1*> \brief \b CPOTF2 computes the Cholesky factorization of a symmetric/Hermitian positive definite matrix (unblocked algorithm).
2*
3*  =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6*            http://www.netlib.org/lapack/explore-html/
7*
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16*> \endhtmlonly
17*
18*  Definition:
19*  ===========
20*
21*       SUBROUTINE CPOTF2( UPLO, N, A, LDA, INFO )
22*
23*       .. Scalar Arguments ..
24*       CHARACTER          UPLO
25*       INTEGER            INFO, LDA, N
26*       ..
27*       .. Array Arguments ..
28*       COMPLEX            A( LDA, * )
29*       ..
30*
31*
32*> \par Purpose:
33*  =============
34*>
35*> \verbatim
36*>
37*> CPOTF2 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 unblocked version of the algorithm, calling Level 2 BLAS.
46*> \endverbatim
47*
48*  Arguments:
49*  ==========
50*
51*> \param[in] UPLO
52*> \verbatim
53*>          UPLO is CHARACTER*1
54*>          Specifies whether the upper or lower triangular part of the
55*>          Hermitian matrix A is stored.
56*>          = 'U':  Upper triangular
57*>          = 'L':  Lower triangular
58*> \endverbatim
59*>
60*> \param[in] N
61*> \verbatim
62*>          N is INTEGER
63*>          The order of the matrix A.  N >= 0.
64*> \endverbatim
65*>
66*> \param[in,out] A
67*> \verbatim
68*>          A is COMPLEX array, dimension (LDA,N)
69*>          On entry, the Hermitian matrix A.  If UPLO = 'U', the leading
70*>          n by n upper triangular part of A contains the upper
71*>          triangular part of the matrix A, and the strictly lower
72*>          triangular part of A is not referenced.  If UPLO = 'L', the
73*>          leading n by n lower triangular part of A contains the lower
74*>          triangular part of the matrix A, and the strictly upper
75*>          triangular part of A is not referenced.
76*>
77*>          On exit, if INFO = 0, the factor U or L from the Cholesky
78*>          factorization A = U**H *U  or A = L*L**H.
79*> \endverbatim
80*>
81*> \param[in] LDA
82*> \verbatim
83*>          LDA is INTEGER
84*>          The leading dimension of the array A.  LDA >= max(1,N).
85*> \endverbatim
86*>
87*> \param[out] INFO
88*> \verbatim
89*>          INFO is INTEGER
90*>          = 0: successful exit
91*>          < 0: if INFO = -k, the k-th argument had an illegal value
92*>          > 0: if INFO = k, the leading minor of order k is not
93*>               positive definite, and the factorization could not be
94*>               completed.
95*> \endverbatim
96*
97*  Authors:
98*  ========
99*
100*> \author Univ. of Tennessee
101*> \author Univ. of California Berkeley
102*> \author Univ. of Colorado Denver
103*> \author NAG Ltd.
104*
105*> \date September 2012
106*
107*> \ingroup complexPOcomputational
108*
109*  =====================================================================
110      SUBROUTINE CPOTF2( UPLO, N, A, LDA, INFO )
111*
112*  -- LAPACK computational routine (version 3.4.2) --
113*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
114*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
115*     September 2012
116*
117*     .. Scalar Arguments ..
118      CHARACTER          UPLO
119      INTEGER            INFO, LDA, N
120*     ..
121*     .. Array Arguments ..
122      COMPLEX            A( LDA, * )
123*     ..
124*
125*  =====================================================================
126*
127*     .. Parameters ..
128      REAL               ONE, ZERO
129      PARAMETER          ( ONE = 1.0E+0, ZERO = 0.0E+0 )
130      COMPLEX            CONE
131      PARAMETER          ( CONE = ( 1.0E+0, 0.0E+0 ) )
132*     ..
133*     .. Local Scalars ..
134      LOGICAL            UPPER
135      INTEGER            J
136      REAL               AJJ
137*     ..
138*     .. External Functions ..
139      LOGICAL            LSAME, SISNAN
140      COMPLEX            CDOTC
141      EXTERNAL           LSAME, CDOTC, SISNAN
142*     ..
143*     .. External Subroutines ..
144      EXTERNAL           CGEMV, CLACGV, CSSCAL, XERBLA
145*     ..
146*     .. Intrinsic Functions ..
147      INTRINSIC          MAX, REAL, SQRT
148*     ..
149*     .. Executable Statements ..
150*
151*     Test the input parameters.
152*
153      INFO = 0
154      UPPER = LSAME( UPLO, 'U' )
155      IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
156         INFO = -1
157      ELSE IF( N.LT.0 ) THEN
158         INFO = -2
159      ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
160         INFO = -4
161      END IF
162      IF( INFO.NE.0 ) THEN
163         CALL XERBLA( 'CPOTF2', -INFO )
164         RETURN
165      END IF
166*
167*     Quick return if possible
168*
169      IF( N.EQ.0 )
170     $   RETURN
171*
172      IF( UPPER ) THEN
173*
174*        Compute the Cholesky factorization A = U**H *U.
175*
176         DO 10 J = 1, N
177*
178*           Compute U(J,J) and test for non-positive-definiteness.
179*
180            AJJ = REAL( A( J, J ) ) - CDOTC( J-1, A( 1, J ), 1,
181     $            A( 1, J ), 1 )
182            IF( AJJ.LE.ZERO.OR.SISNAN( AJJ ) ) THEN
183               A( J, J ) = AJJ
184               GO TO 30
185            END IF
186            AJJ = SQRT( AJJ )
187            A( J, J ) = AJJ
188*
189*           Compute elements J+1:N of row J.
190*
191            IF( J.LT.N ) THEN
192               CALL CLACGV( J-1, A( 1, J ), 1 )
193               CALL CGEMV( 'Transpose', J-1, N-J, -CONE, A( 1, J+1 ),
194     $                     LDA, A( 1, J ), 1, CONE, A( J, J+1 ), LDA )
195               CALL CLACGV( J-1, A( 1, J ), 1 )
196               CALL CSSCAL( N-J, ONE / AJJ, A( J, J+1 ), LDA )
197            END IF
198   10    CONTINUE
199      ELSE
200*
201*        Compute the Cholesky factorization A = L*L**H.
202*
203         DO 20 J = 1, N
204*
205*           Compute L(J,J) and test for non-positive-definiteness.
206*
207            AJJ = REAL( A( J, J ) ) - CDOTC( J-1, A( J, 1 ), LDA,
208     $            A( J, 1 ), LDA )
209            IF( AJJ.LE.ZERO.OR.SISNAN( AJJ ) ) THEN
210               A( J, J ) = AJJ
211               GO TO 30
212            END IF
213            AJJ = SQRT( AJJ )
214            A( J, J ) = AJJ
215*
216*           Compute elements J+1:N of column J.
217*
218            IF( J.LT.N ) THEN
219               CALL CLACGV( J-1, A( J, 1 ), LDA )
220               CALL CGEMV( 'No transpose', N-J, J-1, -CONE, A( J+1, 1 ),
221     $                     LDA, A( J, 1 ), LDA, CONE, A( J+1, J ), 1 )
222               CALL CLACGV( J-1, A( J, 1 ), LDA )
223               CALL CSSCAL( N-J, ONE / AJJ, A( J+1, J ), 1 )
224            END IF
225   20    CONTINUE
226      END IF
227      GO TO 40
228*
229   30 CONTINUE
230      INFO = J
231*
232   40 CONTINUE
233      RETURN
234*
235*     End of CPOTF2
236*
237      END
238