 LAPACK  3.9.1 LAPACK: Linear Algebra PACKage

## ◆ 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 minor of order i is not positive definite, 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 *
logical function disnan(DIN)
DISNAN tests input for NaN.
Definition: disnan.f:59
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine zherk(UPLO, TRANS, N, K, ALPHA, A, LDA, BETA, C, LDC)
ZHERK
Definition: zherk.f:173
subroutine ztrsm(SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
ZTRSM
Definition: ztrsm.f:180
recursive subroutine zpotrf2(UPLO, N, A, LDA, INFO)
ZPOTRF2
Definition: zpotrf2.f:106
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