deal.II version GIT relicensing-2202-g5ed228918a 2024-12-01 17:10:00+00:00
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#include <deal.II/base/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 |
template<typename Number2 > | |
void | value (const Number2 x, const unsigned int n_derivatives, Number2 *values) const |
template<std::size_t n_entries, typename Number2 > | |
void | values_of_array (const std::array< Number2, n_entries > &points, const unsigned int n_derivatives, std::array< Number2, n_entries > *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) |
virtual std::size_t | memory_consumption () const |
EnableObserverPointer functionality | |
Classes derived from EnableObserverPointer provide a facility to subscribe to this object. This is mostly used by the ObserverPointer class. | |
void | subscribe (std::atomic< bool > *const validity, const std::string &identifier="") const |
void | unsubscribe (std::atomic< bool > *const validity, const std::string &identifier="") const |
unsigned int | n_subscriptions () const |
template<typename StreamType > | |
void | list_subscribers (StreamType &stream) const |
void | list_subscribers () const |
Static Public Member Functions | |
static ::ExceptionBase & | ExcInUse (int arg1, std::string arg2, std::string arg3) |
static ::ExceptionBase & | ExcNoSubscriber (std::string arg1, std::string arg2) |
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 |
Private Types | |
using | map_value_type = decltype(counter_map)::value_type |
using | map_iterator = decltype(counter_map)::iterator |
Private Member Functions | |
void | check_no_subscribers () const noexcept |
Private Attributes | |
std::atomic< unsigned int > | counter |
std::map< std::string, unsigned int > | counter_map |
std::vector< std::atomic< bool > * > | validity_pointers |
const std::type_info * | object_info |
Static Private Attributes | |
static std::mutex | mutex |
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.
There are two paths for evaluation of polynomials. One is based on the coefficients which are evaluated through the Horner scheme which is a robust general-purpose scheme. An alternative and more stable evaluation of high-degree polynomials with roots in the unit interval is provided by a product in terms of the roots. This form is available for special polynomials such as Lagrange polynomials or Legendre polynomials and used with the respective constructor. To obtain this more stable evaluation form, the constructor with the roots in form of a Lagrange polynomial must be used. In case a manipulation is done that changes the roots, the representation is switched to the coefficient form.
This class is a typical example of a possible template argument for the TensorProductPolynomials class.
Definition at line 65 of file polynomial.h.
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privateinherited |
The data type used in counter_map.
Definition at line 238 of file enable_observer_pointer.h.
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privateinherited |
The iterator type used in counter_map.
Definition at line 243 of file enable_observer_pointer.h.
Polynomials::Polynomial< number >::Polynomial | ( | const std::vector< number > & | coefficients | ) |
Constructor. The coefficients of the polynomial are passed as arguments, and denote the polynomial \(\sum_i a[i] x^i\), 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.
Definition at line 38 of file polynomial.cc.
Polynomials::Polynomial< number >::Polynomial | ( | const unsigned int | n | ) |
Constructor creating a zero polynomial of degree n
.
Definition at line 47 of file polynomial.cc.
Polynomials::Polynomial< number >::Polynomial | ( | const std::vector< Point< 1 > > & | lagrange_support_points, |
const unsigned int | evaluation_point | ||
) |
Constructor for a Lagrange polynomial and its point of evaluation. The idea is to construct \(\prod_{i\neq j} \frac{x-x_i}{x_j-x_i}\), 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).
Definition at line 56 of file polynomial.cc.
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inline |
Default constructor creating an illegal object.
Definition at line 800 of file polynomial.h.
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inline |
Return the value of this polynomial at the given point.
This function uses the most numerically stable evaluation algorithm for the provided form of the polynomial. If the polynomial is in the product form of roots, the evaluation is based on products of the form (x - x_i), whereas the Horner scheme is used for polynomials in the coefficient form.
Definition at line 826 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 for polynomials in the coefficient form or the product of terms involving the roots if that representation is used.
Definition at line 85 of file polynomial.cc.
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inline |
Return the values and the derivatives of the Polynomial at point x
. values[i], i=0,...,n_derivatives
includes the i
th derivative. The number of derivatives to be computed is determined by n_derivatives
and values
has to provide sufficient space for n_derivatives
+ 1 values.
This function uses the most numerically stable evaluation algorithm for the provided form of the polynomial. If the polynomial is in the product form of roots, the evaluation is based on products of the form (x - x_i), whereas the Horner scheme is used for polynomials in the coefficient form.
The template type Number2
must implement arithmetic operations such as additions or multiplication with the type number
of the polynomial, and must be convertible from number
by operator=
.
Definition at line 856 of file polynomial.h.
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inline |
Similar to the function above, but evaluate the polynomials on several positions at once, as described by the array argument points
. This function is can be faster than the other function when the same polynomial should be evaluated on several positions at once, e.g., the x,y,z coordinates of a point for tensor-product polynomials.
The template type Number2
must implement arithmetic operations such as additions or multiplication with the type number
of the polynomial, and must be convertible from number
by operator=
.
Definition at line 874 of file polynomial.h.
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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 809 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.
Definition at line 150 of file polynomial.cc.
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.
Definition at line 424 of file polynomial.cc.
