LAPACK  3.10.0
LAPACK: Linear Algebra PACKage
strti2.f
Go to the documentation of this file.
1 *> \brief \b STRTI2 computes the inverse of a triangular matrix (unblocked algorithm).
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
8 *> \htmlonly
9 *> Download STRTI2 + dependencies
10 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/strti2.f">
11 *> [TGZ]</a>
12 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/strti2.f">
13 *> [ZIP]</a>
14 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/strti2.f">
15 *> [TXT]</a>
16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE STRTI2( UPLO, DIAG, N, A, LDA, INFO )
22 *
23 * .. Scalar Arguments ..
24 * CHARACTER DIAG, UPLO
25 * INTEGER INFO, LDA, N
26 * ..
27 * .. Array Arguments ..
28 * REAL A( LDA, * )
29 * ..
30 *
31 *
32 *> \par Purpose:
33 * =============
34 *>
35 *> \verbatim
36 *>
37 *> STRTI2 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 REAL 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 *
101 *> \author Univ. of Tennessee
102 *> \author Univ. of California Berkeley
103 *> \author Univ. of Colorado Denver
104 *> \author NAG Ltd.
105 *
106 *> \ingroup realOTHERcomputational
107 *
108 * =====================================================================
109  SUBROUTINE strti2( UPLO, DIAG, N, A, LDA, INFO )
110 *
111 * -- LAPACK computational routine --
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  REAL A( LDA, * )
121 * ..
122 *
123 * =====================================================================
124 *
125 * .. Parameters ..
126  REAL ONE
127  parameter( one = 1.0e+0 )
128 * ..
129 * .. Local Scalars ..
130  LOGICAL NOUNIT, UPPER
131  INTEGER J
132  REAL AJJ
133 * ..
134 * .. External Functions ..
135  LOGICAL LSAME
136  EXTERNAL lsame
137 * ..
138 * .. External Subroutines ..
139  EXTERNAL sscal, strmv, 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( 'STRTI2', -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 strmv( 'Upper', 'No transpose', diag, j-1, a, lda,
180  $ a( 1, j ), 1 )
181  CALL sscal( 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 strmv( 'Lower', 'No transpose', diag, n-j,
199  $ a( j+1, j+1 ), lda, a( j+1, j ), 1 )
200  CALL sscal( n-j, ajj, a( j+1, j ), 1 )
201  END IF
202  20 CONTINUE
203  END IF
204 *
205  RETURN
206 *
207 * End of STRTI2
208 *
209  END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine strti2(UPLO, DIAG, N, A, LDA, INFO)
STRTI2 computes the inverse of a triangular matrix (unblocked algorithm).
Definition: strti2.f:110
subroutine sscal(N, SA, SX, INCX)
SSCAL
Definition: sscal.f:79
subroutine strmv(UPLO, TRANS, DIAG, N, A, LDA, X, INCX)
STRMV
Definition: strmv.f:147