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Image: ubuntu1804
Kernel: Python 3 (Anaconda 2019)
np.diff()#עושה חיסור של איבר קודם ואיבר עכשיו np.heaviside(y,0)#מינוס הופך לאפס ,פלוס הופך לאחד ואפס זה מה שאני בוחרת np.arange() np.array([])#יוצרת מערך
import matplotlib.pyplot as plt import numpy as np b=np.zeros([51]) b[0]=1 b[1]=1 for j in range(2,50): b[j]=b[j-1]+b[j-2] for h in range(len(b)-1): if(b[h]%5==0): print(b[h])
5.0 55.0 610.0 6765.0 75025.0 832040.0 9227465.0 102334155.0 1134903170.0 12586269025.0
#אלגוריתם שיטת הטרפז חישוב שטח
import matplotlib.pyplot as plt import numpy as np x=np.arange(0,1,0.001) y=x**2 myint=np.sum(((y[1:]+y[:-1])/2)*np.diff(x)) print(myint)
0.33233449950000005
#דוגמה לשאלה
import matplotlib.pyplot as plt import numpy as np x=np.arange(3,5,0.001) y=(x-1)*(x-3)*(x-5)*(x-7) myint=np.sum(((y[1:]+y[:-1])/2)*np.diff(x)) print(myint)
11.733322668668595
import matplotlib.pyplot as plt import numpy as np x=np.arange(2,8,0.001) y=x*(x**2-1)*(np.sin(x)-0.5)*(6*x-2) x2=np.arange(7,8,0.001) y2=x2*(x2**2-1)*(np.sin(x2)-0.5)*(6*x2-2) myint=np.sum(((y2[1:]+y2[:-1])/2)*np.diff(x2)) print(myint) plt.plot(x,y)
7439.919927740341
[<matplotlib.lines.Line2D at 0x7efc46d8db90>]
Image in a Jupyter notebook
import matplotlib.pyplot as plt import numpy as np x=np.arange(2,3,0.001) y=(x**3-1)*(np.sin(x)**2-1)*(4*x-4)-np.sin(x)+1 x2=np.arange(2,4,0.001) y2=(x2**3-1)*(np.sin(x2)**2-1)*(4*x2-4)-np.sin(x2)+1 myint=np.sum(((y2[1:]+y2[:-1])/2)*np.diff(x2)) print(myint) plt.plot(x,y)
-402.6129253735211
[<matplotlib.lines.Line2D at 0x7f9124628e90>]
Image in a Jupyter notebook
import matplotlib.pyplot as plt import numpy as np print(np.diff(np.diff([1,1,1,2,2,2])))
[ 0 1 -1 0]
#/////////////////////////////////////////////////////////////////////////////////////////////////////////////// #////////////////////////////////////////////////////////////////////////////////////////////////////////////// #////////////////////////////////////////////////////////////////////////////////////////////////////////////// #/////////////////////////////////////////////////////////////////////////////////////////////////////////////// #////////////////////////////////////////////////////////////////////////////////////////////////////////////// #////////////////////////////////////////////////////////////////////////////////////////////////////////////// #נגזרת
import matplotlib.pyplot as plt import numpy as np x=np.arange(0,2,0.001) y=x**3-9*x**2-23*x-15 y1=np.diff(y)/np.diff(x) plt.plot(x,y) plt.plot(x[1:],y1)
[<matplotlib.lines.Line2D at 0x7efc47936bd0>]
Image in a Jupyter notebook
#/////////////////////////////////////////////////////////////////////////////////////////////////////////////// #////////////////////////////////////////////////////////////////////////////////////////////////////////////// #////////////////////////////////////////////////////////////////////////////////////////////////////////////// #/////////////////////////////////////////////////////////////////////////////////////////////////////////////// #////////////////////////////////////////////////////////////////////////////////////////////////////////////// #////////////////////////////////////////////////////////////////////////////////////////////////////////////// #שורשים ונקודות קיצון
import matplotlib.pyplot as plt import numpy as np x=np.arange(0,3,0.01) y=x**3-4.5*x**2+5.75*x-1.875 z1=np.heaviside(y,0) z2=np.abs(np.diff(z1))#אפשר גם בלי זה פשוט הופך את המינוס לפלוס vec=np.argwhere(z2==1) print(x[vec]) plt.plot(x,y) plt.plot(x[1:],z2)
[[0.5 ] [1.49] [2.5 ]]
[<matplotlib.lines.Line2D at 0x7efc4754cf10>]
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import matplotlib.pyplot as plt import numpy as np x=np.arange(0.5,2.2,0.01) y=x**3-4.5*x**2+6.5*x-3 yroots=np.diff(np.heaviside(y,0)) roots=np.argwhere(yroots!=0) plt.plot(x,y) plt.plot(x[roots],y[roots],'go') print(x[roots])
[[0.99] [1.49] [2. ]]
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#מציאת נקודות קיצון
x=[-1,0,-1,-1] for j in range(2000): x=np.heaviside(np.heaviside(x,-1),-1) print(x)
[-1. 0. -1. -1.]
