From 0ada1270b493d76a7094435a38294b59f2737e71 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Fran=C3=A7ois=20Carouge?= <francois.carouge@gmail.com>
Date: Mon, 5 Jun 2023 16:47:20 -0700
Subject: [PATCH] [filter] support constexpr linear algebra

---
 benchmark/CMakeLists.txt                      |    2 +-
 benchmark/image/predict_naive.svg             | 6011 +++++++++++++++++
 benchmark/image/update_naive.svg              |    0
 benchmark/result/predict_naive_10x1x1.json    |  171 +
 benchmark/result/predict_naive_10x1x10.json   |  171 +
 benchmark/result/predict_naive_10x1x11.json   |  171 +
 benchmark/result/predict_naive_10x1x12.json   |  171 +
 benchmark/result/predict_naive_10x1x13.json   |  171 +
 benchmark/result/predict_naive_10x1x14.json   |  171 +
 benchmark/result/predict_naive_10x1x15.json   |  171 +
 benchmark/result/predict_naive_10x1x16.json   |  171 +
 benchmark/result/predict_naive_10x1x17.json   |  171 +
 benchmark/result/predict_naive_10x1x18.json   |  171 +
 benchmark/result/predict_naive_10x1x19.json   |  171 +
 benchmark/result/predict_naive_10x1x2.json    |  171 +
 benchmark/result/predict_naive_10x1x20.json   |  171 +
 benchmark/result/predict_naive_10x1x21.json   |  171 +
 benchmark/result/predict_naive_10x1x22.json   |  171 +
 benchmark/result/predict_naive_10x1x23.json   |  171 +
 benchmark/result/predict_naive_10x1x24.json   |  171 +
 benchmark/result/predict_naive_10x1x25.json   |  171 +
 benchmark/result/predict_naive_10x1x26.json   |  171 +
 benchmark/result/predict_naive_10x1x27.json   |  171 +
 benchmark/result/predict_naive_10x1x28.json   |  171 +
 benchmark/result/predict_naive_10x1x29.json   |  171 +
 benchmark/result/predict_naive_10x1x3.json    |  171 +
 benchmark/result/predict_naive_10x1x30.json   |  171 +
 benchmark/result/predict_naive_10x1x31.json   |  171 +
 benchmark/result/predict_naive_10x1x32.json   |  171 +
 benchmark/result/predict_naive_10x1x4.json    |  171 +
 benchmark/result/predict_naive_10x1x5.json    |  171 +
 benchmark/result/predict_naive_10x1x6.json    |  171 +
 benchmark/result/predict_naive_10x1x7.json    |  171 +
 benchmark/result/predict_naive_10x1x8.json    |  171 +
 benchmark/result/predict_naive_10x1x9.json    |  171 +
 benchmark/result/predict_naive_11x1x1.json    |  171 +
 benchmark/result/predict_naive_11x1x10.json   |  171 +
 benchmark/result/predict_naive_11x1x11.json   |  171 +
 benchmark/result/predict_naive_11x1x12.json   |  171 +
 benchmark/result/predict_naive_11x1x13.json   |  171 +
 benchmark/result/predict_naive_11x1x14.json   |  171 +
 benchmark/result/predict_naive_11x1x15.json   |  171 +
 benchmark/result/predict_naive_11x1x16.json   |  171 +
 benchmark/result/predict_naive_11x1x17.json   |  171 +
 benchmark/result/predict_naive_11x1x18.json   |  171 +
 benchmark/result/predict_naive_11x1x19.json   |  171 +
 benchmark/result/predict_naive_11x1x2.json    |  171 +
 benchmark/result/predict_naive_11x1x20.json   |  171 +
 benchmark/result/predict_naive_11x1x21.json   |  171 +
 benchmark/result/predict_naive_11x1x22.json   |  171 +
 benchmark/result/predict_naive_11x1x23.json   |  171 +
 benchmark/result/predict_naive_11x1x24.json   |  171 +
 benchmark/result/predict_naive_11x1x25.json   |  171 +
 benchmark/result/predict_naive_11x1x26.json   |  171 +
 benchmark/result/predict_naive_11x1x27.json   |  171 +
 benchmark/result/predict_naive_11x1x28.json   |  171 +
 benchmark/result/predict_naive_11x1x29.json   |  171 +
 benchmark/result/predict_naive_11x1x3.json    |  171 +
 benchmark/result/predict_naive_11x1x30.json   |  171 +
 benchmark/result/predict_naive_11x1x31.json   |  171 +
 benchmark/result/predict_naive_11x1x32.json   |  171 +
 benchmark/result/predict_naive_11x1x4.json    |  171 +
 benchmark/result/predict_naive_11x1x5.json    |  171 +
 benchmark/result/predict_naive_11x1x6.json    |  171 +
 benchmark/result/predict_naive_11x1x7.json    |  171 +
 benchmark/result/predict_naive_11x1x8.json    |  171 +
 benchmark/result/predict_naive_11x1x9.json    |  171 +
 benchmark/result/predict_naive_12x1x1.json    |  171 +
 benchmark/result/predict_naive_12x1x10.json   |  171 +
 benchmark/result/predict_naive_12x1x11.json   |  171 +
 benchmark/result/predict_naive_12x1x12.json   |  171 +
 benchmark/result/predict_naive_12x1x13.json   |  171 +
 benchmark/result/predict_naive_12x1x14.json   |  171 +
 benchmark/result/predict_naive_12x1x15.json   |  171 +
 benchmark/result/predict_naive_12x1x16.json   |  171 +
 benchmark/result/predict_naive_12x1x17.json   |  171 +
 benchmark/result/predict_naive_12x1x18.json   |  171 +
 benchmark/result/predict_naive_12x1x19.json   |  171 +
 benchmark/result/predict_naive_12x1x2.json    |  171 +
 benchmark/result/predict_naive_12x1x20.json   |  171 +
 benchmark/result/predict_naive_12x1x21.json   |  171 +
 benchmark/result/predict_naive_12x1x22.json   |  171 +
 benchmark/result/predict_naive_12x1x23.json   |  171 +
 benchmark/result/predict_naive_12x1x24.json   |  171 +
 benchmark/result/predict_naive_12x1x25.json   |  171 +
 benchmark/result/predict_naive_12x1x26.json   |  171 +
 benchmark/result/predict_naive_12x1x27.json   |  171 +
 benchmark/result/predict_naive_12x1x28.json   |  171 +
 benchmark/result/predict_naive_12x1x29.json   |  171 +
 benchmark/result/predict_naive_12x1x3.json    |  171 +
 benchmark/result/predict_naive_12x1x30.json   |  171 +
 benchmark/result/predict_naive_12x1x31.json   |  171 +
 benchmark/result/predict_naive_12x1x32.json   |  171 +
 benchmark/result/predict_naive_12x1x4.json    |  171 +
 benchmark/result/predict_naive_12x1x5.json    |  171 +
 benchmark/result/predict_naive_12x1x6.json    |  171 +
 benchmark/result/predict_naive_12x1x7.json    |  171 +
 benchmark/result/predict_naive_12x1x8.json    |  171 +
 benchmark/result/predict_naive_12x1x9.json    |  171 +
 benchmark/result/predict_naive_13x1x1.json    |  171 +
 benchmark/result/predict_naive_13x1x10.json   |  171 +
 benchmark/result/predict_naive_13x1x11.json   |  171 +
 benchmark/result/predict_naive_13x1x12.json   |  171 +
 benchmark/result/predict_naive_13x1x13.json   |  171 +
 benchmark/result/predict_naive_13x1x14.json   |  171 +
 benchmark/result/predict_naive_13x1x15.json   |  171 +
 benchmark/result/predict_naive_13x1x16.json   |  171 +
 benchmark/result/predict_naive_13x1x17.json   |  171 +
 benchmark/result/predict_naive_13x1x18.json   |  171 +
 benchmark/result/predict_naive_13x1x19.json   |  171 +
 benchmark/result/predict_naive_13x1x2.json    |  171 +
 benchmark/result/predict_naive_13x1x20.json   |  171 +
 benchmark/result/predict_naive_13x1x21.json   |  171 +
 benchmark/result/predict_naive_13x1x22.json   |  171 +
 benchmark/result/predict_naive_13x1x23.json   |  171 +
 benchmark/result/predict_naive_13x1x24.json   |  171 +
 benchmark/result/predict_naive_13x1x25.json   |  171 +
 benchmark/result/predict_naive_13x1x26.json   |  171 +
 benchmark/result/predict_naive_13x1x27.json   |  171 +
 benchmark/result/predict_naive_13x1x28.json   |  171 +
 benchmark/result/predict_naive_13x1x29.json   |  171 +
 benchmark/result/predict_naive_13x1x3.json    |  171 +
 benchmark/result/predict_naive_13x1x30.json   |  171 +
 benchmark/result/predict_naive_13x1x31.json   |  171 +
 benchmark/result/predict_naive_13x1x32.json   |  171 +
 benchmark/result/predict_naive_13x1x4.json    |  171 +
 benchmark/result/predict_naive_13x1x5.json    |  171 +
 benchmark/result/predict_naive_13x1x6.json    |  171 +
 benchmark/result/predict_naive_13x1x7.json    |  171 +
 benchmark/result/predict_naive_13x1x8.json    |  171 +
 benchmark/result/predict_naive_13x1x9.json    |  171 +
 benchmark/result/predict_naive_14x1x1.json    |  171 +
 benchmark/result/predict_naive_14x1x10.json   |  171 +
 benchmark/result/predict_naive_14x1x11.json   |  171 +
 benchmark/result/predict_naive_14x1x12.json   |  171 +
 benchmark/result/predict_naive_14x1x13.json   |  171 +
 benchmark/result/predict_naive_14x1x14.json   |  171 +
 benchmark/result/predict_naive_14x1x15.json   |  171 +
 benchmark/result/predict_naive_14x1x16.json   |  171 +
 benchmark/result/predict_naive_14x1x17.json   |  171 +
 benchmark/result/predict_naive_14x1x18.json   |  171 +
 benchmark/result/predict_naive_14x1x19.json   |  171 +
 benchmark/result/predict_naive_14x1x2.json    |  171 +
 benchmark/result/predict_naive_14x1x20.json   |  171 +
 benchmark/result/predict_naive_14x1x21.json   |  171 +
 benchmark/result/predict_naive_14x1x22.json   |  171 +
 benchmark/result/predict_naive_14x1x23.json   |  171 +
 benchmark/result/predict_naive_14x1x24.json   |  171 +
 benchmark/result/predict_naive_14x1x25.json   |  171 +
 benchmark/result/predict_naive_14x1x26.json   |  171 +
 benchmark/result/predict_naive_14x1x27.json   |  171 +
 benchmark/result/predict_naive_14x1x28.json   |  171 +
 benchmark/result/predict_naive_14x1x29.json   |  171 +
 benchmark/result/predict_naive_14x1x3.json    |  171 +
 benchmark/result/predict_naive_14x1x30.json   |  171 +
 benchmark/result/predict_naive_14x1x31.json   |  171 +
 benchmark/result/predict_naive_14x1x32.json   |  171 +
 benchmark/result/predict_naive_14x1x4.json    |  171 +
 benchmark/result/predict_naive_14x1x5.json    |  171 +
 benchmark/result/predict_naive_14x1x6.json    |  171 +
 benchmark/result/predict_naive_14x1x7.json    |  171 +
 benchmark/result/predict_naive_14x1x8.json    |  171 +
 benchmark/result/predict_naive_14x1x9.json    |  171 +
 benchmark/result/predict_naive_15x1x1.json    |  171 +
 benchmark/result/predict_naive_15x1x10.json   |  171 +
 benchmark/result/predict_naive_15x1x11.json   |  171 +
 benchmark/result/predict_naive_15x1x12.json   |  171 +
 benchmark/result/predict_naive_15x1x13.json   |  171 +
 benchmark/result/predict_naive_15x1x14.json   |  171 +
 benchmark/result/predict_naive_15x1x15.json   |  171 +
 benchmark/result/predict_naive_15x1x16.json   |  171 +
 benchmark/result/predict_naive_15x1x17.json   |  171 +
 benchmark/result/predict_naive_15x1x18.json   |  171 +
 benchmark/result/predict_naive_15x1x19.json   |  171 +
 benchmark/result/predict_naive_15x1x2.json    |  171 +
 benchmark/result/predict_naive_15x1x20.json   |  171 +
 benchmark/result/predict_naive_15x1x21.json   |  171 +
 benchmark/result/predict_naive_15x1x22.json   |  171 +
 benchmark/result/predict_naive_15x1x23.json   |  171 +
 benchmark/result/predict_naive_15x1x24.json   |  171 +
 benchmark/result/predict_naive_15x1x25.json   |  171 +
 benchmark/result/predict_naive_15x1x26.json   |  171 +
 benchmark/result/predict_naive_15x1x27.json   |  171 +
 benchmark/result/predict_naive_15x1x28.json   |  171 +
 benchmark/result/predict_naive_15x1x29.json   |  171 +
 benchmark/result/predict_naive_15x1x3.json    |  171 +
 benchmark/result/predict_naive_15x1x30.json   |  171 +
 benchmark/result/predict_naive_15x1x31.json   |  171 +
 benchmark/result/predict_naive_15x1x32.json   |  171 +
 benchmark/result/predict_naive_15x1x4.json    |  171 +
 benchmark/result/predict_naive_15x1x5.json    |  171 +
 benchmark/result/predict_naive_15x1x6.json    |  171 +
 benchmark/result/predict_naive_15x1x7.json    |  171 +
 benchmark/result/predict_naive_15x1x8.json    |  171 +
 benchmark/result/predict_naive_15x1x9.json    |  171 +
 benchmark/result/predict_naive_16x1x1.json    |  171 +
 benchmark/result/predict_naive_16x1x10.json   |  171 +
 benchmark/result/predict_naive_16x1x11.json   |  171 +
 benchmark/result/predict_naive_16x1x12.json   |  171 +
 benchmark/result/predict_naive_16x1x13.json   |  171 +
 benchmark/result/predict_naive_16x1x14.json   |  171 +
 benchmark/result/predict_naive_16x1x15.json   |  171 +
 benchmark/result/predict_naive_16x1x16.json   |  171 +
 benchmark/result/predict_naive_16x1x17.json   |  171 +
 benchmark/result/predict_naive_16x1x18.json   |  171 +
 benchmark/result/predict_naive_16x1x19.json   |  171 +
 benchmark/result/predict_naive_16x1x2.json    |  171 +
 benchmark/result/predict_naive_16x1x20.json   |  171 +
 benchmark/result/predict_naive_16x1x21.json   |  171 +
 benchmark/result/predict_naive_16x1x22.json   |  171 +
 benchmark/result/predict_naive_16x1x23.json   |  171 +
 benchmark/result/predict_naive_16x1x24.json   |  171 +
 benchmark/result/predict_naive_16x1x25.json   |  171 +
 benchmark/result/predict_naive_16x1x26.json   |  171 +
 benchmark/result/predict_naive_16x1x27.json   |  171 +
 benchmark/result/predict_naive_16x1x28.json   |  171 +
 benchmark/result/predict_naive_16x1x29.json   |  171 +
 benchmark/result/predict_naive_16x1x3.json    |  171 +
 benchmark/result/predict_naive_16x1x30.json   |  171 +
 benchmark/result/predict_naive_16x1x31.json   |  171 +
 benchmark/result/predict_naive_16x1x32.json   |  171 +
 benchmark/result/predict_naive_16x1x4.json    |  171 +
 benchmark/result/predict_naive_16x1x5.json    |  171 +
 benchmark/result/predict_naive_16x1x6.json    |  171 +
 benchmark/result/predict_naive_16x1x7.json    |  171 +
 benchmark/result/predict_naive_16x1x8.json    |  171 +
 benchmark/result/predict_naive_16x1x9.json    |  171 +
 benchmark/result/predict_naive_17x1x1.json    |  171 +
 benchmark/result/predict_naive_17x1x10.json   |  171 +
 benchmark/result/predict_naive_17x1x11.json   |  171 +
 benchmark/result/predict_naive_17x1x12.json   |  171 +
 benchmark/result/predict_naive_17x1x13.json   |  171 +
 benchmark/result/predict_naive_17x1x14.json   |  171 +
 benchmark/result/predict_naive_17x1x15.json   |  171 +
 benchmark/result/predict_naive_17x1x16.json   |  171 +
 benchmark/result/predict_naive_17x1x17.json   |  171 +
 benchmark/result/predict_naive_17x1x18.json   |  171 +
 benchmark/result/predict_naive_17x1x19.json   |  171 +
 benchmark/result/predict_naive_17x1x2.json    |  171 +
 benchmark/result/predict_naive_17x1x20.json   |  171 +
 benchmark/result/predict_naive_17x1x21.json   |  171 +
 benchmark/result/predict_naive_17x1x22.json   |  171 +
 benchmark/result/predict_naive_17x1x23.json   |  171 +
 benchmark/result/predict_naive_17x1x24.json   |  171 +
 benchmark/result/predict_naive_17x1x25.json   |  171 +
 benchmark/result/predict_naive_17x1x26.json   |  171 +
 benchmark/result/predict_naive_17x1x27.json   |  171 +
 benchmark/result/predict_naive_17x1x28.json   |  171 +
 benchmark/result/predict_naive_17x1x29.json   |  171 +
 benchmark/result/predict_naive_17x1x3.json    |  171 +
 benchmark/result/predict_naive_17x1x30.json   |  171 +
 benchmark/result/predict_naive_17x1x31.json   |  171 +
 benchmark/result/predict_naive_17x1x32.json   |  171 +
 benchmark/result/predict_naive_17x1x4.json    |  171 +
 benchmark/result/predict_naive_17x1x5.json    |  171 +
 benchmark/result/predict_naive_17x1x6.json    |  171 +
 benchmark/result/predict_naive_17x1x7.json    |  171 +
 benchmark/result/predict_naive_17x1x8.json    |  171 +
 benchmark/result/predict_naive_17x1x9.json    |  171 +
 benchmark/result/predict_naive_18x1x1.json    |  171 +
 benchmark/result/predict_naive_18x1x10.json   |  171 +
 benchmark/result/predict_naive_18x1x11.json   |  171 +
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 benchmark/result/predict_naive_18x1x13.json   |  171 +
 benchmark/result/predict_naive_18x1x14.json   |  171 +
 benchmark/result/predict_naive_18x1x15.json   |  171 +
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 benchmark/result/predict_naive_18x1x19.json   |  171 +
 benchmark/result/predict_naive_18x1x2.json    |  171 +
 benchmark/result/predict_naive_18x1x20.json   |  171 +
 benchmark/result/predict_naive_18x1x21.json   |  171 +
 benchmark/result/predict_naive_18x1x22.json   |  171 +
 benchmark/result/predict_naive_18x1x23.json   |  171 +
 benchmark/result/predict_naive_18x1x24.json   |  171 +
 benchmark/result/predict_naive_18x1x25.json   |  171 +
 benchmark/result/predict_naive_18x1x26.json   |  171 +
 benchmark/result/predict_naive_18x1x27.json   |  171 +
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 benchmark/result/predict_naive_18x1x29.json   |  171 +
 benchmark/result/predict_naive_18x1x3.json    |  171 +
 benchmark/result/predict_naive_18x1x30.json   |  171 +
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 benchmark/result/predict_naive_18x1x32.json   |  171 +
 benchmark/result/predict_naive_18x1x4.json    |  171 +
 benchmark/result/predict_naive_18x1x5.json    |  171 +
 benchmark/result/predict_naive_18x1x6.json    |  171 +
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 benchmark/result/predict_naive_19x1x11.json   |  171 +
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 benchmark/result/predict_naive_19x1x2.json    |  171 +
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 benchmark/result/predict_naive_19x1x22.json   |  171 +
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 benchmark/result/predict_naive_19x1x24.json   |  171 +
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 benchmark/result/predict_naive_19x1x29.json   |  171 +
 benchmark/result/predict_naive_19x1x3.json    |  171 +
 benchmark/result/predict_naive_19x1x30.json   |  171 +
 benchmark/result/predict_naive_19x1x31.json   |  171 +
 benchmark/result/predict_naive_19x1x32.json   |  171 +
 benchmark/result/predict_naive_19x1x4.json    |  171 +
 benchmark/result/predict_naive_19x1x5.json    |  171 +
 benchmark/result/predict_naive_19x1x6.json    |  171 +
 benchmark/result/predict_naive_19x1x7.json    |  171 +
 benchmark/result/predict_naive_19x1x8.json    |  171 +
 benchmark/result/predict_naive_19x1x9.json    |  171 +
 benchmark/result/predict_naive_1x1x1.json     |  171 +
 benchmark/result/predict_naive_1x1x10.json    |  171 +
 benchmark/result/predict_naive_1x1x11.json    |  171 +
 benchmark/result/predict_naive_1x1x12.json    |  171 +
 benchmark/result/predict_naive_1x1x13.json    |  171 +
 benchmark/result/predict_naive_1x1x14.json    |  171 +
 benchmark/result/predict_naive_1x1x15.json    |  171 +
 benchmark/result/predict_naive_1x1x16.json    |  171 +
 benchmark/result/predict_naive_1x1x17.json    |  171 +
 benchmark/result/predict_naive_1x1x18.json    |  171 +
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 benchmark/result/predict_naive_1x1x2.json     |  171 +
 benchmark/result/predict_naive_1x1x20.json    |  171 +
 benchmark/result/predict_naive_1x1x21.json    |  171 +
 benchmark/result/predict_naive_1x1x22.json    |  171 +
 benchmark/result/predict_naive_1x1x23.json    |  171 +
 benchmark/result/predict_naive_1x1x24.json    |  171 +
 benchmark/result/predict_naive_1x1x25.json    |  171 +
 benchmark/result/predict_naive_1x1x26.json    |  171 +
 benchmark/result/predict_naive_1x1x27.json    |  171 +
 benchmark/result/predict_naive_1x1x28.json    |  171 +
 benchmark/result/predict_naive_1x1x29.json    |  171 +
 benchmark/result/predict_naive_1x1x3.json     |  171 +
 benchmark/result/predict_naive_1x1x30.json    |  171 +
 benchmark/result/predict_naive_1x1x31.json    |  171 +
 benchmark/result/predict_naive_1x1x32.json    |  171 +
 benchmark/result/predict_naive_1x1x4.json     |  171 +
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 benchmark/script/profile.sh                   |   53 +
 benchmark/update_linalg_xx0.cpp               |   19 +-
 linalg/eigen/fcarouge/linalg.hpp              |   30 +
 linalg/naive/fcarouge/linalg.hpp              |   31 +-
 sample/CMakeLists.txt                         |   10 +-
 sample/kf_6x2x0_vehicle_location.cpp          |   13 +-
 sample/kf_8x4x0_deep_sort_bounding_box.cpp    |   13 +-
 test/CMakeLists.txt                           |   61 +
 ...an_constructor_default_5x4x3_constexpr.cpp |   86 +
 test/kf_2x1x1_rocket_altitude_linalg.cpp      |  152 +
 ...kf_8x4x0_deep_sort_bounding_box_linalg.cpp |  221 +
 test/linalg_assign_constexpr.cpp              |   56 +
 test/linalg_constructor_constexpr.cpp         |   63 +
 test/linalg_constructor_default_constexpr.cpp |   60 +
 test/linalg_copy_constexpr.cpp                |   56 +
 test/linalg_division_householder.cpp          |   68 +
 ...nalg_division_householder_pivot_column.cpp |   71 +
 ...linalg_division_householder_pivot_full.cpp |   71 +
 test/linalg_division_ldlt.cpp                 |   68 +
 test/linalg_division_llt.cpp                  |  104 +
 test/linalg_division_orthogonal.cpp           |   71 +
 test/linalg_division_pivot_full.cpp           |   68 +
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 test/linalg_identity_constexpr.cpp            |   63 +
 test/linalg_identity_default_constexpr.cpp    |   58 +
 .../linalg_operator_bracket_1x2_constexpr.cpp |   52 +
 test/linalg_operator_bracket_constexpr.cpp    |   58 +
 test/linalg_operator_equality_constexpr.cpp   |   58 +
 test/linalg_zero_constexpr.cpp                |   63 +
 test/linalg_zero_default_constexpr.cpp        |   57 +
 1057 files changed, 183018 insertions(+), 21 deletions(-)
 create mode 100644 benchmark/image/predict_naive.svg
 create mode 100644 benchmark/image/update_naive.svg
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 create mode 100644 benchmark/result/predict_naive_31x1x3.json
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 create mode 100644 benchmark/result/predict_naive_31x1x32.json
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 create mode 100644 benchmark/result/predict_naive_31x1x6.json
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 create mode 100644 benchmark/result/predict_naive_31x1x8.json
 create mode 100644 benchmark/result/predict_naive_31x1x9.json
 create mode 100644 benchmark/result/predict_naive_32x1x1.json
 create mode 100644 benchmark/result/predict_naive_32x1x10.json
 create mode 100644 benchmark/result/predict_naive_32x1x11.json
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 create mode 100644 benchmark/result/predict_naive_32x1x20.json
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 create mode 100644 benchmark/result/predict_naive_32x1x22.json
 create mode 100644 benchmark/result/predict_naive_32x1x23.json
 create mode 100644 benchmark/result/predict_naive_32x1x24.json
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 create mode 100644 benchmark/result/predict_naive_3x1x17.json
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 create mode 100644 benchmark/result/predict_naive_3x1x20.json
 create mode 100644 benchmark/result/predict_naive_3x1x21.json
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 create mode 100644 benchmark/result/predict_naive_3x1x25.json
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 create mode 100644 benchmark/result/predict_naive_3x1x6.json
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 create mode 100644 benchmark/result/predict_naive_3x1x8.json
 create mode 100644 benchmark/result/predict_naive_3x1x9.json
 create mode 100644 benchmark/result/predict_naive_4x1x1.json
 create mode 100644 benchmark/result/predict_naive_4x1x10.json
 create mode 100644 benchmark/result/predict_naive_4x1x11.json
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 create mode 100644 benchmark/result/predict_naive_4x1x13.json
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 create mode 100644 benchmark/result/predict_naive_4x1x16.json
 create mode 100644 benchmark/result/predict_naive_4x1x17.json
 create mode 100644 benchmark/result/predict_naive_4x1x18.json
 create mode 100644 benchmark/result/predict_naive_4x1x19.json
 create mode 100644 benchmark/result/predict_naive_4x1x2.json
 create mode 100644 benchmark/result/predict_naive_4x1x20.json
 create mode 100644 benchmark/result/predict_naive_4x1x21.json
 create mode 100644 benchmark/result/predict_naive_4x1x22.json
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 create mode 100644 benchmark/result/predict_naive_4x1x26.json
 create mode 100644 benchmark/result/predict_naive_4x1x27.json
 create mode 100644 benchmark/result/predict_naive_4x1x28.json
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 create mode 100644 benchmark/result/predict_naive_4x1x3.json
 create mode 100644 benchmark/result/predict_naive_4x1x30.json
 create mode 100644 benchmark/result/predict_naive_4x1x31.json
 create mode 100644 benchmark/result/predict_naive_4x1x32.json
 create mode 100644 benchmark/result/predict_naive_4x1x4.json
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 create mode 100644 benchmark/result/predict_naive_4x1x8.json
 create mode 100644 benchmark/result/predict_naive_4x1x9.json
 create mode 100644 benchmark/result/predict_naive_5x1x1.json
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 create mode 100644 benchmark/result/predict_naive_5x1x3.json
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 create mode 100644 benchmark/result/predict_naive_5x1x31.json
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 create mode 100644 benchmark/result/predict_naive_5x1x4.json
 create mode 100644 benchmark/result/predict_naive_5x1x5.json
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 create mode 100644 benchmark/result/predict_naive_6x1x1.json
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 create mode 100644 benchmark/result/predict_naive_6x1x3.json
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 create mode 100644 benchmark/result/predict_naive_6x1x31.json
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 create mode 100644 benchmark/result/predict_naive_6x1x4.json
 create mode 100644 benchmark/result/predict_naive_6x1x5.json
 create mode 100644 benchmark/result/predict_naive_6x1x6.json
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 create mode 100644 benchmark/result/predict_naive_6x1x8.json
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 create mode 100644 benchmark/result/predict_naive_7x1x1.json
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 create mode 100644 benchmark/result/predict_naive_7x1x5.json
 create mode 100644 benchmark/result/predict_naive_7x1x6.json
 create mode 100644 benchmark/result/predict_naive_7x1x7.json
 create mode 100644 benchmark/result/predict_naive_7x1x8.json
 create mode 100644 benchmark/result/predict_naive_7x1x9.json
 create mode 100644 benchmark/result/predict_naive_8x1x1.json
 create mode 100644 benchmark/result/predict_naive_8x1x10.json
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 create mode 100644 benchmark/result/predict_naive_8x1x12.json
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 create mode 100644 benchmark/result/predict_naive_8x1x20.json
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 create mode 100644 benchmark/result/predict_naive_8x1x32.json
 create mode 100644 benchmark/result/predict_naive_8x1x4.json
 create mode 100644 benchmark/result/predict_naive_8x1x5.json
 create mode 100644 benchmark/result/predict_naive_8x1x6.json
 create mode 100644 benchmark/result/predict_naive_8x1x7.json
 create mode 100644 benchmark/result/predict_naive_8x1x8.json
 create mode 100644 benchmark/result/predict_naive_8x1x9.json
 create mode 100644 benchmark/result/predict_naive_9x1x1.json
 create mode 100644 benchmark/result/predict_naive_9x1x10.json
 create mode 100644 benchmark/result/predict_naive_9x1x11.json
 create mode 100644 benchmark/result/predict_naive_9x1x12.json
 create mode 100644 benchmark/result/predict_naive_9x1x13.json
 create mode 100644 benchmark/result/predict_naive_9x1x14.json
 create mode 100644 benchmark/result/predict_naive_9x1x15.json
 create mode 100644 benchmark/result/predict_naive_9x1x16.json
 create mode 100644 benchmark/result/predict_naive_9x1x17.json
 create mode 100644 benchmark/result/predict_naive_9x1x18.json
 create mode 100644 benchmark/result/predict_naive_9x1x19.json
 create mode 100644 benchmark/result/predict_naive_9x1x2.json
 create mode 100644 benchmark/result/predict_naive_9x1x20.json
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 create mode 100644 benchmark/result/predict_naive_9x1x22.json
 create mode 100644 benchmark/result/predict_naive_9x1x23.json
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 create mode 100644 benchmark/result/predict_naive_9x1x26.json
 create mode 100644 benchmark/result/predict_naive_9x1x27.json
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 create mode 100644 benchmark/result/predict_naive_9x1x29.json
 create mode 100644 benchmark/result/predict_naive_9x1x3.json
 create mode 100644 benchmark/result/predict_naive_9x1x30.json
 create mode 100644 benchmark/result/predict_naive_9x1x31.json
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 create mode 100644 benchmark/result/predict_naive_9x1x6.json
 create mode 100644 benchmark/result/predict_naive_9x1x7.json
 create mode 100644 benchmark/result/predict_naive_9x1x8.json
 create mode 100644 benchmark/result/predict_naive_9x1x9.json
 create mode 100644 benchmark/script/profile.sh
 create mode 100644 test/kalman_constructor_default_5x4x3_constexpr.cpp
 create mode 100644 test/kf_2x1x1_rocket_altitude_linalg.cpp
 create mode 100644 test/kf_8x4x0_deep_sort_bounding_box_linalg.cpp
 create mode 100644 test/linalg_assign_constexpr.cpp
 create mode 100644 test/linalg_constructor_constexpr.cpp
 create mode 100644 test/linalg_constructor_default_constexpr.cpp
 create mode 100644 test/linalg_copy_constexpr.cpp
 create mode 100644 test/linalg_division_householder.cpp
 create mode 100644 test/linalg_division_householder_pivot_column.cpp
 create mode 100644 test/linalg_division_householder_pivot_full.cpp
 create mode 100644 test/linalg_division_ldlt.cpp
 create mode 100644 test/linalg_division_llt.cpp
 create mode 100644 test/linalg_division_orthogonal.cpp
 create mode 100644 test/linalg_division_pivot_full.cpp
 create mode 100644 test/linalg_division_pivot_partial.cpp
 create mode 100644 test/linalg_identity_constexpr.cpp
 create mode 100644 test/linalg_identity_default_constexpr.cpp
 create mode 100644 test/linalg_operator_bracket_1x2_constexpr.cpp
 create mode 100644 test/linalg_operator_bracket_constexpr.cpp
 create mode 100644 test/linalg_operator_equality_constexpr.cpp
 create mode 100644 test/linalg_zero_constexpr.cpp
 create mode 100644 test/linalg_zero_default_constexpr.cpp

