Nugroho's blog.

## Friday, November 27, 2015

### 3D (Polar/Cylindrical Coordinate) Animation of 2D Diffusion Equation using Python, Scipy, and Matplotlib

Yup, that same code but in polar coordinate.

I use nabla operator for cylindrical coordinate but ditch the z component.

So, what's the z-axis for? It's represent the u value, in this case, temperature, as function of r and phi (I know I should use rho, but, ...)

`import scipy as spfrom mpl_toolkits.mplot3d import Axes3Dfrom matplotlib import cmfrom matplotlib.ticker import LinearLocator, FormatStrFormatterimport matplotlib.pyplot as pltimport mpl_toolkits.mplot3d.axes3d as p3import matplotlib.animation as animation#dr  = .1#dp  = .1#nr      = int(1/dr)#np      = int(2*sp.pi/dp)nr  = 10np  = 10r       = sp.linspace(0.,1.,nr)p       = sp.linspace(0.,2*sp.pi,np)dr  = r[1]-r[0]dp  = p[1]-p[0]a   = .5tmax    = 100t       = 0.dr2     = dr**2dp2     = dp**2dt      = dr2 * dp2 / (2 * a * (dr2 + dp2) )dt      /=10.print 'dr = ',dr print 'dp = ',dp print 'dt = ',dtut      = sp.zeros([nr,np])u0      = sp.zeros([nr,np])ur      = sp.zeros([nr,np])ur2     = sp.zeros([nr,np])#initialfor i in range(nr):    for j in range(np):        if ((i>4)&(i<6)):            u0[i,j] = 1.#print u0def hitung_ut(ut,u0):    for i in sp.arange (len(r)):        if r[i]!= 0.:            ur[i,:]     = u0[i,:]/r[i]            ur2[i,:]     = u0[i,:]/(r[i]**2)    ut[1:-1, 1:-1]  = u0[1:-1, 1:-1] + a*dt*(            (ur[1:-1, 1:-1] - ur[:-2, 1:-1])/dr+            (u0[2:, 1:-1] - 2*u0[1:-1, 1:-1] + u0[:-2,1:-1])/dr2+            (ur2[1:-1, 2:] - 2*ur2[1:-1, 1:-1] + ur2[1:-1, :-2])/dp2)    #calculate the edge    ut[1:-1, 0]  = u0[1:-1, 0] + a*dt*(            (ur[1:-1, 0] - ur[:-2, 0])/dr+            (u0[2:, 0] - 2*u0[1:-1, 0] + u0[:-2, 0])/dr2+            (ur2[1:-1, 1] - 2*ur2[1:-1, 0] + ur2[1:-1, np-1])/dp2)    ut[1:-1, np-1]  = u0[1:-1, np-1] + a*dt*(            (ur[1:-1, np-1] - ur[:-2, np-1])/dr+            (u0[2:, np-1] - 2*u0[1:-1, np-1] + u0[:-2,np-1])/dr2+            (ur2[1:-1, 0] - 2*ur2[1:-1, np-1] + ur2[1:-1, np-2])/dp2)#hitung_ut(ut,u0)#print utdef data_gen(framenumber, Z ,surf):    global ut    global u0    global t    hitung_ut(ut,u0)    u0[:] = ut[:]    Z = u0    t += 1    print t        ax.clear()    plotset()    surf = ax.plot_surface(X, Y, Z, rstride=1, cstride=1, cmap=cm.coolwarm,                       linewidth=0, antialiased=False, alpha=0.7)    return surf,fig = plt.figure()#ax = fig.gca(projection='3d')ax = fig.add_subplot(111, projection='3d')P,R = sp.meshgrid(p,r)X,Y = R*sp.cos(P),R*sp.sin(P) Z = u0print len(R), len(P)def plotset():    ax.set_xlim3d(-1., 1.)    ax.set_ylim3d(-1., 1.)    ax.set_zlim3d(-1.,1.)    ax.set_autoscalez_on(False)    ax.zaxis.set_major_locator(LinearLocator(10))    ax.zaxis.set_major_formatter(FormatStrFormatter('%.02f'))    cset = ax.contour(X, Y, Z, zdir='x', offset=-1. , cmap=cm.coolwarm)    cset = ax.contour(X, Y, Z, zdir='y', offset=1. , cmap=cm.coolwarm)    cset = ax.contour(X, Y, Z, zdir='z', offset=-1., cmap=cm.coolwarm)plotset()surf = ax.plot_surface(X, Y, Z, rstride=1, cstride=1, cmap=cm.coolwarm,                       linewidth=0, antialiased=False, alpha=0.7)fig.colorbar(surf, shrink=0.5, aspect=5)ani = animation.FuncAnimation(fig, data_gen, fargs=(Z, surf),frames=4096, interval=4, blit=False)#ani.save('2dDiffusionfRadialf1024b512.mp4', bitrate=1024)plt.show()    `
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 100x100 size

