Added Legendre polynomials (preparation for Bergot basis for pyramids)

Numeric/CMakeLists.txt

@@ -9,6 +9,7 @@ set(SRC
     polynomialBasis.cpp
     JacobianBasis.cpp
     jacobiPolynomials.cpp
+    legendrePolynomials.cpp
   GaussIntegration.cpp
     GaussQuadratureLin.cpp
     GaussQuadratureTri.cpp

Numeric/legendrePolynomials.cpp

+#include "legendrePolynomials.h"
+
+LegendrePolynomials::LegendrePolynomials(int o): n(o) {}
+LegendrePolynomials::~LegendrePolynomials() {;}
+
+void LegendrePolynomials::f(double u, double *val) const {
+  val[0] = 1;
+  
+  for (int i=0;i<n;i++) {
+    
+    double a1i = i+1;
+    double a3i = 2.*i+1;
+    double a4i = i;
+    
+    val[i+1] = a3i * u * val[i];
+    if (i>0) val[i+1] -= a4i * val[i-1];
+    val[i+1] /= a1i;
+  }
+}
+
+void LegendrePolynomials::df(double u, double *val) const {
+  double tmp[n+1];
+  f(u,tmp);
+
+  val[0] = 0;  
+  double g2 = (1.-u*u);
+  
+  for (int i=1;i<=n;i++) {
+    double g1 = - u*i;
+    double g0 = (double) i;
+  
+    val[i] = (g1 * tmp[i] + g0 * tmp[i-1])/g2;
+  }
+}

Numeric/legendrePolynomials.h

+#ifndef LEGENDREPOLYNOMIALS_H
+#define LEGENDREPOLYNOMIALS_H
+
+#include "fullMatrix.h"
+
+class LegendrePolynomials {
+
+ public:
+  LegendrePolynomials(int o);
+  ~LegendrePolynomials();
+
+  void f(double u, double *val) const;
+
+  void df(double u, double *val) const;
+
+ private:
+  int n;
+};
+
+
+#endif