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trapz. Integrate along the given axis using the composite trapezoidal rule. If x is provided, the integration happens in sequence along its elements - they are not sorted.
Numpy Vectorization with the numpy.Numpy vectorize function takes in a python function (pyfunc) and returns a vectorized version of the function. The vectorized version of the function takes a sequence of objects or NumPy arrays as input and evaluates the Python function over each element of the input sequence.
Vectorized implementations (numpy) are much faster and more efficient as compared to for-loops. To really see HOW large the difference is, let's try some simple operations used in most machine learnign algorithms (especially deep learning).
The concept of vectorized operations on NumPy allows the use of more optimal and pre-compiled functions and mathematical operations on NumPy array objects and data sequences. The Output and Operations will speed up when compared to simple non-vectorized operations.
I have a vector 
and wish to make another vector of the same length whose k-th component is
The question is: how can we vectorize this for speed? NumPy vectorize() is actually a for loop, so it doesn't count.
Veedrac pointed out that "There is no way to apply a pure Python function to every element of a NumPy array without calling it that many times". Since I'm using NumPy functions rather than "pure Python" ones, I suppose it's possible to vectorize, but I don't know how.
import numpy as np
from scipy.integrate import quad
ws = 2 * np.random.random(10) - 1
n = len(ws)
integrals = np.empty(n)
def f(x, w):
if w < 0: return np.abs(x * w)
else: return np.exp(x) * w
def temp(x): return np.array([f(x, w) for w in ws]).sum()
def integrand(x, w): return f(x, w) * np.log(temp(x))
## Python for loop
for k in range(n):
integrals[k] = quad(integrand, -1, 1, args = ws[k])[0]
## NumPy vectorize
integrals = np.vectorize(quad)(integrand, -1, 1, args = ws)[0]
On a side note, is a Cython for loop always faster than NumPy vectorization?
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