I have system of differential equations. I must do the Jacobian Matrix, and get it to the method, to find the stability step by using 2/max(abs(eigenvalue)) = hst
I am trying to make it like this
x, y, z = symbols("x y z")
J = Function('J')(x, y, z)
#Setting the Jacobian matrix elements
f1_swpx_angle_ball_step1 = 'arctg(x)'
print(f1_swpx_angle_ball_step1)
f1_swpy_angle_ball_step1 = 'y/(x*x+1)'
print(f1_swpx_angle_ball_step1)
f1_swpz_angle_ball_step1 = '0'
print(f1_swpx_angle_ball_step1)
f2_swpx_angle_ball_step1 = '-3*arctg(x)'
print(f2_swpx_angle_ball_step1)
f2_swpy_angle_ball_step1 = '-3*(x+3.27)/(y*y+1)'
print(f2_swpy_angle_ball_step1)
f2_swpz_angle_ball_step1 = '0'
print(f2_swpy_angle_ball_step1)
f3_swpx_angle_ball_step1 = "1/(x*x+1)"
print(f2_swpy_angle_ball_step1)
f3_swpy_angle_ball_step1 = "0"
print(f2_swpy_angle_ball_step1)
f3_swpz_angle_ball_step1 = "(0)"
print(f3_swpz_angle_ball_step1)
#Setting the Jacobian matrix elements
F3_switchball_angle_step1 = Matrix([[f1_swpx_angle_ball_step1, f1_swpy_angle_ball_step1, f1_swpz_angle_ball_step1],
[f2_swpx_angle_ball_step1, f2_swpy_angle_ball_step1, f2_swpz_angle_ball_step1],
[f3_swpx_angle_ball_step1, f3_swpy_angle_ball_step1, f3_swpz_angle_ball_step1]])
getting some values from print
jaceiglist = list(JacobianF_falling_angle_ball_step1.eigenvals())
print(jaceiglist)
[-0.5*sqrt(1.0*arctg(5)**2 - 0.399230769230769*arctg(5) + 0.910556360946746) + 0.5*arctg(5) - 0.477115384615385, 0.5*sqrt(1.0*arctg(5)**2 - 0.399230769230769*arctg(5) + 0.910556360946746) + 0.5*arctg(5) - 0.477115384615385, 0]
#trying to make a method, that get differentiable variables, and substituting the values, will calculate the current Jacobi matrix and the stability step
def hstabilitygetting_angle_ball_step1(MatrixForYacobian, values):
print("Matrix Shape ",MatrixForYacobian.shape)
JacobianF_falling_angle_ball_step1 = Matrix(
MatrixForYacobian.subs([(x, values[0]), (y, values[1]), (z, values[2])]))
print("Jacobian Matrix shape after substitute", JacobianF_falling_angle_ball_step1.shape)
jaceiglist = list(JacobianF_falling_angle_ball_step1.eigenvals())
print("Eigenvalues",jaceiglist)
return 2 / (reduce(lambda x, y: abs(x) if abs(x) > abs(y) else abs(y), jaceiglist))
I can't make this list values to float
JacobianF_falling_angle_ball_step1 = sympy.Matrix(F3_switchball_angle_step1.subs([(x,5),(y,5),(z,0)]))
jaceiglist = list(JacobianF_falling_angle_ball_step1.eigenvals()) print(jaceiglist) eq=sympy.S(str(jaceiglist[0])) eq.subs(sympy.Function('arctg'), sympy.atan ) eq.subs(sympy.Function('sqrt'), math.sqrt)
print((eq).evalf(),'Value')
eq = ((eq).evalf())
getting
-0.5*(1.0*arctg(5)**2 - 0.399230769230769*arctg(5) + 0.910556360946746)**0.5 + 0.5*arctg(5) - 0.477115384615385
This is an expression, and I need to make it float, get max(abs(values list), to have stability step.
print(float((eq).evalf()),'Value') TypeError: Cannot convert expression to float
When expressions involving arctg were sympified, unknown functions of that name were created. You should replace them with atan:
>>> eq=S('-3*arctg(x)')
>>> eq.subs(Function('arctg'), atan)
-3*atan(x)
Maybe like this:
>>> jaceiglist = Tuple(*JacobianF_falling_angle_ball_step1.eigenvals())
... .subs(Function('arctg'), atan)