TensorFlow, PyTorch and Numpy layers for generating multi-dimensional Orthogonal Polynomials

1. Installation
2. Usage
3. Polynomials
4. Base Class(Poly)

Installation:

1. the stable version:
   pip3 install orthnet

2. the dev version:

git clone https://github.com/orcuslc/orthnet.git && cd orthnet
python3 setup.py build_ext --inplace && python3 setup.py install

Usage:

with TensorFlow

import tensorflow as tf
import numpy as np
from orthnet import Legendre

x_data = np.random.random((10, 2))
x = tf.placeholder(dtype = tf.float32, shape = [None, 2])
L = Legendre(x, 5)

with tf.Session() as sess:
    print(L.tensor, feed_dict = {x: x_data})

with PyTorch

import torch
import numpy as np
from orthnet import Legendre

x = torch.DoubleTensor(np.random.random((10, 2)))
L = Legendre(x, 5)
print(L.tensor)

with Numpy

import numpy as np
from orthnet import Legendre

x = np.random.random((10, 2))
L = Legendre(x, 5)
print(L.tensor)

Specify Backend

In some scenarios, users can specify the exact backend compatible with the input x. The backends provided are:

• orthnet.TensorflowBackend()
• orthnet.TorchBackend()
• orthnet.NumpyBackend()

An example to specify the backend is as follows.

import numpy as np
from orthnet import Legendre, NumpyBackend

x = np.random.random((10, 2))
L = Legendre(x, 5, backend = NumpyBackend())
print(L.tensor)

Specify tensor product combinations

In some scenarios, users may provide pre-computed tensor product combinations to save computing time. An example of providing combinations is as follows.

import numpy as np
from orthnet import Legendre, enum_dim

dim = 2
degree = 5
x = np.random.random((10, dim))
L = Legendre(x, degree, combinations = enum_dim(degree, dim))
print(L.tensor)

Polynomials:

Base class:

Class Poly(x, degree, combination = None):

• Inputs:
  • x a tensor
  • degree highest degree for target polynomials
  • combination optional, tensor product combinations
• Attributes:
  • Poly.tensor the tensor of function values (with degree from 0 to Poly.degree(included))
  • Poly.length the number of function basis (columns) in Poly.tensor
  • Poly.index the index of the first combination of each degree in Poly.combinations
  • Poly.combinations all combinations of tensor product
  • Poly.tensor_of_degree(degree) return all polynomials of given degrees
  • Poly.eval(coefficients) return the function values with given coefficients
  • Poly.quadrature(function, weight) return Gauss quadrature with given function and weight