SRC/cptsvx.f(3)

NAME
SRC/cptsvx.f

SYNOPSIS

  Functions/Subroutines
subroutine cptsvx (fact, n, nrhs, d, e, df, ef, b, ldb, x, ldx, rcond, ferr, berr, work, rwork, info)
CPTSVX computes the solution to system of linear equations A * X = B for PT matrices

Function/Subroutine Documentation

  subroutine cptsvx (character fact, integer n, integer nrhs, real, dimension( * ) d, complex, dimension( * ) e, real, dimension( * ) df, complex, dimension( * ) ef, complex, dimension( ldb, * ) b, integer ldb, complex, dimension( ldx, * ) x, integer ldx, real rcond, real, dimension( * ) ferr, real, dimension( * ) berr, complex, dimension( * ) work, real, dimension( * ) rwork, integer info)

CPTSVX computes the solution to system of linear equations A * X = B for PT matrices

Purpose:

    !>
    !> CPTSVX uses the factorization A = L*D*L**H to compute the solution
    !> to a complex system of linear equations A*X = B, where A is an
    !> N-by-N Hermitian positive definite tridiagonal matrix and X and B
    !> are N-by-NRHS matrices.
    !>
    !> Error bounds on the solution and a condition estimate are also
    !> provided.
    !>

Description:

    !>
    !> The following steps are performed:
    !>
    !> 1. If FACT = 'N', the matrix A is factored as A = L*D*L**H, where L
    !>    is a unit lower bidiagonal matrix and D is diagonal.  The
    !>    factorization can also be regarded as having the form
    !>    A = U**H*D*U.
    !>
    !> 2. If the leading principal minor of order i is not positive,
    !>    then the routine returns with INFO = i. Otherwise, the factored
    !>    form of A is used to estimate the condition number of the matrix
    !>    A.  If the reciprocal of the condition number is less than machine
    !>    precision, INFO = N+1 is returned as a warning, but the routine
    !>    still goes on to solve for X and compute error bounds as
    !>    described below.
    !>
    !> 3. The system of equations is solved for X using the factored form
    !>    of A.
    !>
    !> 4. Iterative refinement is applied to improve the computed solution
    !>    matrix and calculate error bounds and backward error estimates
    !>    for it.
    !>

Parameters
    FACT

    !>          FACT is CHARACTER*1
    !>          Specifies whether or not the factored form of the matrix
    !>          A is supplied on entry.
    !>          = 'F':  On entry, DF and EF contain the factored form of A.
    !>                  D, E, DF, and EF will not be modified.
    !>          = 'N':  The matrix A will be copied to DF and EF and
    !>                  factored.
    !>

    N

    !>          N is INTEGER
    !>          The order of the matrix A.  N >= 0.
    !>

    NRHS

    !>          NRHS is INTEGER
    !>          The number of right hand sides, i.e., the number of columns
    !>          of the matrices B and X.  NRHS >= 0.
    !>

    D

    !>          D is REAL array, dimension (N)
    !>          The n diagonal elements of the tridiagonal matrix A.
    !>

    E

    !>          E is COMPLEX array, dimension (N-1)
    !>          The (n-1) subdiagonal elements of the tridiagonal matrix A.
    !>

    DF

    !>          DF is REAL array, dimension (N)
    !>          If FACT = 'F', then DF is an input argument and on entry
    !>          contains the n diagonal elements of the diagonal matrix D
    !>          from the L*D*L**H factorization of A.
    !>          If FACT = 'N', then DF is an output argument and on exit
    !>          contains the n diagonal elements of the diagonal matrix D
    !>          from the L*D*L**H factorization of A.
    !>

    EF

    !>          EF is COMPLEX array, dimension (N-1)
    !>          If FACT = 'F', then EF is an input argument and on entry
    !>          contains the (n-1) subdiagonal elements of the unit
    !>          bidiagonal factor L from the L*D*L**H factorization of A.
    !>          If FACT = 'N', then EF is an output argument and on exit
    !>          contains the (n-1) subdiagonal elements of the unit
    !>          bidiagonal factor L from the L*D*L**H factorization of A.
    !>

    B

    !>          B is COMPLEX array, dimension (LDB,NRHS)
    !>          The N-by-NRHS right hand side matrix B.
    !>

    LDB

    !>          LDB is INTEGER
    !>          The leading dimension of the array B.  LDB >= max(1,N).
    !>

    X

    !>          X is COMPLEX array, dimension (LDX,NRHS)
    !>          If INFO = 0 or INFO = N+1, the N-by-NRHS solution matrix X.
    !>

    LDX

    !>          LDX is INTEGER
    !>          The leading dimension of the array X.  LDX >= max(1,N).
    !>

    RCOND

    !>          RCOND is REAL
    !>          The reciprocal condition number of the matrix A.  If RCOND
    !>          is less than the machine precision (in particular, if
    !>          RCOND = 0), the matrix is singular to working precision.
    !>          This condition is indicated by a return code of INFO > 0.
    !>

    FERR

    !>          FERR is REAL array, dimension (NRHS)
    !>          The forward error bound for each solution vector
    !>          X(j) (the j-th column of the solution matrix X).
    !>          If XTRUE is the true solution corresponding to X(j), FERR(j)
    !>          is an estimated upper bound for the magnitude of the largest
    !>          element in (X(j) - XTRUE) divided by the magnitude of the
    !>          largest element in X(j).
    !>

    BERR

    !>          BERR is REAL array, dimension (NRHS)
    !>          The componentwise relative backward error of each solution
    !>          vector X(j) (i.e., the smallest relative change in any
    !>          element of A or B that makes X(j) an exact solution).
    !>

    WORK

    !>          WORK is COMPLEX array, dimension (N)
    !>

    RWORK

    !>          RWORK is REAL array, dimension (N)
    !>

    INFO

    !>          INFO is INTEGER
    !>          = 0:  successful exit
    !>          < 0:  if INFO = -i, the i-th argument had an illegal value
    !>          > 0:  if INFO = i, and i is
    !>                <= N:  the leading principal minor of order i of A
    !>                       is not positive, so the factorization could not
    !>                       be completed, and the solution has not been
    !>                       computed. RCOND = 0 is returned.
    !>                = N+1: U is nonsingular, but RCOND is less than machine
    !>                       precision, meaning that the matrix is singular
    !>                       to working precision.  Nevertheless, the
    !>                       solution and error bounds are computed because
    !>                       there are a number of situations where the
    !>                       computed solution can be more accurate than the
    !>                       value of RCOND would suggest.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 232 of file cptsvx.f.

Author

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