Test different methods for solving with nleqslv

The function tests different methods and global strategies for solving a system of nonlinear equations with nleqslv

Usage

testnslv(
  x,
  fn,
  jac = NULL,
  ...,
  method = c("Newton", "Broyden"),
  global = c("cline", "qline", "gline", "pwldog", "dbldog", "hook", "none"),
  Nrep = 0L,
  title = NULL
)

Arguments

x: A numeric vector with an initial guess of the root.
fn: A function of x returning the function values.
jac: A function to return the Jacobian for the fn function. For a vector valued function fn the Jacobian must be a numeric matrix of the correct dimensions. For a scalar valued function fn the jac function may return a scalar. If not supplied numerical derivatives will be used.
...: Further arguments to be passed to fn and jac and nleqslv.
method: The methods to use for finding a solution.
global: The global strategies to test. The argument may consist of several possibly abbreviated items.
Nrep: Number of repetitions to apply. Default is no repetitions.
title: a description of this experiment.

Value

testnslv returns an object of class "test.nleqslv" which is a list containing the following elements

call

the matched call

out

a dataframe containing the results with the following columns

Method: method used.
Global: global strategy used.
termcd: termination code of nleqslv.
Fcnt: number of function evaluations used by the method and global strategy. This excludes function evaluations made when computing a numerical Jacobian.
Jcnt: number of Jacobian evaluations.
Iter: number of outer iterations used by the algorithm.
Message: a string describing the termination code in an abbreviated form.
Fnorm: square of the euclidean norm of the vector of function results divided by 2.
cpusecs: CPU seconds used by the requested number of repetitions (only present when argument Nrep is not 0).

title

the description if specified

The abbreviated strings are

Fcrit: Convergence of function values has been achieved.
Xcrit: This means that the relative distance between two consecutive x-values is smaller than xtol.
Stalled: The algorithm cannot find an acceptable new point.
Maxiter: Iteration limit maxit exceeded.
Illcond: Jacobian is too ill-conditioned.
Singular: Jacobian is singular.
BadJac: Jacobian is unusable.
ERROR: nleqslv stopped because of a fatal error.

Details

The function solves the function fn with nleqslv for the specified methods and global strategies. When argument Nrep has been set to a number greater than or equal to 1, repetitions of the solving process are performed and the used CPU time in seconds is recorded.

If checking a user supplied jacobian is enabled, then testnslv will stop immediately when a possibly incorrect jacobian is detected.

Warning

Any nleqslv error message will be displayed immediately and an error for the particular combination of method and global strategy will be recorded in the final dataframe.

Examples


dslnex <- function(x) {
    y <- numeric(2)
    y[1] <- x[1]^2 + x[2]^2 - 2
    y[2] <- exp(x[1]-1) + x[2]^3 - 2
    y
}
xstart <- c(0.5,0.5)
fstart <- dslnex(xstart)
testnslv(xstart,dslnex)
#> Call:
#> testnslv(x = xstart, fn = dslnex)
#> 
#> Results:
#>     Method Global termcd Fcnt Jcnt Iter Message     Fnorm
#> 1   Newton  cline      1    7    6    6   Fcrit 8.550e-23
#> 2   Newton  qline      1    7    6    6   Fcrit 8.550e-23
#> 3   Newton  gline      1    9    5    5   Fcrit 1.501e-20
#> 4   Newton pwldog      1    7    6    6   Fcrit 4.536e-27
#> 5   Newton dbldog      1    7    6    6   Fcrit 4.536e-27
#> 6   Newton   hook      1    7    6    6   Fcrit 2.450e-23
#> 7   Newton   none      1    8    8    8   Fcrit 6.085e-25
#> 8  Broyden  cline      1   12    1    9   Fcrit 4.297e-17
#> 9  Broyden  qline      1   12    1    9   Fcrit 4.297e-17
#> 10 Broyden  gline      1   14    1   10   Fcrit 4.960e-21
#> 11 Broyden pwldog      1   12    1   10   Fcrit 5.156e-21
#> 12 Broyden dbldog      1   12    1   10   Fcrit 3.958e-20
#> 13 Broyden   hook      1   12    1   10   Fcrit 1.127e-19
#> 14 Broyden   none      1   13    1   13   Fcrit 1.783e-22
# this will encounter an error
xstart <- c(2.0,0.5)
fstart <- dslnex(xstart)
testnslv(xstart,dslnex)
#> Error (method=Newton global=none): non-finite value(s) detected in jacobian (row=2,col=1)
#> Call:
#> testnslv(x = xstart, fn = dslnex)
#> 
#> Results:
#>     Method Global termcd Fcnt Jcnt Iter Message     Fnorm
#> 1   Newton  cline      1   11    7    7   Fcrit 4.992e-19
#> 2   Newton  qline      1   10    7    7   Fcrit 2.809e-20
#> 3   Newton  gline      1   17    7    7   Fcrit 6.311e-29
#> 4   Newton pwldog      1    6    5    5   Fcrit 1.543e-18
#> 5   Newton dbldog      1    6    5    5   Fcrit 1.790e-18
#> 6   Newton   hook      1   11    7    7   Fcrit 3.819e-26
#> 7   Newton   none     NA   NA   NA   NA   ERROR        NA
#> 8  Broyden  cline      1   17    1   11   Fcrit 2.900e-18
#> 9  Broyden  qline      1   18    1   13   Fcrit 1.404e-17
#> 10 Broyden  gline      1   25    1   11   Fcrit 4.798e-19
#> 11 Broyden pwldog      1   12    1   10   Fcrit 6.230e-18
#> 12 Broyden dbldog      1   12    1   10   Fcrit 3.239e-18
#> 13 Broyden   hook      1   16    1   12   Fcrit 5.719e-23
#> 14 Broyden   none      4   20    1   20 Maxiter 1.846e-01