mtflib: Multivariate Taylor Function Library
A Python library for creating, manipulating, and composing Multivariate Taylor Functions (MTF/mtf), 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 (optional but recommended for non-default values)
# If skipped, defaults to max_order=4, max_dimension=3.
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:
$\displaystyle 0.00833333 x^{5} - 0.166667 x^{3} + 1.0 x + 1.0 y^{2}$
JSON Serialization
mtflib supports serializing MTF objects to JSON format, preserving all coefficients and properties (including complex values).
# Serialize to JSON string
json_str = f.to_json()
# Deserialize back to object
f_loaded = mtf.from_json(json_str)
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
1 maintainer
Metadata
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Release files for mtflib 1.5.2
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