.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "_auto_examples/performances/plot_benchmarks_samplesloss_3D.py"
.. LINE NUMBERS ARE GIVEN BELOW.
.. only:: html
.. note::
:class: sphx-glr-download-link-note
:ref:`Go to the end <sphx_glr_download__auto_examples_performances_plot_benchmarks_samplesloss_3D.py>`
to download the full example code
.. rst-class:: sphx-glr-example-title
.. _sphx_glr__auto_examples_performances_plot_benchmarks_samplesloss_3D.py:
Benchmark SamplesLoss in 3D
=====================================
Let's compare the performances of our losses and backends
as the number of samples grows from 100 to 1,000,000.
.. GENERATED FROM PYTHON SOURCE LINES 11-13
Setup
---------------------
.. GENERATED FROM PYTHON SOURCE LINES 13-49
.. code-block:: Python
import numpy as np
import time
from matplotlib import pyplot as plt
import importlib
import torch
use_cuda = torch.cuda.is_available()
from geomloss import SamplesLoss
MAXTIME = 10 if use_cuda else 1 # Max number of seconds before we break the loop
REDTIME = (
2 if use_cuda else 0.2
) # Decrease the number of runs if computations take longer than 2s...
D = 3 # Let's do this in 3D
# Number of samples that we'll loop upon
NS = [
100,
200,
500,
1000,
2000,
5000,
10000,
20000,
50000,
100000,
200000,
500000,
1000000,
]
.. GENERATED FROM PYTHON SOURCE LINES 50-52
Synthetic dataset. Feel free to use
a Stanford Bunny, or whatever!
.. GENERATED FROM PYTHON SOURCE LINES 52-80
.. code-block:: Python
def generate_samples(N, device):
"""Create point clouds sampled non-uniformly on a sphere of diameter 1."""
x = torch.randn(N, D, device=device)
x[:, 0] += 1
x = x / (2 * x.norm(dim=1, keepdim=True))
y = torch.randn(N, D, device=device)
y[:, 1] += 2
y = y / (2 * y.norm(dim=1, keepdim=True))
x.requires_grad = True
# Draw random weights:
a = torch.randn(N, device=device)
b = torch.randn(N, device=device)
# And normalize them:
a = a.abs()
b = b.abs()
a = a / a.sum()
b = b / b.sum()
return a, x, b, y
.. GENERATED FROM PYTHON SOURCE LINES 81-82
Benchmarking loops.
.. GENERATED FROM PYTHON SOURCE LINES 82-202
.. code-block:: Python
def benchmark(Loss, dev, N, loops=10):
"""Times a loss computation+gradient on an N-by-N problem."""
# NB: torch does not accept reloading anymore.
# importlib.reload(torch) # In case we had a memory overflow just before...
device = torch.device(dev)
a, x, b, y = generate_samples(N, device)
# We simply benchmark a Loss + gradien wrt. x
code = "L = Loss( a, x, b, y ) ; L.backward()"
Loss.verbose = True
exec(code, locals()) # Warmup run, to compile and load everything
Loss.verbose = False
t_0 = time.perf_counter() # Actual benchmark --------------------
if use_cuda:
torch.cuda.synchronize()
for i in range(loops):
exec(code, locals())
if use_cuda:
torch.cuda.synchronize()
elapsed = time.perf_counter() - t_0 # ---------------------------
print(
"{:3} NxN loss, with N ={:7}: {:3}x{:3.6f}s".format(
loops, N, loops, elapsed / loops
)
)
return elapsed / loops
def bench_config(Loss, dev):
"""Times a loss computation+gradient for an increasing number of samples."""
print("Backend : {}, Device : {} -------------".format(Loss.backend, dev))
times = []
def run_bench():
try:
Nloops = [100, 10, 1]
nloops = Nloops.pop(0)
for n in NS:
elapsed = benchmark(Loss, dev, n, loops=nloops)
times.append(elapsed)
if (nloops * elapsed > MAXTIME) or (
nloops * elapsed > REDTIME and len(Nloops) > 0
):
nloops = Nloops.pop(0)
except IndexError:
print("**\nToo slow !")
