Added the real_eigenvalues() function and also cleaned up a few things.

--HG--
extra : convert_revision : svn%3Afdd8eb12-d10e-0410-9acb-85c331704f74/trunk%402853

dlib/matrix/matrix_la.h

@@ -1508,6 +1508,49 @@ convergence:
         }
     };
 
+// ----------------------------------------------------------------------------------------
+
+    template <typename EXP>
+    const matrix<typename EXP::type, EXP::NR, 1, typename EXP::mem_manager_type, typename EXP::layout_type> real_eigenvalues (
+        const matrix_exp<EXP>& m
+    )
+    {
+        DLIB_ASSERT(m.nr() == m.nc(), 
+            "\tconst matrix real_eigenvalues()"
+            << "\n\tYou have given an invalidly sized matrix"
+            << "\n\tm.nr(): " << m.nr()
+            << "\n\tm.nc(): " << m.nc() 
+            );
+
+        if (m.nr() == 2)
+        {
+            typedef typename EXP::type T;
+            const T m00 = m(0,0);
+            const T m01 = m(0,1);
+            const T m10 = m(1,0);
+            const T m11 = m(1,1);
+
+            const T b = -(m00 + m11);
+            const T c = m00*m11 - m01*m10;
+            matrix<T,EXP::NR,1, typename EXP::mem_manager_type, typename EXP::layout_type> v(2);
+
+
+            T disc = b*b - 4*c;
+            if (disc >= 0)
+                disc = std::sqrt(disc);
+            else
+                disc = 0;
+
+            v(0) = (-b + disc)/2;
+            v(1) = (-b - disc)/2;
+            return v;
+        }
+        else
+        {
+            return eigenvalue_decomposition<EXP>(m).get_real_eigenvalues();
+        }
+    }
+
 // ----------------------------------------------------------------------------------------
 
 }

dlib/matrix/matrix_la_abstract.h

@@ -124,6 +124,22 @@ namespace dlib
             - #v.nc() == m.nc()
     !*/
 
+// ----------------------------------------------------------------------------------------
+
+    const matrix real_eigenvalues (
+        const matrix_exp& m
+    );
+    /*!
+        requires
+            - m.nr() == m.nc()
+        ensures
+            - returns a matrix E such that:
+                - E.nr() == m.nr()
+                - E.nc() == 1
+                - E contains the real part of all eigenvalues of the matrix m.
+                  (note that the eigenvalues are not sorted)
+    !*/
+
 // ----------------------------------------------------------------------------------------
 
     const matrix_exp::type det (

dlib/matrix/matrix_utilities_abstract.h

@@ -423,10 +423,7 @@ namespace dlib
     /*!
         ensures
             - returns a temporary matrix object that is a copy of m. 
-              (This is useful because it allows you to easily force a matrix_exp to 
-              fully evaluate before giving it to some other function that queries
-              the elements of the matrix more than once each, such as the matrix
-              multiplication operator.)
+              (This allows you to easily force a matrix_exp to fully evaluate)
     !*/
 
 // ----------------------------------------------------------------------------------------

dlib/test/matrix_la.cpp

@@ -263,6 +263,12 @@ namespace
         DLIB_CASSERT(equal(real(diag(test.get_d())), test.get_real_eigenvalues(), eps), ""); 
         DLIB_CASSERT(equal(imag(diag(test.get_d())), test.get_imag_eigenvalues(), eps), ""); 
 
+        matrix<type> eig1 ( real_eigenvalues(m));
+        matrix<type> eig2 ( test.get_real_eigenvalues());
+        sort(&eig1(0), &eig1(0) + eig1.size());
+        sort(&eig2(0), &eig2(0) + eig2.size());
+        DLIB_CASSERT(max(abs(eig1 - eig2)) < eps, "");
+
         const matrix<type> V = test.get_pseudo_v();
         const matrix<type> D = test.get_pseudo_d();
         const matrix<complex<type> > CV = test.get_v();