Difference between revisions of "DPL94 derivatives"

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

Revision as of 09:30, 1 September 2014

Jacobian

sympy

as

output

output

from numpy import array, cos, sin, pi, transpose

R1 = 1.1
theta = pi / 4
R1rho_p = 10.
phi_ex = 1100.
kex = 2200.
we = 3300.

d_f_d_R1 = cos(theta)**2
d_f_d_theta = -2*R1*sin(theta)*cos(theta) + 2*(R1rho_p + kex*phi_ex/(kex**2 + we**2))*sin(theta)*cos(theta)
d_f_d_R1rho_p = sin(theta)**2
d_f_d_phi_ex = kex*sin(theta)**2/(kex**2 + we**2)
d_f_d_kex = (-2*kex**2*phi_ex/(kex**2 + we**2)**2 + phi_ex/(kex**2 + we**2))*sin(theta)**2
d_f_d_we = -2*kex*phi_ex*we*sin(theta)**2/(kex**2 + we**2)**2
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