Scientific Visualization

ScientiﬁcVisualization
May 22, 2014

!
PGI-1 / IAS-1 | ScientiﬁcVisualization Workshop | Josef Heinen
MemberoftheHelmholtzAssociation

May 22, 2014 Josef Heinen, Forschungszentrum Jülich, Peter Grünberg Institute, Scientiﬁc IT Systems
✓ Motivation

✓ Scientiﬁc visualization software

✓ Visualization with Python

✓ Python performance optimizations

✓ Development tools

✓ Conclusion

✓ Future plans

✓ Discussion
2
Outline

We need easy-to-use methods for:

✓ visualizing and analyzing two- and three-
dimensional data sets, perhaps with a dynamic
component

✓ creating publication-quality graphics

✓ making glossy ﬁgures for high impact journals or
press releases
3
Motivation

✓ line / bar graphs, curve plots

✓ scatter plots

✓ surface plots, mesh rendering with iso-surface
generation

✓ contour plots

✓ vector / streamline plots

✓ volume graphics

✓ molecule plots
4
Scientiﬁc plotting methods

Scientiﬁc visualization tools
✓ Gnuplot

✓ Xmgrace

✓ OpenDX

✓ ParaView

✓ Mayavi2

✓ MATLAB

✓ Mathematica

✓ Octave, Scilab, Freemat
5

… drawbacks
✓ Gnuplot — limited functionality

✓ Xmgrace — too old, requires OSF/Motif (X11)

✓ OpenDX — no longer maintained (2007)

✓ ParaView — not very intuitive

✓ Mayavi2 — not very responsive

✓ MATLAB — 5 ﬂoating, 3 user licenses (16K €/year)

✓ Mathematica — expensive (~2.500 €/user)

✓ Octave, Scilab, Freemat — no syntax compatibility
6

Scientiﬁc visualization APIs
✓ Matplotlib

✓ mlab,VTK

✓ OpenGL

✓ pgplot

✓ PyQtGraph

✓ PyQwt / PyQwt3D
7

Scientiﬁc visualization APIs
✓ Matplotlib — de-facto standard (“workhorse”)

✓ mlab,VTK — versatile, but difﬁcult to learn; slow

✓ OpenGL — large and complex

✓ pgplot — too old

✓ PyQtGraph — no yet mature

✓ PyQwt / PyQwt3D — currently unmaintained
8

Remaining solutions
GUI + API:
✓ ParaView

✓ Mayavi2

API:
✓ matplotlib

✓ n.n.

←

Let’s talk about this later …
9
both based onVTK
}

May 22, 2014 Josef Heinen, Forschungszentrum Jülich, Peter Grünberg Institute, Scientiﬁc IT Systems 10
ParaView

Mayavi2

matplotlib

Problems so far
✓ separated 2D and (hardware accelerated) 3D
world

✓ some graphics backends "only" produce pictures  
➟ no presentation of continuous data streams

✓ bare minimum level of interoperability  
➟ limited user interaction

✓ poor performance on large data sets

✓ APIs are partly device- and platform-dependent
13

Isn’t there an all-in-one solution?
14
All these components provide powerful APIs 
for Python !

!
There must be a reason for that …

… so let’s push for Python
✓ free and open

✓ dynamic typed language, easy to understand

✓ powerful modules for science, technology, engineering
and mathematics (STEM): NumPy, SciPy, Pandas, SymPy

✓ great visualization libraries: Matplotlib, MayaVi,VTK,
PyOpenGL

✓ techniques to boost execution speed: PyPy, Cython,
PyOpenCL, PyCUDA, Numba

✓ wrapper for GUI toolkits: PyQt4, PyGTK, wxWidgets
15

… get it up and running
16
IPython + NumPy + SciPy + Matplotlib 
What else do we need?

