Faster LU factorisation of collocation matrices

[jipolanco]

This PR adds a port of the LU factorisation by de Boor, which avoids pivoting thanks to the total positivity property of banded collocation matrices used for spline calculations.

This allows to reduce memory usage of the factorisation, since there is no need to allocate extra bands as in the pivoted implementation of BandedMatrices / LAPACK. The factorisation itself seems to be much faster as well.

The implementation is directly based off the Fortran 90 version of de Boor's FORTRAN77 code, made by John Burkardt.

Things to do:

• [x] Implement CollocationMatrix as a BandedMatrix wrapper.
• [x] Then, rename lu_no_pivot! to just LinearAlgebra.lu!, making sure that pivot = Val(false).
• [x] Define lu (without the !).
• [x] collocation_matrix should return a CollocationMatrix, maybe with an optional parameter allowing non-square matrices (which should be regular sparse matrices?).
• [x] Add tests for special cases.
• [ ] Maybe this implementation would make sense in BandedMatrices, where the pivot = Val(false) option is not currently implemented?

[codecov-io]

Codecov Report

Merging #15 (d00c908) into master (34fbbac) will increase coverage by 0.45%. The diff coverage is 97.16%.

@@            Coverage Diff             @@
##           master      #15      +/-   ##
==========================================
+ Coverage   91.81%   92.26%   +0.45%     
==========================================
  Files          18       19       +1     
  Lines         855      957     +102     
==========================================
+ Hits          785      883      +98     
- Misses         70       74       +4     

Impacted Files	Coverage Δ
src/Collocation/matrix.jl	97.00% <97.00%> (ø)
src/Collocation/Collocation.jl	89.28% <100.00%> (+0.82%)	:arrow_up:
src/Interpolations/Interpolations.jl	97.43% <100.00%> (-0.13%)	:arrow_down:
src/Splines/spline.jl	96.84% <0.00%> (-1.06%)	:arrow_down:

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