Polynomial< number > Polynomials::Polynomial< number >::derivative | ( | ) | const |
Compute the derivative of a polynomial.
Definition at line 443 of file polynomial.cc.
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.
Definition at line 472 of file polynomial.cc.
Polynomial< number > & Polynomials::Polynomial< number >::operator*= | ( | const double | s | ) |
Multiply with a scalar.
Definition at line 188 of file polynomial.cc.
Polynomial< number > & Polynomials::Polynomial< number >::operator*= | ( | const Polynomial< number > & | p | ) |
Multiply with another polynomial.
Definition at line 206 of file polynomial.cc.
Polynomial< number > & Polynomials::Polynomial< number >::operator+= | ( | const Polynomial< number > & | p | ) |
Add a second polynomial.
Definition at line 253 of file polynomial.cc.
Polynomial< number > & Polynomials::Polynomial< number >::operator-= | ( | const Polynomial< number > & | p | ) |
Subtract a second polynomial.
Definition at line 295 of file polynomial.cc.
bool Polynomials::Polynomial< number >::operator== | ( | const Polynomial< number > & | p | ) | const |
Test for equality of two polynomials.
Definition at line 331 of file polynomial.cc.
void Polynomials::Polynomial< number >::print | ( | std::ostream & | out | ) | const |
Print coefficients.
Definition at line 499 of file polynomial.cc.
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inline |
Write or read the data of this object to or from a stream for the purpose of serialization using the BOOST serialization library.
Definition at line 1031 of file polynomial.h.
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virtual |
Return an estimate (in bytes) for the memory consumption of this object.
Definition at line 518 of file polynomial.cc.
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staticprotected |
This function performs the actual scaling.
Definition at line 133 of file polynomial.cc.
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staticprotected |
This function performs the actual shift
Definition at line 362 of file polynomial.cc.
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staticprotected |
Multiply polynomial by a factor.
Definition at line 175 of file polynomial.cc.
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protected |
Transform polynomial form of product of linear factors into standard form, \(\sum_i a_i x^i\). Deletes all data structures related to the product form.
Definition at line 96 of file polynomial.cc.
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inherited |
Subscribes a user of the object by storing the pointer validity
. The subscriber may be identified by text supplied as identifier
.
Definition at line 131 of file enable_observer_pointer.cc.
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inherited |
Unsubscribes a user from the object.
identifier
and the validity
pointer must be the same as the one supplied to subscribe(). Definition at line 151 of file enable_observer_pointer.cc.
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inlineinherited |
Return the present number of subscriptions to this object. This allows to use this class for reference counted lifetime determination where the last one to unsubscribe also deletes the object.
Definition at line 322 of file enable_observer_pointer.h.
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inlineinherited |
List the subscribers to the input stream
.
Definition at line 339 of file enable_observer_pointer.h.
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inherited |
List the subscribers to deallog
.
Definition at line 199 of file enable_observer_pointer.cc.
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privatenoexceptinherited |
Check that there are no objects subscribing to this object. If this check passes then it is safe to destroy the current object. It this check fails then this function will either abort or print an error message to deallog (by using the AssertNothrow mechanism), but will not throw an exception.
Definition at line 53 of file enable_observer_pointer.cc.
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protected |
Coefficients of the polynomial \(\sum_i a_i x^i\). 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 305 of file polynomial.h.
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protected |
Stores whether the polynomial is in Lagrange product form, i.e., constructed as a product \((x-x_0) (x-x_1) \ldots (x-x_n)/c\), or not.
Definition at line 311 of file polynomial.h.
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protected |
If the polynomial is in Lagrange product form, i.e., constructed as a product \((x-x_0) (x-x_1) \ldots (x-x_n)/c\), store the shifts \(x_i\).
Definition at line 317 of file polynomial.h.
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protected |
If the polynomial is in Lagrange product form, i.e., constructed as a product \((x-x_0) (x-x_1) \ldots (x-x_n)/c\), store the weight c.
Definition at line 323 of file polynomial.h.
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mutableprivateinherited |
Store the number of objects which subscribed to this object. Initially, this number is zero, and upon destruction it shall be zero again (i.e. all objects which subscribed should have unsubscribed again).
The creator (and owner) of an object is counted in the map below if HE manages to supply identification.
We use the mutable
keyword in order to allow subscription to constant objects also.
This counter may be read from and written to concurrently in multithreaded code: hence we use the std::atomic
class template.
Definition at line 227 of file enable_observer_pointer.h.
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mutableprivateinherited |
In this map, we count subscriptions for each different identification string supplied to subscribe().
Definition at line 233 of file enable_observer_pointer.h.
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mutableprivateinherited |
In this vector, we store pointers to the validity bool in the ObserverPointer objects that subscribe to this class.
Definition at line 249 of file enable_observer_pointer.h.
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mutableprivateinherited |
Pointer to the typeinfo object of this object, from which we can later deduce the class name. Since this information on the derived class is neither available in the destructor, nor in the constructor, we obtain it in between and store it here.
Definition at line 257 of file enable_observer_pointer.h.
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staticprivateinherited |
A mutex used to ensure data consistency when accessing the mutable
members of this class. This lock is used in the subscribe() and unsubscribe() functions, as well as in list_subscribers()
.
Definition at line 280 of file enable_observer_pointer.h.