Sympy Simplify eliminate imaginary numbers











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I'm trying to get the cosine similarity between convolved vectors. Because I'm using fast fourier transform, I am using complex numbers. In the calculation of the cosine similarity, the final value returned should be a real number. However, my output is including imaginary parts: 1.0*(-1.53283653303955 + 6.08703605256546e-17*I)/(sqrt(5.69974497311137 + 5.55111512312578e-17*I)*sqrt(14.2393958011541 - 3.46944695195361e-18*I))



The imaginary portions should be zero (which they effectively are), but I can't get sympy to set the imaginary portions to zero so that I can get a real value as my output.



I've included the code that leads to the output. It's as pared down as I can accomplish.



# import statements
from sympy import *
from numpy import dot,array,random

# sympy initialization
a, b, c, d, e, f, g, h, i, j, k, l = symbols('a b c d e f g h i j k l')

# vector initialization
alpha = [a, b, c, d];
beta = [e, f, g, h];
gamma = [i, j, k, l];

# discrete fourier initialization (dft/idft)
W = [[1, 1, 1, 1], [1, -1j, -1, 1j], [1, -1, 1, -1], [1, 1j, -1, -1j]];
WH = [[1, 1, 1, 1], [1, 1j, -1, -1j], [1, -1, 1, -1], [1, -1j, -1, 1j]];

# i/fft initialization, cosine similarity
def fft(a):
return dot(a,W)
def ifft(a):
return dot(a,WH)/4.0
def cosineSimilarity(a,b):
return dot(a,b)/(sqrt(dot(a,a)) * sqrt(dot(b,b)))

# x&y initialization
x = ifft(fft(alpha)*fft(beta)) + ifft(fft(alpha)*fft(gamma));
y = ifft(fft(alpha)*fft(beta)/fft(gamma)) +
ifft(fft(alpha)*fft(gamma)/fft(beta));

# determine cosine similarity between x&y
random.seed(39843)
current = random.rand(12)
mymap = list(zip(params,current))
print(simplify(diff(cosineSimilarity(x, y), a).subs(mymap)))









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    I'm trying to get the cosine similarity between convolved vectors. Because I'm using fast fourier transform, I am using complex numbers. In the calculation of the cosine similarity, the final value returned should be a real number. However, my output is including imaginary parts: 1.0*(-1.53283653303955 + 6.08703605256546e-17*I)/(sqrt(5.69974497311137 + 5.55111512312578e-17*I)*sqrt(14.2393958011541 - 3.46944695195361e-18*I))



    The imaginary portions should be zero (which they effectively are), but I can't get sympy to set the imaginary portions to zero so that I can get a real value as my output.



    I've included the code that leads to the output. It's as pared down as I can accomplish.



    # import statements
    from sympy import *
    from numpy import dot,array,random

    # sympy initialization
    a, b, c, d, e, f, g, h, i, j, k, l = symbols('a b c d e f g h i j k l')

    # vector initialization
    alpha = [a, b, c, d];
    beta = [e, f, g, h];
    gamma = [i, j, k, l];

    # discrete fourier initialization (dft/idft)
    W = [[1, 1, 1, 1], [1, -1j, -1, 1j], [1, -1, 1, -1], [1, 1j, -1, -1j]];
    WH = [[1, 1, 1, 1], [1, 1j, -1, -1j], [1, -1, 1, -1], [1, -1j, -1, 1j]];

    # i/fft initialization, cosine similarity
    def fft(a):
    return dot(a,W)
    def ifft(a):
    return dot(a,WH)/4.0
    def cosineSimilarity(a,b):
    return dot(a,b)/(sqrt(dot(a,a)) * sqrt(dot(b,b)))

    # x&y initialization
    x = ifft(fft(alpha)*fft(beta)) + ifft(fft(alpha)*fft(gamma));
    y = ifft(fft(alpha)*fft(beta)/fft(gamma)) +
    ifft(fft(alpha)*fft(gamma)/fft(beta));

