@q $Id: vector_function.hweb 431 2005-08-16 15:41:01Z kamenik $ @>
@q Copyright 2005, Ondra Kamenik @>

@*2 Vector function. This is {\tt vector\_function.h} file

This file defines interface for functions taking a vector as an input
and returning a vector (with a different size) as an output. We are
also introducing a parameter signalling; it is a boolean vector which
tracks parameters which were changed from the previous call. The
|VectorFunction| implementation can exploit this information and
evaluate the function more efficiently. The information can be
completely ignored.

From the signalling reason, and from other reasons, the function
evaluation is not |const|.

@s ParameterSignal int
@s VectorFunction int
@s VectorFunctionSet int
@s GaussConverterFunction int

@c
#ifndef VECTOR_FUNCTION_H
#define VECTOR_FUNCTION_H

#include "Vector.h"
#include "GeneralMatrix.h"

#include <vector>

@<|ParameterSignal| class declaration@>;
@<|VectorFunction| class declaration@>;
@<|VectorFunctionSet| class declaration@>;
@<|GaussConverterFunction| class declaration@>;

#endif

@ This is a simple class representing a vector of booleans. The items
night be retrieved or changed, or can be set |true| after some
point. This is useful when we multiply the vector with lower
triangular matrix.

|true| means that a parameter was changed.

@<|ParameterSignal| class declaration@>=
class ParameterSignal {
protected:@;
	bool* data;
	int num;
public:@;
	ParameterSignal(int n);
	ParameterSignal(const ParameterSignal& sig);
	~ParameterSignal()
		{@+ delete [] data;@+}
	void signalAfter(int l);
	const bool& operator[](int i) const
		{@+ return data[i];@+} 
	bool& operator[](int i)
		{@+ return data[i];@+} 
};

@ This is the abstract class for vector function. At this level of
abstraction we only need to know size of input vector and a size of
output vector.

The important thing here is a clone method, we will need to make hard
copies of vector functions since the evaluations are not |const|. The
hardcopies apply for parallelization.

@<|VectorFunction| class declaration@>=
class VectorFunction {
protected:@;
	int in_dim;
	int out_dim;
public:@;
	VectorFunction(int idim, int odim)
		: in_dim(idim), out_dim(odim)@+ {}
	VectorFunction(const VectorFunction& func)
		: in_dim(func.in_dim), out_dim(func.out_dim)@+ {}
	virtual ~VectorFunction()@+ {}
	virtual VectorFunction* clone() const =0;
	virtual void eval(const Vector& point, const ParameterSignal& sig, Vector& out) =0;
	int indim() const
		{@+ return in_dim;@+}
	int outdim() const
		{@+ return out_dim;@+}
};

@ This makes |n| copies of |VectorFunction|. The first constructor
make exactly |n| new copies, the second constructor copies only the
pointer to the first and others are hard (real) copies.

The class is useful for making a given number of copies at once, and
this set can be reused many times if we need mupliple copis of the
function (for example for paralelizing the code).

@<|VectorFunctionSet| class declaration@>=
class VectorFunctionSet {
protected:@;
	std::vector<VectorFunction*> funcs;
	bool first_shallow;
public:@;
	VectorFunctionSet(const VectorFunction& f, int n);
	VectorFunctionSet(VectorFunction& f, int n);
	~VectorFunctionSet();
	VectorFunction& getFunc(int i)
		{@+ return *(funcs[i]);@+}
	int getNum() const
		{@+ return funcs.size(); @+}
};

@ This class wraps another |VectorFunction| to allow integration of a
function through normally distributed inputs. Namely, if one wants to
integrate
$${1\over\sqrt{(2\pi)^n\vert\Sigma\vert}}\int f(x)e^{-{1\over2}x^T\Sigma^{-1}x}{\rm d}x$$
then if we write $\Sigma=AA^T$ and $x=\sqrt{2}Ay$, we get integral
$${1\over\sqrt{(2\pi)^n\vert\Sigma\vert}}
\int f\left(\sqrt{2}Ay\right)e^{-y^Ty}\sqrt{2^n}\vert A\vert{\rm d}y=
{1\over\sqrt{\pi^n}}\int f\left(\sqrt{2}Ay\right)e^{-y^Ty}{\rm d}y,$$
which means that a given function $f$ we have to wrap to yield a function
$$g(y)={1\over\sqrt{\pi^n}}f\left(\sqrt{2}Ay\right).$$
This is exactly what this class is doing. This transformation is
useful since the Gauss--Hermite points and weights are defined for
weighting function $e^{-y^2}$, so this transformation allows using
Gauss--Hermite quadratures seemlessly in a context of integration through
normally distributed inputs.

The class maintains a pointer to the function $f$. When the object is
constructed by the first constructor, the $f$ is not copied. If the
object of this class is copied, then $f$ is copied and we need to
remember to destroy it in the desctructor; hence |delete_flag|. The
second constructor takes a pointer to the function and differs from
the first only by setting |delete_flag| to |true|.

@<|GaussConverterFunction| class declaration@>=
class GaussConverterFunction : public VectorFunction {
protected:@;
	VectorFunction* func;
	bool delete_flag;
	GeneralMatrix A;
	double multiplier;
public:@;
	GaussConverterFunction(VectorFunction& f, const GeneralMatrix& vcov);
	GaussConverterFunction(VectorFunction* f, const GeneralMatrix& vcov);
	GaussConverterFunction(const GaussConverterFunction& f);
	virtual ~GaussConverterFunction()
		{@+ if (delete_flag) delete func; @+}
	virtual VectorFunction* clone() const
		{@+ return new GaussConverterFunction(*this);@+}
	virtual void eval(const Vector& point, const ParameterSignal& sig, Vector& out);	
private:@;
	double calcMultiplier() const;
	void calcCholeskyFactor(const GeneralMatrix& vcov);
};

@ End of {\tt vector\_function.h} file