gif in the README

[basnijholt]

[basnijholt]

Fixed by 9126a70.

[basnijholt]

When holoviz/holoviews#1977 and holoviz/holoviews#2260 are fixed we can add a script that will reproduce these images. ATM I used LICEcap + Photoshop to edit them.

This is the code:

%%output fps=5
offset = random.uniform(-0.3, 0.3)

def f(x, offset=offset):
    a = 0.01
    return x + a**2 / (a**2 + (x - offset)**2)

learner = adaptive.Learner1D(f, bounds=(-1, 1))

def plot(learner):
    learner2 = adaptive.Learner1D(f, bounds=learner.bounds)
    xs = np.linspace(*learner.bounds, len(learner.data))
    learner2.add_data(xs, map(f, xs))
    return (hv.Scatter(learner.data)[-1:1, -1:1].relabel('adaptive') 
            + hv.Scatter(learner2.data).relabel('homogeneous grid')).cols(1)

plots = []
for i in range(100):
    xs, _ = learner.choose_points(1)
    learner.add_data(xs, map(learner.function, xs))
    plots.append((i+1, plot(learner)))

hv.HoloMap(plots, kdims=['N points']).collate()

def ring(xy):
    import numpy as np
    x, y = xy
    a = 0.2
    return x + np.exp(-(x**2 + y**2 - 0.75**2)**2/a**4)

learner = adaptive.Learner2D(ring, bounds=[(-1, 1), (-1, 1)])

import itertools
def plot(learner):
    learner2 = adaptive.Learner2D(ring, bounds=learner.bounds)
    xs = np.linspace(*learner.bounds[0], learner.n**0.5)
    ys = np.linspace(*learner.bounds[1], learner.n**0.5)
    xys = list(itertools.product(xs, ys))
    learner2.add_data(xys, map(ring, xys))
    return (learner2.plot().relabel('Homogeneous grid') 
            + learner.plot().relabel('With adaptive')
            + learner2.plot(tri_alpha=0.5).relabel('Homogeneous grid')
            + learner.plot(tri_alpha=0.5).relabel('With adaptive')).cols(2)


plots = []
for i in range(100):
    N = 10
    xs, _ = learner.choose_points(N)
    learner.add_data(xs, map(learner.function, xs))
    plots.append((learner.n, plot(learner))

[basnijholt]

I am going to put this cooler gif in the README.md:

import adaptive
from functools import partial
import holoviews as hv  # Plotting
import numpy as np
adaptive.notebook_extension()

def f(x, offset=0.07357338543088588):
    a = 0.01
    return x + a**2 / (a**2 + (x - offset)**2)

def plot_loss_interval(learner):
    if learner.npoints >= 2:
        x_0, x_1 = max(learner.losses, key=learner.losses.get)
        y_0, y_1 = learner.data[x_0], learner.data[x_1]
        plot = hv.Scatter(([x_0, x_1], [y_0, y_1]))
    else:
        plot = hv.Scatter([])
    return plot.opts(style=dict(size=6, color='r'))

learner = adaptive.Learner1D(f, bounds=(-1, 1))
plots = {0: learner.plot()}
for n in range(1, 101):
    xs, _ = learner.choose_points(1)
    learner.add_data(xs, map(learner.function, xs))
    plots[n] = (learner.plot() * plot_loss_interval(learner))[:, -1.1:1.1]
hm_plots = hv.HoloMap(plots, kdims=['npoints']).relabel('adaptive')
    
    
hom_learner = adaptive.Learner1D(f, bounds=(-1, 1), loss_per_interval=adaptive.learner.learner1D.uniform_loss)
hom_plots = {0: hom_learner.plot()}
for n in range(1, 101):
    xs, _ = hom_learner.choose_points(1)
    hom_learner.add_data(xs, map(hom_learner.function, xs))
    hom_plots[n] = (hom_learner.plot() * plot_loss_interval(hom_learner))[:, -1.1:1.1]
hm_hom_plots = hv.HoloMap(hom_plots, kdims=['npoints']).relabel('homogeneous')

(hm_hom_plots + hm_plots).cols(1)

Because of holoviews problems I recorded the gif myself and manually removed the bokeh toolbar.

[basnijholt]

I've added these examples in the docs in b1ebe92.

[basnijholt]

This is another one:

def sphere(xyz):
    import numpy as np
    x, y, z = xyz
    a = 0.4
    return np.exp(-(x**2 + y**2 + z**2 - 0.75**2)**2/a**4)

learner = adaptive.LearnerND(sphere, bounds=[(-1, 1), (-1, 1), (-1, 1)])
adaptive.runner.simple(learner, lambda l: l.npoints == 3000)

temp_learner = adaptive.LearnerND(sphere, bounds=[(-1, 1), (-1, 1), (-1, 1)])
for p, v in learner.data.items():
    x, y, z = p
    if not (x > 0 and y > 0):
        temp_learner.tell(p, v)
temp_learner.plot_3D()