try:
run_bench()
except RuntimeError as err:
if str(err)[:4] == "CUDA":
print("**\nMemory overflow !")
else:
# CUDA memory overflows semi-break the internal
# torch state and may cause some strange bugs.
# In this case, best option is simply to re-launch
# the benchmark.
run_bench()
return times + (len(NS) - len(times)) * [np.nan]
def full_bench(loss, *args, **kwargs):
"""Benchmarks the varied backends of a geometric loss function."""
print("Benchmarking : ===============================")
lines = [NS]
backends = ["tensorized", "online", "multiscale"]
for backend in backends:
Loss = SamplesLoss(*args, **kwargs, backend=backend)
lines.append(bench_config(Loss, "cuda" if use_cuda else "cpu"))
benches = np.array(lines).T
# Creates a pyplot figure:
plt.figure()
linestyles = ["o-", "s-", "^-"]
for i, backend in enumerate(backends):
plt.plot(
benches[:, 0],
benches[:, i + 1],
linestyles[i],
linewidth=2,
label='backend="{}"'.format(backend),
)
plt.title('Runtime for SamplesLoss("{}") in dimension {}'.format(Loss.loss, D))
plt.xlabel("Number of samples per measure")
plt.ylabel("Seconds")
plt.yscale("log")
plt.xscale("log")
plt.legend(loc="upper left")
plt.grid(True, which="major", linestyle="-")
plt.grid(True, which="minor", linestyle="dotted")
plt.axis([NS[0], NS[-1], 1e-3, MAXTIME])
plt.tight_layout()
# Save as a .csv to put a nice Tikz figure in the papers:
header = "Npoints " + " ".join(backends)
np.savetxt(
"output/benchmark_" + Loss.loss + "_3D.csv",
benches,
fmt="%-9.5f",
header=header,
comments="",
)
.. GENERATED FROM PYTHON SOURCE LINES 203-206
Gaussian MMD, with a small blur
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
.. GENERATED FROM PYTHON SOURCE LINES 206-210
.. code-block:: Python
full_bench(SamplesLoss, "gaussian", blur=0.1, truncate=3)
.. image-sg:: /_auto_examples/performances/images/sphx_glr_plot_benchmarks_samplesloss_3D_001.png
:alt: Runtime for SamplesLoss("gaussian") in dimension 3
:srcset: /_auto_examples/performances/images/sphx_glr_plot_benchmarks_samplesloss_3D_001.png
:class: sphx-glr-single-img
.. rst-class:: sphx-glr-script-out
.. code-block:: none
Benchmarking : ===============================
Backend : tensorized, Device : cuda -------------
100 NxN loss, with N = 100: 100x0.005299s
100 NxN loss, with N = 200: 100x0.005526s
100 NxN loss, with N = 500: 100x0.005521s
100 NxN loss, with N = 1000: 100x0.005516s
100 NxN loss, with N = 2000: 100x0.005554s
100 NxN loss, with N = 5000: 100x0.008550s
100 NxN loss, with N = 10000: 100x0.033574s
10 NxN loss, with N = 20000: 10x0.145354s
**
Memory overflow !