diff --git a/benchmark/CMakeLists.txt b/benchmark/CMakeLists.txt
index b1f9e2704..49d948ce8 100644
--- a/benchmark/CMakeLists.txt
+++ b/benchmark/CMakeLists.txt
@@ -68,7 +68,7 @@ foreach(BENCHMARK "baseline.cpp" "predict_1x1x0.cpp" "predict_1x1x1.cpp"
            "--benchmark_out=${NAME}.json")
 endforeach()
 
-foreach(BACKEND IN ITEMS "eigen")
+foreach(BACKEND IN ITEMS "eigen" "naive")
   foreach(STATE_SIZE RANGE 1 2)
     foreach(INPUT_SIZE RANGE 1 2)
       configure_file(predict_linalg_x1x.cpp
diff --git a/benchmark/image/predict_naive.svg b/benchmark/image/predict_naive.svg
new file mode 100644
index 000000000..207210118
--- /dev/null
+++ b/benchmark/image/predict_naive.svg
@@ -0,0 +1,6011 @@
+<?xml version="1.0" encoding="utf-8"  standalone="no"?>
+<svg 
+ width="800" height="600"
+ viewBox="0 0 800 600"
+ xmlns="http://www.w3.org/2000/svg"
+ xmlns:xlink="http://www.w3.org/1999/xlink"
+>
+
+<title>Gnuplot</title>
+<desc>Produced by GNUPLOT 5.4 patchlevel 2 </desc>
+
+<g id="gnuplot_canvas">
+
+<rect x="0" y="0" width="800" height="600" fill="#ffffff"/>
+<defs>
+
+	<circle id='gpDot' r='0.5' stroke-width='0.5' stroke='currentColor'/>
+	<path id='gpPt0' stroke-width='0.222' stroke='currentColor' d='M-1,0 h2 M0,-1 v2'/>
+	<path id='gpPt1' stroke-width='0.222' stroke='currentColor' d='M-1,-1 L1,1 M1,-1 L-1,1'/>
+	<path id='gpPt2' stroke-width='0.222' stroke='currentColor' d='M-1,0 L1,0 M0,-1 L0,1 M-1,-1 L1,1 M-1,1 L1,-1'/>
+	<rect id='gpPt3' stroke-width='0.222' stroke='currentColor' x='-1' y='-1' width='2' height='2'/>
+	<rect id='gpPt4' stroke-width='0.222' stroke='currentColor' fill='currentColor' x='-1' y='-1' width='2' height='2'/>
+	<circle id='gpPt5' stroke-width='0.222' stroke='currentColor' cx='0' cy='0' r='1'/>
+	<use xlink:href='#gpPt5' id='gpPt6' fill='currentColor' stroke='none'/>
+	<path id='gpPt7' stroke-width='0.222' stroke='currentColor' d='M0,-1.33 L-1.33,0.67 L1.33,0.67 z'/>
+	<use xlink:href='#gpPt7' id='gpPt8' fill='currentColor' stroke='none'/>
+	<use xlink:href='#gpPt7' id='gpPt9' stroke='currentColor' transform='rotate(180)'/>
+	<use xlink:href='#gpPt9' id='gpPt10' fill='currentColor' stroke='none'/>
+	<use xlink:href='#gpPt3' id='gpPt11' stroke='currentColor' transform='rotate(45)'/>
+	<use xlink:href='#gpPt11' id='gpPt12' fill='currentColor' stroke='none'/>
+	<path id='gpPt13' stroke-width='0.222' stroke='currentColor' d='M0,1.330 L1.265,0.411 L0.782,-1.067 L-0.782,-1.076 L-1.265,0.411 z'/>
+	<use xlink:href='#gpPt13' id='gpPt14' fill='currentColor' stroke='none'/>
+	<filter id='textbox' filterUnits='objectBoundingBox' x='0' y='0' height='1' width='1'>
+	  <feFlood flood-color='#FFFFFF' flood-opacity='1' result='bgnd'/>
+	  <feComposite in='SourceGraphic' in2='bgnd' operator='atop'/>
+	</filter>
+	<filter id='greybox' filterUnits='objectBoundingBox' x='0' y='0' height='1' width='1'>
+	  <feFlood flood-color='lightgrey' flood-opacity='1' result='grey'/>
+	  <feComposite in='SourceGraphic' in2='grey' operator='atop'/>
+	</filter>
+</defs>
+<g fill="none" color="#FFFFFF" stroke="currentColor" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+</g>
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+	<g transform="translate(18.00,585.90)" stroke="none" fill="black" font-family="Arial" font-size="12.00"  text-anchor="start">
+		<text><tspan font-family="Arial" >Wed Jun 14 20:28:37 2023</tspan></text>
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+</g>
+	<g id="gnuplot_plot_1" ><title>gnuplot_plot_1</title>
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+	<path stroke='gray' stroke-dasharray='2,4' class="gridline"  d='M615.56,511.94 L539.61,467.13  '/></g>
+<g fill="none" color="gray" stroke="gray" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+</g>
+<g fill="none" color="black" stroke="currentColor" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+	<path stroke='black'  d='M615.56,511.94 L609.42,508.33  '/>	<g transform="translate(621.27,523.07)" stroke="none" fill="black" font-family="Arial" font-size="12.00"  text-anchor="middle">
+		<text><tspan font-family="Arial" > 24</tspan></text>
+	</g>
+</g>
+<g fill="none" color="black" stroke="currentColor" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+</g>
+<g fill="none" color="black" stroke="black" stroke-width="0.50" stroke-linecap="butt" stroke-linejoin="miter">
+</g>
+<g fill="none" color="gray" stroke="currentColor" stroke-width="0.50" stroke-linecap="butt" stroke-linejoin="miter">
+	<path stroke='gray' stroke-dasharray='2,4' class="gridline"  d='M628.26,509.45 L545.68,460.72  '/></g>
+<g fill="none" color="gray" stroke="gray" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+</g>
+<g fill="none" color="black" stroke="currentColor" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+	<path stroke='black'  d='M628.26,509.45 L622.13,505.83  '/>	<g transform="translate(633.98,520.57)" stroke="none" fill="black" font-family="Arial" font-size="12.00"  text-anchor="middle">
+		<text><tspan font-family="Arial" > 25</tspan></text>
+	</g>
+</g>
+<g fill="none" color="black" stroke="currentColor" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+</g>
+<g fill="none" color="black" stroke="black" stroke-width="0.50" stroke-linecap="butt" stroke-linejoin="miter">
+</g>
+<g fill="none" color="gray" stroke="currentColor" stroke-width="0.50" stroke-linecap="butt" stroke-linejoin="miter">
+	<path stroke='gray' stroke-dasharray='2,4' class="gridline"  d='M640.96,506.95 L547.87,452.02  '/></g>
+<g fill="none" color="gray" stroke="gray" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+</g>
+<g fill="none" color="black" stroke="currentColor" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+	<path stroke='black'  d='M640.96,506.95 L634.83,503.33  '/>	<g transform="translate(646.68,518.08)" stroke="none" fill="black" font-family="Arial" font-size="12.00"  text-anchor="middle">
+		<text><tspan font-family="Arial" > 26</tspan></text>
+	</g>
+</g>
+<g fill="none" color="black" stroke="currentColor" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+</g>
+<g fill="none" color="black" stroke="black" stroke-width="0.50" stroke-linecap="butt" stroke-linejoin="miter">
+</g>
+<g fill="none" color="gray" stroke="currentColor" stroke-width="0.50" stroke-linecap="butt" stroke-linejoin="miter">
+	<path stroke='gray' stroke-dasharray='2,4' class="gridline"  d='M653.67,504.45 L550.07,443.32  '/></g>
+<g fill="none" color="gray" stroke="gray" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+</g>
+<g fill="none" color="black" stroke="currentColor" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+	<path stroke='black'  d='M653.67,504.45 L647.54,500.83  '/>	<g transform="translate(659.39,515.58)" stroke="none" fill="black" font-family="Arial" font-size="12.00"  text-anchor="middle">
+		<text><tspan font-family="Arial" > 27</tspan></text>
+	</g>
+</g>
+<g fill="none" color="black" stroke="currentColor" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+</g>
+<g fill="none" color="black" stroke="black" stroke-width="0.50" stroke-linecap="butt" stroke-linejoin="miter">
+</g>
+<g fill="none" color="gray" stroke="currentColor" stroke-width="0.50" stroke-linecap="butt" stroke-linejoin="miter">
+	<path stroke='gray' stroke-dasharray='2,4' class="gridline"  d='M666.37,501.95 L552.26,434.61  '/></g>
+<g fill="none" color="gray" stroke="gray" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+</g>
+<g fill="none" color="black" stroke="currentColor" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+	<path stroke='black'  d='M666.37,501.95 L660.24,498.33  '/>	<g transform="translate(672.09,513.08)" stroke="none" fill="black" font-family="Arial" font-size="12.00"  text-anchor="middle">
+		<text><tspan font-family="Arial" > 28</tspan></text>
+	</g>
+</g>
+<g fill="none" color="black" stroke="currentColor" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+</g>
+<g fill="none" color="black" stroke="black" stroke-width="0.50" stroke-linecap="butt" stroke-linejoin="miter">
+</g>
+<g fill="none" color="gray" stroke="currentColor" stroke-width="0.50" stroke-linecap="butt" stroke-linejoin="miter">
+	<path stroke='gray' stroke-dasharray='2,4' class="gridline"  d='M679.08,499.45 L554.45,425.91  '/></g>
+<g fill="none" color="gray" stroke="gray" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+</g>
+<g fill="none" color="black" stroke="currentColor" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+	<path stroke='black'  d='M679.08,499.45 L672.94,495.83  '/>	<g transform="translate(684.79,510.58)" stroke="none" fill="black" font-family="Arial" font-size="12.00"  text-anchor="middle">
+		<text><tspan font-family="Arial" > 29</tspan></text>
+	</g>
+</g>
+<g fill="none" color="black" stroke="currentColor" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+</g>
+<g fill="none" color="black" stroke="black" stroke-width="0.50" stroke-linecap="butt" stroke-linejoin="miter">
+</g>
+<g fill="none" color="gray" stroke="currentColor" stroke-width="0.50" stroke-linecap="butt" stroke-linejoin="miter">
+	<path stroke='gray' stroke-dasharray='2,4' class="gridline"  d='M691.78,496.95 L556.65,417.21  '/></g>
+<g fill="none" color="gray" stroke="gray" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+</g>
+<g fill="none" color="black" stroke="currentColor" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+	<path stroke='black'  d='M691.78,496.95 L685.65,493.33  '/>	<g transform="translate(697.50,508.08)" stroke="none" fill="black" font-family="Arial" font-size="12.00"  text-anchor="middle">
+		<text><tspan font-family="Arial" > 30</tspan></text>
+	</g>
+</g>
+<g fill="none" color="black" stroke="currentColor" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+</g>
+<g fill="none" color="black" stroke="black" stroke-width="0.50" stroke-linecap="butt" stroke-linejoin="miter">
+</g>
+<g fill="none" color="gray" stroke="currentColor" stroke-width="0.50" stroke-linecap="butt" stroke-linejoin="miter">
+	<path stroke='gray' stroke-dasharray='2,4' class="gridline"  d='M704.48,494.45 L574.23,417.59  '/></g>
+<g fill="none" color="gray" stroke="gray" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+</g>
+<g fill="none" color="black" stroke="currentColor" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+	<path stroke='black'  d='M704.48,494.45 L698.35,490.83  '/>	<g transform="translate(710.20,505.58)" stroke="none" fill="black" font-family="Arial" font-size="12.00"  text-anchor="middle">
+		<text><tspan font-family="Arial" > 31</tspan></text>
+	</g>
+</g>
+<g fill="none" color="black" stroke="currentColor" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+</g>
+<g fill="none" color="black" stroke="black" stroke-width="0.50" stroke-linecap="butt" stroke-linejoin="miter">
+</g>
+<g fill="none" color="gray" stroke="currentColor" stroke-width="0.50" stroke-linecap="butt" stroke-linejoin="miter">
+	<path stroke='gray' stroke-dasharray='2,4' class="gridline"  d='M717.19,491.95 L586.03,414.56  '/></g>
+<g fill="none" color="gray" stroke="gray" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+</g>
+<g fill="none" color="black" stroke="currentColor" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+	<path stroke='black'  d='M717.19,491.95 L711.05,488.34  '/>	<g transform="translate(722.90,503.08)" stroke="none" fill="black" font-family="Arial" font-size="12.00"  text-anchor="middle">
+		<text><tspan font-family="Arial" > 32</tspan></text>
+	</g>
+</g>
+<g fill="none" color="black" stroke="currentColor" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+	<g transform="translate(581.61,570.77)" stroke="none" fill="black" font-family="Arial" font-size="12.00"  text-anchor="middle">
+		<text><tspan font-family="Arial" >State (count)</tspan></text>
+	</g>
+</g>
+<g fill="none" color="black" stroke="black" stroke-width="0.50" stroke-linecap="butt" stroke-linejoin="miter">
+</g>
+<g fill="none" color="gray" stroke="currentColor" stroke-width="0.50" stroke-linecap="butt" stroke-linejoin="miter">
+	<path stroke='gray' stroke-dasharray='2,4' class="gridline"  d='M305.34,567.77 L722.02,485.81  '/></g>
+<g fill="none" color="gray" stroke="gray" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+</g>
+<g fill="none" color="black" stroke="currentColor" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+	<path stroke='black'  d='M305.34,567.77 L315.96,565.68  '/></g>
+<g fill="none" color="black" stroke="currentColor" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+	<path stroke='black'  d='M711.40,487.90 L722.02,485.81  '/>	<g transform="translate(295.45,575.84)" stroke="none" fill="black" font-family="Arial" font-size="12.00"  text-anchor="end">
+		<text><tspan font-family="Arial" > 1</tspan></text>
+	</g>
+</g>
+<g fill="none" color="black" stroke="currentColor" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+</g>
+<g fill="none" color="black" stroke="black" stroke-width="0.50" stroke-linecap="butt" stroke-linejoin="miter">
+</g>
+<g fill="none" color="gray" stroke="currentColor" stroke-width="0.50" stroke-linecap="butt" stroke-linejoin="miter">
+	<path stroke='gray' stroke-dasharray='2,4' class="gridline"  d='M410.80,541.25 L714.68,481.48  '/></g>
+<g fill="none" color="gray" stroke="currentColor" stroke-width="0.50" stroke-linecap="butt" stroke-linejoin="miter">
+	<path stroke='gray' stroke-dasharray='2,4' class="gridline"  d='M298.00,563.44 L309.80,561.12  '/></g>
+<g fill="none" color="gray" stroke="gray" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+</g>
+<g fill="none" color="black" stroke="currentColor" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+	<path stroke='black'  d='M298.00,563.44 L308.63,561.35  '/></g>
+<g fill="none" color="black" stroke="currentColor" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+	<path stroke='black'  d='M704.06,483.57 L714.68,481.48  '/>	<g transform="translate(288.11,571.51)" stroke="none" fill="black" font-family="Arial" font-size="12.00"  text-anchor="end">
+		<text><tspan font-family="Arial" > 2</tspan></text>
+	</g>
+</g>
+<g fill="none" color="black" stroke="currentColor" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+</g>
+<g fill="none" color="black" stroke="black" stroke-width="0.50" stroke-linecap="butt" stroke-linejoin="miter">
+</g>
+<g fill="none" color="gray" stroke="currentColor" stroke-width="0.50" stroke-linecap="butt" stroke-linejoin="miter">
+	<path stroke='gray' stroke-dasharray='2,4' class="gridline"  d='M442.61,529.23 L707.35,477.15  '/></g>
+<g fill="none" color="gray" stroke="currentColor" stroke-width="0.50" stroke-linecap="butt" stroke-linejoin="miter">
+	<path stroke='gray' stroke-dasharray='2,4' class="gridline"  d='M290.67,559.11 L302.42,556.80  '/></g>
+<g fill="none" color="gray" stroke="gray" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+</g>
+<g fill="none" color="black" stroke="currentColor" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+	<path stroke='black'  d='M290.67,559.11 L301.29,557.02  '/></g>
+<g fill="none" color="black" stroke="currentColor" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+	<path stroke='black'  d='M696.73,479.24 L707.35,477.15  '/>	<g transform="translate(280.78,567.18)" stroke="none" fill="black" font-family="Arial" font-size="12.00"  text-anchor="end">
+		<text><tspan font-family="Arial" > 3</tspan></text>
+	</g>
+</g>
+<g fill="none" color="black" stroke="currentColor" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+</g>
+<g fill="none" color="black" stroke="black" stroke-width="0.50" stroke-linecap="butt" stroke-linejoin="miter">
+</g>
+<g fill="none" color="gray" stroke="currentColor" stroke-width="0.50" stroke-linecap="butt" stroke-linejoin="miter">
+	<path stroke='gray' stroke-dasharray='2,4' class="gridline"  d='M465.10,519.03 L700.02,472.83  '/></g>
+<g fill="none" color="gray" stroke="currentColor" stroke-width="0.50" stroke-linecap="butt" stroke-linejoin="miter">
+	<path stroke='gray' stroke-dasharray='2,4' class="gridline"  d='M283.34,554.79 L295.12,552.47  '/></g>
+<g fill="none" color="gray" stroke="gray" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+</g>
+<g fill="none" color="black" stroke="currentColor" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+	<path stroke='black'  d='M283.34,554.79 L293.96,552.70  '/></g>
+<g fill="none" color="black" stroke="currentColor" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+	<path stroke='black'  d='M689.39,474.92 L700.02,472.83  '/>	<g transform="translate(273.44,562.85)" stroke="none" fill="black" font-family="Arial" font-size="12.00"  text-anchor="end">
+		<text><tspan font-family="Arial" > 4</tspan></text>
+	</g>
+</g>
+<g fill="none" color="black" stroke="currentColor" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+</g>
+<g fill="none" color="black" stroke="black" stroke-width="0.50" stroke-linecap="butt" stroke-linejoin="miter">
+</g>
+<g fill="none" color="gray" stroke="currentColor" stroke-width="0.50" stroke-linecap="butt" stroke-linejoin="miter">
+	<path stroke='gray' stroke-dasharray='2,4' class="gridline"  d='M482.18,509.90 L692.68,468.50  '/></g>
+<g fill="none" color="gray" stroke="currentColor" stroke-width="0.50" stroke-linecap="butt" stroke-linejoin="miter">
+	<path stroke='gray' stroke-dasharray='2,4' class="gridline"  d='M276.00,550.46 L287.80,548.14  '/></g>
+<g fill="none" color="gray" stroke="gray" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+</g>
+<g fill="none" color="black" stroke="currentColor" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+	<path stroke='black'  d='M276.00,550.46 L286.62,548.37  '/></g>
+<g fill="none" color="black" stroke="currentColor" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+	<path stroke='black'  d='M682.06,470.59 L692.68,468.50  '/>	<g transform="translate(266.11,558.53)" stroke="none" fill="black" font-family="Arial" font-size="12.00"  text-anchor="end">
+		<text><tspan font-family="Arial" > 5</tspan></text>
+	</g>
+</g>
+<g fill="none" color="black" stroke="currentColor" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+</g>
+<g fill="none" color="black" stroke="black" stroke-width="0.50" stroke-linecap="butt" stroke-linejoin="miter">
+</g>
+<g fill="none" color="gray" stroke="currentColor" stroke-width="0.50" stroke-linecap="butt" stroke-linejoin="miter">
+	<path stroke='gray' stroke-dasharray='2,4' class="gridline"  d='M495.10,501.59 L685.35,464.17  '/></g>
+<g fill="none" color="gray" stroke="currentColor" stroke-width="0.50" stroke-linecap="butt" stroke-linejoin="miter">
+	<path stroke='gray' stroke-dasharray='2,4' class="gridline"  d='M268.67,546.13 L280.48,543.81  '/></g>
+<g fill="none" color="gray" stroke="gray" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+</g>
+<g fill="none" color="black" stroke="currentColor" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+	<path stroke='black'  d='M268.67,546.13 L279.29,544.04  '/></g>
+<g fill="none" color="black" stroke="currentColor" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+	<path stroke='black'  d='M674.72,466.26 L685.35,464.17  '/>	<g transform="translate(258.77,554.20)" stroke="none" fill="black" font-family="Arial" font-size="12.00"  text-anchor="end">
+		<text><tspan font-family="Arial" > 6</tspan></text>
+	</g>
+</g>
+<g fill="none" color="black" stroke="currentColor" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+</g>
+<g fill="none" color="black" stroke="black" stroke-width="0.50" stroke-linecap="butt" stroke-linejoin="miter">
+</g>
+<g fill="none" color="gray" stroke="currentColor" stroke-width="0.50" stroke-linecap="butt" stroke-linejoin="miter">
+	<path stroke='gray' stroke-dasharray='2,4' class="gridline"  d='M505.66,493.74 L678.01,459.84  '/></g>
+<g fill="none" color="gray" stroke="currentColor" stroke-width="0.50" stroke-linecap="butt" stroke-linejoin="miter">
+	<path stroke='gray' stroke-dasharray='2,4' class="gridline"  d='M261.33,541.80 L273.15,539.48  '/></g>
+<g fill="none" color="gray" stroke="gray" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+</g>
+<g fill="none" color="black" stroke="currentColor" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+	<path stroke='black'  d='M261.33,541.80 L271.96,539.71  '/></g>
+<g fill="none" color="black" stroke="currentColor" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+	<path stroke='black'  d='M667.39,461.93 L678.01,459.84  '/>	<g transform="translate(251.44,549.87)" stroke="none" fill="black" font-family="Arial" font-size="12.00"  text-anchor="end">
+		<text><tspan font-family="Arial" > 7</tspan></text>
+	</g>
+</g>
+<g fill="none" color="black" stroke="currentColor" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+</g>
+<g fill="none" color="black" stroke="black" stroke-width="0.50" stroke-linecap="butt" stroke-linejoin="miter">
+</g>
+<g fill="none" color="gray" stroke="currentColor" stroke-width="0.50" stroke-linecap="butt" stroke-linejoin="miter">
+	<path stroke='gray' stroke-dasharray='2,4' class="gridline"  d='M516.88,485.77 L670.68,455.52  '/></g>
+<g fill="none" color="gray" stroke="currentColor" stroke-width="0.50" stroke-linecap="butt" stroke-linejoin="miter">
+	<path stroke='gray' stroke-dasharray='2,4' class="gridline"  d='M254.00,537.47 L265.85,535.14  '/></g>
+<g fill="none" color="gray" stroke="gray" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+</g>
+<g fill="none" color="black" stroke="currentColor" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+	<path stroke='black'  d='M254.00,537.47 L264.62,535.38  '/></g>
+<g fill="none" color="black" stroke="currentColor" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+	<path stroke='black'  d='M660.05,457.60 L670.68,455.52  '/>	<g transform="translate(244.11,545.54)" stroke="none" fill="black" font-family="Arial" font-size="12.00"  text-anchor="end">
+		<text><tspan font-family="Arial" > 8</tspan></text>
+	</g>
+</g>
+<g fill="none" color="black" stroke="currentColor" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+</g>
+<g fill="none" color="black" stroke="black" stroke-width="0.50" stroke-linecap="butt" stroke-linejoin="miter">
+</g>
+<g fill="none" color="gray" stroke="currentColor" stroke-width="0.50" stroke-linecap="butt" stroke-linejoin="miter">
+	<path stroke='gray' stroke-dasharray='2,4' class="gridline"  d='M527.10,477.99 L663.34,451.19  '/></g>
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+</g>
+<g fill="none" color="black" stroke="black" stroke-width="0.50" stroke-linecap="butt" stroke-linejoin="miter">
+</g>
+<g fill="none" color="gray" stroke="currentColor" stroke-width="0.50" stroke-linecap="butt" stroke-linejoin="miter">
+	<path stroke='gray' stroke-dasharray='2,4' class="gridline"  d='M121.98,459.57 L134.07,457.19  '/></g>
+<g fill="none" color="gray" stroke="gray" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+</g>
+<g fill="none" color="black" stroke="currentColor" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+	<path stroke='black'  d='M121.98,459.57 L132.60,457.48  '/>	<g transform="translate(112.09,467.64)" stroke="none" fill="black" font-family="Arial" font-size="12.00"  text-anchor="end">
+		<text><tspan font-family="Arial" > 26</tspan></text>
+	</g>
+</g>
+<g fill="none" color="black" stroke="currentColor" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+</g>
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+</g>
+<g fill="none" color="gray" stroke="currentColor" stroke-width="0.50" stroke-linecap="butt" stroke-linejoin="miter">
+	<path stroke='gray' stroke-dasharray='2,4' class="gridline"  d='M114.64,455.24 L126.76,452.86  '/></g>
+<g fill="none" color="gray" stroke="gray" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+</g>
+<g fill="none" color="black" stroke="currentColor" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+	<path stroke='black'  d='M114.64,455.24 L125.27,453.15  '/>	<g transform="translate(104.75,463.31)" stroke="none" fill="black" font-family="Arial" font-size="12.00"  text-anchor="end">
+		<text><tspan font-family="Arial" > 27</tspan></text>
+	</g>
+</g>
+<g fill="none" color="black" stroke="currentColor" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+</g>
+<g fill="none" color="black" stroke="black" stroke-width="0.50" stroke-linecap="butt" stroke-linejoin="miter">
+</g>
+<g fill="none" color="gray" stroke="currentColor" stroke-width="0.50" stroke-linecap="butt" stroke-linejoin="miter">
+	<path stroke='gray' stroke-dasharray='2,4' class="gridline"  d='M107.31,450.91 L119.44,448.53  '/></g>
+<g fill="none" color="gray" stroke="gray" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+</g>
+<g fill="none" color="black" stroke="currentColor" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+	<path stroke='black'  d='M107.31,450.91 L117.93,448.83  '/>	<g transform="translate(97.42,458.98)" stroke="none" fill="black" font-family="Arial" font-size="12.00"  text-anchor="end">
+		<text><tspan font-family="Arial" > 28</tspan></text>
+	</g>
+</g>
+<g fill="none" color="black" stroke="currentColor" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+</g>
+<g fill="none" color="black" stroke="black" stroke-width="0.50" stroke-linecap="butt" stroke-linejoin="miter">
+</g>
+<g fill="none" color="gray" stroke="currentColor" stroke-width="0.50" stroke-linecap="butt" stroke-linejoin="miter">
+	<path stroke='gray' stroke-dasharray='2,4' class="gridline"  d='M99.97,446.59 L112.12,444.20  '/></g>
+<g fill="none" color="gray" stroke="gray" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+</g>
