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235 lines
6.7 KiB
235 lines
6.7 KiB
2 years ago
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*> \brief \b ZPOTF2 computes the Cholesky factorization of a symmetric/Hermitian positive definite matrix (unblocked algorithm).
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*
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* =========== DOCUMENTATION ===========
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*
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* Online html documentation available at
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* http://www.netlib.org/lapack/explore-html/
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*
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*> \htmlonly
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*> Download ZPOTF2 + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zpotf2.f">
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*> [TGZ]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zpotf2.f">
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*> [ZIP]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zpotf2.f">
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*> [TXT]</a>
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*> \endhtmlonly
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*
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* Definition:
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* ===========
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*
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* SUBROUTINE ZPOTF2( UPLO, N, A, LDA, INFO )
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*
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* .. Scalar Arguments ..
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* CHARACTER UPLO
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* INTEGER INFO, LDA, N
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* ..
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* .. Array Arguments ..
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* COMPLEX*16 A( LDA, * )
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* ..
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*
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*
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*> \par Purpose:
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* =============
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*>
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*> \verbatim
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*>
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*> ZPOTF2 computes the Cholesky factorization of a complex Hermitian
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*> positive definite matrix A.
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*>
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*> The factorization has the form
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*> A = U**H * U , if UPLO = 'U', or
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*> A = L * L**H, if UPLO = 'L',
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*> where U is an upper triangular matrix and L is lower triangular.
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*>
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*> This is the unblocked version of the algorithm, calling Level 2 BLAS.
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*> \endverbatim
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*
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* Arguments:
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* ==========
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*
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*> \param[in] UPLO
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*> \verbatim
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*> UPLO is CHARACTER*1
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*> Specifies whether the upper or lower triangular part of the
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*> Hermitian matrix A is stored.
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*> = 'U': Upper triangular
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*> = 'L': Lower triangular
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*> \endverbatim
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*>
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*> \param[in] N
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*> \verbatim
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*> N is INTEGER
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*> The order of the matrix A. N >= 0.
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*> \endverbatim
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*>
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*> \param[in,out] A
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*> \verbatim
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*> A is COMPLEX*16 array, dimension (LDA,N)
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*> On entry, the Hermitian matrix A. If UPLO = 'U', the leading
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*> n by n upper triangular part of A contains the upper
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*> triangular part of the matrix A, and the strictly lower
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*> triangular part of A is not referenced. If UPLO = 'L', the
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*> leading n by n lower triangular part of A contains the lower
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*> triangular part of the matrix A, and the strictly upper
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*> triangular part of A is not referenced.
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*>
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*> On exit, if INFO = 0, the factor U or L from the Cholesky
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*> factorization A = U**H *U or A = L*L**H.
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*> \endverbatim
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*>
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*> \param[in] LDA
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*> \verbatim
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*> LDA is INTEGER
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*> The leading dimension of the array A. LDA >= max(1,N).
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*> \endverbatim
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*>
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*> \param[out] INFO
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*> \verbatim
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*> INFO is INTEGER
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*> = 0: successful exit
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*> < 0: if INFO = -k, the k-th argument had an illegal value
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*> > 0: if INFO = k, the leading principal minor of order k
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*> is not positive, and the factorization could not be
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*> completed.
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*> \endverbatim
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*
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* Authors:
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* ========
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*
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*> \author Univ. of Tennessee
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*> \author Univ. of California Berkeley
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*> \author Univ. of Colorado Denver
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*> \author NAG Ltd.
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*
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*> \ingroup complex16POcomputational
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*
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* =====================================================================
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SUBROUTINE ZPOTF2( UPLO, N, A, LDA, INFO )
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*
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* -- LAPACK computational routine --
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* -- LAPACK is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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*
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* .. Scalar Arguments ..
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CHARACTER UPLO
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INTEGER INFO, LDA, N
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* ..
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* .. Array Arguments ..
