LAPACK  3.8.0
LAPACK: Linear Algebra PACKage
dpotrf2.f
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1 *> \brief \b DPOTRF2
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
8 * Definition:
9 * ===========
10 *
11 * RECURSIVE SUBROUTINE DPOTRF2( UPLO, N, A, LDA, INFO )
12 *
13 * .. Scalar Arguments ..
14 * CHARACTER UPLO
15 * INTEGER INFO, LDA, N
16 * ..
17 * .. Array Arguments ..
18 * REAL A( LDA, * )
19 * ..
20 *
21 *
22 *> \par Purpose:
23 * =============
24 *>
25 *> \verbatim
26 *>
27 *> DPOTRF2 computes the Cholesky factorization of a real symmetric
28 *> positive definite matrix A using the recursive algorithm.
29 *>
30 *> The factorization has the form
31 *> A = U**T * U, if UPLO = 'U', or
32 *> A = L * L**T, if UPLO = 'L',
33 *> where U is an upper triangular matrix and L is lower triangular.
34 *>
35 *> This is the recursive version of the algorithm. It divides
36 *> the matrix into four submatrices:
37 *>
38 *> [ A11 | A12 ] where A11 is n1 by n1 and A22 is n2 by n2
39 *> A = [ -----|----- ] with n1 = n/2
40 *> [ A21 | A22 ] n2 = n-n1
41 *>
42 *> The subroutine calls itself to factor A11. Update and scale A21
43 *> or A12, update A22 then calls itself to factor A22.
44 *>
45 *> \endverbatim
46 *
47 * Arguments:
48 * ==========
49 *
50 *> \param[in] UPLO
51 *> \verbatim
52 *> UPLO is CHARACTER*1
53 *> = 'U': Upper triangle of A is stored;
54 *> = 'L': Lower triangle of A is stored.
55 *> \endverbatim
56 *>
57 *> \param[in] N
58 *> \verbatim
59 *> N is INTEGER
60 *> The order of the matrix A. N >= 0.
61 *> \endverbatim
62 *>
63 *> \param[in,out] A
64 *> \verbatim
65 *> A is DOUBLE PRECISION array, dimension (LDA,N)
66 *> On entry, the symmetric matrix A. If UPLO = 'U', the leading
67 *> N-by-N upper triangular part of A contains the upper
68 *> triangular part of the matrix A, and the strictly lower
69 *> triangular part of A is not referenced. If UPLO = 'L', the
70 *> leading N-by-N lower triangular part of A contains the lower
71 *> triangular part of the matrix A, and the strictly upper
72 *> triangular part of A is not referenced.
73 *>
74 *> On exit, if INFO = 0, the factor U or L from the Cholesky
75 *> factorization A = U**T*U or A = L*L**T.
76 *> \endverbatim
77 *>
78 *> \param[in] LDA
79 *> \verbatim
80 *> LDA is INTEGER
81 *> The leading dimension of the array A. LDA >= max(1,N).
82 *> \endverbatim
83 *>
84 *> \param[out] INFO
85 *> \verbatim
86 *> INFO is INTEGER
87 *> = 0: successful exit
88 *> < 0: if INFO = -i, the i-th argument had an illegal value
89 *> > 0: if INFO = i, the leading minor of order i is not
90 *> positive definite, and the factorization could not be
91 *> completed.
92 *> \endverbatim
93 *
94 * Authors:
95 * ========
96 *
97 *> \author Univ. of Tennessee
98 *> \author Univ. of California Berkeley
99 *> \author Univ. of Colorado Denver
100 *> \author NAG Ltd.
101 *
102 *> \date December 2016
103 *
104 *> \ingroup doublePOcomputational
105 *
106 * =====================================================================
107  RECURSIVE SUBROUTINE dpotrf2( UPLO, N, A, LDA, INFO )
108 *
109 * -- LAPACK computational routine (version 3.7.0) --
110 * -- LAPACK is a software package provided by Univ. of Tennessee, --
111 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
112 * December 2016
113 *
114 * .. Scalar Arguments ..
115  CHARACTER UPLO
116  INTEGER INFO, LDA, N
117 * ..
118 * .. Array Arguments ..
