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SUBROUTINE ZGTTRF( N, DL, D, DU, DU2, IPIV, INFO )
*
* -- LAPACK routine (version 2.0) --
* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
* Courant Institute, Argonne National Lab, and Rice University
* September 30, 1994
*
* .. Scalar Arguments ..
INTEGER INFO, N
* ..
* .. Array Arguments ..
INTEGER IPIV( * )
COMPLEX*16 D( * ), DL( * ), DU( * ), DU2( * )
* ..
*
* Purpose
* =======
*
* ZGTTRF computes an LU factorization of a complex 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.
*
* Arguments
* =========
*
* N (input) INTEGER
* The order of the matrix A. N >= 0.
*
* DL (input/output) COMPLEX*16 array, dimension (N-1)
* On entry, DL must contain the (n-1) subdiagonal elements of
* A.
* On exit, DL is overwritten by the (n-1) multipliers that
* define the matrix L from the LU factorization of A.
*
* D (input/output) COMPLEX*16 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.
*
* DU (input/output) COMPLEX*16 array, dimension (N-1)
* On entry, DU must contain the (n-1) superdiagonal elements
* of A.
* On exit, DU is overwritten by the (n-1) elements of the first
* superdiagonal of U.
*
* DU2 (output) COMPLEX*16 array, dimension (N-2)
* On exit, DU2 is overwritten by the (n-2) elements of the
* second superdiagonal of U.
*
* IPIV (output) 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.
*
* INFO (output) INTEGER
* = 0: successful exit
* < 0: if INFO = -i, the i-th argument had an illegal value
* > 0: if INFO = i, U(i,i) 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.
*
* =====================================================================
*
* .. Local Scalars ..
INTEGER I
COMPLEX*16 FACT, TEMP, ZDUM
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, DBLE, DIMAG
* ..
* .. External Subroutines ..
EXTERNAL XERBLA
* ..
* .. Parameters ..
COMPLEX*16 CZERO
PARAMETER ( CZERO = ( 0.0D+0, 0.0D+0 ) )
* ..
* .. Statement Functions ..
DOUBLE PRECISION CABS1
* ..
* .. Statement Function definitions ..
CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) )
* ..
* .. Executable Statements ..
*
INFO = 0
IF( N.LT.0 ) THEN
INFO = -1
CALL XERBLA( 'ZGTTRF', -INFO )
RETURN
END IF
*
* Quick return if possible
*
IF( N.EQ.0 )
$ RETURN
*
* Initialize IPIV(i) = i
*
DO 10 I = 1, N
IPIV( I ) = I
10 CONTINUE
*
DO 20 I = 1, N - 1
IF( DL( I ).EQ.CZERO ) THEN
*
* Subdiagonal is zero, no elimination is required.
*
IF( D( I ).EQ.CZERO .AND. INFO.EQ.0 )
$ INFO = I
IF( I.LT.N-1 )
$ DU2( I ) = CZERO
ELSE IF( CABS1( D( I ) ).GE.CABS1( DL( I ) ) ) THEN
*
* No row interchange required, eliminate DL(I)
*
FACT = DL( I ) / D( I )
DL( I ) = FACT
D( I+1 ) = D( I+1 ) - FACT*DU( I )
IF( I.LT.N-1 )
$ DU2( I ) = CZERO
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 )
IF( I.LT.N-1 ) THEN
DU2( I ) = DU( I+1 )
DU( I+1 ) = -FACT*DU( I+1 )
END IF
IPIV( I ) = IPIV( I ) + 1
END IF
20 CONTINUE
IF( D( N ).EQ.CZERO .AND. INFO.EQ.0 ) THEN
INFO = N
RETURN
END IF
*
RETURN
*
* End of ZGTTRF
*
END
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