Arrays in R Davis Vaughan https://speakerdeck.com/davisvaughan

x matrix(1:3) y matrix(4:6) x [,1] [1,] 1 [2,] 2 [3,] 3 y [,1] [1,] 4 [2,] 5 [3,] 6 x + y [,1] [1,] 5 [2,] 7 [3,] 9 Arithmetic with matrices 2 / 13

x matrix(1:3) y matrix(4:6) x [,1] [1,] 1 [2,] 2 [3,] 3 y [,1] [1,] 4 [2,] 5 [3,] 6 x + y [,1] [1,] 5 [2,] 7 [3,] 9 Arithmetic with matrices Well duh 2 / 13

# 2 is implicitely extended to 3 1 dimension x + 2 [,1] [1,] 3 [2,] 4 [3,] 5 matrix(2, nrow = 3) [,1] [1,] 2 [2,] 2 [3,] 2 x + matrix(2, nrow = 3) [,1] [1,] 3 [2,] 4 [3,] 5 Arithmetic with scalars 3 / 13

x [,1] [1,] 1 [2,] 2 [3,] 3 two matrix(2) two [,1] [1,] 2 # What do you expect? x + two Arithmetic with scalars 4 / 13

x [,1] [1,] 1 [2,] 2 [3,] 3 two matrix(2) two [,1] [1,] 2 # What do you expect? x + two Error in x + two : non conformable arrays Arithmetic with scalars 4 / 13

x [,1] [1,] 1 [2,] 2 [3,] 3 two matrix(2) two [,1] [1,] 2 # What do you expect? x + two Error in x + two : non conformable arrays Arithmetic with scalars 4 / 13

z matrix(1:6, ncol = 2) z [,1] [,2] [1,] 1 4 [2,] 2 5 [3,] 3 6 x [,1] [1,] 1 [2,] 2 [3,] 3 x + z Arithmetic with matrices (2) 5 / 13

z matrix(1:6, ncol = 2) z [,1] [,2] [1,] 1 4 [2,] 2 5 [3,] 3 6 x [,1] [1,] 1 [2,] 2 [3,] 3 x + z Error in x + z: non conformable arrays Arithmetic with matrices (2) 5 / 13

Proposal These are valid and intuitive operations. There is a name for this. Broadcasting. Tried and true from the Python world (numpy) R can benefit from this! More intuitive syntax Can be more memory efficient Can be faster 6 / 13

Why does this work? Dimensions of 2 are broadcasted automatically. x + 2 [,1] [1,] 3 [2,] 4 [3,] 5 Broadcasting 7 / 13

Why does this work? Dimensions of 2 are broadcasted automatically. x + 2 [,1] [1,] 3 [2,] 4 [3,] 5 "Common" dimensions (3, 1) 3 rows, 1 cols (1, ) 1 rows, no cols ------ (3, 1) The 2 is broadcasted from (1, ) to (3, 1) so that it can be added to x using standard R addition rules (matching dimension). Broadcasting 7 / 13

Why does this work? Dimensions of 2 are broadcasted automatically. x + 2 [,1] [1,] 3 [2,] 4 [3,] 5 "Common" dimensions (3, 1) 3 rows, 1 cols (1, ) 1 rows, no cols ------ (3, 1) The 2 is broadcasted from (1, ) to (3, 1) so that it can be added to x using standard R addition rules (matching dimension). x + matrix(c(2, 2, 2)) [,1] [1,] 3 [2,] 4 [3,] 5 Broadcasting 7 / 13

Why does this work? Dimensions of 2 are broadcasted automatically. x + 2 [,1] [1,] 3 [2,] 4 [3,] 5 "Common" dimensions (3, 1) 3 rows, 1 cols (1, ) 1 rows, no cols ------ (3, 1) The 2 is broadcasted from (1, ) to (3, 1) so that it can be added to x using standard R addition rules (matching dimension). x + matrix(c(2, 2, 2)) [,1] [1,] 3 [2,] 4 [3,] 5 So, in theory, this should work: x + matrix(2) Error in x + matrix(2): non conformable arrays (3, 1) 3 rows, 1 cols (1, 1) 1 rows, 1 cols ------ (3, 1) The dimensions of (1, 1) should be broadcasted up to (3, 1) (concretely, the first row should be repeated 3 times). Broadcasting 7 / 13

Three rules of broadcasting 1) Dimensions of size 1 are always recycled up to the other dimension you are comparing to. 2) Implicit dimensions are always appended to the right hand side, and are assumed to be 1’s. 3) If two dimensions do not match, and neither are 1, an error is thrown. 8 / 13

