:)

 Melihat koreografi Bruno Mars dan The Hooligans, jadinya malah teringat Rhoma Irama dan Soneta

iWork Update on El Capitan

 My Pages, Number and Keynote received new feature.

 ...and hey, my view is increased twofold, :D

(And my Keynote on iPhone 4s is upgraded as well)

Belajar.

Dulu belajar berbicara.

Sekarang perlu untuk belajar diam.

(The Tales of Tatonka)

Pasir

Berapa nikmat yang diberikan kepadaku?

Ngawur,

kurang kerjaan.

Sana, mending hitung butiran pasir di pantai saja sana,

tu lebih sedikit, lebih gampang.

(terinspirasi status mbakYu)

Lagrange Interpolation using Python

 Here it is. We could set the order of interpolation by changing the value of k

from pylab import *
from random import uniform
k = 11

def l(t):
    l = []
    for i in arange (len(t)):
        l.append(0.)
        for j in arange(k+1):
            lag = 1.
            for m in arange(k+1):
                if m!=j:
                    lag = lag * (t[i]-x[m])/(x[j]-x[m])
            l[i] = l[i]+y[j]*lag
            

    return l

def f(x):
    f = []
    for i in arange (len(x)):
        f.append(0.)
        f[i] = x[i]+uniform(-10,10)
    return f

x = arange(0.0, 2.0, 0.1)
t = arange(0.,2.,0.001)
y = f(x)
z = l(t)

plot(x,y)
plot(t,z)
xlabel('x')
ylabel('y')
title('interpolasi')
grid(True)
axis([0,2,-111,111])
#savefig("test.png")
show()

.

Walking Sine on Visual Python GDisplay

 Look, the wrong way often provide a beautiful result. Yeah, it's not what the program should be, but still I like it, :)

from __future__ import division, print_function
from visual import *
from visual.graph import *

def f(x):
    f = sin(pi*x+p)
    return f
def g(x):
    g = cos(pi*x)
    return g

graph1 = gdisplay(x=0, y=0, width=600, height=400, 
          title='A vs. t', xtitle='t', ytitle='A', 
          foreground=color.black, background=color.white)
p = 0.
f1 = gcurve(color=color.blue)
f2 = gcurve(color=color.red)

t = arange(-2.,2.,0.01)
s = g(t)
while True:
    rate(100)
    f1.gcurve.pos=[]  #delete this and look at the effect :)
    f2.gcurve.pos=[]
    u = f(t)
    for i in arange(len(s)):
        f2.plot(pos=((i-len(s)/2.)*.01,s[i]))
        f1.plot(pos=((i-len(s)/2.)*.01,u[i]))
    p = p + 0.01
    if p >100:
        p = 0

Fourier Transform using Delphi

 It's not Discrete Fourier Transform.

 Instead, I use continue definition (using Integral, not Sum) to compute the transformation. I know, it's weird, but it's worth a try, :)

 What I did is transform signal with 3 frequency, remove the two frequency and trasform back to time-signal.

unit Unit1;

interface

uses
  Windows, Messages, SysUtils, Variants, Classes, Graphics, Controls, Forms,
  Dialogs, ExtCtrls, StdCtrls;

type
  TForm1 = class(TForm)
    Image1: TImage;
    Timer1: TTimer;
    Memo1: TMemo;
    Image2: TImage;
    Image3: TImage;
    Image4: TImage;
    procedure proses;
    procedure gambarFungsi;
    procedure gambarSumbu;
    procedure gambarTransformasi;
    procedure olahTransformasi;
    procedure gambarOlahTransformasi;
    procedure transformasiBalik;
    procedure gambarTransformasibalik;
    function f(x:real):real;
    procedure Timer1Timer(Sender: TObject);
  private
  public
  end;

const
  a=200;
  b=150;

