Julie
e18d437924
GitHub is now enabling us to track accurately version and date. No need for this anymore.
235 lines
6.1 KiB
FortranFixed
235 lines
6.1 KiB
FortranFixed
*> \brief \b DPOTRF2
|
|
*
|
|
* =========== DOCUMENTATION ===========
|
|
*
|
|
* Online html documentation available at
|
|
* http://www.netlib.org/lapack/explore-html/
|
|
*
|
|
* Definition:
|
|
* ===========
|
|
*
|
|
* RECURSIVE SUBROUTINE DPOTRF2( UPLO, N, A, LDA, INFO )
|
|
*
|
|
* .. Scalar Arguments ..
|
|
* CHARACTER UPLO
|
|
* INTEGER INFO, LDA, N
|
|
* ..
|
|
* .. Array Arguments ..
|
|
* REAL A( LDA, * )
|
|
* ..
|
|
*
|
|
*
|
|
*> \par Purpose:
|
|
* =============
|
|
*>
|
|
*> \verbatim
|
|
*>
|
|
*> DPOTRF2 computes the Cholesky factorization of a real symmetric
|
|
*> positive definite matrix A using the recursive algorithm.
|
|
*>
|
|
*> The factorization has the form
|
|
*> A = U**T * U, if UPLO = 'U', or
|
|
*> A = L * L**T, if UPLO = 'L',
|
|
*> where U is an upper triangular matrix and L is lower triangular.
|
|
*>
|
|
*> This is the recursive version of the algorithm. It divides
|
|
*> the matrix into four submatrices:
|
|
*>
|
|
*> [ A11 | A12 ] where A11 is n1 by n1 and A22 is n2 by n2
|
|
*> A = [ -----|----- ] with n1 = n/2
|
|
*> [ A21 | A22 ] n2 = n-n1
|
|
*>
|
|
*> The subroutine calls itself to factor A11. Update and scale A21
|
|
*> or A12, update A22 then calls itself to factor A22.
|
|
*>
|
|
*> \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 DOUBLE PRECISION array, dimension (LDA,N)
|
|
*> On entry, the symmetric 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**T*U or A = L*L**T.
|
|
*> \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.
|
|
*
|
|
*> \ingroup doublePOcomputational
|
|
*
|
|
* =====================================================================
|
|
RECURSIVE SUBROUTINE DPOTRF2( UPLO, N, A, LDA, INFO )
|
|
*
|
|
* -- LAPACK computational routine --
|
|
* -- LAPACK is a software package provided by Univ. of Tennessee, --
|
|
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
|
*
|
|
* .. Scalar Arguments ..
|
|
CHARACTER UPLO
|
|
INTEGER INFO, LDA, N
|
|
* ..
|
|
* .. Array Arguments ..
|
|
DOUBLE PRECISION A( LDA, * )
|
|
* ..
|
|
*
|
|
* =====================================================================
|
|
*
|
|
* .. Parameters ..
|
|
DOUBLE PRECISION ONE, ZERO
|
|
PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
|
|
* ..
|
|
* .. Local Scalars ..
|
|
LOGICAL UPPER
|
|
INTEGER N1, N2, IINFO
|
|
* ..
|
|
* .. External Functions ..
|
|
LOGICAL LSAME, DISNAN
|
|
EXTERNAL LSAME, DISNAN
|
|
* ..
|
|
* .. External Subroutines ..
|
|
EXTERNAL DSYRK, DTRSM, XERBLA
|
|
* ..
|
|
* .. Intrinsic Functions ..
|
|
INTRINSIC MAX, SQRT
|
|
* ..
|
|
* .. 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( 'DPOTRF2', -INFO )
|
|
RETURN
|
|
END IF
|
|
*
|
|
* Quick return if possible
|
|
*
|
|
IF( N.EQ.0 )
|
|
$ RETURN
|
|
*
|
|
* N=1 case
|
|
*
|
|
IF( N.EQ.1 ) THEN
|
|
*
|
|
* Test for non-positive-definiteness
|
|
*
|
|
IF( A( 1, 1 ).LE.ZERO.OR.DISNAN( A( 1, 1 ) ) ) THEN
|
|
INFO = 1
|
|
RETURN
|
|
END IF
|
|
*
|
|
* Factor
|
|
*
|
|
A( 1, 1 ) = SQRT( A( 1, 1 ) )
|
|
*
|
|
* Use recursive code
|
|
*
|
|
ELSE
|
|
N1 = N/2
|
|
N2 = N-N1
|
|
*
|
|
* Factor A11
|
|
*
|
|
CALL DPOTRF2( UPLO, N1, A( 1, 1 ), LDA, IINFO )
|
|
IF ( IINFO.NE.0 ) THEN
|
|
INFO = IINFO
|
|
RETURN
|
|
END IF
|
|
*
|
|
* Compute the Cholesky factorization A = U**T*U
|
|
*
|
|
IF( UPPER ) THEN
|
|
*
|
|
* Update and scale A12
|
|
*
|
|
CALL DTRSM( 'L', 'U', 'T', 'N', N1, N2, ONE,
|
|
$ A( 1, 1 ), LDA, A( 1, N1+1 ), LDA )
|
|
*
|
|
* Update and factor A22
|
|
*
|
|
CALL DSYRK( UPLO, 'T', N2, N1, -ONE, A( 1, N1+1 ), LDA,
|
|
$ ONE, A( N1+1, N1+1 ), LDA )
|
|
CALL DPOTRF2( UPLO, N2, A( N1+1, N1+1 ), LDA, IINFO )
|
|
IF ( IINFO.NE.0 ) THEN
|
|
INFO = IINFO + N1
|
|
RETURN
|
|
END IF
|
|
*
|
|
* Compute the Cholesky factorization A = L*L**T
|
|
*
|
|
ELSE
|
|
*
|
|
* Update and scale A21
|
|
*
|
|
CALL DTRSM( 'R', 'L', 'T', 'N', N2, N1, ONE,
|
|
$ A( 1, 1 ), LDA, A( N1+1, 1 ), LDA )
|
|
*
|
|
* Update and factor A22
|
|
*
|
|
CALL DSYRK( UPLO, 'N', N2, N1, -ONE, A( N1+1, 1 ), LDA,
|
|
$ ONE, A( N1+1, N1+1 ), LDA )
|
|
CALL DPOTRF2( UPLO, N2, A( N1+1, N1+1 ), LDA, IINFO )
|
|
IF ( IINFO.NE.0 ) THEN
|
|
INFO = IINFO + N1
|
|
RETURN
|
|
END IF
|
|
END IF
|
|
END IF
|
|
RETURN
|
|
*
|
|
* End of DPOTRF2
|
|
*
|
|
END
|