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*> \brief \b SPOTF2 computes the Cholesky factorization of a symmetric/Hermitian positive definite matrix (unblocked algorithm).
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download SPOTF2 + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/spotf2.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/spotf2.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/spotf2.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE SPOTF2( UPLO, N, A, LDA, INFO )
*
* .. Scalar Arguments ..
* CHARACTER UPLO
* INTEGER INFO, LDA, N
* ..
* .. Array Arguments ..
* REAL A( LDA, * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> SPOTF2 computes the Cholesky factorization of a real symmetric
*> positive definite matrix A.
*>
*> 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 unblocked version of the algorithm, calling Level 2 BLAS.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] UPLO
*> \verbatim
*> UPLO is CHARACTER*1
*> Specifies whether the upper or lower triangular part of the
*> symmetric matrix A is stored.
*> = 'U': Upper triangular
*> = 'L': Lower triangular
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The order of the matrix A. N >= 0.
*> \endverbatim
*>
*> \param[in,out] A
*> \verbatim
*> A is REAL 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 = -k, the k-th argument had an illegal value
*> > 0: if INFO = k, the leading minor of order k 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 November 2011
*
*> \ingroup realPOcomputational
*
* =====================================================================
SUBROUTINE SPOTF2( UPLO, N, A, LDA, INFO )
*
* -- LAPACK computational routine (version 3.4.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* November 2011
*
* .. Scalar Arguments ..
CHARACTER UPLO
INTEGER INFO, LDA, N
* ..
* .. Array Arguments ..
REAL A( LDA, * )
* ..
*
* =====================================================================
*
* .. Parameters ..
REAL ONE, ZERO
PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 )
* ..
* .. Local Scalars ..
LOGICAL UPPER
INTEGER J
REAL AJJ
* ..
* .. External Functions ..
LOGICAL LSAME, SISNAN
REAL SDOT
EXTERNAL LSAME, SDOT, SISNAN
* ..
* .. External Subroutines ..
EXTERNAL SGEMV, SSCAL, 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( 'SPOTF2', -INFO )
RETURN
END IF
*
* Quick return if possible
*
IF( N.EQ.0 )
$ RETURN
*
IF( UPPER ) THEN
*
* Compute the Cholesky factorization A = U**T *U.
*
DO 10 J = 1, N
*
* Compute U(J,J) and test for non-positive-definiteness.
*
AJJ = A( J, J ) - SDOT( J-1, A( 1, J ), 1, A( 1, J ), 1 )
IF( AJJ.LE.ZERO.OR.SISNAN( AJJ ) ) THEN
A( J, J ) = AJJ
GO TO 30
END IF
AJJ = SQRT( AJJ )
A( J, J ) = AJJ
*
* Compute elements J+1:N of row J.
*
IF( J.LT.N ) THEN
CALL SGEMV( 'Transpose', J-1, N-J, -ONE, A( 1, J+1 ),
$ LDA, A( 1, J ), 1, ONE, A( J, J+1 ), LDA )
CALL SSCAL( N-J, ONE / AJJ, A( J, J+1 ), LDA )
END IF
10 CONTINUE
ELSE
*
* Compute the Cholesky factorization A = L*L**T.
*
DO 20 J = 1, N
*
* Compute L(J,J) and test for non-positive-definiteness.
*
AJJ = A( J, J ) - SDOT( J-1, A( J, 1 ), LDA, A( J, 1 ),
$ LDA )
IF( AJJ.LE.ZERO.OR.SISNAN( AJJ ) ) THEN
A( J, J ) = AJJ
GO TO 30
END IF
AJJ = SQRT( AJJ )
A( J, J ) = AJJ
*
* Compute elements J+1:N of column J.
*
IF( J.LT.N ) THEN
CALL SGEMV( 'No transpose', N-J, J-1, -ONE, A( J+1, 1 ),
$ LDA, A( J, 1 ), LDA, ONE, A( J+1, J ), 1 )
CALL SSCAL( N-J, ONE / AJJ, A( J+1, J ), 1 )
END IF
20 CONTINUE
END IF
GO TO 40
*
30 CONTINUE
INFO = J
*
40 CONTINUE
RETURN
*
* End of SPOTF2
*
END
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