AHELP for CIAO 4.14 Sherpa

# gauss1d

Context: models

## Synopsis

One-dimensional gaussian function.

## Syntax

`gauss1d`

## Examples

### Example 1

```>>> create_model_component("gauss1d", "mdl")
>>> print(mdl)```

Create a component of the gauss1d model and display its default parameters. The output is:

```mdl
Param        Type          Value          Min          Max      Units
-----        ----          -----          ---          ---      -----
mdl.fwhm     thawed           10  1.17549e-38  3.40282e+38
mdl.pos      thawed            0 -3.40282e+38  3.40282e+38
mdl.ampl     thawed            1 -3.40282e+38  3.40282e+38           ```

### Example 2

Compare the gaussian and normalized gaussian models:

```>>> gauss1d.m1
>>> normgauss1d.m2
>>> m1.pos, m2.pos = 10, 10
>>> m1.ampl, m2.ampl = 10, 10
>>> m1.fwhm, m2.fwhm = 5, 5
>>> m1(10)
10.0
>>> m2(10)
1.8788745573993026
>>> m1.fwhm, m2.fwhm = 1, 1
>>> m1(10)
10.0
>>> m2(10)
9.394372786996513```

### Example 3

The normalised version will sum to the amplitude when given an integrated grid - i.e. both low and high edges rather than points - that covers all the signal (and with a bin size a lot smaller than the FWHM):

```>>> m1.fwhm, m2.fwhm = 12.2, 12.2
>>> grid = np.arange(-90, 110, 0.01)
>>> glo, ghi = grid[:-1], grid[1:]
>>> m1(glo, ghi).sum()
129.86497637060958
>>> m2(glo, ghi).sum()
10.000000000000002```

### ATTRIBUTES

The attributes for this object are:

Attribute Definition
fwhm The Full-Width Half Maximum of the gaussian. It is related to the sigma value by: FWHM = sqrt(8 * log(2)) * sigma.
pos The center of the gaussian.
ampl The amplitude refers to the maximum peak of the model.

The functional form of the model for points is:

`f(x) = ampl * exp(-4 * log(2) * (x - pos)^2 / fwhm^2)`

and for an integrated grid it is the integral of this over the bin.

## Bugs

See the bugs pages on the Sherpa website for an up-to-date listing of known bugs.