Features and fixes

* added the trace function for a SquareMatrix

* added Vector3.hat() and it's counterpart Dcm.vee()
for skewsymskew symmetric matrix operations in relation to the cross product
see https://en.wikipedia.org/wiki/Hat_operator

* Matrix::write_string produced runtime errors when I used it in PX4 posix simulation, i simplified it

* a Matrix3f is a SquareMatrix

* added tests for SquareMatrix.trace, Vector3.hat and Dcm.vee

* added a test for quaternion initialisation from array

* preventing buffer overflows in Matrix.write_string method

test/CMakeLists.txt

@@ -15,6 +15,7 @@ set(tests
 	integration
 	squareMatrix
 	helper
+	hatvee
 	)
 
 add_custom_target(test_build)

test/attitude.cpp

@@ -231,6 +231,12 @@ int main()
     TEST(fabsf(q(2) - q_true(2)) < eps);
     TEST(fabsf(q(3) - q_true(3)) < eps);
 
+    // Quaternion initialisation per array
+    float q_array[] = {0.9833f, -0.0343f, -0.1060f, -0.1436f};
+    Quaternion<float>q_from_array(q_array);
+    for(int i = 0; i < 4; i++)
+        TEST(fabsf(q_from_array(i) - q_array[i]) < eps);
+
 };
 
 /* vim: set et fenc=utf-8 ff=unix sts=0 sw=4 ts=4 : */

test/hatvee.cpp

@@ -0,0 +1,23 @@
+#include <stdio.h>
+#include "test_macros.hpp"
+
+#include <matrix/math.hpp>
+
+using namespace matrix;
+
+template class SquareMatrix<float, 3>;
+
+int main()
+{
+    Euler<float> euler(0.1f, 0.2f, 0.3f);
+    Dcm<float> R(euler);
+    Dcm<float> skew = R - R.T();
+    Vector3<float> w = skew.vee();
+    Vector3<float> w_check(0.1348f, 0.4170f, 0.5647f);
+
+    TEST(isEqual(w, w_check));
+    TEST(isEqual(skew, w.hat()));
+    return 0;
+}
+
+/* vim: set et fenc=utf-8 ff=unix sts=0 sw=4 ts=4 : */

test/squareMatrix.cpp

@@ -17,6 +17,7 @@ int main()
     Vector3<float> diag_check(1, 5, 10);
 
     TEST(isEqual(A.diag(), diag_check));
+    TEST(A.trace() - 16 < 1e-3);
 
     float data_check[9] = {
         1.01158503f,  0.02190432f,  0.03238144f,