212 lines
5.3 KiB
Fortran
212 lines
5.3 KiB
Fortran
*> \brief \b SPTTRF
|
|
*
|
|
* =========== DOCUMENTATION ===========
|
|
*
|
|
* Online html documentation available at
|
|
* http://www.netlib.org/lapack/explore-html/
|
|
*
|
|
*> \htmlonly
|
|
*> Download SPTTRF + dependencies
|
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/spttrf.f">
|
|
*> [TGZ]</a>
|
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/spttrf.f">
|
|
*> [ZIP]</a>
|
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/spttrf.f">
|
|
*> [TXT]</a>
|
|
*> \endhtmlonly
|
|
*
|
|
* Definition:
|
|
* ===========
|
|
*
|
|
* SUBROUTINE SPTTRF( N, D, E, INFO )
|
|
*
|
|
* .. Scalar Arguments ..
|
|
* INTEGER INFO, N
|
|
* ..
|
|
* .. Array Arguments ..
|
|
* REAL D( * ), E( * )
|
|
* ..
|
|
*
|
|
*
|
|
*> \par Purpose:
|
|
* =============
|
|
*>
|
|
*> \verbatim
|
|
*>
|
|
*> SPTTRF computes the L*D*L**T factorization of a real symmetric
|
|
*> positive definite tridiagonal matrix A. The factorization may also
|
|
*> be regarded as having the form A = U**T*D*U.
|
|
*> \endverbatim
|
|
*
|
|
* Arguments:
|
|
* ==========
|
|
*
|
|
*> \param[in] N
|
|
*> \verbatim
|
|
*> N is INTEGER
|
|
*> The order of the matrix A. N >= 0.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in,out] D
|
|
*> \verbatim
|
|
*> D is REAL array, dimension (N)
|
|
*> On entry, the n diagonal elements of the tridiagonal matrix
|
|
*> A. On exit, the n diagonal elements of the diagonal matrix
|
|
*> D from the L*D*L**T factorization of A.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in,out] E
|
|
*> \verbatim
|
|
*> E is REAL array, dimension (N-1)
|
|
*> On entry, the (n-1) subdiagonal elements of the tridiagonal
|
|
*> matrix A. On exit, the (n-1) subdiagonal elements of the
|
|
*> unit bidiagonal factor L from the L*D*L**T factorization of A.
|
|
*> E can also be regarded as the superdiagonal of the unit
|
|
*> bidiagonal factor U from the U**T*D*U factorization of A.
|
|
*> \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, the leading minor of order k is not
|
|
*> positive definite; if k < N, the factorization could not
|
|
*> be completed, while if k = N, the factorization was
|
|
*> completed, but D(N) <= 0.
|
|
*> \endverbatim
|
|
*
|
|
* Authors:
|
|
* ========
|
|
*
|
|
*> \author Univ. of Tennessee
|
|
*> \author Univ. of California Berkeley
|
|
*> \author Univ. of Colorado Denver
|
|
*> \author NAG Ltd.
|
|
*
|
|
*> \date November 2011
|
|
*
|
|
*> \ingroup auxOTHERcomputational
|
|
*
|
|
* =====================================================================
|
|
SUBROUTINE SPTTRF( N, D, E, INFO )
|
|
*
|
|
* -- LAPACK computational routine (version 3.4.0) --
|
|
* -- LAPACK is a software package provided by Univ. of Tennessee, --
|
|
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
|
* November 2011
|
|
*
|
|
* .. Scalar Arguments ..
|
|
INTEGER INFO, N
|
|
* ..
|
|
* .. Array Arguments ..
|
|
REAL D( * ), E( * )
|
|
* ..
|
|
*
|
|
* =====================================================================
|
|
*
|
|
* .. Parameters ..
|
|
REAL ZERO
|
|
PARAMETER ( ZERO = 0.0E+0 )
|
|
* ..
|
|
* .. Local Scalars ..
|
|
INTEGER I, I4
|
|
REAL EI
|
|
* ..
|
|
* .. External Subroutines ..
|
|
EXTERNAL XERBLA
|
|
* ..
|
|
* .. Intrinsic Functions ..
|
|
INTRINSIC MOD
|
|
* ..
|
|
* .. Executable Statements ..
|
|
*
|
|
* Test the input parameters.
|
|
*
|
|
INFO = 0
|
|
IF( N.LT.0 ) THEN
|
|
INFO = -1
|
|
CALL XERBLA( 'SPTTRF', -INFO )
|
|
RETURN
|
|
END IF
|
|
*
|
|
* Quick return if possible
|
|
*
|
|
IF( N.EQ.0 )
|
|
$ RETURN
|
|
*
|
|
* Compute the L*D*L**T (or U**T*D*U) factorization of A.
|
|
*
|
|
I4 = MOD( N-1, 4 )
|
|
DO 10 I = 1, I4
|
|
IF( D( I ).LE.ZERO ) THEN
|
|
INFO = I
|
|
GO TO 30
|
|
END IF
|
|
EI = E( I )
|
|
E( I ) = EI / D( I )
|
|
D( I+1 ) = D( I+1 ) - E( I )*EI
|
|
10 CONTINUE
|
|
*
|
|
DO 20 I = I4 + 1, N - 4, 4
|
|
*
|
|
* Drop out of the loop if d(i) <= 0: the matrix is not positive
|
|
* definite.
|
|
*
|
|
IF( D( I ).LE.ZERO ) THEN
|
|
INFO = I
|
|
GO TO 30
|
|
END IF
|
|
*
|
|
* Solve for e(i) and d(i+1).
|
|
*
|
|
EI = E( I )
|
|
E( I ) = EI / D( I )
|
|
D( I+1 ) = D( I+1 ) - E( I )*EI
|
|
*
|
|
IF( D( I+1 ).LE.ZERO ) THEN
|
|
INFO = I + 1
|
|
GO TO 30
|
|
END IF
|
|
*
|
|
* Solve for e(i+1) and d(i+2).
|
|
*
|
|
EI = E( I+1 )
|
|
E( I+1 ) = EI / D( I+1 )
|
|
D( I+2 ) = D( I+2 ) - E( I+1 )*EI
|
|
*
|
|
IF( D( I+2 ).LE.ZERO ) THEN
|
|
INFO = I + 2
|
|
GO TO 30
|
|
END IF
|
|
*
|
|
* Solve for e(i+2) and d(i+3).
|
|
*
|
|
EI = E( I+2 )
|
|
E( I+2 ) = EI / D( I+2 )
|
|
D( I+3 ) = D( I+3 ) - E( I+2 )*EI
|
|
*
|
|
IF( D( I+3 ).LE.ZERO ) THEN
|
|
INFO = I + 3
|
|
GO TO 30
|
|
END IF
|
|
*
|
|
* Solve for e(i+3) and d(i+4).
|
|
*
|
|
EI = E( I+3 )
|
|
E( I+3 ) = EI / D( I+3 )
|
|
D( I+4 ) = D( I+4 ) - E( I+3 )*EI
|
|
20 CONTINUE
|
|
*
|
|
* Check d(n) for positive definiteness.
|
|
*
|
|
IF( D( N ).LE.ZERO )
|
|
$ INFO = N
|
|
*
|
|
30 CONTINUE
|
|
RETURN
|
|
*
|
|
* End of SPTTRF
|
|
*
|
|
END
|