diff --git a/tests/matrix-test.c b/tests/matrix-test.c new file mode 100644 index 00000000..11c840da --- /dev/null +++ b/tests/matrix-test.c @@ -0,0 +1,271 @@ +/* + * Copyright 2022 Collabora, Ltd. + * + * Permission is hereby granted, free of charge, to any person obtaining + * a copy of this software and associated documentation files (the + * "Software"), to deal in the Software without restriction, including + * without limitation the rights to use, copy, modify, merge, publish, + * distribute, sublicense, and/or sell copies of the Software, and to + * permit persons to whom the Software is furnished to do so, subject to + * the following conditions: + * + * The above copyright notice and this permission notice (including the + * next paragraph) shall be included in all copies or substantial + * portions of the Software. + * + * 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 OR COPYRIGHT HOLDERS + * 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. + */ + +#include "config.h" + +#include +#include +#include "weston-test-client-helper.h" + +/* + * A helper to lay out a matrix in the natural writing order in code + * instead of needing to transpose in your mind every time you read it. + * The matrix is laid out as written: + * ⎡ a11 a12 a13 a14 ⎤ + * ⎢ a21 a22 a23 a24 ⎥ + * ⎢ a31 a32 a33 a34 ⎥ + * ⎣ a41 a42 a43 a44 ⎦ + * where the first digit is row and the second digit is column. + * + * The type field is set to the most pessimistic case possible so that if + * weston_matrix_invert() ever gets special-case code paths, we don't take + * them. + */ +#define MAT(a11, a12, a13, a14, \ + a21, a22, a23, a24, \ + a31, a32, a33, a34, \ + a41, a42, a43, a44) ((struct weston_matrix) \ + { \ + .d[0] = a11, .d[4] = a12, .d[ 8] = a13, .d[12] = a14, \ + .d[1] = a21, .d[5] = a22, .d[ 9] = a23, .d[13] = a24, \ + .d[2] = a31, .d[6] = a32, .d[10] = a33, .d[14] = a34, \ + .d[3] = a41, .d[7] = a42, .d[11] = a43, .d[15] = a44, \ + .type = WESTON_MATRIX_TRANSFORM_TRANSLATE | \ + WESTON_MATRIX_TRANSFORM_SCALE | \ + WESTON_MATRIX_TRANSFORM_ROTATE | \ + WESTON_MATRIX_TRANSFORM_OTHER, \ + }) + +static const struct weston_matrix IDENTITY = + MAT(1, 0, 0, 0, + 0, 1, 0, 0, + 0, 0, 1, 0, + 0, 0, 0, 1); + +static void +subtract_matrix(struct weston_matrix *from, const struct weston_matrix *what) +{ + unsigned i; + + for (i = 0; i < ARRAY_LENGTH(from->d); i++) + from->d[i] -= what->d[i]; +} + +static void +print_matrix(const struct weston_matrix *m) +{ + unsigned r, c; + + for (r = 0; r < 4; ++r) { + for (c = 0; c < 4; ++c) + testlog(" %14.6e", m->d[r + c * 4]); + testlog("\n"); + } +} + +/* + * Matrix infinity norm + * http://www.netlib.org/lapack/lug/node75.html + */ +static double +matrix_inf_norm(const struct weston_matrix *mat) +{ + unsigned row; + double infnorm = -1.0; + + for (row = 0; row < 4; row++) { + unsigned col; + double sum = 0.0; + + for (col = 0; col < 4; col++) + sum += fabs(mat->d[col * 4 + row]); + + if (infnorm < sum) + infnorm = sum; + } + + return infnorm; +} + +struct test_matrix { + /* the matrix to test */ + struct weston_matrix M; + + /* + * Residual error limit; inf norm(M * inv(M) - I) < err_limit + * The residual error as calculated here represents the relative + * error added by transforming a vector with inv(M). + * + * Since weston_matrix stores the inverse matrix in 32-bit floats, + * that limits the precision considerably. + */ + double err_limit; +}; + +static const struct test_matrix matrices[] = { + /* A very trivial case. */ + { + .M = MAT(1, 0, 0, 0, + 0, 2, 0, 0, + 0, 0, 3, 0, + 0, 0, 0, 4), + .err_limit = 0.0, + }, + + /* + * A very likely case in a compositor, being a matrix applying + * just a translation. Surprisingly, fourbyfour-analyze says: + * + * ------------------------------------------------------------------- + * $ ./fourbyfour-analyse 1 0 0 1980 0 1 0 1080 + * Your input matrix A is + * 1 0 0 1980 + * 0 1 0 1080 + * 0 0 1 0 + * 0 0 0 1 + * + * The singular values of A are: 2255.39, 1, 1, 0.000443382 + * The condition number according to 2-norm of A is 5.087e+06. + * + * This means that if you were to solve the linear system Ax=b for vector x, + * in the worst case you would lose 6.7 digits (22.3 bits) of precision. + * The condition number is how much errors in vector b would be amplified + * when solving x even with infinite computational precision. + * + * Compare this to the precision of vectors b and x: + * + * - Single precision floating point has 7.2 digits (24 bits) of precision, + * leaving your result with no correct digits. + * Single precision, matrix A has rank 3 which means that the solution space + * for x has 1 dimension and therefore has many solutions. + * + * - Double precision floating point has 16.0 digits (53 bits) of precision, + * leaving your result with 9.2 correct digits (30 correct bits). + * Double