import matplotlib.pyplot as plt import numpy as np def find_roots(x,y): z=np.diff(np.heaviside(y,0)) return np.argwhere(z!=0) x=np.arange(0,6,0.01) y=x**5-25*x**4+230*x**3-950*x**2+1689*x-945 y1=np.diff(y)/np.diff(x) vec2=find_roots(x[1:],y1) plt.plot(x,y) plt.plot(x[vec2],y[vec2],'go')
[<matplotlib.lines.Line2D at 0x7efc4752d190>]
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#מציאת נק קיצון ושורשים
import matplotlib.pyplot as plt import numpy as np def find_roots(x,y): z=np.diff(np.heaviside(y,0)) return np.argwhere(z!=0) x=np.arange(0.5,2.2,0.01) y=x**3-4.5*x**2+6.5*x-3 yroots=np.diff(np.heaviside(y,0)) roots=np.argwhere(yroots!=0) y1=np.diff(y)/np.diff(x) vec2=find_roots(x[1:],y1) plt.plot(x,y) plt.plot(x[roots],y[roots],'go') plt.plot(x[vec2],y[vec2],'ro')
[<matplotlib.lines.Line2D at 0x7fe6ad2e26d0>]
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import matplotlib.pyplot as plt import numpy as np x=np.arange(-3,3,0.01) y=x*(x+1)*(x+2)*(x-1)*(x-2) yroots=np.diff(np.heaviside(y,0)) roots=np.argwhere(yroots!=0) plt.plot(x[roots],y[roots],'go') plt.plot(x,y) print(x[roots])
[[-2.00000000e+00] [-1.00000000e+00] [-6.39488462e-14] [ 1.00000000e+00] [ 2.00000000e+00]]
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import matplotlib.pyplot as plt import numpy as np def find_roots(x,y): z=np.diff(np.heaviside(y,0)) return np.argwhere(z!=0) x=np.arange(-3,3,0.01) y=x*(x+1)*(x+2)*(x-1)*(x-2) y1=np.diff(y)/np.diff(x) vec2=find_roots(x[1:],y1) plt.plot(x,y) plt.plot(x[vec2],y[vec2],'go')
[<matplotlib.lines.Line2D at 0x7f9117f74d50>]
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import matplotlib.pyplot as plt import numpy as np def find_roots(x,y): z=np.diff(np.heaviside(y,0)) return np.argwhere(z!=0) x=np.arange(-3,3,0.01) y=x*(x+1)*(x+2)*(x-1)*(x-2) g=np.diff(y)/np.diff(x) #g1=np.diff(g)/np.diff(x) yroots=np.diff(np.heaviside(g,0)) roots=np.argwhere(yroots!=0) plt.plot(x[roots],g[roots],'go') plt.plot(x[1:],g) #print(x[roots])
[<matplotlib.lines.Line2D at 0x7f9124091890>]
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import matplotlib.pyplot as plt import numpy as np def find_roots(x,y): z=np.diff(np.heaviside(y,0)) return np.argwhere(z!=0) x=np.arange(-3,3,0.01) y=x*(x+1)*(x+2)*(x-1)*(x-2) y1=np.diff(y)/np.diff(x) x2=x[1:] g=np.diff(y1)/np.diff(x2) vec2=find_roots(x2[1:],g) plt.plot(x[1:],y1) plt.plot(x[vec2],y1[vec2],'go')
[<matplotlib.lines.Line2D at 0x7f91179dfd90>]
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import matplotlib.pyplot as plt import numpy as np def find_roots(x,y1): z=np.diff(np.heaviside(y1,0)) return np.argwhere(z!=0) x=np.arange(-3,3,0.01) y=x*(x+1)*(x+2)*(x-1)*(x-2) y1=np.diff(y)/np.diff(x) #y11=np.diff(y1)/np.diff(x) vec2=find_roots(x[1:],y1) plt.plot(x[1:],y1) plt.plot(x[vec2],y1[vec2],'ro')
[<matplotlib.lines.Line2D at 0x7f9124bfb190>]
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print(np.diff(np.heaviside([1,1,1,2,2,2,1,1,1],0)))
[0. 0. 0. 0. 0. 0. 0. 0.]
