sgttrf()

subroutine sgttrf	(	integer	n,
		real, dimension( * )	dl,
		real, dimension( * )	d,
		real, dimension( * )	du,
		real, dimension( * )	du2,
		integer, dimension( * )	ipiv,
		integer	info
	)

SGTTRF

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Purpose:

 SGTTRF 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.

Parameters

[in]	N	N is INTEGER The order of the matrix A.
[in,out]	DL	DL is REAL 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 REAL 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 REAL 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 REAL 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 123 of file sgttrf.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( * )
      REAL               D( * ), DL( * ), DU( * ), DU2( * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      REAL               ZERO
      parameter( zero = 0.0e+0 )
*     ..
*     .. Local Scalars ..
      INTEGER            I
      REAL               FACT, TEMP
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          abs
*     ..
*     .. External Subroutines ..
      EXTERNAL           xerbla
*     ..
*     .. Executable Statements ..
*
      info = 0
      IF( n.LT.0 ) THEN
         info = -1
         CALL xerbla( 'SGTTRF', -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 SGTTRF
*

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