Three rules of broadcasting 1) Dimensions of size 1 are always recycled up to the other dimension you are comparing to. 2) Implicit dimensions are always appended to the right hand side, and are assumed to be 1’s. 3) If two dimensions do not match, and neither are 1, an error is thrown. These rules explain: (3, 1) (1, ) ------ (3, 1) 3 row VS 1 row = Rule 1 = The 1 row object is broadcasted up to 3. 1 col VS no col = Rule 2 = Implicit dimension of 1, matches the other 1. 8 / 13

Three rules of broadcasting 1) Dimensions of size 1 are always recycled up to the other dimension you are comparing to. 2) Implicit dimensions are always appended to the right hand side, and are assumed to be 1’s. 3) If two dimensions do not match, and neither are 1, an error is thrown. These rules explain: (3, 1) (1, ) ------ (3, 1) 3 row VS 1 row = Rule 1 = The 1 row object is broadcasted up to 3. 1 col VS no col = Rule 2 = Implicit dimension of 1, matches the other 1. rray is a new package that enforces this set of rules, and uses the xtensor C++ library for the underlying operations. 8 / 13

library(rray) x_rray as_rray(x) x_rray [,1][3]> [,1] [1,] 1 [2,] 2 [3,] 3 x_rray + matrix(2) [,1][3]> [,1] [1,] 3 [2,] 4 [3,] 5 z [,1] [,2] [1,] 1 4 [2,] 2 5 [3,] 3 6 x_rray + z [,2][6]> [,1] [,2] [1,] 2 5 [2,] 4 7 [3,] 6 9 rray 9 / 13

x_rray [,1][3]> [,1] [1,] 1 [2,] 2 [3,] 3 t(x_rray) [,3][3]> [,1] [,2] [,3] [1,] 1 2 3 What happens if these are added together? Why is this powerful? 10 / 13

x_rray [,1][3]> [,1] [1,] 1 [2,] 2 [3,] 3 t(x_rray) [,3][3]> [,1] [,2] [,3] [1,] 1 2 3 What happens if these are added together? x_rray + t(x_rray) [,3][9]> [,1] [,2] [,3] [1,] 2 3 4 [2,] 3 4 5 [3,] 4 5 6 (3, 1) (1, 3) ------ (3, 3) 3 row VS 1 row = Broadcast 1 up to 3 1 col VS 3 col = Broadcast 1 up to 3 Why is this powerful? 10 / 13

arr array(1:8, c(1, 4, 2)) rray as_rray(arr) rray [,4,2][8]> , , 1 [,1] [,2] [,3] [,4] [1,] 1 2 3 4 , , 2 [,1] [,2] [,3] [,4] [1,] 5 6 7 8 # choke arr + matrix(1:2) Error in arr + matrix(1 2): non conformable arrays Moar dimensions 11 / 13

arr array(1:8, c(1, 4, 2)) rray as_rray(arr) rray [,4,2][8]> , , 1 [,1] [,2] [,3] [,4] [1,] 1 2 3 4 , , 2 [,1] [,2] [,3] [,4] [1,] 5 6 7 8 # choke arr + matrix(1:2) Error in arr + matrix(1 2): non conformable arrays rray + matrix(1:2) [,4,2][16]> , , 1 [,1] [,2] [,3] [,4] [1,] 2 3 4 5 [2,] 3 4 5 6 , , 2 [,1] [,2] [,3] [,4] [1,] 6 7 8 9 [2,] 7 8 9 10 (1, 4, 2) (2, 1, ) --------- (2, 4, 2) Moar dimensions 11 / 13

common_dim rray_dim_common(rray, matrix(1:2)) common_dim [1] 2 4 2 rray_broadcast(matrix(1:2), common_dim) , , 1 [,1] [,2] [,3] [,4] [1,] 1 1 1 1 [2,] 2 2 2 2 , , 2 [,1] [,2] [,3] [,4] [1,] 1 1 1 1 [2,] 2 2 2 2 Find common dimension Broadcast individually to the common dim Add Moar dimensions 12 / 13

common_dim rray_dim_common(rray, matrix(1:2)) common_dim [1] 2 4 2 rray_broadcast(matrix(1:2), common_dim) , , 1 [,1] [,2] [,3] [,4] [1,] 1 1 1 1 [2,] 2 2 2 2 , , 2 [,1] [,2] [,3] [,4] [1,] 1 1 1 1 [2,] 2 2 2 2 Find common dimension Broadcast individually to the common dim Add rray_broadcast(rray, common_dim) [,4,2][16]> , , 1 [,1] [,2] [,3] [,4] [1,] 1 2 3 4 [2,] 1 2 3 4 , , 2 [,1] [,2] [,3] [,4] [1,] 5 6 7 8 [2,] 5 6 7 8 Moar dimensions 12 / 13

Thank you! 13 / 13