https://github.com/floswald/ApproXD.jl

B-splines and linear approximators in multiple dimensions for Julia
https://github.com/floswald/ApproXD.jl

Last synced: 3 months ago
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B-splines and linear approximators in multiple dimensions for Julia

• Host: GitHub
• URL: https://github.com/floswald/ApproXD.jl
• Owner: floswald
• License: mit
• Created: 2014-07-28T13:34:15.000Z (over 10 years ago)
• Default Branch: master
• Last Pushed: 2019-05-12T07:25:35.000Z (over 5 years ago)
• Last Synced: 2024-05-22T07:35:57.649Z (6 months ago)
• Language: Julia
• Homepage:
• Size: 216 KB
• Stars: 28
• Watchers: 6
• Forks: 6
• Open Issues: 7
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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• awesome-sciml - floswald/ApproXD.jl: B-splines and linear approximators in multiple dimensions for Julia

README

        
# ApproXD

[![Build Status](https://travis-ci.org/floswald/ApproXD.jl.svg?branch=master)](https://travis-ci.org/floswald/ApproXD.jl)

[![Codecov](https://codecov.io/gh/floswald/ApproXD.jl/branch/master/graph/badge.svg)](https://codecov.io/gh/floswald/ApproXD.jl)

* This package implements bspline and linear interpolation in julia

* For most purposes, [Interpolations.jl](https://github.com/JuliaMath/Interpolations.jl) will be preferrable to this package.

* However, there are some features which are available here, and not there.

    - the method `getTensorCoef` is a very efficient algorithm to compute approximating coefficients from a tensor product of basis matrices. it is efficient because it never forms the tensor product.

    - the package allows low-level access to objects such as spline knot vectors. Suppose you want to have a knot vector with a [knot multiplicity](https://pages.mtu.edu/~shene/COURSES/cs3621/NOTES/spline/B-spline/bspline-mod-knot.html) in the interior knot span to approximate a kink. For example,

    ```julia

    knots = vcat(lb,-0.5,0,0,0.5,ub)

    ```

    is a valid knot vector.

* Documentation is non-existent. Please look at the tests. Sorry.

## Example

```julia

using ApproXD

f(x) = abs.(x).^0.5

lb,ub = (-1.0,1.0)

nknots = 13

deg = 3

# standard case: equally spaced knots

params1 = BSpline(nknots,deg,lb,ub)   

nevals = 5 * params1.numKnots # get nBasis < nEvalpoints

# myknots with knot multiplicity at 0

myknots = vcat(range(-1,stop = -0.1,length = 5),0,0,0,  range(0.1,stop = 1,length =5))

params2 = BSpline(myknots,deg)  # 0: no derivative

# get coefficients for each case

eval_points = collect(range(lb,stop = ub,length = nevals))  

c1 = getBasis(eval_points,params1) \ f(eval_points)

c2 = getBasis(eval_points,params2) \ f(eval_points)

# look at errors over entire interval

test_points = collect(range(lb,stop = ub,length = 1000));

truth = f(test_points);

p1 = getBasis(test_points,params1) * c1;

p2 = getBasis(test_points,params2) * c2;

e1 = p1 - truth;

e2 = p2 - truth;

```

![](question_5.png)