… achieve more Python performance
Numba: compiles annotated Python and NumPy code
to LLVM (through decorators)

✓ just-in-time compilation

✓ vectorization

✓ parallelization

NumbaPro: adds support for multicore and GPU
architectures
17
(* Numba (Pro) is part of Anaconda (Accelerate), a (commercial) Python distribution from Continuum Analytics

… achieve more graphics performance and interop
GR framework: a universal framework for cross-
platform visualization (*

✓ procedural graphics backend 
➟ presentation of continuous data streams

✓ coexistent 2D and 3D world

✓ interoperability with GUI toolkits 
➟ good user interaction
18
(* The GR framework is an in-house project initiated by the group Scientiﬁc IT Systems

“Our” Scientiﬁc Python distribution
19
IPython + NumPy + SciPy + Numba + GR framework +
PyOpenGL + PyOpenCL + PyCUDA + PyQt4/PyGTK/wxWidgets 
 
➟ more performance and interoperability

How can we use it?
✓ GR framework (and other mentioned packages)
available on all Linux and OS X machines 
(Python and IPython) at PGI / JCNS: 
% gr 
% igr"
✓ GR framework can also be used with Anaconda: 
% anaconda

✓ Windows version(s) on request
20

Batteries included
✓ NumPy — package for numerical computation

✓ SciPy — collection of numerical algorithms and speciﬁc toolboxes

✓ Matplotlib — popular plotting package

✓ Pandas — provides high-performance, easy to use data structures

✓ SymPy — symbolic mathematics and computer algebra

✓ IPython — rich interactive interface (including IPython notebook)

✓ Mayavi2 — 3D visualization framework, based onVTK

✓ scikit-image — algorithms for image processing

✓ h5py, PyTables — managing hierarchical datasets (HDF5)
21

Visualization with Python
22
GKS logical device drivers
C / C++
GKS
GR
OpenGL (WGL / CGL / GLX)
POV-Ray 
generation
off-screen
rendering
direct
rendering
Browser
JavaScript 
generation
WebGL
IPython / PyPy/ Anaconda
Win32X11
GKSTermgksqt
Java
gksweb
Qt Quartz PDF
C / ObjC
OpenGL ES
glgr / iGR App socket 
communication
Qt / wx 
event loop
0MQ OpenGL
More logical device drivers / plugins:

– CGM, GKSM, GIF, RF, UIL

– WMF, Xﬁg

– GS (BMP, JPEG, PNG,TIFF)
...
HTML5
wx
POV-Ray
GLUT

wxGLCanvas

QGLWidget
...
SVGPS
MOV
GR3
Highlights:

– simultaneous output to multiple output devices

– direct generation of MPEG4 image sequences

– ﬂicker-free display ("double buffering")

Presentation of continuous data streams in 2D ...
23
from numpy import sin, cos, sqrt, pi, array
import gr
!
def rk4(x, h, y, f):
k1 = h * f(x, y)
k2 = h * f(x + 0.5 * h, y + 0.5 * k1)
k3 = h * f(x + 0.5 * h, y + 0.5 * k2)
k4 = h * f(x + h, y + k3)
return x + h, y + (k1 + 2 * (k2 + k3) + k4) / 6.0
!
def damped_pendulum_deriv(t, state):
theta, omega = state
return array([omega, -gamma * omega - 9.81 / L * sin(theta)])
!
def pendulum(t, theta, omega)
gr.clearws()
... # draw pendulum (pivot point, rod, bob, ...)
gr.updatews()
!
theta = 70.0 # initial angle
gamma = 0.1 # damping coefficient
L = 1 # pendulum length
t = 0
dt = 0.04
state = array([theta * pi / 180, 0])
!
while t < 30:
t, state = rk4(t, dt, state, damped_pendulum_deriv)
theta, omega = state
pendulum(t, theta, omega)

... with full 3D functionality
24
from numpy import sin, cos, array
import gr, gr3
!
def rk4(x, h, y, f):
k1 = h * f(x, y)
k2 = h * f(x + 0.5 * h, y + 0.5 * k1)
k3 = h * f(x + 0.5 * h, y + 0.5 * k2)
k4 = h * f(x + h, y + k3)
return x + h, y + (k1 + 2 * (k2 + k3) + k4) / 6.0
!
def pendulum_derivs(t, state):
t1, w1, t2, w2 = state
a = (m1 + m2) * l1
b = m2 * l2 * cos(t1 - t2)
c = m2 * l1 * cos(t1 - t2)
d = m2 * l2
e = -m2 * l2 * w2**2 * sin(t1 - t2) - 9.81 * (m1 + m2) * sin(t1)
f = m2 * l1 * w1**2 * sin(t1 - t2) - m2 * 9.81 * sin(t2)
return array([w1, (e*d-b*f) / (a*d-c*b), w2, (a*f-c*e) / (a*d-c*b)])
!
def double_pendulum(theta, length, mass):
gr.clearws()
gr3.clear()
!
... # draw pivot point, rods, bobs (using 3D meshes)
!
gr3.drawimage(0, 1, 0, 1, 500, 500, gr3.GR3_Drawable.GR3_DRAWABLE_GKS)
gr.updatews()