    # determine cosine similarity between x&y
    random.seed(39843)
    current = random.rand(12)
    mymap = list(zip(params,current))
    print(simplify(diff(cosineSimilarity(x, y), a).subs(mymap)))









    share|improve this question
























      up vote
      1
      down vote

      favorite









      up vote
      1
      down vote

      favorite











      I'm trying to get the cosine similarity between convolved vectors. Because I'm using fast fourier transform, I am using complex numbers. In the calculation of the cosine similarity, the final value returned should be a real number. However, my output is including imaginary parts: 1.0*(-1.53283653303955 + 6.08703605256546e-17*I)/(sqrt(5.69974497311137 + 5.55111512312578e-17*I)*sqrt(14.2393958011541 - 3.46944695195361e-18*I))



      The imaginary portions should be zero (which they effectively are), but I can't get sympy to set the imaginary portions to zero so that I can get a real value as my output.



      I've included the code that leads to the output. It's as pared down as I can accomplish.



      # import statements
      from sympy import *
      from numpy import dot,array,random

      # sympy initialization
      a, b, c, d, e, f, g, h, i, j, k, l = symbols('a b c d e f g h i j k l')

      # vector initialization
      alpha = [a, b, c, d];
      beta = [e, f, g, h];
      gamma = [i, j, k, l];

      # discrete fourier initialization (dft/idft)
      W = [[1, 1, 1, 1], [1, -1j, -1, 1j], [1, -1, 1, -1], [1, 1j, -1, -1j]];
      WH = [[1, 1, 1, 1], [1, 1j, -1, -1j], [1, -1, 1, -1], [1, -1j, -1, 1j]];

      # i/fft initialization, cosine similarity
      def fft(a):
      return dot(a,W)
      def ifft(a):
      return dot(a,WH)/4.0
      def cosineSimilarity(a,b):
      return dot(a,b)/(sqrt(dot(a,a)) * sqrt(dot(b,b)))

      # x&y initialization
      x = ifft(fft(alpha)*fft(beta)) + ifft(fft(alpha)*fft(gamma));
      y = ifft(fft(alpha)*fft(beta)/fft(gamma)) +
      ifft(fft(alpha)*fft(gamma)/fft(beta));

      # determine cosine similarity between x&y
      random.seed(39843)
      current = random.rand(12)
      mymap = list(zip(params,current))
      print(simplify(diff(cosineSimilarity(x, y), a).subs(mymap)))









      share|improve this question













      I'm trying to get the cosine similarity between convolved vectors. Because I'm using fast fourier transform, I am using complex numbers. In the calculation of the cosine similarity, the final value returned should be a real number. However, my output is including imaginary parts: 1.0*(-1.53283653303955 + 6.08703605256546e-17*I)/(sqrt(5.69974497311137 + 5.55111512312578e-17*I)*sqrt(14.2393958011541 - 3.46944695195361e-18*I))



      The imaginary portions should be zero (which they effectively are), but I can't get sympy to set the imaginary portions to zero so that I can get a real value as my output.



      I've included the code that leads to the output. It's as pared down as I can accomplish.



      # import statements
      from sympy import *
      from numpy import dot,array,random

      # sympy initialization
      a, b, c, d, e, f, g, h, i, j, k, l = symbols('a b c d e f g h i j k l')

      # vector initialization
      alpha = [a, b, c, d];
      beta = [e, f, g, h];
      gamma = [i, j, k, l];

      # discrete fourier initialization (dft/idft)
      W = [[1, 1, 1, 1], [1, -1j, -1, 1j], [1, -1, 1, -1], [1, 1j, -1, -1j]];
      WH = [[1, 1, 1, 1], [1, 1j, -1, -1j], [1, -1, 1, -1], [1, -1j, -1, 1j]];