+<g fill="none" color="black" stroke="currentColor" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+	<path stroke='black'  d='M99.97,446.59 L110.60,444.50  '/>	<g transform="translate(90.08,454.66)" stroke="none" fill="black" font-family="Arial" font-size="12.00"  text-anchor="end">
+		<text><tspan font-family="Arial" > 29</tspan></text>
+	</g>
+</g>
+<g fill="none" color="black" stroke="currentColor" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+</g>
+<g fill="none" color="black" stroke="black" stroke-width="0.50" stroke-linecap="butt" stroke-linejoin="miter">
+</g>
+<g fill="none" color="gray" stroke="currentColor" stroke-width="0.50" stroke-linecap="butt" stroke-linejoin="miter">
+	<path stroke='gray' stroke-dasharray='2,4' class="gridline"  d='M92.64,442.26 L104.82,439.86  '/></g>
+<g fill="none" color="gray" stroke="gray" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+</g>
+<g fill="none" color="black" stroke="currentColor" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+	<path stroke='black'  d='M92.64,442.26 L103.26,440.17  '/>	<g transform="translate(82.75,450.33)" stroke="none" fill="black" font-family="Arial" font-size="12.00"  text-anchor="end">
+		<text><tspan font-family="Arial" > 30</tspan></text>
+	</g>
+</g>
+<g fill="none" color="black" stroke="currentColor" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+</g>
+<g fill="none" color="black" stroke="black" stroke-width="0.50" stroke-linecap="butt" stroke-linejoin="miter">
+</g>
+<g fill="none" color="gray" stroke="currentColor" stroke-width="0.50" stroke-linecap="butt" stroke-linejoin="miter">
+	<path stroke='gray' stroke-dasharray='2,4' class="gridline"  d='M85.31,437.93 L97.52,435.53  '/></g>
+<g fill="none" color="gray" stroke="gray" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+</g>
+<g fill="none" color="black" stroke="currentColor" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+	<path stroke='black'  d='M85.31,437.93 L95.93,435.84  '/>	<g transform="translate(75.41,446.00)" stroke="none" fill="black" font-family="Arial" font-size="12.00"  text-anchor="end">
+		<text><tspan font-family="Arial" > 31</tspan></text>
+	</g>
+</g>
+<g fill="none" color="black" stroke="currentColor" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+</g>
+<g fill="none" color="black" stroke="black" stroke-width="0.50" stroke-linecap="butt" stroke-linejoin="miter">
+</g>
+<g fill="none" color="gray" stroke="currentColor" stroke-width="0.50" stroke-linecap="butt" stroke-linejoin="miter">
+	<path stroke='gray' stroke-dasharray='2,4' class="gridline"  d='M77.97,433.60 L90.18,431.20  '/></g>
+<g fill="none" color="gray" stroke="gray" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+</g>
+<g fill="none" color="black" stroke="currentColor" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+	<path stroke='black'  d='M77.97,433.60 L88.59,431.51  '/>	<g transform="translate(68.08,441.67)" stroke="none" fill="black" font-family="Arial" font-size="12.00"  text-anchor="end">
+		<text><tspan font-family="Arial" > 32</tspan></text>
+	</g>
+</g>
+<g fill="none" color="black" stroke="currentColor" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+	<g transform="translate(85.44,525.47)" stroke="none" fill="black" font-family="Arial" font-size="12.00"  text-anchor="middle">
+		<text><tspan font-family="Arial" >Input (count)</tspan></text>
+	</g>
+</g>
+<g fill="none" color="black" stroke="black" stroke-width="0.50" stroke-linecap="butt" stroke-linejoin="miter">
+</g>
+<g fill="none" color="gray" stroke="currentColor" stroke-width="0.50" stroke-linecap="butt" stroke-linejoin="miter">
+	<path stroke='gray' stroke-dasharray='2,4' class="gridline"  d='M71.37,429.71 L165.15,411.26  '/></g>
+<g fill="none" color="gray" stroke="currentColor" stroke-width="0.50" stroke-linecap="butt" stroke-linejoin="miter">
+	<path stroke='gray' stroke-dasharray='2,4' class="gridline"  d='M728.62,489.71 L590.84,408.40  '/></g>
+<g fill="none" color="gray" stroke="gray" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+</g>
+<g fill="none" color="black" stroke="currentColor" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+	<path stroke='black'  d='M80.37,429.71 L71.37,429.71  '/>	<g transform="translate(53.38,433.60)" stroke="none" fill="black" font-family="Arial" font-size="12.00"  text-anchor="end">
+		<text><tspan font-family="Arial" > 0</tspan></text>
+	</g>
+</g>
+<g fill="none" color="black" stroke="currentColor" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+</g>
+<g fill="none" color="black" stroke="black" stroke-width="0.50" stroke-linecap="butt" stroke-linejoin="miter">
+</g>
+<g fill="none" color="gray" stroke="currentColor" stroke-width="0.50" stroke-linecap="butt" stroke-linejoin="miter">
+	<path stroke='gray' stroke-dasharray='2,4' class="gridline"  d='M71.37,376.47 L307.09,330.11  '/></g>
+<g fill="none" color="gray" stroke="currentColor" stroke-width="0.50" stroke-linecap="butt" stroke-linejoin="miter">
+	<path stroke='gray' stroke-dasharray='2,4' class="gridline"  d='M728.62,436.47 L616.99,370.60  '/></g>
+<g fill="none" color="gray" stroke="gray" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+</g>
+<g fill="none" color="black" stroke="currentColor" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+	<path stroke='black'  d='M80.37,376.47 L71.37,376.47  '/>	<g transform="translate(53.38,380.36)" stroke="none" fill="black" font-family="Arial" font-size="12.00"  text-anchor="end">
+		<text><tspan font-family="Arial" > 5000</tspan></text>
+	</g>
+</g>
+<g fill="none" color="black" stroke="currentColor" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+</g>
+<g fill="none" color="black" stroke="black" stroke-width="0.50" stroke-linecap="butt" stroke-linejoin="miter">
+</g>
+<g fill="none" color="gray" stroke="currentColor" stroke-width="0.50" stroke-linecap="butt" stroke-linejoin="miter">
+	<path stroke='gray' stroke-dasharray='2,4' class="gridline"  d='M71.37,323.24 L367.58,264.98  '/></g>
+<g fill="none" color="gray" stroke="currentColor" stroke-width="0.50" stroke-linecap="butt" stroke-linejoin="miter">
+	<path stroke='gray' stroke-dasharray='2,4' class="gridline"  d='M728.62,383.24 L641.25,331.68  '/></g>
+<g fill="none" color="gray" stroke="gray" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+</g>
+<g fill="none" color="black" stroke="currentColor" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+	<path stroke='black'  d='M80.37,323.24 L71.37,323.24  '/>	<g transform="translate(53.38,327.13)" stroke="none" fill="black" font-family="Arial" font-size="12.00"  text-anchor="end">
+		<text><tspan font-family="Arial" > 10000</tspan></text>
+	</g>
+</g>
+<g fill="none" color="black" stroke="currentColor" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+</g>
+<g fill="none" color="black" stroke="black" stroke-width="0.50" stroke-linecap="butt" stroke-linejoin="miter">
+</g>
+<g fill="none" color="gray" stroke="currentColor" stroke-width="0.50" stroke-linecap="butt" stroke-linejoin="miter">
+	<path stroke='gray' stroke-dasharray='2,4' class="gridline"  d='M71.37,270.01 L407.12,203.97  '/></g>
+<g fill="none" color="gray" stroke="currentColor" stroke-width="0.50" stroke-linecap="butt" stroke-linejoin="miter">
+	<path stroke='gray' stroke-dasharray='2,4' class="gridline"  d='M728.62,330.00 L664.10,291.93  '/></g>
+<g fill="none" color="gray" stroke="gray" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+</g>
+<g fill="none" color="black" stroke="currentColor" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+	<path stroke='black'  d='M80.37,270.01 L71.37,270.01  '/>	<g transform="translate(53.38,273.91)" stroke="none" fill="black" font-family="Arial" font-size="12.00"  text-anchor="end">
+		<text><tspan font-family="Arial" > 15000</tspan></text>
+	</g>
+</g>
+<g fill="none" color="black" stroke="currentColor" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+</g>
+<g fill="none" color="black" stroke="black" stroke-width="0.50" stroke-linecap="butt" stroke-linejoin="miter">
+</g>
+<g fill="none" color="gray" stroke="currentColor" stroke-width="0.50" stroke-linecap="butt" stroke-linejoin="miter">
+	<path stroke='gray' stroke-dasharray='2,4' class="gridline"  d='M71.37,216.77 L442.61,143.75  '/></g>
+<g fill="none" color="gray" stroke="currentColor" stroke-width="0.50" stroke-linecap="butt" stroke-linejoin="miter">
+	<path stroke='gray' stroke-dasharray='2,4' class="gridline"  d='M728.62,276.77 L687.11,252.28  '/></g>
+<g fill="none" color="gray" stroke="gray" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+</g>
+<g fill="none" color="black" stroke="currentColor" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+	<path stroke='black'  d='M80.37,216.77 L71.37,216.77  '/>	<g transform="translate(53.38,220.67)" stroke="none" fill="black" font-family="Arial" font-size="12.00"  text-anchor="end">
+		<text><tspan font-family="Arial" > 20000</tspan></text>
+	</g>
+</g>
+<g fill="none" color="black" stroke="currentColor" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
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+</g>
+<g fill="none" color="gray" stroke="currentColor" stroke-width="0.50" stroke-linecap="butt" stroke-linejoin="miter">
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+<g fill="none" color="gray" stroke="currentColor" stroke-width="0.50" stroke-linecap="butt" stroke-linejoin="miter">
+	<path stroke='gray' stroke-dasharray='2,4' class="gridline"  d='M728.62,223.54 L488.05,81.58  '/></g>
+<g fill="none" color="gray" stroke="gray" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+</g>
+<g fill="none" color="black" stroke="currentColor" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+	<path stroke='black'  d='M80.37,163.54 L71.37,163.54  '/>	<g transform="translate(53.38,167.44)" stroke="none" fill="black" font-family="Arial" font-size="12.00"  text-anchor="end">
+		<text><tspan font-family="Arial" > 25000</tspan></text>
+	</g>
+</g>
+<g fill="none" color="black" stroke="currentColor" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+</g>
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+</g>
+<g fill="none" color="gray" stroke="currentColor" stroke-width="0.50" stroke-linecap="butt" stroke-linejoin="miter">
+	<path stroke='gray' stroke-dasharray='2,4' class="gridline"  d='M71.37,110.30 L488.05,28.34  '/></g>
+<g fill="none" color="gray" stroke="currentColor" stroke-width="0.50" stroke-linecap="butt" stroke-linejoin="miter">
+	<path stroke='gray' stroke-dasharray='2,4' class="gridline"  d='M728.62,170.30 L488.05,28.34  '/></g>
+<g fill="none" color="gray" stroke="gray" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+</g>
+<g fill="none" color="black" stroke="currentColor" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+	<path stroke='black'  d='M80.37,110.30 L71.37,110.30  '/>	<g transform="translate(53.38,114.20)" stroke="none" fill="black" font-family="Arial" font-size="12.00"  text-anchor="end">
+		<text><tspan font-family="Arial" > 30000</tspan></text>
+	</g>
+</g>
+<g fill="none" color="black" stroke="currentColor" stroke-width="1.00" stroke-linecap="butt" stroke-linejoin="miter">
+	<g transform="translate(16.55,270.01) rotate(-90)" stroke="none" fill="black" font-family="Arial" font-size="12.00"  text-anchor="middle">
+		<text><tspan font-family="Arial" >Time (ns)</tspan></text>
+	</g>
+	<g stroke='none' shape-rendering='crispEdges'>
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diff --git a/benchmark/result/predict_naive_10x1x1.json b/benchmark/result/predict_naive_10x1x1.json
new file mode 100644
index 000000000..690872f2d
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+      "iterations": 3,
+      "real_time": 6.6825829966226104e+02,
+      "cpu_time": 7.1559081563041173e+02,
+      "time_unit": "ns"
+    },
+    {
+      "name": "predict_linalg_9x1x7/repeats:3/manual_time_max",
+      "family_index": 0,
+      "per_family_instance_index": 0,
+      "run_name": "predict_linalg_9x1x7/repeats:3/manual_time",
+      "run_type": "aggregate",
+      "repetitions": 3,
+      "threads": 1,
+      "aggregate_name": "max",
+      "aggregate_unit": "time",
+      "iterations": 3,
+      "real_time": 6.7553547660863592e+02,
+      "cpu_time": 7.3049895762271183e+02,
+      "time_unit": "ns"
+    }
+  ]
+}
diff --git a/benchmark/result/predict_naive_9x1x8.json b/benchmark/result/predict_naive_9x1x8.json
new file mode 100644
index 000000000..35516a12f
--- /dev/null
+++ b/benchmark/result/predict_naive_9x1x8.json
@@ -0,0 +1,171 @@
+{
+  "context": {
+    "date": "2023-06-14T19:54:33-07:00",
+    "host_name": "FRANCOIS-DESK",
+    "executable": "F:/Drive/Projects/cpp/kalman/build/benchmark/Release/kalman_benchmark_predict_naive_9x1x8_driver.exe",
+    "num_cpus": 8,
+    "mhz_per_cpu": 4008,
+    "caches": [
+      {
+        "type": "Data",
+        "level": 1,
+        "size": 32768,
+        "num_sharing": 2
+      },
+      {
+        "type": "Instruction",
+        "level": 1,
+        "size": 32768,
+        "num_sharing": 2
+      },
+      {
+        "type": "Unified",
+        "level": 2,
+        "size": 262144,
+        "num_sharing": 2
+      },
+      {
+        "type": "Unified",
+        "level": 3,
+        "size": 8388608,
+        "num_sharing": 8
+      }
+    ],
+    "load_avg": [],
+    "library_build_type": "release"
+  },
+  "benchmarks": [
+    {
+      "name": "predict_linalg_9x1x8/repeats:3/manual_time",
+      "family_index": 0,
+      "per_family_instance_index": 0,
+      "run_name": "predict_linalg_9x1x8/repeats:3/manual_time",
+      "run_type": "iteration",
+      "repetitions": 3,
+      "repetition_index": 0,
+      "threads": 1,
+      "iterations": 1056704,
+      "real_time": 6.6166958770165172e+02,
+      "cpu_time": 7.0975410332505601e+02,
+      "time_unit": "ns"
+    },
+    {
+      "name": "predict_linalg_9x1x8/repeats:3/manual_time",
+      "family_index": 0,
+      "per_family_instance_index": 0,
+      "run_name": "predict_linalg_9x1x8/repeats:3/manual_time",
+      "run_type": "iteration",
+      "repetitions": 3,
+      "repetition_index": 1,
+      "threads": 1,
+      "iterations": 1056704,
+      "real_time": 6.6108938738076699e+02,
+      "cpu_time": 7.0975410332505601e+02,
+      "time_unit": "ns"
+    },
+    {
+      "name": "predict_linalg_9x1x8/repeats:3/manual_time",
+      "family_index": 0,
+      "per_family_instance_index": 0,
+      "run_name": "predict_linalg_9x1x8/repeats:3/manual_time",
+      "run_type": "iteration",
+      "repetitions": 3,
+      "repetition_index": 2,
+      "threads": 1,
+      "iterations": 1056704,
+      "real_time": 6.6460617164425321e+02,
+      "cpu_time": 7.2454064714432798e+02,
+      "time_unit": "ns"
+    },
+    {
+      "name": "predict_linalg_9x1x8/repeats:3/manual_time_mean",
+      "family_index": 0,
+      "per_family_instance_index": 0,
+      "run_name": "predict_linalg_9x1x8/repeats:3/manual_time",
+      "run_type": "aggregate",
+      "repetitions": 3,
+      "threads": 1,
+      "aggregate_name": "mean",
+      "aggregate_unit": "time",
+      "iterations": 3,
+      "real_time": 6.6245504890889060e+02,
+      "cpu_time": 7.1468295126481325e+02,
+      "time_unit": "ns"
+    },
+    {
+      "name": "predict_linalg_9x1x8/repeats:3/manual_time_median",
+      "family_index": 0,
+      "per_family_instance_index": 0,
+      "run_name": "predict_linalg_9x1x8/repeats:3/manual_time",
+      "run_type": "aggregate",
+      "repetitions": 3,
+      "threads": 1,
+      "aggregate_name": "median",
+      "aggregate_unit": "time",
+      "iterations": 3,
+      "real_time": 6.6166958770165172e+02,
+      "cpu_time": 7.0975410332505601e+02,
+      "time_unit": "ns"
+    },
+    {
+      "name": "predict_linalg_9x1x8/repeats:3/manual_time_stddev",
+      "family_index": 0,
+      "per_family_instance_index": 0,
+      "run_name": "predict_linalg_9x1x8/repeats:3/manual_time",
+      "run_type": "aggregate",
+      "repetitions": 3,
+      "threads": 1,
+      "aggregate_name": "stddev",
+      "aggregate_unit": "time",
+      "iterations": 3,
+      "real_time": 1.8853792377372356e+00,
+      "cpu_time": 8.5370150544399142e+00,
+      "time_unit": "ns"
+    },
+    {
+      "name": "predict_linalg_9x1x8/repeats:3/manual_time_cv",
+      "family_index": 0,
+      "per_family_instance_index": 0,
+      "run_name": "predict_linalg_9x1x8/repeats:3/manual_time",
+      "run_type": "aggregate",
+      "repetitions": 3,
+      "threads": 1,
+      "aggregate_name": "cv",
+      "aggregate_unit": "percentage",
+      "iterations": 3,
+      "real_time": 2.8460485595854178e-03,
+      "cpu_time": 1.1945177983232280e-02,
+      "time_unit": "ns"
+    },
+    {
+      "name": "predict_linalg_9x1x8/repeats:3/manual_time_min",
+      "family_index": 0,
+      "per_family_instance_index": 0,
+      "run_name": "predict_linalg_9x1x8/repeats:3/manual_time",
+      "run_type": "aggregate",
+      "repetitions": 3,
+      "threads": 1,
+      "aggregate_name": "min",
+      "aggregate_unit": "time",
+      "iterations": 3,
+      "real_time": 6.6108938738076688e+02,
+      "cpu_time": 7.0975410332505601e+02,
+      "time_unit": "ns"
+    },
+    {
+      "name": "predict_linalg_9x1x8/repeats:3/manual_time_max",
+      "family_index": 0,
+      "per_family_instance_index": 0,
+      "run_name": "predict_linalg_9x1x8/repeats:3/manual_time",
+      "run_type": "aggregate",
+      "repetitions": 3,
+      "threads": 1,
+      "aggregate_name": "max",
+      "aggregate_unit": "time",
+      "iterations": 3,
+      "real_time": 6.6460617164425332e+02,
+      "cpu_time": 7.2454064714432798e+02,
+      "time_unit": "ns"
+    }
+  ]
+}
diff --git a/benchmark/result/predict_naive_9x1x9.json b/benchmark/result/predict_naive_9x1x9.json
new file mode 100644
index 000000000..a7caaf94c
--- /dev/null
+++ b/benchmark/result/predict_naive_9x1x9.json
@@ -0,0 +1,171 @@
+{
+  "context": {
+    "date": "2023-06-14T19:54:35-07:00",
+    "host_name": "FRANCOIS-DESK",
+    "executable": "F:/Drive/Projects/cpp/kalman/build/benchmark/Release/kalman_benchmark_predict_naive_9x1x9_driver.exe",
+    "num_cpus": 8,
+    "mhz_per_cpu": 4008,
+    "caches": [
+      {
+        "type": "Data",
+        "level": 1,
+        "size": 32768,
+        "num_sharing": 2
+      },
+      {
+        "type": "Instruction",
+        "level": 1,
+        "size": 32768,
+        "num_sharing": 2
+      },
+      {
+        "type": "Unified",
+        "level": 2,
+        "size": 262144,
+        "num_sharing": 2
+      },
+      {
+        "type": "Unified",
+        "level": 3,
+        "size": 8388608,
+        "num_sharing": 8
+      }
+    ],
+    "load_avg": [],
+    "library_build_type": "release"
+  },
+  "benchmarks": [
+    {
+      "name": "predict_linalg_9x1x9/repeats:3/manual_time",
+      "family_index": 0,
+      "per_family_instance_index": 0,
+      "run_name": "predict_linalg_9x1x9/repeats:3/manual_time",
+      "run_type": "iteration",
+      "repetitions": 3,
+      "repetition_index": 0,
+      "threads": 1,
+      "iterations": 996200,
+      "real_time": 6.7870397510663508e+02,
+      "cpu_time": 7.3717626982533625e+02,
+      "time_unit": "ns"
+    },
+    {
+      "name": "predict_linalg_9x1x9/repeats:3/manual_time",
+      "family_index": 0,
+      "per_family_instance_index": 0,
+      "run_name": "predict_linalg_9x1x9/repeats:3/manual_time",
+      "run_type": "iteration",
+      "repetitions": 3,
+      "repetition_index": 1,
+      "threads": 1,
+      "iterations": 996200,
+      "real_time": 6.7757428227407024e+02,
+      "cpu_time": 7.3717626982533625e+02,
+      "time_unit": "ns"
+    },
+    {
+      "name": "predict_linalg_9x1x9/repeats:3/manual_time",
+      "family_index": 0,
+      "per_family_instance_index": 0,
+      "run_name": "predict_linalg_9x1x9/repeats:3/manual_time",
+      "run_type": "iteration",
+      "repetitions": 3,
+      "repetition_index": 2,
+      "threads": 1,
+      "iterations": 996200,
+      "real_time": 6.7398112828905130e+02,
+      "cpu_time": 7.2149166833969082e+02,
+      "time_unit": "ns"
+    },
+    {
+      "name": "predict_linalg_9x1x9/repeats:3/manual_time_mean",
+      "family_index": 0,
+      "per_family_instance_index": 0,
+      "run_name": "predict_linalg_9x1x9/repeats:3/manual_time",
+      "run_type": "aggregate",
+      "repetitions": 3,
+      "threads": 1,
+      "aggregate_name": "mean",
+      "aggregate_unit": "time",
+      "iterations": 3,
+      "real_time": 6.7675312855658547e+02,
+      "cpu_time": 7.3194806933012114e+02,
+      "time_unit": "ns"
+    },
+    {
+      "name": "predict_linalg_9x1x9/repeats:3/manual_time_median",
+      "family_index": 0,
+      "per_family_instance_index": 0,
+      "run_name": "predict_linalg_9x1x9/repeats:3/manual_time",
+      "run_type": "aggregate",
+      "repetitions": 3,
+      "threads": 1,
+      "aggregate_name": "median",
+      "aggregate_unit": "time",
+      "iterations": 3,
+      "real_time": 6.7757428227407024e+02,
+      "cpu_time": 7.3717626982533636e+02,
+      "time_unit": "ns"
+    },
+    {
+      "name": "predict_linalg_9x1x9/repeats:3/manual_time_stddev",
+      "family_index": 0,
+      "per_family_instance_index": 0,
+      "run_name": "predict_linalg_9x1x9/repeats:3/manual_time",
+      "run_type": "aggregate",
+      "repetitions": 3,
+      "threads": 1,
+      "aggregate_name": "stddev",
+      "aggregate_unit": "time",
+      "iterations": 3,
+      "real_time": 2.4661793500301434e+00,
+      "cpu_time": 9.0555088898776415e+00,
+      "time_unit": "ns"
+    },
+    {
+      "name": "predict_linalg_9x1x9/repeats:3/manual_time_cv",
+      "family_index": 0,
+      "per_family_instance_index": 0,
+      "run_name": "predict_linalg_9x1x9/repeats:3/manual_time",
+      "run_type": "aggregate",
+      "repetitions": 3,
+      "threads": 1,
+      "aggregate_name": "cv",
+      "aggregate_unit": "percentage",
+      "iterations": 3,
+      "real_time": 3.6441343910594694e-03,
+      "cpu_time": 1.2371791482646090e-02,
+      "time_unit": "ns"
+    },
+    {
+      "name": "predict_linalg_9x1x9/repeats:3/manual_time_min",
+      "family_index": 0,
+      "per_family_instance_index": 0,
+      "run_name": "predict_linalg_9x1x9/repeats:3/manual_time",
+      "run_type": "aggregate",
+      "repetitions": 3,
+      "threads": 1,
+      "aggregate_name": "min",
+      "aggregate_unit": "time",
+      "iterations": 3,
+      "real_time": 6.7398112828905130e+02,
+      "cpu_time": 7.2149166833969093e+02,
+      "time_unit": "ns"
+    },
+    {
+      "name": "predict_linalg_9x1x9/repeats:3/manual_time_max",
+      "family_index": 0,
+      "per_family_instance_index": 0,
+      "run_name": "predict_linalg_9x1x9/repeats:3/manual_time",
+      "run_type": "aggregate",
+      "repetitions": 3,
+      "threads": 1,
+      "aggregate_name": "max",
+      "aggregate_unit": "time",
+      "iterations": 3,
+      "real_time": 6.7870397510663520e+02,
+      "cpu_time": 7.3717626982533636e+02,
+      "time_unit": "ns"
+    }
+  ]
+}
diff --git a/benchmark/script/profile.sh b/benchmark/script/profile.sh
new file mode 100644
index 000000000..d3349aeba
--- /dev/null
+++ b/benchmark/script/profile.sh
@@ -0,0 +1,53 @@
+#!/bin/bash
+#  _  __          _      __  __          _   _
+# | |/ /    /\   | |    |  \/  |   /\   | \ | |
+# | ' /    /  \  | |    | \  / |  /  \  |  \| |
+# |  <    / /\ \ | |    | |\/| | / /\ \ | . ` |
+# | . \  / ____ \| |____| |  | |/ ____ \| |\  |
+# |_|\_\/_/    \_\______|_|  |_/_/    \_\_| \_|
+
+# Kalman Filter
+# Version 0.2.0
+# https://github.com/FrancoisCarouge/Kalman
+
+# SPDX-License-Identifier: Unlicense
+
+# This is free and unencumbered software released into the public domain.
+
+# Anyone is free to copy, modify, publish, use, compile, sell, or
+# distribute this software, either in source code form or as a compiled
+# binary, for any purpose, commercial or non-commercial, and by any
+# means.
+
+# In jurisdictions that recognize copyright laws, the author or authors
+# of this software dedicate any and all copyright interest in the
+# software to the public domain. We make this dedication for the benefit
+# of the public at large and to the detriment of our heirs and
+# successors. We intend this dedication to be an overt act of
+# relinquishment in perpetuity of all present and future rights to this
+# software under copyright law.
+
+# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+# EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
+# MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
+# IN NO EVENT SHALL THE AUTHORS BE LIABLE FOR ANY CLAIM, DAMAGES OR
+# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
+# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
+# OTHER DEALINGS IN THE SOFTWARE.
+
+# For more information, please refer to <https://unlicense.org>
+
+# Usage: ./profile.sh path/to/executable/file
+# Then: kcachegrind callgrind.out.xyz
+
+set -e
+
+/usr/local/bin/valgrind \
+  --tool=callgrind \
+  --dump-instr=yes \
+  --collect-jumps=yes \
+  --callgrind-out-file="callgrind.out" \
+  --log-file="callgrind.log" \
+  ./$1 > $(basename $1).log 2>&1
+
+kcachegrind callgrind.out &
diff --git a/benchmark/update_linalg_xx0.cpp b/benchmark/update_linalg_xx0.cpp
index 569b446f1..6006b21e8 100644
--- a/benchmark/update_linalg_xx0.cpp
+++ b/benchmark/update_linalg_xx0.cpp
@@ -52,12 +52,19 @@ For more information, please refer to <https://unlicense.org> */
 #include <random>
 
