Annotation of rpl/lapack/lapack/dtrti2.f, revision 1.18
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: *
106: *> \ingroup doubleOTHERcomputational
107: *
108: * =====================================================================
1.1 bertrand 109: SUBROUTINE DTRTI2( UPLO, DIAG, N, A, LDA, INFO )
110: *
1.18 ! bertrand 111: * -- LAPACK computational routine --
1.1 bertrand 112: * -- LAPACK is a software package provided by Univ. of Tennessee, --
113: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
114: *
115: * .. Scalar Arguments ..
116: CHARACTER DIAG, UPLO
117: INTEGER INFO, LDA, N
118: * ..
119: * .. Array Arguments ..
120: DOUBLE PRECISION A( LDA, * )
121: * ..
122: *
123: * =====================================================================
124: *
125: * .. Parameters ..
126: DOUBLE PRECISION ONE
127: PARAMETER ( ONE = 1.0D+0 )
128: * ..
129: * .. Local Scalars ..
130: LOGICAL NOUNIT, UPPER
131: INTEGER J
132: DOUBLE PRECISION AJJ
133: * ..
134: * .. External Functions ..
135: LOGICAL LSAME
136: EXTERNAL LSAME
137: * ..
138: * .. External Subroutines ..
139: EXTERNAL DSCAL, DTRMV, XERBLA
140: * ..
141: * .. Intrinsic Functions ..
142: INTRINSIC MAX
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( 'DTRTI2', -INFO )
162: RETURN
163: END IF
164: *
165: IF( UPPER ) THEN
166: *
167: * Compute inverse of upper triangular matrix.
168: *
169: DO 10 J = 1, N
170: IF( NOUNIT ) THEN
171: A( J, J ) = ONE / A( J, J )
172: AJJ = -A( J, J )
173: ELSE
174: AJJ = -ONE
175: END IF
176: *
177: * Compute elements 1:j-1 of j-th column.
178: *
179: CALL DTRMV( 'Upper', 'No transpose', DIAG, J-1, A, LDA,
180: $ A( 1, J ), 1 )
181: CALL DSCAL( J-1, AJJ, A( 1, J ), 1 )
182: 10 CONTINUE
183: ELSE
184: *
185: * Compute inverse of lower triangular matrix.
186: *
187: DO 20 J = N, 1, -1
188: IF( NOUNIT ) THEN
189: A( J, J ) = ONE / A( J, J )
190: AJJ = -A( J, J )
191: ELSE
192: AJJ = -ONE
193: END IF
194: IF( J.LT.N ) THEN
195: *
196: * Compute elements j+1:n of j-th column.
197: *
198: CALL DTRMV( 'Lower', 'No transpose', DIAG, N-J,
199: $ A( J+1, J+1 ), LDA, A( J+1, J ), 1 )
200: CALL DSCAL( N-J, AJJ, A( J+1, J ), 1 )
201: END IF
202: 20 CONTINUE
203: END IF
204: *
205: RETURN
206: *
207: * End of DTRTI2
208: *
209: END
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