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

Generated automatically by Doxygen for LAPACK from the source code.