LAPACK  3.7.0 LAPACK: Linear Algebra PACKage
dpotf2.f
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1 *> \brief \b DPOTF2 computes the Cholesky factorization of a symmetric/Hermitian positive definite matrix (unblocked algorithm).
2 *
3 * =========== DOCUMENTATION ===========
4 *
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17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE DPOTF2( UPLO, N, A, LDA, INFO )
22 *
23 * .. Scalar Arguments ..
24 * CHARACTER UPLO
25 * INTEGER INFO, LDA, N
26 * ..
27 * .. Array Arguments ..
28 * DOUBLE PRECISION A( LDA, * )
29 * ..
30 *
31 *
32 *> \par Purpose:
33 * =============
34 *>
35 *> \verbatim
36 *>
37 *> DPOTF2 computes the Cholesky factorization of a real symmetric
38 *> positive definite matrix A.
39 *>
40 *> The factorization has the form
41 *> A = U**T * U , if UPLO = 'U', or
42 *> A = L * L**T, if UPLO = 'L',
43 *> where U is an upper triangular matrix and L is lower triangular.
44 *>
45 *> This is the unblocked version of the algorithm, calling Level 2 BLAS.
46 *> \endverbatim
47 *
48 * Arguments:
49 * ==========
50 *
51 *> \param[in] UPLO
52 *> \verbatim
53 *> UPLO is CHARACTER*1
54 *> Specifies whether the upper or lower triangular part of the
55 *> symmetric matrix A is stored.
56 *> = 'U': Upper triangular
57 *> = 'L': Lower triangular
58 *> \endverbatim
59 *>
60 *> \param[in] N
61 *> \verbatim
62 *> N is INTEGER
63 *> The order of the matrix A. N >= 0.
64 *> \endverbatim
65 *>
66 *> \param[in,out] A
67 *> \verbatim
68 *> A is DOUBLE PRECISION array, dimension (LDA,N)
69 *> On entry, the symmetric matrix A. If UPLO = 'U', the leading
70 *> n by n upper triangular part of A contains the upper
71 *> triangular part of the matrix A, and the strictly lower
72 *> triangular part of A is not referenced. If UPLO = 'L', the
73 *> leading n by n lower triangular part of A contains the lower
74 *> triangular part of the matrix A, and the strictly upper
75 *> triangular part of A is not referenced.
76 *>
77 *> On exit, if INFO = 0, the factor U or L from the Cholesky
78 *> factorization A = U**T *U or A = L*L**T.
79 *> \endverbatim
80 *>
81 *> \param[in] LDA
82 *> \verbatim
83 *> LDA is INTEGER
84 *> The leading dimension of the array A. LDA >= max(1,N).
85 *> \endverbatim
86 *>
87 *> \param[out] INFO
88 *> \verbatim
89 *> INFO is INTEGER
90 *> = 0: successful exit
91 *> < 0: if INFO = -k, the k-th argument had an illegal value
92 *> > 0: if INFO = k, the leading minor of order k is not
93 *> positive definite, and the factorization could not be
94 *> completed.
95 *> \endverbatim
96 *
97 * Authors:
98 * ========
99 *
100 *> \author Univ. of Tennessee
101 *> \author Univ. of California Berkeley
102 *> \author Univ. of Colorado Denver
103 *> \author NAG Ltd.
104 *
105 *> \date December 2016
106 *
107 *> \ingroup doublePOcomputational
108 *
109 * =====================================================================
110  SUBROUTINE dpotf2( UPLO, N, A, LDA, INFO )
111 *
112 * -- LAPACK computational routine (version 3.7.0) --
113 * -- LAPACK is a software package provided by Univ. of Tennessee, --
114 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
115 * December 2016
116 *
117 * .. Scalar Arguments ..
118  CHARACTER UPLO
119  INTEGER INFO, LDA, N
120 * ..
121 * .. Array Arguments ..
122  DOUBLE PRECISION A( lda, * )
123 * ..
