Universal Functions

import numpy as np

a = np.array([0.0, 0.5, 1.0, 1.5, 2.0])
b = np.array([1.0, 1.0, 1.0, 1.0, 1.0])

# 1) Element-wise math — all run in C, no Python loop
np.sqrt(a)
np.exp(a)
np.log(np.where(a > 0, a, 1))      # avoid log(0)
np.sin(a) ** 2 + np.cos(a) ** 2     # ≈ 1

# 2) Element-wise comparison + selection
np.maximum(a, b)                    # element-wise max
np.where(a > 1, a, 0)               # ternary: a if a>1 else 0
np.clip(a, 0.5, 1.5)                # squeeze to a range

# 3) Broadcasting works on every ufunc
m = np.arange(6).reshape(2, 3)
m + np.array([10, 20, 30])          # (2,3) + (3,) → (2,3)

# 4) Reductions — collapse an axis
a.sum()        a.mean()        a.std()
a.max()        a.argmax()      a.argmin()
m.sum(axis=0)   # column sums
m.mean(axis=1)  # row means

# 5) Accumulations — cumulative versions
np.cumsum([1, 2, 3])    # [1, 3, 6]
np.cumprod([1, 2, 3])   # [1, 2, 6]

# 6) Custom vectorisation — np.vectorize wraps a Python fn (still loop, but cleaner)
f = np.vectorize(lambda x: 'big' if x > 1 else 'small')
print(f(a))

# 7) The 'out=' trick — write in place, no extra allocation
result = np.empty_like(a)
np.multiply(a, 100, out=result)

import numpy as np
x = np.array([1.0, 4.0, 9.0])
print(np.sqrt(x))
print(np.exp(x))
print(np.log(x))