The compositor will likely do an order of magnitude less matrix
inversions than point transformations with an inverse, hence we do not
really need the optimised path for single-shot invert-and-transform.
Expose only the computing of the explicit inverse matrix in the API.
However, the matrix inversion tests need access to the internal
functions. Designate a unit test build by #defining UNIT_TEST, and
export the internal functions in that case.
Signed-off-by: Pekka Paalanen <ppaalanen@gmail.com>
Add a new directory tests/ for unit test applications. This directory
will be built only if --enable-tests is given to ./configure.
Add matrix-test application. It excercises especially the
weston_matrix_invert() and weston_matrix_inverse_transform() functions.
It has one test for correctness and precision, and other tests for
measuring the speed of various matrix operations.
For the record, the correctness test prints:
a random matrix:
1.112418e-02 2.628150e+00 8.205844e+02 -1.147526e-04
4.943677e-04 -1.117819e-04 -9.158849e-06 3.678122e-02
7.915063e-03 -3.093254e-04 -4.376583e+02 3.424706e-02
-2.504038e+02 2.481788e+03 -7.545445e+01 1.752909e-03
The matrix multiplied by its inverse, error:
0.000000e+00 -0.000000e+00 -0.000000e+00 -0.000000e+00
0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
-0.000000e+00 -0.000000e+00 0.000000e+00 -0.000000e+00
0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
max abs error: 0, original determinant 11595.2
Running a test loop for 10 seconds...
test fail, det: -0.00464805, error sup: inf
test fail, det: -0.0424053, error sup: 1.30787e-06
test fail, det: 5.15191, error sup: 1.15956e-06
tests: 6791767 ok, 1 not invertible but ok, 3 failed.
Total: 6791771 iterations.
These results are expected with the current precision thresholds in
src/matrix.c and tests/matrix-test.c. The random number generator is
seeded with a constant, so the random numbers should be the same on
every run. Machine speed and scheduling affect how many iterations are
run.
Signed-off-by: Pekka Paalanen <ppaalanen@gmail.com>
Implement 4x4 matrix inversion based on LU-decomposition with partial
pivoting.
Instead of simply computing the inverse matrix explicitly, introduce the
type struct weston_inverse_matrix for storing the LU-decomposition and
the permutation from pivoting. Using doubles, this struct has greater
precision than struct weston_matrix.
If you need only few (less than 5, presumably) multiplications with the
inverse matrix, is it cheaper to use weston_inverse_matrix, and not
compute the inverse matrix explicitly into a weston_matrix.
Signed-off-by: Pekka Paalanen <ppaalanen@gmail.com>
Remove the inverse matrix member from struct weston_transform. It is
easier (and probably faster, too) to create and store only forward
transformation matrices in a list, multiply them once, and then invert
the final matrix, rather than creating both forward and inverse
matrices, and multiplying both.
Add a stub for the 4x4 matrix inversion function.
Signed-off-by: Pekka Paalanen <ppaalanen@gmail.com>
Rob Bradford
John Kåre Alsaker
Pekka Paalanen