*> \brief \b CPOTRF
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
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*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE CPOTRF( UPLO, N, A, LDA, INFO )
*
* .. Scalar Arguments ..
* CHARACTER UPLO
* INTEGER INFO, LDA, N
* ..
* .. Array Arguments ..
* COMPLEX A( LDA, * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> CPOTRF 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.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] UPLO
*> \verbatim
*> UPLO is CHARACTER*1
*> = 'U': Upper triangle of A is stored;
*> = 'L': Lower triangle of A is stored.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The order of the matrix A. N >= 0.
*> \endverbatim
*>
*> \param[in,out] A
*> \verbatim
*> A is COMPLEX 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.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is INTEGER
*> The leading dimension of the array A. LDA >= max(1,N).
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*> 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.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date December 2016
*
*> \ingroup complexPOcomputational
*
* =====================================================================
SUBROUTINE CPOTRF( UPLO, N, A, LDA, INFO )
*
* -- LAPACK computational routine (version 3.7.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* December 2016
*
* .. Scalar Arguments ..
CHARACTER UPLO
INTEGER INFO, LDA, N
* ..
* .. Array Arguments ..
COMPLEX A( LDA, * )
* ..
*
* =====================================================================
*
* .. Parameters ..
REAL ONE
COMPLEX CONE
PARAMETER ( ONE = 1.0E+0, CONE = ( 1.0E+0, 0.0E+0 ) )
* ..
* .. Local Scalars ..
LOGICAL UPPER
INTEGER J, JB, NB
* ..
* .. External Functions ..
LOGICAL LSAME
INTEGER ILAENV
EXTERNAL LSAME, ILAENV
* ..
* .. External Subroutines ..
EXTERNAL CGEMM, CHERK, CPOTRF2, CTRSM, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX, MIN
* ..
* .. Executable Statements ..
*
* Test the input parameters.
*
INFO = 0
UPPER = LSAME( UPLO, 'U' )
IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
INFO = -1
ELSE IF( N.LT.0 ) THEN
INFO = -2
ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
INFO = -4
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'CPOTRF', -INFO )
RETURN
END IF
*
* Quick return if possible
*
IF( N.EQ.0 )
$ RETURN
*
* Determine the block size for this environment.
*
NB = ILAENV( 1, 'CPOTRF', UPLO, N, -1, -1, -1 )
IF( NB.LE.1 .OR. NB.GE.N ) THEN
*
* Use unblocked code.
*
CALL CPOTRF2( UPLO, N, A, LDA, INFO )
ELSE
*
* Use blocked code.
*
IF( UPPER ) THEN
*
* Compute the Cholesky factorization A = U**H *U.
*
DO 10 J = 1, N, NB
*
* Update and factorize the current diagonal block and test
* for non-positive-definiteness.
*
JB = MIN( NB, N-J+1 )
CALL CHERK( 'Upper', 'Conjugate transpose', JB, J-1,
$ -ONE, A( 1, J ), LDA, ONE, A( J, J ), LDA )
CALL CPOTRF2( 'Upper', JB, A( J, J ), LDA, INFO )
IF( INFO.NE.0 )
$ GO TO 30
IF( J+JB.LE.N ) THEN
*
* Compute the current block row.
*
CALL CGEMM( 'Conjugate transpose', 'No transpose', JB,
$ N-J-JB+1, J-1, -CONE, A( 1, J ), LDA,
$ A( 1, J+JB ), LDA, CONE, A( J, J+JB ),
$ LDA )
CALL CTRSM( 'Left', 'Upper', 'Conjugate transpose',
$ 'Non-unit', JB, N-J-JB+1, CONE, A( J, J ),
$ LDA, A( J, J+JB ), LDA )
END IF
10 CONTINUE
*
ELSE
*
* Compute the Cholesky factorization A = L*L**H.
*
DO 20 J = 1, N, NB
*
* Update and factorize the current diagonal block and test
* for non-positive-definiteness.
*
JB = MIN( NB, N-J+1 )
CALL CHERK( 'Lower', 'No transpose', JB, J-1, -ONE,
$ A( J, 1 ), LDA, ONE, A( J, J ), LDA )
CALL CPOTRF2( 'Lower', JB, A( J, J ), LDA, INFO )
IF( INFO.NE.0 )
$ GO TO 30
IF( J+JB.LE.N ) THEN
*
* Compute the current block column.
*
CALL CGEMM( 'No transpose', 'Conjugate transpose',
$ N-J-JB+1, JB, J-1, -CONE, A( J+JB, 1 ),
$ LDA, A( J, 1 ), LDA, CONE, A( J+JB, J ),
$ LDA )
CALL CTRSM( 'Right', 'Lower', 'Conjugate transpose',
$ 'Non-unit', N-J-JB+1, JB, CONE, A( J, J ),
$ LDA, A( J+JB, J ), LDA )
END IF
20 CONTINUE
END IF
END IF
GO TO 40
*
30 CONTINUE
INFO = INFO + J - 1
*
40 CONTINUE
RETURN
*
* End of CPOTRF
*
END