missed opportunity for cse in Function hierarchies

casadi / casadi

CasADi is a symbolic framework for numeric optimization implementing automatic differentiation in forward and reverse modes on sparse matrix-valued computational graphs. It supports self-contained C-code generation and interfaces state-of-the-art codes such as SUNDIALS, IPOPT etc. It can be used from C++, Python or Matlab/Octave.

GNU Lesser General Public License v3.0

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# Physical constants g = 9.81 # gravitation [m/s^2] L = 0.2 # pendulum length [m] m = 1 # pendulum mass [kg] mcart = 0.5 # cart mass [kg] T = 2.0 # control horizon [s] dt = T/N # length of 1 control interval [s] # System is composed of 4 states nx = 4 # Construct a CasADi function for the ODE right-hand side x = MX.sym('x',nx) # states: pos [m], theta [rad], dpos [m/s], dtheta [rad/s] u = MX.sym('u') # control force [N] ddpos = ((u+m*L*x[3]*x[3]*sin(x[1])-m*g*sin(x[1])*cos(x[1]))/(mcart+m-m*cos(x[1])*cos(x[1]))) rhs = vertcat(x[2],x[3],ddpos,g/L*sin(x[1])-cos(x[1])*ddpos) # Continuous system dynamics as a CasADi Function f = Function('f', [x, u],[rhs]) k1 = f(x, u) k2 = f(x + dt/2 * f(x, u), u) k3 = f(x + dt/2 * f(x + dt/2 * f(x, u), u), u) k4 = f(x + dt * f(x + dt/2 * f(x + dt/2 * f(x, u), u), u), u) x_next = x+dt/6*(k1 +2*k2 +2*k3 +k4) F = Function('F',[x,u],[x_next])

With #3183 implemented, this looks a lot better already. Let's keep this issue open and steer it new something new:

from casadi import *

N = 10

# Physical constants
g = 9.81    # gravitation [m/s^2]
L = 0.2     # pendulum length [m]
m = 1       # pendulum mass [kg]
mcart = 0.5 # cart mass [kg]

T = 2.0 # control horizon [s]

dt = T/N # length of 1 control interval [s]

# System is composed of 4 states
nx = 4

# Construct a CasADi function for the ODE right-hand side
x = MX.sym('x',nx) # states: pos [m], theta [rad], dpos [m/s], dtheta [rad/s]
u = MX.sym('u') # control force [N]
ddpos = ((u+m*L*x[3]*x[3]*sin(x[1])-m*g*sin(x[1])*cos(x[1]))/(mcart+m-m*cos(x[1])*cos(x[1])))
rhs = vertcat(x[2],x[3],ddpos,g/L*sin(x[1])-cos(x[1])*ddpos)

# Continuous system dynamics as a CasADi Function
f = Function('f', [x, u],[rhs])
f = f.expand()

k1 = f(x, u)
k2 = f(x + dt/2 * f(x, u), u)
k3 = f(x + dt/2 * f(x + dt/2 * f(x, u), u), u)
k4 = f(x + dt * f(x + dt/2 * f(x + dt/2 * f(x, u), u), u), u)
x_next = x+dt/6*(k1 +2*k2 +2*k3 +k4)

y = cse(x_next)

g = Function('g',[x,u],[y])

f_recovered =g.find_functions()[0]
f_recovered.disp(True) # Missed cse opportunities

casadi / casadi

missed opportunity for cse in Function hierarchies #3503