124 *
125 * =====================================================================
126 *
127 * .. Parameters ..
128  DOUBLE PRECISION ONE, ZERO
129  parameter ( one = 1.0d+0, zero = 0.0d+0 )
130 * ..
131 * .. Local Scalars ..
132  LOGICAL UPPER
133  INTEGER J
134  DOUBLE PRECISION AJJ
135 * ..
136 * .. External Functions ..
137  LOGICAL LSAME, DISNAN
138  DOUBLE PRECISION DDOT
139  EXTERNAL lsame, ddot, disnan
140 * ..
141 * .. External Subroutines ..
142  EXTERNAL dgemv, dscal, xerbla
143 * ..
144 * .. Intrinsic Functions ..
145  INTRINSIC max, sqrt
146 * ..
147 * .. Executable Statements ..
148 *
149 * Test the input parameters.
150 *
151  info = 0
152  upper = lsame( uplo, 'U' )
153  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
154  info = -1
155  ELSE IF( n.LT.0 ) THEN
156  info = -2
157  ELSE IF( lda.LT.max( 1, n ) ) THEN
158  info = -4
159  END IF
160  IF( info.NE.0 ) THEN
161  CALL xerbla( 'DPOTF2', -info )
162  RETURN
163  END IF
164 *
165 * Quick return if possible
166 *
167  IF( n.EQ.0 )
168  \$ RETURN
169 *
170  IF( upper ) THEN
171 *
172 * Compute the Cholesky factorization A = U**T *U.
173 *
174  DO 10 j = 1, n
175 *
176 * Compute U(J,J) and test for non-positive-definiteness.
177 *
178  ajj = a( j, j ) - ddot( j-1, a( 1, j ), 1, a( 1, j ), 1 )
179  IF( ajj.LE.zero.OR.disnan( ajj ) ) THEN
180  a( j, j ) = ajj
181  GO TO 30
182  END IF
183  ajj = sqrt( ajj )
184  a( j, j ) = ajj
185 *
186 * Compute elements J+1:N of row J.
187 *
188  IF( j.LT.n ) THEN
189  CALL dgemv( 'Transpose', j-1, n-j, -one, a( 1, j+1 ),
190  \$ lda, a( 1, j ), 1, one, a( j, j+1 ), lda )
191  CALL dscal( n-j, one / ajj, a( j, j+1 ), lda )
192  END IF
193  10 CONTINUE
194  ELSE
195 *
196 * Compute the Cholesky factorization A = L*L**T.
197 *
198  DO 20 j = 1, n
199 *
200 * Compute L(J,J) and test for non-positive-definiteness.
201 *
202  ajj = a( j, j ) - ddot( j-1, a( j, 1 ), lda, a( j, 1 ),
203  \$ lda )
204  IF( ajj.LE.zero.OR.disnan( ajj ) ) THEN
205  a( j, j ) = ajj
206  GO TO 30
207  END IF
208  ajj = sqrt( ajj )
209  a( j, j ) = ajj
210 *
211 * Compute elements J+1:N of column J.
212 *
213  IF( j.LT.n ) THEN
214  CALL dgemv( 'No transpose', n-j, j-1, -one, a( j+1, 1 ),
215  \$ lda, a( j, 1 ), lda, one, a( j+1, j ), 1 )
216  CALL dscal( n-j, one / ajj, a( j+1, j ), 1 )
217  END IF
218  20 CONTINUE
219  END IF
220  GO TO 40
221 *
222  30 CONTINUE
223  info = j
224 *
225  40 CONTINUE
226  RETURN
227 *
228 * End of DPOTF2
229 *
230  END
subroutine dgemv(TRANS, M, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
DGEMV
Definition: dgemv.f:158
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
subroutine dscal(N, DA, DX, INCX)
DSCAL
Definition: dscal.f:55
subroutine dpotf2(UPLO, N, A, LDA, INFO)
DPOTF2 computes the Cholesky factorization of a symmetric/Hermitian positive definite matrix (unblock...
Definition: dpotf2.f:111