Changed the pinv() function so that it doesn't get slow when operating on

matrices with many more columns than rows.

--HG--
extra : convert_revision : svn%3Afdd8eb12-d10e-0410-9acb-85c331704f74/trunk%403029

dlib/matrix/matrix_la.h

@@ -1278,9 +1278,15 @@ convergence:
     template <
         typename EXP
         >
-    inline const matrix<typename EXP::type,EXP::NC,EXP::NR,typename EXP::mem_manager_type> pinv ( 
+    const matrix<typename EXP::type,EXP::NC,EXP::NR,typename EXP::mem_manager_type> pinv_helper ( 
         const matrix_exp<EXP>& m
     )
+    /*!
+        ensures
+            - computes the results of pinv(m) but does so using a method that is fastest
+              when m.nc() <= m.nr().  So if m.nc() > m.nr() then it is best to use
+              trans(pinv_helper(trans(m))) to compute pinv(m).
+    !*/
     { 
         typename matrix_exp<EXP>::matrix_type u;
         typedef typename EXP::mem_manager_type MM1;
@@ -1307,6 +1313,21 @@ convergence:
         return tmp(scale_columns(v,reciprocal(round_zeros(w,eps))))*trans(u);
     }
 
+    template <
+        typename EXP
+        >
+    const matrix<typename EXP::type,EXP::NC,EXP::NR,typename EXP::mem_manager_type> pinv ( 
+        const matrix_exp<EXP>& m
+    )
+    { 
+        // if m has more columns then rows then it is more efficient to
+        // compute the pseudo-inverse of its transpose (given the way I'm doing it below).
+        if (m.nc() > m.nr())
+            return trans(pinv_helper(trans(m)));
+        else
+            return pinv_helper(m);
+    }
+
 // ----------------------------------------------------------------------------------------
 
     template <

dlib/test/matrix.cpp

@@ -121,7 +121,6 @@ namespace
             DLIB_TEST((equal(round_zeros(mi*m,0.000001) , identity_matrix<double,5>())));
         }
 
-
         {
             matrix<double,5,2,MM,column_major_layout> m;
 
@@ -162,6 +161,46 @@ namespace
             DLIB_TEST((equal(round_zeros(mi*m,0.000001) , identity_matrix<double,2>())));
         }
 
+        {
+            matrix<double,5,2,MM,column_major_layout> m;
+
+            for (long r = 0; r < m.nr(); ++r)
+            {
+                for (long c = 0; c < m.nc(); ++c)
+                {
+                    m(r,c) = r*c; 
+                }
+            }
+
+            m = cos(exp(m));
+
+
+            matrix<double> mi = trans(pinv(trans(m) )); 
+            DLIB_TEST(mi.nr() == m.nc());
+            DLIB_TEST(mi.nc() == m.nr());
+            DLIB_TEST((equal(round_zeros(mi*m,0.000001) , identity_matrix<double,2>())));
+        }
+
+        {
+            matrix<double> m(5,2);
+
+            for (long r = 0; r < m.nr(); ++r)
+            {
+                for (long c = 0; c < m.nc(); ++c)
+                {
+                    m(r,c) = r*c; 
+                }
+            }
+
+            m = cos(exp(m));
+
+
+            matrix<double> mi = trans(pinv(trans(m) )); 
+            DLIB_TEST(mi.nr() == m.nc());
+            DLIB_TEST(mi.nc() == m.nr());
+            DLIB_TEST((equal(round_zeros(mi*m,0.000001) , identity_matrix<double,2>())));
+        }
+
         {
             matrix<long> a1(5,1);
             matrix<long,0,0,MM,column_major_layout> a2(1,5);