 LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ zpotrf()

 subroutine zpotrf ( character UPLO, integer N, complex*16, dimension( lda, * ) A, integer LDA, integer INFO )

ZPOTRF

Purpose:
``` ZPOTRF computes the Cholesky factorization of a complex Hermitian
positive definite matrix A.

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 block version of the algorithm, calling Level 3 BLAS.```
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 106 of file zpotrf.f.

107*
108* -- LAPACK computational routine --
109* -- LAPACK is a software package provided by Univ. of Tennessee, --
110* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
111*
112* .. Scalar Arguments ..
113 CHARACTER UPLO
114 INTEGER INFO, LDA, N
115* ..
116* .. Array Arguments ..
117 COMPLEX*16 A( LDA, * )
118* ..
119*
120* =====================================================================
121*
122* .. Parameters ..
123 DOUBLE PRECISION ONE
124 COMPLEX*16 CONE
125 parameter( one = 1.0d+0, cone = ( 1.0d+0, 0.0d+0 ) )
126* ..
127* .. Local Scalars ..
128 LOGICAL UPPER
129 INTEGER J, JB, NB
130* ..
131* .. External Functions ..
132 LOGICAL LSAME
133 INTEGER ILAENV
134 EXTERNAL lsame, ilaenv
135* ..
136* .. External Subroutines ..
137 EXTERNAL xerbla, zgemm, zherk, zpotrf2, ztrsm
138* ..
139* .. Intrinsic Functions ..
140 INTRINSIC max, min
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( 'ZPOTRF', -info )
157 RETURN
158 END IF
159*
160* Quick return if possible
161*
162 IF( n.EQ.0 )
163 \$ RETURN
164*
165* Determine the block size for this environment.
166*
167 nb = ilaenv( 1, 'ZPOTRF', uplo, n, -1, -1, -1 )
168 IF( nb.LE.1 .OR. nb.GE.n ) THEN
169*
170* Use unblocked code.
171*
172 CALL zpotrf2( uplo, n, a, lda, info )
173 ELSE
174*
175* Use blocked code.
176*
177 IF( upper ) THEN
178*
179* Compute the Cholesky factorization A = U**H *U.
180*
181 DO 10 j = 1, n, nb
182*
183* Update and factorize the current diagonal block and test
184* for non-positive-definiteness.
185*
186 jb = min( nb, n-j+1 )
187 CALL zherk( 'Upper', 'Conjugate transpose', jb, j-1,
188 \$ -one, a( 1, j ), lda, one, a( j, j ), lda )
189 CALL zpotrf2( 'Upper', jb, a( j, j ), lda, info )
190 IF( info.NE.0 )
191 \$ GO TO 30
192 IF( j+jb.LE.n ) THEN
193*
194* Compute the current block row.
195*
196 CALL zgemm( 'Conjugate transpose', 'No transpose', jb,
197 \$ n-j-jb+1, j-1, -cone, a( 1, j ), lda,
198 \$ a( 1, j+jb ), lda, cone, a( j, j+jb ),
199 \$ lda )
200 CALL ztrsm( 'Left', 'Upper', 'Conjugate transpose',
201 \$ 'Non-unit', jb, n-j-jb+1, cone, a( j, j ),
202 \$ lda, a( j, j+jb ), lda )
203 END IF
204 10 CONTINUE
205*
206 ELSE
207*
208* Compute the Cholesky factorization A = L*L**H.
209*
210 DO 20 j = 1, n, nb
211*
212* Update and factorize the current diagonal block and test
213* for non-positive-definiteness.
214*
215 jb = min( nb, n-j+1 )
216 CALL zherk( 'Lower', 'No transpose', jb, j-1, -one,
217 \$ a( j, 1 ), lda, one, a( j, j ), lda )
218 CALL zpotrf2( 'Lower', jb, a( j, j ), lda, info )
219 IF( info.NE.0 )
220 \$ GO TO 30
221 IF( j+jb.LE.n ) THEN
222*
223* Compute the current block column.
224*
225 CALL zgemm( 'No transpose', 'Conjugate transpose',
226 \$ n-j-jb+1, jb, j-1, -cone, a( j+jb, 1 ),
227 \$ lda, a( j, 1 ), lda, cone, a( j+jb, j ),
228 \$ lda )
229 CALL ztrsm( 'Right', 'Lower', 'Conjugate transpose',
230 \$ 'Non-unit', n-j-jb+1, jb, cone, a( j, j ),
231 \$ lda, a( j+jb, j ), lda )
232 END IF
233 20 CONTINUE
234 END IF
235 END IF
236 GO TO 40
237*
238 30 CONTINUE
239 info = info + j - 1
240*
241 40 CONTINUE
242 RETURN
243*
244* End of ZPOTRF
245*
integer function ilaenv(ISPEC, NAME, OPTS, N1, N2, N3, N4)
ILAENV
Definition: ilaenv.f:162
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine zgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
ZGEMM
Definition: zgemm.f:187
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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