LAPACK  3.10.0
LAPACK: Linear Algebra PACKage
ztrtri.f
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1 *> \brief \b ZTRTRI
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
8 *> \htmlonly
9 *> Download ZTRTRI + dependencies
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13 *> [ZIP]</a>
14 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ztrtri.f">
15 *> [TXT]</a>
16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE ZTRTRI( UPLO, DIAG, N, A, LDA, INFO )
22 *
23 * .. Scalar Arguments ..
24 * CHARACTER DIAG, UPLO
25 * INTEGER INFO, LDA, N
26 * ..
27 * .. Array Arguments ..
28 * COMPLEX*16 A( LDA, * )
29 * ..
30 *
31 *
32 *> \par Purpose:
33 * =============
34 *>
35 *> \verbatim
36 *>
37 *> ZTRTRI computes the inverse of a complex 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 COMPLEX*16 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 complex16OTHERcomputational
106 *
107 * =====================================================================
108  SUBROUTINE ztrtri( 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  COMPLEX*16 A( LDA, * )
120 * ..
121 *
122 * =====================================================================
123 *
124 * .. Parameters ..
125  COMPLEX*16 ONE, ZERO
126  parameter( one = ( 1.0d+0, 0.0d+0 ),
127  $ zero = ( 0.0d+0, 0.0d+0 ) )
128 * ..
129 * .. Local Scalars ..
130  LOGICAL NOUNIT, UPPER
131  INTEGER J, JB, NB, NN
132 * ..
133 * .. External Functions ..
134  LOGICAL LSAME
135  INTEGER ILAENV
136  EXTERNAL lsame, ilaenv
137 * ..
138 * .. External Subroutines ..
139  EXTERNAL xerbla, ztrmm, ztrsm, ztrti2
140 * ..
141 * .. Intrinsic Functions ..
142  INTRINSIC max, min
143 * ..
144 * .. Executable Statements ..
145 *
146 * Test the input parameters.
147 *
148  info = 0
149  upper = lsame( uplo, 'U' )
150  nounit = lsame( diag, 'N' )
151  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
152  info = -1
153  ELSE IF( .NOT.nounit .AND. .NOT.lsame( diag, 'U' ) ) THEN
154  info = -2
155  ELSE IF( n.LT.0 ) THEN
156  info = -3
157  ELSE IF( lda.LT.max( 1, n ) ) THEN
158  info = -5
159  END IF
160  IF( info.NE.0 ) THEN
161  CALL xerbla( 'ZTRTRI', -info )
162  RETURN
163  END IF
164 *
165 * Quick return if possible
166 *
167  IF( n.EQ.0 )
168  $ RETURN
169 *
170 * Check for singularity if non-unit.
171 *
172  IF( nounit ) THEN
173  DO 10 info = 1, n
174  IF( a( info, info ).EQ.zero )
175  $ RETURN
176  10 CONTINUE
177  info = 0
178  END IF
179 *
180 * Determine the block size for this environment.
181 *
182  nb = ilaenv( 1, 'ZTRTRI', uplo // diag, n, -1, -1, -1 )
183  IF( nb.LE.1 .OR. nb.GE.n ) THEN
184 *
185 * Use unblocked code
186 *
187  CALL ztrti2( uplo, diag, n, a, lda, info )
188  ELSE
189 *
190 * Use blocked code
191 *
192  IF( upper ) THEN
193 *
194 * Compute inverse of upper triangular matrix
195 *
196  DO 20 j = 1, n, nb
197  jb = min( nb, n-j+1 )
198 *
199 * Compute rows 1:j-1 of current block column
200 *
201  CALL ztrmm( 'Left', 'Upper', 'No transpose', diag, j-1,
202  $ jb, one, a, lda, a( 1, j ), lda )
203  CALL ztrsm( 'Right', 'Upper', 'No transpose', diag, j-1,
204  $ jb, -one, a( j, j ), lda, a( 1, j ), lda )
205 *
206 * Compute inverse of current diagonal block
207 *
208  CALL ztrti2( 'Upper', diag, jb, a( j, j ), lda, info )
209  20 CONTINUE
210  ELSE
211 *
212 * Compute inverse of lower triangular matrix
213 *
214  nn = ( ( n-1 ) / nb )*nb + 1
215  DO 30 j = nn, 1, -nb
216  jb = min( nb, n-j+1 )
217  IF( j+jb.LE.n ) THEN
218 *
219 * Compute rows j+jb:n of current block column
220 *
221  CALL ztrmm( 'Left', 'Lower', 'No transpose', diag,
222  $ n-j-jb+1, jb, one, a( j+jb, j+jb ), lda,
223  $ a( j+jb, j ), lda )
224  CALL ztrsm( 'Right', 'Lower', 'No transpose', diag,
225  $ n-j-jb+1, jb, -one, a( j, j ), lda,
226  $ a( j+jb, j ), lda )
227  END IF
228 *
229 * Compute inverse of current diagonal block
230 *
231  CALL ztrti2( 'Lower', diag, jb, a( j, j ), lda, info )
232  30 CONTINUE
233  END IF
234  END IF
235 *
236  RETURN
237 *
238 * End of ZTRTRI
239 *
240  END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine ztrsm(SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
ZTRSM
Definition: ztrsm.f:180
subroutine ztrmm(SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
ZTRMM
Definition: ztrmm.f:177
subroutine ztrti2(UPLO, DIAG, N, A, LDA, INFO)
ZTRTI2 computes the inverse of a triangular matrix (unblocked algorithm).
Definition: ztrti2.f:110
subroutine ztrtri(UPLO, DIAG, N, A, LDA, INFO)
ZTRTRI
Definition: ztrtri.f:109