... in real-time
25
import wave, pyaudio
import numpy
import gr
!
SAMPLES=1024
FS=44100 # Sampling frequency
!
f = [FS/float(SAMPLES)*t for t in range(1, SAMPLES/2+1)]
!
wf = wave.open('Monty_Python.wav', 'rb')
pa = pyaudio.PyAudio()
stream = pa.open(format=pa.get_format_from_width(wf.getsampwidth()),
channels=wf.getnchannels(), rate=wf.getframerate(),
output=True)
!
...
!
data = wf.readframes(SAMPLES)
while data != '' and len(data) == SAMPLES * wf.getsampwidth():
stream.write(data)
amplitudes = numpy.fromstring(data, dtype=numpy.short)
power = abs(numpy.fft.fft(amplitudes / 65536.0))[:SAMPLES/2]
!
gr.clearws()
...
gr.polyline(SAMPLES/2, f, power)
gr.updatews()
data = wf.readframes(SAMPLES)

... with user interaction
26
import gr3
from OpenGL.GLUT import *
# ... Read MRI data 
width = height = 1000
isolevel = 100
angle = 0
!
def display():
vertices, normals = gr3.triangulate(data, (1.0/160, 1.0/160, 1.0/200), (-0.5, -0.5, -0.5), isolevel)
mesh = gr3.createmesh(len(vertices)*3, vertices, normals, np.ones(vertices.shape))
gr3.drawmesh(mesh, 1, (0,0,0), (0,0,1), (0,1,0), (1,1,1), (1,1,1))
gr3.cameralookat(-2*math.cos(angle), -2*math.sin(angle), -0.25, 0, 0, -0.25, 0, 0, -1)
gr3.drawimage(0, width, 0, height, width, height, gr3.GR3_Drawable.GR3_DRAWABLE_OPENGL)
glutSwapBuffers()
gr3.clear()
gr3.deletemesh(ctypes.c_int(mesh.value))
def motion(x, y):
isolevel = 256*y/height
angle = -math.pi + 2*math.pi*x/width
glutPostRedisplay()
glutInit()
glutInitWindowSize(width, height)
glutCreateWindow("Marching Cubes Demo")
!
glutDisplayFunc(display)
glutMotionFunc(motion)
glutMainLoop()

... with Qt
27

... and wxWidgets
28

Scalable graphics in Web browsers
29

Import PDF
30
import gr
(w, h, data) = gr.readimage("fs.pdf")
if w < h:
r = float(w)/h
gr.setviewport(0.5*(1-r), 0.5*(1+r), 0, 1);
else:
r = float(h)/w
gr.setviewport(0, 1, 0.5*(1-r), 0.5*(1+r));
gr.drawimage(0, 1, 0, 1, w, h, data)
gr.updatews()

Success stories (I)
31
World’s most powerful laboratory
small-angle X-ray scattering facility at
Forschungszentrum Jülich

Success stories (II)
32
BornAgain

A software to simulate and ﬁt neutron
and x-ray scattering at grazing incidence
(GISANS and GISAXS), using distorted-
wave Born approximation (DWBA)
Nframes = 100
radius = 1
height = 4
distance = 5
!def RunSimulation():
# defining materials
mAir = HomogeneousMaterial("Air", 0.0, 0.0)
mSubstrate = HomogeneousMaterial("Substrate", 6e-6, 2e-8)
mParticle = HomogeneousMaterial("Particle", 6e-4, 2e-8)
# collection of particles
cylinder_ff = FormFactorCylinder(radius, height)
cylinder = Particle(mParticle, cylinder_ff)
particle_layout = ParticleLayout()
particle_layout.addParticle(cylinder)
# interference function
interference = InterferenceFunction1DParaCrystal(distance, 3 * nanometer)
particle_layout.addInterferenceFunction(interference)
# air layer with particles and substrate form multi layer
air_layer = Layer(mAir)
air_layer.setLayout(particle_layout)
substrate_layer = Layer(mSubstrate)
multi_layer = MultiLayer()
multi_layer.addLayer(air_layer)
multi_layer.addLayer(substrate_layer)
# build and run experiment
simulation = Simulation()
simulation.setDetectorParameters(250, -4*degree, 4*degree, 250, 0*degree, 8*degree)
simulation.setBeamParameters(1.0 * angstrom, 0.2 * degree, 0.0 * degree)
simulation.setSample(multi_layer)
simulation.runSimulation()
return simulation.getIntensityData().getArray()
def SetParameters(i):
radius = (1. + (3.0/Nframes)*i) * nanometer
height = (1. + (4.0/Nframes)*i) * nanometer
distance = (10. - (1.0/Nframes)*i) * nanometer
!for i in range(100):
SetParameters(i)
result = RunSimulation()
gr.pygr.imshow(numpy.log10(numpy.rot90(result, 1)), cmap=gr.COLORMAP_PILATUS)

