subroutine spotf2	(	character	UPLO,
		integer	N,
		real, dimension( lda, * )	A,
		integer	LDA,
		integer	INFO
	)

SPOTF2 computes the Cholesky factorization of a symmetric/Hermitian positive definite matrix (unblocked algorithm).

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Purpose:

 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.

Parameters

[in]	UPLO	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
[in]	N	N is INTEGER The order of the matrix A. N >= 0.
[in,out]	A	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.
[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 = -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.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date

September 2012

Definition at line 111 of file spotf2.f.

*
*  -- LAPACK computational routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. 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
*

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