summaryrefslogtreecommitdiff
path: root/SRC/cpotrf2.f
blob: 789843c41dcb791a1ee6db52e54e3a4034c4b519 (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
*> \brief \b CPOTRF2
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
*  Definition:
*  ===========
*
*       RECURSIVE SUBROUTINE CPOTRF2( UPLO, N, A, LDA, INFO )
*
*       .. Scalar Arguments ..
*       CHARACTER          UPLO
*       INTEGER            INFO, LDA, N
*       ..
*       .. Array Arguments ..
*       COMPLEX            A( LDA, * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> CPOTRF2 computes the Cholesky factorization of a real symmetric
*> positive definite matrix A using the recursive algorithm.
*>
*> The factorization has the form
*>    A = U**H * U,  if UPLO = 'U', or
*>    A = L  * L**H,  if UPLO = 'L',
*> where U is an upper triangular matrix and L is lower triangular.
*>
*> This is the recursive version of the algorithm. It divides
*> the matrix into four submatrices:
*>
*>        [  A11 | A12  ]  where A11 is n1 by n1 and A22 is n2 by n2
*>    A = [ -----|----- ]  with n1 = n/2
*>        [  A21 | A22  ]       n2 = n-n1
*>
*> The subroutine calls itself to factor A11. Update and scale A21
*> or A12, update A22 then calls itself to factor A22.
*>
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] UPLO
*> \verbatim
*>          UPLO is CHARACTER*1
*>          = 'U':  Upper triangle of A is stored;
*>          = 'L':  Lower triangle of A is stored.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>          The order of the matrix A.  N >= 0.
*> \endverbatim
*>
*> \param[in,out] A
*> \verbatim
*>          A is COMPLEX array, dimension (LDA,N)
*>          On entry, the symmetric matrix A.  If UPLO = 'U', the leading
*>          N-by-N upper triangular part of A contains the upper
*>          triangular part of the matrix A, and the strictly lower
*>          triangular part of A is not referenced.  If UPLO = 'L', the
*>          leading N-by-N lower triangular part of A contains the lower
*>          triangular part of the matrix A, and the strictly upper
*>          triangular part of A is not referenced.
*>
*>          On exit, if INFO = 0, the factor U or L from the Cholesky
*>          factorization A = U**H*U or A = L*L**H.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*>          LDA is INTEGER
*>          The leading dimension of the array A.  LDA >= max(1,N).
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*>          INFO is INTEGER
*>          = 0:  successful exit
*>          < 0:  if INFO = -i, the i-th argument had an illegal value
*>          > 0:  if INFO = i, the leading minor of order i is not
*>                positive definite, and the factorization could not be
*>                completed.
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date June 2016
*
*> \ingroup complexPOcomputational
*
*  =====================================================================
      RECURSIVE SUBROUTINE CPOTRF2( UPLO, N, A, LDA, INFO )
*
*  -- LAPACK computational routine (version 3.7.0) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     June 2016
*
*     .. Scalar Arguments ..
      CHARACTER          UPLO
      INTEGER            INFO, LDA, N
*     ..
*     .. Array Arguments ..
      COMPLEX            A( LDA, * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      REAL               ONE, ZERO
      PARAMETER          ( ONE = 1.0E+0, ZERO = 0.0E+0 )
      COMPLEX            CONE
      PARAMETER          ( CONE = (1.0E+0, 0.0E+0) )
*     ..
*     .. Local Scalars ..
      LOGICAL            UPPER
      INTEGER            N1, N2, IINFO
      REAL               AJJ
*     ..
*     .. External Functions ..
      LOGICAL            LSAME, SISNAN
      EXTERNAL           LSAME, SISNAN
*     ..
*     .. External Subroutines ..
      EXTERNAL           CHERK, CTRSM, XERBLA
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          MAX, REAL, SQRT
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters
*
      INFO = 0
      UPPER = LSAME( UPLO, 'U' )
      IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
         INFO = -1
      ELSE IF( N.LT.0 ) THEN
         INFO = -2
      ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
         INFO = -4
      END IF
      IF( INFO.NE.0 ) THEN
         CALL XERBLA( 'CPOTRF2', -INFO )
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( N.EQ.0 )
     $   RETURN
*
*     N=1 case
*
      IF( N.EQ.1 ) THEN
*
*        Test for non-positive-definiteness
*
         AJJ = REAL( A( 1, 1 ) )
         IF( AJJ.LE.ZERO.OR.SISNAN( AJJ ) ) THEN
            INFO = 1
            RETURN
         END IF
*
*        Factor
*
         A( 1, 1 ) = SQRT( AJJ )
*
*     Use recursive code
*
      ELSE
         N1 = N/2
         N2 = N-N1
*
*        Factor A11
*
         CALL CPOTRF2( UPLO, N1, A( 1, 1 ), LDA, IINFO )
         IF ( IINFO.NE.0 ) THEN
            INFO = IINFO
            RETURN
         END IF
*
*        Compute the Cholesky factorization A = U**H*U
*
         IF( UPPER ) THEN
*
*           Update and scale A12
*
            CALL CTRSM( 'L', 'U', 'C', 'N', N1, N2, CONE,
     $                  A( 1, 1 ), LDA, A( 1, N1+1 ), LDA )
*
*           Update and factor A22
*
            CALL CHERK( UPLO, 'C', N2, N1, -ONE, A( 1, N1+1 ), LDA,
     $                  ONE, A( N1+1, N1+1 ), LDA )
*
            CALL CPOTRF2( UPLO, N2, A( N1+1, N1+1 ), LDA, IINFO )
*
            IF ( IINFO.NE.0 ) THEN
               INFO = IINFO + N1
               RETURN
            END IF
*
*        Compute the Cholesky factorization A = L*L**H
*
         ELSE
*
*           Update and scale A21
*
            CALL CTRSM( 'R', 'L', 'C', 'N', N2, N1, CONE,
     $                  A( 1, 1 ), LDA, A( N1+1, 1 ), LDA )
*
*           Update and factor A22
*
            CALL CHERK( UPLO, 'N', N2, N1, -ONE, A( N1+1, 1 ), LDA,
     $                  ONE, A( N1+1, N1+1 ), LDA )
*
            CALL CPOTRF2( UPLO, N2, A( N1+1, N1+1 ), LDA, IINFO )
*
            IF ( IINFO.NE.0 ) THEN
               INFO = IINFO + N1
               RETURN
            END IF
*
         END IF
      END IF
      RETURN
*
*     End of CPOTRF2
*
      END