Success stories (III)
33
NICOS

a network-based control
system written for
neutron scattering
instruments at the FRM II

Coming soon: 
Python moldyn package …
34

… with video output
35

… and POV-Ray output
36

… in highest resolution
37

Performance optimizations
✓ NumPy 
module for handling multi-dimensional arrays (ndarray)

✓ Numba (Anaconda)
✓ just-in-time compilation driven by @autojit- or @jit-
decorators (LLVM)

✓ vectorization of ndarray based functions (ufuncs)

✓ Numba Pro (Anaconda Accelerate)
✓ parallel loops and ufuncs

✓ execution of ufunfs on GPUs

✓ “Python” GPU kernels

✓ GPU optimized libraries (cuBLAS, cuFFT, cuRAND)
38

Realization
✓ NumPy 
vector operations on ndarrays instead of loops 
➟ works in any NumPy Python environment

✓ Numba (Anaconda) 
add @jit and @autojit decorators 
➟ useful for “many” function calls with “big” arrays

✓ Numba Pro (Anaconda Accelerate) 
add @vectorize decorators 
implementation of multi-core / GPU kernels in "Python"  
switch to GPU-optimized features 
➟ useful only for "large" arrays 
performance
39

Particle simulation
40
import numpy as np
!
!
N = 300 # number of particles
M = 0.05 * np.ones(N) # masses
size = 0.04 # particle size
!
!
def step(dt, size, a):
a[0] += dt * a[1] # update positions
!
n = a.shape[1]
D = np.empty((n, n), dtype=np.float)
for i in range(n):
for j in range(n):
dx = a[0, i, 0] - a[0, j, 0]
dy = a[0, i, 1] - a[0, j, 1]
D[i, j] = np.sqrt(dx*dx + dy*dy)
!
... # find pairs of particles undergoing a collision
... # check for crossing boundary
return a
...
!
a[0, :] = -0.5 + np.random.random((N, 2)) # positions
a[1, :] = -0.5 + np.random.random((N, 2)) # velocities
a[0, :] *= (4 - 2*size)
dt = 1. / 30
!
while True:
a = step(dt, size, a)
....
!
from numba.decorators import autojit
!
!
!
!
!
@autojit
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!

Diffusion
41
import numpy
!
!
dx = 0.005
dy = 0.005
a = 0.5
dt = dx*dx*dy*dy/(2*a*(dx*dx+dy*dy))
timesteps = 300
!
nx = int(1/dx)
ny = int(1/dy)
ui = numpy.zeros([nx,ny])
u = numpy.zeros([nx,ny])
!
!
def diff_step(u, ui):
for i in range(1,nx-1):
for j in range(1,ny-1):
uxx = ( ui[i+1,j] - 2*ui[i,j] + ui[i-1, j] )/(dx*dx)
uyy = ( ui[i,j+1] - 2*ui[i,j] + ui[i, j-1] )/(dy*dy)
u[i,j] = ui[i,j]+dt*a*(uxx+uyy)
!
!
!
for m in range(timesteps):
diff_step (u, ui)
ui = numpy.copy(u)
...
!
from numba.decorators import jit
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
diff_step_numba = jit('void(f8[:,:], f8[:,:])')(diff_step)
!
!
diff_step_numba(u, ui)
!

