mtflib 1.5.0

A library for working with Multivariate Taylor Functions.

mtflib: Multivariate Taylor Function Library

[!IMPORTANT] Version 1.5.0 is a major release with significant improvements and breaking changes. It is NOT backward compatible with previous versions. Please see the CHANGELOG.md for more details.

A Python library for creating, manipulating, and composing Multivariate Taylor Functions, with a C++ backend for performance-critical applications.

Installation

The recommended way to install mtflib is from PyPI:

pip install mtflib

Installation from Source

Alternatively, you can install mtflib directly from the source repository using pip. Ensure you have a C++17 compliant compiler (e.g., GCC, Clang, MSVC) for building the backend extensions.

pip install .

Quick Start

Here's a simple example to get you started with mtflib:

import numpy as np
from mtflib import mtf
from IPython.display import display

# 1. Initialize global settings (must be done once)
# This sets the max order of the Taylor series and the number of variables.
mtf.initialize_mtf(max_order=5, max_dimension=2)

# 2. Define symbolic variables
# var(1) corresponds to x, var(2) to y
x = mtf.var(1)
y = mtf.var(2)

# 3. Create a Taylor series expression
# This creates a Taylor series for sin(x) + y^2
f = mtf.sin(x) + y**2

# 4. Evaluate the result at a point
# Let's evaluate f at (x=0.5, y=2.0)
eval_point = np.array([0.5, 2.0])
result = f.eval(eval_point)

print(f"\nf(x, y) = sin(x) + y^2")
print(f"Result of f(0.5, 2.0): {result[0]}")

# For comparison, the exact value is sin(0.5) + 2.0^2
exact_value = np.sin(0.5) + 4.0
print(f"Exact value: {exact_value}")

# You can also view the Taylor series coefficients
print("\nTaylor Series Representation:")
print(f)

print("Symbolic representation of the function:")
display(f.symprint())  # This will print the series in a human-readable format

output:

Initializing MTF globals with: _MAX_ORDER=5, _MAX_DIMENSION=2
Loading/Precomputing Taylor coefficients up to order 5
Global precomputed coefficients loading/generation complete.
Size of precomputed_coefficients dictionary in memory: 464 bytes, 0.45 KB, 0.00 MB
MTF globals initialized: _MAX_ORDER=5, _MAX_DIMENSION=2, _INITIALIZED=True
Max coefficient count (order=5, nvars=2): 21
Precomputed coefficients loaded and ready for use.

f(x, y) = sin(x) + y^2
Result of f(0.5, 2.0): 4.479427083333333
Exact value: 4.479425538604203

Taylor Series Representation:
          Coefficient  Order Exponents
0  1.000000000000e+00      1    (1, 0)
1  1.000000000000e+00      2    (0, 2)
2 -1.666666666667e-01      3    (3, 0)
3  8.333333333333e-03      5    (5, 0)

Symbolic representation of the function:

$\displaystyle 0.00833333 x^{5} - 0.166667 x^{3} + 1.0 x + 1.0 y^{2}$

Running Tests

The project uses pytest for testing. First, install the test dependencies:

pip install -e .[test]

Then, run the test suite from the root of the repository:

pytest