Vector Operations

The vector library provides operations on vectors represented as Python lists of Real numbers.

Construction

fpy2.libraries.vector.zeros(n)

Create a zero vector of length n.

Parameters:

n (int) – Vector length

Returns:

Zero vector

Return type:

list[Real]

fpy2.libraries.vector.ones(n)

Create a vector of ones of length n.

Parameters:

n (int) – Vector length

Returns:

Vector of ones

Return type:

list[Real]

Element-wise Operations

fpy2.libraries.vector.add(x, y)

Element-wise addition of two vectors.

Parameters:

• x (list[Real]) – First vector

• y (list[Real]) – Second vector

Returns:

Result vector x + y

Return type:

list[Real]

fpy2.libraries.vector.sub(x, y)

Element-wise subtraction of two vectors.

Parameters:

• x (list[Real]) – First vector

• y (list[Real]) – Second vector

Returns:

Result vector x - y

Return type:

list[Real]

fpy2.libraries.vector.hadamard(x, y)

Element-wise multiplication (Hadamard product) of two vectors.

Parameters:

• x (list[Real]) – First vector

• y (list[Real]) – Second vector

Returns:

Result vector x ⊙ y

Return type:

list[Real]

fpy2.libraries.vector.scale(a, x)

Scale a vector by a scalar.

Parameters:

• a (Real) – Scalar multiplier

• x (list[Real]) – Input vector

Returns:

Result vector a*x

Return type:

list[Real]

Products

fpy2.libraries.vector.dot(x, y)

Compute the dot product of two vectors.

Parameters:

• x (list[Real]) – First vector

• y (list[Real]) – Second vector

Returns:

Dot product of x and y

Return type:

Real

fpy2.libraries.vector.dot_add(x, y, c)

Compute xy + c, dot product with addition.

Parameters:

• x (list[Real]) – First vector

• y (list[Real]) – Second vector

• c (Real) – Scalar to add

Returns:

Result x·y + c

Return type:

Real

fpy2.libraries.vector.cross(x, y)

Compute cross product of two 3D vectors.

Parameters:

• x (list[Real]) – First 3D vector

• y (list[Real]) – Second 3D vector

Returns:

Cross product x × y

Return type:

list[Real]

BLAS-like Operations

fpy2.libraries.vector.axpy(a, x, y)

Compute a*x + y (AXPY operation).

Parameters:

• a (Real) – Scalar multiplier

• x (list[Real]) – First vector

• y (list[Real]) – Second vector

Returns:

Result vector a*x + y

Return type:

list[Real]

Norms

fpy2.libraries.vector.norm1(x)

Compute the L1 norm (Manhattan norm) of a vector.

Parameters:

x (list[Real]) – Input vector

Returns:

L1 norm of x

Return type:

Real

fpy2.libraries.vector.norm2(x)

Compute the L2 norm (Euclidean norm) of a vector.

Parameters:

x (list[Real]) – Input vector

Returns:

L2 norm of x

Return type:

Real

fpy2.libraries.vector.norm_inf(x)

Compute the infinity norm (maximum norm) of a vector.

Parameters:

x (list[Real]) – Input vector

Returns:

Infinity norm of x

Return type:

Real

fpy2.libraries.vector.norm_p(x, p)

Compute the p-norm of a vector.

Parameters:

• x (list[Real]) – Input vector

• p (Real) – Norm parameter (p >= 1)

Returns:

p-norm of x

Return type:

Real

Normalization

fpy2.libraries.vector.normalize(x)

Normalize a vector to unit length (L2 norm).

Parameters:

x (list[Real]) – Input vector

Returns:

Unit vector in direction of x

Return type:

list[Real]

fpy2.libraries.vector.normalize_p(x, p)

Normalize a vector using p-norm.

Parameters:

• x (list[Real]) – Input vector

• p (Real) – Norm parameter

Returns:

Vector normalized by p-norm

Return type:

list[Real]

Similarity and Distance

fpy2.libraries.vector.cosine_similarity(x, y)

Compute cosine similarity between two vectors.

Parameters:

• x (list[Real]) – First vector

• y (list[Real]) – Second vector

Returns:

Cosine similarity x·y / (||x|| ||y||)

Return type:

Real

Statistics

fpy2.libraries.vector.mean(x)

Compute the mean of vector elements.

Parameters:

x (list[Real]) – Input vector

Returns:

Mean of elements

Return type:

Real

fpy2.libraries.vector.min_element(x)

Find minimum element in vector.

Parameters:

x (list[Real]) – Input vector

Returns:

Minimum element

Return type:

Real

fpy2.libraries.vector.max_element(x)

Find maximum element in vector.

Parameters:

x (list[Real]) – Input vector

Returns:

Maximum element

Return type:

Real