LAPACK  3.8.0
LAPACK: Linear Algebra PACKage
dpotrf.f
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1 C> \brief \b DPOTRF VARIANT: right looking block version of the algorithm, calling Level 3 BLAS.
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
8 * Definition:
9 * ===========
10 *
11 * SUBROUTINE DPOTRF ( UPLO, N, A, LDA, INFO )
12 *
13 * .. Scalar Arguments ..
14 * CHARACTER UPLO
15 * INTEGER INFO, LDA, N
16 * ..
17 * .. Array Arguments ..
18 * DOUBLE PRECISION A( LDA, * )
19 * ..
20 *
21 * Purpose
22 * =======
23 *
24 C>\details \b Purpose:
25 C>\verbatim
26 C>
27 C> DPOTRF computes the Cholesky factorization of a real symmetric
28 C> positive definite matrix A.
29 C>
30 C> The factorization has the form
31 C> A = U**T * U, if UPLO = 'U', or
32 C> A = L * L**T, if UPLO = 'L',
33 C> where U is an upper triangular matrix and L is lower triangular.
34 C>
35 C> This is the right looking block version of the algorithm, calling Level 3 BLAS.
36 C>
37 C>\endverbatim
38 *
39 * Arguments:
40 * ==========
41 *
42 C> \param[in] UPLO
43 C> \verbatim
44 C> UPLO is CHARACTER*1
45 C> = 'U': Upper triangle of A is stored;
46 C> = 'L': Lower triangle of A is stored.
47 C> \endverbatim
48 C>
49 C> \param[in] N
50 C> \verbatim
51 C> N is INTEGER
52 C> The order of the matrix A. N >= 0.
53 C> \endverbatim
54 C>
55 C> \param[in,out] A
56 C> \verbatim
57 C> A is DOUBLE PRECISION array, dimension (LDA,N)
58 C> On entry, the symmetric matrix A. If UPLO = 'U', the leading
59 C> N-by-N upper triangular part of A contains the upper
60 C> triangular part of the matrix A, and the strictly lower
61 C> triangular part of A is not referenced. If UPLO = 'L', the
62 C> leading N-by-N lower triangular part of A contains the lower
63 C> triangular part of the matrix A, and the strictly upper
64 C> triangular part of A is not referenced.
65 C> \endverbatim
66 C> \verbatim
67 C> On exit, if INFO = 0, the factor U or L from the Cholesky
68 C> factorization A = U**T*U or A = L*L**T.
69 C> \endverbatim
70 C>
71 C> \param[in] LDA
72 C> \verbatim
73 C> LDA is INTEGER
74 C> The leading dimension of the array A. LDA >= max(1,N).
75 C> \endverbatim
76 C>
77 C> \param[out] INFO
78 C> \verbatim
79 C> INFO is INTEGER
80 C> = 0: successful exit
81 C> < 0: if INFO = -i, the i-th argument had an illegal value
82 C> > 0: if INFO = i, the leading minor of order i is not
83 C> positive definite, and the factorization could not be
84 C> completed.
85 C> \endverbatim
86 C>
87 *
88 * Authors:
89 * ========
90 *
91 C> \author Univ. of Tennessee
92 C> \author Univ. of California Berkeley
93 C> \author Univ. of Colorado Denver
94 C> \author NAG Ltd.
95 *
96 C> \date December 2016
97 *
98 C> \ingroup variantsPOcomputational
99 *
100 * =====================================================================
101  SUBROUTINE dpotrf ( UPLO, N, A, LDA, INFO )
102 *
103 * -- LAPACK computational routine (version 3.1) --
104 * -- LAPACK is a software package provided by Univ. of Tennessee, --
105 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
106 * December 2016
107 *
108 * .. Scalar Arguments ..
109  CHARACTER UPLO
110  INTEGER INFO, LDA, N
111 * ..
112 * .. Array Arguments ..
113  DOUBLE PRECISION A( lda, * )
114 * ..
115 *
116 * =====================================================================
117 *
118 * .. Parameters ..
119  DOUBLE PRECISION ONE
120  parameter( one = 1.0d+0 )
121 * ..
122 * .. Local Scalars ..
123  LOGICAL UPPER
124  INTEGER J, JB, NB
125 * ..
126 * .. External Functions ..
