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SUBROUTINE DPPTRF( UPLO, N, AP, INFO )
*
* -- LAPACK routine (version 2.0) --
* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
* Courant Institute, Argonne National Lab, and Rice University
* March 31, 1993
*
* .. Scalar Arguments ..
CHARACTER UPLO
INTEGER INFO, N
* ..
* .. Array Arguments ..
DOUBLE PRECISION AP( * )
* ..
*
* Purpose
* =======
*
* DPPTRF computes the Cholesky factorization of a real symmetric
* positive definite matrix A stored in packed format.
*
* 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.
*
* Arguments
* =========
*
* UPLO (input) CHARACTER*1
* = 'U': Upper triangle of A is stored;
* = 'L': Lower triangle of A is stored.
*
* N (input) INTEGER
* The order of the matrix A. N >= 0.
*
* AP (input/output) DOUBLE PRECISION array, dimension (N*(N+1)/2)
* On entry, the upper or lower triangle of the symmetric matrix
* A, packed columnwise in a linear array. The j-th column of A
* is stored in the array AP as follows:
* if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
* if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
* See below for further details.
*
* On exit, if INFO = 0, the triangular factor U or L from the
* Cholesky factorization A = U**T*U or A = L*L**T, in the same
* storage format as A.
*
* INFO (output) 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.
*
* Further Details
* ======= =======
*
* The packed storage scheme is illustrated by the following example
* when N = 4, UPLO = 'U':
*
* Two-dimensional storage of the symmetric matrix A:
*
* a11 a12 a13 a14
* a22 a23 a24
* a33 a34 (aij = aji)
* a44
*
* Packed storage of the upper triangle of A:
*
* AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ONE, ZERO
PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
* ..
* .. Local Scalars ..
LOGICAL UPPER
INTEGER J, JC, JJ
DOUBLE PRECISION AJJ
* ..
* .. External Functions ..
LOGICAL LSAME
DOUBLE PRECISION DDOT
EXTERNAL LSAME, DDOT
* ..
* .. External Subroutines ..
EXTERNAL DSCAL, DSPR, DTPSV, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC 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
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'DPPTRF', -INFO )
RETURN
END IF
*
* Quick return if possible
*
IF( N.EQ.0 )
$ RETURN
*
IF( UPPER ) THEN
*
* Compute the Cholesky factorization A = U'*U.
*
JJ = 0
DO 10 J = 1, N
JC = JJ + 1
JJ = JJ + J
*
* Compute elements 1:J-1 of column J.
*
IF( J.GT.1 )
$ CALL DTPSV( 'Upper', 'Transpose', 'Non-unit', J-1, AP,
$ AP( JC ), 1 )
*
* Compute U(J,J) and test for non-positive-definiteness.
*
AJJ = AP( JJ ) - DDOT( J-1, AP( JC ), 1, AP( JC ), 1 )
IF( AJJ.LE.ZERO ) THEN
AP( JJ ) = AJJ
GO TO 30
END IF
AP( JJ ) = SQRT( AJJ )
10 CONTINUE
ELSE
*
* Compute the Cholesky factorization A = L*L'.
*
JJ = 1
DO 20 J = 1, N
*
* Compute L(J,J) and test for non-positive-definiteness.
*
AJJ = AP( JJ )
IF( AJJ.LE.ZERO ) THEN
AP( JJ ) = AJJ
GO TO 30
END IF
AJJ = SQRT( AJJ )
AP( JJ ) = AJJ
*
* Compute elements J+1:N of column J and update the trailing
* submatrix.
*
IF( J.LT.N ) THEN
CALL DSCAL( N-J, ONE / AJJ, AP( JJ+1 ), 1 )
CALL DSPR( 'Lower', N-J, -ONE, AP( JJ+1 ), 1,
$ AP( JJ+N-J+1 ) )
JJ = JJ + N - J + 1
END IF
20 CONTINUE
END IF
GO TO 40
*
30 CONTINUE
INFO = J
*
40 CONTINUE
RETURN
*
* End of DPPTRF
*
END
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