Regular simpsons rule in numerical methods












0












$begingroup$


In the following code I have implemented simpsons rule. It is working correctly for my first function but for my second function I am getting an error.



So,



Is it possible to do this code without using np.linspace? and if not how do I fix it so my second function works? 



def simps(f,a,b,N):

    dx = (b-a)/N

    x = np.linspace(a,b,N+1)

    y = f(x)

    S = dx/3 * np.sum(y[0:-1:2] + 4*y[1::2] + y[2::2])

    return S



print(simps(lambda x:x**2, 5, 10, 100))

print(simps(lambda x: sin(x),0,pi/2,100))


which gives the output:



291.6666666666667



---------------------------------------------------------------------------

TypeError                                 Traceback (most recent call last)

<ipython-input-143-40325ae966e9> in <module>()

  1 print(simps(lambda x:x**2, 5, 10, 100))

----> 2 print(simps(lambda x: sin(x),0,pi/2,100))



<ipython-input-142-860ce9822b06> in simps(f, a, b, N)

  3     dx = (b-a)/N

  4     x = np.linspace(a,b,N+1)

----> 5     y = f(x)

  6     S = dx/3 * np.sum(y[0:-1:2] + 4*y[1::2] + y[2::2])

  7     return S



<ipython-input-143-40325ae966e9> in <lambda>(x)

  1 print(simps(lambda x:x**2, 5, 10, 100))

---->2 print(simps(lambda x: sin(x),0,pi/2,100))



TypeError: only size-1 arrays can be converted to Python scalars





numerical-methods







share|cite|improve this question









$endgroup$

















    0












    $begingroup$


    In the following code I have implemented simpsons rule. It is working correctly for my first function but for my second function I am getting an error.



    So,



    Is it possible to do this code without using np.linspace? and if not how do I fix it so my second function works? 



    def simps(f,a,b,N):
    
    dx = (b-a)/N
    
    x = np.linspace(a,b,N+1)
    
    y = f(x)
    
    S = dx/3 * np.sum(y[0:-1:2] + 4*y[1::2] + y[2::2])
    
    return S
    

    
print(simps(lambda x:x**2, 5, 10, 100))
    
print(simps(lambda x: sin(x),0,pi/2,100))


    which gives the output:



    291.6666666666667
    

    
---------------------------------------------------------------------------
    
TypeError                                 Traceback (most recent call last)
    
<ipython-input-143-40325ae966e9> in <module>()
    
  1 print(simps(lambda x:x**2, 5, 10, 100))
    
----> 2 print(simps(lambda x: sin(x),0,pi/2,100))
    

    
<ipython-input-142-860ce9822b06> in simps(f, a, b, N)
    
  3     dx = (b-a)/N
    
  4     x = np.linspace(a,b,N+1)
    
----> 5     y = f(x)
    
  6     S = dx/3 * np.sum(y[0:-1:2] + 4*y[1::2] + y[2::2])
    
  7     return S
    

    
<ipython-input-143-40325ae966e9> in <lambda>(x)
    
  1 print(simps(lambda x:x**2, 5, 10, 100))
    
---->2 print(simps(lambda x: sin(x),0,pi/2,100))
    

    
TypeError: only size-1 arrays can be converted to Python scalars





    numerical-methods







    share|cite|improve this question









    $endgroup$















      0












      0








      0





      $begingroup$


      In the following code I have implemented simpsons rule. It is working correctly for my first function but for my second function I am getting an error.



      So,



      Is it possible to do this code without using np.linspace? and if not how do I fix it so my second function works? 



      def simps(f,a,b,N):
      
    dx = (b-a)/N
      
    x = np.linspace(a,b,N+1)
      
    y = f(x)
      
    S = dx/3 * np.sum(y[0:-1:2] + 4*y[1::2] + y[2::2])
      
    return S
      

      
print(simps(lambda x:x**2, 5, 10, 100))
      
print(simps(lambda x: sin(x),0,pi/2,100))


      which gives the output:



      291.6666666666667
      

      
---------------------------------------------------------------------------
      
TypeError                                 Traceback (most recent call last)
      
<ipython-input-143-40325ae966e9> in <module>()
      
  1 print(simps(lambda x:x**2, 5, 10, 100))
      
----> 2 print(simps(lambda x: sin(x),0,pi/2,100))
      

      
<ipython-input-142-860ce9822b06> in simps(f, a, b, N)
      
  3     dx = (b-a)/N
      
  4     x = np.linspace(a,b,N+1)
      
----> 5     y = f(x)
      
  6     S = dx/3 * np.sum(y[0:-1:2] + 4*y[1::2] + y[2::2])
      
  7     return S
      

      
<ipython-input-143-40325ae966e9> in <lambda>(x)
      
  1 print(simps(lambda x:x**2, 5, 10, 100))
      
---->2 print(simps(lambda x: sin(x),0,pi/2,100))
      

      
TypeError: only size-1 arrays can be converted to Python scalars





      numerical-methods







      share|cite|improve this question









      $endgroup$




      In the following code I have implemented simpsons rule. It is working correctly for my first function but for my second function I am getting an error.



      So,



      Is it possible to do this code without using np.linspace? and if not how do I fix it so my second function works? 



      def simps(f,a,b,N):
      
    dx = (b-a)/N
      
    x = np.linspace(a,b,N+1)
      
    y = f(x)
      
    S = dx/3 * np.sum(y[0:-1:2] + 4*y[1::2] + y[2::2])
      
    return S
      

      
print(simps(lambda x:x**2, 5, 10, 100))
      
print(simps(lambda x: sin(x),0,pi/2,100))


      which gives the output:



      291.6666666666667
      

      
---------------------------------------------------------------------------
      
TypeError                                 Traceback (most recent call last)
      
<ipython-input-143-40325ae966e9> in <module>()
      
  1 print(simps(lambda x:x**2, 5, 10, 100))
      
----> 2 print(simps(lambda x: sin(x),0,pi/2,100))
      

      
<ipython-input-142-860ce9822b06> in simps(f, a, b, N)
      
  3     dx = (b-a)/N
      
  4     x = np.linspace(a,b,N+1)
      
----> 5     y = f(x)
      
  6     S = dx/3 * np.sum(y[0:-1:2] + 4*y[1::2] + y[2::2])
      
  7     return S
      

      
<ipython-input-143-40325ae966e9> in <lambda>(x)
      
  1 print(simps(lambda x:x**2, 5, 10, 100))
      
---->2 print(simps(lambda x: sin(x),0,pi/2,100))
      

      
TypeError: only size-1 arrays can be converted to Python scalars





      numerical-methods




      numerical-methods






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      share|cite|improve this question











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      asked Dec 4 '18 at 2:04









      fr14fr14

      38318




      38318






















          1 Answer
          1






          active

          oldest

          votes


















          1












          $begingroup$

          linspace is a very useful function to generate uniformly separated points. Remember to use function from numpy to efficiently map operations on arrays



          import numpy as np
          
def simps(f,a,b,N):
          
    dx = (b-a)/N
          
    x = np.linspace(a,b,N+1)
          
    y = f(x)
          
    S = dx/3 * np.sum(y[0:-1:2] + 4*y[1::2] + y[2::2])
          
    return S
          

          
print(simps(lambda x:x**2, 5, 10, 100))
          
print(simps(lambda x: np.sin(x),0,np.pi/2,100))


          With result



          291.6666666666667
          
1.000000000338236





          share|cite|improve this answer









          $endgroup$













          • $begingroup$
            you have all the answers to my problems haha I appreciate it!
            $endgroup$
            – fr14
            Dec 4 '18 at 2:09










          • $begingroup$
            @fr14 Glad I could help
            $endgroup$
            – caverac
            Dec 4 '18 at 2:11











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          active

          oldest

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          1












          $begingroup$

          linspace is a very useful function to generate uniformly separated points. Remember to use function from numpy to efficiently map operations on arrays



          import numpy as np
          
def simps(f,a,b,N):
          
    dx = (b-a)/N
          
    x = np.linspace(a,b,N+1)
          
    y = f(x)
          
