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I have a function for calculating probability like below:

def multinormpdf(x, mu, var): # calculate probability of multi Gaussian distribution

    k = len(x)

    det = np.linalg.det(var)

    inv = np.linalg.inv(var)

    denominator = math.sqrt(((2*math.pi)**k)*det)

    numerator = np.dot((x - mean).transpose(), inv)

    numerator = np.dot(numerator, (x - mean))

    numerator = math.exp(-0.5 * numerator)

    return numerator/denominator

and I have mean vector, covariance matrix and 2D numpy array for test

mu = np.array([100, 105, 42]) # mean vector

var = np.array([[100, 124, 11], # covariance matrix

               [124, 150, 44],

               [11, 44, 130]])



arr = np.array([[42, 234, 124],  # arr is 43923794 x 3 matrix

                [123, 222, 112],

                [42, 213, 11],

                ...(so many values about 40,000,000 rows),

                [23, 55, 251]])

I have to calculate for probability for each value, so I used this code

for i in arr:

    print(multinormpdf(i, mu, var)) # I already know mean_vector and variance_matrix

But it is so slow...

Is there any faster way to calculate probability?
Or is there any way to calculate probability for test arr at once like 'batch'?

You can vectorize your function easily:

import numpy as np



def fast_multinormpdf(x, mu, var):

    mu = np.asarray(mu)

    var = np.asarray(var)

    k = x.shape[-1]

    det = np.linalg.det(var)

    inv = np.linalg.inv(var)

    denominator = np.sqrt(((2*np.pi)**k)*det)

    numerator = np.dot((x - mu), inv)

    numerator = np.sum((x - mu) * numerator, axis=-1)

    numerator = np.exp(-0.5 * numerator)

    return numerator/denominator





arr = np.array([[42, 234, 124],

                [123, 222, 112],

                [42, 213, 11],

                [42, 213, 11]])



mu = [0, 0, 1]

var = [[1, 100, 100],

       [100, 1, 100],

       [100, 100, 1]]



slow_out = np.array([multinormpdf(i, mu, var) for i in arr])

fast_out = fast_multinormpdf(arr, mu, var)



np.allclose(slow_out, fast_out) # True

With fast_multinormpdf being about 1000 times faster than your unvectorized function:

long_arr = np.tile(arr, (10000, 1))



%timeit np.array([multinormpdf(i, mu, var) for i in long_arr])

# 2.12 s ± 93.4 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)

%timeit fast_multinormpdf(long_arr, mu, var)

# 2.56 ms ± 76.9 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)

You can try numba. Just decorate your function with @numba.vectorize.

@numba.vectorize

def multinormpdf(x, mu, var):

    # ...

    return caculated_probability



new_arr = multinormpdf(arr)

If your multinormpdf doesn't contains any unsupported functions, it can be accelerated. See here: https://numba.pydata.org/numba-doc/dev/reference/numpysupported.html

Moreover, you can use the experimental feature target='parallel' like this.

@numba.vectorize(target='parallel')