You can not select more than 25 topics Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
 
 
 
 
weston/tests/matrix-test.c

424 lines
8.8 KiB

/*
* Copyright © 2012 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 <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <unistd.h>
#include <signal.h>
#include <time.h>
#include "../shared/matrix.h"
struct inverse_matrix {
double LU[16]; /* column-major */
unsigned perm[4]; /* permutation */
};
static struct timespec begin_time;
static void
reset_timer(void)
{
clock_gettime(CLOCK_MONOTONIC, &begin_time);
}
static double
read_timer(void)
{
struct timespec t;
clock_gettime(CLOCK_MONOTONIC, &t);
return (double)(t.tv_sec - begin_time.tv_sec) +
1e-9 * (t.tv_nsec - begin_time.tv_nsec);
}
static double
det3x3(const float *c0, const float *c1, const float *c2)
{
return (double)
c0[0] * c1[1] * c2[2] +
c1[0] * c2[1] * c0[2] +
c2[0] * c0[1] * c1[2] -
c0[2] * c1[1] * c2[0] -
c1[2] * c2[1] * c0[0] -
c2[2] * c0[1] * c1[0];
}
static double
determinant(const struct weston_matrix *m)
{
double det = 0;
#if 1
/* develop on last row */
det -= m->d[3 + 0 * 4] * det3x3(&m->d[4], &m->d[8], &m->d[12]);
det += m->d[3 + 1 * 4] * det3x3(&m->d[0], &m->d[8], &m->d[12]);
det -= m->d[3 + 2 * 4] * det3x3(&m->d[0], &m->d[4], &m->d[12]);
det += m->d[3 + 3 * 4] * det3x3(&m->d[0], &m->d[4], &m->d[8]);
#else
/* develop on first row */
det += m->d[0 + 0 * 4] * det3x3(&m->d[5], &m->d[9], &m->d[13]);
det -= m->d[0 + 1 * 4] * det3x3(&m->d[1], &m->d[9], &m->d[13]);
det += m->d[0 + 2 * 4] * det3x3(&m->d[1], &m->d[5], &m->d[13]);
det -= m->d[0 + 3 * 4] * det3x3(&m->d[1], &m->d[5], &m->d[9]);
#endif
return det;
}
static void
print_permutation_matrix(const struct inverse_matrix *m)
{
const unsigned *p = m->perm;
const char *row[4] = {
"1 0 0 0\n",
"0 1 0 0\n",
"0 0 1 0\n",
"0 0 0 1\n"
};
printf(" P =\n%s%s%s%s", row[p[0]], row[p[1]], row[p[2]], row[p[3]]);
}
static void
print_LU_decomposition(const struct inverse_matrix *m)
{
unsigned r, c;
printf(" L "
" U\n");
for (r = 0; r < 4; ++r) {
double v;
for (c = 0; c < 4; ++c) {
if (c < r)
v = m->LU[r + c * 4];
else if (c == r)
v = 1.0;
else
v = 0.0;
printf(" %12.6f", v);
}
printf(" | ");
for (c = 0; c < 4; ++c) {
if (c >= r)
v = m->LU[r + c * 4];
else
v = 0.0;
printf(" %12.6f", v);
}
printf("\n");
}
}
static void
print_inverse_data_matrix(const struct inverse_matrix *m)
{
unsigned r, c;
for (r = 0; r < 4; ++r) {
for (c = 0; c < 4; ++c)
printf(" %12.6f", m->LU[r + c * 4]);
printf("\n");
}
printf("permutation: ");
for (r = 0; r < 4; ++r)
printf(" %u", m->perm[r]);
printf("\n");
}
static void
print_matrix(const struct weston_matrix *m)
{
unsigned r, c;
for (r = 0; r < 4; ++r) {
for (c = 0; c < 4; ++c)
printf(" %14.6e", m->d[r + c * 4]);
printf("\n");
}
}
static double
frand(void)
{
double r = random();
return r / (double)(RAND_MAX / 2) - 1.0f;
}
static void
randomize_matrix(struct weston_matrix *m)
{
unsigned i;
for (i = 0; i < 16; ++i)
#if 1
m->d[i] = frand() * exp(10.0 * frand());
#else
m->d[i] = frand();
#endif
}
/* Take a matrix, compute inverse, multiply together
* and subtract the identity matrix to get the error matrix.
* Return the largest absolute value from the error matrix.
*/
static double
test_inverse(struct weston_matrix *m)
{
unsigned i;
struct inverse_matrix q;
double errsup = 0.0;
if (matrix_invert(q.LU, q.perm, m) != 0)
return INFINITY;
for (i = 0; i < 4; ++i)
inverse_transform(q.LU, q.perm, &m->d[i * 4]);
m->d[0] -= 1.0f;
m->d[5] -= 1.0f;
m->d[10] -= 1.0f;
m->d[15] -= 1.0f;
for (i = 0; i < 16; ++i) {
double err = fabs(m->d[i]);
if (err > errsup)
errsup = err;
}
return errsup;
}
enum {
TEST_OK,
TEST_NOT_INVERTIBLE_OK,
TEST_FAIL,
TEST_COUNT
};
static int
test(void)
{
struct weston_matrix m;
double det, errsup;
randomize_matrix(&m);
