PolynomialParam.h

A Polynomial is described by a set of coefficients; its fundamental operation is evaluating itself at some "x". The number of coefficients is the order of the polynomial plus one.

Since the Polynomial is a Function, the derivatives can be obtained as well.

The parameter interface (see FunctionParam class), is used to provide an interface to the Fitting classes.

This class is in general used implicitly by the Polynomial class only.

Example

  Polynomial<Float> pf(3);  // Third order polynomial - coeffs 0 by default
  pf.setCoefficient(1, 1.0);
  pf[2] = 2.0;
  pf.setCoefficient(3, 3.0);  // 3x^3 + 2x^2 + x
  pf(2); // == 34

Template Type Argument Requirements (T)

T should have standard numerical operators. Current implementation only tested for real types (and their AutoDiffs).

Thrown Exceptions

Assertion in debug mode if attempt is made to address incorrect coefficients

To Do

Global functions to make various ``special'' polynomials of various orders will be useful eventually.

Member Description

PolynomialParam()

Constructs a zero'th order polynomial, with a coeficcient of 0.0.

explicit PolynomialParam(uInt order)

Makes a polynomial of the given order, with all coeficcients set to zero.

PolynomialParam(const PolynomialParam<T> &other)
PolynomialParam<T> &operator=(const PolynomialParam<T> &other)

Make this a copy of other (deep copy).

~PolynomialParam()

Destructor

Bool operator==(const PolynomialParam<T> &other) const
Bool operator!=(const PolynomialParam<T> &other) const

Comparisons. Polynomials are equal if they are the same order

uInt order() const

What is the order of the polynomial, i.e. maximum exponent of "x".

T coefficient(uInt which) const

What is the which'th coefficient of the polynomial. For an nth degree polynomial, which varies between zero and n.

const Vector<T> &coefficients() const

Return all the coefficients as a vector.

void setCoefficient(uInt which, const T value)

Set the which'th coefficient to value.

void setCoefficients(const Vector<T> &coefficients)

Set all the coefficients at once, throw away all existing coefficients.