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SUBROUTINE DPOTF2( UPLO, N, A, LDA, INFO )
*
* -- LAPACK routine (version 3.1) --
* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
* November 2006
*
* .. Scalar Arguments ..
CHARACTER UPLO
INTEGER INFO, LDA, N
* ..
* .. Array Arguments ..
DOUBLE PRECISION A( LDA, * )
* ..
*
* Purpose
* =======
*
* DPOTF2 computes the Cholesky factorization of a real symmetric
* positive definite matrix A.
*
* The factorization has the form
* A = U' * U , if UPLO = 'U', or
* A = L * L', 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.
*
* Arguments
* =========
*
* UPLO (input) CHARACTER*1
* Specifies whether the upper or lower triangular part of the
* symmetric matrix A is stored.
* = 'U': Upper triangular
* = 'L': Lower triangular
*
* N (input) INTEGER
* The order of the matrix A. N >= 0.
*
* A (input/output) 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'*U or A = L*L'.
*
* LDA (input) INTEGER
* The leading dimension of the array A. LDA >= max(1,N).
*
* INFO (output) 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.
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ONE, ZERO
PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
* ..
* .. Local Scalars ..
LOGICAL UPPER
INTEGER J
DOUBLE PRECISION AJJ
* ..
* .. External Functions ..
LOGICAL LSAME
DOUBLE PRECISION DDOT
EXTERNAL LSAME, DDOT
* ..
* .. External Subroutines ..
EXTERNAL DGEMV, DSCAL, 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( 'DPOTF2', -INFO )
RETURN
END IF
*
* Quick return if possible
*
IF( N.EQ.0 )
$ RETURN
*
IF( UPPER ) THEN
*
* Compute the Cholesky factorization A = U'*U.
*
DO 10 J = 1, N
*
* Compute U(J,J) and test for non-positive-definiteness.
*
AJJ = A( J, J ) - DDOT( J-1, A( 1, J ), 1, A( 1, J ), 1 )
IF( AJJ.LE.ZERO ) 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 DGEMV( 'Transpose', J-1, N-J, -ONE, A( 1, J+1 ),
$ LDA, A( 1, J ), 1, ONE, A( J, J+1 ), LDA )
CALL DSCAL( N-J, ONE / AJJ, A( J, J+1 ), LDA )
END IF
10 CONTINUE
ELSE
*
* Compute the Cholesky factorization A = L*L'.
*
DO 20 J = 1, N
*
* Compute L(J,J) and test for non-positive-definiteness.
*
AJJ = A( J, J ) - DDOT( J-1, A( J, 1 ), LDA, A( J, 1 ),
$ LDA )
IF( AJJ.LE.ZERO ) 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 DGEMV( 'No transpose', N-J, J-1, -ONE, A( J+1, 1 ),
$ LDA, A( J, 1 ), LDA, ONE, A( J+1, J ), 1 )
CALL DSCAL( 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 DPOTF2
*
END
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