Taylor models utilities

#include <audi/taylor_model_utilities.hpp>

std::vector<std::vector<double>> matmul(const std::vector<std::vector<double>> &A, const std::vector<std::vector<double>> &B)

Matrix multiplication.

Computes the matrix product \( C = A \cdot B \) where

• A is of shape (m x p)

• B is of shape (p x n)

The result C has shape (m x n).

Parameters:

• A – left-hand matrix of shape (m x p)

• B – right-hand matrix of shape (p x n)

Throws:

std::out_of_range – if A and B have incompatible dimensions

Returns:

matrix product C of shape (m x n)

std::vector<std::vector<double>> transpose(const std::vector<std::vector<double>> &M)

Matrix transpose.

Computes the transpose of a given matrix \(M\).

• If M has shape (rows x cols), the result has shape (cols x rows).

Parameters:

M – input matrix

Returns:

transpose of M

std::ostream &operator<<(std::ostream &os, const var_map_d &m)

Overloaded stream insertion operator for var_map_d.

Outputs the contents of a var_map_d (mapping variable names to doubles) to the given output stream in a human-readable format.

Example output: {“x”: 1.23, “y”: 4.56}

Parameters:

• os – the output stream

• m – the var_map_d mapping variable names to double values

Returns:

a reference to the output stream with the formatted contents inserted

std::ostream &operator<<(std::ostream &os, const var_map_i &m)

Overloaded stream insertion operator for var_map_i.

Outputs the contents of a var_map_i (mapping variable names to intervals) to the given output stream in a human-readable format.

Each interval is displayed as [lower, upper]. Example output: {“x”:[0, 1], “y”:[2, 5]}

Parameters:

• os – the output stream

• m – the var_map_i mapping variable names to int_d intervals

Returns:

a reference to the output stream with the formatted contents inserted