det = determinant(&m);
errsup = test_inverse(&m);
if (errsup < 1e-6)
return TEST_OK;
if (fabs(det) < 1e-5 && isinf(errsup))
return TEST_NOT_INVERTIBLE_OK;
printf("test fail, det: %g, error sup: %g\n", det, errsup);
return TEST_FAIL;
}
static int running;
static void
stopme(int n)
{
running = 0;
}
static void
test_loop_precision(void)
{
int counts[TEST_COUNT] = { 0 };
printf("\nRunning a test loop for 10 seconds...\n");
running = 1;
alarm(10);
while (running) {
counts[test()]++;
}
printf("tests: %d ok, %d not invertible but ok, %d failed.\n"
"Total: %d iterations.\n",
counts[TEST_OK], counts[TEST_NOT_INVERTIBLE_OK],
counts[TEST_FAIL],
counts[TEST_OK] + counts[TEST_NOT_INVERTIBLE_OK] +
counts[TEST_FAIL]);
}
static void __attribute__((noinline))
test_loop_speed_matrixvector(void)
{
struct weston_matrix m;
struct weston_vector v = { { 0.5, 0.5, 0.5, 1.0 } };
unsigned long count = 0;
double t;
printf("\nRunning 3 s test on weston_matrix_transform()...\n");
weston_matrix_init(&m);
running = 1;
alarm(3);
reset_timer();
while (running) {
weston_matrix_transform(&m, &v);
count++;
}
t = read_timer();
printf("%lu iterations in %f seconds, avg. %.1f ns/iter.\n",
count, t, 1e9 * t / count);
}
static void __attribute__((noinline))
test_loop_speed_inversetransform(void)
{
struct weston_matrix m;
struct inverse_matrix inv;
struct weston_vector v = { { 0.5, 0.5, 0.5, 1.0 } };
unsigned long count = 0;
double t;
printf("\nRunning 3 s test on inverse_transform()...\n");
weston_matrix_init(&m);
matrix_invert(inv.LU, inv.perm, &m);
running = 1;
alarm(3);
reset_timer();
while (running) {
inverse_transform(inv.LU, inv.perm, v.f);
count++;
}
t = read_timer();
printf("%lu iterations in %f seconds, avg. %.1f ns/iter.\n",
count, t, 1e9 * t / count);
}
static void __attribute__((noinline))
test_loop_speed_invert(void)
{
struct weston_matrix m;
struct inverse_matrix inv;
unsigned long count = 0;
double t;
printf("\nRunning 3 s test on matrix_invert()...\n");
weston_matrix_init(&m);
running = 1;
alarm(3);
reset_timer();
while (running) {
matrix_invert(inv.LU, inv.perm, &m);
count++;
}
t = read_timer();
printf("%lu iterations in %f seconds, avg. %.1f ns/iter.\n",
count, t, 1e9 * t / count);
}
static void __attribute__((noinline))
test_loop_speed_invert_explicit(void)
{
struct weston_matrix m;
unsigned long count = 0;
double t;
printf("\nRunning 3 s test on weston_matrix_invert()...\n");
weston_matrix_init(&m);
running = 1;
alarm(3);
reset_timer();
while (running) {
weston_matrix_invert(&m, &m);
count++;
}
t = read_timer();
printf("%lu iterations in %f seconds, avg. %.1f ns/iter.\n",
count, t, 1e9 * t / count);
}
int main(void)
{
struct sigaction ding;
struct weston_matrix M;
struct inverse_matrix Q;
int ret;
double errsup;
double det;
ding.sa_handler = stopme;
sigemptyset(&ding.sa_mask);
ding.sa_flags = 0;
sigaction(SIGALRM, &ding, NULL);
srandom(13);
M.d[0] = 3.0; M.d[4] = 17.0; M.d[8] = 10.0; M.d[12] = 0.0;
M.d[1] = 2.0; M.d[5] = 4.0; M.d[9] = -2.0; M.d[13] = 0.0;
M.d[2] = 6.0; M.d[6] = 18.0; M.d[10] = -12; M.d[14] = 0.0;
M.d[3] = 0.0; M.d[7] = 0.0; M.d[11] = 0.0; M.d[15] = 1.0;
ret = matrix_invert(Q.LU, Q.perm, &M);
printf("ret = %d\n", ret);
printf("det = %g\n\n", determinant(&M));
if (ret != 0)
return 1;
print_inverse_data_matrix(&Q);
printf("P * A = L * U\n");
print_permutation_matrix(&Q);
print_LU_decomposition(&Q);
printf("a random matrix:\n");
randomize_matrix(&M);
det = determinant(&M);
print_matrix(&M);
errsup = test_inverse(&M);
printf("\nThe matrix multiplied by its inverse, error:\n");
print_matrix(&M);
printf("max abs error: %g, original determinant %g\n", errsup, det);
test_loop_precision();
test_loop_speed_matrixvector();
test_loop_speed_inversetransform();
test_loop_speed_invert();
test_loop_speed_invert_explicit();
return 0;
}