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fixmatrix_unittests.c
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fixmatrix_unittests.c
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#include <stdio.h>
#include "unittests.h"
#include "fixmatrix.h"
#include "fixstring.h"
fix16_t max_delta(const mf16 *a, const mf16 *b)
{
fix16_t max = 0;
int i, j;
if (a->rows != b->rows || a->columns != b->columns ||
a->errors || b->errors)
{
return fix16_maximum;
}
for (i = 0; i < a->rows; i++)
{
for (j = 0; j < a->columns; j++)
{
fix16_t diff = a->data[i][j] - b->data[i][j];
if (diff < 0) diff = -diff;
if (diff > max) max = diff;
}
}
return max;
}
int main()
{
int status = 0;
{
mf16 a = {3, 3, 0,
{{fix16_from_int(1), fix16_from_int(2), fix16_from_int(3)},
{fix16_from_int(4), fix16_from_int(5), fix16_from_int(6)},
{fix16_from_int(7), fix16_from_int(8), fix16_from_int(9)}}};
mf16 r, r2;
COMMENT("Test 3x3 matrix multiplication");
mf16_mul(&r, &a, &a);
TEST(r.errors == 0);
TEST(r.rows == 3 && r.columns == 3);
TEST(r.data[0][0] == fix16_from_int(30));
TEST(r.data[0][1] == fix16_from_int(36));
TEST(r.data[0][2] == fix16_from_int(42));
TEST(r.data[1][0] == fix16_from_int(66));
TEST(r.data[1][1] == fix16_from_int(81));
TEST(r.data[1][2] == fix16_from_int(96));
TEST(r.data[2][0] == fix16_from_int(102));
TEST(r.data[2][1] == fix16_from_int(126));
TEST(r.data[2][2] == fix16_from_int(150));
COMMENT("Test 3x3 matrix multiplication with aliasing");
r2 = a;
mf16_mul(&r2, &r2, &r2);
TEST(max_delta(&r, &r2) == 0);
}
{
mf16 a = {3, 3, 0,
{{fix16_from_int(1000), fix16_from_int(100), fix16_from_int(100)},
{fix16_from_int(100), fix16_from_int(5), fix16_from_int(6)},
{fix16_from_int(100), fix16_from_int(8), fix16_from_int(9)}}};
mf16 r;
COMMENT("Test overflow detection in multiplication");
// Overflow in the multiplication
mf16_mul(&r, &a, &a);
TEST(r.errors == FIXMATRIX_OVERFLOW);
// Overflow in summation
a.data[0][0] = fix16_from_int(150);
mf16_mul(&r, &a, &a);
TEST(r.errors == FIXMATRIX_OVERFLOW);
// No overflow
a.data[0][0] = fix16_from_int(100);
mf16_mul(&r, &a, &a);
TEST(r.errors == 0);
}
{
mf16 a = {5, 1, 0,
{{fix16_from_int(101)},
{fix16_from_int(102)},
{fix16_from_int(103)},
{fix16_from_int(104)},
{fix16_from_int(105)}}};
mf16 b = {5, 1, 0,
{{fix16_from_int(51)},
{fix16_from_int(52)},
{fix16_from_int(53)},
{fix16_from_int(54)},
{fix16_from_int(55)}}};
mf16 atb, abt;
COMMENT("Test mf16_mul_at");
mf16_mul_at(&atb, &a, &b);
TEST(atb.rows == 1);
TEST(atb.columns == 1);
TEST(atb.errors == 0);
TEST(atb.data[0][0] == fix16_from_int(27305));
COMMENT("Test mf16_mul_bt");
mf16_mul_bt(&abt, &a, &b);
TEST(abt.rows == 5);
TEST(abt.columns == 5);
TEST(abt.errors == 0);
TEST(abt.data[0][0] == fix16_from_int(101 * 51));
}
{
mf16 a = {4, 3, 0,
{{fix16_from_int(101), fix16_from_int(102), fix16_from_int(103)},
{fix16_from_int(104), fix16_from_int(105), fix16_from_int(106)},
{fix16_from_int(107), fix16_from_int(108), fix16_from_int(109)},
{fix16_from_int(110), fix16_from_int(111), fix16_from_int(112)}
}};
mf16 b = {4, 3, 0,
