SUBROUTINE DDTTRF( N, DL, D, DU, INFO ) * * Written by Andrew J. Cleary, November 1996. * Modified from DGTTRF: * -- LAPACK routine (preliminary version) -- * Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., * Courant Institute, Argonne National Lab, and Rice University * * .. Scalar Arguments .. INTEGER INFO, N * .. * .. Array Arguments .. DOUBLE PRECISION D( * ), DL( * ), DU( * ) * .. * * Purpose * ======= * * DDTTRF computes an LU factorization of a complex tridiagonal matrix A * using elimination without partial pivoting. * * The factorization has the form * A = L * U * where L is a product of unit lower bidiagonal * matrices and U is upper triangular with nonzeros in only the main * diagonal and first superdiagonal. * * Arguments * ========= * * N (input) INTEGER * The order of the matrix A. N >= 0. * * DL (input/output) COMPLEX 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 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 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. * * 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 DOUBLE PRECISION FACT * .. * .. Intrinsic Functions .. INTRINSIC ABS * .. * .. External Subroutines .. EXTERNAL XERBLA * .. * .. Parameters .. DOUBLE PRECISION ZERO PARAMETER ( ZERO = 0.0D+0 ) * .. * .. Executable Statements .. * INFO = 0 IF( N.LT.0 ) THEN INFO = -1 CALL XERBLA( 'DDTTRF', -INFO ) RETURN END IF * * Quick return if possible * IF( N.EQ.0 ) $ RETURN * DO 20 I = 1, N - 1 IF( DL( I ).EQ.ZERO ) THEN * * Subdiagonal is zero, no elimination is required. * IF( D( I ).EQ.ZERO .AND. INFO.EQ.0 ) $ INFO = I ELSE * FACT = DL( I ) / D( I ) DL( I ) = FACT D( I+1 ) = D( I+1 ) - FACT*DU( I ) END IF 20 CONTINUE IF( D( N ).EQ.ZERO .AND. INFO.EQ.0 ) THEN INFO = N RETURN END IF * RETURN * * End of DDTTRF * END