View on GitHub

Glossary

Throughout this course we will use a variety of different functions available in the base Python library, but also many other libraries in the scientific computing stack. Here we provide a list of all of the functions that are used across the various notebooks. It can be a helpful reference when you are learning Python about the types of things you can do with various packages. Remember you can always view the docstrings for any function by adding a ? to the end of the function name.

Jupyter Cell Magic

Magics are specific to and provided by the IPython kernel. Whether Magics are available on a kernel is a decision that is made by the kernel developer on a per-kernel basis. To work properly, Magics must use a syntax element which is not valid in the underlying language. For example, the IPython kernel uses the % syntax element for Magics as % is not a valid unary operator in Python. However, % might have meaning in other languages.

:::{glossary}

%conda

Run the conda package manager within the current kernel. API docs

%debug

Activate the interactive debugger. This magic command supports two ways of activating debugger. One is to activate debugger before executing code. This way, you can set a break point, to step through the code from the point. The other one is to activate debugger in post-mortem mode. You can activate this mode simply running %debug without any argument. If an exception has just occurred, this lets you inspect its stack frames interactively. API docs

%matplotlib

Set up matplotlib to work interactively. Example: %matplotlib inline. This function lets you activate matplotlib interactive support at any point during an IPython session. It does not import anything into the interactive namespace. API docs

%timeit

Time execution of a Python statement or expression using the timeit module. This function can be used both as a line and cell magic. API docs

! (shell execute)

Shell execute — run shell command and capture output (!! is short-hand). Example: !pip. API docs

:::

Base Python Functions

These functions are all bundled with Python.

:::{glossary}

any

Test if any of the elements are true. API docs

bool

Cast as boolean type. API docs

dict

Cast as dictionary type. API docs

enumerate

Return an enumerate object. iterable must be a sequence, an iterator, or some other object which supports iteration. The __next__() method of the iterator returned by enumerate() returns a tuple containing a count (from start which defaults to 0) and the values obtained from iterating over iterable. API docs

float

Return a floating point number constructed from a number or string x. API docs

import

Import python module into namespace. API docs

int

Cast as integer type. API docs

len

Return the length (the number of items) of an object. The argument may be a sequence (such as a string, bytes, tuple, list, or range) or a collection (such as a dictionary, set, or frozen set). API docs

glob.glob

The glob module finds all the pathnames matching a specified pattern according to the rules used by the Unix shell, although results are returned in arbitrary order. No tilde expansion is done, but *, ?, and character ranges expressed with [] will be correctly matched. API docs

list

Cast as list type. API docs

max

Return the largest item in an iterable or the largest of two or more arguments. API docs

min

Return the smallest item in an iterable or the smallest of two or more arguments. API docs

os.path.basename

Return the base name of pathname path. This is the second element of the pair returned by passing path to the function split(). API docs

os.path.join

Join one or more path components intelligently. The return value is the concatenation of path and any members of paths with exactly one directory separator (os.sep) following each non-empty part except the last. API docs

print

Print strings. Recommend using f-strings formatting. Example: print(f'Results: {variable}'). API docs

pwd

Print current working directory. API docs

sorted

Return a new sorted list from the items in iterable. API docs

str

Cast as string type. API docs

range

Rather than being a function, range is actually an immutable sequence type, as documented in Ranges and Sequence Types — list, tuple, range. API docs

tuple

Cast as tuple type. API docs

type

Return the type of the object. API docs

zip

Make an iterator that aggregates elements from each of the iterables. API docs

:::

Pandas

pandas is an open source, BSD-licensed library providing high-performance, easy-to-use data structures and data analysis tools for the Python programming language.

import pandas as pd

:::{glossary}

pd.read_csv

Read a comma-separated values (csv) file into DataFrame. API docs

pd.concat

Concatenate pandas objects along a particular axis with optional set logic along the other axes. API docs

pd.DataFrame.isnull

Detect missing values. API docs

pd.DataFrame.mean

Return the mean of the values for the requested axis. API docs

pd.DataFrame.std

Return sample standard deviation over requested axis. API docs

pd.DataFrame.plot

Plot data using matplotlib. API docs

pd.DataFrame.map

Map values of Series according to input correspondence. API docs

pd.DataFrame.groupby

Group DataFrame or Series using a mapper or by a Series of columns. API docs

pd.DataFrame.fillna

Fill NA/NaN values using the specified method. API docs

pd.DataFrame.replace

Replace values given in to_replace with value. API docs

:::

NumPy

NumPy is the fundamental package for scientific computing with Python. It contains among other things: - a powerful N-dimensional array object - sophisticated (broadcasting) functions - tools for integrating C/C++ and Fortran code - useful linear algebra, Fourier transform, and random number capabilities

