# 4. Technical specifications¶

In this page we summarize the assumptions that are made in **galario** and the specifications for the input quantities.

Full details are presented in Section 3 of Tazzari, Beaujean and Testi (2018) MNRAS **476** 4527
[MNRAS]
[arXiv]
[ADS].

## 4.1. Image specifications¶

Following the Figure below, there are two fundamental coordinate systems that define the input image for the
`sampleImage()`

and `chi2Image()`

functions:

the

matrix axes\([i, j]\) mapping the pixel coordinates, running from`0`

to`Nxy-1`

(`Nxy`

is the number of pixels on each axis).the

physical axes\((R.A., Dec.)\) mapping Right Ascension and Declination coordinates.

The origin `[i, j] = [0, 0]`

of the matrix axes can be put either in the **upper left** or in the **lower left** corner of the matrix.
By default **galario** assumes the origin is in the **upper left** corner of the matrix, but it can be changed to the
lower corner by specifying the optional parameter `origin='lower'`

in the `sampleImage()`

and `chi2Image()`

functions.

The origin \((R.A., Dec.)=(0,0)\) of the physical axes is always in the center of the `[Nxy/2, Nxy/2]`

pixel
(grey pixel in the Figure below) for any value of `origin`

. The \(R.A.\) axis always increases leftwards, following the usual convention
of having East to the left and West to the right: therefore, the \(R.A.\) axis always decreases with increasing `j`

index.
Note that, with `origin='upper'`

, both the \((R.A., Dec.)\) axes **decrease** with increasing `i`

, `j`

index (see Figure below).

Warning

**galario** assumes that the values of the input image are evaluated in the **pixel centers** (not in the pixel edges).

For instructions on how to compute the correct \((R.A., Dec.)\) coordinate meshgrid to create the image, see the Cookbook.

The left and right panels of the Figure below show the relative orientations of matrix and physical axes
for the `origin='upper'`

and `origin='lower'`

cases, respectively (click on the images for a larger version).

Note

The `origin`

parameter in **galario** follows the same definition as in the `matshow`

and `imshow`

commands of the
`matplotlib`

library.
To get the desired orientation of the Declination axis in **galario**, use the same `origin`

parameter that produces
the desired image orientation with `matshow`

or `imshow`

.