import matplotlib.pyplot as plt import numpy as np x=np.arange(-3,3,0.01) y=x*(x+1)*(x+2)*(x-1)*(x-2) yroots=np.diff(np.heaviside(y,0)) roots=np.argwhere(yroots!=0) plt.plot(x[roots],y[roots],'go') plt.plot(x,y) print(x[roots])
[[-2.00000000e+00] [-1.00000000e+00] [-6.39488462e-14] [ 1.00000000e+00] [ 2.00000000e+00]]
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import matplotlib.pyplot as plt import numpy as np def mse(x): b=np.sum(x**2) c=b/len(x) print(c) mse(np.array([1,2,3,4,5]))
11.0
import matplotlib.pyplot as plt import numpy as np x=np.arange(2,3,0.001) y=(x**3-1)*(np.sin(x)**2-1)*(4*x-4)-np.sin(x)+1 x2=np.arange(2,4,0.001) y2=(x2**3-1)*(np.sin(x2)**2-1)*(4*x2-4)-np.sin(x2)+1 myint=np.abs(np.sum(((y2[1:]+y2[:-1])/2)*np.diff(x2))) print(myint) plt.plot(x,y)
402.6129253735211
[<matplotlib.lines.Line2D at 0x7f9117c462d0>]
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import matplotlib.pyplot as plt import numpy as np x=np.array([1,2,3]) y=x[1:]*x[:-1]-x[0] print(y)
[1 5]
import matplotlib.pyplot as plt import numpy as np def mse(x): b=np.sum(x**2) c=b/len(x) print(c) y1=np.array([1,2,3]) y2=np.array([3,4,5]) t=y1-y2 mse(t)
4.0
#/////////////////////////////////////////////////////////////////////////////////////////////////////////////// #////////////////////////////////////////////////////////////////////////////////////////////////////////////// #////////////////////////////////////////////////////////////////////////////////////////////////////////////// #/////////////////////////////////////////////////////////////////////////////////////////////////////////////// #////////////////////////////////////////////////////////////////////////////////////////////////////////////// #////////////////////////////////////////////////////////////////////////////////////////////////////////////// #טור טיילור
import matplotlib.pyplot as plt import numpy as np der=np.array([np.cos(0),-np.sin(0),-np.cos(0),np.sin(0)]) x= np.arange(0,0.1,0.01) y=x*0 for n in range(20): y=y+der[n%4]*(x**n)/np.math.factorial(n) plt.plot(x,y)
[<matplotlib.lines.Line2D at 0x7efc47499210>]
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import matplotlib.pyplot as plt import numpy as np der=np.array([np.sin(0),2*np.cos(0),-4*np.sin(0),-8*np.cos(0)]) x= np.arange(0.0001,12.56,0.01) y=x*0 plt.figure(figsize=(15,15)) for n in range(20): y=y+der[n%4]*(2*x**n)/np.math.factorial(n) plt.subplot(5,4,n+1) plt.plot(x,y)
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#/////////////////////////////////////////////////////////////////////////////////////////////////////////////// #////////////////////////////////////////////////////////////////////////////////////////////////////////////// #////////////////////////////////////////////////////////////////////////////////////////////////////////////// #/////////////////////////////////////////////////////////////////////////////////////////////////////////////// #////////////////////////////////////////////////////////////////////////////////////////////////////////////// #////////////////////////////////////////////////////////////////////////////////////////////////////////////// #משוואות דיפרנציליות
import matplotlib.pyplot as plt#y1=0.6y-1 import numpy as np h=5/100 x=np.linspace(0,5,100) y=x*0 y[0]=-6 for j in range (len(x)-1): y[j+1]=h*(0.6*y[j]-1)+y[j] plt.plot(x,y,'r')