Besides its obvious scientific uses, NumPy can also be used as an efficient multi-dimensional container of generic data. Arbitrary data-types can be defined. This allows NumPy to seamlessly and speedily integrate with a wide variety of databases.

import numpy as np

:::{glossary}

np.arange

Return evenly spaced values within a given interval. API docs

np.array

Create an array. API docs

np.convolve

Returns the discrete, linear convolution of two one-dimensional sequences. API docs

np.cos

Trigonometric cosine element-wise. API docs

np.diag

Extract a diagonal or construct a diagonal array. API docs

np.diag_indices

Return the indices to access the main diagonal of an array. API docs

np.dot

Dot product of two arrays. API docs

np.exp

Calculate the exponential of all elements in the input array. API docs

np.fft.fft

Compute the one-dimensional discrete Fourier Transform. API docs

np.fft.ifft

Compute the one-dimensional inverse discrete Fourier Transform. API docs

np.hstack

Stack arrays in sequence horizontally (column wise). API docs

np.linalg.pinv

Compute the (Moore-Penrose) pseudo-inverse of a matrix. API docs

np.mean

Compute the arithmetic mean along the specified axis. API docs

np.nan

IEEE 754 floating point representation of Not a Number (NaN). API docs

np.ones

Return a new array of given shape and type, filled with ones. API docs

np.pi

Return pi 3.1415926535897932384626433... API docs

np.random.randint

Return random integers from low (inclusive) to high (exclusive). API docs

np.random.randn

Return a sample (or samples) from the "standard normal" distribution. API docs

np.real

Return the real part of the complex argument. API docs

np.sin

Trigonometric sine, element-wise. API docs

np.sqrt

Return the non-negative square-root of an array, element-wise. API docs

np.squeeze

Remove single-dimensional entries from the shape of an array. API docs

np.std

Compute the standard deviation along the specified axis. API docs

np.vstack

Stack arrays in sequence vertically (row wise). API docs

np.zeros

Return a new array of given shape and type, filled with zeros. API docs

:::

SciPy

SciPy is one of the core packages that make up the SciPy stack. It provides many user-friendly and efficient numerical routines, such as routines for numerical integration, interpolation, optimization, linear algebra, and statistics.

:::{glossary}

scipy.stats.binom

A binomial discrete random variable. API docs

scipy.signal.butter

Butterworth digital and analog filter design. API docs

scipy.signal.filtfilt

Apply a digital filter forward and backward to a signal. API docs

scipy.signal.freqz

Compute the frequency response of a digital filter. API docs

scipy.signal.sosfreqz

Compute the frequency response of a digital filter in SOS format. API docs

scipy.stats.ttest_1samp

Calculate the T-test for the mean of ONE group of scores. API docs

:::

Matplotlib

Matplotlib is a Python 2D plotting library which produces publication quality figures in a variety of hardcopy formats and interactive environments across platforms. Matplotlib can be used in Python scripts, the Python and IPython shells, the Jupyter notebook, web application servers, and four graphical user interface toolkits.

import matplotlib.pyplot as plt

:::{glossary}

plt.bar

Make a bar plot. API docs

plt.figure

Create a new figure. API docs

plt.hist

Plot a histogram. API docs

plt.imshow

Display an image, i.e. data on a 2D regular raster. API docs

plt.legend

Place a legend on the axes. API docs

plt.savefig

Save the current figure. API docs

plt.scatter

A scatter plot of y vs x with varying marker size and/or color. API docs

plt.subplots

Create a figure and a set of subplots. API docs

plt.tight_layout

Automatically adjust subplot parameters to give specified padding. API docs

ax.axvline

Add a vertical line across the axes. API docs

ax.set_xlabel

Set the label for the x-axis. API docs

ax.set_xlim

Set the x-axis view limits. API docs

ax.set_xticklabels

Set the x-tick labels with list of string labels. API docs

ax.set_ylim

Set the y-axis view limits. API docs

ax.set_yticklabels

Set the y-tick labels with list of string labels. API docs

ax.set_ylabel

Set the label for the y-axis. API docs

ax.set_title

Set a title for the axes. API docs

:::

Seaborn

Seaborn is a Python data visualization library based on matplotlib. It provides a high-level interface for drawing attractive and informative statistical graphics.

import seaborn as sns

:::{glossary}

sns.heatmap

Plot rectangular data as a color-encoded matrix. API docs

sns.catplot

Figure-level interface for drawing categorical plots onto a FacetGrid. API docs

sns.jointplot

Draw a plot of two variables with bivariate and univariate graphs. API docs

sns.regplot

Plot data and a linear regression model fit. API docs

:::

scikit-learn

Scikit-learn is an open source machine learning library that supports supervised and unsupervised learning. It also provides various tools for model fitting, data preprocessing, model selection and evaluation, and many other utilities.

:::{glossary}

sklearn.metrics.pairwise_distances

This method takes either a vector array or a distance matrix, and returns a distance matrix. If the input is a vector array, the distances are computed. If the input is a distances matrix, it is returned instead. API docs

sklearn.metrics.balanced_accuracy_score

Compute the balanced accuracy. The balanced accuracy in binary and multiclass classification problems to deal with imbalanced datasets. It is defined as the average of recall obtained on each class. API docs

:::

networkx

NetworkX is a Python package for the creation, manipulation, and study of the structure, dynamics, and functions of complex networks.

import networkx as nx

:::{glossary}

nx.draw_kamada_kawai

Draw the graph G with a Kamada-Kawai force-directed layout. API docs

nx.degree

Return the degree of a node or nodes. The node degree is the number of edges adjacent to that node. API docs

:::

NiBabel

nibabel is a package to help read/write access to some common neuroimaging file formats, including: ANALYZE (plain, SPM99, SPM2 and later), GIFTI, NIfTI1, NIfTI2, CIFTI-2, MINC1, MINC2, AFNI BRIK/HEAD, MGH and ECAT as well as Philips PAR/REC. We can read and write FreeSurfer geometry, annotation and morphometry files. There is some very limited support for DICOM. NiBabel is the successor of PyNIfTI.

The various image format classes give full or selective access to header (meta) information and access to the image data is made available via NumPy arrays.

import nibabel as nib

:::{glossary}

nib.load

Load file given filename, guessing at file type. API docs

nib.save

Save an image to file adapting format to filename. API docs

data.get_data

Return image data from image with any necessary scaling applied. API docs

data.get_shape

Return shape for image. API docs

data.header

The header of an image contains the image metadata. The information in the header will differ between different image formats. For example, the header information for a NIfTI1 format file differs from the header information for a MINC format file. API docs

data.affine

Homogenous affine giving relationship between voxel coordinates and world coordinates. Affine can also be None. In this case, obj.affine also returns None, and the affine as written to disk will depend on the file format. API docs

:::

NiLearn

nilearn is a Python module for fast and easy statistical learning on NeuroImaging data.

It leverages the scikit-learn Python toolbox for multivariate statistics with applications such as predictive modelling, classification, decoding, or connectivity analysis.

:::{glossary}

nilearn.plotting.plot_anat

Plot cuts of an anatomical image (by default 3 cuts: Frontal, Axial, and Lateral). API docs

nilearn.plotting.view_img

Interactive html viewer of a statistical map, with optional background. API docs

nilearn.plotting.plot_glass_brain

Plot 2d projections of an ROI/mask image (by default 3 projections: Frontal, Axial, and Lateral). The brain glass schematics are added on top of the image. API docs

nilearn.plotting.plot_stat_map

Plot cuts of an ROI/mask image (by default 3 cuts: Frontal, Axial, and Lateral). API docs

:::

nltools

NLTools is a Python package for analyzing neuroimaging data. It is the analysis engine powering neuro-learn. There are tools to perform data manipulation and analyses such as univariate GLMs, predictive multivariate modeling, and representational similarity analyses.

Data Classes

Adjacency

:::{glossary}

Adjacency

A class to represent Adjacency matrices as a vector rather than a 2-dimensional matrix. This makes it easier to perform data manipulation and analyses. This tool is particularly useful for performing Representational Similarity Analyses. API docs

Adjacency.distance

Calculate distance between images within an Adjacency() instance. API docs

Adjacency.distance_to_similarity

Convert distance matrix to similarity matrix. API docs

Adjacency.plot

Create Heatmap of Adjacency Matrix. API docs

Adjacency.plot_mds

Plot Multidimensional Scaling. API docs

Adjacency.to_graph

Convert Adjacency into networkx graph. Only works on single_matrix for now. API docs

:::

Brain_Data

:::{glossary}

Brain_Data

A class to represent neuroimaging data in python as a vector rather than a 3-dimensional matrix. This makes it easier to perform data manipulation and analyses. This is the main tool for working with neuroimaging data. API docs

