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| | === sympy === | | === sympy === |
| | <source lang="python"> | | <source lang="python"> |
| − | from sympy import *
| + | as |
| − |
| |
| − | # In contrast to other Computer Algebra Systems, in SymPy you have to declare symbolic variables explicitly:
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| − | R1 = Symbol('R1')
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| − | theta = Symbol('theta')
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| − | R1rho_p = Symbol('R1rho_p')
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| − | phi_ex = Symbol('phi_ex')
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| − | kex = Symbol('kex')
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| − | we = Symbol('we')
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| − | | |
| − | # Define function
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| − | f = R1 * cos(theta)**2 + (R1rho_p + ( (phi_ex * kex) / (kex**2 + we**2) ) ) * sin(theta)**2
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| − | | |
| − | print("Now calculate the Jacobian. The partial derivative matrix.\n")
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| − | print("Jacobian is m rows with function derivatives and n columns of parameters.")
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| − | | |
| − | d_f_d_R1 = diff(f, R1)
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| − | d_f_d_theta = diff(f, theta)
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| − | d_f_d_R1rho_p = diff(f, R1rho_p)
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| − | d_f_d_phi_ex = diff(f, phi_ex)
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| − | d_f_d_kex = diff(f, kex)
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| − | d_f_d_we = diff(f, we)
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| − | | |
| − | print("""Form the Jacobian matrix by:
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| − | ------------------------------------------------------------------------------
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| − | from numpy import array, cos, sin, pi, transpose
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| − | | |
| − | R1 = 1.1
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| − | theta = pi / 4
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| − | R1rho_p = 10.
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| − | phi_ex = 1100.
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| − | kex = 2200.
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| − | we = 3300.
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| − | | |
| − | d_f_d_R1 = %s
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| − | d_f_d_theta = %s
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| − | d_f_d_R1rho_p = %s
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| − | d_f_d_phi_ex = %s
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| − | d_f_d_kex = %s
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| − | d_f_d_we = %s
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| − | jacobian_matrix = transpose(array( [d_f_d_R1 , d_f_d_theta, d_f_d_R1rho_p, d_f_d_phi_ex, d_f_d_kex, d_f_d_we] ) )
| |
| − | | |
| − | print jacobian_matrix
| |
| − | ------------------------------------------------------------------------------
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| − | """ % (d_f_d_R1, d_f_d_theta, d_f_d_R1rho_p, d_f_d_phi_ex, d_f_d_kex, d_f_d_we) )
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| − | | |
| − | #### Method 2
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| − | # http://docs.sympy.org/0.7.2/modules/matrices/matrices.html
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| − | | |
| − | # The vectorial function.
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| − | X = Matrix([R1 * cos(theta)**2 + (R1rho_p + ( (phi_ex * kex) / (kex**2 + we**2) ) ) * sin(theta)**2])
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| − | # What to derive for.
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| − | Y = Matrix([R1, theta, R1rho_p, phi_ex, kex, we])
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| − | | |
| − | # Make the Jacobian
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| − | Jacobian = X.jacobian(Y)
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| − | | |
| − | jac_string = str(Jacobian)
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| − | jac_string_arr = jac_string.replace("Matrix", "array")
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| − | | |
| − | print("""Form the Jacobian matrix by:
| |
| − | ------------------------------------------------------------------------------
| |
| − | from numpy import array, cos, sin, pi, transpose
| |
| − | | |
| − | R1 = 1.1
| |
| − | theta = pi / 4
| |
| − | R1rho_p = 10.
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| − | phi_ex = 1100.
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| − | kex = 2200.
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| − | we = 3300.
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| − | | |
| − | jacobian_matrix_2 = %s
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| − | | |
| − | print jacobian_matrix_2
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| − | ------------------------------------------------------------------------------
| |
| − | """ % (jac_string_arr) )
| |
| | </source> | | </source> |
| | | | |
