the matrix A.  N >= 0.
60*> \endverbatim
61*>
62*> \param[in,out] A
63*> \verbatim
64*>          A is DOUBLE PRECISION array, dimension (LDA,N)
65*>          On entry, the block diagonal matrix D and the multipliers
66*>          used to obtain the factor U or L as computed by DSYTRF.
67*>
68*>          On exit, if INFO = 0, the (symmetric) inverse of the original
69*>          matrix.  If UPLO = 'U', the upper triangular part of the
70*>          inverse is formed and the part of A below the diagonal is not
71*>          referenced; if UPLO = 'L' the lower triangular part of the
72*>          inverse is formed and the part of A above the diagonal is
73*>          not referenced.
74*> \endverbatim
75*>
76*> \param[in] LDA
77*> \verbatim
78*>          LDA is INTEGER
79*>          The leading dimension of the array A.  LDA >= max(1,N).
80*> \endverbatim
81*>
82*> \param[in] IPIV
83*> \verbatim
84*>          IPIV is INTEGER array, dimension (N)
85*>          Details of the interchanges and the block structure of D
86*>          as determined by DSYTRF.
87*> \endverbatim
88*>
89*> \param[out] WORK
90*> \verbatim
91*>          WORK is DOUBLE PRECISION array, dimension (N+NB+1)*(NB+3)
92*> \endverbatim
93*>
94*> \param[in] LWORK
95*> \verbatim
96*>          LWORK is INTEGER
97*>          The dimension of the array WORK.
98*>          WORK is size >= (N+NB+1)*(NB+3)
99*>          If LWORK = -1, then a workspace query is assumed; the routine
100*>           calculates:
101*>              - the optimal size of the WORK array, returns
102*>          this value as the first entry of the WORK array,
103*>              - and no error message related to LWORK is issued by XERBLA.
104*> \endverbatim
105*>
106*> \param[out] INFO
107*> \verbatim
108*>          INFO is INTEGER
109*>          = 0: successful exit
110*>          < 0: if INFO = -i, the i-th argument had an illegal value
111*>          > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its
112*>               inverse could not be computed.
113*> \endverbatim
114*
115*  Authors:
116*  ========
117*
118*> \author Univ. of Tennessee
119*> \author Univ. of California Berkeley
120*> \author Univ. of Colorado Denver
121*> \author NAG Ltd.
122*
123*> \ingroup doubleSYcomputational
124*
125*  =====================================================================
126      SUBROUTINE DSYTRI2( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
127*
128*  -- LAPACK computational routine --
129*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
130*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
131*
132*     .. Scalar Arguments ..
133      CHARACTER          UPLO
134      INTEGER            INFO, LDA, LWORK, N
135*     ..
136*     .. Array Arguments ..
137      INTEGER            IPIV( * )
138      DOUBLE PRECISION   A( LDA, * ), WORK( * )
139*     ..
140*
141*  =====================================================================
142*
143*     .. Local Scalars ..
144      LOGICAL            UPPER, LQUERY
145      INTEGER            MINSIZE, NBMAX
146*     ..
147*     .. External Functions ..
148      LOGICAL            LSAME
149      INTEGER            ILAENV
150      EXTERNAL           LSAME, ILAENV
151*     ..
152*     .. External Subroutines ..
153      EXTERNAL           DSYTRI, DSYTRI2X, XERBLA
154*     ..
155*     .. Executable Statements ..
156*
157*     Test the input parameters.
158*
159      INFO = 0
160      UPPER = LSAME( UPLO, 'U' )
161      LQUERY = ( LWORK.EQ.-1 )
162*     Get blocksize
163      NBMAX = ILAENV( 1, 'DSYTRI2', UPLO, N, -1, -1, -1 )
164      IF ( NBMAX .GE. N ) THEN
165         MINSIZE = N
166      ELSE
167         MINSIZE = (N+NBMAX+1)*(NBMAX+3)
168      END IF
169*
170      IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
171         INFO = -1
172      ELSE IF( N.LT.0 ) THEN
173         INFO = -2
174      ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
175         INFO = -4
176      ELSE IF (LWORK .LT. MINSIZE .AND. .NOT.LQUERY ) THEN
177         INFO = -7
178      END IF
179*
180*     Quick return if possible
181*
182*
183      IF( INFO.NE.0 ) THEN
184         CALL XERBLA( 'DSYTRI2', -INFO )
185         RETURN
186      ELSE IF( LQUERY ) THEN
187         WORK(1)=MINSIZE
188         RETURN
189      END IF
190      IF( N.EQ.0 )
191     $   RETURN
192
193      IF( NBMAX .GE. N ) THEN
194         CALL DSYTRI( UPLO, N, A, LDA, IPIV, WORK, INFO )
195      ELSE
196         CALL DSYTRI2X( UPLO, N, A, LDA, IPIV, WORK, NBMAX, INFO )
197      END IF
198      RETURN
199*
200*     End of DSYTRI2
201*
202      END
203