https://github.com/gridap/tensorpolynomialbases.jl

++REPO NOT MAINTAINED++ Gallery of tensor-valued multivariate polynomial bases for the julia language
https://github.com/gridap/tensorpolynomialbases.jl

Last synced: 7 months ago
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++REPO NOT MAINTAINED++ Gallery of tensor-valued multivariate polynomial bases for the julia language

• Host: GitHub
• URL: https://github.com/gridap/tensorpolynomialbases.jl
• Owner: gridap
• License: mit
• Created: 2019-05-15T15:54:48.000Z (about 7 years ago)
• Default Branch: master
• Last Pushed: 2023-08-09T15:39:27.000Z (almost 3 years ago)
• Last Synced: 2025-01-20T22:51:10.658Z (over 1 year ago)
• Language: Julia
• Homepage:
• Size: 62.5 KB
• Stars: 3
• Watchers: 3
• Forks: 3
• Open Issues: 2
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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README

          
# TensorPolynomialBases

[![Build Status](https://travis-ci.com/gridap/TensorPolynomialBases.jl.svg?branch=master)](https://travis-ci.com/gridap/TensorPolynomialBases.jl)

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[![](https://img.shields.io/badge/docs-stable-blue.svg)](https://gridap.github.io/TensorPolynomialBases.jl/stable)

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The **TensorPolynomialBases** package provides a collection of different types representing tensor-valued multivariate polynomial bases. It provides a common interface, called `TensorPolynomialBasis`, and several concrete implementations. At the moment, only a concrete implementation, called `MonomialBasis` is available, which implements a tensor-valued multivariate monomial basis. For representing the tensor values arising in the evaluation of tensor-valued polynomails, the user can either use the [StaticArrays](https://github.com/JuliaArrays/StaticArrays.jl) or the [TensorValues](https://github.com/gridap/TensorValues.jl) packages.

## Quick start

### Create a vector-valued monomial basis of P-polynomials in 2 variables

```julia

using TensorPolynomialBases

using StaticArrays

# Define a filter to select the monomials in the P-space

filter(e,order) = sum(e) <= order

order= 4

P = SVector{2,Float64} # type of the evaluation point

V = SVector{3,Float64} # type of the value

basis = MonomialBasis{P,V}(filter,order)

# Create scratch data that can be reused between evaluations

cache = ScratchData(basis)

# Evaluation point

x = @SVector rand(3)

# Evaluation

v = zeros(V,length(basis))

evaluate!(v,basis,x,cache) # No memory allocation here

@show v

# Evaluation of the gradient

G = gradient_type(basis)

# G == SMatrix{2,3,T,6}

v = zeros(G,length(basis))

gradient!(v,basis,x,cache) # No memory allocation here

@show v

```

### Create a Tensor-valued monomial basis of the "serendipity" space in 3 variables (this time using the types of the TensorValues package)

```julia

using TensorValues

# Define the filter for the serendipity space

filter(e,order) = sum( ( i for i in e if i>1 ) ) <= order

order= 3

P = VectorValue{3,Float64} # type of the evaluation point

V = TensorValue{3,Float64,9} # type of the value (3x3 tensor)

basis = MonomialBasis{P,V}(filter,order)

# Create scratch data that can be reused between evaluations

cache = ScratchData(basis)

# Evaluation point

x = VectorValue(0.1,2.0,3.1)

# Evaluation

v = zeros(V,length(basis))

evaluate!(v,basis,x,cache) # No memory allocation here

@show v

```