 template <typename Numerator, fcarouge::algebraic Denominator>
-constexpr auto fcarouge::operator/(const Numerator &lhs, const Denominator &rhs)
-    -> fcarouge::quotient<Numerator, Denominator> {
-  return rhs.transpose()
-      .fullPivHouseholderQr()
-      .solve(lhs.transpose())
-      .transpose();
+constexpr auto
+fcarouge::operator/(const Numerator &lhs, const Denominator &rhs) -> fcarouge::quotient<Numerator, Denominator> {
+  if constexpr (fcarouge::eigen<Denominator>) {
+    return rhs.transpose()
+        .fullPivHouseholderQr()
+        .solve(lhs.transpose())
+        .transpose();
+  } else {
+    assert(false);
+    static_cast<void>(lhs);
+    static_cast<void>(rhs);
+    return {};
+  }
 }
 
 namespace fcarouge::benchmark {
diff --git a/linalg/eigen/fcarouge/linalg.hpp b/linalg/eigen/fcarouge/linalg.hpp
index 19c4a8999..7f5f92ef1 100644
--- a/linalg/eigen/fcarouge/linalg.hpp
+++ b/linalg/eigen/fcarouge/linalg.hpp
@@ -50,6 +50,8 @@ For more information, please refer to <https://unlicense.org> */
 
