|
| 1 | +// Copyright 2019-2020 CERN and copyright holders of ALICE O2. |
| 2 | +// See https://alice-o2.web.cern.ch/copyright for details of the copyright holders. |
| 3 | +// All rights not expressly granted are reserved. |
| 4 | +// |
| 5 | +// This software is distributed under the terms of the GNU General Public |
| 6 | +// License v3 (GPL Version 3), copied verbatim in the file "COPYING". |
| 7 | +// |
| 8 | +// In applying this license CERN does not waive the privileges and immunities |
| 9 | +// granted to it by virtue of its status as an Intergovernmental Organization |
| 10 | +// or submit itself to any jurisdiction. |
| 11 | + |
| 12 | +/// \file testChebyshev3D.cxx |
| 13 | +/// \brief Accuracy of the Chebyshev3D evaluation kernel. |
| 14 | +/// |
| 15 | +/// Guards `Chebyshev3DCalc::Eval` / `chebyshevEvaluation1D` (the Clenshaw |
| 16 | +/// recurrence that dominates magnetic-field evaluation in track extrapolation). |
| 17 | +/// We build an in-memory parameterization of a known smooth function and check |
| 18 | +/// that `Eval` reproduces it to the requested precision over many random points, |
| 19 | +/// and that the per-dimension and double-precision overloads agree with the |
| 20 | +/// float vector overload. Any breakage of the recurrence (e.g. a wrong FMA |
| 21 | +/// regrouping) makes the reproduction error explode and fails the test. |
| 22 | + |
| 23 | +#define BOOST_TEST_MODULE Test Chebyshev3D |
| 24 | +#define BOOST_TEST_MAIN |
| 25 | +#define BOOST_TEST_DYN_LINK |
| 26 | +#include <boost/test/unit_test.hpp> |
| 27 | +#include <cmath> |
| 28 | +#include <random> |
| 29 | +#include "MathUtils/Chebyshev3D.h" |
| 30 | + |
| 31 | +using o2::math_utils::Chebyshev3D; |
| 32 | + |
| 33 | +namespace |
| 34 | +{ |
| 35 | +// A smooth, low-degree (≤3 per variable) vector function over the fit box, of |
| 36 | +// the kind a Chebyshev parameterization reproduces to ~float precision. Stands |
| 37 | +// in for a slowly-varying magnetic field B(x,y,z). |
| 38 | +void referenceField(float* in, float* out) |
| 39 | +{ |
| 40 | + const float x = in[0], y = in[1], z = in[2]; |
| 41 | + out[0] = 0.50f + 0.020f * x - 1.0e-4f * x * y + 3.0e-3f * z - 2.0e-6f * x * x * z; |
| 42 | + out[1] = -0.30f + 0.015f * y + 5.0e-5f * y * z - 1.0e-3f * x; |
| 43 | + out[2] = 5.00f - 4.0e-4f * x * x + 6.0e-4f * y * y + 1.0e-3f * x * y - 2.0e-6f * x * y * z; |
| 44 | +} |
| 45 | +} // namespace |
| 46 | + |
| 47 | +BOOST_AUTO_TEST_CASE(Chebyshev3D_eval_accuracy) |
| 48 | +{ |
| 49 | + const Float_t bmin[3] = {-40.f, -40.f, -200.f}; |
| 50 | + const Float_t bmax[3] = {40.f, 40.f, 200.f}; |
| 51 | + const Int_t np[3] = {7, 7, 7}; // > polynomial degree in every dimension |
| 52 | + const Float_t fitPrec = 1.0e-5f; |
| 53 | + |
| 54 | + Chebyshev3D cheb(referenceField, 3, bmin, bmax, np, fitPrec); |
| 55 | + |
| 56 | + // Deterministic interior sampling (fixed seed -> no flakiness). Stay a hair |
| 57 | + // inside the box so we never hit the boundary-clamping branch. |
| 58 | + std::mt19937 rng(20260604u); |
| 59 | + std::uniform_real_distribution<float> ux(bmin[0] + 1.f, bmax[0] - 1.f); |
| 60 | + std::uniform_real_distribution<float> uy(bmin[1] + 1.f, bmax[1] - 1.f); |
| 61 | + std::uniform_real_distribution<float> uz(bmin[2] + 1.f, bmax[2] - 1.f); |
| 62 | + |
| 63 | + float maxAbsErr = 0.f; // |cheb - reference| (kernel reproduces the function) |
| 64 | + float maxDimMismatch = 0.f; // |vector overload - per-dim overload| |
| 65 | + float maxDoubleMismatch = 0.f; // |float overload - double overload| |
| 66 | + |
| 67 | + for (int i = 0; i < 20000; ++i) { |
| 68 | + float par[3] = {ux(rng), uy(rng), uz(rng)}; |
| 69 | + float ref[3]; |
| 70 | + referenceField(par, ref); |
| 71 | + |
| 72 | + float res[3]; |
| 73 | + cheb.Eval(par, res); |
| 74 | + |
| 75 | + double pard[3] = {par[0], par[1], par[2]}; |
| 76 | + double resd[3]; |
| 77 | + cheb.Eval(pard, resd); |
| 78 | + |
| 79 | + for (int d = 0; d < 3; ++d) { |
| 80 | + BOOST_REQUIRE(std::isfinite(res[d])); |
| 81 | + maxAbsErr = std::max(maxAbsErr, std::abs(res[d] - ref[d])); |
| 82 | + // Single-component overload must match the vector overload (same kernel). |
| 83 | + maxDimMismatch = std::max(maxDimMismatch, std::abs(res[d] - cheb.Eval(par, d))); |
| 84 | + // Double overload differs only by intermediate precision. |
| 85 | + maxDoubleMismatch = std::max(maxDoubleMismatch, std::abs(static_cast<float>(resd[d]) - res[d])); |
| 86 | + } |
| 87 | + } |
| 88 | + |
| 89 | + BOOST_TEST_MESSAGE("Chebyshev3D max |eval - reference| = " << maxAbsErr); |
| 90 | + BOOST_TEST_MESSAGE("Chebyshev3D max vector-vs-perdim = " << maxDimMismatch); |
| 91 | + BOOST_TEST_MESSAGE("Chebyshev3D max float-vs-double = " << maxDoubleMismatch); |
| 92 | + |
| 93 | + // Reproduction of the known function: fit precision (1e-5) plus a little float |
| 94 | + // slack from the three nested Clenshaw sums (observed ~1.4e-6). A broken |
| 95 | + // recurrence misses this by orders of magnitude (coefficient-scale error / NaN). |
| 96 | + BOOST_CHECK_SMALL(maxAbsErr, 1.0e-4f); |
| 97 | + // The two float entry points share the kernel: expect bit-for-bit agreement. |
| 98 | + BOOST_CHECK_SMALL(maxDimMismatch, 1.0e-6f); |
| 99 | + // float vs double evaluation of the same coefficients: within float epsilon. |
| 100 | + BOOST_CHECK_SMALL(maxDoubleMismatch, 1.0e-3f); |
| 101 | +} |
0 commit comments