[<matplotlib.lines.Line2D at 0x7efc46f89050>]
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import matplotlib.pyplot as plt#y1=0.6y-1 import numpy as np h=0.0001 x=np.arange(2,5,h) y=x*0 y[2]=2 y1=np.diff(y)/np.diff(x) for j in range (len(x)-1): y[j+1]=2*h*y[j]+y[j] plt.plot(x,y,'r') plt.plot(x[1:],y1,'r')
[<matplotlib.lines.Line2D at 0x7f9124c09c10>]
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import matplotlib.pyplot as plt#y1=0.6y-1 import numpy as np h=2/100 x=np.linspace(0,2,100) y=x*0 y[0]= 1 for j in range (len(x)-1): y[j+1]=h*(y[j]+np.cos(y[j]))+y[j] plt.plot(x,y,'r')
[<matplotlib.lines.Line2D at 0x7fe6acf3cfd0>]
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#/////////////////////////////////////////////////////////////////////////////////////////////////////////////// #////////////////////////////////////////////////////////////////////////////////////////////////////////////// #////////////////////////////////////////////////////////////////////////////////////////////////////////////// #/////////////////////////////////////////////////////////////////////////////////////////////////////////////// #////////////////////////////////////////////////////////////////////////////////////////////////////////////// #////////////////////////////////////////////////////////////////////////////////////////////////////////////// #וקטורים
#כפל מספר קדימה ועכשווי import numpy as np y=np.array([1,2,3,4,5]) b=y[1:]*y[:-1] print(b)
[ 2 6 12 20]
#כפל שלוש מספרים קדימה ועכשווי import numpy as np y=np.array([1,2,3,4,5,6,7,8,9,10,11,12]) b=y[3:]*y[:-3] print(b)
[ 4 10 18 28 40 54 70 88 108]
import numpy as np y=np.array([1,2,3,4,5,6,7,8,9,10,11,12]) b=np.zeros(y) b=y[2:]*y[1:-1]*y[:-2] print(b)
[ 6 24 60 120 210 336 504 720 990 1320]
import numpy as np x=np.array([1,2,3,4,5,6,7,8,9,10,11,12]) b=x[:-2]+x[2:] #d=np.sum(b) print(b)
[ 4 6 8 10 12 14 16 18 20 22]
import numpy as np x=np.array([1,2,3,4,5,6,7,8,9,10,11,12]) j=x[:-1] f=x[1:] u=x[:-2]+x[2:] print(j) print(f) print(u)
[ 1 2 3 4 5 6 7 8 9 10 11] [ 2 3 4 5 6 7 8 9 10 11 12] [ 4 6 8 10 12 14 16 18 20 22]
#/////////////////////////////////////////////////////////////////////////////////////////////////////////////// #////////////////////////////////////////////////////////////////////////////////////////////////////////////// #////////////////////////////////////////////////////////////////////////////////////////////////////////////// #/////////////////////////////////////////////////////////////////////////////////////////////////////////////// #////////////////////////////////////////////////////////////////////////////////////////////////////////////// #////////////////////////////////////////////////////////////////////////////////////////////////////////////// #ציורים
import matplotlib.pyplot as plt#זה עיגול עם פרצוף import numpy as np a= np.arange(0,6.29,0.01) plt.plot(2*np.cos(a),2*np.sin(a))
[<matplotlib.lines.Line2D at 0x7efc473df250>]
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import matplotlib.pyplot as plt#זה עיגול עם פרצוף import numpy as np #a= np.arange(0,6.29,0.01) #plt.plot(2*np.cos(a),2*np.sin(a)) #b=np.arange(0,6.29,0.01) #plt.plot(0.3*np.cos(b)-0.5,0.3*np.sin(b)+0.5) p=5 c=np.arange(0,p*6.29,0.01) r=c/np.max(c) plt.plot(r*(0.3*np.cos(c))+0.5,r*(0.3*np.sin(c))+0.5) #d=np.arange(0,3.14,0.01) #plt.plot(1*np.cos(d),-1*np.sin(d))
