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Reference documentation for deal.II version 8.1.0
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#include <polynomial.h>
Public Member Functions | |
Polynomial (const std::vector< number > &coefficients) | |
Polynomial (const unsigned int n) | |
Polynomial (const std::vector< Point< 1 > > &lagrange_support_points, const unsigned int evaluation_point) | |
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) |
bool | operator== (const Polynomial< number > &p) const |
void | print (std::ostream &out) const |
template<class Archive > | |
void | serialize (Archive &ar, const unsigned int version) |
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Subscriptor () | |
Subscriptor (const Subscriptor &) | |
virtual | ~Subscriptor () |
Subscriptor & | operator= (const Subscriptor &) |
void | subscribe (const char *identifier=0) const |
void | unsubscribe (const char *identifier=0) const |
unsigned int | n_subscriptions () const |
void | list_subscribers () const |
DeclException3 (ExcInUse, int, char *, std::string &,<< "Object of class "<< arg2<< " is still used by "<< arg1<< " other objects.\n"<< "(Additional information: "<< arg3<< ")\n"<< "Note the entry in the Frequently Asked Questions of "<< "deal.II (linked to from http://www.dealii.org/) for "<< "more information on what this error means.") | |
DeclException2 (ExcNoSubscriber, char *, char *,<< "No subscriber with identifier \""<< arg2<< "\" did subscribe to this object of class "<< arg1) | |
template<class Archive > | |
void | serialize (Archive &ar, const unsigned int version) |
Protected Member Functions | |
void | transform_into_standard_form () |
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 |
bool | in_lagrange_product_form |
std::vector< number > | lagrange_support_points |
number | lagrange_weight |
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.
Definition at line 54 of file polynomial.h.
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 | ( | const unsigned int | n | ) |
Constructor creating a zero polynomial of degree n
.
Polynomials::Polynomial< number >::Polynomial | ( | const std::vector< Point< 1 > > & | lagrange_support_points, |
const unsigned int | evaluation_point | ||
) |
Constructor for Lagrange polynomial and its point of evaluation. The idea is to construct , where j is the evaluation point specified as argument and the support points contain all points (including x_j, which will internally not be stored).
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inline |
Default constructor creating an illegal object.
Definition at line 666 of file polynomial.h.
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Return the value of this polynomial at the given point.
This function uses the Horner scheme for numerical stability of the evaluation.
Definition at line 695 of file polynomial.h.
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.
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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.
Definition at line 677 of file polynomial.h.
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 | ) |
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.
bool Polynomials::Polynomial< number >::operator== | ( | const Polynomial< number > & | p | ) | const |
Test for equality of two polynomials.
void Polynomials::Polynomial< number >::print | ( | std::ostream & | out | ) | const |
Print coefficients.
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inline |
Write or read the data of this object to or from a stream for the purpose of serialization.
Definition at line 726 of file polynomial.h.
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staticprotected |
This function performs the actual scaling.
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staticprotected |
This function performs the actual shift
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staticprotected |
Multiply polynomial by a factor.
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Transforms polynomial form of product of linear factors into standard form, . Deletes all data structures related to the product form.
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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.
Definition at line 225 of file polynomial.h.
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Stores whether the polynomial is in Lagrange product form, i.e., constructed as a product , or not.
Definition at line 231 of file polynomial.h.
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If the polynomial is in Lagrange product form, i.e., constructed as a product , store the shifts
.
Definition at line 237 of file polynomial.h.
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If the polynomial is in Lagrange product form, i.e., constructed as a product , store the weight c.
Definition at line 243 of file polynomial.h.