LAPACK  3.10.1
LAPACK: Linear Algebra PACKage
cpotrf2.f
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1 *> \brief \b CPOTRF2
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 CPOTRF2( UPLO, N, A, LDA, INFO )
12 *
13 * .. Scalar Arguments ..
14 * CHARACTER UPLO
15 * INTEGER INFO, LDA, N
16 * ..
17 * .. Array Arguments ..
18 * COMPLEX A( LDA, * )
19 * ..
20 *
21 *
22 *> \par Purpose:
23 * =============
24 *>
25 *> \verbatim
26 *>
27 *> CPOTRF2 computes the Cholesky factorization of a Hermitian
28 *> positive definite matrix A using the recursive algorithm.
29 *>
30 *> The factorization has the form
31 *> A = U**H * U, if UPLO = 'U', or
32 *> A = L * L**H, 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 COMPLEX array, dimension (LDA,N)
66 *> On entry, the Hermitian 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**H*U or A = L*L**H.
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 *> \ingroup complexPOcomputational
103 *
104 * =====================================================================
105  RECURSIVE SUBROUTINE cpotrf2( UPLO, N, A, LDA, INFO )
106 *
107 * -- LAPACK computational routine --
108 * -- LAPACK is a software package provided by Univ. of Tennessee, --
109 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
110 *
111 * .. Scalar Arguments ..
112  CHARACTER uplo
113  INTEGER info, lda, n
114 * ..
115 * .. Array Arguments ..
116  COMPLEX a( lda, * )
117 * ..
118 *
119 * =====================================================================
120 *
121 * .. Parameters ..
122  REAL one, zero
123  parameter( one = 1.0e+0, zero = 0.0e+0 )
124  COMPLEX cone
125  parameter( cone = (1.0e+0, 0.0e+0) )
126 * ..
127 * .. Local Scalars ..
128  LOGICAL upper
129  INTEGER n1, n2, iinfo
130  REAL ajj
131 * ..
132 * .. External Functions ..
133  LOGICAL lsame, sisnan
134  EXTERNAL lsame, sisnan
135 * ..
136 * .. External Subroutines ..
137  EXTERNAL cherk, ctrsm, xerbla
138 * ..
139 * .. Intrinsic Functions ..
140  INTRINSIC max, real, 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( 'CPOTRF2', -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  ajj = real( a( 1, 1 ) )
172  IF( ajj.LE.zero.OR.sisnan( ajj ) ) THEN
173  info = 1
174  RETURN
175  END IF
176 *
177 * Factor
178 *
179  a( 1, 1 ) = sqrt( ajj )
180 *
181 * Use recursive code
182 *
183  ELSE
184  n1 = n/2
185  n2 = n-n1
186 *
187 * Factor A11
188 *
189  CALL cpotrf2( uplo, n1, a( 1, 1 ), lda, iinfo )
190  IF ( iinfo.NE.0 ) THEN
191  info = iinfo
192  RETURN
193  END IF
194 *
195 * Compute the Cholesky factorization A = U**H*U
196 *
197  IF( upper ) THEN
198 *
199 * Update and scale A12
200 *
201  CALL ctrsm( 'L', 'U', 'C', 'N', n1, n2, cone,
202  $ a( 1, 1 ), lda, a( 1, n1+1 ), lda )
203 *
204 * Update and factor A22
205 *
206  CALL cherk( uplo, 'C', n2, n1, -one, a( 1, n1+1 ), lda,
207  $ one, a( n1+1, n1+1 ), lda )
208 *
209  CALL cpotrf2( uplo, n2, a( n1+1, n1+1 ), lda, iinfo )
210 *
211  IF ( iinfo.NE.0 ) THEN
212  info = iinfo + n1
213  RETURN
214  END IF
215 *
216 * Compute the Cholesky factorization A = L*L**H
217 *
218  ELSE
219 *
220 * Update and scale A21
221 *
222  CALL ctrsm( 'R', 'L', 'C', 'N', n2, n1, cone,
223  $ a( 1, 1 ), lda, a( n1+1, 1 ), lda )
224 *
225 * Update and factor A22
226 *
227  CALL cherk( uplo, 'N', n2, n1, -one, a( n1+1, 1 ), lda,
228  $ one, a( n1+1, n1+1 ), lda )
229 *
230  CALL cpotrf2( uplo, n2, a( n1+1, n1+1 ), lda, iinfo )
231 *
232  IF ( iinfo.NE.0 ) THEN
233  info = iinfo + n1
234  RETURN
235  END IF
236 *
237  END IF
238  END IF
239  RETURN
240 *
241 * End of CPOTRF2
242 *
243  END
logical function sisnan(SIN)
SISNAN tests input for NaN.
Definition: sisnan.f:59
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine cherk(UPLO, TRANS, N, K, ALPHA, A, LDA, BETA, C, LDC)
CHERK
Definition: cherk.f:173
subroutine ctrsm(SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
CTRSM
Definition: ctrsm.f:180
recursive subroutine cpotrf2(UPLO, N, A, LDA, INFO)
CPOTRF2
Definition: cpotrf2.f:106