## Thursday, November 26, 2015

### The Wrong Code Will often Provide Beautiful Result, :)

It means to compute 2d diffusion equation just like previous post in polar/cylindrical coordinate, and all went to wrong direction, :)

Still trying to understand matplotlib mplot3d behavior

`import scipy as spfrom mpl_toolkits.mplot3d import Axes3Dfrom matplotlib import cmfrom matplotlib.ticker import LinearLocator, FormatStrFormatterimport matplotlib.pyplot as pltimport mpl_toolkits.mplot3d.axes3d as p3import matplotlib.animation as animation#dr  = .1#dp  = .1#nr      = int(1/dr)#np      = int(2*sp.pi/dp)nr  = 10np  = 10dr  = 1./nrdp  = 2*sp.pi/npa   = .5tmax    = 100t       = 0.dr2     = dr**2dp2     = dp**2dt      = dr2 * dp2 / (2 * a * (dr2 + dp2) )dt      /=10.print dtut      = sp.zeros([nr,np])u0      = sp.zeros([nr,np])ur      = sp.zeros([nr,np])ur2     = sp.zeros([nr,np])r       = sp.arange(0.,1.,dr)p       = sp.arange(0.,2*sp.pi,dp)#initialfor i in range(nr):    for j in range(np):        if ( (i>(2*nr/5.)) & (i<(3.*nr/3.)) ):            u0[i,j] = 1.#print u0def hitung_ut(ut,u0):    for i in sp.arange (len(r)):        if r[i]!= 0.:            ur[i,:]     = u0[i,:]/r[i]            ur2[i,:]     = u0[i,:]/(r[i]**2)    ut[1:-1, 1:-1]  = u0[1:-1, 1:-1] + a*dt*(            (ur[1:-1, 1:-1] - ur[:-2, 1:-1])/dr+            (u0[2:, 1:-1] - 2*u0[1:-1, 1:-1] + u0[:-2,1:-1])/dr2+            (ur2[1:-1, 2:] - 2*ur2[1:-1, 1:-1] + ur2[1:-1, :-2])/dp2)#hitung_ut(ut,u0)#print utdef data_gen(framenumber, Z ,surf):    global ut    global u0    hitung_ut(ut,u0)    u0[:] = ut[:]    Z = u0        ax.clear()    plotset()    surf = ax.plot_surface(X, Y, Z, rstride=1, cstride=1, cmap=cm.coolwarm,                       linewidth=0, antialiased=False, alpha=0.7)    return surf,fig = plt.figure()#ax = fig.gca(projection='3d')ax = fig.add_subplot(111, projection='3d')R = sp.arange(0,1,dr)P = sp.arange(0,2*sp.pi,dp)R,P = sp.meshgrid(R,P)X,Y = R*sp.cos(P),R*sp.sin(P) Z = u0print len(R), len(P)def plotset():    ax.set_xlim3d(-1., 1.)    ax.set_ylim3d(-1., 1.)    ax.set_zlim3d(-1.,1.)    ax.set_autoscalez_on(False)    ax.zaxis.set_major_locator(LinearLocator(10))    ax.zaxis.set_major_formatter(FormatStrFormatter('%.02f'))    cset = ax.contour(X, Y, Z, zdir='x', offset=0. , cmap=cm.coolwarm)    cset = ax.contour(X, Y, Z, zdir='y', offset=1. , cmap=cm.coolwarm)    cset = ax.contour(X, Y, Z, zdir='z', offset=-1., cmap=cm.coolwarm)plotset()surf = ax.plot_surface(X, Y, Z, rstride=1, cstride=1, cmap=cm.coolwarm,                       linewidth=0, antialiased=False, alpha=0.7)fig.colorbar(surf, shrink=0.5, aspect=5)ani = animation.FuncAnimation(fig, data_gen, fargs=(Z, surf),frames=500, interval=30, blit=False)#ani.save('2dDiffusionf500b512.mp4', bitrate=512)plt.show()    `
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### Miss Lay.

Baca komen seperti  "Permainan gitar Eross pecah banget...." di Youtube, hati langsung panas.

Berani-beraninya menghina sang maestro, sana, ke comberan sana, tempat asalmu, ...

Eh, tunggu...

Itu bukan hinaan, itu pujian...

Pecah? Pujian?

Yeah, beberapa dari kita sering menggunakan kata tak pada tempatnya, :)

Penggunaan kata 'pecah' sebagai pujian datang dari Maia Estianty saat menjadi juri The Remix.