precision, matrix A has full rank which means the solution x is + * unique. + * + * NOTE! The above gives you only an upper limit on errors. + * If the upper limit is low, you can be confident of your computations. But, + * if the upper limit is high, it does not necessarily imply that your + * computations will be doomed. + * ------------------------------------------------------------------- + * + * This is one example where the condition number is highly pessimistic, + * while the actual inversion results in no error at all. + * + * https://gitlab.freedesktop.org/pq/fourbyfour + */ + { + .M = MAT(1, 0, 0, 1980, + 0, 1, 0, 1080, + 0, 0, 1, 0, + 0, 0, 0, 1), + .err_limit = 0.0, + }, + + /* + * The following matrices have been generated with + * fourbyfour-generate using parameters out of a hat as listed below. + * + * If you want to verify the matrices in Octave, type this: + * M = [ ] + * mat = reshape(M, 4, 4) + * det(mat) + * cond(mat) + */ + + /* cond = 1e3 */ + { + .M = MAT(-4.12798022231678357619e-02, -7.93301899046665176529e-02, 2.49367040174418935772e-01, -2.22400462135059429070e-01, + 2.02416121867255743849e-01, -2.25754422240346010187e-02, -2.91283152417864787953e-01, 1.49354988316431153139e-01, + 6.18473094065821293874e-01, 5.81511312950217934548e-02, -1.18363610818063924590e+00, 8.00087538947595322547e-01, + 1.25723127083294305972e-01, 7.72723720984487272290e-02, -3.76023220287807879991e-01, 2.82473279931768073148e-01), + .err_limit = 1e-5, + }, + + /* cond = 1e3, abs det = 15 */ + { + .M = MAT(6.84154939885726509630e+00, -6.87241565273813304060e+00, -2.56772939909334070308e+01, -2.52185055099662420730e+01, + 2.04511561406330022450e+00, -3.67551043874248994925e+00, -1.96421641406619129633e+00, -2.40644091603848320204e+00, + 5.83631095663641819016e+00, -9.31051765621826277197e+00, -1.80402129629135217215e+01, -1.78475057662460052654e+01, + -9.88588496379959025262e+00, 1.49790516545410774540e+01, 2.64975800675967363418e+01, 2.65795891678410747261e+01), + .err_limit = 1e-4, + }, + + /* cond = 700, abs det = 1e-6, invertible regardless of det */ + { + .M = MAT(1.32125189257677579449e-03, -1.67411409720826992453e-01, 1.07940907587735196449e-01, -1.22163309792902186057e-01, + -5.42113793774764013422e-02, 5.30455105336593901733e-01, -2.59607412684229155175e-01, 4.36480803188117993940e-01, + 2.88175168292948129939e-03, -1.85262537685181277736e-01, 1.46265858042118279680e-01, -9.41398969709369287662e-02, + -2.88900393087768159184e-03, 1.57987202530630227448e-01, -1.20781192010860280450e-01, 8.95194304475115387731e-02), + .err_limit = 1e-4, + }, + + /* cond = 1e6, this is a little more challenging */ + { + .M = MAT(-4.41851445093878913983e-01, -5.16386185043831491548e-01, 2.86186055948129847160e-01, -5.79440137716940473211e-01, + 2.49798696238173301154e-01, 2.84965614532234345901e-01, -1.65729639683955931595e-01, 3.12568045963485974248e-01, + 3.15253213984537428161e-01, 3.71270066781250074328e-01, -2.02675623845341434937e-01, 4.19969870491003371971e-01, + 5.60818677658178832424e-01, 6.45373659426444201692e-01, -3.68902466471524526082e-01, 7.13785795079988516498e-01), + .err_limit = 0.02, + }, + + /* cond = 15, abs det = 1e-9, should be well invertible */ + { + .M = MAT(-5.37536200142514660589e-05, 7.92552373388843642288e-03, -3.90554524958281433500e-03, 2.68892064500873568395e-03, + -9.72329428437283989350e-03, 8.32075145342783470404e-03, 6.52648485926096092596e-03, 1.06707947887298994737e-03, + 1.04453728969657322345e-02, -1.03627268579679666927e-02, -3.56835980207569763989e-03, -3.95935925157862422114e-03, + 5.37160838929722633805e-03, 6.13466744624343262009e-05, -1.23695935407398946090e-04, 8.21231194921675112380e-04), + .err_limit = 1e-6, + }, +}; + +TEST_P(matrix_inversion_precision, matrices) +{ + const struct test_matrix *tm = data; + struct weston_matrix rr; + double err; + + /* Compute rr = M * inv(M) */ + weston_matrix_invert(&rr, &tm->M); + weston_matrix_multiply(&rr, &tm->M); + + /* Residual: subtract identity matrix (expected result) */ + subtract_matrix(&rr, &IDENTITY); + + /* + * Infinity norm of the residual is our measure. + * See https://gitlab.freedesktop.org/pq/fourbyfour/-/blob/master/README.d/precision_testing.md + */ + err = matrix_inf_norm(&rr); + testlog("Residual error %g (%.1f bits precision), limit %g.\n", + err, -log2(err), tm->err_limit); + + if (err > tm->err_limit) { + testlog("Error is too high for matrix\n"); + print_matrix(&tm->M); + assert(0); + } +} diff --git a/tests/meson.build b/tests/meson.build index 190255a7..388dcc9a 100644 --- a/tests/meson.build +++ b/tests/meson.build @@ -157,6 +157,10 @@ tests = [ linux_explicit_synchronization_unstable_v1_protocol_c, ], }, + { + 'name': 'matrix', + 'dep_objs': [ dep_libm ] + }, { 'name': 'output-damage', }, { 'name': 'output-transforms', }, { 'name': 'plugin-registry', },