241 lines
6.6 KiB
Fortran
241 lines
6.6 KiB
Fortran
*> \brief \b ZGTTRF
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*
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* =========== DOCUMENTATION ===========
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*
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* Online html documentation available at
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* http://www.netlib.org/lapack/explore-html/
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*
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*> \htmlonly
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*> Download ZGTTRF + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zgttrf.f">
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*> [TGZ]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zgttrf.f">
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*> [ZIP]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zgttrf.f">
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*> [TXT]</a>
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*> \endhtmlonly
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*
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* Definition:
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* ===========
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*
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* SUBROUTINE ZGTTRF( N, DL, D, DU, DU2, IPIV, INFO )
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*
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* .. Scalar Arguments ..
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* INTEGER INFO, N
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* ..
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* .. Array Arguments ..
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* INTEGER IPIV( * )
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* COMPLEX*16 D( * ), DL( * ), DU( * ), DU2( * )
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* ..
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*
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*
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*> \par Purpose:
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* =============
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*>
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*> \verbatim
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*>
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*> ZGTTRF computes an LU factorization of a complex tridiagonal matrix A
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*> using elimination with partial pivoting and row interchanges.
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*>
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*> The factorization has the form
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*> A = L * U
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*> where L is a product of permutation and unit lower bidiagonal
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*> matrices and U is upper triangular with nonzeros in only the main
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*> diagonal and first two superdiagonals.
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*> \endverbatim
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*
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* Arguments:
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* ==========
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*
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*> \param[in] N
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*> \verbatim
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*> N is INTEGER
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*> The order of the matrix A.
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*> \endverbatim
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*>
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*> \param[in,out] DL
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*> \verbatim
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*> DL is COMPLEX*16 array, dimension (N-1)
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*> On entry, DL must contain the (n-1) sub-diagonal elements of
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*> A.
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*>
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*> On exit, DL is overwritten by the (n-1) multipliers that
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*> define the matrix L from the LU factorization of A.
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*> \endverbatim
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*>
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*> \param[in,out] D
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*> \verbatim
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*> D is COMPLEX*16 array, dimension (N)
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*> On entry, D must contain the diagonal elements of A.
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*>
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*> On exit, D is overwritten by the n diagonal elements of the
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*> upper triangular matrix U from the LU factorization of A.
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*> \endverbatim
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*>
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*> \param[in,out] DU
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*> \verbatim
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*> DU is COMPLEX*16 array, dimension (N-1)
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*> On entry, DU must contain the (n-1) super-diagonal elements
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*> of A.
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*>
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*> On exit, DU is overwritten by the (n-1) elements of the first
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*> super-diagonal of U.
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*> \endverbatim
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*>
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*> \param[out] DU2
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*> \verbatim
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*> DU2 is COMPLEX*16 array, dimension (N-2)
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*> On exit, DU2 is overwritten by the (n-2) elements of the
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*> second super-diagonal of U.
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*> \endverbatim
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*>
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*> \param[out] IPIV
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*> \verbatim
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*> IPIV is INTEGER array, dimension (N)
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*> The pivot indices; for 1 <= i <= n, row i of the matrix was
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*> interchanged with row IPIV(i). IPIV(i) will always be either
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*> i or i+1; IPIV(i) = i indicates a row interchange was not
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*> required.
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*> \endverbatim
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*>
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*> \param[out] INFO
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*> \verbatim
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*> INFO is INTEGER
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*> = 0: successful exit
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*> < 0: if INFO = -k, the k-th argument had an illegal value
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*> > 0: if INFO = k, U(k,k) is exactly zero. The factorization
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*> has been completed, but the factor U is exactly
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*> singular, and division by zero will occur if it is used
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*> to solve a system of equations.
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*> \endverbatim
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*
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* Authors:
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* ========
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*
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*> \author Univ. of Tennessee
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*> \author Univ. of California Berkeley
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*> \author Univ. of Colorado Denver
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*> \author NAG Ltd.
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*
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*> \ingroup complex16GTcomputational
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*
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* =====================================================================
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SUBROUTINE ZGTTRF( N, DL, D, DU, DU2, IPIV, INFO )
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*
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* -- LAPACK computational routine --
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* -- LAPACK is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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*
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* .. Scalar Arguments ..
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INTEGER INFO, N
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* ..
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* .. Array Arguments ..
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INTEGER IPIV( * )
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COMPLEX*16 D( * ), DL( * ), DU( * ), DU2( * )
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* ..
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*
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* =====================================================================
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*
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* .. Parameters ..
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DOUBLE PRECISION ZERO
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PARAMETER ( ZERO = 0.0D+0 )
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* ..
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* .. Local Scalars ..
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INTEGER I
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COMPLEX*16 FACT, TEMP, ZDUM
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* ..
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* .. External Subroutines ..
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EXTERNAL XERBLA
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC ABS, DBLE, DIMAG
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* ..
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* .. Statement Functions ..
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DOUBLE PRECISION CABS1
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* ..
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* .. Statement Function definitions ..
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CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) )
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* ..
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* .. Executable Statements ..
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*
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INFO = 0
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IF( N.LT.0 ) THEN
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INFO = -1
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CALL XERBLA( 'ZGTTRF', -INFO )
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RETURN
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END IF
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*
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* Quick return if possible
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*
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IF( N.EQ.0 )
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$ RETURN
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*
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* Initialize IPIV(i) = i and DU2(i) = 0
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*
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DO 10 I = 1, N
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IPIV( I ) = I
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10 CONTINUE
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DO 20 I = 1, N - 2
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DU2( I ) = ZERO
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20 CONTINUE
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*
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DO 30 I = 1, N - 2
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IF( CABS1( D( I ) ).GE.CABS1( DL( I ) ) ) THEN
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*
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* No row interchange required, eliminate DL(I)
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*
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IF( CABS1( D( I ) ).NE.ZERO ) THEN
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FACT = DL( I ) / D( I )
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DL( I ) = FACT
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D( I+1 ) = D( I+1 ) - FACT*DU( I )
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END IF
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ELSE
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*
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* Interchange rows I and I+1, eliminate DL(I)
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*
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FACT = D( I ) / DL( I )
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D( I ) = DL( I )
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DL( I ) = FACT
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TEMP = DU( I )
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DU( I ) = D( I+1 )
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D( I+1 ) = TEMP - FACT*D( I+1 )
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DU2( I ) = DU( I+1 )
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DU( I+1 ) = -FACT*DU( I+1 )
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IPIV( I ) = I + 1
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END IF
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30 CONTINUE
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IF( N.GT.1 ) THEN
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I = N - 1
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IF( CABS1( D( I ) ).GE.CABS1( DL( I ) ) ) THEN
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IF( CABS1( D( I ) ).NE.ZERO ) THEN
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FACT = DL( I ) / D( I )
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DL( I ) = FACT
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D( I+1 ) = D( I+1 ) - FACT*DU( I )
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END IF
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ELSE
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FACT = D( I ) / DL( I )
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D( I ) = DL( I )
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DL( I ) = FACT
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TEMP = DU( I )
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DU( I ) = D( I+1 )
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D( I+1 ) = TEMP - FACT*D( I+1 )
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IPIV( I ) = I + 1
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END IF
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END IF
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*
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* Check for a zero on the diagonal of U.
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*
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DO 40 I = 1, N
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IF( CABS1( D( I ) ).EQ.ZERO ) THEN
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INFO = I
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GO TO 50
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END IF
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40 CONTINUE
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50 CONTINUE
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*
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RETURN
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*
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* End of ZGTTRF
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*
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END
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