How To Pick Points Under The Curve?

What I'm trying to do is make a gaussian function graph. then pick random numbers anywhere in a space say y=[0,1] (because its normalized) & x=[0,200]. Then, I want it to ignor

Solution 1:

The immediate cause of the error you're seeing is presumably this line (which should be identified by the full traceback -- it's generally quite helpful to post that):

Lower = numpy.where(foos[Upper]>(method[Upper]))

because the confusingly-named variable method is actually a set, as returned by your function method2. Actually, on second thought, foos is also a set, so it's probably failing on that first. Sets don't support indexing with something like the_set[index]; that's what the complaint about __getitem__ means.

I'm not entirely sure what all the parts of your code are intended to do; variable names like "foos" don't really help like that. So here's how I might do what you're trying to do:

# generate sample points
num_pts = 500
sample_xs = np.random.uniform(0, 200, size=num_pts)
sample_ys = np.random.uniform(0, 1, size=num_pts)

# define distribution
mean = 50
sigma = 10

# figure out "normalized" pdf vals at sample points
max_pdf = mlab.normpdf(mean, mean, sigma)
sample_pdf_vals = mlab.normpdf(sample_xs, mean, sigma) / max_pdf

# which ones are under the curve?
under_curve = sample_ys < sample_pdf_vals

# get pdf vals to plot
x = np.linspace(0, 200, 1000)
pdf_vals = mlab.normpdf(x, mean, sigma) / max_pdf

# plot the samples and the curve
colors = np.array(['cyan' if b else 'red' for b in under_curve])
scatter(sample_xs, sample_ys, c=colors)
plot(x, pdf_vals)

Of course, you should also realize that if you only want the points under the curve, this is equivalent to (but much less efficient than) just sampling from the normal distribution and then randomly selecting a y for each sample uniformly from 0 to the pdf value there:

sample_xs = np.random.normal(mean, sigma, size=num_pts)
max_pdf = mlab.normpdf(mean, mean, sigma)
sample_pdf_vals = mlab.normpdf(sample_xs, mean, sigma) / max_pdf
sample_ys = np.array([np.random.uniform(0, pdf_val) for pdf_val in sample_pdf_vals])

Solution 2:

It's hard to read your code.. Anyway, you can't access a set using [], that is, foos[Upper], method[Upper], etc are all illegal. I don't see why you convert foo, x into set. In addition, for a point produced by method2, say (x0, y0), it is very likely that x0 is not present in x.

I'm not familiar with numpy, but this is what I'll do for the purpose you specified:

def undercurve(size):
    result = []
    for i in xrange(size):
        x = random()
        y = random()
        if y < scipy.stats.norm(0, 200).pdf(x): # here's the 'undercurve'
        result.append((x, y))
    return results