{{fix16_from_int(-1), fix16_from_int(-2), fix16_from_int(-3)},
{fix16_from_int(-4), fix16_from_int(-5), fix16_from_int(-6)},
{fix16_from_int(-7), fix16_from_int(-8), fix16_from_int(-9)},
{fix16_from_int(-10), fix16_from_int(-11), fix16_from_int(-12)}
}};
mf16 ref = {4, 3, 0,
{{fix16_from_int(100), fix16_from_int(100), fix16_from_int(100)},
{fix16_from_int(100), fix16_from_int(100), fix16_from_int(100)},
{fix16_from_int(100), fix16_from_int(100), fix16_from_int(100)},
{fix16_from_int(100), fix16_from_int(100), fix16_from_int(100)}
}};
mf16 r;
COMMENT("Test mf16_add with 4x3 matrices");
mf16_add(&r, &a, &b);
TEST(max_delta(&r, &ref) == 0);
COMMENT("Test mf16_add with 4x3 matrices and aliasing");
r = a;
mf16_add(&r, &r, &b);
TEST(max_delta(&r, &ref) == 0);
COMMENT("Test mf16_sub with 4x3 matrices and aliasing");
mf16_sub(&r, &r, &b);
TEST(max_delta(&r, &a) == 0);
}
{
mf16 a = {5, 1, 0,
{{fix16_from_int(1)},
{fix16_from_int(2)},
{fix16_from_int(20000)},
{fix16_from_int(-20000)},
{fix16_from_int(4)}}};
mf16 b = {5, 1, 0,
{{fix16_from_int(1)},
{fix16_from_int(2)},
{fix16_from_int(20000)},
{fix16_from_int(3)},
{fix16_from_int(4)}}};
mf16 c = {5, 1, 0,
{{fix16_from_int(1)},
{fix16_from_int(2)},
{fix16_from_int(3)},
{fix16_from_int(20000)},
{fix16_from_int(4)}}};
mf16 r;
COMMENT("Test overflow detection in addition");
mf16_add(&r, &a, &b);
TEST(r.errors == FIXMATRIX_OVERFLOW);
mf16_add(&r, &a, &c);
TEST(r.errors == 0);
mf16_add(&r, &b, &c);
TEST(r.errors == 0);
COMMENT("Test overflow detection in subtraction");
mf16_sub(&r, &a, &c);
TEST(r.errors == FIXMATRIX_OVERFLOW);
mf16_sub(&r, &a, &b);
TEST(r.errors == 0);
mf16_sub(&r, &b, &c);
TEST(r.errors == 0);
}
{
mf16 a = {3, 3, 0,
{{fix16_from_int(1), fix16_from_int(2), fix16_from_int(3)},
{fix16_from_int(4), fix16_from_int(5), fix16_from_int(6)},
{fix16_from_int(7), fix16_from_int(8), fix16_from_int(9)}}};
mf16 b = {3, 3, 0,
{{fix16_from_int(10), fix16_from_int(20), fix16_from_int(30)},
{fix16_from_int(40), fix16_from_int(50), fix16_from_int(60)},
{fix16_from_int(70), fix16_from_int(80), fix16_from_int(90)}}};
mf16 r;
COMMENT("Test multiplication and division by a scalar");
mf16_mul_s(&r, &a, fix16_from_int(10));
TEST(max_delta(&r, &b) == 0);
mf16_div_s(&r, &r, fix16_from_int(10));
TEST(max_delta(&r, &a) == 0);
}
{
mf16 a = {5, 1, 0,
{{fix16_from_int(1)},
{fix16_from_int(2)},
{fix16_from_int(20000)},
{fix16_from_int(-20000)},
{fix16_from_int(4)}}};
mf16 r;
COMMENT("Test 5x1 transposition");
mf16_transpose(&r, &a);
TEST(r.errors == 0);
TEST(r.rows == 1);
TEST(r.columns == 5);
TEST(r.data[0][0] == a.data[0][0]);
TEST(r.data[0][1] == a.data[1][0]);
TEST(r.data[0][2] == a.data[2][0]);
TEST(r.data[0][3] == a.data[3][0]);
TEST(r.data[0][4] == a.data[4][0]);
COMMENT("Test 1x5 transposition with aliasing");
mf16_transpose(&r, &r);
TEST(max_delta(&r, &a) == 0);
}
{
mf16 a = {3, 3, 0,
{{fix16_from_int(1), fix16_from_int(2), fix16_from_int(3)},
{fix16_from_int(4), fix16_from_int(5), fix16_from_int(6)},
{fix16_from_int(7), fix16_from_int(8), fix16_from_int(10)}}};
mf16 q, r, qtq, qr;
