Fix RecombineMatrix for asymmetric boundary conditions

[fintzij]

Summary

Two bugs in RecombineMatrix (src/Recombinations/matrices.jl) that manifest when the left and right boundary conditions differ (cₗ ≠ cᵣ). Both are one-line fixes; symmetric BCs (cₗ = cᵣ) are unaffected.

Bug 1: getindex — wrong row offset for right-boundary block

# Before (line 446):
ii = i - h - cr    # BUG: uses right constraint count

# After:
ii = i - h - cl    # FIX: uses left constraint count

The right-block row index into the lower-right submatrix Lᵣ should be i - h - cₗ (matching what 3-arg mul! computes), not i - h - cᵣ. When cₗ ≠ cᵣ, getindex returns incorrect values, which corrupts:

• Matrix{T}(R) (dense conversion)
• replace_in_print_matrix (display)
• evaluate and evaluate_all in bases.jl (basis function evaluation)

Derivation: The first row of Lᵣ corresponds to parent B-spline row N - nᵣ - cᵣ + 1. Substituting N = M + cₗ + cᵣ and h = M - nᵣ:

ii = i - (N - nᵣ - cᵣ + 1) + 1
   = i - (M + cₗ + cᵣ) + nᵣ + cᵣ
   = i - (M - nᵣ) - cₗ
   = i - h - cₗ       ← correct

Bug 2: 5-arg mul! — wrong SVector size for right-boundary block

# Before (line 501):
y[js] = α * lr * view(x, (h+1):M) + β * SVector{n1}(view(y, js))
#                                             n1 = nl + cl (LEFT corner size)

# After:
n2 = nr + cr
y[js] = α * lr * view(x, (h+1):M) + β * SVector{n2}(view(y, js))
#                                             n2 = nr + cr (RIGHT corner size)

The right-boundary range js has length nr + cr, but the code wrapped it in SVector{n1} where n1 = nl + cl. When nl + cl ≠ nr + cr, this throws DimensionMismatch.

Why existing tests don't catch this

test_recombine_matrix explicitly asserts bcleft === bcright and nl == nr && cl == cr. The only asymmetric test ("Hybrid BCs") tests spline evaluation but never tests getindex, mul!, or matrix conversion.

Tests added

New "Asymmetric BC RecombineMatrix" test set covering 6 asymmetric BC combinations × 2 spline orders (4, 6). For each case:

• Matrix{Float64}(R) matches ground-truth from 3-arg mul!
• Every R[i,j] entry is verified individually
• 5-arg mul!(y, R, x, α, β) runs without error and produces correct results

Minimal working example (click to expand)

using BSplineKit, LinearAlgebra

# Cubic B-spline basis with 8 functions
B = BSplineBasis(BSplineOrder(4), 0.0:0.2:1.0)

# Asymmetric BCs: Free left (cₗ=0), Neumann right (cᵣ=1)
R = RecombineMatrix(B, (), (Derivative(1),))  # size 8×7

x = ones(7)

# 3-arg mul! is correct:
y_mul = zeros(8); mul!(y_mul, R, x)

# Matrix conversion uses getindex — had the bug:
R_dense = Matrix{Float64}(R)
y_idx = R_dense * x

println("Match? ", y_mul ≈ y_idx)
# Before fix: false (R[7,7] returns 0 instead of 1)
# After fix:  true

# 5-arg mul! — had DimensionMismatch for nl+cl ≠ nr+cr:
y5 = ones(8)
mul!(y5, R, x, 2.0, 3.0)  # Before fix: ERROR; After fix: works

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 95.18%. Comparing base (401af69) to head (4676d9b).
⚠️ Report is 1 commits behind head on master.

Additional details and impacted files

@@           Coverage Diff           @@
##           master     #116   +/-   ##
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  Coverage   95.17%   95.18%           
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  Files          36       36           
  Lines        2344     2346    +2     
=======================================
+ Hits         2231     2233    +2     
  Misses        113      113           

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[jipolanco]

This looks great! Thanks for catching the issue and fixing it.