Vector / Matrix / Tensor

Instance of: algebraic object / data structure

AKA: array, matrices

Distinct from: list

English: Vectors, matrices, and tensors are like lists in that they are a collection of objects which are indexed. They differ in that the index can be multi-dimensional, where vectors are 1-d indexed, matrices are 2-d indexed, and tensors are m-d indexed. They also are typically constrained to have objects that share the same type, e.g. numbers or strings.

Formalization:

\[ \]

Cites:

Array:

Wikipedia

3Blue1Brown: Vectors | Chapter 1, Essence of linear algebra 3Blue1Brown: Linear combinations, span, and basis vectors | Chapter 2, Essence of linear algebra

https://superstudy.guide/algorithms-data-structures/data-structures/arrays-strings *Kadane’s algorithm

Matrix:

Wikipedia

3Blue1Brown: Linear transformations and matrices | Chapter 3, Essence of linear algebra

Tensor:

Wikipedia

Code

Vector

Note unlike matrix and array, the basic vector function initializes an empty vector and you have to actually use as.vector to coerce something else to vector as the constructor.

vector: Vectors

example_vector <- as.vector(c(1,2,3,4))
class(example_vector)

[1] "numeric"

example_vector

[1] 1 2 3 4

Matrix

Note we can choose which direction to fill the matrix with, either by row1-col1, row1-col2, row1-col3, row1-col4

matrix: Matrices

example_matrix <- matrix(c(1,2,3,4,"A","B","C","D"), nrow = 2, ncol = 4, byrow = TRUE,
               dimnames = list(c("row1", "row2"),
                               c("C.1", "C.2", "C.3", "C.4")))
class(example_matrix)

[1] "matrix" "array"

example_matrix

     C.1 C.2 C.3 C.4
row1 "1" "2" "3" "4"
row2 "A" "B" "C" "D"

Arrays

Note array dimensions are ordered, row, column, depth, …, M , and elements are filled row1-col1-depth1, row2-col1-depth1, row1-col2-depth1,… and so on. Note this was coerced to a string because any of the elements were a string.

array: Multi-way Arrays

example_tensor= array(c(1,2,3,4,"A","B","C","D","+","-","*","/"),dim=c(2,3,2,2)) 
class(example_tensor)

[1] "array"

example_tensor

, , 1, 1

     [,1] [,2] [,3]
[1,] "1"  "3"  "A" 
[2,] "2"  "4"  "B" 

, , 2, 1

     [,1] [,2] [,3]
[1,] "C"  "+"  "*" 
[2,] "D"  "-"  "/" 

, , 1, 2

     [,1] [,2] [,3]
[1,] "1"  "3"  "A" 
[2,] "2"  "4"  "B" 

, , 2, 2

     [,1] [,2] [,3]
[1,] "C"  "+"  "*" 
[2,] "D"  "-"  "/"

Documentation:

Examples:

Documentation:

library(DBI)
# Create an ephemeral in-memory RSQLite database
#con <- dbConnect(RSQLite::SQLite(), dbname = ":memory:")
#dbListTables(con)
#dbWriteTable(con, "mtcars", mtcars)
#dbListTables(con)

#Configuration failed because libpq was not found. Try installing:
#* deb: libpq-dev libssl-dev (Debian, Ubuntu, etc)
#install.packages('RPostgres')
#remotes::install_github("r-dbi/RPostgres")
#Took forever because my file permissions were broken
#pg_lsclusters
require(RPostgres)

Loading required package: RPostgres

# Connect to the default postgres database
#I had to follow these instructions and create both a username and database that matched my ubuntu name
#https://www.digitalocean.com/community/tutorials/how-to-install-postgresql-on-ubuntu-20-04-quickstart
con <- dbConnect(RPostgres::Postgres())

“JAX provides a multidimensional array data structure called DeviceArray that implements many typical properties and methods of the numpy.ndarray”

import torch

import torch