127  LOGICAL LSAME
128  INTEGER ILAENV
129  EXTERNAL lsame, ilaenv
130 * ..
131 * .. External Subroutines ..
132  EXTERNAL dgemm, dpotf2, dsyrk, dtrsm, xerbla
133 * ..
134 * .. Intrinsic Functions ..
135  INTRINSIC max, min
136 * ..
137 * .. Executable Statements ..
138 *
139 * Test the input parameters.
140 *
141  info = 0
142  upper = lsame( uplo, 'U' )
143  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
144  info = -1
145  ELSE IF( n.LT.0 ) THEN
146  info = -2
147  ELSE IF( lda.LT.max( 1, n ) ) THEN
148  info = -4
149  END IF
150  IF( info.NE.0 ) THEN
151  CALL xerbla( 'DPOTRF', -info )
152  RETURN
153  END IF
154 *
155 * Quick return if possible
156 *
157  IF( n.EQ.0 )
158  $ RETURN
159 *
160 * Determine the block size for this environment.
161 *
162  nb = ilaenv( 1, 'DPOTRF', uplo, n, -1, -1, -1 )
163  IF( nb.LE.1 .OR. nb.GE.n ) THEN
164 *
165 * Use unblocked code.
166 *
167  CALL dpotf2( uplo, n, a, lda, info )
168  ELSE
169 *
170 * Use blocked code.
171 *
172  IF( upper ) THEN
173 *
174 * Compute the Cholesky factorization A = U'*U.
175 *
176  DO 10 j = 1, n, nb
177 *
178 * Update and factorize the current diagonal block and test
179 * for non-positive-definiteness.
180 *
181  jb = min( nb, n-j+1 )
182 
183  CALL dpotf2( 'Upper', jb, a( j, j ), lda, info )
184 
185  IF( info.NE.0 )
186  $ GO TO 30
187 
188  IF( j+jb.LE.n ) THEN
189 *
190 * Updating the trailing submatrix.
191 *
192  CALL dtrsm( 'Left', 'Upper', 'Transpose', 'Non-unit',
193  $ jb, n-j-jb+1, one, a( j, j ), lda,
194  $ a( j, j+jb ), lda )
195  CALL dsyrk( 'Upper', 'Transpose', n-j-jb+1, jb, -one,
196  $ a( j, j+jb ), lda,
197  $ one, a( j+jb, j+jb ), lda )
198  END IF
199  10 CONTINUE
200 *
201  ELSE
202 *
203 * Compute the Cholesky factorization A = L*L'.
204 *
205  DO 20 j = 1, n, nb
206 *
207 * Update and factorize the current diagonal block and test
208 * for non-positive-definiteness.
209 *
210  jb = min( nb, n-j+1 )
211 
212  CALL dpotf2( 'Lower', jb, a( j, j ), lda, info )
213 
214  IF( info.NE.0 )
215  $ GO TO 30
216 
217  IF( j+jb.LE.n ) THEN
218 *
219 * Updating the trailing submatrix.
220 *
221  CALL dtrsm( 'Right', 'Lower', 'Transpose', 'Non-unit',
222  $ n-j-jb+1, jb, one, a( j, j ), lda,
223  $ a( j+jb, j ), lda )
224 
225  CALL dsyrk( 'Lower', 'No Transpose', n-j-jb+1, jb,
226  $ -one, a( j+jb, j ), lda,
227  $ one, a( j+jb, j+jb ), lda )
228  END IF
229  20 CONTINUE
230  END IF
231  END IF
232  GO TO 40
233 *
234  30 CONTINUE
235  info = info + j - 1
236 *
237  40 CONTINUE
238  RETURN
239 *
240 * End of DPOTRF
241 *
242  END
subroutine dtrsm(SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
DTRSM
Definition: dtrsm.f:183
subroutine dpotrf(UPLO, N, A, LDA, INFO)
DPOTRF
Definition: dpotrf.f:109
subroutine dgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
DGEMM
Definition: dgemm.f:189
subroutine dsyrk(UPLO, TRANS, N, K, ALPHA, A, LDA, BETA, C, LDC)
DSYRK
Definition: dsyrk.f:171
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
subroutine dpotf2(UPLO, N, A, LDA, INFO)
DPOTF2 computes the Cholesky factorization of a symmetric/Hermitian positive definite matrix (unblock...
Definition: dpotf2.f:111