Added a version of poly_min_extrap() that uses a 2nd degree model.

dlib/optimization/optimization_line_search.h

@@ -193,6 +193,24 @@ namespace dlib
         return put_in_range(0,1,x);
     }
 
+// ----------------------------------------------------------------------------------------
+
+    inline double poly_min_extrap (
+        double f0,
+        double d0,
+        double f1
+    )
+    {
+        const double temp = 2*(f1 - f0 - d0);
+        if (std::abs(temp) <= d0*std::numeric_limits<double>::epsilon())
+            return 0.5;
+
+        const double alpha = -d0/temp;
+
+        // now make sure the minimum is within the allowed range of (0,1) 
+        return put_in_range(0,1,alpha);
+    }
+
 // ----------------------------------------------------------------------------------------
 
     inline double lagrange_poly_min_extrap (

dlib/optimization/optimization_line_search_abstract.h

@@ -103,6 +103,22 @@ namespace dlib
             - returns the point in the range [0,1] that minimizes the polynomial c(x) 
     !*/
 
+// ----------------------------------------------------------------------------------------
+
+    inline double poly_min_extrap (
+        double f0,
+        double d0,
+        double f1
+    );
+    /*!
+        ensures
+            - let c(x) be a 2nd degree polynomial such that:
+                - c(0) == f0
+                - c(1) == f1
+                - derivative of c(x) at x==0 is d0
+            - returns the point in the range [0,1] that minimizes the polynomial c(x) 
+    !*/
+
 // ----------------------------------------------------------------------------------------
 
     inline double lagrange_poly_min_extrap (

dlib/test/optimization.cpp

@@ -917,6 +917,21 @@ namespace
     }
 
 
+    void test_poly_min_extract_2nd()
+    {
+        double off;
+
+        off = 0.0; DLIB_TEST(std::abs( poly_min_extrap(off*off, -2*off, (1-off)*(1-off)) - off) < 1e-13); 
+        off = 0.1; DLIB_TEST(std::abs( poly_min_extrap(off*off, -2*off, (1-off)*(1-off)) - off) < 1e-13); 
+        off = 0.2; DLIB_TEST(std::abs( poly_min_extrap(off*off, -2*off, (1-off)*(1-off)) - off) < 1e-13); 
+        off = 0.3; DLIB_TEST(std::abs( poly_min_extrap(off*off, -2*off, (1-off)*(1-off)) - off) < 1e-13); 
+        off = 0.4; DLIB_TEST(std::abs( poly_min_extrap(off*off, -2*off, (1-off)*(1-off)) - off) < 1e-13); 
+        off = 0.5; DLIB_TEST(std::abs( poly_min_extrap(off*off, -2*off, (1-off)*(1-off)) - off) < 1e-13); 
+        off = 0.6; DLIB_TEST(std::abs( poly_min_extrap(off*off, -2*off, (1-off)*(1-off)) - off) < 1e-13); 
+        off = 0.8; DLIB_TEST(std::abs( poly_min_extrap(off*off, -2*off, (1-off)*(1-off)) - off) < 1e-13); 
+        off = 0.9; DLIB_TEST(std::abs( poly_min_extrap(off*off, -2*off, (1-off)*(1-off)) - off) < 1e-13); 
+        off = 1.0; DLIB_TEST(std::abs( poly_min_extrap(off*off, -2*off, (1-off)*(1-off)) - off) < 1e-13); 
+    }
 
     class optimization_tester : public tester
     {
@@ -930,6 +945,7 @@ namespace
         void perform_test (
         )
         {
+            test_poly_min_extract_2nd();
             optimization_test();
         }
     } a;