1_histo_vlad

def custom_histogram(data, bins, density = False):
    """
    A custom function to compute histogram data without using np.histogram, with an option to scale the histogram
    to represent a probability distribution.

    Parameters:
    - data: array-like, the input data.
    - bins: int, the number of bins.
    - density: bool, if True, scale the histogram counts to represent a probability distribution.

    Returns:
    - counts: array of the counts in each bin, or the probability densities if density=True.
    - bin_edges: array of the bin edges.
    """
    counts = [0] * bins # create array of zeros



    bin_edges = [0] * (bins + 1)

    # YOUR CODE HERE

    Min, Max = 1e9, -1e9
    for point in data:
        Min = min(Min, point)
        Max = max(Max, point)

    bin_width = (Max - Min) / bins # All bins have the same width

    bin_edges[0]= Min
    bin_edges[bins] = Max
    for i in range(1, bins): # For all bins beside the last one: l <= x < r (inclusive left, exclusive right)
        bin_edges[i] = bin_edges[i - 1] + bin_width

    for i in range(bins - 1):
        l, r = bin_edges[i], bin_edges[i + 1] # bounds of the bin
        cnt = 0
        for point in data:
            if l <= point < r:
                cnt += 1
        counts[i] = cnt

    i = bins - 1 # Edge case: last bin: inclusidve to the right
    l, r = bin_edges[i], bin_edges[i + 1] # bounds of the bin
    cnt = 0
    for point in data:
        if l <= point <= r:
            cnt += 1
    counts[i] = cnt

    if density: # Create histogram w/ density scaling
        area_histogram = sum([counts[i] * bin_width for i in range(bins)])
    else: # NO density scaling
        area_histogram = 1

    counts = [counts[i] / area_histogram for i in range(len(counts))]


    return counts, bin_edges

# Example usage with density=True
samples = np.random.randn(10000)  # Generate some data
n_bins = 10  # Number of bins

# Generate histogram data with density scaling
hist, bin_edges = custom_histogram(samples, n_bins, density = True)

# Generate reference histogram data with density scaling, using NumPy
reference_hist, reference_bin_edges = np.histogram(samples, bins = n_bins, density = True)

# Plotting the histogram as a probability distribution
fig, ax = plt.subplots(1, 2, figsize = (15, 7))
bin_centers = (np.diff(bin_edges) / 2 + bin_edges[:-1])
ax[0].bar(bin_centers, hist, width = np.diff(bin_centers)[0])
ax[0].set_xlabel('Value')
ax[0].set_ylabel('Probability Density')
ax[0].set_title('Custom Histogram as Probability Distribution')

# Checking the answer using plt.hist()
ax[1].hist(samples, bins = n_bins, density = True)
ax[1].set_xlabel('Value')
ax[1].set_ylabel('Probability Density')
ax[1].set_title('Actual Histogram as Probability Distribution')
plt.show()

assert len(hist) == len(reference_hist) and (np.abs(hist - reference_hist) < 1e-6).all() # histogram
assert len(bin_edges) == len(reference_bin_edges) and (np.abs(bin_edges - reference_bin_edges) < 1e-6).all() # bin edges