 #include <Eigen/Eigen>
 
+#include <format>
+
 namespace fcarouge {
 //! @name Algebraic Types
 //! @{
@@ -75,6 +77,34 @@ inline const auto identity_v<Matrix>{Matrix::Identity()};
 //! @brief The zero matrix Eigen specialization.
 template <eigen Matrix> inline const auto zero_v<Matrix>{Matrix::Zero()};
 //! @}
+
+[[nodiscard]] inline auto transpose(const auto &other) {
+  return other.transpose();
+}
+
+[[nodiscard]] inline auto llt(const auto &A) { return A.llt(); }
+
+[[nodiscard]] inline auto solve(const auto &lhs, const auto &rhs) {
+
+  return lhs.solve(rhs);
+  // Eigen::Solve< Decomposition, RhsType >
+}
 } // namespace fcarouge
 
+// // Until Eigen catches up.
+// template <fcarouge::eigen Matrix, typename Char>
+// struct std::formatter<Matrix, Char> : public std::formatter<> {
+//   constexpr auto parse(std::basic_format_parse_context<Char> &parse_context)
+//   {
+//     return parse_context.begin();
+//   }
+
+//   template <typename OutputIt>
+//   auto format(const Matrix &m,
+//               std::basic_format_context<OutputIt, Char> &format_context)
+//       -> OutputIt {
+//     return format_context.out();
+//   }
+// };
+
 #endif // FCAROUGE_LINALG_HPP
diff --git a/linalg/naive/fcarouge/linalg.hpp b/linalg/naive/fcarouge/linalg.hpp
index 43057edf2..8b91d89c8 100644
--- a/linalg/naive/fcarouge/linalg.hpp
+++ b/linalg/naive/fcarouge/linalg.hpp
@@ -311,17 +311,44 @@ template <typename Type, auto Row>
 
 template <typename Type, auto Row, auto Column>
 [[nodiscard]] inline constexpr auto
-transpose(const matrix<Type, Row, Column> &lhs) {
+transpose(const matrix<Type, Row, Column> &other) {
   matrix<Type, Column, Row> result;
 
   for (decltype(Row) i{0}; i < Row; ++i) {
     for (decltype(Column) j{0}; j < Column; ++j) {
-      result.data[j][i] = lhs.data[i][j];
+      result.data[j][i] = other.data[i][j];
     }
   }
 
   return result;
 }
+
+[[nodiscard]] inline auto llt(const auto &A) {
+  std::remove_cvref_t<decltype(A)> L;
+
+  for (int i = 0; i < 2; i++) {
+    for (int j = 0; j <= i; j++) {
+      double sum = 0;
+      for (int k = 0; k < j; k++)
+        sum += L(i, k) * L(j, k);
+
+      if (i == j)
+        L.data[i][j] = sqrt(A(i, i) - sum);
+      else
+        L.data[i][j] = (1.0 / L(j, j) * (A(i, j) - sum));
+    }
+  }
+
+  return L;
+}
+
+[[nodiscard]] inline auto solve(const auto &lhs, const auto &rhs) {
+  static_cast<void>(lhs);
+  static_cast<void>(rhs);
+  matrix<double, 2, 6> m;
+  return m;
+}
+
 } // namespace fcarouge
 
 #endif // FCAROUGE_LINALG_HPP
diff --git a/sample/CMakeLists.txt b/sample/CMakeLists.txt
index 7aab55ebe..34c92d65e 100644
--- a/sample/CMakeLists.txt
+++ b/sample/CMakeLists.txt
@@ -52,10 +52,12 @@ foreach(SAMPLE "kf_1x1x0_building_height.cpp" "kf_1x1x0_liquid_temperature.cpp"
             $<TARGET_FILE:kalman_sample_${NAME}_driver>)
 endforeach()
 
-foreach(BACKEND IN ITEMS "eigen")
-  foreach(SAMPLE
-          "ekf_4x1x0_soaring.cpp" "kf_2x1x1_rocket_altitude.cpp"
-          "kf_6x2x0_vehicle_location.cpp" "kf_8x4x0_deep_sort_bounding_box.cpp")
+foreach(BACKEND IN ITEMS "eigen" "naive")
+  foreach(
+    SAMPLE
+    "ekf_4x1x0_soaring.cpp" "kf_2x1x1_rocket_altitude.cpp"
+    # "kf_6x2x0_vehicle_location.cpp" "kf_8x4x0_deep_sort_bounding_box.cpp"
+  )
     get_filename_component(NAME ${SAMPLE} NAME_WE)
     add_executable(kalman_sample_${BACKEND}_${NAME}_driver ${SAMPLE})
     set_target_properties(kalman_sample_${BACKEND}_${NAME}_driver
diff --git a/sample/kf_6x2x0_vehicle_location.cpp b/sample/kf_6x2x0_vehicle_location.cpp
index aa9aae6b8..e6ddcface 100644
--- a/sample/kf_6x2x0_vehicle_location.cpp
+++ b/sample/kf_6x2x0_vehicle_location.cpp
@@ -7,10 +7,15 @@
 template <typename Numerator, fcarouge::algebraic Denominator>
 constexpr auto fcarouge::operator/(const Numerator &lhs, const Denominator &rhs)
     -> fcarouge::quotient<Numerator, Denominator> {
-  return rhs.transpose()
-      .fullPivHouseholderQr()
-      .solve(lhs.transpose())
-      .transpose();
+  if constexpr (fcarouge::eigen<Denominator>) {
+    return rhs.transpose()
+        .fullPivHouseholderQr()
+        .solve(lhs.transpose())
+        .transpose();
+  } else {
+    assert(false && "TODO");
+    return {};
+  }
 }
 
 namespace fcarouge::sample {
diff --git a/sample/kf_8x4x0_deep_sort_bounding_box.cpp b/sample/kf_8x4x0_deep_sort_bounding_box.cpp
index bd5ed1f19..78388f616 100644
--- a/sample/kf_8x4x0_deep_sort_bounding_box.cpp
+++ b/sample/kf_8x4x0_deep_sort_bounding_box.cpp
@@ -7,10 +7,15 @@
 template <typename Numerator, fcarouge::algebraic Denominator>
 constexpr auto fcarouge::operator/(const Numerator &lhs, const Denominator &rhs)
     -> fcarouge::quotient<Numerator, Denominator> {
-  return rhs.transpose()
-      .fullPivHouseholderQr()
-      .solve(lhs.transpose())
-      .transpose();
+  if constexpr (fcarouge::eigen<Denominator>) {
+    return rhs.transpose()
+        .fullPivHouseholderQr()
+        .solve(lhs.transpose())
+        .transpose();
+  } else {
+    assert(false && "TODO");
+    return {};
+  }
 }
 
 namespace fcarouge::sample {
diff --git a/test/CMakeLists.txt b/test/CMakeLists.txt
index 6e509f951..f98adedcf 100644
--- a/test/CMakeLists.txt
+++ b/test/CMakeLists.txt
@@ -76,7 +76,66 @@ foreach(
             $<TARGET_FILE:kalman_test_${NAME}_driver>)
 endforeach()
 
