LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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## ◆ zpotrf2()

 recursive subroutine zpotrf2 ( character uplo, integer n, complex*16, dimension( lda, * ) a, integer lda, integer info )

ZPOTRF2

Purpose:
``` ZPOTRF2 computes the Cholesky factorization of a Hermitian
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 call 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*16 array, dimension (LDA,N) On entry, the Hermitian 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 principal minor of order i is not positive, and the factorization could not be completed.```

Definition at line 105 of file zpotrf2.f.

106*
107* -- LAPACK computational routine --
108* -- LAPACK is a software package provided by Univ. of Tennessee, --
109* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
110*
111* .. Scalar Arguments ..
112 CHARACTER UPLO
113 INTEGER INFO, LDA, N
114* ..
115* .. Array Arguments ..
116 COMPLEX*16 A( LDA, * )
117* ..
118*
119* =====================================================================
120*
121* .. Parameters ..
122 DOUBLE PRECISION ONE, ZERO
123 parameter( one = 1.0d+0, zero = 0.0d+0 )
124 COMPLEX*16 CONE
125 parameter( cone = (1.0d+0, 0.0d+0) )
126* ..
127* .. Local Scalars ..
128 LOGICAL UPPER
129 INTEGER N1, N2, IINFO
130 DOUBLE PRECISION AJJ
131* ..
132* .. External Functions ..
133 LOGICAL LSAME, DISNAN
134 EXTERNAL lsame, disnan
135* ..
136* .. External Subroutines ..
137 EXTERNAL zherk, ztrsm, xerbla
138* ..
139* .. Intrinsic Functions ..
140 INTRINSIC max, dble, sqrt
141* ..
142* .. Executable Statements ..
143*
144* Test the input parameters
145*
146 info = 0
147 upper = lsame( uplo, 'U' )
148 IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
149 info = -1
150 ELSE IF( n.LT.0 ) THEN
151 info = -2
152 ELSE IF( lda.LT.max( 1, n ) ) THEN
153 info = -4
154 END IF
155 IF( info.NE.0 ) THEN
156 CALL xerbla( 'ZPOTRF2', -info )
157 RETURN
158 END IF
159*
160* Quick return if possible
161*
162 IF( n.EQ.0 )
163 \$ RETURN
164*
165* N=1 case
166*
167 IF( n.EQ.1 ) THEN
168*
169* Test for non-positive-definiteness
170*
171 ajj = dble( a( 1, 1 ) )
172 IF( ajj.LE.zero.OR.disnan( ajj ) ) THEN
173 info = 1
174 RETURN
175 END IF
176*
177* Factor
178*
179 a( 1, 1 ) = sqrt( ajj )
180*
181* Use recursive code
182*
183 ELSE
184 n1 = n/2
185 n2 = n-n1
186*
187* Factor A11
188*
189 CALL zpotrf2( uplo, n1, a( 1, 1 ), lda, iinfo )
190 IF ( iinfo.NE.0 ) THEN
191 info = iinfo
192 RETURN
193 END IF
194*
195* Compute the Cholesky factorization A = U**H*U
196*
197 IF( upper ) THEN
198*
199* Update and scale A12
200*
201 CALL ztrsm( 'L', 'U', 'C', 'N', n1, n2, cone,
202 \$ a( 1, 1 ), lda, a( 1, n1+1 ), lda )
203*
204* Update and factor A22
205*
206 CALL zherk( uplo, 'C', n2, n1, -one, a( 1, n1+1 ), lda,
207 \$ one, a( n1+1, n1+1 ), lda )
208 CALL zpotrf2( uplo, n2, a( n1+1, n1+1 ), lda, iinfo )
209 IF ( iinfo.NE.0 ) THEN
210 info = iinfo + n1
211 RETURN
212 END IF
213*
214* Compute the Cholesky factorization A = L*L**H
215*
216 ELSE
217*
218* Update and scale A21
219*
220 CALL ztrsm( 'R', 'L', 'C', 'N', n2, n1, cone,
221 \$ a( 1, 1 ), lda, a( n1+1, 1 ), lda )
222*
223* Update and factor A22
224*
225 CALL zherk( uplo, 'N', n2, n1, -one, a( n1+1, 1 ), lda,
226 \$ one, a( n1+1, n1+1 ), lda )
227 CALL zpotrf2( uplo, n2, a( n1+1, n1+1 ), lda, iinfo )
228 IF ( iinfo.NE.0 ) THEN
229 info = iinfo + n1
230 RETURN
231 END IF
232 END IF
233 END IF
234 RETURN
235*
236* End of ZPOTRF2
237*
subroutine xerbla(srname, info)
Definition cblat2.f:3285
subroutine zherk(uplo, trans, n, k, alpha, a, lda, beta, c, ldc)
ZHERK
Definition zherk.f:173
logical function disnan(din)
DISNAN tests input for NaN.
Definition disnan.f:59
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
recursive subroutine zpotrf2(uplo, n, a, lda, info)
ZPOTRF2
Definition zpotrf2.f:106
subroutine ztrsm(side, uplo, transa, diag, m, n, alpha, a, lda, b, ldb)
ZTRSM
Definition ztrsm.f:180
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