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lagts(3) Library Functions Manual 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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