+foreach(BACKEND IN ITEMS "naive")
+  foreach(
+    TEST
+    "kalman_constructor_default_5x4x3_constexpr.cpp"
+    "linalg_assign_constexpr.cpp"
+    "linalg_constructor_constexpr.cpp"
+    "linalg_constructor_default_constexpr.cpp"
+    "linalg_copy_constexpr.cpp"
+    "linalg_identity_constexpr.cpp"
+    "linalg_identity_default_constexpr.cpp"
+    "linalg_operator_bracket_constexpr.cpp"
+    "linalg_operator_bracket_1x2_constexpr.cpp"
+    "linalg_operator_equality_constexpr.cpp"
+    "linalg_zero_constexpr.cpp"
+    "linalg_zero_default_constexpr.cpp")
+    get_filename_component(NAME ${TEST} NAME_WE)
+    add_executable(kalman_test_${BACKEND}_${NAME}_driver ${TEST})
+    set_target_properties(kalman_test_${BACKEND}_${NAME}_driver
+                          PROPERTIES CXX_STANDARD 23)
+    set_target_properties(kalman_test_${BACKEND}_${NAME}_driver
+                          PROPERTIES CXX_EXTENSIONS OFF)
+    target_link_libraries(kalman_test_${BACKEND}_${NAME}_driver
+                          PRIVATE kalman kalman_main kalman_linalg_${BACKEND})
+    add_test(kalman_test_${BACKEND}_${NAME}
+             kalman_test_${BACKEND}_${NAME}_driver)
+    add_test(
+      NAME kalman_${BACKEND}_valgrind_${NAME}
+      COMMAND valgrind --error-exitcode=1 --leak-check=full --track-origins=yes
+              $<TARGET_FILE:kalman_test_${BACKEND}_${NAME}_driver>)
+  endforeach()
+endforeach()
+
 foreach(BACKEND IN ITEMS "eigen")
+  foreach(
+    TEST
+    "linalg_division_householder_pivot_column.cpp"
+    "linalg_division_householder_pivot_full.cpp"
+    "linalg_division_householder.cpp"
+    "linalg_division_ldlt.cpp"
+    "linalg_division_orthogonal.cpp"
+    "linalg_division_pivot_full.cpp"
+    "linalg_division_pivot_partial.cpp")
+    get_filename_component(NAME ${TEST} NAME_WE)
+    add_executable(kalman_test_${BACKEND}_${NAME}_driver ${TEST})
+    set_target_properties(kalman_test_${BACKEND}_${NAME}_driver
+                          PROPERTIES CXX_STANDARD 23)
+    set_target_properties(kalman_test_${BACKEND}_${NAME}_driver
+                          PROPERTIES CXX_EXTENSIONS OFF)
+    target_link_libraries(kalman_test_${BACKEND}_${NAME}_driver
+                          PRIVATE kalman kalman_main kalman_linalg_${BACKEND})
+    add_test(kalman_test_${BACKEND}_${NAME}
+             kalman_test_${BACKEND}_${NAME}_driver)
+    add_test(
+      NAME kalman_${BACKEND}_valgrind_${NAME}
+      COMMAND valgrind --error-exitcode=1 --leak-check=full --track-origins=yes
+              $<TARGET_FILE:kalman_test_${BACKEND}_${NAME}_driver>)
+  endforeach()
+endforeach()
+
+foreach(BACKEND IN ITEMS "eigen" "naive")
   foreach(
     TEST
     "kalman_constructor_default_1x1x3.cpp"
@@ -107,6 +166,8 @@ endforeach()
 foreach(BACKEND IN ITEMS "eigen" "lazy" "naive")
   foreach(
     TEST
+    # "kf_2x1x1_rocket_altitude_linalg.cpp"
+    # "kf_8x4x0_deep_sort_bounding_box_linalg.cpp"
     "linalg_addition.cpp"
     "linalg_assign.cpp"
     "linalg_constructor_1x1_array.cpp"
diff --git a/test/kalman_constructor_default_5x4x3_constexpr.cpp b/test/kalman_constructor_default_5x4x3_constexpr.cpp
new file mode 100644
index 000000000..38ddb1ec4
--- /dev/null
+++ b/test/kalman_constructor_default_5x4x3_constexpr.cpp
@@ -0,0 +1,86 @@
+/*  __          _      __  __          _   _
+| |/ /    /\   | |    |  \/  |   /\   | \ | |
+| ' /    /  \  | |    | \  / |  /  \  |  \| |
+|  <    / /\ \ | |    | |\/| | / /\ \ | . ` |
+| . \  / ____ \| |____| |  | |/ ____ \| |\  |
+|_|\_\/_/    \_\______|_|  |_/_/    \_\_| \_|
+
+Kalman Filter
+Version 0.2.0
+https://github.com/FrancoisCarouge/Kalman
+
+SPDX-License-Identifier: Unlicense
+
+This is free and unencumbered software released into the public domain.
+
+Anyone is free to copy, modify, publish, use, compile, sell, or
+distribute this software, either in source code form or as a compiled
+binary, for any purpose, commercial or non-commercial, and by any
+means.
+
+In jurisdictions that recognize copyright laws, the author or authors
+of this software dedicate any and all copyright interest in the
+software to the public domain. We make this dedication for the benefit
+of the public at large and to the detriment of our heirs and
+successors. We intend this dedication to be an overt act of
+relinquishment in perpetuity of all present and future rights to this
+software under copyright law.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
+MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
+IN NO EVENT SHALL THE AUTHORS BE LIABLE FOR ANY CLAIM, DAMAGES OR
+OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
+ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
+OTHER DEALINGS IN THE SOFTWARE.
+
+For more information, please refer to <https://unlicense.org> */
+
+#include "fcarouge/kalman.hpp"
+#include "fcarouge/linalg.hpp"
+
+#include <cassert>
+
+namespace fcarouge::test {
+namespace {
+template <auto Size> using vector = column_vector<double, Size>;
+
+template <auto RowSize, auto ColumnSize>
+using matrix = matrix<double, RowSize, ColumnSize>;
+
+//! @test Verifies default values are initialized for multi-dimension filters.
+//!
+//! @todo Make the lambda `consteval` when MSVC supports it.
+[[maybe_unused]] constexpr auto test{[] {
+  using kalman = kalman<vector<5>, vector<4>, vector<3>>;
+
+  kalman filter;
+
+  constexpr auto z3x1{zero_v<vector<3>>};
+  constexpr auto i4x4{identity_v<matrix<4, 4>>};
+  constexpr auto i4x5{identity_v<matrix<4, 5>>};
+  constexpr auto i5x3{identity_v<matrix<5, 3>>};
+  constexpr auto i5x4{identity_v<matrix<5, 4>>};
+  constexpr auto i5x5{identity_v<matrix<5, 5>>};
+  constexpr auto z4x1{zero_v<vector<4>>};
+  constexpr auto z4x4{zero_v<matrix<4, 4>>};
+  constexpr auto z5x1{zero_v<vector<5>>};
+  constexpr auto z5x5{zero_v<matrix<5, 5>>};
+
+  assert(filter.f() == i5x5);
+  assert(filter.g() == i5x3);
+  assert(filter.h() == i4x5);
+  assert(filter.k() == i5x4);
+  assert(filter.p() == i5x5);
+  assert(filter.q() == z5x5 && "No process noise by default.");
+  assert(filter.r() == z4x4 && "No observation noise by default.");
+  assert(filter.s() == i4x4);
+  assert(filter.u() == z3x1 && "No initial control.");
+  assert(filter.x() == z5x1 && "Origin state.");
+  assert(filter.y() == z4x1);
+  assert(filter.z() == z4x1);
+
+  return 0;
+}()};
+} // namespace
+} // namespace fcarouge::test
diff --git a/test/kf_2x1x1_rocket_altitude_linalg.cpp b/test/kf_2x1x1_rocket_altitude_linalg.cpp
new file mode 100644
index 000000000..4a73c8e9b
--- /dev/null
+++ b/test/kf_2x1x1_rocket_altitude_linalg.cpp
@@ -0,0 +1,152 @@
+#include "fcarouge/kalman.hpp"
+#include "fcarouge/linalg.hpp"
+
+#include <cassert>
+#include <chrono>
+#include <cmath>
+
+// #include <iostream> ////////////////////////////////////////////////////////
+
+namespace fcarouge::sample {
+namespace {
+template <auto Size> using vector = column_vector<double, Size>;
+using state = vector<2>;
+using output = vector<1>;
+using input = vector<1>;
+
+//! @brief
+[[maybe_unused]] /*constexpr*/ auto kf_2x1x1_rocket_altitude{[] {
+  using kalman = kalman<state, output, input, std::tuple<>,
+                        std::tuple<std::chrono::milliseconds>>;
+
+  kalman filter;
+
+  filter.x(0., 0.);
+  filter.p(kalman::estimate_uncertainty{{500, 0}, {0, 500}});
+  filter.q([]([[maybe_unused]] const kalman::state &x,
+              const std::chrono::milliseconds &delta_time) {
+    const auto dt{std::chrono::duration<double>(delta_time).count()};
+    return kalman::process_uncertainty{
+        {0.1 * 0.1 * dt * dt * dt * dt / 4, 0.1 * 0.1 * dt * dt * dt / 2},
+        {0.1 * 0.1 * dt * dt * dt / 2, 0.1 * 0.1 * dt * dt}};
+  });
+  filter.f([]([[maybe_unused]] const kalman::state &x,
+              [[maybe_unused]] const kalman::input &u,
+              const std::chrono::milliseconds &delta_time) {
+    const auto dt{std::chrono::duration<double>(delta_time).count()};
+    return kalman::state_transition{{1, dt}, {0, 1}};
+  });
+  filter.g([](const std::chrono::milliseconds &delta_time) {
+    const auto dt{std::chrono::duration<double>(delta_time).count()};
+    return kalman::input_control{0.0313, dt};
+  });
+  const double gravity{-9.8};
+  const std::chrono::milliseconds delta_time{250};
+  filter.predict(delta_time, -gravity);
+
+  //   std::cout << "Result: " << filter.p()(0, 0) << std::endl;
+  //   ////////////////////
+
+  assert(std::abs(1 - filter.x()[0] / 0.3) < 0.03 &&
+         std::abs(1 - filter.x()[1] / 2.45) < 0.03 &&
+         "The state estimates expected at 3% accuracy.");
+  assert(std::abs(1 - filter.p()(0, 0) / 531.25) < 0.001 &&
+         std::abs(1 - filter.p()(0, 1) / 125) < 0.001 &&
+         std::abs(1 - filter.p()(1, 0) / 125) < 0.001 &&
+         std::abs(1 - filter.p()(1, 1) / 500) < 0.001 &&
+         "The estimate uncertainty expected at 0.1% accuracy.");
+
+  filter.h(kalman::output_model{1., 0.});
+  filter.r(kalman::output_uncertainty{400.});
+
+  filter.update(-32.4);
+
+  assert(std::abs(1 - filter.x()[0] / -18.35) < 0.001 &&
+         std::abs(1 - filter.x()[1] / -1.94) < 0.001 &&
+         "The state estimates expected at 0.1% accuracy.");
+  assert(std::abs(1 - filter.p()(0, 0) / 228.2) < 0.001 &&
+         std::abs(1 - filter.p()(0, 1) / 53.7) < 0.001 &&
+         std::abs(1 - filter.p()(1, 0) / 53.7) < 0.001 &&
+         std::abs(1 - filter.p()(1, 1) / 483.2) < 0.001 &&
+         "The estimate uncertainty expected at 0.1% accuracy.");
+
+  filter.predict(delta_time, 39.72 + gravity);
+
+  assert(std::abs(1 - filter.x()[0] / -17.9) < 0.001 &&
+         std::abs(1 - filter.x()[1] / 5.54) < 0.001 &&
+         "The state estimates expected at 0.1% accuracy.");
+  assert(std::abs(1 - filter.p()(0, 0) / 285.2) < 0.001 &&
+         std::abs(1 - filter.p()(0, 1) / 174.5) < 0.001 &&
+         std::abs(1 - filter.p()(1, 0) / 174.5) < 0.001 &&
+         std::abs(1 - filter.p()(1, 1) / 483.2) < 0.001 &&
+         "The estimate uncertainty expected at 0.1% accuracy.");
+
+  const auto step{[&filter](double altitude,
+                            std::chrono::milliseconds step_time,
+                            double acceleration) {
+    filter.update(altitude);
+    filter.predict(step_time, acceleration);
+  }};
+
+  step(-11.1, delta_time, 40.02 + gravity);
+
+  assert(std::abs(1 - filter.x()[0] / -12.3) < 0.002 &&
+         std::abs(1 - filter.x()[1] / 14.8) < 0.002 &&
+         "The state estimates expected at 0.2% accuracy.");
+  assert(std::abs(1 - filter.p()(0, 0) / 244.9) < 0.001 &&
+         std::abs(1 - filter.p()(0, 1) / 211.6) < 0.001 &&
+         std::abs(1 - filter.p()(1, 0) / 211.6) < 0.001 &&
+         std::abs(1 - filter.p()(1, 1) / 438.8) < 0.001 &&
+         "The estimate uncertainty expected at 0.1% accuracy.");
+
+  step(18., delta_time, 39.97 + gravity);
+  step(22.9, delta_time, 39.81 + gravity);
+  step(19.5, delta_time, 39.75 + gravity);
+  step(28.5, delta_time, 39.6 + gravity);
+  step(46.5, delta_time, 39.77 + gravity);
+  step(68.9, delta_time, 39.83 + gravity);
+  step(48.2, delta_time, 39.73 + gravity);
+  step(56.1, delta_time, 39.87 + gravity);
+  step(90.5, delta_time, 39.81 + gravity);
+  step(104.9, delta_time, 39.92 + gravity);
+  step(140.9, delta_time, 39.78 + gravity);
+  step(148., delta_time, 39.98 + gravity);
+  step(187.6, delta_time, 39.76 + gravity);
+  step(209.2, delta_time, 39.86 + gravity);
+  step(244.6, delta_time, 39.61 + gravity);
+  step(276.4, delta_time, 39.86 + gravity);
+  step(323.5, delta_time, 39.74 + gravity);
+  step(357.3, delta_time, 39.87 + gravity);
+  step(357.4, delta_time, 39.63 + gravity);
+  step(398.3, delta_time, 39.67 + gravity);
+  step(446.7, delta_time, 39.96 + gravity);
+  step(465.1, delta_time, 39.8 + gravity);
+  step(529.4, delta_time, 39.89 + gravity);
+  step(570.4, delta_time, 39.85 + gravity);
+  step(636.8, delta_time, 39.9 + gravity);
+  step(693.3, delta_time, 39.81 + gravity);
+  step(707.3, delta_time, 39.81 + gravity);
+
+  filter.update(748.5);
+
+  assert(std::abs(1 - filter.p()(0, 0) / 49.3) < 0.001 &&
+         "At this point, the altitude uncertainty px = 49.3, which means that "
+         "the standard deviation of the prediction is square root of 49.3: "
+         "7.02m (remember that the standard deviation of the measurement is "
+         "20m).");
+
+  filter.predict(delta_time, 39.68 + gravity);
+
+  assert(std::abs(1 - filter.x()[0] / 831.5) < 0.001 &&
+         std::abs(1 - filter.x()[1] / 222.94) < 0.001 &&
+         "The state estimates expected at 0.1% accuracy.");
+  assert(std::abs(1 - filter.p()(0, 0) / 54.3) < 0.01 &&
+         std::abs(1 - filter.p()(0, 1) / 10.4) < 0.01 &&
+         std::abs(1 - filter.p()(1, 0) / 10.4) < 0.01 &&
+         std::abs(1 - filter.p()(1, 1) / 2.6) < 0.01 &&
+         "The estimate uncertainty expected at 1% accuracy.");
+
+  return 0;
+}()};
+} // namespace
+} // namespace fcarouge::sample
diff --git a/test/kf_8x4x0_deep_sort_bounding_box_linalg.cpp b/test/kf_8x4x0_deep_sort_bounding_box_linalg.cpp
new file mode 100644
index 000000000..ee92fdabb
--- /dev/null
+++ b/test/kf_8x4x0_deep_sort_bounding_box_linalg.cpp
@@ -0,0 +1,221 @@
+#include "fcarouge/kalman.hpp"
+#include "fcarouge/linalg.hpp"
+
+#include <cassert>
+#include <cmath>
+
+template <typename Numerator, fcarouge::algebraic Denominator>
+constexpr auto fcarouge::operator/(const Numerator &lhs, const Denominator &rhs)
+    -> fcarouge::quotient<Numerator, Denominator> {
+  //   assert(false);
+  static_cast<void>(lhs);
+  static_cast<void>(rhs);
+  return {};
+}
+
+namespace fcarouge::sample {
+namespace {
+template <auto Size> using vector = column_vector<float, Size>;
+using state = vector<8>;
+using output = vector<4>;
+using no_input = void;
+
+//! @brief
+[[maybe_unused]] /*constexpr*/ auto kf_8x4x0_deep_sort_bounding_box{[] {
+  using kalman = kalman<state, output, no_input>;
+
+  kalman filter;
+
+  const kalman::output measured[]{{603.5F, 251.5F, 0.187335092348285F, 379},
+                                  {599, 241, 0.24390243902439F, 328},
+                                  {599, 239.5F, 0.257234726688103F, 311},
+                                  {602.5F, 244, 0.240131578947368F, 304},
+                                  {598, 248.5F, 0.272425249169435F, 301},
+                                  {596.5F, 240.5F, 0.283276450511945F, 293},
+                                  {601, 227, 0.301587301587302F, 252},
+                                  {603.5F, 235.5F, 0.282868525896414F, 251},
+                                  {602, 242.5F, 0.292490118577075F, 253},
+                                  {602.5F, 253, 0.218562874251497F, 334},
+                                  {593, 254, 0.273291925465838F, 322},
+                                  {603, 264, 0.22360248447205F, 322},
+                                  {600.5F, 278.5F, 0.198966408268734F, 387},
+                                  {593, 280, 0.237113402061856F, 388},
+                                  {588.5F, 269, 0.267195767195767F, 378},
+                                  {579, 260, 0.311111111111111F, 360},
+                                  {565.5F, 268.5F, 0.339130434782609F, 345},
+                                  {558.5F, 255.5F, 0.366568914956012F, 341},
+                                  {544, 268, 0.364705882352941F, 340},
+                                  {533, 258.5F, 0.356083086053412F, 337},
+                                  {519, 258, 0.353293413173653F, 334},
+                                  {511.5F, 252.5F, 0.333333333333333F, 333},
+                                  {515.5F, 252.5F, 0.31306990881459F, 329},
+                                  {523.5F, 251, 0.298192771084337F, 332},
+                                  {540, 252.5F, 0.318318318318318F, 333},
+                                  {574, 262, 0.344827586206897F, 348},
+                                  {590.5F, 265, 0.278735632183908F, 348},
+                                  {613, 268, 0.164556962025316F, 316},
+                                  {617, 260.5F, 0.161172161172161F, 273},
+                                  {615.5F, 261.5F, 0.15210355987055F, 309},
+                                  {605.5F, 259, 0.226351351351351F, 296},
+                                  {595.5F, 258.5F, 0.289036544850498F, 301},
+                                  {588, 257.5F, 0.350515463917526F, 291},
+                                  {579.5F, 254, 0.343537414965986F, 294},
+                                  {569.5F, 258.5F, 0.353535353535354F, 297},
+                                  {565.5F, 257, 0.37248322147651F, 298},
+                                  {555, 250, 0.388157894736842F, 304},
+                                  {546.5F, 249, 0.336666666666667F, 300},
+                                  {535, 251, 0.30718954248366F, 306},
+                                  {530, 246, 0.308724832214765F, 298},
+                                  {521, 252, 0.278145695364238F, 302},
+                                  {521.5F, 254.5F, 0.331010452961672F, 287},
+                                  {521, 258.5F, 0.32280701754386F, 285},
+                                  {519.5F, 255, 0.316326530612245F, 294},
+                                  {518.5F, 255, 0.304794520547945F, 292},
+                                  {511, 253, 0.310810810810811F, 296},
+                                  {506, 255, 0.319727891156463F, 294},
+                                  {499, 256, 0.352112676056338F, 284},
+                                  {492.5F, 256.5F, 0.349152542372881F, 295},
+                                  {489.5F, 257, 0.362068965517241F, 290},
+                                  {481, 251.5F, 0.357894736842105F, 285},
+                                  {474, 249, 0.324137931034483F, 290},
+                                  {466, 250, 0.306122448979592F, 294},
+                                  {461.5F, 248, 0.304794520547945F, 292},
+                                  {450.5F, 248.5F, 0.323843416370107F, 281},
+                                  {442, 260.5F, 0.32280701754386F, 285},
+                                  {437, 255.5F, 0.329824561403509F, 285},
+                                  {427, 251.5F, 0.329896907216495F, 291},
+                                  {419, 251, 0.330985915492958F, 284},
+                                  {411, 251, 0.328671328671329F, 286},
+                                  {411, 251.5F, 0.325259515570934F, 289},
+                                  {410, 249, 0.324137931034483F, 290},
+                                  {407, 247.5F, 0.346020761245675F, 289},
+                                  {398.5F, 248.5F, 0.356890459363958F, 283},
+                                  {393, 249, 0.347222222222222F, 288},
+                                  {390.5F, 246.5F, 0.331058020477816F, 293},
+                                  {387, 246, 0.308724832214765F, 298},
+                                  {379.5F, 244.5F, 0.303754266211604F, 293},
+                                  {370, 255.5F, 0.258899676375404F, 309},
+                                  {372, 252.5F, 0.307167235494881F, 293},
+                                  {368, 254.5F, 0.311418685121107F, 289},
+                                  {365.5F, 251, 0.322916666666667F, 288},
+                                  {360.5F, 250.5F, 0.301694915254237F, 295},
+                                  {353, 251.5F, 0.316151202749141F, 291},
+                                  {349.5F, 248.5F, 0.32404181184669F, 287},
+                                  {343.5F, 246, 0.327464788732394F, 284},
+                                  {334.5F, 251.5F, 0.335689045936396F, 283},
+                                  {328.5F, 249.5F, 0.342960288808664F, 277},
+                                  {321.5F, 256.5F, 0.328621908127208F, 283},
+                                  {321.5F, 259.5F, 0.317073170731707F, 287},
+                                  {319.5F, 252, 0.313380281690141F, 284},
+                                  {317.5F, 247.5F, 0.314487632508834F, 283},
+                                  {314.5F, 248, 0.313380281690141F, 284},
+                                  {318.5F, 255, 0.311188811188811F, 286},
+                                  {324.5F, 252, 0.317857142857143F, 280},
+                                  {328.5F, 249, 0.311188811188811F, 286},
+                                  {330, 248, 0.318840579710145F, 276},
+                                  {334.5F, 245, 0.320143884892086F, 278},
+                                  {342.5F, 248, 0.324817518248175F, 274},
+                                  {348, 247.5F, 0.312727272727273F, 275},
+                                  {349.5F, 245.5F, 0.326007326007326F, 273},
+                                  {350, 250, 0.321167883211679F, 274},
+                                  {350.5F, 252.5F, 0.323636363636364F, 275},
+                                  {356.5F, 249, 0.31294964028777F, 278},
+                                  {356.5F, 245, 0.320143884892086F, 278},
+                                  {357, 245, 0.314285714285714F, 280},
+                                  {361, 246, 0.318840579710145F, 276},
+                                  {364, 251.5F, 0.308771929824561F, 285},
+                                  {368, 252.5F, 0.303886925795053F, 283},
+                                  {369, 250.5F, 0.29757785467128F, 289}};
+
+  const kalman::output initial_box{605.0F, 248.0F, 0.20481927710843373F,
+                                   332.0f};
+  filter.x(initial_box(0), initial_box(1), initial_box(2), initial_box(3), 0.F,
+           0.F, 0.F, 0.f);
+
+  const float position_weight{1.f / 20.f};
+  const float velocity_weight{1.f / 160.f};
+
+  filter.p(
+      kalman::estimate_uncertainty{{2 * position_weight * initial_box(3) * 2 *
+                                        position_weight * initial_box(3),
+                                    0, 0, 0, 0, 0, 0, 0},
+                                   {0,
+                                    2 * position_weight * initial_box(3) * 2 *
+                                        position_weight * initial_box(3),
+                                    0, 0, 0, 0, 0, 0},
+                                   {0, 0, 1e-2f * 1e-2F, 0, 0, 0, 0, 0},
+                                   {0, 0, 0,
+                                    2 * position_weight * initial_box(3) * 2 *
+                                        position_weight * initial_box(3),
+                                    0, 0, 0, 0},
+                                   {0, 0, 0, 0,
+                                    10 * velocity_weight * initial_box(3) * 10 *
+                                        velocity_weight * initial_box(3),
+                                    0, 0, 0},
+                                   {0, 0, 0, 0, 0,
+                                    10 * velocity_weight * initial_box(3) * 10 *
+                                        velocity_weight * initial_box(3),
+                                    0, 0},
+                                   {0, 0, 0, 0, 0, 0, 1e-5f * 1e-5F, 0},
+                                   {0, 0, 0, 0, 0, 0, 0,
+                                    10 * velocity_weight * initial_box(3) * 10 *
+                                        velocity_weight * initial_box(3)}});
+
+  const float delta_time{1};
+  filter.f(kalman::state_transition{{1, 0, 0, 0, delta_time, 0, 0, 0},
+                                    {0, 1, 0, 0, 0, delta_time, 0, 0},
+                                    {0, 0, 1, 0, 0, 0, delta_time, 0},
+                                    {0, 0, 0, 1, 0, 0, 0, delta_time},
+                                    {0, 0, 0, 0, 1, 0, 0, 0},
+                                    {0, 0, 0, 0, 0, 1, 0, 0},
+                                    {0, 0, 0, 0, 0, 0, 1, 0},
+                                    {0, 0, 0, 0, 0, 0, 0, 1}});
+
+  filter.q([position_weight, velocity_weight](
+               const kalman::state &x) -> kalman::process_uncertainty {
+    return kalman::process_uncertainty{
+        {position_weight * x(3) * position_weight * x(3), 0, 0, 0, 0, 0, 0, 0},
+        {0, position_weight * x(3) * position_weight * x(3), 0, 0, 0, 0, 0, 0},
+        {0, 0, 1e-2f * 1e-2F, 0, 0, 0, 0, 0},
+        {0, 0, 0, position_weight * x(3) * position_weight * x(3), 0, 0, 0, 0},
+        {0, 0, 0, 0, velocity_weight * x(3) * velocity_weight * x(3), 0, 0, 0},
+        {0, 0, 0, 0, 0, velocity_weight * x(3) * velocity_weight * x(3), 0, 0},
+        {0, 0, 0, 0, 0, 0, 1e-5f * 1e-5F, 0},
+        {0, 0, 0, 0, 0, 0, 0, velocity_weight * x(3) * velocity_weight * x(3)}};
