Mathematical functions
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
axisis not provided, compute the mean of the flattened array - If
axisis provided, compute the means across the axis.
- Compute the mean of
arr.std(axis=None)- Compute the standard deviation of
arr - If
axisis not provided, compute the standard deviation of the flattened array - If
axisis provided, compute the standard deviations across the axis.
- Compute the standard deviation of
arr.var(axis=None)- Compute the variance of
arr - If
axisis not provided, compute the variance of the flattened array - If
axisis provided, compute the variances across the axis.
- Compute the variance of
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).
Others
These functions can be applied to arrays in an elementwise fashion.
np.floor(arr): Floor functionnp.round(arr): Round functionnp.exp(arr): Exponential functionnp.sqrt(arr): Square rootnp.sin(arr): Sin functionnp.cos(arr): Cos function