recursive subroutine dpotrf2	(	character	UPLO,
		integer	N,
		double precision, dimension( lda, * )	A,
		integer	LDA,
		integer	INFO
	)

DPOTRF2

Purpose:

 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.

Parameters

[in]	UPLO	UPLO is CHARACTER*1 = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored.
[in]	N	N is INTEGER The order of the matrix A. N >= 0.
[in,out]	A	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.
[in]	LDA	LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).
[out]	INFO	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.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date

November 2015

Definition at line 108 of file dpotrf2.f.

*
*  -- LAPACK computational routine (version 3.6.0) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     November 2015
*
*     .. 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
*

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