diagnostics.bvpSolve: Prints Diagnostic Characteristics of BVP Solvers

Description

Prints several diagnostics of the simulation to the screen, e.g. conditioning parameters

Usage

# S3 method for bvpSolve
diagnostics(obj, ...)
# S3 method for bvpSolve
approx(x, xout = NULL, ...)

Value

S3 method diagnostics prints diagnostic features of the simulation.

What exactly is printed will depend on the solution method.

The diagnostics of all solvers include the number of function evaluations, the number of jacobian evaluations, and the number of steps. The diagnostics of both bvptwp and bvpcol also include the the number of boundary evaluations and the number of boundary jacobian evaluations. In case the problem was solved with bvpshoot, the diagnostics of the initial value problem solver will also be written to screen.

Note that the number of function evaluations are *without* the extra calls performed to generate the ordinary output variables (if present).

In case the method used was

bvptwp, will also return the conditioning parameters. They are: kappa, kappa1, kappa2, sigma and gamma1.

See https://www.scpe.org/index.php/scpe/article/view/626

the kappa's are based on the Inf-norm, gamma1 is based on the 1-norm, If kappa, kappa1 and gamma1 are of moderate size, the problem is well conditioned. If large, the problem is ill-conditioned. If kappa1 is large and gamma1 is small, the problem is ill-conditioned in the maximum and well conditioned in the 1-norm. This is typical for problems that involve different time scales ("stiff" problems). If kappa1 is small and kappa, kappa2 are large the problem has not the correct dichotomy.

S3 method approx calculates an approximate solution vector at points inbetween the original x-values. If beyond the integration interval, it will not extrapolate, but just return the values at the edges. This works only when the solution was generated with bvpcol, and usses information in the arrays rwork and iwork, stored as attributes. The returned matrix will be of class "bvpSolve"

Arguments

obj: the output as produced by bvptwp, bvpcol or bvpshoot.
x: the output as produced by bvpcol
xout: points x for which new variable values should be generated.
...: optional arguments to the generic function.

Details

When the integration output is saved as a data.frame, then the required attributes are lost and method diagnostics will not work anymore.

Examples

Run this code

## =============================================================================
## Diagnostic messages
## =============================================================================
f2 <- function(x, y, parms) {
 dy  <- y[2]
 dy2 <- -1/x*y[2] - (1-1/(4*x^2))*y[1] + sqrt(x)*cos(x)
 list(c(dy, dy2))
}

x    <- seq(1, 6, 0.1)
yini <- c(y = 1, dy = NA)
yend <- c(-0.5, NA)

sol   <- bvptwp(yini = yini, yend = yend, x = x, func = f2)
sol2  <- bvpcol(yini = yini, yend = yend, x = x, func = f2)
sol3  <- bvpshoot(yini = yini, yend = yend, x = x, func = f2, guess = 0)

plot(sol, which = "y")
diagnostics(sol)
diagnostics(sol2)
diagnostics(sol3)

## =============================================================================
## approx
## =============================================================================

soldetail <- approx(sol2, xout = seq(2,4,0.01))
plot(soldetail)

# beyond the interval
approx(sol2, xout = c(0,1,2))
approx(sol2, xout = c(6,100))