zgttrf()

subroutine zgttrf	(	integer	n,
		complex*16, dimension( * )	dl,
		complex*16, dimension( * )	d,
		complex*16, dimension( * )	du,
		complex*16, dimension( * )	du2,
		integer, dimension( * )	ipiv,
		integer	info )

ZGTTRF

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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.
!> 

Parameters

[in]	N	!> N is INTEGER !> The order of the matrix A. !>
[in,out]	DL	!> DL is COMPLEX*16 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. !>
[in,out]	D	!> D is 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. !>
[in,out]	DU	!> DU is COMPLEX*16 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. !>
[out]	DU2	!> DU2 is COMPLEX*16 array, dimension (N-2) !> On exit, DU2 is overwritten by the (n-2) elements of the !> second super-diagonal of U. !>
[out]	IPIV	!> 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. !>
[out]	INFO	!> 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. !>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 121 of file zgttrf.f.

*
*  -- 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( * )
      COMPLEX*16         D( * ), DL( * ), DU( * ), DU2( * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ZERO
      parameter( zero = 0.0d+0 )
*     ..
*     .. Local Scalars ..
      INTEGER            I
      COMPLEX*16         FACT, TEMP, ZDUM
*     ..
*     .. External Subroutines ..
      EXTERNAL           xerbla
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          abs, dble, dimag
*     ..
*     .. 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 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( cabs1( d( i ) ).GE.cabs1( dl( i ) ) ) THEN
*
*           No row interchange required, eliminate DL(I)
*
            IF( cabs1( 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( cabs1( d( i ) ).GE.cabs1( dl( i ) ) ) THEN
            IF( cabs1( 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( cabs1( d( i ) ).EQ.zero ) THEN
            info = i
            GO TO 50
         END IF
   40 CONTINUE
   50 CONTINUE
*
      RETURN
*
*     End of ZGTTRF
*

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