lagts(3)

NAME
lagts - lagts: LU solve of (T - λI) x = y

SYNOPSIS

  Functions
subroutine dlagts (job, n, a, b, c, d, in, y, tol, info)
DLAGTS solves the system of equations (T-λI)x = y or (T-λI)^Tx = y, where T is a general tridiagonal matrix and λ a scalar, using the LU factorization computed by slagtf.
subroutine slagts (job, n, a, b, c, d, in, y, tol, info)
SLAGTS solves the system of equations (T-λI)x = y or (T-λI)^Tx = y, where T is a general tridiagonal matrix and λ a scalar, using the LU factorization computed by slagtf.

Detailed Description

Function Documentation

  subroutine dlagts (integer job, integer n, double precision, dimension( * ) a, double precision, dimension( * ) b, double precision, dimension( * ) c, double precision, dimension( * ) d, integer, dimension( * ) in, double precision, dimension( * ) y, double precision tol, integer info)

DLAGTS solves the system of equations (T-λI)x = y or (T-λI)^Tx = y, where T is a general tridiagonal matrix and λ a scalar, using the LU factorization computed by slagtf.

Purpose:

    !>
    !> DLAGTS may be used to solve one of the systems of equations
    !>
    !>    (T - lambda*I)*x = y   or   (T - lambda*I)**T*x = y,
    !>
    !> where T is an n by n tridiagonal matrix, for x, following the
    !> factorization of (T - lambda*I) as
    !>
    !>    (T - lambda*I) = P*L*U ,
    !>
    !> by routine DLAGTF. The choice of equation to be solved is
    !> controlled by the argument JOB, and in each case there is an option
    !> to perturb zero or very small diagonal elements of U, this option
    !> being intended for use in applications such as inverse iteration.
    !>

Parameters
    JOB

    !>          JOB is INTEGER
    !>          Specifies the job to be performed by DLAGTS as follows:
    !>          =  1: The equations  (T - lambda*I)x = y  are to be solved,
    !>                but diagonal elements of U are not to be perturbed.
    !>          = -1: The equations  (T - lambda*I)x = y  are to be solved
    !>                and, if overflow would otherwise occur, the diagonal
    !>                elements of U are to be perturbed. See argument TOL
    !>                below.
    !>          =  2: The equations  (T - lambda*I)**Tx = y  are to be solved,
    !>                but diagonal elements of U are not to be perturbed.
    !>          = -2: The equations  (T - lambda*I)**Tx = y  are to be solved
    !>                and, if overflow would otherwise occur, the diagonal
    !>                elements of U are to be perturbed. See argument TOL
    !>                below.
    !>

    N

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

    A

    !>          A is DOUBLE PRECISION array, dimension (N)
    !>          On entry, A must contain the diagonal elements of U as
    !>          returned from DLAGTF.
    !>

    B

    !>          B is DOUBLE PRECISION array, dimension (N-1)
    !>          On entry, B must contain the first super-diagonal elements of
    !>          U as returned from DLAGTF.
    !>

    C

    !>          C is DOUBLE PRECISION array, dimension (N-1)
    !>          On entry, C must contain the sub-diagonal elements of L as
    !>          returned from DLAGTF.
    !>

    D

    !>          D is DOUBLE PRECISION array, dimension (N-2)
    !>          On entry, D must contain the second super-diagonal elements
    !>          of U as returned from DLAGTF.
    !>

    IN

    !>          IN is INTEGER array, dimension (N)
    !>          On entry, IN must contain details of the matrix P as returned
    !>          from DLAGTF.
    !>

    Y

    !>          Y is DOUBLE PRECISION array, dimension (N)
    !>          On entry, the right hand side vector y.
    !>          On exit, Y is overwritten by the solution vector x.
    !>

    TOL

    !>          TOL is DOUBLE PRECISION
    !>          On entry, with  JOB < 0, TOL should be the minimum
    !>          perturbation to be made to very small diagonal elements of U.
    !>          TOL should normally be chosen as about eps*norm(U), where eps
    !>          is the relative machine precision, but if TOL is supplied as
    !>          non-positive, then it is reset to eps*max( abs( u(i,j) ) ).
    !>          If  JOB > 0  then TOL is not referenced.
    !>
    !>          On exit, TOL is changed as described above, only if TOL is
    !>          non-positive on entry. Otherwise TOL is unchanged.
    !>