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COMPLEX*16 A( LDA, * )
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* ..
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*
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* =====================================================================
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*
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* .. Parameters ..
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DOUBLE PRECISION ONE, ZERO
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PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
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COMPLEX*16 CONE
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PARAMETER ( CONE = ( 1.0D+0, 0.0D+0 ) )
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* ..
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* .. Local Scalars ..
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LOGICAL UPPER
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INTEGER J
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DOUBLE PRECISION AJJ
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* ..
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* .. External Functions ..
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LOGICAL LSAME, DISNAN
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COMPLEX*16 ZDOTC
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EXTERNAL LSAME, ZDOTC, DISNAN
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* ..
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* .. External Subroutines ..
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EXTERNAL XERBLA, ZDSCAL, ZGEMV, ZLACGV
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC DBLE, MAX, SQRT
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* ..
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* .. Executable Statements ..
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*
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* Test the input parameters.
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*
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INFO = 0
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UPPER = LSAME( UPLO, 'U' )
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IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
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INFO = -1
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ELSE IF( N.LT.0 ) THEN
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INFO = -2
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ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
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INFO = -4
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END IF
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'ZPOTF2', -INFO )
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RETURN
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END IF
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*
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* Quick return if possible
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*
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IF( N.EQ.0 )
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$ RETURN
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*
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IF( UPPER ) THEN
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*
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* Compute the Cholesky factorization A = U**H *U.
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*
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DO 10 J = 1, N
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*
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* Compute U(J,J) and test for non-positive-definiteness.
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*
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AJJ = DBLE( A( J, J ) ) - DBLE( ZDOTC( J-1, A( 1, J ), 1,
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$ A( 1, J ), 1 ) )
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IF( AJJ.LE.ZERO.OR.DISNAN( AJJ ) ) THEN
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A( J, J ) = AJJ
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GO TO 30
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END IF
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AJJ = SQRT( AJJ )
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A( J, J ) = AJJ
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*
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* Compute elements J+1:N of row J.
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*
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IF( J.LT.N ) THEN
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CALL ZLACGV( J-1, A( 1, J ), 1 )
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CALL ZGEMV( 'Transpose', J-1, N-J, -CONE, A( 1, J+1 ),
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$ LDA, A( 1, J ), 1, CONE, A( J, J+1 ), LDA )
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CALL ZLACGV( J-1, A( 1, J ), 1 )
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CALL ZDSCAL( N-J, ONE / AJJ, A( J, J+1 ), LDA )
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END IF
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10 CONTINUE
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ELSE
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*
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* Compute the Cholesky factorization A = L*L**H.
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*
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DO 20 J = 1, N
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*
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* Compute L(J,J) and test for non-positive-definiteness.
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*
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AJJ = DBLE( A( J, J ) ) - DBLE( ZDOTC( J-1, A( J, 1 ), LDA,
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$ A( J, 1 ), LDA ) )
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IF( AJJ.LE.ZERO.OR.DISNAN( AJJ ) ) THEN
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A( J, J ) = AJJ
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GO TO 30
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END IF
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AJJ = SQRT( AJJ )
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A( J, J ) = AJJ
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*
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* Compute elements J+1:N of column J.
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*
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IF( J.LT.N ) THEN
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CALL ZLACGV( J-1, A( J, 1 ), LDA )
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CALL ZGEMV( 'No transpose', N-J, J-1, -CONE, A( J+1, 1 ),
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$ LDA, A( J, 1 ), LDA, CONE, A( J+1, J ), 1 )
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CALL ZLACGV( J-1, A( J, 1 ), LDA )
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CALL ZDSCAL( N-J, ONE / AJJ, A( J+1, J ), 1 )
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END IF
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20 CONTINUE
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END IF
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GO TO 40
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*
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30 CONTINUE
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INFO = J
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*
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40 CONTINUE
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RETURN
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*
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* End of ZPOTF2
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*
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END
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