Simple example of how to work with h2tools

Let assume, we need to approximate functional matrix $A_{ij} = f(x_i, y_j)$ for some given sets of objects $X=\{x_1, \ldots, x_N\}$ and $Y=\{y_1, \ldots, y_M\}$. Obviously, $X$ corresponds to rows and $Y$ corresponds to columns. Let additionally denote $X$ and $Y$ as a destination and source sets accordingly. For simplicity, we assume interaction function $f$ returns only scalar values. Then, following steps are required to build approximation with MCBH method:

1. Prepare cluster trees $\mathcal{T}_{I}$ and $\mathcal{T}_{J}$ for destination and source sets correspondingly,
2. Prepare block cluster tree by finding admissibly far and close nodes for $\mathcal{T}_{I}$ and $\mathcal{T}_{J}$,
3. Build approximation with given parameters.

To make each step clearer, we show it in following example:

# At first, we generate 10000 particles's positions randomly with given
# random seed
import numpy as np
np.random.seed(0)
position = np.random.randn(3, 10000)
# We use predefined `particles` submodule of `h2tools.collections`
# This submodule contains data class, cluster division code and
# interaction function
from h2tools.collections import particles
# Create particles data object
data = particles.ParticlesData(position)
# Initialize cluster tree with data object
from h2tools import ClusterTree
tree = ClusterTree(data, block_size=25)
# Use function inv_distance, which returns inverse of distance
# between particles
func = particles.inv_distance
# Create object for whole problem (block cluster tree + function)
from h2tools import Problem
problem = Problem(func, tree, tree, symmetric=1, verbose=0)
# Build approximation of matrix in H^2 format
# with relative accuracy parameter 1e-4,
# 0 (zero) iterations of MCBH algorithm
# and with True verbose flag
from h2tools.mcbh import mcbh
matrix = mcbh(problem, tau=1e-4, iters=0, verbose=1)
# If you have package `pypropack` installed,
# you can measure relative error of approximation
# in spectral norm
matrix.diffnorm()