    INFO

    !>          INFO is INTEGER
    !>          = 0:  successful exit
    !>          < 0:  if INFO = -i, the i-th argument had an illegal value
    !>          > 0:  overflow would occur when computing the INFO(th)
    !>                element of the solution vector x. This can only occur
    !>                when JOB is supplied as positive and either means
    !>                that a diagonal element of U is very small, or that
    !>                the elements of the right-hand side vector y are very
    !>                large.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 162 of file dlagts.f.

  subroutine slagts (integer job, integer n, real, dimension( * ) a, real, dimension( * ) b, real, dimension( * ) c, real, dimension( * ) d, integer, dimension( * ) in, real, dimension( * ) y, real tol, integer info)

SLAGTS solves the system of equations (T-λI)x = y or (T-λI)^Tx = y, where T is a general tridiagonal matrix and λ a scalar, using the LU factorization computed by slagtf.

Purpose:

    !>
    !> SLAGTS may be used to solve one of the systems of equations
    !>
    !>    (T - lambda*I)*x = y   or   (T - lambda*I)**T*x = y,
    !>
    !> where T is an n by n tridiagonal matrix, for x, following the
    !> factorization of (T - lambda*I) as
    !>
    !>    (T - lambda*I) = P*L*U ,
    !>
    !> by routine SLAGTF. The choice of equation to be solved is
    !> controlled by the argument JOB, and in each case there is an option
    !> to perturb zero or very small diagonal elements of U, this option
    !> being intended for use in applications such as inverse iteration.
    !>

Parameters
    JOB

    !>          JOB is INTEGER
    !>          Specifies the job to be performed by SLAGTS as follows:
    !>          =  1: The equations  (T - lambda*I)x = y  are to be solved,
    !>                but diagonal elements of U are not to be perturbed.
    !>          = -1: The equations  (T - lambda*I)x = y  are to be solved
    !>                and, if overflow would otherwise occur, the diagonal
    !>                elements of U are to be perturbed. See argument TOL
    !>                below.
    !>          =  2: The equations  (T - lambda*I)**Tx = y  are to be solved,
    !>                but diagonal elements of U are not to be perturbed.
    !>          = -2: The equations  (T - lambda*I)**Tx = y  are to be solved
    !>                and, if overflow would otherwise occur, the diagonal
    !>                elements of U are to be perturbed. See argument TOL
    !>                below.
    !>

    N

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

    A

    !>          A is REAL array, dimension (N)
    !>          On entry, A must contain the diagonal elements of U as
    !>          returned from SLAGTF.
    !>

    B

    !>          B is REAL array, dimension (N-1)
    !>          On entry, B must contain the first super-diagonal elements of
    !>          U as returned from SLAGTF.
    !>

    C

    !>          C is REAL array, dimension (N-1)
    !>          On entry, C must contain the sub-diagonal elements of L as
    !>          returned from SLAGTF.
    !>

    D

    !>          D is REAL array, dimension (N-2)
    !>          On entry, D must contain the second super-diagonal elements
    !>          of U as returned from SLAGTF.
    !>

    IN

    !>          IN is INTEGER array, dimension (N)
    !>          On entry, IN must contain details of the matrix P as returned
    !>          from SLAGTF.
    !>

    Y

    !>          Y is REAL array, dimension (N)
    !>          On entry, the right hand side vector y.
    !>          On exit, Y is overwritten by the solution vector x.
    !>

    TOL

    !>          TOL is REAL
    !>          On entry, with  JOB < 0, TOL should be the minimum
    !>          perturbation to be made to very small diagonal elements of U.
    !>          TOL should normally be chosen as about eps*norm(U), where eps
    !>          is the relative machine precision, but if TOL is supplied as
    !>          non-positive, then it is reset to eps*max( abs( u(i,j) ) ).
    !>          If  JOB > 0  then TOL is not referenced.
    !>
    !>          On exit, TOL is changed as described above, only if TOL is
    !>          non-positive on entry. Otherwise TOL is unchanged.
    !>

    INFO

    !>          INFO is INTEGER
    !>          = 0: successful exit
    !>          < 0: if INFO = -i, the i-th argument had an illegal value
    !>          > 0: overflow would occur when computing the INFO(th)
    !>               element of the solution vector x. This can only occur
    !>               when JOB is supplied as positive and either means
    !>               that a diagonal element of U is very small, or that
    !>               the elements of the right-hand side vector y are very
    !>               large.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 162 of file slagts.f.

Author

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