LAPACK  3.10.0
LAPACK: Linear Algebra PACKage
cpotrf.f
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1 *> \brief \b CPOTRF
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
8 *> \htmlonly
9 *> Download CPOTRF + dependencies
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13 *> [ZIP]</a>
14 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cpotrf.f">
15 *> [TXT]</a>
16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE CPOTRF( UPLO, N, A, LDA, INFO )
22 *
23 * .. Scalar Arguments ..
24 * CHARACTER UPLO
25 * INTEGER INFO, LDA, N
26 * ..
27 * .. Array Arguments ..
28 * COMPLEX A( LDA, * )
29 * ..
30 *
31 *
32 *> \par Purpose:
33 * =============
34 *>
35 *> \verbatim
36 *>
37 *> CPOTRF computes the Cholesky factorization of a complex Hermitian
38 *> positive definite matrix A.
39 *>
40 *> The factorization has the form
41 *> A = U**H * U, if UPLO = 'U', or
42 *> A = L * L**H, if UPLO = 'L',
43 *> where U is an upper triangular matrix and L is lower triangular.
44 *>
45 *> This is the block version of the algorithm, calling Level 3 BLAS.
46 *> \endverbatim
47 *
48 * Arguments:
49 * ==========
50 *
51 *> \param[in] UPLO
52 *> \verbatim
53 *> UPLO is CHARACTER*1
54 *> = 'U': Upper triangle of A is stored;
55 *> = 'L': Lower triangle of A is stored.
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] A
65 *> \verbatim
66 *> A is COMPLEX array, dimension (LDA,N)
67 *> On entry, the Hermitian matrix A. If UPLO = 'U', the leading
68 *> N-by-N upper triangular part of A contains the upper
69 *> triangular part of the matrix A, and the strictly lower
70 *> triangular part of A is not referenced. If UPLO = 'L', the
71 *> leading N-by-N lower triangular part of A contains the lower
72 *> triangular part of the matrix A, and the strictly upper
73 *> triangular part of A is not referenced.
74 *>
75 *> On exit, if INFO = 0, the factor U or L from the Cholesky
76 *> factorization A = U**H*U or A = L*L**H.
77 *> \endverbatim
78 *>
79 *> \param[in] LDA
80 *> \verbatim
81 *> LDA is INTEGER
82 *> The leading dimension of the array A. LDA >= max(1,N).
83 *> \endverbatim
84 *>
85 *> \param[out] INFO
86 *> \verbatim
87 *> INFO is INTEGER
88 *> = 0: successful exit
89 *> < 0: if INFO = -i, the i-th argument had an illegal value
90 *> > 0: if INFO = i, the leading minor of order i is not
91 *> positive definite, and the factorization could not be
92 *> completed.
93 *> \endverbatim
94 *
95 * Authors:
96 * ========
97 *
98 *> \author Univ. of Tennessee
99 *> \author Univ. of California Berkeley
100 *> \author Univ. of Colorado Denver
101 *> \author NAG Ltd.
102 *
103 *> \ingroup complexPOcomputational
104 *
105 * =====================================================================
106  SUBROUTINE cpotrf( UPLO, N, A, LDA, INFO )
107 *
108 * -- LAPACK computational routine --
109 * -- LAPACK is a software package provided by Univ. of Tennessee, --
110 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
111 *
112 * .. Scalar Arguments ..
113  CHARACTER UPLO
114  INTEGER INFO, LDA, N
115 * ..
116 * .. Array Arguments ..
117  COMPLEX A( LDA, * )
118 * ..
119 *
120 * =====================================================================
121 *
122 * .. Parameters ..
123  REAL ONE
124  COMPLEX CONE
125  parameter( one = 1.0e+0, cone = ( 1.0e+0, 0.0e+0 ) )
126 * ..
127 * .. Local Scalars ..
128  LOGICAL UPPER
129  INTEGER J, JB, NB
130 * ..
131 * .. External Functions ..
132  LOGICAL LSAME
133  INTEGER ILAENV
134  EXTERNAL lsame, ilaenv
135 * ..
136 * .. External Subroutines ..
137  EXTERNAL cgemm, cherk, cpotrf2, ctrsm, xerbla
138 * ..
139 * .. Intrinsic Functions ..
140  INTRINSIC max, min
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( 'CPOTRF', -info )
157  RETURN
158  END IF
159 *
160 * Quick return if possible
161 *
162  IF( n.EQ.0 )
163  $ RETURN
164 *
165 * Determine the block size for this environment.
166 *
167  nb = ilaenv( 1, 'CPOTRF', uplo, n, -1, -1, -1 )
168  IF( nb.LE.1 .OR. nb.GE.n ) THEN
169 *
170 * Use unblocked code.
171 *
172  CALL cpotrf2( uplo, n, a, lda, info )
173  ELSE
174 *
175 * Use blocked code.
176 *
177  IF( upper ) THEN
178 *
179 * Compute the Cholesky factorization A = U**H *U.
180 *
181  DO 10 j = 1, n, nb
182 *
183 * Update and factorize the current diagonal block and test
184 * for non-positive-definiteness.
185 *
186  jb = min( nb, n-j+1 )
187  CALL cherk( 'Upper', 'Conjugate transpose', jb, j-1,
188  $ -one, a( 1, j ), lda, one, a( j, j ), lda )
189  CALL cpotrf2( 'Upper', jb, a( j, j ), lda, info )
190  IF( info.NE.0 )
191  $ GO TO 30
192  IF( j+jb.LE.n ) THEN
193 *
194 * Compute the current block row.
195 *
196  CALL cgemm( 'Conjugate transpose', 'No transpose', jb,
197  $ n-j-jb+1, j-1, -cone, a( 1, j ), lda,
198  $ a( 1, j+jb ), lda, cone, a( j, j+jb ),
199  $ lda )
200  CALL ctrsm( 'Left', 'Upper', 'Conjugate transpose',
201  $ 'Non-unit', jb, n-j-jb+1, cone, a( j, j ),
202  $ lda, a( j, j+jb ), lda )
203  END IF
204  10 CONTINUE
205 *
206  ELSE
207 *
208 * Compute the Cholesky factorization A = L*L**H.
209 *
210  DO 20 j = 1, n, nb
211 *
212 * Update and factorize the current diagonal block and test
213 * for non-positive-definiteness.
214 *
215  jb = min( nb, n-j+1 )
216  CALL cherk( 'Lower', 'No transpose', jb, j-1, -one,
217  $ a( j, 1 ), lda, one, a( j, j ), lda )
218  CALL cpotrf2( 'Lower', jb, a( j, j ), lda, info )
219  IF( info.NE.0 )
220  $ GO TO 30
221  IF( j+jb.LE.n ) THEN
222 *
223 * Compute the current block column.
224 *
225  CALL cgemm( 'No transpose', 'Conjugate transpose',
226  $ n-j-jb+1, jb, j-1, -cone, a( j+jb, 1 ),
227  $ lda, a( j, 1 ), lda, cone, a( j+jb, j ),
228  $ lda )
229  CALL ctrsm( 'Right', 'Lower', 'Conjugate transpose',
230  $ 'Non-unit', n-j-jb+1, jb, cone, a( j, j ),
231  $ lda, a( j+jb, j ), lda )
232  END IF
233  20 CONTINUE
234  END IF
235  END IF
236  GO TO 40
237 *
238  30 CONTINUE
239  info = info + j - 1
240 *
241  40 CONTINUE
242  RETURN
243 *
244 * End of CPOTRF
245 *
246  END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine cgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
CGEMM
Definition: cgemm.f:187
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
subroutine cpotrf(UPLO, N, A, LDA, INFO)
CPOTRF
Definition: cpotrf.f:107