## Visualize Function Minimum

### Description

Visualizes multivariate functions around a point or along a line between two points in R^n.

### Usage

fminviz(fn, x0, nlines = 2*length(x0),
npoints = 51, scaled = 1.0)

flineviz(fn, x1, x2, npoints = 51, scaled = 0.1)

### Arguments

 fn multivariate function to be visualized. x0, x1, x2 points in n-dimensional space. nlines number of lines to plot. npoints number of points used to plot a line. scaled scale factor to extend the line(s).

### Details

fminviz vizualizes the behavior of a multivariate function fn around a point x0. It randomly selects nlines lines through x0 in R^n and draws the curves of the function along these lines in one graph.

Curves that have at least one point below fn(x0) are drawn in red, all others in blue. The scale on the x-axis is the Euclidean distance in R^n. The scale factor can change it.

flineviz vizualizes the behavior of a multivariate function fn along the straight line between the points x1 and x2. Points x1 and x2 are also plotted.

### Value

Plots a line graph and returns NULL (invisibly).

### Examples

## Not run:
f1 <- function(x) x[1]^2 - x[2]^2
fminviz(f1, c(0, 0), nlines = 10)

f2 <- function(x) (1 - x[1])^2 + 100*(x[2] - x[1]^2)^2
flineviz(f2, c(0, 0), c(1, 1))

## End(Not run)