Public Member Functions | |
Polynomial (const std::vector< number > &coefficients) | |
Polynomial () | |
number | value (const number x) const |
void | value (const number x, std::vector< number > &values) const |
unsigned int | degree () const |
void | scale (const number factor) |
template<typename number2 > | |
void | shift (const number2 offset) |
Polynomial< number > | derivative () const |
Polynomial< number > | primitive () const |
Polynomial< number > & | operator*= (const double s) |
Polynomial< number > & | operator*= (const Polynomial< number > &p) |
Polynomial< number > & | operator+= (const Polynomial< number > &p) |
Polynomial< number > & | operator-= (const Polynomial< number > &p) |
void | print (std::ostream &out) const |
Static Protected Member Functions | |
static void | scale (std::vector< number > &coefficients, const number factor) |
template<typename number2 > | |
static void | shift (std::vector< number > &coefficients, const number2 shift) |
static void | multiply (std::vector< number > &coefficients, const number factor) |
Protected Attributes | |
std::vector< number > | coefficients |
Base class for all 1D polynomials. A polynomial is represented in this class by its coefficients, which are set through the constructor or by derived classes. Evaluation of a polynomial happens through the Horner scheme which provides both numerical stability and a minimal number of numerical operations.
Polynomials::Polynomial< number >::Polynomial | ( | const std::vector< number > & | coefficients | ) |
Constructor. The coefficients of the polynomial are passed as arguments, and denote the polynomial , i.e. the first element of the array denotes the constant term, the second the linear one, and so on. The degree of the polynomial represented by this object is thus the number of elements in the
coefficient
array minus one.
Polynomials::Polynomial< number >::Polynomial | ( | ) | [inline] |
Default constructor creating an illegal object.
number Polynomials::Polynomial< number >::value | ( | const number | x | ) | const |
Return the value of this polynomial at the given point.
This function uses the Horner scheme for numerical stability of the evaluation.
void Polynomials::Polynomial< number >::value | ( | const number | x, | |
std::vector< number > & | values | |||
) | const |
Return the values and the derivatives of the Polynomial at point x
. values[i], i=0,...,values.size()-1
includes the i
th derivative. The number of derivatives to be computed is thus determined by the size of the array passed.
This function uses the Horner scheme for numerical stability of the evaluation.
unsigned int Polynomials::Polynomial< number >::degree | ( | ) | const [inline] |
Degree of the polynomial. This is the degree reflected by the number of coefficients provided by the constructor. Leading non-zero coefficients are not treated separately.
References Assert, and Polynomials::Polynomial< number >::coefficients.
void Polynomials::Polynomial< number >::scale | ( | const number | factor | ) |
Scale the abscissa of the polynomial. Given the polynomial p(t) and the scaling t = ax, then the result of this operation is the polynomial q, such that q(x) = p(t).
The operation is performed in place.
void Polynomials::Polynomial< number >::shift | ( | const number2 | offset | ) | [inline] |
Shift the abscissa oft the polynomial. Given the polynomial p(t) and the shift t = x + a, then the result of this operation is the polynomial q, such that q(x) = p(t).
The template parameter allows to compute the new coefficients with higher accuracy, since all computations are performed with type number2
. This may be necessary, since this operation involves a big number of additions. On a Sun Sparc Ultra with Solaris 2.8, the difference between double
and long double
was not significant, though.
The operation is performed in place, i.e. the coefficients of the present object are changed.
Polynomial<number> Polynomials::Polynomial< number >::derivative | ( | ) | const |
Compute the derivative of a polynomial.
Polynomial<number> Polynomials::Polynomial< number >::primitive | ( | ) | const |
Compute the primitive of a polynomial. the coefficient of the zero order term of the polynomial is zero.
Polynomial<number>& Polynomials::Polynomial< number >::operator*= | ( | const double | s | ) |
Multiply with a scalar.
Polynomial<number>& Polynomials::Polynomial< number >::operator*= | ( | const Polynomial< number > & | p | ) |
Multiply with another polynomial.
Polynomial<number>& Polynomials::Polynomial< number >::operator+= | ( | const Polynomial< number > & | p | ) |
Add a second polynomial.
Polynomial<number>& Polynomials::Polynomial< number >::operator-= | ( | const Polynomial< number > & | p | ) |
Subtract a second polynomial.
void Polynomials::Polynomial< number >::print | ( | std::ostream & | out | ) | const |
Print coefficients.
static void Polynomials::Polynomial< number >::scale | ( | std::vector< number > & | coefficients, | |
const number | factor | |||
) | [static, protected] |
This function performs the actual scaling.
static void Polynomials::Polynomial< number >::shift | ( | std::vector< number > & | coefficients, | |
const number2 | shift | |||
) | [inline, static, protected] |
This function performs the actual shift
static void Polynomials::Polynomial< number >::multiply | ( | std::vector< number > & | coefficients, | |
const number | factor | |||
) | [static, protected] |
Multiply polynomial by a factor.
std::vector<number> Polynomials::Polynomial< number >::coefficients [protected] |
Coefficients of the polynomial . This vector is filled by the constructor of this class and may be passed down by derived classes.
This vector cannot be constant since we want to allow copying of polynomials.
Referenced by Polynomials::Polynomial< number >::degree().