[<matplotlib.lines.Line2D at 0x7efc46ac7e10>]
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import matplotlib.pyplot as plt import numpy as np a= np.arange(0,29,0.01) for i in range(5): i=i/9.0 plt.plot(i*np.cos(a),i*np.sin(a))
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import matplotlib.pyplot as plt import numpy as np #a= np.arange(0,6.29,6.28/7) for i in range(3,8,1): a= np.arange(0,6.29,6.28/i) plt.plot(2*np.cos(a),2*np.sin(a))
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import matplotlib.pyplot as plt import numpy as np for i in range(20): a= np.arange(0,6.29,6.28/3) plt.plot(i*np.sin(a),i*np.cos(a))
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import matplotlib.pyplot as plt import numpy as np for i in range(20): a= np.arange(0,6.29,6.28/10) plt.plot(i*np.cos(a),i*np.sin(a))
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import matplotlib.pyplot as plt import numpy as np x=np.array([-1,-1,1,1,1,-1]) y=np.array([1,-1,-1,1,1,1]) for i in np.arange (10): plt.plot(x*i,y*i)
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import matplotlib.pyplot as plt import numpy as np a= np.arange(0,6.29,0.01) plt.plot(2*np.cos(a),2*np.sin(a)) x=np.array([-2,-2,2,2,2,-2]) y=np.array([2,-2,-2,2,2,2]) plt.plot(x,y)
[<matplotlib.lines.Line2D at 0x7f9124e47310>]
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x=np.array([-2,-2,2,2,2,-2]) y=np.array([2,-2,-2,2,2,2]) x2=np.array([-2,-2,1,-2]) y2=np.array([-2,-6,-6,-2]) plt.plot(x,y) plt.plot(x2,y2) a= np.arange(0,6.29,0.01) plt.plot(np.cos(a)-2,np.sin(a)-6)
[<matplotlib.lines.Line2D at 0x7f9124119d10>]
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import matplotlib.pyplot as plt import numpy as np b=np.zeros([51]) b[0]=0 b[1]=1 for j in range(2,50): b[j]=b[j-1]+b[j-2] for h in range(len(b)-1): if(b[h]%5==0): print(b[h])
0.0 5.0 55.0 610.0 6765.0 75025.0 832040.0 9227465.0 102334155.0 1134903170.0
import matplotlib.pyplot as plt import numpy as np a= np.arange(0,3.14,0.000001) plt.plot(np.cos(a),np.sin(a))
[<matplotlib.lines.Line2D at 0x7efc46eed450>]
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import matplotlib.pyplot as plt import numpy as np x=[-1,-1,1,1,0,-1] y=[2,0,0,2,6,2] plt.plot(x,y)
[<matplotlib.lines.Line2D at 0x7efc471ba0d0>]
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import matplotlib.pyplot as plt import numpy as np for i in range(20): a= np.arange(0,6.29,6.28/9) plt.plot(i*np.cos(a),i*np.sin(a))
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import matplotlib.pyplot as plt import numpy as np x=[-2,-1,-1,1,1,2,0,-2] y=[0,0,-3,-3,0,0,6,0] plt.plot(x,y)
[<matplotlib.lines.Line2D at 0x7f91246d1b90>]
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import matplotlib.pyplot as plt import numpy as np #t=np.arange(-1,1,0.001) x=[-2,-1,-1,1,1,2,0,-2] y=[0,0,-3,-3,0,0,6,0] x2=np.sin(x)*np.cos(x)*np.log(np.abs(x)) y2=np.abs(x)**0.4*np.cos(x) r=np.sqrt(x2**2+y**2) b=(40/360)*6.29 x1=x*np.cos(b)-y*np.sin(b) y1=x*np.sin(b)+y*np.cos(b) plt.plot(x1,y1)
[<matplotlib.lines.Line2D at 0x7f9117c72ed0>]
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