var
  Form1: TForm1;
  x0,y0,xm,ym:integer;
  s,ss:array[-a..a]of real;
  ft:array[-b..b]of real;
implementation
{$R *.dfm}
function tform1.f(x:real):real;
begin
  f:=cos(PI*x)+cos(2*PI*x)+cos(4*PI*x);
end;
procedure tform1.transformasiBalik;
var i,j:integer;
t,w,dt:real;
begin{}
  dt:=0.1;
  for i:=-a to a do begin
    w:=i/10;
    ss[i]:=0;
    for j:=-b to b do begin
      t:=j/10;
      ss[i]:=ss[i]+ft[j]*cos(w*t)*dt
    end;
  end;
  gambarTransformasiBalik;
end;

procedure tform1.olahTransformasi;
var i:integer;
begin
  for i:=-b to b do begin
    if abs(i)>50 then ft[i]:=0;
  end;
  gambarOlahTransformasi;
end;

procedure tform1.proses;
var i,j:integer;
t,w,dt:real;
begin
  form1.Caption:='transformasi';
  gambarSumbu;
  {transformasi}
  dt:=0.1;
  for i:=-a to a do begin
    s[i]:=f(i/30);
  end;
  for i:=-b to b do begin
    w:=i/10;
    ft[i]:=0;
    for j:=-a to a do begin
      t:=j/10;
      ft[i]:=ft[i]+f(t)*cos(w*t)*dt
    end;
  end;
  gambarFungsi;
  gambarTransformasi;
  olahTransformasi;
  transformasiBalik;
end;

procedure tform1.gambarFungsi;
var i,xo,yo,xt,yt:integer;
begin
  xo:=-a; yo:=0;
  for i:=-a to a do begin
    xt:=i;
    yt:=round(10*s[i]);
    with image1.Canvas do begin
      moveto(x0+xo,y0-yo);lineto(x0+xt,y0-yt);
    end;
    xo:=xt;
    yo:=yt;
  end;
end;

procedure tform1.gambarTransformasibalik;
var i,xo,yo,xt,yt:integer;
begin
  xo:=-a; yo:=0;
  for i:=-a to a do begin
    xt:=i;
    yt:=round(10*ss[i]);
    with image4.Canvas do begin
      moveto(x0+xo,y0-yo);lineto(x0+xt,y0-yt);
    end;
    xo:=xt;
    yo:=yt;
  end;
end;

procedure tform1.gambarOlahTransformasi;
var i,xo,yo,xt,yt:integer;
begin
{}
  xo:=-b; yo:=0;
  for i:=-b to b do begin
    xt:=i;
    yt:=round(10*ft[i]);
    with image3.Canvas do begin
      moveto(x0+xo,y0-yo);lineto(x0+xt,y0-yt);
    end;
    xo:=xt;
    yo:=yt;
  end;
end;

procedure tform1.gambarTransformasi;
var i,xo,yo,xt,yt:integer;
begin
  xo:=-b;yo:=0;
  for i:=-b to b do begin
    xt:=i;
    yt:=round(10*ft[i]);
    with image2.Canvas do begin
      moveto(x0+xo,y0-yo);lineto(x0+xt,y0-yt);
    end;
    xo:=xt;
    yo:=yt;
  end;
end;

procedure tform1.gambarSumbu;
begin
  x0:=image1.Width div 2;
  y0:=image1.Height div 2;
  xm:=image1.Width;
  ym:=image1.Height;
  with image1.Canvas do begin
    moveto(0,y0);lineto(xm,y0);moveto(x0,0);lineto(x0,ym);
  end;
  with image2.Canvas do begin
    moveto(0,y0);lineto(xm,y0);moveto(x0,0);lineto(x0,ym);
  end;
  with image3.Canvas do begin
    moveto(0,y0);lineto(xm,y0);moveto(x0,0);lineto(x0,ym);
  end;
  with image4.Canvas do begin
    moveto(0,y0);lineto(xm,y0);moveto(x0,0);lineto(x0,ym);
  end;
end;

procedure TForm1.Timer1Timer(Sender: TObject);
begin
  timer1.Enabled:=false;
  proses;
end;

end.