SUBROUTINE ZGTTRF( N, DL, D, DU, DU2, IPIV, INFO ) * * -- LAPACK routine (version 3.1) -- * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. * November 2006 * * .. 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. * * DL (input/output) 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. * * 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) super-diagonal elements * of A. * * On exit, DU is overwritten by the (n-1) elements of the first * super-diagonal of U. * * DU2 (output) COMPLEX*16 array, dimension (N-2) * On exit, DU2 is overwritten by the (n-2) elements of the * second super-diagonal 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 = -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. * * ===================================================================== * * .. 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 * END