COMMENT("Test 3x3 QR-decomposition");
mf16_qr_decomposition(&q, &r, &a, 1);
printf("q =\n");
print_mf16(stdout, &q);
printf("r =\n");
print_mf16(stdout, &r);
mf16_mul_at(&qtq, &q, &q);
printf("q'q =\n");
print_mf16(stdout, &qtq);
mf16_mul(&qr, &q, &r);
printf("qr =\n");
print_mf16(stdout, &qr);
fix16_t one = fix16_from_int(1);
const mf16 identity = {3, 3, 0,
{{one, 0, 0}, {0, one, 0}, {0, 0, one}}
};
TEST(max_delta(&qtq, &identity) < 5);
TEST(max_delta(&qr, &a) < 5);
COMMENT("Test 3x3 QR-decomposition without reorthogonalization");
mf16_qr_decomposition(&q, &r, &a, 0);
printf("q =\n");
print_mf16(stdout, &q);
printf("r =\n");
print_mf16(stdout, &r);
mf16_mul_at(&qtq, &q, &q);
printf("q'q =\n");
print_mf16(stdout, &qtq);
mf16_mul(&qr, &q, &r);
printf("qr =\n");
print_mf16(stdout, &qr);
TEST(max_delta(&qtq, &identity) < 10);
TEST(max_delta(&qr, &a) < 10);
}
{
mf16 a = {4, 3, 0,
{{fix16_from_int(1), fix16_from_int(2), fix16_from_int(3)},
{fix16_from_int(4), fix16_from_int(5), fix16_from_int(6)},
{fix16_from_int(7), fix16_from_int(8), fix16_from_int(9)},
{fix16_from_int(10), fix16_from_int(11), fix16_from_int(13)},
}};
mf16 q, r, qtq, qr;
q = a;
COMMENT("Test 4x3 QR-decomposition with aliasing q = matrix");
mf16_qr_decomposition(&q, &r, &q, 1);
printf("q =\n");
print_mf16(stdout, &q);
printf("r =\n");
print_mf16(stdout, &r);
mf16_mul_at(&qtq, &q, &q);
printf("q'q =\n");
print_mf16(stdout, &qtq);
mf16_mul(&qr, &q, &r);
printf("qr =\n");
print_mf16(stdout, &qr);
fix16_t one = fix16_from_int(1);
const mf16 identity = {3, 3, 0,
{{one, 0, 0}, {0, one, 0}, {0, 0, one}}
};
TEST(max_delta(&qtq, &identity) < 5);
TEST(max_delta(&qr, &a) < 10);
COMMENT("Test 4x3 QR-decomposition with aliasing r = matrix");
r = a;
mf16_qr_decomposition(&q, &r, &r, 1);
mf16_mul_at(&qtq, &q, &q);
mf16_mul(&qr, &q, &r);
TEST(max_delta(&qtq, &identity) < 5);
TEST(max_delta(&qr, &a) < 10);
}
{
mf16 a = {8, 5, 0,
{{ 10, 0, 0, 0, 982},
{ 0, 6, -1383, 0, 0},
{ 0, 15, 580, 0, 0},
{ 0, 0, 0, 284, -3},
{-56, 0, 0, 0, 284},
{ 64, 0, 0, 0, 0},
{ 0, 64, 0, 0, 0},
{ 0, 0, 64, 0, 0}}
};
mf16 q, r, qr;
COMMENT("Test 8x5 QR-decomposition with small values");
mf16_qr_decomposition(&q, &r, &a, 1);
printf("q =\n");
print_mf16(stdout, &q);
printf("r =\n");
print_mf16(stdout, &r);
TEST(q.errors == 0);
TEST(r.errors == 0);
mf16_mul(&qr, &q, &r);
TEST(max_delta(&qr, &a) < 10);
}
{
mf16 a = {8, 1, 0,
{{fix16_from_int(1)},
{fix16_from_int(2)},
{fix16_from_int(3)},
{fix16_from_int(4)},
{fix16_from_int(5)},
{fix16_from_int(6)},
{fix16_from_int(7)},
{fix16_from_int(8)},
}};
mf16 q, r, qtq, qr;
COMMENT("Test 8x1 QR-decomposition");
mf16_qr_decomposition(&q, &r, &a, 1);
printf("q =\n");
print_mf16(stdout, &q);
printf("r =\n");
print_mf16(stdout, &r);
mf16_mul_at(&qtq, &q, &q);
printf("q'q =\n");
print_mf16(stdout, &qtq);
mf16_mul(&qr, &q, &r);
printf("qr =\n");
print_mf16(stdout, &qr);
const mf16 identity = {1, 1, 0,
{{fix16_from_int(1)}}
};
TEST(max_delta(&qtq, &identity) < 10);
TEST(max_delta(&qr, &a) < 20);
}
{
// Carefully chosen to trigger overflow in subtract_projection.