Tentu saja penggunaan kata 'pecah' di dunia DJ atau remix sangat cocok; merujuk pada sunyi yang lambat laun menjadi semakin ramai seiring dengan penumpukan nada-nada sampling yang makin banyak, tempo yang makin cepat dan diakhiri dengan sebuah hentakan..., pecah...,

OK, itu pujian, bagaimana kalo kata 'pecah' digunakan di permainan gitar. Yeah, kami menganggap kata pecah sebagai kata berkonotasi buruk; merujuk pada suara gitar yang seharusnya clean namun karena setting yang buruk jadi terdengar 'brebet' atau 'pecah'.

Bukannya efek gitar Telecaster-nya Eross mempunya karakter pecah?  Ehm, EDrive-nya Eross, seperti namanya, 'drive', hanya bertugas sebagai booster saat permainan lead, bahkan kalo kita lihat di penampilan live, Eross jarang sekali menggunakan stompbox, dia memainkan knob volume untuk efek crunch atau crisp. Jika  ingin suara clean, dia mengecilkan volume gitarnya.

Suara Telecaster Eross 'pecah'? Well, lebih baik pakai kata crunchy, crispy, ..., lebih diterima oleh banyak gitaris, :)

## Wednesday, November 25, 2015

### 3D Animation of 2D Diffusion Equation using Python, Scipy, and Matplotlib

I wrote the code on OS X El Capitan, use a small mesh-grid.  Basically it's same code like the previous post.

I use surface plot mode for the graphic output and animate it.

Because my Macbook Air is suffered from running laborious code, I save the animation on my Linux environment, 1024 bitrate, 1000 frames.

story
```import scipy as sp
import time
from mpl_toolkits.mplot3d import Axes3D
from matplotlib import cm
from matplotlib.ticker import LinearLocator, FormatStrFormatter
import matplotlib.pyplot as plt

import mpl_toolkits.mplot3d.axes3d as p3
import matplotlib.animation as animation

dx=0.01
dy=0.01
a=0.5
timesteps=500
t=0.

nx = int(1/dx)
ny = int(1/dy)

dx2=dx**2
dy2=dy**2

dt = dx2*dy2/( 2*a*(dx2+dy2) )

ui = sp.zeros([nx,ny])
u = sp.zeros([nx,ny])

for i in range(nx):
for j in range(ny):
if ( ( (i*dx-0.5)**2+(j*dy-0.5)**2 <= 0.1)
& ((i*dx-0.5)**2+(j*dy-0.5)**2>=.05) ):
ui[i,j] = 1
def evolve_ts(u, ui):
u[1:-1, 1:-1] = ui[1:-1, 1:-1] + a*dt*(
(ui[2:, 1:-1] - 2*ui[1:-1, 1:-1] + ui[:-2, 1:-1])/dx2 +
(ui[1:-1, 2:] - 2*ui[1:-1, 1:-1] + ui[1:-1, :-2])/dy2 )

global u
global ui
evolve_ts(u,ui)
ui[:] = u[:]
Z = ui

ax.clear()
plotset()
surf = ax.plot_surface(X, Y, Z, rstride=1, cstride=1, cmap=cm.coolwarm,
linewidth=0, antialiased=False, alpha=0.7)
return surf,

fig = plt.figure()

X = sp.arange(0,1,dx)
Y = sp.arange(0,1,dy)
X,Y= sp.meshgrid(X,Y)

Z = ui

def plotset():
ax.set_xlim3d(0., 1.)
ax.set_ylim3d(0., 1.)
ax.set_zlim3d(-1.,1.)
ax.set_autoscalez_on(False)
ax.zaxis.set_major_locator(LinearLocator(10))
ax.zaxis.set_major_formatter(FormatStrFormatter('%.02f'))
cset = ax.contour(X, Y, Z, zdir='x', offset=0. , cmap=cm.coolwarm)
cset = ax.contour(X, Y, Z, zdir='y', offset=1. , cmap=cm.coolwarm)
cset = ax.contour(X, Y, Z, zdir='z', offset=-1., cmap=cm.coolwarm)

plotset()
surf = ax.plot_surface(X, Y, Z, rstride=1, cstride=1, cmap=cm.coolwarm,
linewidth=0, antialiased=False, alpha=0.7)

fig.colorbar(surf, shrink=0.5, aspect=5)

ani = animation.FuncAnimation(fig, data_gen, fargs=(Z, surf),frames=1000, interval=30, blit=False)
ani.save("2dDiffusion.mp4", bitrate=1024)

#plt.show()
```
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## Tuesday, November 24, 2015

### 2D Diffusion Equation using Python, Scipy, and VPython

I got it from here, but modify it here and there.

