The GAUSSINT function evaluates the integral of the Gaussian probability function.

The Gaussian integral is defined as:

## Examples

Plot the Gaussian probability function for a range of numbers raised to one of several exponents:

`; Generate our base values.`

X = FINDGEN(50)/100.

`; Plot the base values against their Gaussian probability integrals.`

`; Then plot the base values raised to an exponent against their `

`; Gaussian probability integrals.`

p1 = PLOT(X, GAUSSINT(X), XTITLE='Numbers', $

` YTITLE='Gaussian Integral', $`

` TITLE="Gaussian Integrals for Numbers", $`

COLOR='red', NAME='Number to the Power of 1')

p1 = PLOT((X^2), GAUSSINT(X), COLOR='blue', $

` NAME='Number to the Power of 2', /OVERPLOT)`

p1 = PLOT((X^3), GAUSSINT(X), COLOR='purple', $

` NAME='Number to the Power of 3', /OVERPLOT)`

p1 = PLOT((X^4), GAUSSINT(X), COLOR='green', $

` NAME='Number to the Power of 4', /OVERPLOT)`

p1 = PLOT((X^5), GAUSSINT(X), COLOR='chocolate', $

` NAME='Number to the Power of 5', /OVERPLOT)`

L = LEGEND(POSITION=[0.4,90], /DATA)

## Syntax

*Result* = GAUSSINT(*X [, Y]*)

## Return Value

Returns the result of the Gaussian probability function integral evaluation.

If *Y* is supplied, the result is for a two-dimensional integral. If either *X* or *Y* is double-precision, the result is double-precision, otherwise the argument is converted to single-precision and the result is single-precision.

If both *X* and *Y* are scalars, the result is a scalar. If both *X* and *Y* are arrays, the result is an array with the structure of the shorter of the arrays and excess elements are ignored. If *X* is a scalar and *Y* is an array or vice versa, the result has the structure of the array.

## Arguments

### X

The upper limit of integration in the first dimension at which the Gaussian integral is evaluated.

### Y

The upper limit of integration in the second dimension at which the Gaussian integral is evaluated.

## Keywords

### Thread Pool Keywords

This routine is written to make use of IDL’s *thread pool*, which can increase execution speed on systems with multiple CPUs. The values stored in the !CPU system variable control whether IDL uses the thread pool for a given computation. In addition, you can use the thread pool keywords TPOOL_MAX_ELTS, TPOOL_MIN_ELTS, and TPOOL_NOTHREAD to override the defaults established by !CPU for a single invocation of this routine. See Thread Pool Keywords for details.

## Version History

Original |
Introduced |