119  DOUBLE PRECISION A( lda, * )
120 * ..
121 *
122 * =====================================================================
123 *
124 * .. Parameters ..
125  DOUBLE PRECISION ONE, ZERO
126  parameter( one = 1.0d+0, zero = 0.0d+0 )
127 * ..
128 * .. Local Scalars ..
129  LOGICAL UPPER
130  INTEGER N1, N2, IINFO
131 * ..
132 * .. External Functions ..
133  LOGICAL LSAME, DISNAN
134  EXTERNAL lsame, disnan
135 * ..
136 * .. External Subroutines ..
137  EXTERNAL dsyrk, dtrsm, xerbla
138 * ..
139 * .. Intrinsic Functions ..
140  INTRINSIC max, sqrt
141 * ..
142 * .. Executable Statements ..
143 *
144 * Test the input parameters
145 *
146  info = 0
147  upper = lsame( uplo, 'U' )
148  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
149  info = -1
150  ELSE IF( n.LT.0 ) THEN
151  info = -2
152  ELSE IF( lda.LT.max( 1, n ) ) THEN
153  info = -4
154  END IF
155  IF( info.NE.0 ) THEN
156  CALL xerbla( 'DPOTRF2', -info )
157  RETURN
158  END IF
159 *
160 * Quick return if possible
161 *
162  IF( n.EQ.0 )
163  $ RETURN
164 *
165 * N=1 case
166 *
167  IF( n.EQ.1 ) THEN
168 *
169 * Test for non-positive-definiteness
170 *
171  IF( a( 1, 1 ).LE.zero.OR.disnan( a( 1, 1 ) ) ) THEN
172  info = 1
173  RETURN
174  END IF
175 *
176 * Factor
177 *
178  a( 1, 1 ) = sqrt( a( 1, 1 ) )
179 *
180 * Use recursive code
181 *
182  ELSE
183  n1 = n/2
184  n2 = n-n1
185 *
186 * Factor A11
187 *
188  CALL dpotrf2( uplo, n1, a( 1, 1 ), lda, iinfo )
189  IF ( iinfo.NE.0 ) THEN
190  info = iinfo
191  RETURN
192  END IF
193 *
194 * Compute the Cholesky factorization A = U**T*U
195 *
196  IF( upper ) THEN
197 *
198 * Update and scale A12
199 *
200  CALL dtrsm( 'L', 'U', 'T', 'N', n1, n2, one,
201  $ a( 1, 1 ), lda, a( 1, n1+1 ), lda )
202 *
203 * Update and factor A22
204 *
205  CALL dsyrk( uplo, 'T', n2, n1, -one, a( 1, n1+1 ), lda,
206  $ one, a( n1+1, n1+1 ), lda )
207  CALL dpotrf2( uplo, n2, a( n1+1, n1+1 ), lda, iinfo )
208  IF ( iinfo.NE.0 ) THEN
209  info = iinfo + n1
210  RETURN
211  END IF
212 *
213 * Compute the Cholesky factorization A = L*L**T
214 *
215  ELSE
216 *
217 * Update and scale A21
218 *
219  CALL dtrsm( 'R', 'L', 'T', 'N', n2, n1, one,
220  $ a( 1, 1 ), lda, a( n1+1, 1 ), lda )
221 *
222 * Update and factor A22
223 *
224  CALL dsyrk( uplo, 'N', n2, n1, -one, a( n1+1, 1 ), lda,
225  $ one, a( n1+1, n1+1 ), lda )
226  CALL dpotrf2( uplo, n2, a( n1+1, n1+1 ), lda, iinfo )
227  IF ( iinfo.NE.0 ) THEN
228  info = iinfo + n1
229  RETURN
230  END IF
231  END IF
232  END IF
233  RETURN
234 *
235 * End of DPOTRF2
236 *
237  END
subroutine dtrsm(SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
DTRSM
Definition: dtrsm.f:183
recursive subroutine dpotrf2(UPLO, N, A, LDA, INFO)
DPOTRF2
Definition: dpotrf2.f:108
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
subroutine dsyrk(UPLO, TRANS, N, K, ALPHA, A, LDA, BETA, C, LDC)
DSYRK
Definition: dsyrk.f:171