LAPACK  3.4.2 LAPACK: Linear Algebra PACKage
dtptri.f
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1 *> \brief \b DTPTRI
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
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15 *> [TXT]</a>
16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE DTPTRI( UPLO, DIAG, N, AP, INFO )
22 *
23 * .. Scalar Arguments ..
24 * CHARACTER DIAG, UPLO
25 * INTEGER INFO, N
26 * ..
27 * .. Array Arguments ..
28 * DOUBLE PRECISION AP( * )
29 * ..
30 *
31 *
32 *> \par Purpose:
33 * =============
34 *>
35 *> \verbatim
36 *>
37 *> DTPTRI computes the inverse of a real 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 DOUBLE PRECISION 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 *> \date November 2011
95 *
96 *> \ingroup doubleOTHERcomputational
97 *
98 *> \par Further Details:
99 * =====================
100 *>
101 *> \verbatim
102 *>
103 *> A triangular matrix A can be transferred to packed storage using one
104 *> of the following program segments:
105 *>
106 *> UPLO = 'U': UPLO = 'L':
107 *>
108 *> JC = 1 JC = 1
109 *> DO 2 J = 1, N DO 2 J = 1, N
110 *> DO 1 I = 1, J DO 1 I = J, N
111 *> AP(JC+I-1) = A(I,J) AP(JC+I-J) = A(I,J)
112 *> 1 CONTINUE 1 CONTINUE
113 *> JC = JC + J JC = JC + N - J + 1
114 *> 2 CONTINUE 2 CONTINUE
115 *> \endverbatim
116 *>
117 * =====================================================================
118  SUBROUTINE dtptri( UPLO, DIAG, N, AP, INFO )
119 *
120 * -- LAPACK computational routine (version 3.4.0) --
121 * -- LAPACK is a software package provided by Univ. of Tennessee, --
122 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
123 * November 2011
124 *
125 * .. Scalar Arguments ..
126  CHARACTER diag, uplo
127  INTEGER info, n
128 * ..
129 * .. Array Arguments ..
130  DOUBLE PRECISION ap( * )
131 * ..
132 *
133 * =====================================================================
134 *
135 * .. Parameters ..
136  DOUBLE PRECISION one, zero
137  parameter( one = 1.0d+0, zero = 0.0d+0 )
138 * ..
139 * .. Local Scalars ..
140  LOGICAL nounit, upper
141  INTEGER j, jc, jclast, jj
142  DOUBLE PRECISION ajj
143 * ..
144 * .. External Functions ..
145  LOGICAL lsame
146  EXTERNAL lsame
147 * ..
148 * .. External Subroutines ..
149  EXTERNAL dscal, dtpmv, xerbla
150 * ..
151 * .. Executable Statements ..
152 *
153 * Test the input parameters.
154 *
155  info = 0
156  upper = lsame( uplo, 'U' )
157  nounit = lsame( diag, 'N' )
158  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
159  info = -1
160  ELSE IF( .NOT.nounit .AND. .NOT.lsame( diag, 'U' ) ) THEN
161  info = -2
162  ELSE IF( n.LT.0 ) THEN
163  info = -3
164  END IF
165  IF( info.NE.0 ) THEN
166  CALL xerbla( 'DTPTRI', -info )
167  return
168  END IF
169 *
170 * Check for singularity if non-unit.
171 *
172  IF( nounit ) THEN
173  IF( upper ) THEN
174  jj = 0
175  DO 10 info = 1, n
176  jj = jj + info
177  IF( ap( jj ).EQ.zero )
178  \$ return
179  10 continue
180  ELSE
181  jj = 1
182  DO 20 info = 1, n
183  IF( ap( jj ).EQ.zero )
184  \$ return
185  jj = jj + n - info + 1
186  20 continue
187  END IF
188  info = 0
189  END IF
190 *
191  IF( upper ) THEN
192 *
193 * Compute inverse of upper triangular matrix.
194 *
195  jc = 1
196  DO 30 j = 1, n
197  IF( nounit ) THEN
198  ap( jc+j-1 ) = one / ap( jc+j-1 )
199  ajj = -ap( jc+j-1 )
200  ELSE
201  ajj = -one
202  END IF
203 *
204 * Compute elements 1:j-1 of j-th column.
205 *
206  CALL dtpmv( 'Upper', 'No transpose', diag, j-1, ap,
207  \$ ap( jc ), 1 )
208  CALL dscal( j-1, ajj, ap( jc ), 1 )
209  jc = jc + j
210  30 continue
211 *
212  ELSE
213 *
214 * Compute inverse of lower triangular matrix.
215 *
216  jc = n*( n+1 ) / 2
217  DO 40 j = n, 1, -1
218  IF( nounit ) THEN
219  ap( jc ) = one / ap( jc )
220  ajj = -ap( jc )
221  ELSE
222  ajj = -one
223  END IF
224  IF( j.LT.n ) THEN
225 *
226 * Compute elements j+1:n of j-th column.
227 *
228  CALL dtpmv( 'Lower', 'No transpose', diag, n-j,
229  \$ ap( jclast ), ap( jc+1 ), 1 )
230  CALL dscal( n-j, ajj, ap( jc+1 ), 1 )
231  END IF
232  jclast = jc
233  jc = jc - n + j - 2
234  40 continue
235  END IF
236 *
237  return
238 *
239 * End of DTPTRI
240 *
241  END