1 #ifndef MATH_QUADRATURE_H 2 #define MATH_QUADRATURE_H 15 typedef Real (*QuadratureFunction) (RealFunction&, Real, Real);
21 Real
Quadrature(RealFunction& f,
const Real* c,
const Real* x,
int k);
22 void Quadrature(VectorFunction& f,
const Real* c,
const Real* x,
int k,Vector& res);
32 Real
simpsons(RealFunction& f, Real a, Real b);
33 Real
simpsons(Real f0, Real f1, Real f2);
42 Real
NC4(RealFunction& f, Real a, Real b);
43 Real
NC4(Real f0, Real f1, Real f2, Real f3, Real f4);
51 extern const Real cGaussian3[2],xGaussian3[2];
52 extern const Real cGaussian4[2],xGaussian4[2];
53 extern const Real cGaussian5[3],xGaussian5[3];
54 extern const Real cGaussian6[3],xGaussian6[3];
55 extern const Real cGaussian7[4],xGaussian7[4];
56 extern const Real cGaussian8[4],xGaussian8[4];
57 extern const Real cGaussian10[5],xGaussian10[5];
63 extern const Real cGaussian3_x_unit[3],xGaussian3_x_unit[3];
66 extern const Real cGaussian3_x2_unit[3],xGaussian3_x2_unit[3];
69 extern const Real cGaussian3_x1x_unit[3],xGaussian3_x1x_unit[3];
72 Real
Gaussian(RealFunction& f,
int k);
73 Real
Gaussian(RealFunction& f,Real a,Real b,
int k);
85 Real
composite(QuadratureFunction q, RealFunction& f, Real a, Real b,
int n);
88 Real
trapezoidal2D(RealFunction2& f, Real a, Real b, Real c, Real d);
92 Real
simpsons2D(RealFunction2& f, Real a, Real b, Real c, Real d);
96 Real
simpsons2D(RealFunction2& f, Real a, Real b, RealFunction& c, RealFunction& d);
Real simpsons(RealFunction &f, Real a, Real b)
Definition: quadrature.cpp:38
Abstract base classes for function interfaces.
Real compositeTrapezoidal(RealFunction &f, Real a, Real b, int n)
Definition: quadrature.cpp:175
Real composite(QuadratureFunction q, RealFunction &f, Real a, Real b, int n)
composite integration for an arbitrary quadrature function
Definition: quadrature.cpp:209
Real trapezoidal2D(RealFunction2 &f, Real a, Real b, Real c, Real d)
integral[a,b]x[c,d] f dA = 1/4(b-a)(c-d) (f(a,c) + f(b,c) + f(a,d) + f(b,d)) + O(h^2) ...
Definition: quadrature.cpp:218
Real simpsons2D(RealFunction2 &f, Real a, Real b, Real c, Real d)
Definition: quadrature.cpp:224
Real NC4(RealFunction &f, Real a, Real b)
Definition: quadrature.cpp:63
Real Quadrature(RealFunction &f, const Real *c, const Real *x, int k)
General purpose summation routine, returns sum[i=0..k-1]ci*f(xi)
Definition: quadrature.cpp:9
Real trapezoidal(RealFunction &f, Real a, Real b)
Definition: quadrature.cpp:27
const Real cGaussian2[1]
Definition: quadrature.cpp:77
const Real cGaussian2_x_unit[2]
Definition: quadrature.cpp:94
Real simpsons_3_8(RealFunction &f, Real a, Real b)
Definition: quadrature.cpp:50
const Real cGaussian2_x2_unit[2]
f*x^2 on [0,1]
Definition: quadrature.cpp:100
const Real cGaussian2_x1x_unit[2]
f*x(x-1) on [0,1]
Definition: quadrature.cpp:106
Real Gaussian(RealFunction &f, int k)
Gaussian quadrature rule with k points on [-1,1], [a,b] respectively.
Definition: quadrature.cpp:119
Real compositeSimpsons(RealFunction &f, Real a, Real b, int n)
Definition: quadrature.cpp:192
Contains all definitions in the Math package.
Definition: WorkspaceBound.h:12