# Name

avgvar - Calculates average and variance for an image series.

# Usage

Calculate average and variance of image stack without using current alignment parameters:

- avgvar(data, mode='b')

Calculate average and variance of image stack using current alignment parameters:

- avgvar(data, mode='a')

Calculate average and variance of only the even numbered images without using current alignment parameters:

- avgvar(data, mode='b', use_odd = False)

Calculate average and variance of only the odd numbered images between images 3 and 57, inclusive, using current alignment parameters:

- avgvar(data, mode='a', i1 = 3, i2 = 57, use_even=False)

## Input

- data
- image stack, can be 2D or 3D, must be in real space
- mode
- whether to apply alignment parameters. Default mode='a' means apply parameters
- ali_params
- name of the attribute alignment parameters are stored under in image headers
- rot_method
- specifies the function by which images are rotated/shifted if alignment parameters are to be applied. This is only relevant for the case where images are 2D, in which case rot_method can be either rot_shift2D or rotshift2dg, with the default being rot_shift2D. If images are 3D, rot_shift3D will be used to rotate/shift the images.
- interp
- interpolation method to use for rot_method when applying alignment parameters.
- i1
- index of first image to be used.
- i2
- index of last image to be used. If i2 = 0, then i2 defaults to one less than number of images in the data
- use_odd
- images with indices between i1 and i2 which are odd are used if and only if use_odd is set to True. Default is True.
- use_even
- images with indices between i1 and i2 which are even are used if and only if use_even is set to True. Default is True.

## Output

- ave
- the average of the image series in real space
- var
- the variance of the image series in real space

# Description

The output average is calculated as the sum of the images divided by the number of images used in the calculation (as determined by i1, i2, use_even and use_odd). If mode='a', the average is calculated from the images after alignment parameters have been applied.

The variance is calculated as: `` (sum_i O_i^2 - ave*ave*n)/(n-1) ``, where the sum ranges over all images used in the calculations, n is the number of images used in the calculations, and O_i denotes the i-th image.

# Author / Maintainer

Jia Fang

# Keywords

- category 1
- UTILITIES

# Files

statistics.py

# See also

mad_scalar, mul_scalar, add_img2, sub_img, mul_img

# Maturity

- Works for author