Backend : online, Device : cuda -------------
100 NxN loss, with N = 100: 100x0.009200s
100 NxN loss, with N = 200: 100x0.009534s
100 NxN loss, with N = 500: 100x0.009619s
100 NxN loss, with N = 1000: 100x0.009683s
100 NxN loss, with N = 2000: 100x0.009820s
100 NxN loss, with N = 5000: 100x0.010222s
100 NxN loss, with N = 10000: 100x0.010767s
100 NxN loss, with N = 20000: 100x0.012666s
100 NxN loss, with N = 50000: 100x0.025210s
10 NxN loss, with N = 100000: 10x0.061954s
10 NxN loss, with N = 200000: 10x0.221864s
1 NxN loss, with N = 500000: 1x1.335791s
1 NxN loss, with N =1000000: 1x5.302837s
Backend : multiscale, Device : cuda -------------
82x69 clusters, computed at scale = 0.782
100 NxN loss, with N = 100: 100x0.017255s
145x113 clusters, computed at scale = 0.781
100 NxN loss, with N = 200: 100x0.017660s
266x173 clusters, computed at scale = 0.786
100 NxN loss, with N = 500: 100x0.017636s
378x224 clusters, computed at scale = 0.791
100 NxN loss, with N = 1000: 100x0.017902s
486x306 clusters, computed at scale = 0.792
100 NxN loss, with N = 2000: 100x0.018219s
591x408 clusters, computed at scale = 0.793
100 NxN loss, with N = 5000: 100x0.019684s
640x465 clusters, computed at scale = 0.793
100 NxN loss, with N = 10000: 100x0.020147s
657x535 clusters, computed at scale = 0.794
10 NxN loss, with N = 20000: 10x0.022367s
692x618 clusters, computed at scale = 0.794
10 NxN loss, with N = 50000: 10x0.034833s
702x651 clusters, computed at scale = 0.794
10 NxN loss, with N = 100000: 10x0.048888s
712x674 clusters, computed at scale = 0.794
10 NxN loss, with N = 200000: 10x0.135483s
720x694 clusters, computed at scale = 0.794
10 NxN loss, with N = 500000: 10x0.713417s
725x707 clusters, computed at scale = 0.794
1 NxN loss, with N =1000000: 1x2.705595s
.. GENERATED FROM PYTHON SOURCE LINES 211-214
Energy Distance MMD
~~~~~~~~~~~~~~~~~~~~~~
.. GENERATED FROM PYTHON SOURCE LINES 214-218
.. code-block:: Python
full_bench(SamplesLoss, "energy")
.. image-sg:: /_auto_examples/performances/images/sphx_glr_plot_benchmarks_samplesloss_3D_002.png
:alt: Runtime for SamplesLoss("energy") in dimension 3
:srcset: /_auto_examples/performances/images/sphx_glr_plot_benchmarks_samplesloss_3D_002.png
:class: sphx-glr-single-img
.. rst-class:: sphx-glr-script-out
.. code-block:: none
Benchmarking : ===============================
Backend : tensorized, Device : cuda -------------
100 NxN loss, with N = 100: 100x0.005103s
100 NxN loss, with N = 200: 100x0.005535s
100 NxN loss, with N = 500: 100x0.005526s
100 NxN loss, with N = 1000: 100x0.005533s
100 NxN loss, with N = 2000: 100x0.005587s
100 NxN loss, with N = 5000: 100x0.009383s
100 NxN loss, with N = 10000: 100x0.036845s
10 NxN loss, with N = 20000: 10x0.159529s
**
Memory overflow !
Backend : online, Device : cuda -------------
100 NxN loss, with N = 100: 100x0.008582s
100 NxN loss, with N = 200: 100x0.008939s
100 NxN loss, with N = 500: 100x0.009056s
100 NxN loss, with N = 1000: 100x0.009137s
100 NxN loss, with N = 2000: 100x0.009277s
100 NxN loss, with N = 5000: 100x0.009685s
100 NxN loss, with N = 10000: 100x0.010421s
100 NxN loss, with N = 20000: 100x0.012155s
100 NxN loss, with N = 50000: 100x0.023538s
10 NxN loss, with N = 100000: 10x0.057045s
10 NxN loss, with N = 200000: 10x0.205460s
1 NxN loss, with N = 500000: 1x1.239322s
1 NxN loss, with N =1000000: 1x4.925361s
Backend : multiscale, Device : cuda -------------
100 NxN loss, with N = 100: 100x0.008248s
