LAPACK  3.10.0 LAPACK: Linear Algebra PACKage
dtrtri.f
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1 *> \brief \b DTRTRI
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
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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
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine dtrsm(SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
DTRSM
Definition: dtrsm.f:181
subroutine dtrmm(SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
DTRMM
Definition: dtrmm.f:177
subroutine dtrti2(UPLO, DIAG, N, A, LDA, INFO)
DTRTI2 computes the inverse of a triangular matrix (unblocked algorithm).
Definition: dtrti2.f:110
subroutine dtrtri(UPLO, DIAG, N, A, LDA, INFO)
DTRTRI
Definition: dtrtri.f:109