Find closest convex function for piecewise linear data #513
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Implement make_convex and make_concave functions using the Pool Adjacent Violators Algorithm (PAVA) for isotonic regression. This provides an optimal O(n) solution for finding the closest convex/concave approximation to non-convex PiecewiseLinearData and PiecewiseStepData. New functions: - isotonic_regression / antitonic_regression: Core PAVA implementation - make_convex / make_concave: Convert piecewise data to convex/concave form - convexity_violations: Find indices where convexity is violated - convexity_gap: Measure the maximum convexity violation - approximation_error: Compute error between original and approximated data Features: - Multiple weighting schemes (:uniform, :length, custom) - Multiple anchor options for PiecewiseLinearData (:first, :last, :centroid) - Support for L1, L2, and Linf error metrics
Remove antitonic_regression, make_concave for PiecewiseStepData and PiecewiseLinearData, and related tests. The library only needs conversion from concave to convex (make_convex), not the reverse.
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| return _get_x_lengths(x_coords) | ||
| elseif weights isa Vector{Float64} | ||
| length(weights) == n_segments || | ||
| throw(ArgumentError("Custom weights must have length $n_segments, got $(length(weights))")) |
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| throw(ArgumentError("Custom weights must have length $n_segments, got $(length(weights))")) | |
| throw( | |
| ArgumentError( | |
| "Custom weights must have length $n_segments, got $(length(weights))", | |
| ), | |
| ) |
| approximated = IS.PiecewiseStepData([0.0, 1.0, 2.0, 3.0], [7.5, 7.5, 15.0]) | ||
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| # L2 error with uniform weights | ||
| err_l2 = IS.approximation_error(original, approximated; metric = :L2, weights = :uniform) |
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| err_l2 = IS.approximation_error(original, approximated; metric = :L2, weights = :uniform) | |
| err_l2 = | |
| IS.approximation_error(original, approximated; metric = :L2, weights = :uniform) |
| @test err_l2 ≈ expected_l2 | ||
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| # L1 error | ||
| err_l1 = IS.approximation_error(original, approximated; metric = :L1, weights = :uniform) |
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| err_l1 = IS.approximation_error(original, approximated; metric = :L1, weights = :uniform) | |
| err_l1 = | |
| IS.approximation_error(original, approximated; metric = :L1, weights = :uniform) |
| @test err_l1 ≈ expected_l1 | ||
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| # Linf error | ||
| err_linf = IS.approximation_error(original, approximated; metric = :Linf, weights = :uniform) |
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| err_linf = IS.approximation_error(original, approximated; metric = :Linf, weights = :uniform) | |
| err_linf = | |
| IS.approximation_error(original, approximated; metric = :Linf, weights = :uniform) |
| @test err ≈ expected | ||
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| # Test invalid metric | ||
| @test_throws ArgumentError IS.approximation_error(original, approximated; metric = :invalid) |
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| @test_throws ArgumentError IS.approximation_error(original, approximated; metric = :invalid) | |
| @test_throws ArgumentError IS.approximation_error( | |
| original, | |
| approximated; | |
| metric = :invalid, | |
| ) |
Refactor approximation_error functions to use Julia's standard LinearAlgebra functions instead of manually implementing norms: - L2 norm: Use norm() with weighted scaling - L1 norm: Use dot() for weighted sum - L∞ norm: Use norm(diff, Inf) This makes the code more idiomatic and leverages optimized implementations from Julia's standard library.
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Implement make_convex and make_concave functions using the Pool Adjacent Violators Algorithm (PAVA) for isotonic regression. This provides an optimal O(n) solution for finding the closest convex/concave approximation to non-convex PiecewiseLinearData and PiecewiseStepData.
New functions:
Features: