13 releases (8 breaking)

0.9.0 May 19, 2023
0.8.0 Aug 4, 2022
0.7.0 Jun 6, 2022
0.6.2 Oct 16, 2021
0.6.0 Feb 6, 2021

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ndhistogram : multi-dimensional histogramming for Rust

Main Build status Develop status Documentation Codecov Dependency status Crate License Last commit Last release

ndhistogram implements multi-dimensional histograms for Rust.

This library aims to provide a similar feature set to the C++ library boost-histogram but with an idomatic pure-Rust implementation.

Features include:

  • Histograms with any number of dimensions from 1 up to 21 dimensions.
  • Continuous (eg represented by a floating point number) and discrete axis (eg a category represented by a string value or enum) types that are composable (eg you may mix discrete and continuous axes).
  • Flexible bin values including any primitive number type, or a user-defined type.
  • Unweighted and weighted filling of histograms.
  • Flexible, user-definable axis types.
  • Sparse histograms to reduce the memory footprint of high bin count, mostly empty, histograms.

Table of Contents

  1. Usage
  2. Quick-start
  3. Overview
    1. Histogram Implementations
    2. Axis Implementations
    3. Histogram Bin Values
  4. How to Guide
    1. Customize the Bin Value Type
    2. Create and Use a 2D Histogram
    3. Create a Histogram with a Discrete Axis
    4. Create a Histogram with Variable Sized Bins
    5. Create a Histogram with a Periodic or Cyclic Axis
    6. Create a Sparse Histogram
    7. Merge Histograms
    8. Iterate over Histogram Bins in Parallel
  5. Crate Feature Flags


Add this to your Cargo.toml:

ndhistogram = "0.9.0"

See the change log for differences between releases. Please report any bugs in the issues tracker.


use ndhistogram::{Histogram, ndhistogram, axis::Uniform};

// create a 1D histogram with 10 equally sized bins between -5 and 5
let mut hist = ndhistogram!(Uniform::new(10, -5.0, 5.0));
// fill this histogram with a single value
// fill this histogram with weights
hist.fill_with(&2.0, 4.0);
// read the histogram values
let x1 = hist.value(&1.0);
let also_x1 = hist.value_at_index(7);
assert_eq!(x1, also_x1);
// iterate the histogram values
for item in hist.iter() {
    println!("{}, {}, {}", item.index, item.bin, item.value)
// print the histogram to stdout
println!("{}", hist);


A Histogram is composed of two components:

  • The Axes which is a set of Axis corresponding to each dimension of the histogram. The Axes and Axis define the binning of the histogram and are responsible for mapping from coordinate space (eg [x,y,z]) to an integer bin number.
  • The histogram bin value storage. Valid bin value types include any integer and floating number type as well as user defined types that implement Fill, FillWith or FillWithWeighted.

Histogram Implementations

  • VecHistogram: bin values are stored in a Vec. Created with the ndhistogram macro. This is the recommended implementation for most use cases. However, as memory is allocated even for empty bins, this may not be practical for very high dimension histograms.
  • HashHistogram: bin values are stored in a HashMap. Created with the sparsehistogram macro. Useful for high dimension, mostly empty, histograms as empty bins take up no memory.

Alternative implementations are possible by implementing the Histogram trait.

Axis Implementations

User defined axes types are possible by implementing the Axis trait.

Histogram Bin Values

Histograms may be filled with values of the following types:

This crate defines the following bin value types:

  • Sum : a simple bin count that counts the number of times it has been filled.
  • WeightedSum : as Sum but with weighted fills.
  • Mean : computes the mean of the values it is filled with.
  • WeightedMean : as Mean but with weighted fills.

User defined bin value types are possible by implementing the Fill, FillWith or FillWithWeighted traits.

How to Guide

Customize the Bin Value Type

use ndhistogram::{Histogram, ndhistogram, axis::Uniform, value::Mean};
// Create a histogram whose bin values are i32
let mut hist = ndhistogram!(Uniform::new(10, -5.0, 5.0); i32);
hist.fill_with(&1.0, 2);
let value: Option<&i32> = hist.value(&1.0);
assert_eq!(value, Some(&2));

// More complex value types beyond primitives are available
// "Mean" calculates the average of values it is filled with
let mut hist = ndhistogram!(Uniform::new(10, -5.0, 5.0); Mean);
hist.fill_with(&1.0, 1.0);
hist.fill_with(&1.0, 3.0);
assert_eq!(hist.value(&1.0).unwrap().mean(), 2.0);

// for other examples see the documentation of Sum, WeightedSum and WeightedMean

// user defined value types are possible by implementing
// Fill, FillWith or FillWithWeighted traits

Create and Use a 2D Histogram

use ndhistogram::{Histogram, ndhistogram, axis::Uniform};
// create a 2D histogram
let mut hist = ndhistogram!(Uniform::new(10, -5.0, 5.0), Uniform::new(10, -5.0, 5.0));
// fill 2D histogram
hist.fill(&(1.0, 2.0));
// read back the histogram values
let x1_y2 = hist.value(&(1.0, 2.0));
// higher dimensions are possible with additional arguments to ndhistogram

Create a Histogram with a Discrete Axis

use ndhistogram::{Histogram, ndhistogram, axis::Category};
let mut hist = ndhistogram!(Category::new(vec![0, 2, 4]));
hist.fill_with(&2, 42.0);
hist.fill_with(&1, 128.0);
assert_eq!(hist.value(&2), Some(&42.0));
assert_eq!(hist.value(&1), Some(&128.0));
assert_eq!(hist.value(&3), Some(&128.0));
// 1 and 3 give the same answer as they are both mapped to the overflow bin
// For a version with no overflow bins use CategoryNoFlow

// The Category type can be any hashable type, for example string
let mut hist = ndhistogram!(Category::new(vec!["Red", "Blue", "Green"]));
assert_eq!(hist.value(&"Red"), Some(&1.0));

Create a Histogram with Variable Sized Bins

use ndhistogram::{Histogram, ndhistogram, axis::Variable};
let mut hist = ndhistogram!(Variable::new(vec![0.0, 1.0, 3.0, 6.0]));
for x in 0..6 {
assert_eq!(hist.value(&0.0), Some(&1.0));
assert_eq!(hist.value(&1.0), Some(&2.0));
assert_eq!(hist.value(&3.0), Some(&3.0));

Create a Histogram with a Periodic or Cyclic Axis

use std::f64::consts::PI;
use ndhistogram::{Histogram, ndhistogram, axis::UniformCyclic};
let mut hist = ndhistogram!(UniformCyclic::<f64>::new(10, 0.0, 2.0*PI));
// +pi and -pi are mapped onto the same value
assert_eq!(hist.value(&-PI), Some(&2.0));
assert_eq!(hist.value(&PI), Some(&2.0));

Create a Sparse Histogram

use ndhistogram::{Histogram, sparsehistogram, axis::Uniform};
// This histogram has 1e18 bins, too many to allocate with a normal histogram
let mut histogram_with_lots_of_bins = sparsehistogram!(
    Uniform::new(1_000_000, -5.0, 5.0),
    Uniform::new(1_000_000, -5.0, 5.0),
    Uniform::new(1_000_000, -5.0, 5.0)
histogram_with_lots_of_bins.fill(&(1.0, 2.0, 3.0));
// read back the filled value
assert_eq!(histogram_with_lots_of_bins.value(&(1.0, 2.0, 3.0)).unwrap(), &1.0);
// unfilled bins will return None
assert!(histogram_with_lots_of_bins.value(&(0.0, 0.0, 0.0)).is_none());

Merge Histograms

use ndhistogram::{Histogram, ndhistogram, axis::Uniform};
let mut hist1 = ndhistogram!(Uniform::<f64>::new(10, -5.0, 5.0));
let mut hist2 = ndhistogram!(Uniform::<f64>::new(10, -5.0, 5.0));
hist1.fill_with(&0.0, 2.0);
hist2.fill_with(&0.0, 3.0);
let combined_hist = (hist1 + &hist2).expect("Axes are compatible");

Iterate over Histogram Bins in Parallel

use rayon::prelude::*;
use ndhistogram::{Histogram, ndhistogram, axis::Uniform};
let mut histogram = ndhistogram!(Uniform::<f64>::new(10, -5.0, 5.0));
let sum: f64 = histogram.par_iter().map(|bin| bin.value).sum();
// see also: par_iter_mut, par_values, par_values_mut.
assert_eq!(sum, 0.0);

Requires "rayon" feature enabled.

Crate Feature Flags

All cargo features of this crate are off by default. The following features can be enabled in your Cargo.toml:

  • [serde] : enable support for histogram serialization and deserialization.
  • [rayon] : enable parallel iteration over histograms.


Licensed under either of

at your option.


Unless you explicitly state otherwise, any contribution intentionally submitted for inclusion in the work by you, as defined in the Apache-2.0 license, shall be dual licensed as above, without any additional terms or conditions.


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