diff --git a/dlib/svm/krls.h b/dlib/svm/krls.h
index f18db21db..77cf17587 100644
--- a/dlib/svm/krls.h
+++ b/dlib/svm/krls.h
@@ -115,40 +115,24 @@ namespace dlib
 
                     // update K_inv by computing the new one in the temp matrix (equation 3.14)
                     matrix<scalar_type,0,0,mem_manager_type> temp(K_inv.nr()+1, K_inv.nc()+1);
-                    for (long r = 0; r < K_inv.nr(); ++r)
-                    {
-                        for (long c = 0; c < K_inv.nc(); ++c)
-                        {
-                            temp(r,c) = (K_inv + a*trans(a)/delta)(r,c);
-                        }
-                    }
+                    // update the middle part of the matrix
+                    set_subm(temp, get_rect(K_inv)) = K_inv + a*trans(a)/delta;
+                    // update the right column of the matrix
+                    set_subm(temp, 0, K_inv.nr(),K_inv.nr(),1) = -a/delta;
+                    // update the bottom row of the matrix
+                    set_subm(temp, K_inv.nr(), 0, 1, K_inv.nr()) = trans(-a/delta);
+                    // update the bottom right corner of the matrix
                     temp(K_inv.nr(), K_inv.nc()) = 1/delta;
-
-                    // update the new sides of K_inv
-                    for (long i = 0; i < K_inv.nr(); ++i)
-                    {
-                        temp(K_inv.nr(),i) = -a(i)/delta;
-                        temp(i,K_inv.nr()) = -a(i)/delta;
-                    }
                     // put temp into K_inv
                     temp.swap(K_inv);
 
 
                     // Now update the P matrix (equation 3.15)
                     temp.set_size(P.nr()+1, P.nc()+1);
-                    for (long r = 0; r < P.nr(); ++r)
-                    {
-                        for (long c = 0; c < P.nc(); ++c)
-                        {
-                            temp(r,c) = P(r,c);
-                        }
-                    }
+                    set_subm(temp, get_rect(P)) = P;
                     // initialize the new sides of P 
-                    for (long i = 0; i < P.nr(); ++i)
-                    {
-                        temp(P.nr(),i) = 0;
-                        temp(i,P.nc()) = 0;
-                    }
+                    set_rowm(temp,P.nr()) = 0;
+                    set_colm(temp,P.nr()) = 0;
                     temp(P.nr(), P.nc()) = 1;
                     temp.swap(P);