mf16 a = {3, 3, 0,
{{fix16_from_int(1), fix16_from_int(32767), fix16_from_int(1)},
{fix16_from_int(2), fix16_from_int(-32768), fix16_from_int(0)},
{fix16_from_int(-1), fix16_from_int(32767), fix16_from_int(0)}}};
mf16 q, r, qtq;
COMMENT("Test intermediate result overflow detection in QR decomp.");
mf16_qr_decomposition(&q, &r, &a, 0);
mf16_mul_at(&qtq, &q, &q);
printf("q'q =\n");
print_mf16(stdout, &qtq);
fix16_t one = fix16_from_int(1);
const mf16 identity = {3, 3, 0,
{{one, 0, 0}, {0, one, 0}, {0, 0, one}}
};
TEST(q.errors == FIXMATRIX_OVERFLOW || max_delta(&qtq, &identity) < 50);
}
{
mf16 a = {3, 3, 0,
{{fix16_from_int(535), fix16_from_int(32767), fix16_from_int(1)},
{fix16_from_int(2), fix16_from_int(23), fix16_from_int(400)},
{fix16_from_int(324), fix16_from_int(5), fix16_from_int(0)}}};
mf16 q, r, qtq;
COMMENT("Test large value handling in QR decomp.");
mf16_qr_decomposition(&q, &r, &a, 0);
mf16_mul_at(&qtq, &q, &q);
printf("q =\n");
print_mf16(stdout, &q);
printf("q'q =\n");
print_mf16(stdout, &qtq);
fix16_t one = fix16_from_int(1);
const mf16 identity = {3, 3, 0,
{{one, 0, 0}, {0, one, 0}, {0, 0, one}}
};
TEST(max_delta(&qtq, &identity) < 50);
}
{
mf16 a = {3, 3, 0,
{{fix16_from_int(1), fix16_from_int(2), fix16_from_int(3)},
{fix16_from_int(4), fix16_from_int(5), fix16_from_int(6)},
{fix16_from_int(7), fix16_from_int(8), fix16_from_int(10)}}};
mf16 b = {3, 1, 0,
{{fix16_from_int(-1)}, {fix16_from_int(-2)}, {fix16_from_int(-3)}}};
mf16 q, r, x, ax;
COMMENT("Test 3x3 equation solving");
mf16_qr_decomposition(&q, &r, &a, 1);
mf16_solve(&x, &q, &r, &b);
printf("x = \n");
print_mf16(stdout, &x);
mf16_mul(&ax, &a, &x);
printf("Ax = \n");
print_mf16(stdout, &ax);
TEST(max_delta(&ax, &b) < 10);
}
{
mf16 a = {4, 3, 0,
{{fix16_from_int(31), fix16_from_int(41), fix16_from_int(59)},
{fix16_from_int(26), fix16_from_int(53), fix16_from_int(58)},
{fix16_from_int(97), fix16_from_int(93), fix16_from_int(23)},
{fix16_from_int(84), fix16_from_int(62), fix16_from_int(64)},
}};
mf16 b = {4, 1, 0,
{{fix16_from_int(100)},
{fix16_from_int(100)},
{fix16_from_int(100)},
{fix16_from_int(100)}
}};
mf16 q, r, x;
COMMENT("Test 4x3 least squares solving");
mf16_qr_decomposition(&q, &r, &a, 1);
mf16_solve(&x, &q, &r, &b);
printf("x = \n");
print_mf16(stdout, &x);
// Reference result computed using Octave A\b
mf16 ref = {3, 1, 0,
{{fix16_from_float(-0.31426f)},
{fix16_from_float( 1.16055f)},
{fix16_from_float( 0.90470f)}}};
TEST(max_delta(&x, &ref) < 20);
}
{
mf16 a = {3, 3, 0,
{{fix16_from_int(15), fix16_from_int(-12), fix16_from_int(99)},
{fix16_from_int(42), fix16_from_int(57), fix16_from_int(6)},
{fix16_from_int(72), fix16_from_int(-8), fix16_from_int(10)}}};
mf16 b = {3, 2, 0,
{{fix16_from_int(10), fix16_from_int(-12)},
{fix16_from_int(20), fix16_from_int(15)},
{fix16_from_int(30), fix16_from_int(99)}}};
mf16 q, r, x, ax;
COMMENT("Test 3x3 equation solving with multiple columns");
mf16_qr_decomposition(&q, &r, &a, 1);
mf16_solve(&x, &q, &r, &b);
printf("x = \n");
print_mf16(stdout, &x);
mf16_mul(&ax, &a, &x);
printf("Ax = \n");
print_mf16(stdout, &ax);
// Note: large delta due to large values in matrix.
