#include <EquationsSolver.h>

Static Public Member Functions
static bool	solveLinearEquation (const Float &a, const Float &b, Float &x1)
static bool	solveLinearEquations2 (const Float &a1, const Float &b1, const Float &c1, const Float &a2, const Float &b2, const Float &c2, Float &x, Float &y)
static bool	solveLinearEquations3 (const Float &a1, const Float &b1, const Float &c1, const Float &d1, const Float &a2, const Float &b2, const Float &c2, const Float &d2, const Float &a3, const Float &b3, const Float &c3, const Float &d3, Float &x, Float &y, Float &z)
static bool	solveLinearEquations (const TMatrix &rAVars, const TVector &rDVars, TVector &rResults)
static Int	solveQuadraticEquationReal (const Float &a, const Float &b, const Float &c, Float &x1, Float &x2)
static bool	findRoot (RealRealFunction pFunction, const Float &fInitialValue, Float &fRoot, Int iMaxIterations=100000)

Detailed Description

TEquationsSolver is a static class encapsulating equations solving capabilities supported by the zeus math package.

Member Function Documentation

bool zeus::TEquationsSolver::findRoot	(	RealRealFunction	pFunction,
		const Float &	fInitialValue,
		Float &	fRoot,
		Int	iMaxIterations = `100000`
	)		`[static]`

Numerically approximate a root (German: Nullstelle) of a function from the real numbers to the real numbers:

y = f(x)

Parameters:

pFunction	[IN] : Pointer to a real real function.
fInitialValue	[IN] : Initial value to start the approximation of the root.
fRoot	[OUT]: Solution for the root.
iMaxIterations	[IN] : The maximum number of iterations for the numerical approximation.

Returns:: The solution for the root was found.

bool zeus::TEquationsSolver::solveLinearEquation	(	const Float &	a,
		const Float &	b,
		Float &	x
	)		`[static]`

Solves a simple equation of type ax+b = 0.

Parameters:

a	[IN] : Equation coefficient a, see above.
b	[IN] : Equation coefficient b, see above.
x	[OUT]: Solution.

Returns:: : Solution exists.

bool zeus::TEquationsSolver::solveLinearEquations	(	const TMatrix &	rAVars,
		const TVector &	rDVars,
		TVector &	rResults
	)		`[static]`

Solves a linear system with n linear equations of the form a11*[x1] + a12*[x2] ... a1n*[xn] + d1 = 0
a21*[x1] + a22*[x2] ... a2n*[xn] + d2 = 0
...
where as a11, a12 ... ann are components of the rAVars matrix, d1 ..dn are components of the rDVars vector. The result is returned as a vector, which must be interpreted like [x1] = v1, [x2] = v2, with v1, v2 ..vn are components of the result vector.

Parameters:

rAVars	: Components of the variables
rDVars	: d-components
rResults	: result vector

Return values:

true	: A solution has been found
false,:	No solution or the dimensions of matrix and vectors are not the same. Make sure the matrix is n x n and the vector has n components. The result will be created by this method and must not be initialized.

bool zeus::TEquationsSolver::solveLinearEquations2	(	const Float &	a1,
		const Float &	b1,
		const Float &	c1,
		const Float &	a2,
		const Float &	b2,
		const Float &	c2,
		Float &	x,
		Float &	y
	)		`[static]`

Solve a system of 2 linear equations of the form

a1*x + b1*y + c1 = 0
a2*x + b2*y + c2 = 0

for x and y.

Parameters:

a1	[IN] : Equation coefficient a1, see above.
b1	[IN] : Equation coefficient b1, see above.
c1	[IN] : Equation coefficient c1, see above.
a2	[IN] : Equation coefficient a2, see above.
b2	[IN] : Equation coefficient b2, see above.
c2	[IN] : Equation coefficient c2, see above.
x1	[OUT]: Solution 1.
x2	[OUT]: Solution 2.

Return values:

true	: A unique solution exists.
false	: No solution exists.

bool zeus::TEquationsSolver::solveLinearEquations3	(	const Float &	a1,
		const Float &	b1,
		const Float &	c1,
		const Float &	d1,
		const Float &	a2,
		const Float &	b2,
		const Float &	c2,
		const Float &	d2,
		const Float &	a3,
		const Float &	b3,
		const Float &	c3,
		const Float &	d3,
		Float &	x,
		Float &	y,
		Float &	z
	)		`[static]`

Solve a system of 3 linear equations of the form

a1*x + b1*y + c1*z + d1 = 0 a2*x + b2*y + c2*z + d2 = 0 a3*x + b3*y + c3*z + d3 = 0
for x, y and z.

Parameters:

a1	[IN] : Equation coefficient a1, see above.
b1	[IN] : Equation coefficient b1, see above.
c1	[IN] : Equation coefficient c1, see above.
d1	[IN] : Equation coefficient d1, see above.
a2	[IN] : Equation coefficient a2, see above.
b2	[IN] : Equation coefficient b2, see above.
c2	[IN] : Equation coefficient c2, see above.
d2	[IN] : Equation coefficient d2, see above.
a3	[IN] : Equation coefficient a3, see above.
b3	[IN] : Equation coefficient b3, see above.
c3	[IN] : Equation coefficient c3, see above.
d3	[IN] : Equation coefficient d3, see above.
x	[OUT]: Solution 1.
y	[OUT]: Solution 2.
z	[OUT]: Solution 3.

Return values:

true	: A unique solution exists.
false	: No solution exists.

Int zeus::TEquationsSolver::solveQuadraticEquationReal	(	const Float &	a,
		const Float &	b,
		const Float &	c,
		Float &	x1,
		Float &	x2
	)		`[static]`

Solve a quadratic equation of the form

a*x^2 + b*x + c = 0
for x over the real numbers.

Parameters:

a	[IN] : Equation coefficient a, see above.
b	[IN] : Equation coefficient b, see above.
c	[IN] : Equation coefficient c, see above.
x1	[OUT]: Solution 1.
x2	[OUT]: Solution 2.

Returns:: : The number of distinct solutions over the real numbers.

The documentation for this class was generated from the following files:

zeus::TEquationsSolver Class Reference

Static Public Member Functions

Detailed Description

Member Function Documentation