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meritFuncsHelpers.hpp
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00005 //    GlobiPack: Collection of Scalar 1D globalizaton utilities
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00043 
00044 
00045 #include "GlobiPack_TestLagrPolyMeritFunc1D.hpp"
00046 #include "Teuchos_Tuple.hpp"
00047 
00048 
00049 namespace {
00050 
00051 
00052 using GlobiPack::TestLagrPolyMeritFunc1D;
00053 using GlobiPack::testLagrPolyMeritFunc1D;
00054 using GlobiPack::PointEval1D;
00055 using Teuchos::RCP;
00056 using Teuchos::Array;
00057 using Teuchos::tuple;
00058 
00059 
00060 template<class Scalar>
00061 inline Scalar sqr(const Scalar &x) { return x*x; }
00062 
00063 
00064 template<class Scalar>
00065 inline Scalar cube(const Scalar &x) { return x*x*x; }
00066 
00067 
00068 //
00069 // Set up a quadratic merit function with minimizer at alpha=2.0, phi=3.0.
00070 //
00071 
00072 template<class Scalar>
00073 const RCP<TestLagrPolyMeritFunc1D<Scalar> > quadPhi()
00074 {
00075   typedef Teuchos::ScalarTraits<Scalar> ST;
00076   typedef typename ST::magnitudeType ScalarMag;
00077   Array<Scalar> alphaPoints = tuple<Scalar>(0.0, 2.0, 4.0);
00078   Array<ScalarMag> phiPoints = tuple<ScalarMag>(6.0, 3.0, 6.0);
00079   return testLagrPolyMeritFunc1D<Scalar>(alphaPoints, phiPoints);
00080 }
00081 
00082 
00083 //
00084 // Set up a cubic merit function with minimizer at alpha=2.0, phi=3.0;
00085 //
00086 // The function being represented approximated is:
00087 //
00088 //   phi(alpha) = (alpha - 2.0)^2 + 1e-3 * (alpha - 2.0)^3 + 3.0
00089 //
00090 // This function has the first and second derivatives derivatives:
00091 //
00092 //   Dphi(alpha) = 2.0 * (alpha - 2.0) + 3e-3 * (alpha - 2.0)^2
00093 //
00094 //   D2phi(alpha) = 2.0 + 6e-3 * (alpha - 2.0)
00095 //
00096 // At alpha=2.0, the function has Dphi=0.0 and D2phi = 2.0 and therefore, this
00097 // is a local minimum.
00098 //
00099 
00100 
00101 const double cubicMut = 1e-3;
00102 
00103 
00104 template<class Scalar>
00105 inline Scalar cubicPhiVal(const Scalar &alpha)
00106 { return sqr(alpha - 2.0) + cubicMut * cube(alpha - 2.0) + 3.0; }
00107 
00108 
00109 template<class Scalar>
00110 const RCP<TestLagrPolyMeritFunc1D<Scalar> > cubicPhi()
00111 {
00112   typedef Teuchos::ScalarTraits<Scalar> ST;
00113   typedef typename ST::magnitudeType ScalarMag;
00114   Array<Scalar> alphaPoints =
00115     tuple<Scalar>(0.0, 1.0, 3.0, 4.0);
00116   Array<ScalarMag> phiPoints =
00117     tuple<ScalarMag>(
00118       cubicPhiVal(alphaPoints[0]),
00119       cubicPhiVal(alphaPoints[1]),
00120       cubicPhiVal(alphaPoints[2]),
00121       cubicPhiVal(alphaPoints[3])
00122       );
00123   return testLagrPolyMeritFunc1D<Scalar>(alphaPoints, phiPoints);
00124 }
00125 
00126 
00127 } // namespace
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