      # i/fft initialization, cosine similarity
      def fft(a):
      return dot(a,W)
      def ifft(a):
      return dot(a,WH)/4.0
      def cosineSimilarity(a,b):
      return dot(a,b)/(sqrt(dot(a,a)) * sqrt(dot(b,b)))

      # x&y initialization
      x = ifft(fft(alpha)*fft(beta)) + ifft(fft(alpha)*fft(gamma));
      y = ifft(fft(alpha)*fft(beta)/fft(gamma)) +
      ifft(fft(alpha)*fft(gamma)/fft(beta));

      # determine cosine similarity between x&y
      random.seed(39843)
      current = random.rand(12)
      mymap = list(zip(params,current))
      print(simplify(diff(cosineSimilarity(x, y), a).subs(mymap)))






      python fft sympy complex-numbers






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      asked Nov 21 at 22:45









      masterccioli

      82




      82
























          1 Answer
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          If you know the imaginary part is 0 then you can just take the real part of the evaluation, else use "chop=True" with caution to discard relatively small imaginary parts:



          >>> q
          (-1.53283653303955 + 6.08703605256546e-17*I)/(sqrt(5.69974497311137 +
          5.55111512312578e-17*I)*sqrt(14.2393958011541 - 3.46944695195361e-18*I))
          >>> q.n(chop=True)
          -0.170146237401735
          >>> re(q.n())
          -0.170146237401735





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            1 Answer
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            active

            oldest

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            1 Answer
            1






            active

            oldest

            votes









            active

            oldest

            votes






            active

            oldest

            votes








            up vote
            0
            down vote



            accepted










            If you know the imaginary part is 0 then you can just take the real part of the evaluation, else use "chop=True" with caution to discard relatively small imaginary parts:



            >>> q
            (-1.53283653303955 + 6.08703605256546e-17*I)/(sqrt(5.69974497311137 +
            5.55111512312578e-17*I)*sqrt(14.2393958011541 - 3.46944695195361e-18*I))
            >>> q.n(chop=True)
            -0.170146237401735
            >>> re(q.n())
            -0.170146237401735





            share|improve this answer

























              up vote
              0
              down vote



              accepted










              If you know the imaginary part is 0 then you can just take the real part of the evaluation, else use "chop=True" with caution to discard relatively small imaginary parts:



              >>> q
              (-1.53283653303955 + 6.08703605256546e-17*I)/(sqrt(5.69974497311137 +
              5.55111512312578e-17*I)*sqrt(14.2393958011541 - 3.46944695195361e-18*I))
              >>> q.n(chop=True)
              -0.170146237401735
              >>> re(q.n())
              -0.170146237401735





              share|improve this answer























                up vote
                0
                down vote



                accepted







                up vote
                0
                down vote



                accepted






                If you know the imaginary part is 0 then you can just take the real part of the evaluation, else use "chop=True" with caution to discard relatively small imaginary parts:



                >>> q
                (-1.53283653303955 + 6.08703605256546e-17*I)/(sqrt(5.69974497311137 +
                5.55111512312578e-17*I)*sqrt(14.2393958011541 - 3.46944695195361e-18*I))
                >>> q.n(chop=True)
                -0.170146237401735
                >>> re(q.n())
                -0.170146237401735





                share|improve this answer












                If you know the imaginary part is 0 then you can just take the real part of the evaluation, else use "chop=True" with caution to discard relatively small imaginary parts:



                >>> q
                (-1.53283653303955 + 6.08703605256546e-17*I)/(sqrt(5.69974497311137 +
                5.55111512312578e-17*I)*sqrt(14.2393958011541 - 3.46944695195361e-18*I))
                >>> q.n(chop=True)
                -0.170146237401735
                >>> re(q.n())
                -0.170146237401735






                share|improve this answer












                share|improve this answer



                share|improve this answer










                answered Nov 22 at 13:31









                smichr

                3,368710




                3,368710






























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