C> \brief \b SPOTRF VARIANT: top-looking block version of the algorithm, calling Level 3 BLAS.
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE SPOTRF ( UPLO, N, A, LDA, INFO )
*
* .. Scalar Arguments ..
* CHARACTER UPLO
* INTEGER INFO, LDA, N
* ..
* .. Array Arguments ..
* REAL A( LDA, * )
* ..
*
* Purpose
* =======
*
C>\details \b Purpose:
C>\verbatim
C>
C> SPOTRF computes the Cholesky factorization of a real symmetric
C> positive definite matrix A.
C>
C> The factorization has the form
C> A = U**T * U, if UPLO = 'U', or
C> A = L * L**T, if UPLO = 'L',
C> where U is an upper triangular matrix and L is lower triangular.
C>
C> This is the top-looking block version of the algorithm, calling Level 3 BLAS.
C>
C>\endverbatim
*
* Arguments:
* ==========
*
C> \param[in] UPLO
C> \verbatim
C> UPLO is CHARACTER*1
C> = 'U': Upper triangle of A is stored;
C> = 'L': Lower triangle of A is stored.
C> \endverbatim
C>
C> \param[in] N
C> \verbatim
C> N is INTEGER
C> The order of the matrix A. N >= 0.
C> \endverbatim
C>
C> \param[in,out] A
C> \verbatim
C> A is REAL array, dimension (LDA,N)
C> On entry, the symmetric matrix A. If UPLO = 'U', the leading
C> N-by-N upper triangular part of A contains the upper
C> triangular part of the matrix A, and the strictly lower
C> triangular part of A is not referenced. If UPLO = 'L', the
C> leading N-by-N lower triangular part of A contains the lower
C> triangular part of the matrix A, and the strictly upper
C> triangular part of A is not referenced.
C> \endverbatim
C> \verbatim
C> On exit, if INFO = 0, the factor U or L from the Cholesky
C> factorization A = U**T*U or A = L*L**T.
C> \endverbatim
C>
C> \param[in] LDA
C> \verbatim
C> LDA is INTEGER
C> The leading dimension of the array A. LDA >= max(1,N).
C> \endverbatim
C>
C> \param[out] INFO
C> \verbatim
C> INFO is INTEGER
C> = 0: successful exit
C> < 0: if INFO = -i, the i-th argument had an illegal value
C> > 0: if INFO = i, the leading principal minor of order i
C> is not positive, and the factorization could not be
C> completed.
C> \endverbatim
C>
*
* Authors:
* ========
*
C> \author Univ. of Tennessee
C> \author Univ. of California Berkeley
C> \author Univ. of Colorado Denver
C> \author NAG Ltd.
*
C> \date December 2016
*
C> \ingroup variantsPOcomputational
*
* =====================================================================
SUBROUTINE SPOTRF ( 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 ..
REAL A( LDA, * )
* ..
*
* =====================================================================
*
* .. Parameters ..
REAL ONE
PARAMETER ( ONE = 1.0E+0 )
* ..
* .. Local Scalars ..
LOGICAL UPPER
INTEGER J, JB, NB
* ..
* .. External Functions ..
LOGICAL LSAME
INTEGER ILAENV
EXTERNAL LSAME, ILAENV
* ..
* .. External Subroutines ..
EXTERNAL SGEMM, SPOTF2, SSYRK, STRSM, 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( 'SPOTRF', -INFO )
RETURN
END IF
*
* Quick return if possible
*
IF( N.EQ.0 )
$ RETURN
*
* Determine the block size for this environment.
*
NB = ILAENV( 1, 'SPOTRF', UPLO, N, -1, -1, -1 )
IF( NB.LE.1 .OR. NB.GE.N ) THEN
*
* Use unblocked code.
*
CALL SPOTF2( UPLO, N, A, LDA, INFO )
ELSE
*
* Use blocked code.
*
IF( UPPER ) THEN
*
* Compute the Cholesky factorization A = U'*U.
*
DO 10 J = 1, N, NB
JB = MIN( NB, N-J+1 )
*
* Compute the current block.
*
CALL STRSM( 'Left', 'Upper', 'Transpose', 'Non-unit',
$ J-1, JB, ONE, A( 1, 1 ), LDA,
$ A( 1, J ), LDA )
CALL SSYRK( 'Upper', 'Transpose', JB, J-1, -ONE,
$ A( 1, J ), LDA,
$ ONE, A( J, J ), LDA )
*
* Update and factorize the current diagonal block and test
* for non-positive-definiteness.
*
CALL SPOTF2( 'Upper', JB, A( J, J ), LDA, INFO )
IF( INFO.NE.0 )
$ GO TO 30
10 CONTINUE
*
ELSE
*
* Compute the Cholesky factorization A = L*L'.
*
DO 20 J = 1, N, NB
JB = MIN( NB, N-J+1 )
*
* Compute the current block.
*
CALL STRSM( 'Right', 'Lower', 'Transpose', 'Non-unit',
$ JB, J-1, ONE, A( 1, 1 ), LDA,
$ A( J, 1 ), LDA )
CALL SSYRK( 'Lower', 'No Transpose', JB, J-1,
$ -ONE, A( J, 1 ), LDA,
$ ONE, A( J, J ), LDA )
*
* Update and factorize the current diagonal block and test
* for non-positive-definiteness.
*
CALL SPOTF2( 'Lower', JB, A( J, J ), LDA, INFO )
IF( INFO.NE.0 )
$ GO TO 30
20 CONTINUE
END IF
END IF
GO TO 40
*
30 CONTINUE
INFO = INFO + J - 1
*
40 CONTINUE
RETURN
*
* End of SPOTRF
*
END