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Vectors & FloatArray

Part of the math library. These functions treat lists of numbers as vectors and matrices; math.array() converts a list into a FloatArray for efficient numerical storage.

Vector and Matrix Functions

dist(p, q)

Returns the Euclidean distance between two points.

Parameters:

  • p (list): First point, as a list of numbers.
  • q (list): Second point, as a list of numbers with the same length as p.

Returns: float

Raises: Error: if p and q have different lengths.

import math
result = math.dist([0, 0], [3, 4])        # 5.0
result = math.dist([1, 2, 3], [4, 6, 3])  # 5.0

softmax(x)

Returns the numerically stable softmax of a vector.

Parameters:

  • x (list or FloatArray): Values to transform. Must be 1D and non-empty.

Returns: list of float, or FloatArray if the input was a FloatArray: a probability distribution summing to 1.0.

import math
result = math.softmax([1.0, 2.0, 3.0])
print(result)  # [0.0900..., 0.2447..., 0.6652...]

a = math.array([1.0, 2.0, 3.0])
result = math.softmax(a)  # Returns FloatArray

dot(a, b)

Returns the dot product of two vectors.

Parameters:

  • a (list or FloatArray): First vector (1D).
  • b (list or FloatArray): Second vector (1D), same length as a.

Returns: float

Raises: Error: if a and b have different lengths.

import math
result = math.dot([1, 2, 3], [4, 5, 6])  # 32.0

a = math.array([1.0, 2.0, 3.0])
b = math.array([4.0, 5.0, 6.0])
result = math.dot(a, b)  # 32.0

matmul(a, b)

Matrix-matrix multiply. a is (M x K), b is (K x N).

Parameters:

  • a (list of list, or 2D FloatArray): Matrix of shape (M, K).
  • b (list of list, or 2D FloatArray): Matrix of shape (K, N).

Returns: list of list (or FloatArray if either input was a FloatArray): matrix of shape (M, N).

Raises: Error: if the inner dimensions don’t match.

import math
a = [[1, 2], [3, 4]]
b = [[5, 6], [7, 8]]
result = math.matmul(a, b)  # [[19.0, 22.0], [43.0, 50.0]]

fa = math.array([[1.0, 2.0], [3.0, 4.0]])
fb = math.array([[5.0, 6.0], [7.0, 8.0]])
result = math.matmul(fa, fb)  # Returns 2D FloatArray

transpose(m)

Transposes a 2D matrix: rows become columns.

Parameters:

  • m (list of list, or 2D FloatArray): Matrix to transpose.

Returns: list of list (or FloatArray if input was a FloatArray): the transposed matrix.

import math
m = [[1, 2, 3], [4, 5, 6]]
result = math.transpose(m)  # [[1.0, 4.0], [2.0, 5.0], [3.0, 6.0]]

fa = math.array([[1.0, 2.0, 3.0], [4.0, 5.0, 6.0]])
result = math.transpose(fa)  # Returns 2D FloatArray with shape [3, 2]

mat_add(a, b)

Element-wise addition of two matrices.

Parameters:

  • a (list of list, or 2D FloatArray): First matrix.
  • b (list of list, or 2D FloatArray): Second matrix, same shape as a.

Returns: list of list (or FloatArray if either input was a FloatArray): element-wise sum.

Raises: Error: if a and b have different shapes.

import math
a = [[1, 2], [3, 4]]
b = [[5, 6], [7, 8]]
result = math.mat_add(a, b)  # [[6.0, 8.0], [10.0, 12.0]]

array(data)

Creates an efficient FloatArray from a list. Accepts a 1D list of numbers, a 2D list of lists, or an existing FloatArray (returned unchanged).

Parameters:

  • data (list or FloatArray): 1D list of numbers, or 2D list of equal-length lists of numbers.

Returns: FloatArray

import math

a = math.array([1.0, 2.0, 3.0])
print(a[0])    # 1.0
print(len(a))  # 3

m = math.array([[1.0, 2.0], [3.0, 4.0]])
print(m[0])     # [1.0, 2.0]
print(m[0][1])  # 2.0
print(len(m))   # 2 (number of rows)

m[0][1] = 9.0
m[1] = [5.0, 6.0]

result = math.matmul(m, math.array([[1.0], [2.0]]))

shape(a)

Returns the shape of a FloatArray as a list of integers.

Parameters:

  • a (FloatArray): Array to inspect.

Returns: list of int: one entry per dimension.

import math
a = math.array([1.0, 2.0, 3.0])
print(math.shape(a))  # [3]

m = math.array([[1.0, 2.0, 3.0], [4.0, 5.0, 6.0]])
print(math.shape(m))  # [2, 3]

FloatArray

The FloatArray type, returned by math.array(), provides efficient storage and operations for numerical data, avoiding per-element boxing overhead.

FloatArray Methods

.tolist()

Converts a FloatArray to a plain list.

Parameters: None

Returns: list of float (1D), or list of list of float (2D).

import math

a = math.array([1.0, 2.0, 3.0])
plain = a.tolist()  # [1.0, 2.0, 3.0]

m = math.array([[1.0, 2.0], [3.0, 4.0]])
rows = m.tolist()   # [[1.0, 2.0], [3.0, 4.0]]

.shape()

Returns the shape of the FloatArray as a list of integers. Method equivalent of math.shape().

Parameters: None

Returns: list of int

import math

a = math.array([1.0, 2.0, 3.0])
print(a.shape())  # [3]

m = math.array([[1.0, 2.0, 3.0], [4.0, 5.0, 6.0]])
print(m.shape())  # [2, 3]

FloatArray Operators

+ (concatenation)

Concatenates two FloatArrays. For 1D arrays, joins the elements. For 2D arrays with matching column counts, stacks the rows.

Parameters:

  • other (FloatArray): Array to concatenate. For 2D arrays, must have the same number of columns.

Returns: FloatArray

import math

a = math.array([1.0, 2.0])
b = math.array([3.0, 4.0])
c = a + b  # math.array([1.0, 2.0, 3.0, 4.0])

m = math.array([[1.0, 2.0], [3.0, 4.0]])
row = math.array([[5.0, 6.0]])
result = m + row  # shape [3, 2]

FloatArray List Comprehensions

FloatArray supports list comprehensions for both 1D and 2D arrays:

import math

a = math.array([1.0, 2.0, 3.0, 4.0])
doubled = [v * 2 for v in a]    # [2.0, 4.0, 6.0, 8.0]
big = [v for v in a if v > 2.5] # [3.0, 4.0]

m = math.array([[1.0, 2.0, 3.0], [4.0, 5.0, 6.0]])
firsts = [row[0] for row in m]  # [1.0, 4.0]
rows_as_lists = [row.tolist() for row in m]

See Also

  • math: the scalar math functions and constants.
  • statistics: mean, median, variance, and other statistical functions.