100 NxN loss, with N = 200: 100x0.008605s
100 NxN loss, with N = 500: 100x0.008733s
100 NxN loss, with N = 1000: 100x0.008973s
100 NxN loss, with N = 2000: 100x0.009160s
100 NxN loss, with N = 5000: 100x0.009586s
100 NxN loss, with N = 10000: 100x0.010308s
100 NxN loss, with N = 20000: 100x0.012044s
100 NxN loss, with N = 50000: 100x0.023436s
10 NxN loss, with N = 100000: 10x0.056971s
10 NxN loss, with N = 200000: 10x0.205727s
1 NxN loss, with N = 500000: 1x1.238967s
1 NxN loss, with N =1000000: 1x4.933789s
.. GENERATED FROM PYTHON SOURCE LINES 219-224
Sinkhorn divergence
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
With a medium blurring scale, at one twentieth of the
configuration's diameter:
.. GENERATED FROM PYTHON SOURCE LINES 224-228
.. code-block:: Python
full_bench(SamplesLoss, "sinkhorn", p=2, blur=0.05, diameter=1)
.. image-sg:: /_auto_examples/performances/images/sphx_glr_plot_benchmarks_samplesloss_3D_003.png
:alt: Runtime for SamplesLoss("sinkhorn") in dimension 3
:srcset: /_auto_examples/performances/images/sphx_glr_plot_benchmarks_samplesloss_3D_003.png
:class: sphx-glr-single-img
.. rst-class:: sphx-glr-script-out
.. code-block:: none
Benchmarking : ===============================
Backend : tensorized, Device : cuda -------------
100 NxN loss, with N = 100: 100x0.007079s
100 NxN loss, with N = 200: 100x0.006703s
100 NxN loss, with N = 500: 100x0.006941s
100 NxN loss, with N = 1000: 100x0.006722s
100 NxN loss, with N = 2000: 100x0.009562s
100 NxN loss, with N = 5000: 100x0.052947s
10 NxN loss, with N = 10000: 10x0.223527s
1 NxN loss, with N = 20000: 1x1.611537s
**
Memory overflow !
Backend : online, Device : cuda -------------
100 NxN loss, with N = 100: 100x0.012902s
100 NxN loss, with N = 200: 100x0.013262s
100 NxN loss, with N = 500: 100x0.013530s
100 NxN loss, with N = 1000: 100x0.014121s
100 NxN loss, with N = 2000: 100x0.015427s
100 NxN loss, with N = 5000: 100x0.019439s
100 NxN loss, with N = 10000: 100x0.024867s
10 NxN loss, with N = 20000: 10x0.045086s
10 NxN loss, with N = 50000: 10x0.178711s
10 NxN loss, with N = 100000: 10x0.593134s
1 NxN loss, with N = 200000: 1x2.175571s
1 NxN loss, with N = 500000: 1x13.285897s
**
Too slow !
Backend : multiscale, Device : cuda -------------
91x92 clusters, computed at scale = 0.046
Successive scales : 1.000, 1.000, 0.500, 0.250, 0.125, 0.063, 0.050
Extrapolate from coarse to fine after the last iteration.
100 NxN loss, with N = 100: 100x0.014569s
181x159 clusters, computed at scale = 0.046
Successive scales : 1.000, 1.000, 0.500, 0.250, 0.125, 0.063, 0.050
Extrapolate from coarse to fine after the last iteration.
100 NxN loss, with N = 200: 100x0.014862s
384x301 clusters, computed at scale = 0.046
Successive scales : 1.000, 1.000, 0.500, 0.250, 0.125, 0.063, 0.050
Extrapolate from coarse to fine after the last iteration.
100 NxN loss, with N = 500: 100x0.015084s
633x424 clusters, computed at scale = 0.046
Successive scales : 1.000, 1.000, 0.500, 0.250, 0.125, 0.063, 0.050
Extrapolate from coarse to fine after the last iteration.
100 NxN loss, with N = 1000: 100x0.015415s
919x595 clusters, computed at scale = 0.046
Successive scales : 1.000, 1.000, 0.500, 0.250, 0.125, 0.063, 0.050
Extrapolate from coarse to fine after the last iteration.
100 NxN loss, with N = 2000: 100x0.016064s
1327x847 clusters, computed at scale = 0.046
Successive scales : 1.000, 1.000, 0.500, 0.250, 0.125, 0.063, 0.050
Extrapolate from coarse to fine after the last iteration.
