LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
zpotf2.f
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1 *> \brief \b ZPOTF2 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 ZPOTF2( UPLO, N, A, LDA, INFO )
22 *
23 * .. Scalar Arguments ..
24 * CHARACTER UPLO
25 * INTEGER INFO, LDA, N
26 * ..
27 * .. Array Arguments ..
28 * COMPLEX*16 A( LDA, * )
29 * ..
30 *
31 *
32 *> \par Purpose:
33 * =============
34 *>
35 *> \verbatim
36 *>
37 *> ZPOTF2 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*16 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 *> \date September 2012
106 *
107 *> \ingroup complex16POcomputational
108 *
109 * =====================================================================
110  SUBROUTINE zpotf2( UPLO, N, A, LDA, INFO )
111 *
112 * -- LAPACK computational routine (version 3.4.2) --
113 * -- LAPACK is a software package provided by Univ. of Tennessee, --
114 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
115 * September 2012
116 *
117 * .. Scalar Arguments ..
118  CHARACTER UPLO
119  INTEGER INFO, LDA, N
120 * ..
121 * .. Array Arguments ..
122  COMPLEX*16 A( lda, * )
123 * ..
124 *
125 * =====================================================================
126 *
127 * .. Parameters ..
128  DOUBLE PRECISION ONE, ZERO
129  parameter ( one = 1.0d+0, zero = 0.0d+0 )
130  COMPLEX*16 CONE
131  parameter ( cone = ( 1.0d+0, 0.0d+0 ) )
132 * ..
133 * .. Local Scalars ..
134  LOGICAL UPPER
135  INTEGER J
136  DOUBLE PRECISION AJJ
137 * ..
138 * .. External Functions ..
139  LOGICAL LSAME, DISNAN
140  COMPLEX*16 ZDOTC
141  EXTERNAL lsame, zdotc, disnan
142 * ..
143 * .. External Subroutines ..
144  EXTERNAL xerbla, zdscal, zgemv, zlacgv
145 * ..
146 * .. Intrinsic Functions ..
147  INTRINSIC dble, max, sqrt
148 * ..
149 * .. Executable Statements ..
150 *
151 * Test the input parameters.
152 *
153  info = 0
154  upper = lsame( uplo, 'U' )
155  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
156  info = -1
157  ELSE IF( n.LT.0 ) THEN
158  info = -2
159  ELSE IF( lda.LT.max( 1, n ) ) THEN
160  info = -4
161  END IF
162  IF( info.NE.0 ) THEN
163  CALL xerbla( 'ZPOTF2', -info )
164  RETURN
165  END IF
166 *
167 * Quick return if possible
168 *
169  IF( n.EQ.0 )
170  \$ RETURN
171 *
172  IF( upper ) THEN
173 *
174 * Compute the Cholesky factorization A = U**H *U.
175 *
176  DO 10 j = 1, n
177 *
178 * Compute U(J,J) and test for non-positive-definiteness.
179 *
180  ajj = dble( a( j, j ) ) - zdotc( j-1, a( 1, j ), 1,
181  \$ a( 1, j ), 1 )
182  IF( ajj.LE.zero.OR.disnan( ajj ) ) THEN
183  a( j, j ) = ajj
184  GO TO 30
185  END IF
186  ajj = sqrt( ajj )
187  a( j, j ) = ajj
188 *
189 * Compute elements J+1:N of row J.
190 *
191  IF( j.LT.n ) THEN
192  CALL zlacgv( j-1, a( 1, j ), 1 )
193  CALL zgemv( 'Transpose', j-1, n-j, -cone, a( 1, j+1 ),
194  \$ lda, a( 1, j ), 1, cone, a( j, j+1 ), lda )
195  CALL zlacgv( j-1, a( 1, j ), 1 )
196  CALL zdscal( n-j, one / ajj, a( j, j+1 ), lda )
197  END IF
198  10 CONTINUE
199  ELSE
200 *
201 * Compute the Cholesky factorization A = L*L**H.
202 *
203  DO 20 j = 1, n
204 *
205 * Compute L(J,J) and test for non-positive-definiteness.
206 *
207  ajj = dble( a( j, j ) ) - zdotc( j-1, a( j, 1 ), lda,
208  \$ a( j, 1 ), lda )
209  IF( ajj.LE.zero.OR.disnan( ajj ) ) THEN
210  a( j, j ) = ajj
211  GO TO 30
212  END IF
213  ajj = sqrt( ajj )
214  a( j, j ) = ajj
215 *
216 * Compute elements J+1:N of column J.
217 *
218  IF( j.LT.n ) THEN
219  CALL zlacgv( j-1, a( j, 1 ), lda )
220  CALL zgemv( 'No transpose', n-j, j-1, -cone, a( j+1, 1 ),
221  \$ lda, a( j, 1 ), lda, cone, a( j+1, j ), 1 )
222  CALL zlacgv( j-1, a( j, 1 ), lda )
223  CALL zdscal( n-j, one / ajj, a( j+1, j ), 1 )
224  END IF
225  20 CONTINUE
226  END IF
227  GO TO 40
228 *
229  30 CONTINUE
230  info = j
231 *
232  40 CONTINUE
233  RETURN
234 *
235 * End of ZPOTF2
236 *
237  END
subroutine zgemv(TRANS, M, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
ZGEMV
Definition: zgemv.f:160
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
subroutine zdscal(N, DA, ZX, INCX)
ZDSCAL
Definition: zdscal.f:54
subroutine zpotf2(UPLO, N, A, LDA, INFO)
ZPOTF2 computes the Cholesky factorization of a symmetric/Hermitian positive definite matrix (unblock...
Definition: zpotf2.f:111
subroutine zlacgv(N, X, INCX)
ZLACGV conjugates a complex vector.
Definition: zlacgv.f:76