LAPACK  3.10.0
LAPACK: Linear Algebra PACKage
cpotf2.f
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1 *> \brief \b CPOTF2 computes the Cholesky factorization of a symmetric/Hermitian positive definite matrix (unblocked algorithm).
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
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15 *> [TXT]</a>
16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE CPOTF2( 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 *> CPOTF2 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 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 *> Hermitian 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 COMPLEX array, dimension (LDA,N)
69 *> On entry, the Hermitian 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**H *U or A = L*L**H.
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 *> \ingroup complexPOcomputational
106 *
107 * =====================================================================
108  SUBROUTINE cpotf2( UPLO, N, A, LDA, INFO )
109 *
110 * -- LAPACK computational routine --
111 * -- LAPACK is a software package provided by Univ. of Tennessee, --
112 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
113 *
114 * .. Scalar Arguments ..
115  CHARACTER UPLO
116  INTEGER INFO, LDA, N
117 * ..
118 * .. Array Arguments ..
119  COMPLEX A( LDA, * )
120 * ..
121 *
122 * =====================================================================
123 *
124 * .. Parameters ..
125  REAL ONE, ZERO
126  parameter( one = 1.0e+0, zero = 0.0e+0 )
127  COMPLEX CONE
128  parameter( cone = ( 1.0e+0, 0.0e+0 ) )
129 * ..
130 * .. Local Scalars ..
131  LOGICAL UPPER
132  INTEGER J
133  REAL AJJ
134 * ..
135 * .. External Functions ..
136  LOGICAL LSAME, SISNAN
137  COMPLEX CDOTC
138  EXTERNAL lsame, cdotc, sisnan
139 * ..
140 * .. External Subroutines ..
141  EXTERNAL cgemv, clacgv, csscal, xerbla
142 * ..
143 * .. Intrinsic Functions ..
144  INTRINSIC max, real, sqrt
145 * ..
146 * .. Executable Statements ..
147 *
148 * Test the input parameters.
149 *
150  info = 0
151  upper = lsame( uplo, 'U' )
152  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
153  info = -1
154  ELSE IF( n.LT.0 ) THEN
155  info = -2
156  ELSE IF( lda.LT.max( 1, n ) ) THEN
157  info = -4
158  END IF
159  IF( info.NE.0 ) THEN
160  CALL xerbla( 'CPOTF2', -info )
161  RETURN
162  END IF
163 *
164 * Quick return if possible
165 *
166  IF( n.EQ.0 )
167  $ RETURN
168 *
169  IF( upper ) THEN
170 *
171 * Compute the Cholesky factorization A = U**H *U.
172 *
173  DO 10 j = 1, n
174 *
175 * Compute U(J,J) and test for non-positive-definiteness.
176 *
177  ajj = real( real( a( j, j ) ) - cdotc( j-1, a( 1, j ), 1,
178  $ a( 1, j ), 1 ) )
179  IF( ajj.LE.zero.OR.sisnan( 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 clacgv( j-1, a( 1, j ), 1 )
190  CALL cgemv( 'Transpose', j-1, n-j, -cone, a( 1, j+1 ),
191  $ lda, a( 1, j ), 1, cone, a( j, j+1 ), lda )
192  CALL clacgv( j-1, a( 1, j ), 1 )
193  CALL csscal( n-j, one / ajj, a( j, j+1 ), lda )
194  END IF
195  10 CONTINUE
196  ELSE
197 *
198 * Compute the Cholesky factorization A = L*L**H.
199 *
200  DO 20 j = 1, n
201 *
202 * Compute L(J,J) and test for non-positive-definiteness.
203 *
204  ajj = real( real( a( j, j ) ) - cdotc( j-1, a( j, 1 ), lda,
205  $ a( j, 1 ), lda ) )
206  IF( ajj.LE.zero.OR.sisnan( ajj ) ) THEN
207  a( j, j ) = ajj
208  GO TO 30
209  END IF
210  ajj = sqrt( ajj )
211  a( j, j ) = ajj
212 *
213 * Compute elements J+1:N of column J.
214 *
215  IF( j.LT.n ) THEN
216  CALL clacgv( j-1, a( j, 1 ), lda )
217  CALL cgemv( 'No transpose', n-j, j-1, -cone, a( j+1, 1 ),
218  $ lda, a( j, 1 ), lda, cone, a( j+1, j ), 1 )
219  CALL clacgv( j-1, a( j, 1 ), lda )
220  CALL csscal( n-j, one / ajj, a( j+1, j ), 1 )
221  END IF
222  20 CONTINUE
223  END IF
224  GO TO 40
225 *
226  30 CONTINUE
227  info = j
228 *
229  40 CONTINUE
230  RETURN
231 *
232 * End of CPOTF2
233 *
234  END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine csscal(N, SA, CX, INCX)
CSSCAL
Definition: csscal.f:78
subroutine cgemv(TRANS, M, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
CGEMV
Definition: cgemv.f:158
subroutine clacgv(N, X, INCX)
CLACGV conjugates a complex vector.
Definition: clacgv.f:74
subroutine cpotf2(UPLO, N, A, LDA, INFO)
CPOTF2 computes the Cholesky factorization of a symmetric/Hermitian positive definite matrix (unblock...
Definition: cpotf2.f:109