1DGTTRF(1)                LAPACK routine (version 3.1)                DGTTRF(1)
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NAME

6       DGTTRF - an LU factorization of a real tridiagonal matrix A using elim‐
7       ination with partial pivoting and row interchanges
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SYNOPSIS

10       SUBROUTINE DGTTRF( N, DL, D, DU, DU2, IPIV, INFO )
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12           INTEGER        INFO, N
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14           INTEGER        IPIV( * )
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16           DOUBLE         PRECISION D( * ), DL( * ), DU( * ), DU2( * )
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PURPOSE

19       DGTTRF computes an LU factorization of  a  real  tridiagonal  matrix  A
20       using elimination with partial pivoting and row interchanges.
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22       The factorization has the form
23          A = L * U
24       where  L is a product of permutation and unit lower bidiagonal matrices
25       and U is upper triangular with nonzeros in only the main  diagonal  and
26       first two superdiagonals.
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ARGUMENTS

30       N       (input) INTEGER
31               The order of the matrix A.
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33       DL      (input/output) DOUBLE PRECISION array, dimension (N-1)
34               On entry, DL must contain the (n-1) sub-diagonal elements of A.
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36               On exit, DL is overwritten by the (n-1) multipliers that define
37               the matrix L from the LU factorization of A.
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39       D       (input/output) DOUBLE PRECISION array, dimension (N)
40               On entry, D must contain the diagonal elements of A.
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42               On exit, D is overwritten by the n  diagonal  elements  of  the
43               upper triangular matrix U from the LU factorization of A.
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45       DU      (input/output) DOUBLE PRECISION array, dimension (N-1)
46               On  entry, DU must contain the (n-1) super-diagonal elements of
47               A.
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49               On exit, DU is overwritten by the (n-1) elements of  the  first
50               super-diagonal of U.
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52       DU2     (output) DOUBLE PRECISION array, dimension (N-2)
53               On exit, DU2 is overwritten by the (n-2) elements of the second
54               super-diagonal of U.
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56       IPIV    (output) INTEGER array, dimension (N)
57               The pivot indices; for 1 <= i <= n, row i  of  the  matrix  was
58               interchanged with row IPIV(i).  IPIV(i) will always be either i
59               or i+1; IPIV(i)  =  i  indicates  a  row  interchange  was  not
60               required.
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62       INFO    (output) INTEGER
63               = 0:  successful exit
64               < 0:  if INFO = -k, the k-th argument had an illegal value
65               >  0:   if  INFO = k, U(k,k) is exactly zero. The factorization
66               has been completed, but the factor U is exactly  singular,  and
67               division  by zero will occur if it is used to solve a system of
68               equations.
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72 LAPACK routine (version 3.1)    November 2006                       DGTTRF(1)
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