gttrf(3)

NAME
gttrf - gttrf: triangular factor

SYNOPSIS

  Functions

subroutine cgttrf (n, dl, d, du, du2, ipiv, info)
CGTTRF
subroutine dgttrf (n, dl, d, du, du2, ipiv, info)
DGTTRF
subroutine sgttrf (n, dl, d, du, du2, ipiv, info)
SGTTRF
subroutine zgttrf (n, dl, d, du, du2, ipiv, info)
ZGTTRF

Detailed Description

Function Documentation

  subroutine cgttrf (integer n, complex, dimension( * ) dl, complex, dimension( * ) d, complex, dimension( * ) du, complex, dimension( * ) du2, integer, dimension( * ) ipiv, integer info)

CGTTRF

Purpose:

    !>
    !> CGTTRF 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.
    !>

Parameters
    N

    !>          N is INTEGER
    !>          The order of the matrix A.
    !>

    DL

    !>          DL is COMPLEX 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

    !>          D is 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

    !>          DU is COMPLEX 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

    !>          DU2 is COMPLEX array, dimension (N-2)
    !>          On exit, DU2 is overwritten by the (n-2) elements of the
    !>          second super-diagonal of U.
    !>

    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.
    !>

    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.

  subroutine dgttrf (integer n, double precision, dimension( * ) dl, double precision, dimension( * ) d, double precision, dimension( * ) du, double precision, dimension( * ) du2, integer, dimension( * ) ipiv, integer info)

DGTTRF

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.
    !>

Parameters
    N

    !>          N is INTEGER
    !>          The order of the matrix A.
    !>

    DL

    !>          DL is 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

    !>          D is 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

    !>          DU is 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

    !>          DU2 is DOUBLE PRECISION array, dimension (N-2)
    !>          On exit, DU2 is overwritten by the (n-2) elements of the
    !>          second super-diagonal of U.
    !>

    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.
    !>

    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.

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

SGTTRF

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
    N

    !>          N is INTEGER
    !>          The order of the matrix A.
    !>

    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.
    !>

    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.
    !>

    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.
    !>

    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.
    !>

    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.
    !>

    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.

  subroutine zgttrf (integer n, complex*16, dimension( * ) dl, complex*16, dimension( * ) d, complex*16, dimension( * ) du, complex*16, dimension( * ) du2, integer, dimension( * ) ipiv, integer info)

ZGTTRF

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.
    !>

Parameters
    N

    !>          N is INTEGER
    !>          The order of the matrix A.
    !>

    DL

    !>          DL is 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

    !>          D is 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

    !>          DU is 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

    !>          DU2 is COMPLEX*16 array, dimension (N-2)
    !>          On exit, DU2 is overwritten by the (n-2) elements of the
    !>          second super-diagonal of U.
    !>

    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.
    !>

    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.

Author

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