Kernel: Python 3 (Ubuntu Linux)
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%matplotlib inline import ipywidgets as widgets from ipywidgets import interact,interactive,fixed from IPython.display import display,Math,clear_output #import test #import sympy import src.lagrange as lg import src.leastSquares as ls import src.splines as sp import matplotlib.pyplot as plt from numpy import linspace,sin,shape from pandas import DataFrame from IPython.display import HTML #l=lg.Lagrange() #l1=ls.LeastSquares() #l2=sp.SplineParab()
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HTML('''<script> code_show=true; function code_toggle() { if (code_show){ $('div.input').hide(); } else { $('div.input').show(); } code_show = !code_show } $( document ).ready(code_toggle); </script> <form action="javascript:code_toggle()"><input type="submit" value="Click here to toggle on/off the raw code."></form>''')
Newton's divided differences interpolation polynomial and socket multiplication algorithms
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button=widgets.Button(description="click me") buttonDiffSock=widgets.Button(description="click me") strPoints = widgets.Text(description='points',value='-1,-1,1,1') strFunct=widgets.Text(description=r'f(x)=',value='sin(pi*x)') strPointsDiffSock = widgets.Text(description='points',value='') strFunctDiffSock=widgets.Text(description=r'f(x)=',value='sin(x)') strPointDiffSock=widgets.Text(description='x0=',value='0') def on_button_cliked(event): l=lg.Lagrange() clear_output() #display(Math(r'$\begin{pmatrix}1 & 2 \\ 3 & 4\end{pmatrix}$')) plt.cla() points=[float(s) for s in list(strPoints.value.split(','))] f=strFunct.value l.lagrangeInterp(points=points,func=f) l.showInNotebook() display(l.dataFrameD) l.plot() display(Math("interp\ f(x)="+lg.latex(l.iF))) def on_button_clikedDiffSock(event): l=lg.Lagrange() clear_output() if len(strPointsDiffSock.value)==0: points=[] else: points=[float(s) for s in list(strPointsDiffSock.value.split(','))] f=strFunctDiffSock.value if len(strPointDiffSock.value)==0: x0=0 else: x0=float(strPointDiffSock.value) l.diffSocket() l.showInNotebook() display(l.dataFrameDD) #display(Math("interp\ f(x)="+lg.latex(l.iF))) button.on_click(on_button_cliked) buttonDiffSock.on_click(on_button_clikedDiffSock) page1 = widgets.Box(children=[button, strPoints,strFunct]) page2 = widgets.Box(children=[buttonDiffSock,strPointsDiffSock, strFunctDiffSock,strPointDiffSock]) #display(container) tabs = widgets.Tab(children=[page1, page2]) display(tabs) tabs.set_title(0, 'Lagrange interpolation') tabs.set_title(1, 'Socket multiplication algoriphm')
| f(xi) | f(xi;xj) | ... | ... | f(xi;...;xj) | |
|---|---|---|---|---|---|
| -1 | -0.841471 | 0.540302 | 0.150584 | -0.150584 | 0.248014 |
| -1 | -0.841471 | 0.841471 | -0.150584 | 0.345443 | NaN |
| 1 | 0.841471 | 0.540302 | 0.540302 | NaN | NaN |
| 1 | 0.841471 | 0.540302 | NaN | NaN | NaN |
| 1 | 0.841471 | NaN | NaN | NaN | NaN |
interp f(x)=0.248013831069444x4−0.150584339469878x3−0.496027662138887x2+0.992055324277775x+0.248013831069444
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Least Squares algorithm with Head function or Jacobi for basis
