Annotation of rpl/lapack/lapack/dtrti2.f, revision 1.17
1.11 bertrand 1: *> \brief \b DTRTI2 computes the inverse of a triangular matrix (unblocked algorithm).
1.8 bertrand 2: *
3: * =========== DOCUMENTATION ===========
4: *
1.15 bertrand 5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
1.8 bertrand 7: *
8: *> \htmlonly
1.15 bertrand 9: *> Download DTRTI2 + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dtrti2.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dtrti2.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dtrti2.f">
1.8 bertrand 15: *> [TXT]</a>
1.15 bertrand 16: *> \endhtmlonly
1.8 bertrand 17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE DTRTI2( UPLO, DIAG, N, A, LDA, INFO )
1.15 bertrand 22: *
1.8 bertrand 23: * .. Scalar Arguments ..
24: * CHARACTER DIAG, UPLO
25: * INTEGER INFO, LDA, N
26: * ..
27: * .. Array Arguments ..
28: * DOUBLE PRECISION A( LDA, * )
29: * ..
1.15 bertrand 30: *
1.8 bertrand 31: *
32: *> \par Purpose:
33: * =============
34: *>
35: *> \verbatim
36: *>
37: *> DTRTI2 computes the inverse of a real upper or lower triangular
38: *> matrix.
39: *>
40: *> This is the Level 2 BLAS version of the algorithm.
41: *> \endverbatim
42: *
43: * Arguments:
44: * ==========
45: *
46: *> \param[in] UPLO
47: *> \verbatim
48: *> UPLO is CHARACTER*1
49: *> Specifies whether the matrix A is upper or lower triangular.
50: *> = 'U': Upper triangular
51: *> = 'L': Lower triangular
52: *> \endverbatim
53: *>
54: *> \param[in] DIAG
55: *> \verbatim
56: *> DIAG is CHARACTER*1
57: *> Specifies whether or not the matrix A is unit triangular.
58: *> = 'N': Non-unit triangular
59: *> = 'U': Unit triangular
60: *> \endverbatim
61: *>
62: *> \param[in] N
63: *> \verbatim
64: *> N is INTEGER
65: *> The order of the matrix A. N >= 0.
66: *> \endverbatim
67: *>
68: *> \param[in,out] A
69: *> \verbatim
70: *> A is DOUBLE PRECISION array, dimension (LDA,N)
71: *> On entry, the triangular matrix A. If UPLO = 'U', the
72: *> leading n by n upper triangular part of the array A contains
73: *> the upper triangular matrix, and the strictly lower
74: *> triangular part of A is not referenced. If UPLO = 'L', the
75: *> leading n by n lower triangular part of the array A contains
76: *> the lower triangular matrix, and the strictly upper
77: *> triangular part of A is not referenced. If DIAG = 'U', the
78: *> diagonal elements of A are also not referenced and are
79: *> assumed to be 1.
80: *>
81: *> On exit, the (triangular) inverse of the original matrix, in
82: *> the same storage format.
83: *> \endverbatim
84: *>
85: *> \param[in] LDA
86: *> \verbatim
87: *> LDA is INTEGER
88: *> The leading dimension of the array A. LDA >= max(1,N).
89: *> \endverbatim
90: *>
91: *> \param[out] INFO
92: *> \verbatim
93: *> INFO is INTEGER
94: *> = 0: successful exit
95: *> < 0: if INFO = -k, the k-th argument had an illegal value
96: *> \endverbatim
97: *
98: * Authors:
99: * ========
100: *
1.15 bertrand 101: *> \author Univ. of Tennessee
102: *> \author Univ. of California Berkeley
103: *> \author Univ. of Colorado Denver
104: *> \author NAG Ltd.
1.8 bertrand 105: *
1.15 bertrand 106: *> \date December 2016
1.8 bertrand 107: *
108: *> \ingroup doubleOTHERcomputational
109: *
110: * =====================================================================
1.1 bertrand 111: SUBROUTINE DTRTI2( UPLO, DIAG, N, A, LDA, INFO )
112: *
1.15 bertrand 113: * -- LAPACK computational routine (version 3.7.0) --
1.1 bertrand 114: * -- LAPACK is a software package provided by Univ. of Tennessee, --
115: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.15 bertrand 116: * December 2016
1.1 bertrand 117: *
118: * .. Scalar Arguments ..
119: CHARACTER DIAG, UPLO
120: INTEGER INFO, LDA, N
121: * ..
122: * .. Array Arguments ..
123: DOUBLE PRECISION A( LDA, * )
124: * ..
125: *
126: * =====================================================================
127: *
128: * .. Parameters ..
129: DOUBLE PRECISION ONE
130: PARAMETER ( ONE = 1.0D+0 )
131: * ..
132: * .. Local Scalars ..
133: LOGICAL NOUNIT, UPPER
134: INTEGER J
135: DOUBLE PRECISION AJJ
136: * ..
137: * .. External Functions ..
138: LOGICAL LSAME
139: EXTERNAL LSAME
140: * ..
141: * .. External Subroutines ..
142: EXTERNAL DSCAL, DTRMV, XERBLA
143: * ..
144: * .. Intrinsic Functions ..
145: INTRINSIC MAX
146: * ..
147: * .. Executable Statements ..
148: *
149: * Test the input parameters.
150: *
151: INFO = 0
152: UPPER = LSAME( UPLO, 'U' )
153: NOUNIT = LSAME( DIAG, 'N' )
154: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
155: INFO = -1
156: ELSE IF( .NOT.NOUNIT .AND. .NOT.LSAME( DIAG, 'U' ) ) THEN
157: INFO = -2
158: ELSE IF( N.LT.0 ) THEN
159: INFO = -3
160: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
161: INFO = -5
162: END IF
163: IF( INFO.NE.0 ) THEN
164: CALL XERBLA( 'DTRTI2', -INFO )
165: RETURN
166: END IF
167: *
168: IF( UPPER ) THEN
169: *
170: * Compute inverse of upper triangular matrix.
171: *
172: DO 10 J = 1, N
173: IF( NOUNIT ) THEN
174: A( J, J ) = ONE / A( J, J )
175: AJJ = -A( J, J )
176: ELSE
177: AJJ = -ONE
178: END IF
179: *
180: * Compute elements 1:j-1 of j-th column.
181: *
182: CALL DTRMV( 'Upper', 'No transpose', DIAG, J-1, A, LDA,
183: $ A( 1, J ), 1 )
184: CALL DSCAL( J-1, AJJ, A( 1, J ), 1 )
185: 10 CONTINUE
186: ELSE
187: *
188: * Compute inverse of lower triangular matrix.
189: *
190: DO 20 J = N, 1, -1
191: IF( NOUNIT ) THEN
192: A( J, J ) = ONE / A( J, J )
193: AJJ = -A( J, J )
194: ELSE
195: AJJ = -ONE
196: END IF
197: IF( J.LT.N ) THEN
198: *
199: * Compute elements j+1:n of j-th column.
200: *
201: CALL DTRMV( 'Lower', 'No transpose', DIAG, N-J,
202: $ A( J+1, J+1 ), LDA, A( J+1, J ), 1 )
203: CALL DSCAL( N-J, AJJ, A( J+1, J ), 1 )
204: END IF
205: 20 CONTINUE
206: END IF
207: *
208: RETURN
209: *
210: * End of DTRTI2
211: *
212: END
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