Mandelbrot set
42
from numbapro import vectorize
import numpy as np
!
@vectorize(['uint8(uint32, f8, f8, f8, f8, uint32, uint32, uint32)'], target='gpu')
def mandel(tid, min_x, max_x, min_y, max_y, width, height, iters):
pixel_size_x = (max_x - min_x) / width
pixel_size_y = (max_y - min_y) / height
!
x = tid % width
y = tid / width
!
real = min_x + x * pixel_size_x
imag = min_y + y * pixel_size_y
!
c = complex(real, imag)
z = 0.0j
!
for i in range(iters):
z = z * z + c
if (z.real * z.real + z.imag * z.imag) >= 4:
return i
!
return 255
!
!
def create_fractal(min_x, max_x, min_y, max_y, width, height, iters):
tids = np.arange(width * height, dtype=np.uint32)
return mandel(tids, np.float64(min_x), np.float64(max_x), np.float64(min_y),
np.float64(max_y), np.uint32(height), np.uint32(width),
np.uint32(iters))

Performance comparison
43
Calculation of Mandelbrot set

Numba (Pro) review
44
✓ functions with numerical code can be compiled with little effort
and lead to impressive results

✓ numerical code should be separated from logic statements (and
processing of lists, dictionaries)

✓ advanced Technologie due to LLVM intermediate language
(LLVM IR)

✓ easy installation and maintenance 
Download link (Continuum Analytics): http://www.continuum.io/downloads
% bash Anaconda-1.x.x-[Linux|MacOSX]-x86[_64].sh
% conda update conda
% conda update anaconda

Development tools
45
You can use your favorite editor and start Python in a shell. But 
the impatient user should chose a development environment:

IPython console
46

IPython notebook
47

Spyder
48

PyCharm
49

Bokeh
50
import numpy as np
from scipy.integrate import odeint
from bokeh.plotting import *
!
sigma = 10
rho = 28
beta = 8.0/3
theta = 3 * np.pi / 4
!
def lorenz(xyz, t):
x, y, z = xyz
x_dot = sigma * (y - x)
y_dot = x * rho - x * z - y
z_dot = x * y - beta* z
return [x_dot, y_dot, z_dot]
!
initial = (-10, -7, 35)
t = np.arange(0, 100, 0.006)
!
solution = odeint(lorenz, initial, t)
!
x = solution[:, 0]
y = solution[:, 1]
z = solution[:, 2]
xprime = np.cos(theta) * x - np.sin(theta) * y
!
colors = ["#C6DBEF", "#9ECAE1", "#6BAED6", “#4292C6",
"#2171B5", "#08519C", "#08306B",]
!
output_file("lorenz.html", title="lorenz.py example")
!
multi_line(np.array_split(xprime, 7), np.array_split(z, 7),
line_color=colors, line_alpha=0.8, line_width=1.5,
tools=“pan,wheel_zoom,box_zoom,reset,previewsave",
title="lorenz example", name="lorenz_example")
!
show() # open a browser

Resources
✓ Website: http://gr-framework.org

✓ PyPI: https://pypi.python.org/pypi/gr

✓ Git Repository: http://github.com/jheinen/gr

✓ Binstar: https://binstar.org/jheinen/gr

✓ Talk: ScientiﬁcVisualization Workshop (PDF, HTML)
51

Website
52

Git-Repo
53

PyPI
54

Binstar
55

Conclusion
✓ The use of Python with the GR framework and Numba (Pro)
extensions allows the realization of high-performance
visualization applications in scientiﬁc and technical environments

✓ The GR framework can seamlessly be integrated into "foreign"
Python environments, e.g.Anaconda, by using the ctypes
mechanism

✓ Anaconda (Accelerate) is an easy to manage (commercial)
Python distribution that can be enhanced by the use of the GR
framework with its functions for real-time or 3D visualization
applications
56

Future plans
✓ implement your(!) feature requests

✓ moldyn package for Python

✓ more

✓ tutorials

✓ convenience functions

✓ documentation

✓ examples (gallery)

✓ IPython notebook integration

✓ Bokeh integration
57

Thank you for your attention
References:
Numba, A Dynamic Python compiler for Science: http://lanyrd.com/2013/pycon/scdyzh 
Continuum Analytics: http://www.continuum.io

!
Contact:
j.heinen@fz-juelich.de 
@josef_heinen"
!
Thanks to:
Florian Rhiem, Ingo Heimbach, Christian Felder, David Knodt, Jörg Winkler, Fabian Beule, 
Marcel Dück, Marvin Goblet, et al.
58

Scientific Visualization

Recommandé

Recommandé

Contenu connexe

En vedette

En vedette (20)

Similaire à Scientific Visualization

Similaire à Scientific Visualization (20)

Dernier

Dernier (20)

Scientific Visualization