100 NxN loss, with N = 5000: 100x0.016333s
1632x1031 clusters, computed at scale = 0.046
Successive scales : 1.000, 1.000, 0.500, 0.250, 0.125, 0.063, 0.050
Extrapolate from coarse to fine after the last iteration.
100 NxN loss, with N = 10000: 100x0.016842s
1832x1247 clusters, computed at scale = 0.046
Successive scales : 1.000, 1.000, 0.500, 0.250, 0.125, 0.063, 0.050
Extrapolate from coarse to fine after the last iteration.
100 NxN loss, with N = 20000: 100x0.017265s
2003x1563 clusters, computed at scale = 0.046
Successive scales : 1.000, 1.000, 0.500, 0.250, 0.125, 0.063, 0.050
Extrapolate from coarse to fine after the last iteration.
100 NxN loss, with N = 50000: 100x0.018045s
2073x1765 clusters, computed at scale = 0.046
Successive scales : 1.000, 1.000, 0.500, 0.250, 0.125, 0.063, 0.050
Extrapolate from coarse to fine after the last iteration.
100 NxN loss, with N = 100000: 100x0.019364s
2124x1910 clusters, computed at scale = 0.046
Successive scales : 1.000, 1.000, 0.500, 0.250, 0.125, 0.063, 0.050
Extrapolate from coarse to fine after the last iteration.
100 NxN loss, with N = 200000: 100x0.020637s
2172x2053 clusters, computed at scale = 0.046
Successive scales : 1.000, 1.000, 0.500, 0.250, 0.125, 0.063, 0.050
Extrapolate from coarse to fine after the last iteration.
10 NxN loss, with N = 500000: 10x0.026567s
2185x2113 clusters, computed at scale = 0.046
Successive scales : 1.000, 1.000, 0.500, 0.250, 0.125, 0.063, 0.050
Extrapolate from coarse to fine after the last iteration.
10 NxN loss, with N =1000000: 10x0.035292s
.. GENERATED FROM PYTHON SOURCE LINES 229-231
With a small blurring scale, at one hundredth of the
configuration's diameter:
.. GENERATED FROM PYTHON SOURCE LINES 231-235
.. code-block:: Python
full_bench(SamplesLoss, "sinkhorn", p=2, blur=0.01, diameter=1)
plt.show()
.. image-sg:: /_auto_examples/performances/images/sphx_glr_plot_benchmarks_samplesloss_3D_004.png
:alt: Runtime for SamplesLoss("sinkhorn") in dimension 3
:srcset: /_auto_examples/performances/images/sphx_glr_plot_benchmarks_samplesloss_3D_004.png
:class: sphx-glr-single-img
.. rst-class:: sphx-glr-script-out
.. code-block:: none
Benchmarking : ===============================
Backend : tensorized, Device : cuda -------------
100 NxN loss, with N = 100: 100x0.007561s
100 NxN loss, with N = 200: 100x0.007817s
100 NxN loss, with N = 500: 100x0.007656s
100 NxN loss, with N = 1000: 100x0.007682s
100 NxN loss, with N = 2000: 100x0.011329s
100 NxN loss, with N = 5000: 100x0.062733s
10 NxN loss, with N = 10000: 10x0.264870s
1 NxN loss, with N = 20000: 1x1.909170s
**
Memory overflow !
Backend : online, Device : cuda -------------
100 NxN loss, with N = 100: 100x0.015015s
100 NxN loss, with N = 200: 100x0.015341s
100 NxN loss, with N = 500: 100x0.015877s
100 NxN loss, with N = 1000: 100x0.016754s
100 NxN loss, with N = 2000: 100x0.018445s
100 NxN loss, with N = 5000: 100x0.023053s
10 NxN loss, with N = 10000: 10x0.029969s
10 NxN loss, with N = 20000: 10x0.054050s
10 NxN loss, with N = 50000: 10x0.214230s
1 NxN loss, with N = 100000: 1x0.711520s
1 NxN loss, with N = 200000: 1x2.624156s
1 NxN loss, with N = 500000: 1x16.047510s
**
Too slow !