Brain_Data.append

Append data to Brain_Data instance. API docs

Brain_Data.apply_mask

Mask Brain_Data instance. API docs

Brain_Data.copy

Create a copy of a Brain_Data instance. API docs

Brain_Data.decompose

Decompose Brain_Data object. API docs

Brain_Data.distance

Calculate distance between images within a Brain_Data() instance. API docs

Brain_Data.extract_roi

Extract activity from mask. API docs

Brain_Data.find_spikes

Function to identify spikes from Time Series Data. API docs

Brain_Data.iplot

Create an interactive brain viewer for the current brain data instance. API docs

Brain_Data.mean

Get mean of each voxel across images. API docs

Brain_Data.plot

Create a quick plot of self.data. Will plot each image separately. API docs

Brain_Data.predict

Run prediction. API docs

Brain_Data.regress

Run a mass-univariate regression across voxels. Three types of regressions can be run: 1) Standard OLS (default) 2) Robust OLS (heteroscedasticity and/or auto-correlation robust errors) 3) ARMA (auto-regressive and moving-average lags = 1 by default; experimental). API docs

Brain_Data.shape

Get images by voxels shape. API docs

Brain_Data.similarity

Calculate similarity of Brain_Data() instance with single Brain_Data or Nibabel image. API docs

Brain_Data.smooth

Apply spatial smoothing using nilearn smooth_img(). API docs

Brain_Data.std

Get standard deviation of each voxel across images. API docs

Brain_Data.threshold

Threshold Brain_Data instance. API docs

Brain_Data.to_nifti

Convert Brain_Data Instance into Nifti Object. API docs

Brain_Data.ttest

Calculate one sample t-test across each voxel (two-sided). API docs

Brain_Data.write

Write out Brain_Data object to Nifti or HDF5 File. API docs

:::

Design_Matrix

:::{glossary}

Design_Matrix

A class to represent design matrices with special methods for data processing (e.g. convolution, upsampling, downsampling) and also intelligent and flexible appending (e.g. automatically keep certain columns or polynomial terms separated during concatenation). It plays nicely with Brain_Data and can be used to build an experimental design to pass to Brain_Data's X attribute. It is essentially an enhanced pandas DataFrame, with extra attributes and methods. API docs

Design_Matrix.add_dct_basis

Adds unit scaled cosine basis functions to Design_Matrix columns, based on spm-style discrete cosine transform for use in high-pass filtering. Does not add intercept/constant. Care is recommended if using this along with .add_poly(), as some columns will be highly correlated. API docs

Design_Matrix.add_poly

Add nth order Legendre polynomial terms as columns to design matrix. Good for adding constant/intercept to model (order = 0) and accounting for slow-frequency nuisance artifacts e.g. linear, quadratic, etc drifts. API docs

Design_Matrix.clean

Method to fill NaNs in Design Matrix and remove duplicate columns based on data values, NOT names. Columns are dropped if they are correlated >= the requested threshold (default = .95). API docs

Design_Matrix.convolve

Perform convolution using an arbitrary function. API docs

Design_Matrix.heatmap

Visualize Design Matrix spm style. Use .plot() for typical pandas plotting functionality. Can pass optional keyword args to seaborn heatmap. API docs

Design_Matrix.head

This function returns the first n rows for the object based on position. It is useful for quickly testing if your object has the right type of data in it. API docs

Design_Matrix.info

Print a concise summary of a DataFrame. API docs

Design_Matrix.vif

Compute variance inflation factor amongst columns of design matrix, ignoring polynomial terms. Much faster than statsmodel and more reliable too. Uses the same method as Matlab and R (diagonal elements of the inverted correlation matrix). API docs

Design_Matrix.zscore

Z-score the design matrix, but ensures that returned object is a design matrix. API docs

:::

Statistics Functions

:::{glossary}

stats.fdr

Determine FDR threshold given a p value array and desired false discovery rate q. API docs

stats.find_spikes

Function to identify spikes from fMRI Time Series Data. API docs

stats.fisher_r_to_z

Use Fisher transformation to convert correlation to z score. API docs

stats.one_sample_permutation

One sample permutation test using randomization. API docs

stats.threshold

Threshold test image by p-value from p image. API docs

stats.regress

This is a flexible function to run several types of regression models provided X and Y numpy arrays. Y can be a 1d numpy array or 2d numpy array. In the latter case, results will be output with shape 1 x Y.shape[1], in other words fitting a separate regression model to each column of Y. API docs

stats.zscore

Z-score every column in a pandas dataframe or series. API docs

:::

Miscellaneous Functions

:::{glossary}

SimulateGrid

A class to simulate signal and noise within 2D grid. API docs

external.hrf.glover_hrf

Implementation of the Glover hemodynamic response function (HRF) model. API docs

datasets.fetch_pain

Download and loads pain dataset from neurovault. API docs

:::