Find a Minimum nD (Downhill Simplex) (G Dataflow)

Version:

Uses the downhill simplex method to determine a local minimum of a function of n independent variables.

formula

Function under investigation. The formula can contain any number of valid variables.

Entering Valid Variables

This node accepts variables that use the following format rule: variables must start with a letter or an underscore followed by any number of alphanumeric characters or underscores.

start

Points at which the optimization process starts. These points form a simplex in n dimension.

error in

Error conditions that occur before this node runs.

The node responds to this input according to standard error behavior.

Standard Error Behavior

Many nodes provide an error in input and an error out output so that the node can respond to and communicate errors that occur while code is running. The value of error in specifies whether an error occurred before the node runs. Most nodes respond to values of error in in a standard, predictable way.

error in does not contain an error error in contains an error
If no error occurred before the node runs, the node begins execution normally.

If no error occurs while the node runs, it returns no error. If an error does occur while the node runs, it returns that error information as error out.

If an error occurred before the node runs, the node does not execute. Instead, it returns the error in value as error out.

Default: No error

accuracy

Accuracy of the minimum of the formula.

The node stops running if the difference between two consecutive approximations equals to or is less than the value of accuracy.

Default: 1E-08

minimum

Local minimum in n dimension.

f(minimum)

Function value at the local minimum.

error out

Error information.

The node produces this output according to standard error behavior.

Standard Error Behavior

Many nodes provide an error in input and an error out output so that the node can respond to and communicate errors that occur while code is running. The value of error in specifies whether an error occurred before the node runs. Most nodes respond to values of error in in a standard, predictable way.

error in does not contain an error error in contains an error
If no error occurred before the node runs, the node begins execution normally.

If no error occurs while the node runs, it returns no error. If an error does occur while the node runs, it returns that error information as error out.

If an error occurred before the node runs, the node does not execute. Instead, it returns the error in value as error out.

How the Downhill Simplex Method Works

The downhill simplex method, also called the Nelder-Mead method, works without partial derivatives. The downhill simplex method consists of catching the minimum of the function f(x) with the help of simple geometrical bodies, specifically a simplex.

A simplex in 2D is a triangle; a simplex in 3D is a tetrahedron, and so on. You must have (n + 1) starting points, each of dimension n, forming the initial simplex. You must enter only one point of these (n + 1) starting points. The (n + 1) dimensional simplex is constructed automatically.

For the function defined by equation f(x, y) = x2 + y2, you must enter two numbers, describing exactly one point in 2D. The method generates a new simplex by some elementary operations such as reflections, expansions, and contractions. In the end, the minimum is concentrated in a very small simplex.

To find the simplex sequence tending to the minimum (0, 0) of the preceding function, enter the following values on the panel:

 formula [x*x + y*y] start [3.2, 1]

The following illustration shows the simplex sequence tending to the minimum (0, 0) of the preceding function.

Where This Node Can Run:

Desktop OS: Windows

FPGA: This product does not support FPGA devices