CONTENTS
3
8.1.5 Create 2D matrix (columns first, row output) . . . . . . . . . . . . . . . . . 15
8.1.6 Create 2D matrix (rows first, column output) . . . . . . . . . . . . . . . . . 16
8.1.7 Create 2D matrix (rows first, row output) . . . . . . . . . . . . . . . . . . . 16
8.2 Stacking and unstacking pages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
9 Rotating matrices and arrays 17
9.1 Rotating 2D matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
9.2 Rotating ND arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
9.3 Rotating ND arrays around an arbitrary axis . . . . . . . . . . . . . . . . . . . . . . 18
9.4 Block-rotating 2D matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
9.4.1 “Inner” vs “outer” block rotation . . . . . . . . . . . . . . . . . . . . . . . . 19
9.4.2 “Inner” block rotation 90 degrees counterclockwise . . . . . . . . . . . . . . 20
9.4.3 “Inner” block rotation 180 degrees . . . . . . . . . . . . . . . . . . . . . . . 21
9.4.4 “Inner” block rotation 90 degrees clockwise . . . . . . . . . . . . . . . . . . 22
9.4.5 “Outer” block rotation 90 degrees counterclockwise . . . . . . . . . . . . . 23
9.4.6 “Outer” block rotation 180 degrees . . . . . . . . . . . . . . . . . . . . . . 24
9.4.7 “Outer” block rotation 90 degrees clockwise . . . . . . . . . . . . . . . . . 25
9.5 Blocktransposing a 2D matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
9.5.1 “Inner” blocktransposing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
9.5.2 “Outer” blocktransposing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
10 Multiply arrays 26
10.1 Multiply each 2D slice with the same matrix (element-by-element) . . . . . . . . . . 26
10.2 Multiply each 2D slice with the same matrix (left) . . . . . . . . . . . . . . . . . . . 26
10.3 Multiply each 2D slice with the same matrix (right) . . . . . . . . . . . . . . . . . . 26
10.4 Multiply matrix with every element of a vector . . . . . . . . . . . . . . . . . . . . 27
10.5 Multiply each 2D slice with corresponding element of a vector . . . . . . . . . . . . 28
10.6 Outer product of all rows in a matrix . . . . . . . . . . . . . . . . . . . . . . . . . . 28
10.7 Keeping only diagonal elements of multiplication . . . . . . . . . . . . . . . . . . . 28
10.8 Products involving the Kronecker product . . . . . . . . . . . . . . . . . . . . . . . 29
11 Divide arrays 29
11.1 Divide each 2D slice with the same matrix (element-by-element) . . . . . . . . . . . 29
11.2 Divide each 2D slice with the same matrix (left) . . . . . . . . . . . . . . . . . . . . 29
11.3 Divide each 2D slice with the same matrix (right) . . . . . . . . . . . . . . . . . . . 30
12 Calculating distances 30
12.1 Euclidean distance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
12.2 Distance between two points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
12.3 Euclidean distance vector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
12.4 Euclidean distance matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
12.5 Special case when both matrices are identical . . . . . . . . . . . . . . . . . . . . . 31
12.6 Mahalanobis distance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
13 Statistics, probability and combinatorics 33
13.1 Discrete uniform sampling with replacement . . . . . . . . . . . . . . . . . . . . . . 33
13.2 Discrete weighted sampling with replacement . . . . . . . . . . . . . . . . . . . . . 33
13.3 Discrete uniform sampling without replacement . . . . . . . . . . . . . . . . . . . . 33
13.4 Combinations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
13.4.1 Counting combinations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
