1*> \brief \b ZPOTRF
2*
3*  =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6*            http://www.netlib.org/lapack/explore-html/
7*
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15*> [TXT]</a>
16*> \endhtmlonly
17*
18*  Definition:
19*  ===========
20*
21*       SUBROUTINE ZPOTRF( 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*> ZPOTRF 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 block version of the algorithm, calling Level 3 BLAS.
46*> \endverbatim
47*
48*  Arguments:
49*  ==========
50*
51*> \param[in] UPLO
52*> \verbatim
53*>          UPLO is CHARACTER*1
54*>          = 'U':  Upper triangle of A is stored;
55*>          = 'L':  Lower triangle of A is stored.
56*> \endverbatim
57*>
58*> \param[in] N
59*> \verbatim
60*>          N is INTEGER
61*>          The order of the matrix A.  N >= 0.
62*> \endverbatim
63*>
64*> \param[in,out] A
65*> \verbatim
66*>          A is COMPLEX*16 array, dimension (LDA,N)
67*>          On entry, the Hermitian matrix A.  If UPLO = 'U', the leading
68*>          N-by-N upper triangular part of A contains the upper
69*>          triangular part of the matrix A, and the strictly lower
70*>          triangular part of A is not referenced.  If UPLO = 'L', the
71*>          leading N-by-N lower triangular part of A contains the lower
72*>          triangular part of the matrix A, and the strictly upper
73*>          triangular part of A is not referenced.
74*>
75*>          On exit, if INFO = 0, the factor U or L from the Cholesky
76*>          factorization A = U**H *U or A = L*L**H.
77*> \endverbatim
78*>
79*> \param[in] LDA
80*> \verbatim
81*>          LDA is INTEGER
82*>          The leading dimension of the array A.  LDA >= max(1,N).
83*> \endverbatim
84*>
85*> \param[out] INFO
86*> \verbatim
87*>          INFO is INTEGER
88*>          = 0:  successful exit
89*>          < 0:  if INFO = -i, the i-th argument had an illegal value
90*>          > 0:  if INFO = i, the leading minor of order i is not
91*>                positive definite, and the factorization could not be
92*>                completed.
93*> \endverbatim
94*
95*  Authors:
96*  ========
97*
98*> \author Univ. of Tennessee
99*> \author Univ. of California Berkeley
100*> \author Univ. of Colorado Denver
101*> \author NAG Ltd.
102*
103*> \date November 2015
104*
105*> \ingroup complex16POcomputational
106*
107*  =====================================================================
108      SUBROUTINE ZPOTRF( UPLO, N, A, LDA, INFO )
109*
110*  -- LAPACK computational routine (version 3.6.0) --
111*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
112*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
113*     November 2015
114*
115*     .. Scalar Arguments ..
116      CHARACTER          UPLO
117      INTEGER            INFO, LDA, N
118*     ..
119*     .. Array Arguments ..
120      COMPLEX*16         A( LDA, * )
121*     ..
122*
123*  =====================================================================
124*
125*     .. Parameters ..
126      DOUBLE PRECISION   ONE
127      COMPLEX*16         CONE
128      PARAMETER          ( ONE = 1.0D+0, CONE = ( 1.0D+0, 0.0D+0 ) )
129*     ..
130*     .. Local Scalars ..
131      LOGICAL            UPPER
132      INTEGER            J, JB, NB
133*     ..
134*     .. External Functions ..
135      LOGICAL            LSAME
136      INTEGER            ILAENV
137      EXTERNAL           LSAME, ILAENV
138*     ..
139*     .. External Subroutines ..
140      EXTERNAL           XERBLA, ZGEMM, ZHERK, ZPOTRF2, ZTRSM
141*     ..
142*     .. Intrinsic Functions ..
143      INTRINSIC          MAX, MIN
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( 'ZPOTRF', -INFO )
160         RETURN
161      END IF
162*
163*     Quick return if possible
164*
165      IF( N.EQ.0 )
166     $   RETURN
167*
168*     Determine the block size for this environment.
169*
170      NB = ILAENV( 1, 'ZPOTRF', UPLO, N, -1, -1, -1 )
171      IF( NB.LE.1 .OR. NB.GE.N ) THEN
172*
173*        Use unblocked code.
174*
175         CALL ZPOTRF2( UPLO, N, A, LDA, INFO )
176      ELSE
177*
178*        Use blocked code.
179*
180         IF( UPPER ) THEN
181*
182*           Compute the Cholesky factorization A = U**H *U.
183*
184            DO 10 J = 1, N, NB
185*
186*              Update and factorize the current diagonal block and test
187*              for non-positive-definiteness.
188*
189               JB = MIN( NB, N-J+1 )
190               CALL ZHERK( 'Upper', 'Conjugate transpose', JB, J-1,
191     $                     -ONE, A( 1, J ), LDA, ONE, A( J, J ), LDA )
192               CALL ZPOTRF2( 'Upper', JB, A( J, J ), LDA, INFO )
193               IF( INFO.NE.0 )
194     $            GO TO 30
195               IF( J+JB.LE.N ) THEN
196*
197*                 Compute the current block row.
198*
199                  CALL ZGEMM( 'Conjugate transpose', 'No transpose', JB,
200     $                        N-J-JB+1, J-1, -CONE, A( 1, J ), LDA,
201     $                        A( 1, J+JB ), LDA, CONE, A( J, J+JB ),
202     $                        LDA )
203                  CALL ZTRSM( 'Left', 'Upper', 'Conjugate transpose',
204     $                        'Non-unit', JB, N-J-JB+1, CONE, A( J, J ),
205     $                        LDA, A( J, J+JB ), LDA )
206               END IF
207   10       CONTINUE
208*
209         ELSE
210*
211*           Compute the Cholesky factorization A = L*L**H.
212*
213            DO 20 J = 1, N, NB
214*
215*              Update and factorize the current diagonal block and test
216*              for non-positive-definiteness.
217*
218               JB = MIN( NB, N-J+1 )
219               CALL ZHERK( 'Lower', 'No transpose', JB, J-1, -ONE,
220     $                     A( J, 1 ), LDA, ONE, A( J, J ), LDA )
221               CALL ZPOTRF2( 'Lower', JB, A( J, J ), LDA, INFO )
222               IF( INFO.NE.0 )
223     $            GO TO 30
224               IF( J+JB.LE.N ) THEN
225*
226*                 Compute the current block column.
227*
228                  CALL ZGEMM( 'No transpose', 'Conjugate transpose',
229     $                        N-J-JB+1, JB, J-1, -CONE, A( J+JB, 1 ),
230     $                        LDA, A( J, 1 ), LDA, CONE, A( J+JB, J ),
231     $                        LDA )
232                  CALL ZTRSM( 'Right', 'Lower', 'Conjugate transpose',
233     $                        'Non-unit', N-J-JB+1, JB, CONE, A( J, J ),
234     $                        LDA, A( J+JB, J ), LDA )
235               END IF
236   20       CONTINUE
237         END IF
238      END IF
239      GO TO 40
240*
241   30 CONTINUE
242      INFO = INFO + J - 1
243*
244   40 CONTINUE
245      RETURN
246*
247*     End of ZPOTRF
248*
249      END
250