Python Programming

NumPy provides many mathematical functions that can be used in a vectorised manner.

Min and Max

You can use the ndarray methods .max() or .min() to compute the maximum/minimum values in an array.

np.max(arr) and np.min(arr) also works.

a = np.array([[4,7,3],[1,2,5]])

# Compute overall min/max
print(a.min())  ## 1
print(a.max())  ## 7

# Compute min/max across rows
print(a.min(axis=0))  ## [1 2 3]
print(a.max(axis=0))  ## [4 7 5]

# Compute min/max across columns
print(a.min(axis=1))  ## [3 1]
print(a.max(axis=1))  ## [7 5]

To get the indices for the min/max values, use .argmax() and .argmin().

a = np.array([[4,7,3],[1,2,5]])

# Get (flattened) indices of overall min/max
print(a.argmin())  ## 3 (index of "1")
print(a.argmax())  ## 1 (index of "7")

# Get row indices of min/max across rows
print(a.argmin(axis=0))  ## [1 1 0]
print(a.argmax(axis=0))  ## [0 0 1]

# Get column indices of min/max across columns
print(a.argmin(axis=1))  ## [2 0]
print(a.argmax(axis=1))  ## [1 2]

Statistical methods for arrays

• arr.mean(axis=None)
  • Compute the mean of arr.
  • If axis is not provided, compute the mean of the flattened array
  • If axis is provided, compute the means across the axis.
• arr.std(axis=None)
  • Compute the standard deviation of arr
  • If axis is not provided, compute the standard deviation of the flattened array
  • If axis is provided, compute the standard deviations across the axis.
• arr.var(axis=None)
  • Compute the variance of arr
  • If axis is not provided, compute the variance of the flattened array
  • If axis is provided, compute the variances across the axis.

Sum and Cumulative Sum

Like .min() and .max(), .sum() can be used to sum up a flattened array, or compute the sum across a specified axis. Explore the output for below yourself and try to make sense of it! Draw out the 3D array and the axis direction on a piece of paper if you are confused.

a = np.arange(24).reshape((2,3,4))
print(a)
## [[[ 0  1  2  3]
##   [ 4  5  6  7]
##   [ 8  9 10 11]]
##
##  [[12 13 14 15]
##   [16 17 18 19]
##   [20 21 22 23]]]

print(a.sum())
## 276

print(a.sum(axis=0))
## [[12 14 16 18]
##  [20 22 24 26]
##  [28 30 32 34]]

print(a.sum(axis=1))
## [[12 15 18 21]
##  [48 51 54 57]]

print(a.sum(axis=2))
## [[ 6 22 38]
##  [54 70 86]]

.cumsum() computes the cumulative sum of an array.

a = np.array([1, 2, 3, 4, 5])
print(a.cumsum())  ### [1 3 6 10 15]

Like .sum(), you can compute the cumulative sum across a specific axis.

a = np.array([[1,2,3], [4,5,6]])
print(a)
## [[1 2 3]
##  [4 5 6]]

print(a.cumsum())
## [ 1  3  6 10 15 21]
 
print(a.cumsum(axis=0))
## [[1 2 3]
##  [5 7 9]]

print(a.cumsum(axis=1))
## [[ 1  3  6]
##  [ 4  9 15]]

Product and Cumulative Product

Just like .sum() and .cumsum(), .prod() amd .cumsum() computes the product and cumulative product of an array respectively.

I will not provide examples for these as they are essentially similar to the above (just multiply instead of adding). And frankly, are you bored reading these just as I am bored writing these by now?🥱

Others

These functions can be applied to arrays in an elementwise fashion.

• np.floor(arr): Floor function
• np.round(arr): Round function
• np.exp(arr): Exponential function
• np.sqrt(arr): Square root
• np.sin(arr): Sin function
• np.cos(arr): Cos function