Reference · Vectors

vec.matmul

vec.matmul(list, list) -> list

What it does

Matrix multiplication. A matrix is a list of rows, each a list of numbers of one length. a with n rows and k columns times b with k rows and m columns gives n rows of m floats. When b is a plain list of k numbers it is taken as a column, and the result is a list of n floats. The result is always floats.

Examples

let a = [[1, 2], [3, 4]]print(vec.matmul(a, [[5, 6], [7, 8]]))print(vec.matmul(a, [1, 1]))print(vec.matmul([[1, 2, 3]], [[1], [2], [3]]))

[[19.0, 22.0], [43.0, 50.0]][3.0, 7.0][[14.0]]

Edge cases

• Ints come back as floats: the identity times [[1, 2], [3, 4]] is [[1.0, 2.0], [3.0, 4.0]], which still equals a, since 1 == 1.0.
• A column times a row is their outer product.
• Two empty matrices, or null for both, give the empty list.
• A row of numbers as a is not a matrix: wrap it, [[1, 2]].

let a = [[1, 2], [3, 4]]print(vec.matmul(a, [[1, 0], [0, 1]]), vec.matmul(a, [[1, 0], [0, 1]]) == a)print(vec.matmul([[1], [2]], [[1, 2, 3]]))print(vec.matmul([], []), vec.matmul(null, null))

[[1.0, 2.0], [3.0, 4.0]] true[[1.0, 2.0, 3.0], [2.0, 4.0, 6.0]][] []

Errors

Shapes that do not fit (the columns of a against the rows of b, or the length of the column), rows of different lengths, an item that is not a number, and an a that is not a list of lists are runtime errors, not error values.

print(vec.matmul([[1, 2]], [[1, 2]]))

line 1: `vec.matmul`: a has 2 columns, b has 1 rows

print(vec.matmul([1, 2], [[1], [2]]))

line 1: `vec.matmul` expects a list of rows, but row 0 is int

Chaining

In a pipeline the left side is a, the matrix: weights | vec.matmul(inputs) applies a linear model with two weights per output to a column of inputs.

let weights = [[0.5, 1], [2, -1]]print(weights | vec.matmul([3, 4]))print(weights | vec.matmul(vec.transpose(weights)))

[5.5, 2.0][[1.25, 0.0], [0.0, 5.0]]

See also

vec.transpose, vec.dot, vec.column, vec.mul

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