1*> \brief \b DTRTRI
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 DTRTRI( UPLO, DIAG, N, A, LDA, INFO )
22*
23*       .. Scalar Arguments ..
24*       CHARACTER          DIAG, UPLO
25*       INTEGER            INFO, LDA, N
26*       ..
27*       .. Array Arguments ..
28*       DOUBLE PRECISION   A( LDA, * )
29*       ..
30*
31*
32*> \par Purpose:
33*  =============
34*>
35*> \verbatim
36*>
37*> DTRTRI computes the inverse of a real upper or lower triangular
38*> matrix A.
39*>
40*> This is the Level 3 BLAS version of the algorithm.
41*> \endverbatim
42*
43*  Arguments:
44*  ==========
45*
46*> \param[in] UPLO
47*> \verbatim
48*>          UPLO is CHARACTER*1
49*>          = 'U':  A is upper triangular;
50*>          = 'L':  A is lower triangular.
51*> \endverbatim
52*>
53*> \param[in] DIAG
54*> \verbatim
55*>          DIAG is CHARACTER*1
56*>          = 'N':  A is non-unit triangular;
57*>          = 'U':  A is unit triangular.
58*> \endverbatim
59*>
60*> \param[in] N
61*> \verbatim
62*>          N is INTEGER
63*>          The order of the matrix A.  N >= 0.
64*> \endverbatim
65*>
66*> \param[in,out] A
67*> \verbatim
68*>          A is DOUBLE PRECISION array, dimension (LDA,N)
69*>          On entry, the triangular matrix A.  If UPLO = 'U', the
70*>          leading N-by-N upper triangular part of the array A contains
71*>          the upper triangular matrix, and the strictly lower
72*>          triangular part of A is not referenced.  If UPLO = 'L', the
73*>          leading N-by-N lower triangular part of the array A contains
74*>          the lower triangular matrix, and the strictly upper
75*>          triangular part of A is not referenced.  If DIAG = 'U', the
76*>          diagonal elements of A are also not referenced and are
77*>          assumed to be 1.
78*>          On exit, the (triangular) inverse of the original matrix, in
79*>          the same storage format.
80*> \endverbatim
81*>
82*> \param[in] LDA
83*> \verbatim
84*>          LDA is INTEGER
85*>          The leading dimension of the array A.  LDA >= max(1,N).
86*> \endverbatim
87*>
88*> \param[out] INFO
89*> \verbatim
90*>          INFO is INTEGER
91*>          = 0: successful exit
92*>          < 0: if INFO = -i, the i-th argument had an illegal value
93*>          > 0: if INFO = i, A(i,i) is exactly zero.  The triangular
94*>               matrix is singular and its inverse can not be computed.
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 doubleOTHERcomputational
106*
107*  =====================================================================
108      SUBROUTINE DTRTRI( UPLO, DIAG, N, A, LDA, INFO )
109*
110*  -- LAPACK computational routine --
111*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
112*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
113*
114*     .. Scalar Arguments ..
115      CHARACTER          DIAG, UPLO
116      INTEGER            INFO, LDA, N
117*     ..
118*     .. Array Arguments ..
119      DOUBLE PRECISION   A( LDA, * )
120*     ..
121*
122*  =====================================================================
123*
124*     .. Parameters ..
125      DOUBLE PRECISION   ONE, ZERO
126      PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
127*     ..
128*     .. Local Scalars ..
129      LOGICAL            NOUNIT, UPPER
130      INTEGER            J, JB, NB, NN
131*     ..
132*     .. External Functions ..
133      LOGICAL            LSAME
134      INTEGER            ILAENV
135      EXTERNAL           LSAME, ILAENV
136*     ..
137*     .. External Subroutines ..
138      EXTERNAL           DTRMM, DTRSM, DTRTI2, XERBLA
139*     ..
140*     .. Intrinsic Functions ..
141      INTRINSIC          MAX, MIN
142*     ..
143*     .. Executable Statements ..
144*
145*     Test the input parameters.
146*
147      INFO = 0
148      UPPER = LSAME( UPLO, 'U' )
149      NOUNIT = LSAME( DIAG, 'N' )
150      IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
151         INFO = -1
152      ELSE IF( .NOT.NOUNIT .AND. .NOT.LSAME( DIAG, 'U' ) ) THEN
153         INFO = -2
154      ELSE IF( N.LT.0 ) THEN
155         INFO = -3
156      ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
157         INFO = -5
158      END IF
159      IF( INFO.NE.0 ) THEN
160         CALL XERBLA( 'DTRTRI', -INFO )
161         RETURN
162      END IF
163*
164*     Quick return if possible
165*
166      IF( N.EQ.0 )
167     $   RETURN
168*
169*     Check for singularity if non-unit.
170*
171      IF( NOUNIT ) THEN
172         DO 10 INFO = 1, N
173            IF( A( INFO, INFO ).EQ.ZERO )
174     $         RETURN
175   10    CONTINUE
176         INFO = 0
177      END IF
178*
179*     Determine the block size for this environment.
180*
181      NB = ILAENV( 1, 'DTRTRI', UPLO // DIAG, N, -1, -1, -1 )
182      IF( NB.LE.1 .OR. NB.GE.N ) THEN
183*
184*        Use unblocked code
185*
186         CALL DTRTI2( UPLO, DIAG, N, A, LDA, INFO )
187      ELSE
188*
189*        Use blocked code
190*
191         IF( UPPER ) THEN
192*
193*           Compute inverse of upper triangular matrix
194*
195            DO 20 J = 1, N, NB
196               JB = MIN( NB, N-J+1 )
197*
198*              Compute rows 1:j-1 of current block column
199*
200               CALL DTRMM( 'Left', 'Upper', 'No transpose', DIAG, J-1,
201     $                     JB, ONE, A, LDA, A( 1, J ), LDA )
202               CALL DTRSM( 'Right', 'Upper', 'No transpose', DIAG, J-1,
203     $                     JB, -ONE, A( J, J ), LDA, A( 1, J ), LDA )
204*
205*              Compute inverse of current diagonal block
206*
207               CALL DTRTI2( 'Upper', DIAG, JB, A( J, J ), LDA, INFO )
208   20       CONTINUE
209         ELSE
210*
211*           Compute inverse of lower triangular matrix
212*
213            NN = ( ( N-1 ) / NB )*NB + 1
214            DO 30 J = NN, 1, -NB
215               JB = MIN( NB, N-J+1 )
216               IF( J+JB.LE.N ) THEN
217*
218*                 Compute rows j+jb:n of current block column
219*
220                  CALL DTRMM( 'Left', 'Lower', 'No transpose', DIAG,
221     $                        N-J-JB+1, JB, ONE, A( J+JB, J+JB ), LDA,
222     $                        A( J+JB, J ), LDA )
223                  CALL DTRSM( 'Right', 'Lower', 'No transpose', DIAG,
224     $                        N-J-JB+1, JB, -ONE, A( J, J ), LDA,
225     $                        A( J+JB, J ), LDA )
226               END IF
227*
228*              Compute inverse of current diagonal block
229*
230               CALL DTRTI2( 'Lower', DIAG, JB, A( J, J ), LDA, INFO )
231   30       CONTINUE
232         END IF
233      END IF
234*
235      RETURN
236*
237*     End of DTRTRI
238*
239      END
240