+  });
+
+  filter.predict();
+  filter.h(kalman::output_model{{1, 0, 0, 0, 0, 0, 0, 0},
+                                {0, 1, 0, 0, 0, 0, 0, 0},
+                                {0, 0, 1, 0, 0, 0, 0, 0},
+                                {0, 0, 0, 1, 0, 0, 0, 0}});
+  filter.r([position_weight](const kalman::state &x,
+                             [[maybe_unused]] const kalman::output &z)
+               -> kalman::output_uncertainty {
+    return kalman::output_uncertainty{
+        {position_weight * x(3) * position_weight * x(3), 0, 0, 0},
+        {0, position_weight * x(3) * position_weight * x(3), 0, 0},
+        {0, 0, 1e-1f * 1e-1F, 0},
+        {0, 0, 0, position_weight * x(3) * position_weight * x(3)}};
+  });
+
+  for (const auto &measure : measured) {
+    filter.update(measure);
+    filter.predict();
+  }
+
+  //   assert(std::abs(1 - filter.x()[0] / 370.932041394761f) < 0.001f &&
+  //          std::abs(1 - filter.x()[1] / 251.173174229878f) < 0.001f &&
+  //          std::abs(1 - filter.x()[2] / 0.314757138075364f) < 0.001f &&
+  //          std::abs(1 - filter.x()[3] / 287.859996019444f) < 0.001f &&
+  //          std::abs(1 - filter.x()[4] / 1.95865368159518f) < 0.001f &&
+  //          std::abs(1 - filter.x()[5] / 0.229282868701086f) < 0.001f &&
+  //          std::abs(1 - filter.x()[6] / 2.46138628550094E-06f) < 0.5f &&
+  //          std::abs(1 - filter.x()[7] / 0.81402529074969f) < 0.001f &&
+  //          "The estimated states expected to meet Nwojke's Deep SORT filter's
+  //          " "MOT16 sample tracker #201 dataset at 0.1% accuracy.");
+
+  return 0;
+}()};
+} // namespace
+} // namespace fcarouge::sample
diff --git a/test/linalg_assign_constexpr.cpp b/test/linalg_assign_constexpr.cpp
new file mode 100644
index 000000000..766133e67
--- /dev/null
+++ b/test/linalg_assign_constexpr.cpp
@@ -0,0 +1,56 @@
+/*  __          _      __  __          _   _
+| |/ /    /\   | |    |  \/  |   /\   | \ | |
+| ' /    /  \  | |    | \  / |  /  \  |  \| |
+|  <    / /\ \ | |    | |\/| | / /\ \ | . ` |
+| . \  / ____ \| |____| |  | |/ ____ \| |\  |
+|_|\_\/_/    \_\______|_|  |_/_/    \_\_| \_|
+
+Kalman Filter
+Version 0.2.0
+https://github.com/FrancoisCarouge/Kalman
+
+SPDX-License-Identifier: Unlicense
+
+This is free and unencumbered software released into the public domain.
+
+Anyone is free to copy, modify, publish, use, compile, sell, or
+distribute this software, either in source code form or as a compiled
+binary, for any purpose, commercial or non-commercial, and by any
+means.
+
+In jurisdictions that recognize copyright laws, the author or authors
+of this software dedicate any and all copyright interest in the
+software to the public domain. We make this dedication for the benefit
+of the public at large and to the detriment of our heirs and
+successors. We intend this dedication to be an overt act of
+relinquishment in perpetuity of all present and future rights to this
+software under copyright law.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
+MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
+IN NO EVENT SHALL THE AUTHORS BE LIABLE FOR ANY CLAIM, DAMAGES OR
+OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
+ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
+OTHER DEALINGS IN THE SOFTWARE.
+
+For more information, please refer to <https://unlicense.org> */
+
+#include "fcarouge/linalg.hpp"
+
+namespace fcarouge::test {
+namespace {
+//! @test Verifies the assignment operator.
+//!
+//! @todo Make the lambda `consteval` when MSVC supports it.
+//! @todo Rewrite this test as a property-based test.
+[[maybe_unused]] constexpr auto test{[] {
+  constexpr auto m{identity_v<matrix<double, 5, 5>>};
+  constexpr auto c = m;
+
+  static_assert(c == identity_v<matrix<double, 5, 5>>);
+
+  return 0;
+}()};
+} // namespace
+} // namespace fcarouge::test
diff --git a/test/linalg_constructor_constexpr.cpp b/test/linalg_constructor_constexpr.cpp
new file mode 100644
index 000000000..1d386773e
--- /dev/null
+++ b/test/linalg_constructor_constexpr.cpp
@@ -0,0 +1,63 @@
+/*  __          _      __  __          _   _
+| |/ /    /\   | |    |  \/  |   /\   | \ | |
+| ' /    /  \  | |    | \  / |  /  \  |  \| |
+|  <    / /\ \ | |    | |\/| | / /\ \ | . ` |
+| . \  / ____ \| |____| |  | |/ ____ \| |\  |
+|_|\_\/_/    \_\______|_|  |_/_/    \_\_| \_|
+
+Kalman Filter
+Version 0.2.0
+https://github.com/FrancoisCarouge/Kalman
+
+SPDX-License-Identifier: Unlicense
+
+This is free and unencumbered software released into the public domain.
+
+Anyone is free to copy, modify, publish, use, compile, sell, or
+distribute this software, either in source code form or as a compiled
+binary, for any purpose, commercial or non-commercial, and by any
+means.
+
+In jurisdictions that recognize copyright laws, the author or authors
+of this software dedicate any and all copyright interest in the
+software to the public domain. We make this dedication for the benefit
+of the public at large and to the detriment of our heirs and
+successors. We intend this dedication to be an overt act of
+relinquishment in perpetuity of all present and future rights to this
+software under copyright law.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
+MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
+IN NO EVENT SHALL THE AUTHORS BE LIABLE FOR ANY CLAIM, DAMAGES OR
+OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
+ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
+OTHER DEALINGS IN THE SOFTWARE.
+
+For more information, please refer to <https://unlicense.org> */
+
+#include "fcarouge/linalg.hpp"
+
+namespace fcarouge::test {
+namespace {
+//! @test Verifies the initializer lists constructor.
+//!
+//! @todo Make the lambda `consteval` when MSVC supports it.
+//! @todo Rewrite this test as a property-based test.
+[[maybe_unused]] constexpr auto test{[] {
+  constexpr matrix<double, 3, 3> m{{1, 2, 3}, {4, 5, 6}, {7, 8, 9}};
+
+  static_assert(m(0, 0) == 1.0);
+  static_assert(m(0, 1) == 2.0);
+  static_assert(m(0, 2) == 3.0);
+  static_assert(m(1, 0) == 4.0);
+  static_assert(m(1, 1) == 5.0);
+  static_assert(m(1, 2) == 6.0);
+  static_assert(m(2, 0) == 7.0);
+  static_assert(m(2, 1) == 8.0);
+  static_assert(m(2, 2) == 9.0);
+
+  return 0;
+}()};
+} // namespace
+} // namespace fcarouge::test
diff --git a/test/linalg_constructor_default_constexpr.cpp b/test/linalg_constructor_default_constexpr.cpp
new file mode 100644
index 000000000..6c4139d47
--- /dev/null
+++ b/test/linalg_constructor_default_constexpr.cpp
@@ -0,0 +1,60 @@
+/*  __          _      __  __          _   _
+| |/ /    /\   | |    |  \/  |   /\   | \ | |
+| ' /    /  \  | |    | \  / |  /  \  |  \| |
+|  <    / /\ \ | |    | |\/| | / /\ \ | . ` |
+| . \  / ____ \| |____| |  | |/ ____ \| |\  |
+|_|\_\/_/    \_\______|_|  |_/_/    \_\_| \_|
+
+Kalman Filter
+Version 0.2.0
+https://github.com/FrancoisCarouge/Kalman
+
+SPDX-License-Identifier: Unlicense
+
+This is free and unencumbered software released into the public domain.
+
+Anyone is free to copy, modify, publish, use, compile, sell, or
+distribute this software, either in source code form or as a compiled
+binary, for any purpose, commercial or non-commercial, and by any
+means.
+
+In jurisdictions that recognize copyright laws, the author or authors
+of this software dedicate any and all copyright interest in the
+software to the public domain. We make this dedication for the benefit
+of the public at large and to the detriment of our heirs and
+successors. We intend this dedication to be an overt act of
+relinquishment in perpetuity of all present and future rights to this
+software under copyright law.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
+MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
+IN NO EVENT SHALL THE AUTHORS BE LIABLE FOR ANY CLAIM, DAMAGES OR
+OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
+ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
+OTHER DEALINGS IN THE SOFTWARE.
+
+For more information, please refer to <https://unlicense.org> */
+
+#include "fcarouge/linalg.hpp"
+
+#include <type_traits>
+
+namespace fcarouge::test {
+namespace {
+//! @test Verifies the 1x1 deduced default constructed matrix.
+//!
+//! @todo Make the lambda `consteval` when MSVC supports it.
+[[maybe_unused]] constexpr auto test{[] {
+  constexpr matrix m;
+
+  static_assert(sizeof(double) == sizeof(m));
+  static_assert(0.0 == m);
+  static_assert(std::is_same_v<decltype(m), const matrix<>>);
+  static_assert(std::is_same_v<row_vector<>, matrix<>>);
+  static_assert(std::is_same_v<column_vector<>, matrix<>>);
+
+  return 0;
+}()};
+} // namespace
+} // namespace fcarouge::test
diff --git a/test/linalg_copy_constexpr.cpp b/test/linalg_copy_constexpr.cpp
new file mode 100644
index 000000000..74d2d9c37
--- /dev/null
+++ b/test/linalg_copy_constexpr.cpp
@@ -0,0 +1,56 @@
+/*  __          _      __  __          _   _
+| |/ /    /\   | |    |  \/  |   /\   | \ | |
+| ' /    /  \  | |    | \  / |  /  \  |  \| |
+|  <    / /\ \ | |    | |\/| | / /\ \ | . ` |
+| . \  / ____ \| |____| |  | |/ ____ \| |\  |
+|_|\_\/_/    \_\______|_|  |_/_/    \_\_| \_|
+
+Kalman Filter
+Version 0.2.0
+https://github.com/FrancoisCarouge/Kalman
+
+SPDX-License-Identifier: Unlicense
+
+This is free and unencumbered software released into the public domain.
+
+Anyone is free to copy, modify, publish, use, compile, sell, or
+distribute this software, either in source code form or as a compiled
+binary, for any purpose, commercial or non-commercial, and by any
+means.
+
+In jurisdictions that recognize copyright laws, the author or authors
+of this software dedicate any and all copyright interest in the
+software to the public domain. We make this dedication for the benefit
+of the public at large and to the detriment of our heirs and
+successors. We intend this dedication to be an overt act of
+relinquishment in perpetuity of all present and future rights to this
+software under copyright law.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
+MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
+IN NO EVENT SHALL THE AUTHORS BE LIABLE FOR ANY CLAIM, DAMAGES OR
+OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
+ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
+OTHER DEALINGS IN THE SOFTWARE.
+
+For more information, please refer to <https://unlicense.org> */
+
+#include "fcarouge/linalg.hpp"
+
+namespace fcarouge::test {
+namespace {
+//! @test Verifies the copy constructor.
+//!
+//! @todo Make the lambda `consteval` when MSVC supports it.
+//! @todo Rewrite this test as a property-based test.
+[[maybe_unused]] constexpr auto test{[] {
+  constexpr auto m{identity_v<matrix<double, 5, 5>>};
+  constexpr auto c{m};
+
+  static_assert(c == identity_v<matrix<double, 5, 5>>);
+
+  return 0;
+}()};
+} // namespace
+} // namespace fcarouge::test
diff --git a/test/linalg_division_householder.cpp b/test/linalg_division_householder.cpp
new file mode 100644
index 000000000..af4ea51e3
--- /dev/null
+++ b/test/linalg_division_householder.cpp
@@ -0,0 +1,68 @@
+/*  __          _      __  __          _   _
+| |/ /    /\   | |    |  \/  |   /\   | \ | |
+| ' /    /  \  | |    | \  / |  /  \  |  \| |
+|  <    / /\ \ | |    | |\/| | / /\ \ | . ` |
+| . \  / ____ \| |____| |  | |/ ____ \| |\  |
+|_|\_\/_/    \_\______|_|  |_/_/    \_\_| \_|
+
+Kalman Filter
+Version 0.2.0
+https://github.com/FrancoisCarouge/Kalman
+
+SPDX-License-Identifier: Unlicense
+
+This is free and unencumbered software released into the public domain.
+
+Anyone is free to copy, modify, publish, use, compile, sell, or
+distribute this software, either in source code form or as a compiled
+binary, for any purpose, commercial or non-commercial, and by any
+means.
+
+In jurisdictions that recognize copyright laws, the author or authors
+of this software dedicate any and all copyright interest in the
+software to the public domain. We make this dedication for the benefit
+of the public at large and to the detriment of our heirs and
+successors. We intend this dedication to be an overt act of
+relinquishment in perpetuity of all present and future rights to this
+software under copyright law.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
+MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
+IN NO EVENT SHALL THE AUTHORS BE LIABLE FOR ANY CLAIM, DAMAGES OR
+OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
+ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
+OTHER DEALINGS IN THE SOFTWARE.
+
+For more information, please refer to <https://unlicense.org> */
+
+#include "fcarouge/kalman.hpp"
+#include "fcarouge/linalg.hpp"
+
+#include <cassert>
+
+template <typename Numerator, fcarouge::algebraic Denominator>
+constexpr auto fcarouge::operator/(const Numerator &lhs, const Denominator &rhs)
+    -> fcarouge::quotient<Numerator, Denominator> {
+  return rhs.transpose().householderQr().solve(lhs.transpose()).transpose();
+}
+
+namespace fcarouge::test {
+namespace {
+template <auto Row, auto Column> using matrix = matrix<double, Row, Column>;
+
+//! @test Verifies the Eigen decomposition solver.
+//!
+//! @todo Rewrite this test as a property-based test.
+[[maybe_unused]] auto test{[] {
+  matrix<6, 2> a{{204.882, 0}, {253.979, 0}, {143.824, 0},
+                 {0, 204.882}, {0, 253.979}, {0, 143.824}};
+  matrix<2, 2> r{{213.882, 0}, {0, 213.882}};
+  matrix<6, 2> q{a / r};
+
+  assert(a.isApprox(q * r));
+
+  return 0;
+}()};
+} // namespace
+} // namespace fcarouge::test
diff --git a/test/linalg_division_householder_pivot_column.cpp b/test/linalg_division_householder_pivot_column.cpp
new file mode 100644
index 000000000..ca4605579
--- /dev/null
+++ b/test/linalg_division_householder_pivot_column.cpp
@@ -0,0 +1,71 @@
+/*  __          _      __  __          _   _
+| |/ /    /\   | |    |  \/  |   /\   | \ | |
+| ' /    /  \  | |    | \  / |  /  \  |  \| |
+|  <    / /\ \ | |    | |\/| | / /\ \ | . ` |
+| . \  / ____ \| |____| |  | |/ ____ \| |\  |
+|_|\_\/_/    \_\______|_|  |_/_/    \_\_| \_|
+
+Kalman Filter
+Version 0.2.0
+https://github.com/FrancoisCarouge/Kalman
+
+SPDX-License-Identifier: Unlicense
+
+This is free and unencumbered software released into the public domain.
+
+Anyone is free to copy, modify, publish, use, compile, sell, or
+distribute this software, either in source code form or as a compiled
+binary, for any purpose, commercial or non-commercial, and by any
+means.
+
+In jurisdictions that recognize copyright laws, the author or authors
+of this software dedicate any and all copyright interest in the
+software to the public domain. We make this dedication for the benefit
+of the public at large and to the detriment of our heirs and
+successors. We intend this dedication to be an overt act of
+relinquishment in perpetuity of all present and future rights to this
+software under copyright law.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
+MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
+IN NO EVENT SHALL THE AUTHORS BE LIABLE FOR ANY CLAIM, DAMAGES OR
+OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
+ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
+OTHER DEALINGS IN THE SOFTWARE.
+
+For more information, please refer to <https://unlicense.org> */
+
+#include "fcarouge/kalman.hpp"
+#include "fcarouge/linalg.hpp"
+
+#include <cassert>
+
+template <typename Numerator, fcarouge::algebraic Denominator>
+constexpr auto fcarouge::operator/(const Numerator &lhs, const Denominator &rhs)
+    -> fcarouge::quotient<Numerator, Denominator> {
+  return rhs.transpose()
+      .colPivHouseholderQr()
+      .solve(lhs.transpose())
+      .transpose();
+}
+
+namespace fcarouge::test {
+namespace {
+template <auto Row, auto Column> using matrix = matrix<double, Row, Column>;
+
+//! @test Verifies the Eigen decomposition solver.
+//!
+//! @todo Rewrite this test as a property-based test.
+[[maybe_unused]] auto test{[] {
+  matrix<6, 2> a{{204.882, 0}, {253.979, 0}, {143.824, 0},
+                 {0, 204.882}, {0, 253.979}, {0, 143.824}};
+  matrix<2, 2> r{{213.882, 0}, {0, 213.882}};
+  matrix<6, 2> q{a / r};
+
+  assert(a.isApprox(q * r));
+
+  return 0;
+}()};
+} // namespace
+} // namespace fcarouge::test
diff --git a/test/linalg_division_householder_pivot_full.cpp b/test/linalg_division_householder_pivot_full.cpp
new file mode 100644
index 000000000..75daf8eb9
--- /dev/null
+++ b/test/linalg_division_householder_pivot_full.cpp
@@ -0,0 +1,71 @@
+/*  __          _      __  __          _   _
+| |/ /    /\   | |    |  \/  |   /\   | \ | |
+| ' /    /  \  | |    | \  / |  /  \  |  \| |
+|  <    / /\ \ | |    | |\/| | / /\ \ | . ` |
+| . \  / ____ \| |____| |  | |/ ____ \| |\  |
+|_|\_\/_/    \_\______|_|  |_/_/    \_\_| \_|
+
+Kalman Filter
+Version 0.2.0
+https://github.com/FrancoisCarouge/Kalman
+
+SPDX-License-Identifier: Unlicense
+
+This is free and unencumbered software released into the public domain.
+
+Anyone is free to copy, modify, publish, use, compile, sell, or
+distribute this software, either in source code form or as a compiled
+binary, for any purpose, commercial or non-commercial, and by any
+means.
+
+In jurisdictions that recognize copyright laws, the author or authors
+of this software dedicate any and all copyright interest in the
+software to the public domain. We make this dedication for the benefit
+of the public at large and to the detriment of our heirs and
+successors. We intend this dedication to be an overt act of
+relinquishment in perpetuity of all present and future rights to this
+software under copyright law.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
+MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
+IN NO EVENT SHALL THE AUTHORS BE LIABLE FOR ANY CLAIM, DAMAGES OR
+OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
+ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
+OTHER DEALINGS IN THE SOFTWARE.
+
+For more information, please refer to <https://unlicense.org> */
+
+#include "fcarouge/kalman.hpp"
+#include "fcarouge/linalg.hpp"
+
+#include <cassert>
+
+template <typename Numerator, fcarouge::algebraic Denominator>
+constexpr auto fcarouge::operator/(const Numerator &lhs, const Denominator &rhs)
+    -> fcarouge::quotient<Numerator, Denominator> {
+  return rhs.transpose()
+      .fullPivHouseholderQr()
+      .solve(lhs.transpose())
+      .transpose();
+}
+
+namespace fcarouge::test {
+namespace {
+template <auto Row, auto Column> using matrix = matrix<double, Row, Column>;
+
+//! @test Verifies the Eigen decomposition solver.
+//!
+//! @todo Rewrite this test as a property-based test.
+[[maybe_unused]] auto test{[] {
+  matrix<6, 2> a{{204.882, 0}, {253.979, 0}, {143.824, 0},
+                 {0, 204.882}, {0, 253.979}, {0, 143.824}};
+  matrix<2, 2> r{{213.882, 0}, {0, 213.882}};
+  matrix<6, 2> q{a / r};
+
+  assert(a.isApprox(q * r));
+
+  return 0;
+}()};
+} // namespace
+} // namespace fcarouge::test
diff --git a/test/linalg_division_ldlt.cpp b/test/linalg_division_ldlt.cpp
new file mode 100644
index 000000000..46825ec1f
--- /dev/null
+++ b/test/linalg_division_ldlt.cpp
@@ -0,0 +1,68 @@
+/*  __          _      __  __          _   _
+| |/ /    /\   | |    |  \/  |   /\   | \ | |
+| ' /    /  \  | |    | \  / |  /  \  |  \| |
+|  <    / /\ \ | |    | |\/| | / /\ \ | . ` |
+| . \  / ____ \| |____| |  | |/ ____ \| |\  |
+|_|\_\/_/    \_\______|_|  |_/_/    \_\_| \_|
+
+Kalman Filter
+Version 0.2.0
+https://github.com/FrancoisCarouge/Kalman
+
+SPDX-License-Identifier: Unlicense
+
+This is free and unencumbered software released into the public domain.
+
+Anyone is free to copy, modify, publish, use, compile, sell, or
+distribute this software, either in source code form or as a compiled
+binary, for any purpose, commercial or non-commercial, and by any
+means.
+
+In jurisdictions that recognize copyright laws, the author or authors
+of this software dedicate any and all copyright interest in the
+software to the public domain. We make this dedication for the benefit
+of the public at large and to the detriment of our heirs and
+successors. We intend this dedication to be an overt act of
+relinquishment in perpetuity of all present and future rights to this
+software under copyright law.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
+MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
+IN NO EVENT SHALL THE AUTHORS BE LIABLE FOR ANY CLAIM, DAMAGES OR
+OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
+ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
+OTHER DEALINGS IN THE SOFTWARE.
+
+For more information, please refer to <https://unlicense.org> */
+
+#include "fcarouge/kalman.hpp"
+#include "fcarouge/linalg.hpp"
+
+#include <cassert>
+
+template <typename Numerator, fcarouge::algebraic Denominator>
+constexpr auto fcarouge::operator/(const Numerator &lhs, const Denominator &rhs)
+    -> fcarouge::quotient<Numerator, Denominator> {
+  return rhs.transpose().ldlt().solve(lhs.transpose()).transpose();
+}
+
+namespace fcarouge::test {
+namespace {
+template <auto Row, auto Column> using matrix = matrix<double, Row, Column>;
+
+//! @test Verifies the Eigen decomposition solver.
+//!
+//! @todo Rewrite this test as a property-based test.
+[[maybe_unused]] auto test{[] {
+  matrix<6, 2> a{{204.882, 0}, {253.979, 0}, {143.824, 0},
+                 {0, 204.882}, {0, 253.979}, {0, 143.824}};
+  matrix<2, 2> r{{213.882, 0}, {0, 213.882}};
+  matrix<6, 2> q{a / r};
+
+  assert(a.isApprox(q * r));
+
+  return 0;
+}()};
+} // namespace
+} // namespace fcarouge::test
diff --git a/test/linalg_division_llt.cpp b/test/linalg_division_llt.cpp
new file mode 100644
index 000000000..f8a520f79
--- /dev/null
+++ b/test/linalg_division_llt.cpp
@@ -0,0 +1,104 @@
+/*  __          _      __  __          _   _
+| |/ /    /\   | |    |  \/  |   /\   | \ | |
+| ' /    /  \  | |    | \  / |  /  \  |  \| |
+|  <    / /\ \ | |    | |\/| | / /\ \ | . ` |
+| . \  / ____ \| |____| |  | |/ ____ \| |\  |
+|_|\_\/_/    \_\______|_|  |_/_/    \_\_| \_|
+
+Kalman Filter
+Version 0.2.0
+https://github.com/FrancoisCarouge/Kalman
+
+SPDX-License-Identifier: Unlicense
+
+This is free and unencumbered software released into the public domain.
+
+Anyone is free to copy, modify, publish, use, compile, sell, or
+distribute this software, either in source code form or as a compiled
+binary, for any purpose, commercial or non-commercial, and by any
+means.
+
+In jurisdictions that recognize copyright laws, the author or authors
+of this software dedicate any and all copyright interest in the
+software to the public domain. We make this dedication for the benefit
+of the public at large and to the detriment of our heirs and
+successors. We intend this dedication to be an overt act of
+relinquishment in perpetuity of all present and future rights to this
+software under copyright law.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
+MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
+IN NO EVENT SHALL THE AUTHORS BE LIABLE FOR ANY CLAIM, DAMAGES OR
+OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
+ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
+OTHER DEALINGS IN THE SOFTWARE.
+
+For more information, please refer to <https://unlicense.org> */
+
+#include "fcarouge/kalman.hpp"
+#include "fcarouge/linalg.hpp"
+
+#include <cassert>
+
+#include <format>
+#include <iostream>
+#include <print>
+
+template <typename Numerator, fcarouge::algebraic Denominator>
+constexpr auto fcarouge::operator/(const Numerator &lhs, const Denominator &rhs)
+    -> fcarouge::quotient<Numerator, Denominator> {
+  // return rhs.transpose().llt().solve(lhs.transpose()).transpose();
+  auto trhs{transpose(rhs)};
+  auto decomp{llt(trhs)};
+  auto tlhs{transpose(lhs)};
+  auto sol{solve(decomp, tlhs)};
+  auto tsol{transpose(sol)};
+  return tsol;
+}
+
+namespace fcarouge::test {
+namespace {
+template <auto Row, auto Column> using matrix = matrix<double, Row, Column>;
+
+//! @test Verifies the Eigen decomposition solver.
+//!
+//! @todo Rewrite this test as a property-based test.
+[[maybe_unused]] auto test{[] {
+  matrix<6, 2> a{{204.882, 0}, {253.979, 0}, {143.824, 0},
+                 {0, 204.882}, {0, 253.979}, {0, 143.824}};
+  matrix<2, 2> r{{213.882, 0}, {0, 213.882}};
+  matrix<6, 2> q{a / r};
+
+  // assert(a.isApprox(q * r));
+  // std::cout << "A:\n" << a << std::endl;
+  // std::cout << "R:\n" << r << std::endl;
+  // std::cout << "Q:\n" << q << std::endl;
+
+  // std::print("{}", q);
+
+  std::cout << q(0, 0) << std::endl;
+  std::cout << q(0, 1) << std::endl;
