LAPACK  3.4.2 LAPACK: Linear Algebra PACKage
cpotrf.f
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1 *> \brief \b CPOTRF
2 *
3 * =========== DOCUMENTATION ===========
4 *
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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 *> \date November 2011
104 *
105 *> \ingroup complexPOcomputational
106 *
107 * =====================================================================
108  SUBROUTINE cpotrf( UPLO, N, A, LDA, INFO )
109 *
110 * -- LAPACK computational routine (version 3.4.0) --
111 * -- LAPACK is a software package provided by Univ. of Tennessee, --
112 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
113 * November 2011
114 *
115 * .. Scalar Arguments ..
116  CHARACTER uplo
117  INTEGER info, lda, n
118 * ..
119 * .. Array Arguments ..
120  COMPLEX a( lda, * )
121 * ..
122 *
123 * =====================================================================
124 *
125 * .. Parameters ..
126  REAL one
127  COMPLEX cone
128  parameter( one = 1.0e+0, cone = ( 1.0e+0, 0.0e+0 ) )
129 * ..
130 * .. Local Scalars ..
131  LOGICAL upper
132  INTEGER j, jb, nb
133 * ..
134 * .. External Functions ..
135  LOGICAL lsame
136  INTEGER ilaenv
137  EXTERNAL lsame, ilaenv
138 * ..
139 * .. External Subroutines ..
140  EXTERNAL cgemm, cherk, cpotf2, ctrsm, xerbla
141 * ..
142 * .. Intrinsic Functions ..
143  INTRINSIC max, min
144 * ..
145 * .. Executable Statements ..
146 *
147 * Test the input parameters.
148 *
149  info = 0
150  upper = lsame( uplo, 'U' )
151  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
152  info = -1
153  ELSE IF( n.LT.0 ) THEN
154  info = -2
155  ELSE IF( lda.LT.max( 1, n ) ) THEN
156  info = -4
157  END IF
158  IF( info.NE.0 ) THEN
159  CALL xerbla( 'CPOTRF', -info )
160  return
161  END IF
162 *
163 * Quick return if possible
164 *
165  IF( n.EQ.0 )
166  \$ return
167 *
168 * Determine the block size for this environment.
169 *
170  nb = ilaenv( 1, 'CPOTRF', uplo, n, -1, -1, -1 )
171  IF( nb.LE.1 .OR. nb.GE.n ) THEN
172 *
173 * Use unblocked code.
174 *
175  CALL cpotf2( uplo, n, a, lda, info )
176  ELSE
177 *
178 * Use blocked code.
179 *
180  IF( upper ) THEN
181 *
182 * Compute the Cholesky factorization A = U**H *U.
183 *
184  DO 10 j = 1, n, nb
185 *
186 * Update and factorize the current diagonal block and test
187 * for non-positive-definiteness.
188 *
189  jb = min( nb, n-j+1 )
190  CALL cherk( 'Upper', 'Conjugate transpose', jb, j-1,
191  \$ -one, a( 1, j ), lda, one, a( j, j ), lda )
192  CALL cpotf2( 'Upper', jb, a( j, j ), lda, info )
193  IF( info.NE.0 )
194  \$ go to 30
195  IF( j+jb.LE.n ) THEN
196 *
197 * Compute the current block row.
198 *
199  CALL cgemm( 'Conjugate transpose', 'No transpose', jb,
200  \$ n-j-jb+1, j-1, -cone, a( 1, j ), lda,
201  \$ a( 1, j+jb ), lda, cone, a( j, j+jb ),
202  \$ lda )
203  CALL ctrsm( 'Left', 'Upper', 'Conjugate transpose',
204  \$ 'Non-unit', jb, n-j-jb+1, cone, a( j, j ),
205  \$ lda, a( j, j+jb ), lda )
206  END IF
207  10 continue
208 *
209  ELSE
210 *
211 * Compute the Cholesky factorization A = L*L**H.
212 *
213  DO 20 j = 1, n, nb
214 *
215 * Update and factorize the current diagonal block and test
216 * for non-positive-definiteness.
217 *
218  jb = min( nb, n-j+1 )
219  CALL cherk( 'Lower', 'No transpose', jb, j-1, -one,
220  \$ a( j, 1 ), lda, one, a( j, j ), lda )
221  CALL cpotf2( 'Lower', jb, a( j, j ), lda, info )
222  IF( info.NE.0 )
223  \$ go to 30
224  IF( j+jb.LE.n ) THEN
225 *
226 * Compute the current block column.
227 *
228  CALL cgemm( 'No transpose', 'Conjugate transpose',
229  \$ n-j-jb+1, jb, j-1, -cone, a( j+jb, 1 ),
230  \$ lda, a( j, 1 ), lda, cone, a( j+jb, j ),
231  \$ lda )
232  CALL ctrsm( 'Right', 'Lower', 'Conjugate transpose',
233  \$ 'Non-unit', n-j-jb+1, jb, cone, a( j, j ),
234  \$ lda, a( j+jb, j ), lda )
235  END IF
236  20 continue
237  END IF
238  END IF
239  go to 40
240 *
241  30 continue
242  info = info + j - 1
243 *
244  40 continue
245  return
246 *
247 * End of CPOTRF
248 *
249  END