LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
 recursive subroutine cpotrf2 ( character UPLO, integer N, complex, dimension( lda, * ) A, integer LDA, integer INFO )

CPOTRF2

Purpose:
``` CPOTRF2 computes the Cholesky factorization of a real symmetric
positive definite matrix A using the recursive algorithm.

The factorization has the form
A = U**H * U,  if UPLO = 'U', or
A = L  * L**H,  if UPLO = 'L',
where U is an upper triangular matrix and L is lower triangular.

This is the recursive version of the algorithm. It divides
the matrix into four submatrices:

[  A11 | A12  ]  where A11 is n1 by n1 and A22 is n2 by n2
A = [ -----|----- ]  with n1 = n/2
[  A21 | A22  ]       n2 = n-n1

The subroutine calls itself to factor A11. Update and scale A21
or A12, update A22 then calls itself to factor A22.```
Parameters
 [in] UPLO ``` UPLO is CHARACTER*1 = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored.``` [in] N ``` N is INTEGER The order of the matrix A. N >= 0.``` [in,out] A ``` A is COMPLEX array, dimension (LDA,N) On entry, the symmetric matrix A. If UPLO = 'U', the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. On exit, if INFO = 0, the factor U or L from the Cholesky factorization A = U**H*U or A = L*L**H.``` [in] LDA ``` LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).``` [out] INFO ``` INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: if INFO = i, the leading minor of order i is not positive definite, and the factorization could not be completed.```
Date
June 2016

Definition at line 108 of file cpotrf2.f.

108 *
109 * -- LAPACK computational routine (version 3.6.1) --
110 * -- LAPACK is a software package provided by Univ. of Tennessee, --
111 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
112 * June 2016
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 n1, n2, iinfo
133  REAL ajj
134 * ..
135 * .. External Functions ..
136  LOGICAL lsame, sisnan
137  EXTERNAL lsame, sisnan
138 * ..
139 * .. External Subroutines ..
140  EXTERNAL cherk, ctrsm, xerbla
141 * ..
142 * .. Intrinsic Functions ..
143  INTRINSIC max, REAL, sqrt
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( 'CPOTRF2', -info )
160  RETURN
161  END IF
162 *
163 * Quick return if possible
164 *
165  IF( n.EQ.0 )
166  \$ RETURN
167 *
168 * N=1 case
169 *
170  IF( n.EQ.1 ) THEN
171 *
172 * Test for non-positive-definiteness
173 *
174  ajj = REAL( A( 1, 1 ) )
175  IF( ajj.LE.zero.OR.sisnan( ajj ) ) THEN
176  info = 1
177  RETURN
178  END IF
179 *
180 * Factor
181 *
182  a( 1, 1 ) = sqrt( ajj )
183 *
184 * Use recursive code
185 *
186  ELSE
187  n1 = n/2
188  n2 = n-n1
189 *
190 * Factor A11
191 *
192  CALL cpotrf2( uplo, n1, a( 1, 1 ), lda, iinfo )
193  IF ( iinfo.NE.0 ) THEN
194  info = iinfo
195  RETURN
196  END IF
197 *
198 * Compute the Cholesky factorization A = U**H*U
199 *
200  IF( upper ) THEN
201 *
202 * Update and scale A12
203 *
204  CALL ctrsm( 'L', 'U', 'C', 'N', n1, n2, cone,
205  \$ a( 1, 1 ), lda, a( 1, n1+1 ), lda )
206 *
207 * Update and factor A22
208 *
209  CALL cherk( uplo, 'C', n2, n1, -one, a( 1, n1+1 ), lda,
210  \$ one, a( n1+1, n1+1 ), lda )
211 *
212  CALL cpotrf2( uplo, n2, a( n1+1, n1+1 ), lda, iinfo )
213 *
214  IF ( iinfo.NE.0 ) THEN
215  info = iinfo + n1
216  RETURN
217  END IF
218 *
219 * Compute the Cholesky factorization A = L*L**H
220 *
221  ELSE
222 *
223 * Update and scale A21
224 *
225  CALL ctrsm( 'R', 'L', 'C', 'N', n2, n1, cone,
226  \$ a( 1, 1 ), lda, a( n1+1, 1 ), lda )
227 *
228 * Update and factor A22
229 *
230  CALL cherk( uplo, 'N', n2, n1, -one, a( n1+1, 1 ), lda,
231  \$ one, a( n1+1, n1+1 ), lda )
232 *
233  CALL cpotrf2( uplo, n2, a( n1+1, n1+1 ), lda, iinfo )
234 *
235  IF ( iinfo.NE.0 ) THEN
236  info = iinfo + n1
237  RETURN
238  END IF
239 *
240  END IF
241  END IF
242  RETURN
243 *
244 * End of CPOTRF2
245 *
logical function sisnan(SIN)
SISNAN tests input for NaN.
Definition: sisnan.f:61
subroutine cherk(UPLO, TRANS, N, K, ALPHA, A, LDA, BETA, C, LDC)
CHERK
Definition: cherk.f:175
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
subroutine ctrsm(SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
CTRSM
Definition: ctrsm.f:182
recursive subroutine cpotrf2(UPLO, N, A, LDA, INFO)
CPOTRF2
Definition: cpotrf2.f:108
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55

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