I also add animation using vpython but can't find 3d or surface version, so I planned to go to matplotlib surface plot route, :)

(update: here it is, :) )

`#!/usr/bin/env python"""A program which uses an explicit finite differencescheme to solve the diffusion equation with fixedboundary values and a given initial value for thedensity.Two steps of the solution are stored: the currentsolution, u, and the previous step, ui. At each time-step, u is calculated from ui. u is moved to ui at theend of each time-step to move forward in time.http://www.timteatro.net/2010/10/29/performance-python-solving-the-2d-diffusion-equation-with-numpy/he uses matplotlibI use visual python"""import scipy as spimport timefrom visual import *from visual.graph import *graph1 = gdisplay(x=0, y=0, width=600, height=400,           title='x vs. T', xtitle='x', ytitle='T',           foreground=color.black, background=color.white)# Declare some variables:dx=0.01        # Interval size in x-direction.dy=0.01        # Interval size in y-direction.a=0.5          # Diffusion constant.timesteps=500  # Number of time-steps to evolve system.t=0.nx = int(1/dx)ny = int(1/dy)dx2=dx**2 # To save CPU cycles, we'll compute Delta x^2dy2=dy**2 # and Delta y^2 only once and store them.# For stability, this is the largest interval possible# for the size of the time-step:dt = dx2*dy2/( 2*a*(dx2+dy2) )# Start u and ui off as zero matrices:ui = sp.zeros([nx,ny])u = sp.zeros([nx,ny])# Now, set the initial conditions (ui).for i in range(nx): for j in range(ny):  if ( ( (i*dx-0.5)**2+(j*dy-0.5)**2 <= 0.1)   & ((i*dx-0.5)**2+(j*dy-0.5)**2>=.05) ):    ui[i,j] = 1'''def evolve_ts(u, ui): global nx, ny """ This function uses two plain Python loops to evaluate the derivatives in the Laplacian, and calculates u[i,j] based on ui[i,j]. """ 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] )/dx2   uyy = ( ui[i,j+1] - 2*ui[i,j] + ui[i, j-1] )/dy2   u[i,j] = ui[i,j]+dt*a*(uxx+uyy)'''def evolve_ts(u, ui): """ This function uses a numpy expression to evaluate the derivatives in the Laplacian, and calculates u[i,j] based on ui[i,j]. """ u[1:-1, 1:-1] = ui[1:-1, 1:-1] + a*dt*(                 (ui[2:, 1:-1] - 2*ui[1:-1, 1:-1] + ui[:-2, 1:-1])/dx2 +                 (ui[1:-1, 2:] - 2*ui[1:-1, 1:-1] + ui[1:-1, :-2])/dy2 )        # Now, start the time evolution calculation...#tstart = time.time()f1 = gcurve(color=color.blue)while True:    rate(60)    #for m in range(1, timesteps+1):    if t<timesteps:        t+=dt evolve_ts(u, ui)        ui[:] = u[:] # I add this line to update ui value (not present in original code) #print "Computing u for m =", m    f1.gcurve.pos   =   []    for i in arange(nx):        f1.plot(pos=(i,u[nx/2,i]))    #tfinish = time.time()#print "Done."#print "Total time: ", tfinish-tstart, "s"#print "Average time per time-step using numpy: ", ( tfinish - tstart )/timesteps, "s."`
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## Monday, November 23, 2015

### Numpy Slice Expression

Suppossed we have two array a and b

If we want to set b as finite difference result of a, we may tempted to do this

`for i in range (9): b[i] = a[i+1]-a[i]`

There's another (faster) way. The performance's close to the pure C, :)

b[:-1] = a[1:]-a[:-1]

What's that?

Numpy has slice form for array. If we have an array with length 10, the a[:] refers to all value in a.

a[1:] refers to a[1] to a[9] (without a[0])
a[3:] refers to a[3] to a[9]
a[:-1] refers to a[0] to a[8]
a[:-3] refers to a[0] to a[6]
a[1:-1] refers to a[1] to a[8]
...
and so on

Here's my tinkering with slice expression
`>>> from numpy import *>>> a = zeros(10)>>> b = zeros(10)>>> a[5]=1.>>> aarray([ 0.,  0.,  0.,  0.,  0.,  1.,  0.,  0.,  0.,  0.])>>> barray([ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.])>>> a[6]=2.>>> aarray([ 0.,  0.,  0.,  0.,  0.,  1.,  2.,  0.,  0.,  0.])>>> b[:-1]=a[:-1]-a[1:]>>> barray([ 0.,  0.,  0.,  0., -1., -1.,  2.,  0.,  0.,  0.])>>> b[:-1]=a[:-1]+a[1:]>>> barray([ 0.,  0.,  0.,  0.,  1.,  3.,  2.,  0.,  0.,  0.])>>> `
I like Python, :)

## Friday, November 20, 2015

### Car Free Day

Sepertinya ada (banyak) yang mengartikan sebagai kendaraan bebas berjalan di manapun, bahkan di tempat yang saat normal gak bisa dimasuki, :(

(hampir ketabrak sepeda motor yang dikendarai mahasiswa berboncengan  di jalan antara gedung MIPA dan Fisika)

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