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buttonH=widgets.Button(description="click me") buttonJ=widgets.Button(description="click me") buttonEps=widgets.Button(description="click me") strPointsH = widgets.Text(description='points',value='') strPointsJ = widgets.Text(description='points',value='-1,1') strFunctH=widgets.Text(description=r'f(x)=',value='sin(x)') strFunctJ=widgets.Text(description=r'f(x)=',value='Piecewise((x+1,x>0),(-x+1,x<0),(1,True))') strEps= widgets.Text(description='Eps',value='1') strFunctEps=widgets.Text(description=r'f(x)=',value='Piecewise((x+1,x>0),(-x+1,x<0),(1,True))') def on_button_clikedH(event,x): l1=ls.LeastSquares() clear_output() #display(Math(r'$\begin{pmatrix}1 & 2 \\ 3 & 4\end{pmatrix}$')) plt.cla() if x==0: if len(strPointsH.value)!=0: l1.points=[float(s) for s in list(strPointsH.value.split(','))] l1.f=strFunctH.value l1.createBasisH() elif x==1: #if len(strPointsJ.value)!=0: l1.points=[-1,1] l1.f=strFunctJ.value l1.createBasisJ() else: pass l1.leastSquares() #print(l1.points) #print(l1.f) #print(l1.iF) l1.showInNotebook() if x!=0: display(Math("interp\ f(x)="+l1.texF)) #display(l.dataFrameD) #l.plot() #display(Math("interp\ f(x)="+l1.texF)) display("Basis:") for b in l1.texBasis: display(Math(b)) def on_button_clikedEps(event): l1=ls.LeastSquares() clear_output() plt.cla() eps=float(strEps.value) for n in range(12): l1=ls.LeastSquares() l1.f=strFunctJ.value l1.forEps(n=n) if l1.eps()<=eps: break if(n>10): print("fail") break l1.showInNotebook() display(Math("interp\ f(x)="+l1.texF)) display("Basis:") for b in l1.texBasis: display(Math(b)) p=lambda event,x:on_button_clikedH(event,x) pH=lambda event:p(event,0) pJ=lambda event:p(event,1) buttonH.on_click(pH)#on_button_clikedH buttonJ.on_click(pJ)#on_button_clikedJ buttonEps.on_click(on_button_clikedEps) page1 = widgets.Box(children=[buttonH, strPointsH,strFunctH]) page2 = widgets.Box(children=[buttonJ,strPointsJ,strFunctJ]) page3 = widgets.Box(children=[buttonEps,strEps,strFunctEps]) #display(container) tabs = widgets.Tab(children=[page3, page1,page2]) display(tabs) tabs.set_title(0, 'Jacoby basis eps') tabs.set_title(1, 'Head function basis') tabs.set_title(2, 'Jacoby basis')
spline algorithm with use parabolas polinom (i.e. polinom degree of 2)
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button=widgets.Button(description="click me") buttonJ=widgets.Button(description="click me") strPointsX = widgets.Text(description='points X',value='0,1,2,3,4') strPointsY = widgets.Text(description='points Y',value='0,0,1,0,0') strFunct=widgets.Text(description=r'f(x)=',value='sin(x)') def on_button_cliked(event): l2=sp.SplineParab() clear_output() #display(Math(r'$\begin{pmatrix}1 & 2 \\ 3 & 4\end{pmatrix}$')) plt.cla() if len(strPointsX.value)!=0: pointsX=[float(s) for s in list(strPointsX.value.split(','))] if len(strPointsY.value)!=0: pointsY=[float(s) for s in list(strPointsY.value.split(','))] f=strFunct.value l2.splineParab(points=pointsX,y=pointsY,f=f) l2.showInNotebook() for i in range(l2.n): display(Math(r'$ p_{%s}(x),g(x),h(x), p_{%s}(x):$'%(i,i+1))) display(l2.dataFrames[i]) l2.plot(i) #display(Math("interp\ f(x)="+l1.texF)) #display(l.dataFrameD) #l.plot() #display(Math("interp\ f(x)="+l1.texF)) button.on_click(on_button_cliked) page1 = widgets.Box(children=[button, strPointsX,strPointsY,strFunct]) display(page1)
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