Backend : multiscale, Device : cuda -------------
96x81 clusters, computed at scale = 0.046
Successive scales : 1.000, 1.000, 0.500, 0.250, 0.125, 0.063, 0.031, 0.016, 0.010
Jump from coarse to fine between indices 5 (σ=0.063) and 6 (σ=0.031).
Keep 1273/7776 = 16.4% of the coarse cost matrix.
Keep 1208/9216 = 13.1% of the coarse cost matrix.
Keep 1793/6561 = 27.3% of the coarse cost matrix.
100 NxN loss, with N = 100: 100x0.020246s
178x159 clusters, computed at scale = 0.046
Successive scales : 1.000, 1.000, 0.500, 0.250, 0.125, 0.063, 0.031, 0.016, 0.010
Jump from coarse to fine between indices 5 (σ=0.063) and 6 (σ=0.031).
Keep 3885/28302 = 13.7% of the coarse cost matrix.
Keep 3754/31684 = 11.8% of the coarse cost matrix.
Keep 5067/25281 = 20.0% of the coarse cost matrix.
10 NxN loss, with N = 200: 10x0.020553s
379x295 clusters, computed at scale = 0.046
Successive scales : 1.000, 1.000, 0.500, 0.250, 0.125, 0.063, 0.031, 0.016, 0.010
Jump from coarse to fine between indices 5 (σ=0.063) and 6 (σ=0.031).
Keep 14892/111805 = 13.3% of the coarse cost matrix.
Keep 15537/143641 = 10.8% of the coarse cost matrix.
Keep 16697/87025 = 19.2% of the coarse cost matrix.
10 NxN loss, with N = 500: 10x0.021149s
630x435 clusters, computed at scale = 0.046
Successive scales : 1.000, 1.000, 0.500, 0.250, 0.125, 0.063, 0.031, 0.016, 0.010
Jump from coarse to fine between indices 5 (σ=0.063) and 6 (σ=0.031).
Keep 34578/274050 = 12.6% of the coarse cost matrix.
Keep 40168/396900 = 10.1% of the coarse cost matrix.
Keep 32093/189225 = 17.0% of the coarse cost matrix.
10 NxN loss, with N = 1000: 10x0.021868s
934x603 clusters, computed at scale = 0.046
Successive scales : 1.000, 1.000, 0.500, 0.250, 0.125, 0.063, 0.031, 0.016, 0.010
Jump from coarse to fine between indices 5 (σ=0.063) and 6 (σ=0.031).
Keep 63295/563202 = 11.2% of the coarse cost matrix.
Keep 79926/872356 = 9.2% of the coarse cost matrix.
Keep 53179/363609 = 14.6% of the coarse cost matrix.
10 NxN loss, with N = 2000: 10x0.023026s
1359x843 clusters, computed at scale = 0.046
Successive scales : 1.000, 1.000, 0.500, 0.250, 0.125, 0.063, 0.031, 0.016, 0.010
Jump from coarse to fine between indices 5 (σ=0.063) and 6 (σ=0.031).
Keep 115167/1145637 = 10.1% of the coarse cost matrix.
Keep 153739/1846881 = 8.3% of the coarse cost matrix.
Keep 85789/710649 = 12.1% of the coarse cost matrix.
10 NxN loss, with N = 5000: 10x0.025470s
1609x1044 clusters, computed at scale = 0.046
Successive scales : 1.000, 1.000, 0.500, 0.250, 0.125, 0.063, 0.031, 0.016, 0.010
Jump from coarse to fine between indices 5 (σ=0.063) and 6 (σ=0.031).
Keep 162316/1679796 = 9.7% of the coarse cost matrix.
Keep 210177/2588881 = 8.1% of the coarse cost matrix.
Keep 118852/1089936 = 10.9% of the coarse cost matrix.
