Added the length and length_squared functions. Also cleaned up

the sigmoid function's code and spec

--HG--
extra : convert_revision : svn%3Afdd8eb12-d10e-0410-9acb-85c331704f74/trunk%402453

dlib/matrix/matrix_math_functions.h

@@ -67,9 +67,7 @@ DLIB_MATRIX_SIMPLE_STD_FUNCTION(atan)
             template <typename M>
             static type apply ( const M& m, long r, long c)
             { 
-                const double e = 2.718281828459045235360287471352; 
-                double temp = std::pow(e,-m(r,c));
-                return static_cast<type>(1.0/(1.0 + temp));
+                return static_cast<type>(1/(1 + std::exp(-m(r,c))));
             }
         };
     };

dlib/matrix/matrix_math_functions_abstract.h

@@ -129,7 +129,7 @@ namespace dlib
                 - R::type == the same type that was in m
                 - R has the same dimensions as m
                 - for all valid r and c:
-                  R(r,c) == 1/(1 + pow(e,-m(r,c))) 
+                  R(r,c) == 1/(1 + exp(-m(r,c))) 
     !*/
 
 // ----------------------------------------------------------------------------------------

dlib/matrix/matrix_utilities.h

@@ -220,6 +220,42 @@ namespace dlib
         return val;
     }
 
+// ----------------------------------------------------------------------------------------
+
+    template <
+        typename EXP
+        >
+    const typename matrix_exp<EXP>::type length (
+        const matrix_exp<EXP>& m
+    )
+    {
+        DLIB_ASSERT(m.nr() == 1 || m.nc() == 1, 
+            "\ttype length(const matrix_exp& m)"
+            << "\n\tm must be a row or column vector"
+            << "\n\tm.nr():     " << m.nr() 
+            << "\n\tm.nc():     " << m.nc() 
+            );
+        return std::sqrt(sum(squared(m)));
+    }
+
+// ----------------------------------------------------------------------------------------
+
+    template <
+        typename EXP
+        >
+    const typename matrix_exp<EXP>::type length_squared (
+        const matrix_exp<EXP>& m
+    )
+    {
+        DLIB_ASSERT(m.nr() == 1 || m.nc() == 1, 
+            "\ttype length_squared(const matrix_exp& m)"
+            << "\n\tm must be a row or column vector"
+            << "\n\tm.nr():     " << m.nr() 
+            << "\n\tm.nc():     " << m.nc() 
+            );
+        return sum(squared(m));
+    }
+
 // ----------------------------------------------------------------------------------------
 // ----------------------------------------------------------------------------------------
 // ----------------------------------------------------------------------------------------

dlib/matrix/matrix_utilities_abstract.h

@@ -595,6 +595,34 @@ namespace dlib
                   the corresponding scalar in v.
     !*/
 
+// ----------------------------------------------------------------------------------------
+
+    const matrix_exp::type length_squared (
+        const matrix_exp& m
+    );
+    /*!
+        requires
+            - m.nr() == 1 || m.nc() == 1
+              (i.e. m must be a vector)
+        ensures
+            - returns sum(squared(m))
+              (i.e. returns the square of the length of the vector m)
+    !*/
+
+// ----------------------------------------------------------------------------------------
+
+    const matrix_exp::type length (
+        const matrix_exp& m
+    );
+    /*!
+        requires
+            - m.nr() == 1 || m.nc() == 1
+              (i.e. m must be a vector)
+        ensures
+            - returns sqrt(sum(squared(m)))
+              (i.e. returns the length of the vector m)
+    !*/
+
 // ----------------------------------------------------------------------------------------
 // ----------------------------------------------------------------------------------------
 //                             Linear algebra functions