// This is one of the shortcomings of fixed point format.
TEST(max_delta(&ax, &b) < 100);
}
{
mf16 a = {4, 4, 0,
{{fix16_from_int(7), fix16_from_int(-11), fix16_from_int(80), fix16_from_int(15)},
{fix16_from_int(11), fix16_from_int(-59), fix16_from_int(57), fix16_from_int(72)},
{fix16_from_int(79), fix16_from_int(57), fix16_from_int(-8), fix16_from_int(24)},
{fix16_from_int(-23), fix16_from_int(32), fix16_from_int(0), fix16_from_int(56)},
}};
fix16_t one = fix16_from_int(1);
mf16 identity = {4, 4, 0,
{{one,0,0,0}, {0,one,0,0}, {0,0,one,0}, {0,0,0,one}}};
mf16 q, r, result, inv_a;
COMMENT("Test 4x4 matrix inversion");
mf16_qr_decomposition(&q, &r, &a, 1);
printf("q =\n");
print_mf16(stdout, &q);
printf("r =\n");
print_mf16(stdout, &r);
mf16_solve(&inv_a, &q, &r, &identity);
printf("inv(a) =\n");
print_mf16(stdout, &inv_a);
mf16_mul(&result, &a, &inv_a);
printf("a*inv(a) =\n");
print_mf16(stdout, &result);
TEST(max_delta(&result, &identity) < 100);
mf16_mul(&result, &inv_a, &a);
printf("inv(a)*a =\n");
print_mf16(stdout, &result);
TEST(max_delta(&result, &identity) < 100);
COMMENT("Test 4x4 matrix inversion with aliasing dest = matrix");
inv_a = identity;
mf16_solve(&inv_a, &q, &r, &inv_a);
printf("inv(a) =\n");
print_mf16(stdout, &inv_a);
mf16_mul(&result, &a, &inv_a);
TEST(max_delta(&result, &identity) < 100);
COMMENT("Test 4x4 matrix inversion with aliasing dest = q");
inv_a = q;
mf16_solve(&inv_a, &inv_a, &r, &identity);
printf("inv(a) =\n");
print_mf16(stdout, &inv_a);
mf16_mul(&result, &a, &inv_a);
TEST(max_delta(&result, &identity) < 100);
}
{
mf16 a = {3, 3, 0,
{{fix16_from_int(66), fix16_from_int(78), fix16_from_int(90)},
{fix16_from_int(78), fix16_from_int(93), fix16_from_int(108)},
{fix16_from_int(90), fix16_from_int(108), fix16_from_int(126)}}};
mf16 l, l2, llt;
COMMENT("Test 3x3 Cholesky factorization");
mf16_cholesky(&l, &a);
mf16_mul_bt(&llt, &l, &l);
printf("L =\n");
print_mf16(stdout, &l);
printf("L L' =\n");
print_mf16(stdout, &llt);
TEST(max_delta(&a, &llt) < 10);
COMMENT("Test Cholesky factorization with aliasing");
l2 = a;
mf16_cholesky(&l2, &l2);
TEST(max_delta(&l, &l2) == 0);
}
{
mf16 a = {3, 3, 0,
{{fix16_from_int(2), fix16_from_int(-1), fix16_from_int(0)},
{fix16_from_int(-1), fix16_from_int(2), fix16_from_int(-1)},
{fix16_from_int(0), fix16_from_int(-1), fix16_from_int(2)}}};
mf16 l;
fix16_t one = fix16_from_int(1);
mf16 identity = {3, 3, 0,
{{one,0,0}, {0,one,0}, {0,0,one}}};
COMMENT("Test mf16_invert_lt");
printf("A =\n");
print_mf16(stdout, &a);
mf16_cholesky(&l, &a);
printf("L =\n");
print_mf16(stdout, &l);
mf16_invert_lt(&l, &l);
printf("inv A =\n");
print_mf16(stdout, &l);
mf16_mul(&a, &l, &a);
printf("inv A * A =\n");
print_mf16(stdout, &a);
TEST(max_delta(&a, &identity) < 10);
}
if (status != 0)
fprintf(stdout, "\n\nSome tests FAILED!\n");
return status;
}