FixedPoint (version 0.6.3)

ConvergenceFig: A function for plotting the convergence change over a series of iterates.

Description

On the x axis is the index of each iterate. On the y axis are different convergence metric values.

Usage

ConvergenceFig(
  Inputs,
  Outputs,
  Input_Convergence = c(),
  LinesToDraw = c("Sup_Norm", "Euclidean_Norm", "Sum_Of_Absolute_Value_Of_Residuals",
    "Smallest_Residual"),
  LogScale = TRUE,
  FromIterate = 1,
  ToIterate = c()
)

Value

This function returns nothing. It just shows a plot in the console.

Arguments

Inputs

The Inputs matrix returned by FixedPoint.

Outputs

The Outputs matrix returned by FixedPoint.

Input_Convergence

Convergence vector to be used in the figure. Often makes sense for it to be the same as that used in the Fixedpoint function.

LinesToDraw

A vector describing which convergence metrics to draw. This vector can contain anything in c("Sup_Norm", "Euclidean_Norm", "Sum_Of_Absolute_Value_Of_Residuals", "Smallest_Residual", "Input_Convergence"). Here "Input_Convergence" draws the input convergence vector. "Sup_Norm" gives the greatest residual (in absolute value), "Euclidean_Norm" is the eucleadean norm of the residuals, "Sum_Of_Absolute_Value_Of_Residuals" sums up the absolute value of the residuals and "Smallest_Residual" is the smallest residual by absolute value. Clearly if the function takes and returns a scalar (rather than a vector) then all of these are identical.

LogScale

This is whether or not to use a log scale. If so instead of convergence, log(1+convergence) is shown on the y axis. By default this is true.

FromIterate

This describes the first iterate on the figure.

ToIterate

This describes the last iterate on the figure.

Examples

Inputs = seq(1,10)
Function = function(x){ cos(x) }
A = FixedPoint(Function, Inputs, Method = "Anderson")
ConvergenceFig(A$Inputs, A$Outputs)
# And now to only show a median norm:
Differences = A$Inputs - A$Outputs
Convergence = apply(Differences,2,function(x){median(abs(x))})
ConvergenceFig(A$Inputs, A$Outputs, Convergence, LinesToDraw = "Input_Convergence")