2.  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 sp

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

#dr  = .1
#dp  = .1
#nr      = int(1/dr)
#np      = int(2*sp.pi/dp)


nr  = 10
np  = 10

r       = sp.linspace(0.,1.,nr)
p       = sp.linspace(0.,2*sp.pi,np)

dr  = r[1]-r[0]
dp  = p[1]-p[0]

a   = .5

tmax    = 100
t       = 0.


dr2     = dr**2
dp2     = dp**2

dt      = dr2 * dp2 / (2 * a * (dr2 + dp2) )
dt      /=10.
print 'dr = ',dr 
print 'dp = ',dp 
print 'dt = ',dt



ut      = sp.zeros([nr,np])
u0      = sp.zeros([nr,np])

ur      = sp.zeros([nr,np])
ur2     = sp.zeros([nr,np])


#initial

for i in range(nr):
    for j in range(np):
        if ((i>4)&(i<6)):
            u0[i,j] = 1.
#print u0

def 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 ut

def 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 = u0
print 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()
    .






    100x100 size

    Posted by Unknown
    Labels: programming Python
    0

    Add a comment

  3.  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 sp

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

#dr  = .1
#dp  = .1
#nr      = int(1/dr)
#np      = int(2*sp.pi/dp)

nr  = 10
np  = 10

dr  = 1./nr
dp  = 2*sp.pi/np

a   = .5

tmax    = 100
t       = 0.


dr2     = dr**2
dp2     = dp**2

dt      = dr2 * dp2 / (2 * a * (dr2 + dp2) )
dt      /=10.
print dt



ut      = 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)

#initial

for i in range(nr):
    for j in range(np):
        if ( (i>(2*nr/5.)) & (i<(3.*nr/3.)) ):
            u0[i,j] = 1.
#print u0

def 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 ut


def 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 = u0
print 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()
    .








    Posted by Unknown
    Labels: programming Python
    0

    Add a comment

  4.  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, :)



    Posted by Unknown
    Labels: diary
    0

    Add a comment

  6.  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 )
        

def data_gen(framenumber, Z ,surf):
    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()
ax = fig.add_subplot(111, projection='3d')

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()
    .

    Posted by Unknown
    Labels: programming Python
    0

    Add a comment

  7.  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 difference
scheme to solve the diffusion equation with fixed
boundary values and a given initial value for the
density.

Two steps of the solution are stored: the current
solution, u, and the previous step, ui. At each time-
step, u is calculated from ui. u is moved to ui at the
end 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 matplotlib

I use visual python

"""
import scipy as sp
import time
from 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^2
dy2=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."
    .


    Posted by Unknown
    Labels: programming Python
    0

    Add a comment

  8.  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.
>>> a
array([ 0.,  0.,  0.,  0.,  0.,  1.,  0.,  0.,  0.,  0.])
>>> b
array([ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.])
>>> a[6]=2.
>>> a
array([ 0.,  0.,  0.,  0.,  0.,  1.,  2.,  0.,  0.,  0.])
>>> b[:-1]=a[:-1]-a[1:]
>>> b
array([ 0.,  0.,  0.,  0., -1., -1.,  2.,  0.,  0.,  0.])
>>> b[:-1]=a[:-1]+a[1:]
>>> b
array([ 0.,  0.,  0.,  0.,  1.,  3.,  2.,  0.,  0.,  0.])
>>>
    I like Python, :)




    Posted by Unknown
    Labels: programming Python
    0

    Add a comment

  10.  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)

     #EdisiError
    Posted by Unknown
    Labels: diary
    0

    Add a comment

  11.  I used textfile variable to write to a file (or create it if it don't exist).

     CSV file? Just make sure that the name at assignfile  command had .csv extension, :)

     Of course we have to format the output to meet the CSV standart; separated by comma.


    procedure TForm1.Button1Click(Sender: TObject);
var
    fileku:textfile;
    i,j,n:integer;
begin
  n:=10;
  assignfile(fileku,'data.csv');
  rewrite(fileku);
  writeln(fileku,'tadaa...');
  for i:=1 to n do begin
    for j:=1 to n do begin
      writeln(fileku,i,',',j,',','data',i,j);
    end;
  end;
  closefile(fileku);
end;
    .









    Posted by Unknown
    Labels: delphi programming
    0

    Add a comment

  12.  “I definitely didn’t have time to get my soul cast into a place I couldn’t even pronounce.”

     Typical Rick, :)
    Posted by Unknown
    Labels: diary
    0

    Add a comment

  14.  Sepatu basah kena hujan.

     Gak bawa serep.

     Nyalakan AC, gantung di depan kipas, tunggu dua jam, :)





    Posted by Unknown
    Labels: diary
    0

    Add a comment

Archive
Archive
Label
Label
Popular Posts
Popular Posts
Loading