# Find a Minimum nD (Conjugate Gradient) (G Dataflow)

Uses the conjugate gradient method to determine a local minimum of a function of n independent variables.

## line minimization

Value that determines whether this node uses the derivatives in the algorithm.

Name Value Description
Without Derivatives 0 Does not use the derivatives in the algorithm.
With Derivatives 1 Uses the derivatives in the algorithm.

Default: Without Derivatives

Algorithm this node uses to compute the derivatives.

Name Value Description
Fletcher-Reeves 0 Uses the Fletcher-Reeves method.
Polak-Ribiere 1 Uses the Polak-Ribiere method.

Default: Fletcher-Reeves

## 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

Point in n dimension at which the optimization process starts.

## 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 Conjugate Gradient Method Works

The conjugate-gradient method uses the derivatives of a function to update the conjugate direction. This node uses the Fletcher-Reeves algorithm or the Polak-Ribiere algorithm to calculate the conjugate direction, depending on gradient method.

The following illustration shows a start point and a start direction. New points and new directions are calculated by this node.

Where This Node Can Run:

Desktop OS: Windows

FPGA: This product does not support FPGA devices