human
I am working on the file "Intercept Distribution .ipynb".
The first task is:
Now let's define a pytry.Trial to let us explore the accuracy of the system.  As we vary the number of dimensions, we will see how well we can decode a constant function ($1$), linear value ($x_i$), squared value ($x_i^2$), and other quadratic combinatons ($x_i y_i$).
Can you write Python program for it?
 ... What is a the Python program you requested?
assistant
#Here is the Python program you requested.

class AreaInterceptTrial(pytry.Trial):
    def params(self):
        self.param('number of neurons per dimension', n_per_d=50)
        self.param('number of dimensions', d=1)
        self.param('use AreaIntercept distribution', use_area=False)
        
    def evaluate(self, p):
        model = nengo.Network(seed=p.seed)
        intercepts = nengo.dists.Uniform(-1, 1)
        if p.use_area:
            intercepts = AreaIntercepts(p.d, base=intercepts)
        n_neurons = p.n_per_d * p.d    
        with model:
            ens = nengo.Ensemble(n_neurons, p.d, intercepts=intercepts)

            def func_constant(x):
                return 1
            constant = nengo.Node(size_in=1)
            c_constant = nengo.Connection(ens, constant, function=func_constant)

            def func_linear(x):
                return x
            linear = nengo.Node(size_in=p.d)
            c_linear = nengo.Connection(ens, linear, function=func_linear)

            def func_square(x):
                return x**2
            square = nengo.Node(size_in=p.d)
            c_square = nengo.Connection(ens, square, function=func_square)

            def func_quad(x):
                r = []
                for i, xx in enumerate(x):
                    for j, yy in enumerate(x[i+1:]):
                        r.append(xx*yy)
                return r
            count = len(func_quad(np.zeros(p.d))) 
            if count > 0:
                quad = nengo.Node(size_in=count)
                c_quad = nengo.Connection(ens, quad, function=func_quad)
            else:
                c_quad = None

        sim = nengo.Simulator(model)
        return dict(
            constant = np.mean(sim.data[c_constant].solver_info['rmses']),
            linear = np.mean(sim.data[c_linear].solver_info['rmses']),
            square = np.mean(sim.data[c_square].solver_info['rmses']),
            quad = np.mean(sim.data[c_quad].solver_info['rmses']) if c_quad is not None else 0,
            )