# Uneven Numeric Integration (G Dataflow)

Version:

Performs numeric integration on unevenly spaced values in the input data using the trapezoidal integration method.

## f(x)

Data to integrate.

You obtain the data by computing the integrand value at sampling points t0, t1, t2, and so on.

## x

Sampling points this node uses to compute data from the integrand. The sampling points can be spaced unevenly. This input must be the same length as f(x).

## 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

## integral

Numeric integral.

## 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.

## Algorithm for Calculating the Integral

Before performing numeric integration, this node reorders x in ascending order and reorders f(x) to correspond to x. The node then performs numeric integration using the following equation:

$\text{integral}=\underset{i=0}{\overset{n-2}{\sum }}\frac{\left(x\left[i\right]+x\left[i+1\right]\right)}{2}*\left(t\left[i+1\right]-t\left[i\right]\right)$

where n is the number of data points.

Where This Node Can Run:

Desktop OS: Windows

FPGA: This product does not support FPGA devices