*> \brief \b DGTTRF
*
* =========== DOCUMENTATION ===========
*
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* http://www.netlib.org/lapack/explore-html/
*
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*
* Definition:
* ===========
*
* SUBROUTINE DGTTRF( N, DL, D, DU, DU2, IPIV, INFO )
*
* .. Scalar Arguments ..
* INTEGER INFO, N
* ..
* .. Array Arguments ..
* INTEGER IPIV( * )
* DOUBLE PRECISION D( * ), DL( * ), DU( * ), DU2( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> DGTTRF computes an LU factorization of a real tridiagonal matrix A
*> using elimination with partial pivoting and row interchanges.
*>
*> The factorization has the form
*> A = L * U
*> where L is a product of permutation and unit lower bidiagonal
*> matrices and U is upper triangular with nonzeros in only the main
*> diagonal and first two superdiagonals.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The order of the matrix A.
*> \endverbatim
*>
*> \param[in,out] DL
*> \verbatim
*> DL is DOUBLE PRECISION array, dimension (N-1)
*> On entry, DL must contain the (n-1) sub-diagonal elements of
*> A.
*>
*> On exit, DL is overwritten by the (n-1) multipliers that
*> define the matrix L from the LU factorization of A.
*> \endverbatim
*>
*> \param[in,out] D
*> \verbatim
*> D is DOUBLE PRECISION array, dimension (N)
*> On entry, D must contain the diagonal elements of A.
*>
*> On exit, D is overwritten by the n diagonal elements of the
*> upper triangular matrix U from the LU factorization of A.
*> \endverbatim
*>
*> \param[in,out] DU
*> \verbatim
*> DU is DOUBLE PRECISION array, dimension (N-1)
*> On entry, DU must contain the (n-1) super-diagonal elements
*> of A.
*>
*> On exit, DU is overwritten by the (n-1) elements of the first
*> super-diagonal of U.
*> \endverbatim
*>
*> \param[out] DU2
*> \verbatim
*> DU2 is DOUBLE PRECISION array, dimension (N-2)
*> On exit, DU2 is overwritten by the (n-2) elements of the
*> second super-diagonal of U.
*> \endverbatim
*>
*> \param[out] IPIV
*> \verbatim
*> IPIV is INTEGER array, dimension (N)
*> The pivot indices; for 1 <= i <= n, row i of the matrix was
*> interchanged with row IPIV(i). IPIV(i) will always be either
*> i or i+1; IPIV(i) = i indicates a row interchange was not
*> required.
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit
*> < 0: if INFO = -k, the k-th argument had an illegal value
*> > 0: if INFO = k, U(k,k) is exactly zero. The factorization
*> has been completed, but the factor U is exactly
*> singular, and division by zero will occur if it is used
*> to solve a system of equations.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup gttrf
*
* =====================================================================
SUBROUTINE DGTTRF( N, DL, D, DU, DU2, IPIV, 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 ..
INTEGER INFO, N
* ..
* .. Array Arguments ..
INTEGER IPIV( * )
DOUBLE PRECISION D( * ), DL( * ), DU( * ), DU2( * )
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ZERO
PARAMETER ( ZERO = 0.0D+0 )
* ..
* .. Local Scalars ..
INTEGER I
DOUBLE PRECISION FACT, TEMP
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS
* ..
* .. External Subroutines ..
EXTERNAL XERBLA
* ..
* .. Executable Statements ..
*
INFO = 0
IF( N.LT.0 ) THEN
INFO = -1
CALL XERBLA( 'DGTTRF', -INFO )
RETURN
END IF
*
* Quick return if possible
*
IF( N.EQ.0 )
$ RETURN
*
* Initialize IPIV(i) = i and DU2(I) = 0
*
DO 10 I = 1, N
IPIV( I ) = I
10 CONTINUE
DO 20 I = 1, N - 2
DU2( I ) = ZERO
20 CONTINUE
*
DO 30 I = 1, N - 2
IF( ABS( D( I ) ).GE.ABS( DL( I ) ) ) THEN
*
* No row interchange required, eliminate DL(I)
*
IF( D( I ).NE.ZERO ) THEN
FACT = DL( I ) / D( I )
DL( I ) = FACT
D( I+1 ) = D( I+1 ) - FACT*DU( I )
END IF
ELSE
*
* Interchange rows I and I+1, eliminate DL(I)
*
FACT = D( I ) / DL( I )
D( I ) = DL( I )
DL( I ) = FACT
TEMP = DU( I )
DU( I ) = D( I+1 )
D( I+1 ) = TEMP - FACT*D( I+1 )
DU2( I ) = DU( I+1 )
DU( I+1 ) = -FACT*DU( I+1 )
IPIV( I ) = I + 1
END IF
30 CONTINUE
IF( N.GT.1 ) THEN
I = N - 1
IF( ABS( D( I ) ).GE.ABS( DL( I ) ) ) THEN
IF( D( I ).NE.ZERO ) THEN
FACT = DL( I ) / D( I )
DL( I ) = FACT
D( I+1 ) = D( I+1 ) - FACT*DU( I )
END IF
ELSE
FACT = D( I ) / DL( I )
D( I ) = DL( I )
DL( I ) = FACT
TEMP = DU( I )
DU( I ) = D( I+1 )
D( I+1 ) = TEMP - FACT*D( I+1 )
IPIV( I ) = I + 1
END IF
END IF
*
* Check for a zero on the diagonal of U.
*
DO 40 I = 1, N
IF( D( I ).EQ.ZERO ) THEN
INFO = I
GO TO 50
END IF
40 CONTINUE
50 CONTINUE
*
RETURN
*
* End of DGTTRF
*
END