10 NxN loss, with N = 10000: 10x0.028603s
1858x1255 clusters, computed at scale = 0.046
Successive scales : 1.000, 1.000, 0.500, 0.250, 0.125, 0.063, 0.031, 0.016, 0.010
Jump from coarse to fine between indices 5 (σ=0.063) and 6 (σ=0.031).
Keep 216719/2331790 = 9.3% of the coarse cost matrix.
Keep 275990/3452164 = 8.0% of the coarse cost matrix.
Keep 157385/1575025 = 10.0% of the coarse cost matrix.
10 NxN loss, with N = 20000: 10x0.034766s
2004x1562 clusters, computed at scale = 0.046
Successive scales : 1.000, 1.000, 0.500, 0.250, 0.125, 0.063, 0.031, 0.016, 0.010
Jump from coarse to fine between indices 5 (σ=0.063) and 6 (σ=0.031).
Keep 279293/3130248 = 8.9% of the coarse cost matrix.
Keep 321418/4016016 = 8.0% of the coarse cost matrix.
Keep 224342/2439844 = 9.2% of the coarse cost matrix.
10 NxN loss, with N = 50000: 10x0.057913s
2065x1742 clusters, computed at scale = 0.046
Successive scales : 1.000, 1.000, 0.500, 0.250, 0.125, 0.063, 0.031, 0.016, 0.010
Jump from coarse to fine between indices 5 (σ=0.063) and 6 (σ=0.031).
Keep 310590/3597230 = 8.6% of the coarse cost matrix.
Keep 341841/4264225 = 8.0% of the coarse cost matrix.
Keep 269452/3034564 = 8.9% of the coarse cost matrix.
10 NxN loss, with N = 100000: 10x0.110885s
2128x1927 clusters, computed at scale = 0.046
Successive scales : 1.000, 1.000, 0.500, 0.250, 0.125, 0.063, 0.031, 0.016, 0.010
Jump from coarse to fine between indices 5 (σ=0.063) and 6 (σ=0.031).
Keep 345694/4100656 = 8.4% of the coarse cost matrix.
Keep 363590/4528384 = 8.0% of the coarse cost matrix.
Keep 326729/3713329 = 8.8% of the coarse cost matrix.
10 NxN loss, with N = 200000: 10x0.267706s
2166x2060 clusters, computed at scale = 0.046
Successive scales : 1.000, 1.000, 0.500, 0.250, 0.125, 0.063, 0.031, 0.016, 0.010
Jump from coarse to fine between indices 5 (σ=0.063) and 6 (σ=0.031).
Keep 370323/4461960 = 8.3% of the coarse cost matrix.
Keep 377652/4691556 = 8.0% of the coarse cost matrix.
Keep 375630/4243600 = 8.9% of the coarse cost matrix.
1 NxN loss, with N = 500000: 1x1.228583s
2183x2115 clusters, computed at scale = 0.046
Successive scales : 1.000, 1.000, 0.500, 0.250, 0.125, 0.063, 0.031, 0.016, 0.010
Jump from coarse to fine between indices 5 (σ=0.063) and 6 (σ=0.031).
Keep 380326/4617045 = 8.2% of the coarse cost matrix.
Keep 383841/4765489 = 8.1% of the coarse cost matrix.
Keep 397855/4473225 = 8.9% of the coarse cost matrix.
1 NxN loss, with N =1000000: 1x4.436718s
.. rst-class:: sphx-glr-timing
**Total running time of the script:** (4 minutes 56.952 seconds)
.. _sphx_glr_download__auto_examples_performances_plot_benchmarks_samplesloss_3D.py:
.. only:: html
.. container:: sphx-glr-footer sphx-glr-footer-example
.. container:: sphx-glr-download sphx-glr-download-jupyter
:download:`Download Jupyter notebook: plot_benchmarks_samplesloss_3D.ipynb <plot_benchmarks_samplesloss_3D.ipynb>`
.. container:: sphx-glr-download sphx-glr-download-python
:download:`Download Python source code: plot_benchmarks_samplesloss_3D.py <plot_benchmarks_samplesloss_3D.py>`
.. only:: html
.. rst-class:: sphx-glr-signature
`Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_