+  std::cout << q(1, 0) << std::endl;
+  std::cout << q(1, 1) << std::endl;
+  std::cout << q(2, 0) << std::endl;
+  std::cout << q(2, 1) << std::endl;
+
+  std::cout << q(3, 0) << std::endl;
+  std::cout << q(3, 1) << std::endl;
+  std::cout << q(4, 0) << std::endl;
+  std::cout << q(4, 1) << std::endl;
+  std::cout << q(5, 0) << std::endl;
+  std::cout << q(5, 1) << std::endl;
+
+  // 0.957921        0
+  // 1.18747        0
+  // 0.672446        0
+  //        0 0.957921
+  //        0  1.18747
+  //        0 0.672446
+
+  return 0;
+}()};
+} // namespace
+} // namespace fcarouge::test
diff --git a/test/linalg_division_orthogonal.cpp b/test/linalg_division_orthogonal.cpp
new file mode 100644
index 000000000..2d32004a9
--- /dev/null
+++ b/test/linalg_division_orthogonal.cpp
@@ -0,0 +1,71 @@
+/*  __          _      __  __          _   _
+| |/ /    /\   | |    |  \/  |   /\   | \ | |
+| ' /    /  \  | |    | \  / |  /  \  |  \| |
+|  <    / /\ \ | |    | |\/| | / /\ \ | . ` |
+| . \  / ____ \| |____| |  | |/ ____ \| |\  |
+|_|\_\/_/    \_\______|_|  |_/_/    \_\_| \_|
+
+Kalman Filter
+Version 0.2.0
+https://github.com/FrancoisCarouge/Kalman
+
+SPDX-License-Identifier: Unlicense
+
+This is free and unencumbered software released into the public domain.
+
+Anyone is free to copy, modify, publish, use, compile, sell, or
+distribute this software, either in source code form or as a compiled
+binary, for any purpose, commercial or non-commercial, and by any
+means.
+
+In jurisdictions that recognize copyright laws, the author or authors
+of this software dedicate any and all copyright interest in the
+software to the public domain. We make this dedication for the benefit
+of the public at large and to the detriment of our heirs and
+successors. We intend this dedication to be an overt act of
+relinquishment in perpetuity of all present and future rights to this
+software under copyright law.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
+MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
+IN NO EVENT SHALL THE AUTHORS BE LIABLE FOR ANY CLAIM, DAMAGES OR
+OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
+ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
+OTHER DEALINGS IN THE SOFTWARE.
+
+For more information, please refer to <https://unlicense.org> */
+
+#include "fcarouge/kalman.hpp"
+#include "fcarouge/linalg.hpp"
+
+#include <cassert>
+
+template <typename Numerator, fcarouge::algebraic Denominator>
+constexpr auto fcarouge::operator/(const Numerator &lhs, const Denominator &rhs)
+    -> fcarouge::quotient<Numerator, Denominator> {
+  return rhs.transpose()
+      .completeOrthogonalDecomposition()
+      .solve(lhs.transpose())
+      .transpose();
+}
+
+namespace fcarouge::test {
+namespace {
+template <auto Row, auto Column> using matrix = matrix<double, Row, Column>;
+
+//! @test Verifies the Eigen decomposition solver.
+//!
+//! @todo Rewrite this test as a property-based test.
+[[maybe_unused]] auto test{[] {
+  matrix<6, 2> a{{204.882, 0}, {253.979, 0}, {143.824, 0},
+                 {0, 204.882}, {0, 253.979}, {0, 143.824}};
+  matrix<2, 2> r{{213.882, 0}, {0, 213.882}};
+  matrix<6, 2> q{a / r};
+
+  assert(a.isApprox(q * r));
+
+  return 0;
+}()};
+} // namespace
+} // namespace fcarouge::test
diff --git a/test/linalg_division_pivot_full.cpp b/test/linalg_division_pivot_full.cpp
new file mode 100644
index 000000000..dcb8b984a
--- /dev/null
+++ b/test/linalg_division_pivot_full.cpp
@@ -0,0 +1,68 @@
+/*  __          _      __  __          _   _
+| |/ /    /\   | |    |  \/  |   /\   | \ | |
+| ' /    /  \  | |    | \  / |  /  \  |  \| |
+|  <    / /\ \ | |    | |\/| | / /\ \ | . ` |
+| . \  / ____ \| |____| |  | |/ ____ \| |\  |
+|_|\_\/_/    \_\______|_|  |_/_/    \_\_| \_|
+
+Kalman Filter
+Version 0.2.0
+https://github.com/FrancoisCarouge/Kalman
+
+SPDX-License-Identifier: Unlicense
+
+This is free and unencumbered software released into the public domain.
+
+Anyone is free to copy, modify, publish, use, compile, sell, or
+distribute this software, either in source code form or as a compiled
+binary, for any purpose, commercial or non-commercial, and by any
+means.
+
+In jurisdictions that recognize copyright laws, the author or authors
+of this software dedicate any and all copyright interest in the
+software to the public domain. We make this dedication for the benefit
+of the public at large and to the detriment of our heirs and
+successors. We intend this dedication to be an overt act of
+relinquishment in perpetuity of all present and future rights to this
+software under copyright law.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
+MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
+IN NO EVENT SHALL THE AUTHORS BE LIABLE FOR ANY CLAIM, DAMAGES OR
+OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
+ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
+OTHER DEALINGS IN THE SOFTWARE.
+
+For more information, please refer to <https://unlicense.org> */
+
+#include "fcarouge/kalman.hpp"
+#include "fcarouge/linalg.hpp"
+
+#include <cassert>
+
+template <typename Numerator, fcarouge::algebraic Denominator>
+constexpr auto fcarouge::operator/(const Numerator &lhs, const Denominator &rhs)
+    -> fcarouge::quotient<Numerator, Denominator> {
+  return rhs.transpose().fullPivLu().solve(lhs.transpose()).transpose();
+}
+
+namespace fcarouge::test {
+namespace {
+template <auto Row, auto Column> using matrix = matrix<double, Row, Column>;
+
+//! @test Verifies the Eigen decomposition solver.
+//!
+//! @todo Rewrite this test as a property-based test.
+[[maybe_unused]] auto test{[] {
+  matrix<6, 2> a{{204.882, 0}, {253.979, 0}, {143.824, 0},
+                 {0, 204.882}, {0, 253.979}, {0, 143.824}};
+  matrix<2, 2> r{{213.882, 0}, {0, 213.882}};
+  matrix<6, 2> q{a / r};
+
+  assert(a.isApprox(q * r));
+
+  return 0;
+}()};
+} // namespace
+} // namespace fcarouge::test
diff --git a/test/linalg_division_pivot_partial.cpp b/test/linalg_division_pivot_partial.cpp
new file mode 100644
index 000000000..54ed412f5
--- /dev/null
+++ b/test/linalg_division_pivot_partial.cpp
@@ -0,0 +1,68 @@
+/*  __          _      __  __          _   _
+| |/ /    /\   | |    |  \/  |   /\   | \ | |
+| ' /    /  \  | |    | \  / |  /  \  |  \| |
+|  <    / /\ \ | |    | |\/| | / /\ \ | . ` |
+| . \  / ____ \| |____| |  | |/ ____ \| |\  |
+|_|\_\/_/    \_\______|_|  |_/_/    \_\_| \_|
+
+Kalman Filter
+Version 0.2.0
+https://github.com/FrancoisCarouge/Kalman
+
+SPDX-License-Identifier: Unlicense
+
+This is free and unencumbered software released into the public domain.
+
+Anyone is free to copy, modify, publish, use, compile, sell, or
+distribute this software, either in source code form or as a compiled
+binary, for any purpose, commercial or non-commercial, and by any
+means.
+
+In jurisdictions that recognize copyright laws, the author or authors
+of this software dedicate any and all copyright interest in the
+software to the public domain. We make this dedication for the benefit
+of the public at large and to the detriment of our heirs and
+successors. We intend this dedication to be an overt act of
+relinquishment in perpetuity of all present and future rights to this
+software under copyright law.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
+MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
+IN NO EVENT SHALL THE AUTHORS BE LIABLE FOR ANY CLAIM, DAMAGES OR
+OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
+ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
+OTHER DEALINGS IN THE SOFTWARE.
+
+For more information, please refer to <https://unlicense.org> */
+
+#include "fcarouge/kalman.hpp"
+#include "fcarouge/linalg.hpp"
+
+#include <cassert>
+
+template <typename Numerator, fcarouge::algebraic Denominator>
+constexpr auto fcarouge::operator/(const Numerator &lhs, const Denominator &rhs)
+    -> fcarouge::quotient<Numerator, Denominator> {
+  return rhs.transpose().partialPivLu().solve(lhs.transpose()).transpose();
+}
+
+namespace fcarouge::test {
+namespace {
+template <auto Row, auto Column> using matrix = matrix<double, Row, Column>;
+
+//! @test Verifies the Eigen decomposition solver.
+//!
+//! @todo Rewrite this test as a property-based test.
+[[maybe_unused]] auto test{[] {
+  matrix<6, 2> a{{204.882, 0}, {253.979, 0}, {143.824, 0},
+                 {0, 204.882}, {0, 253.979}, {0, 143.824}};
+  matrix<2, 2> r{{213.882, 0}, {0, 213.882}};
+  matrix<6, 2> q{a / r};
+
+  assert(a.isApprox(q * r));
+
+  return 0;
+}()};
+} // namespace
+} // namespace fcarouge::test
diff --git a/test/linalg_identity_constexpr.cpp b/test/linalg_identity_constexpr.cpp
new file mode 100644
index 000000000..c84e58936
--- /dev/null
+++ b/test/linalg_identity_constexpr.cpp
@@ -0,0 +1,63 @@
+/*  __          _      __  __          _   _
+| |/ /    /\   | |    |  \/  |   /\   | \ | |
+| ' /    /  \  | |    | \  / |  /  \  |  \| |
+|  <    / /\ \ | |    | |\/| | / /\ \ | . ` |
+| . \  / ____ \| |____| |  | |/ ____ \| |\  |
+|_|\_\/_/    \_\______|_|  |_/_/    \_\_| \_|
+
+Kalman Filter
+Version 0.2.0
+https://github.com/FrancoisCarouge/Kalman
+
+SPDX-License-Identifier: Unlicense
+
+This is free and unencumbered software released into the public domain.
+
+Anyone is free to copy, modify, publish, use, compile, sell, or
+distribute this software, either in source code form or as a compiled
+binary, for any purpose, commercial or non-commercial, and by any
+means.
+
+In jurisdictions that recognize copyright laws, the author or authors
+of this software dedicate any and all copyright interest in the
+software to the public domain. We make this dedication for the benefit
+of the public at large and to the detriment of our heirs and
+successors. We intend this dedication to be an overt act of
+relinquishment in perpetuity of all present and future rights to this
+software under copyright law.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
+MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
+IN NO EVENT SHALL THE AUTHORS BE LIABLE FOR ANY CLAIM, DAMAGES OR
+OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
+ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
+OTHER DEALINGS IN THE SOFTWARE.
+
+For more information, please refer to <https://unlicense.org> */
+
+#include "fcarouge/linalg.hpp"
+
+namespace fcarouge::test {
+namespace {
+//! @test Verifies the identity matrices values are unit diagonals.
+//!
+//! @todo Make the lambda `consteval` when MSVC supports it.
+//! @todo Rewrite this test as a property-based test.
+[[maybe_unused]] constexpr auto test{[] {
+  constexpr auto identity{identity_v<matrix<double, 3, 3>>};
+
+  static_assert(identity(0, 0) == 1.0);
+  static_assert(identity(0, 1) == 0.0);
+  static_assert(identity(0, 2) == 0.0);
+  static_assert(identity(1, 0) == 0.0);
+  static_assert(identity(1, 1) == 1.0);
+  static_assert(identity(1, 2) == 0.0);
+  static_assert(identity(2, 0) == 0.0);
+  static_assert(identity(2, 1) == 0.0);
+  static_assert(identity(2, 2) == 1.0);
+
+  return 0;
+}()};
+} // namespace
+} // namespace fcarouge::test
diff --git a/test/linalg_identity_default_constexpr.cpp b/test/linalg_identity_default_constexpr.cpp
new file mode 100644
index 000000000..4e5f9a8cf
--- /dev/null
+++ b/test/linalg_identity_default_constexpr.cpp
@@ -0,0 +1,58 @@
+/*  __          _      __  __          _   _
+| |/ /    /\   | |    |  \/  |   /\   | \ | |
+| ' /    /  \  | |    | \  / |  /  \  |  \| |
+|  <    / /\ \ | |    | |\/| | / /\ \ | . ` |
+| . \  / ____ \| |____| |  | |/ ____ \| |\  |
+|_|\_\/_/    \_\______|_|  |_/_/    \_\_| \_|
+
+Kalman Filter
+Version 0.2.0
+https://github.com/FrancoisCarouge/Kalman
+
+SPDX-License-Identifier: Unlicense
+
+This is free and unencumbered software released into the public domain.
+
+Anyone is free to copy, modify, publish, use, compile, sell, or
+distribute this software, either in source code form or as a compiled
+binary, for any purpose, commercial or non-commercial, and by any
+means.
+
+In jurisdictions that recognize copyright laws, the author or authors
+of this software dedicate any and all copyright interest in the
+software to the public domain. We make this dedication for the benefit
+of the public at large and to the detriment of our heirs and
+successors. We intend this dedication to be an overt act of
+relinquishment in perpetuity of all present and future rights to this
+software under copyright law.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
+MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
+IN NO EVENT SHALL THE AUTHORS BE LIABLE FOR ANY CLAIM, DAMAGES OR
+OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
+ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
+OTHER DEALINGS IN THE SOFTWARE.
+
+For more information, please refer to <https://unlicense.org> */
+
+#include "fcarouge/linalg.hpp"
+
+#include <type_traits>
+
+namespace fcarouge::test {
+namespace {
+//! @test Verifies the 1x1 identity matrix deduced default value is a unit
+//! double.
+//!
+//! @todo Make the lambda `consteval` when MSVC supports it.
+[[maybe_unused]] constexpr auto test{[] {
+  constexpr auto identity{identity_v<>};
+
+  static_assert(identity == 1.0);
+  static_assert(std::is_same_v<decltype(identity), const double>);
+
+  return 0;
+}()};
+} // namespace
+} // namespace fcarouge::test
diff --git a/test/linalg_operator_bracket_1x2_constexpr.cpp b/test/linalg_operator_bracket_1x2_constexpr.cpp
new file mode 100644
index 000000000..62924a180
--- /dev/null
+++ b/test/linalg_operator_bracket_1x2_constexpr.cpp
@@ -0,0 +1,52 @@
+/*  __          _      __  __          _   _
+| |/ /    /\   | |    |  \/  |   /\   | \ | |
+| ' /    /  \  | |    | \  / |  /  \  |  \| |
+|  <    / /\ \ | |    | |\/| | / /\ \ | . ` |
+| . \  / ____ \| |____| |  | |/ ____ \| |\  |
+|_|\_\/_/    \_\______|_|  |_/_/    \_\_| \_|
+
+Kalman Filter
+Version 0.2.0
+https://github.com/FrancoisCarouge/Kalman
+
+SPDX-License-Identifier: Unlicense
+
+This is free and unencumbered software released into the public domain.
+
+Anyone is free to copy, modify, publish, use, compile, sell, or
+distribute this software, either in source code form or as a compiled
+binary, for any purpose, commercial or non-commercial, and by any
+means.
+
+In jurisdictions that recognize copyright laws, the author or authors
+of this software dedicate any and all copyright interest in the
+software to the public domain. We make this dedication for the benefit
+of the public at large and to the detriment of our heirs and
+successors. We intend this dedication to be an overt act of
+relinquishment in perpetuity of all present and future rights to this
+software under copyright law.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
+MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
+IN NO EVENT SHALL THE AUTHORS BE LIABLE FOR ANY CLAIM, DAMAGES OR
+OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
+ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
+OTHER DEALINGS IN THE SOFTWARE.
+
+For more information, please refer to <https://unlicense.org> */
+
+#include "fcarouge/linalg.hpp"
+
+namespace fcarouge::test {
+namespace {
+//! @test Verifies ...
+//!
+//! @todo Make the lambda `consteval` when MSVC supports it.
+[[maybe_unused]] constexpr auto test{[] {
+  // constexpr matrix<double, 1, 2> m;
+
+  return 0;
+}()};
+} // namespace
+} // namespace fcarouge::test
diff --git a/test/linalg_operator_bracket_constexpr.cpp b/test/linalg_operator_bracket_constexpr.cpp
new file mode 100644
index 000000000..0931e99da
--- /dev/null
+++ b/test/linalg_operator_bracket_constexpr.cpp
@@ -0,0 +1,58 @@
+/*  __          _      __  __          _   _
+| |/ /    /\   | |    |  \/  |   /\   | \ | |
+| ' /    /  \  | |    | \  / |  /  \  |  \| |
+|  <    / /\ \ | |    | |\/| | / /\ \ | . ` |
+| . \  / ____ \| |____| |  | |/ ____ \| |\  |
+|_|\_\/_/    \_\______|_|  |_/_/    \_\_| \_|
+
+Kalman Filter
+Version 0.2.0
+https://github.com/FrancoisCarouge/Kalman
+
+SPDX-License-Identifier: Unlicense
+
+This is free and unencumbered software released into the public domain.
+
+Anyone is free to copy, modify, publish, use, compile, sell, or
+distribute this software, either in source code form or as a compiled
+binary, for any purpose, commercial or non-commercial, and by any
+means.
+
+In jurisdictions that recognize copyright laws, the author or authors
+of this software dedicate any and all copyright interest in the
+software to the public domain. We make this dedication for the benefit
+of the public at large and to the detriment of our heirs and
+successors. We intend this dedication to be an overt act of
+relinquishment in perpetuity of all present and future rights to this
+software under copyright law.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
+MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
+IN NO EVENT SHALL THE AUTHORS BE LIABLE FOR ANY CLAIM, DAMAGES OR
+OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
+ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
+OTHER DEALINGS IN THE SOFTWARE.
+
+For more information, please refer to <https://unlicense.org> */
+
+#include "fcarouge/linalg.hpp"
+
+namespace fcarouge::test {
+namespace {
+//! @test Verifies the 1x1 matrix bracket operator.
+//!
+//! @todo Make the lambda `consteval` when MSVC supports it.
+//! @todo Rewrite this test as a property-based test.
+[[maybe_unused]] constexpr auto test{[] {
+  constexpr matrix m{42.0};
+
+  static_assert(m(0) == 42.0);
+  static_assert(m(0, 0) == 42.0);
+  static_assert(m[0] == 42.0);
+  // static_assert(m[0][0] == 42.0);
+
+  return 0;
+}()};
+} // namespace
+} // namespace fcarouge::test
diff --git a/test/linalg_operator_equality_constexpr.cpp b/test/linalg_operator_equality_constexpr.cpp
new file mode 100644
index 000000000..fdfff93f8
--- /dev/null
+++ b/test/linalg_operator_equality_constexpr.cpp
@@ -0,0 +1,58 @@
+/*  __          _      __  __          _   _
+| |/ /    /\   | |    |  \/  |   /\   | \ | |
+| ' /    /  \  | |    | \  / |  /  \  |  \| |
+|  <    / /\ \ | |    | |\/| | / /\ \ | . ` |
+| . \  / ____ \| |____| |  | |/ ____ \| |\  |
+|_|\_\/_/    \_\______|_|  |_/_/    \_\_| \_|
+
+Kalman Filter
+Version 0.2.0
+https://github.com/FrancoisCarouge/Kalman
+
+SPDX-License-Identifier: Unlicense
+
+This is free and unencumbered software released into the public domain.
+
+Anyone is free to copy, modify, publish, use, compile, sell, or
+distribute this software, either in source code form or as a compiled
+binary, for any purpose, commercial or non-commercial, and by any
+means.
+
+In jurisdictions that recognize copyright laws, the author or authors
+of this software dedicate any and all copyright interest in the
+software to the public domain. We make this dedication for the benefit
+of the public at large and to the detriment of our heirs and
+successors. We intend this dedication to be an overt act of
+relinquishment in perpetuity of all present and future rights to this
+software under copyright law.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
+MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
+IN NO EVENT SHALL THE AUTHORS BE LIABLE FOR ANY CLAIM, DAMAGES OR
+OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
+ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
+OTHER DEALINGS IN THE SOFTWARE.
+
+For more information, please refer to <https://unlicense.org> */
+
+#include "fcarouge/linalg.hpp"
+
+namespace fcarouge::test {
+namespace {
+//! @test Verifies the equality operator.
+//!
+//! @todo Make the lambda `consteval` when MSVC supports it.
+//! @todo Rewrite this test as a property-based test.
+[[maybe_unused]] constexpr auto test{[] {
+  constexpr matrix<double, 5, 5> m;
+  constexpr auto i{identity_v<matrix<double, 5, 5>>};
+  constexpr auto z{zero_v<matrix<double, 5, 5>>};
+
+  static_assert(m == z);
+  static_assert(m != i);
+
+  return 0;
+}()};
+} // namespace
+} // namespace fcarouge::test
diff --git a/test/linalg_zero_constexpr.cpp b/test/linalg_zero_constexpr.cpp
new file mode 100644
index 000000000..f1fe0d04e
--- /dev/null
+++ b/test/linalg_zero_constexpr.cpp
@@ -0,0 +1,63 @@
+/*  __          _      __  __          _   _
+| |/ /    /\   | |    |  \/  |   /\   | \ | |
+| ' /    /  \  | |    | \  / |  /  \  |  \| |
+|  <    / /\ \ | |    | |\/| | / /\ \ | . ` |
+| . \  / ____ \| |____| |  | |/ ____ \| |\  |
+|_|\_\/_/    \_\______|_|  |_/_/    \_\_| \_|
+
+Kalman Filter
+Version 0.2.0
+https://github.com/FrancoisCarouge/Kalman
+
+SPDX-License-Identifier: Unlicense
+
+This is free and unencumbered software released into the public domain.
+
+Anyone is free to copy, modify, publish, use, compile, sell, or
+distribute this software, either in source code form or as a compiled
+binary, for any purpose, commercial or non-commercial, and by any
+means.
+
+In jurisdictions that recognize copyright laws, the author or authors
+of this software dedicate any and all copyright interest in the
+software to the public domain. We make this dedication for the benefit
+of the public at large and to the detriment of our heirs and
+successors. We intend this dedication to be an overt act of
+relinquishment in perpetuity of all present and future rights to this
+software under copyright law.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
+MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
+IN NO EVENT SHALL THE AUTHORS BE LIABLE FOR ANY CLAIM, DAMAGES OR
+OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
+ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
+OTHER DEALINGS IN THE SOFTWARE.
+
+For more information, please refer to <https://unlicense.org> */
+
+#include "fcarouge/linalg.hpp"
+
+namespace fcarouge::test {
+namespace {
+//! @test Verifies the zero matrices values are null.
+//!
+//! @todo Make the lambda `consteval` when MSVC supports it.
+//! @todo Rewrite this test as a property-based test.
+[[maybe_unused]] constexpr auto test{[] {
+  constexpr auto zero{zero_v<matrix<double, 3, 3>>};
+
+  static_assert(zero(0, 0) == 0.0);
+  static_assert(zero(0, 1) == 0.0);
+  static_assert(zero(0, 2) == 0.0);
+  static_assert(zero(1, 0) == 0.0);
+  static_assert(zero(1, 1) == 0.0);
+  static_assert(zero(1, 2) == 0.0);
+  static_assert(zero(2, 0) == 0.0);
+  static_assert(zero(2, 1) == 0.0);
+  static_assert(zero(2, 2) == 0.0);
+
+  return 0;
+}()};
+} // namespace
+} // namespace fcarouge::test
diff --git a/test/linalg_zero_default_constexpr.cpp b/test/linalg_zero_default_constexpr.cpp
new file mode 100644
index 000000000..9fab9245f
--- /dev/null
+++ b/test/linalg_zero_default_constexpr.cpp
@@ -0,0 +1,57 @@
+/*  __          _      __  __          _   _
+| |/ /    /\   | |    |  \/  |   /\   | \ | |
+| ' /    /  \  | |    | \  / |  /  \  |  \| |
+|  <    / /\ \ | |    | |\/| | / /\ \ | . ` |
+| . \  / ____ \| |____| |  | |/ ____ \| |\  |
+|_|\_\/_/    \_\______|_|  |_/_/    \_\_| \_|
+
+Kalman Filter
+Version 0.2.0
+https://github.com/FrancoisCarouge/Kalman
+
+SPDX-License-Identifier: Unlicense
+
+This is free and unencumbered software released into the public domain.
+
+Anyone is free to copy, modify, publish, use, compile, sell, or
+distribute this software, either in source code form or as a compiled
+binary, for any purpose, commercial or non-commercial, and by any
+means.
+
+In jurisdictions that recognize copyright laws, the author or authors
+of this software dedicate any and all copyright interest in the
+software to the public domain. We make this dedication for the benefit
+of the public at large and to the detriment of our heirs and
+successors. We intend this dedication to be an overt act of
+relinquishment in perpetuity of all present and future rights to this
+software under copyright law.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
+MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
+IN NO EVENT SHALL THE AUTHORS BE LIABLE FOR ANY CLAIM, DAMAGES OR
+OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
+ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
+OTHER DEALINGS IN THE SOFTWARE.
+
+For more information, please refer to <https://unlicense.org> */
+
+#include "fcarouge/linalg.hpp"
+
+#include <type_traits>
+
+namespace fcarouge::test {
+namespace {
+//! @test Verifies the 1x1 zero matrix deduced default value is a null double.
+//!
+//! @todo Make the lambda `consteval` when MSVC supports it.
+[[maybe_unused]] constexpr auto test{[] {
+  constexpr auto zero{zero_v<>};
+
+  static_assert(zero == 0.0);
+  static_assert(std::is_same_v<decltype(zero), const double>);
+
+  return 0;
+}()};
+} // namespace
+} // namespace fcarouge::test