LAPACK  3.10.0
LAPACK: Linear Algebra PACKage
ctptri.f
Go to the documentation of this file.
1 *> \brief \b CTPTRI
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
8 *> \htmlonly
9 *> Download CTPTRI + dependencies
10 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ctptri.f">
11 *> [TGZ]</a>
12 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ctptri.f">
13 *> [ZIP]</a>
14 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ctptri.f">
15 *> [TXT]</a>
16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE CTPTRI( UPLO, DIAG, N, AP, INFO )
22 *
23 * .. Scalar Arguments ..
24 * CHARACTER DIAG, UPLO
25 * INTEGER INFO, N
26 * ..
27 * .. Array Arguments ..
28 * COMPLEX AP( * )
29 * ..
30 *
31 *
32 *> \par Purpose:
33 * =============
34 *>
35 *> \verbatim
36 *>
37 *> CTPTRI computes the inverse of a complex upper or lower triangular
38 *> matrix A stored in packed format.
39 *> \endverbatim
40 *
41 * Arguments:
42 * ==========
43 *
44 *> \param[in] UPLO
45 *> \verbatim
46 *> UPLO is CHARACTER*1
47 *> = 'U': A is upper triangular;
48 *> = 'L': A is lower triangular.
49 *> \endverbatim
50 *>
51 *> \param[in] DIAG
52 *> \verbatim
53 *> DIAG is CHARACTER*1
54 *> = 'N': A is non-unit triangular;
55 *> = 'U': A is unit triangular.
56 *> \endverbatim
57 *>
58 *> \param[in] N
59 *> \verbatim
60 *> N is INTEGER
61 *> The order of the matrix A. N >= 0.
62 *> \endverbatim
63 *>
64 *> \param[in,out] AP
65 *> \verbatim
66 *> AP is COMPLEX array, dimension (N*(N+1)/2)
67 *> On entry, the upper or lower triangular matrix A, stored
68 *> columnwise in a linear array. The j-th column of A is stored
69 *> in the array AP as follows:
70 *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
71 *> if UPLO = 'L', AP(i + (j-1)*((2*n-j)/2) = A(i,j) for j<=i<=n.
72 *> See below for further details.
73 *> On exit, the (triangular) inverse of the original matrix, in
74 *> the same packed storage format.
75 *> \endverbatim
76 *>
77 *> \param[out] INFO
78 *> \verbatim
79 *> INFO is INTEGER
80 *> = 0: successful exit
81 *> < 0: if INFO = -i, the i-th argument had an illegal value
82 *> > 0: if INFO = i, A(i,i) is exactly zero. The triangular
83 *> matrix is singular and its inverse can not be computed.
84 *> \endverbatim
85 *
86 * Authors:
87 * ========
88 *
89 *> \author Univ. of Tennessee
90 *> \author Univ. of California Berkeley
91 *> \author Univ. of Colorado Denver
92 *> \author NAG Ltd.
93 *
94 *> \ingroup complexOTHERcomputational
95 *
96 *> \par Further Details:
97 * =====================
98 *>
99 *> \verbatim
100 *>
101 *> A triangular matrix A can be transferred to packed storage using one
102 *> of the following program segments:
103 *>
104 *> UPLO = 'U': UPLO = 'L':
105 *>
106 *> JC = 1 JC = 1
107 *> DO 2 J = 1, N DO 2 J = 1, N
108 *> DO 1 I = 1, J DO 1 I = J, N
109 *> AP(JC+I-1) = A(I,J) AP(JC+I-J) = A(I,J)
110 *> 1 CONTINUE 1 CONTINUE
111 *> JC = JC + J JC = JC + N - J + 1
112 *> 2 CONTINUE 2 CONTINUE
113 *> \endverbatim
114 *>
115 * =====================================================================
116  SUBROUTINE ctptri( UPLO, DIAG, N, AP, INFO )
117 *
118 * -- LAPACK computational routine --
119 * -- LAPACK is a software package provided by Univ. of Tennessee, --
120 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
121 *
122 * .. Scalar Arguments ..
123  CHARACTER DIAG, UPLO
124  INTEGER INFO, N
125 * ..
126 * .. Array Arguments ..
127  COMPLEX AP( * )
128 * ..
129 *
130 * =====================================================================
131 *
132 * .. Parameters ..
133  COMPLEX ONE, ZERO
134  parameter( one = ( 1.0e+0, 0.0e+0 ),
135  $ zero = ( 0.0e+0, 0.0e+0 ) )
136 * ..
137 * .. Local Scalars ..
138  LOGICAL NOUNIT, UPPER
139  INTEGER J, JC, JCLAST, JJ
140  COMPLEX AJJ
141 * ..
142 * .. External Functions ..
143  LOGICAL LSAME
144  EXTERNAL lsame
145 * ..
146 * .. External Subroutines ..
147  EXTERNAL cscal, ctpmv, xerbla
148 * ..
149 * .. Executable Statements ..
150 *
151 * Test the input parameters.
152 *
153  info = 0
154  upper = lsame( uplo, 'U' )
155  nounit = lsame( diag, 'N' )
156  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
157  info = -1
158  ELSE IF( .NOT.nounit .AND. .NOT.lsame( diag, 'U' ) ) THEN
159  info = -2
160  ELSE IF( n.LT.0 ) THEN
161  info = -3
162  END IF
163  IF( info.NE.0 ) THEN
164  CALL xerbla( 'CTPTRI', -info )
165  RETURN
166  END IF
167 *
168 * Check for singularity if non-unit.
169 *
170  IF( nounit ) THEN
171  IF( upper ) THEN
172  jj = 0
173  DO 10 info = 1, n
174  jj = jj + info
175  IF( ap( jj ).EQ.zero )
176  $ RETURN
177  10 CONTINUE
178  ELSE
179  jj = 1
180  DO 20 info = 1, n
181  IF( ap( jj ).EQ.zero )
182  $ RETURN
183  jj = jj + n - info + 1
184  20 CONTINUE
185  END IF
186  info = 0
187  END IF
188 *
189  IF( upper ) THEN
190 *
191 * Compute inverse of upper triangular matrix.
192 *
193  jc = 1
194  DO 30 j = 1, n
195  IF( nounit ) THEN
196  ap( jc+j-1 ) = one / ap( jc+j-1 )
197  ajj = -ap( jc+j-1 )
198  ELSE
199  ajj = -one
200  END IF
201 *
202 * Compute elements 1:j-1 of j-th column.
203 *
204  CALL ctpmv( 'Upper', 'No transpose', diag, j-1, ap,
205  $ ap( jc ), 1 )
206  CALL cscal( j-1, ajj, ap( jc ), 1 )
207  jc = jc + j
208  30 CONTINUE
209 *
210  ELSE
211 *
212 * Compute inverse of lower triangular matrix.
213 *
214  jc = n*( n+1 ) / 2
215  DO 40 j = n, 1, -1
216  IF( nounit ) THEN
217  ap( jc ) = one / ap( jc )
218  ajj = -ap( jc )
219  ELSE
220  ajj = -one
221  END IF
222  IF( j.LT.n ) THEN
223 *
224 * Compute elements j+1:n of j-th column.
225 *
226  CALL ctpmv( 'Lower', 'No transpose', diag, n-j,
227  $ ap( jclast ), ap( jc+1 ), 1 )
228  CALL cscal( n-j, ajj, ap( jc+1 ), 1 )
229  END IF
230  jclast = jc
231  jc = jc - n + j - 2
232  40 CONTINUE
233  END IF
234 *
235  RETURN
236 *
237 * End of CTPTRI
238 *
239  END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine cscal(N, CA, CX, INCX)
CSCAL
Definition: cscal.f:78
subroutine ctpmv(UPLO, TRANS, DIAG, N, AP, X, INCX)
CTPMV
Definition: ctpmv.f:142
subroutine ctptri(UPLO, DIAG, N, AP, INFO)
CTPTRI
Definition: ctptri.f:117