dgttrf.f

Go to the documentation of this file.

      SUBROUTINE DGTTRF( N, DL, D, DU, DU2, IPIV, INFO )
*
*  -- LAPACK routine (version 3.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     November 2006
*
*     .. Scalar Arguments ..
      INTEGER            INFO, N
*     ..
*     .. Array Arguments ..
      INTEGER            IPIV( * )
      DOUBLE PRECISION   D( * ), DL( * ), DU( * ), DU2( * )
*     ..
*
*  Purpose
*  =======
*
*  DGTTRF computes an LU factorization of a real 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) DOUBLE PRECISION 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) DOUBLE PRECISION 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) DOUBLE PRECISION 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) DOUBLE PRECISION 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
      DOUBLE PRECISION   FACT, TEMP
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          ABS
*     ..
*     .. External Subroutines ..
      EXTERNAL           XERBLA
*     ..
*     .. Executable Statements ..
*
      INFO = 0
      IF( N.LT.0 ) THEN
         INFO = -1
         CALL XERBLA( 'DGTTRF', -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( ABS( D( I ) ).GE.ABS( DL( I ) ) ) THEN
*
*           No row interchange required, eliminate DL(I)
*
            IF( 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( ABS( D( I ) ).GE.ABS( DL( I ) ) ) THEN
            IF( 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( D( I ).EQ.ZERO ) THEN
            INFO = I
            GO TO 50
         END IF
   40 CONTINUE
   50 CONTINUE
*
      RETURN
*
*     End of DGTTRF
*
      END