Matrix Multiplication and solve_ivp

Question

I try to simulate a LTI system using Python. The structure is xDot = Ax. I defined the system dynamics as a function I then call using solve_ivp . Calling the function itself works, but simulating the system results in the following error

ValueError: matmul: Input operand 1 does not have enough dimensions (has 0, gufunc core with signature (n?,k),(k,m?)->(n?,m?) requires 1)

for the line with the matrix multiplication in the system dynamics definition. Below is the code.

import numpy as np
from scipy import integrate
import matplotlib.pyplot as plt

# System Parameters
l = 1 # Pendulum length
g = 9.81 # gravity

# Initial Conditions
x0 = np.array([np.pi/2, 0])

# Simulation parameters
tStart = 0
tEnd = 4
t_span = [tStart, tEnd]
t = np.linspace(tStart,tEnd,10) # Simulation time

# System matrices
A = np.array([[0, 1],[-g/l, 0]])

def dynamics(x, t):
    xdot = -A@x
    return xdot

y = integrate.solve_ivp(dynamics, t_span, x0)

How do I need to adjust the system definition to make this work?

Answer 1

According to the docs the signature of the dynamics should be dynamics(t, x) with the scalar t as the first argument. This is how scipy.integrate.solve_ivp calls the given dynamics.

In your case, the error is caused by the fact that the matrix A is multiplied with the scalar t and the error message Input operand 1 does not have enough dimensions indicates that the matrix multiplication goes wrong.

The solution therefore is to switch the arguments to dynamics(t, x) . Inside dynamics you can ignore the parameter t as long as your matrix A is not time-dependent.