    S = dx/3 * np.sum(y[0:-1:2] + 4*y[1::2] + y[2::2])
          
    return S
          

          
print(simps(lambda x:x**2, 5, 10, 100))
          
print(simps(lambda x: np.sin(x),0,np.pi/2,100))


          With result



          291.6666666666667
          
1.000000000338236





          share|cite|improve this answer









          $endgroup$













          • $begingroup$
            you have all the answers to my problems haha I appreciate it!
            $endgroup$
            – fr14
            Dec 4 '18 at 2:09










          • $begingroup$
            @fr14 Glad I could help
            $endgroup$
            – caverac
            Dec 4 '18 at 2:11
















          1












          $begingroup$

          linspace is a very useful function to generate uniformly separated points. Remember to use function from numpy to efficiently map operations on arrays



          import numpy as np
          
def simps(f,a,b,N):
          
    dx = (b-a)/N
          
    x = np.linspace(a,b,N+1)
          
    y = f(x)
          
    S = dx/3 * np.sum(y[0:-1:2] + 4*y[1::2] + y[2::2])
          
    return S
          

          
print(simps(lambda x:x**2, 5, 10, 100))
          
print(simps(lambda x: np.sin(x),0,np.pi/2,100))


          With result



          291.6666666666667
          
1.000000000338236





          share|cite|improve this answer









          $endgroup$













          • $begingroup$
            you have all the answers to my problems haha I appreciate it!
            $endgroup$
            – fr14
            Dec 4 '18 at 2:09










          • $begingroup$
            @fr14 Glad I could help
            $endgroup$
            – caverac
            Dec 4 '18 at 2:11














          1












          1








          1





          $begingroup$

          linspace is a very useful function to generate uniformly separated points. Remember to use function from numpy to efficiently map operations on arrays



          import numpy as np
          
def simps(f,a,b,N):
          
    dx = (b-a)/N
          
    x = np.linspace(a,b,N+1)
          
    y = f(x)
          
    S = dx/3 * np.sum(y[0:-1:2] + 4*y[1::2] + y[2::2])
          
    return S
          

          
print(simps(lambda x:x**2, 5, 10, 100))
          
print(simps(lambda x: np.sin(x),0,np.pi/2,100))


          With result



          291.6666666666667
          
1.000000000338236





          share|cite|improve this answer









          $endgroup$



          linspace is a very useful function to generate uniformly separated points. Remember to use function from numpy to efficiently map operations on arrays



          import numpy as np
          
def simps(f,a,b,N):
          
    dx = (b-a)/N
          
    x = np.linspace(a,b,N+1)
          
    y = f(x)
          
    S = dx/3 * np.sum(y[0:-1:2] + 4*y[1::2] + y[2::2])
          
    return S
          

          
print(simps(lambda x:x**2, 5, 10, 100))
          
print(simps(lambda x: np.sin(x),0,np.pi/2,100))


          With result



          291.6666666666667
          
1.000000000338236






          share|cite|improve this answer












          share|cite|improve this answer



          share|cite|improve this answer










          answered Dec 4 '18 at 2:07









          caveraccaverac

          14.4k31130




          14.4k31130












          • $begingroup$
            you have all the answers to my problems haha I appreciate it!
            $endgroup$
            – fr14
            Dec 4 '18 at 2:09










          • $begingroup$
            @fr14 Glad I could help
            $endgroup$
            – caverac
            Dec 4 '18 at 2:11


















          • $begingroup$
            you have all the answers to my problems haha I appreciate it!
            $endgroup$
            – fr14
            Dec 4 '18 at 2:09










          • $begingroup$
            @fr14 Glad I could help
            $endgroup$
            – caverac
            Dec 4 '18 at 2:11
















          $begingroup$
          you have all the answers to my problems haha I appreciate it!
          $endgroup$
          – fr14
          Dec 4 '18 at 2:09




          $begingroup$
          you have all the answers to my problems haha I appreciate it!
          $endgroup$
          – fr14
          Dec 4 '18 at 2:09












          $begingroup$
          @fr14 Glad I could help
          $endgroup$
          – caverac
          Dec 4 '18 at 2:11




          $begingroup$
          @fr14 Glad I could help
          $endgroup$
          – caverac
          Dec 4 '18 at 2:11


















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