Reference documentation for deal.II version GIT b8135fa6eb 2023-03-25 15:55:02+00:00
IntegratedLegendreSZ Class Reference

#include <deal.II/base/polynomials_integrated_legendre_sz.h>

Inheritance diagram for IntegratedLegendreSZ:
[legend]

## Public Member Functions

IntegratedLegendreSZ (const unsigned int p)

double value (const double x) const

void value (const double x, std::vector< double > &values) const

void value (const Number2 x, const unsigned int n_derivatives, Number2 *values) const

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 double factor)

void shift (const number2 offset)

Polynomial< doublederivative () const

Polynomial< doubleprimitive () const

Polynomial< double > & operator*= (const double s)

Polynomial< double > & operator*= (const Polynomial< double > &p)

Polynomial< double > & operator+= (const Polynomial< double > &p)

Polynomial< double > & operator-= (const Polynomial< double > &p)

bool operator== (const Polynomial< double > &p) const

void print (std::ostream &out) const

void serialize (Archive &ar, const unsigned int version)

virtual std::size_t memory_consumption () const

Subscriptor functionality

Classes derived from Subscriptor provide a facility to subscribe to this object. This is mostly used by the SmartPointer 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 std::vector< Polynomials::Polynomial< double > > generate_complete_basis (const unsigned int degree)

static ::ExceptionBaseExcInUse (int arg1, std::string arg2, std::string arg3)

static ::ExceptionBaseExcNoSubscriber (std::string arg1, std::string arg2)

## Protected Member Functions

void transform_into_standard_form ()

## Static Protected Member Functions

static void scale (std::vector< double > &coefficients, const double factor)

static void shift (std::vector< double > &coefficients, const number2 shift)

static void multiply (std::vector< double > &coefficients, const double factor)

## Protected Attributes

std::vector< doublecoefficients

bool in_lagrange_product_form

std::vector< doublelagrange_support_points

double 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

## Static Private Member Functions

static const std::vector< doubleget_coefficients (const unsigned int k)

## 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

## Detailed Description

Class implementing the integrated Legendre polynomials described in the PhD thesis of Sabine Zaglmayr.

This class was written based upon the existing deal.II Legendre class as a base, but with the coefficients adjusted so that the recursive formula is for the integrated Legendre polynomials described in the PhD thesis of Sabine Zaglmayr. The polynomials can be generated recursively from:

• $$L_{0}(x) = -1$$ (added so that it can be generated recursively from 0)
• $$L_{1}(x) = x$$
• $$L_{2}(x) = \frac{(x^2 - 1)}{2}$$
• $$(n+1)L_{n+1} = (2n-1)L_{n} - (n-2)L_{n-1}$$.

However, it is also possible to generate them directly from the Legendre polynomials:

$$L_{n} = \frac{l_{n} - l_{n-2}}{2n-1)}$$

Definition at line 47 of file polynomials_integrated_legendre_sz.h.

## ◆ map_value_type

 using Subscriptor::map_value_type = decltype(counter_map)::value_type
privateinherited

The data type used in counter_map.

Definition at line 230 of file subscriptor.h.

## ◆ map_iterator

 using Subscriptor::map_iterator = decltype(counter_map)::iterator
privateinherited

The iterator type used in counter_map.

Definition at line 235 of file subscriptor.h.

## ◆ IntegratedLegendreSZ()

 IntegratedLegendreSZ::IntegratedLegendreSZ ( const unsigned int p )

Constructor generating the coefficients of the polynomials at degree p.

Definition at line 21 of file polynomials_integrated_legendre_sz.cc.

## ◆ generate_complete_basis()

 std::vector< Polynomials::Polynomial< double > > IntegratedLegendreSZ::generate_complete_basis ( const unsigned int degree )
static

Return the complete set of Integrated Legendre polynomials up to the given degree.

Definition at line 76 of file polynomials_integrated_legendre_sz.cc.

## ◆ get_coefficients()

 const std::vector< double > IntegratedLegendreSZ::get_coefficients ( const unsigned int k )
staticprivate

Main function to compute the co-efficients of the polynomial at degree p.

Definition at line 28 of file polynomials_integrated_legendre_sz.cc.

## ◆ value() [1/3]

 double Polynomials::Polynomial< double >::value ( const double x ) const
inlineinherited

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 108 of file polynomial.h.

## ◆ value() [2/3]

 void Polynomials::Polynomial< double >::value ( const double x, std::vector< double > & values ) const
inherited

Return the values and the derivatives of the Polynomial at point x. values[i], i=0,...,values.size()-1 includes the ith 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 121 of file polynomial.cc.

## ◆ value() [3/3]

 void Polynomials::Polynomial< double >::value ( const Number2 x, const unsigned int n_derivatives, Number2 * values ) const
inlineinherited

Return the values and the derivatives of the Polynomial at point x. values[i], i=0,...,n_derivatives includes the ith 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 143 of file polynomial.h.

## ◆ values_of_array()

 void Polynomials::Polynomial< double >::values_of_array ( const std::array< Number2, n_entries > & points, const unsigned int n_derivatives, std::array< Number2, n_entries > * values ) const
inlineinherited

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 161 of file polynomial.h.

## ◆ degree()

 unsigned int Polynomials::Polynomial< double >::degree
inlineinherited

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 171 of file polynomial.h.

## ◆ scale() [1/2]

 void Polynomials::Polynomial< double >::scale ( const double factor )
inherited

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 181 of file polynomial.cc.

## ◆ scale() [2/2]

 void Polynomials::Polynomial< double >::scale ( std::vector< double > & coefficients, const double factor )
staticprotectedinherited

This function performs the actual scaling.

Definition at line 271 of file polynomial.cc.

## ◆ shift() [1/2]

 void Polynomials::Polynomial< double >::shift ( const number2 offset )
inherited

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 200 of file polynomial.cc.

## ◆ shift() [2/2]

 void Polynomials::Polynomial< double >::shift ( std::vector< double > & coefficients, const number2 shift )
staticprotectedinherited

This function performs the actual shift

Definition at line 278 of file polynomial.cc.

## ◆ derivative()

 Polynomial< double > Polynomials::Polynomial< double >::derivative
inherited

Compute the derivative of a polynomial.

Definition at line 206 of file polynomial.cc.

## ◆ primitive()

 Polynomial< double > Polynomials::Polynomial< double >::primitive
inherited

Compute the primitive of a polynomial. the coefficient of the zero order term of the polynomial is zero.

Definition at line 213 of file polynomial.cc.

## ◆ operator*=() [1/2]

 Polynomial< double > & Polynomials::Polynomial< double >::operator*= ( const double s )
inherited

Multiply with a scalar.

Definition at line 219 of file polynomial.cc.

## ◆ operator*=() [2/2]

 Polynomial< double > & Polynomials::Polynomial< double >::operator*= ( const Polynomial< double > & p )
inherited

Multiply with another polynomial.

Definition at line 225 of file polynomial.cc.

## ◆ operator+=()

 Polynomial< double > & Polynomials::Polynomial< double >::operator+= ( const Polynomial< double > & p )
inherited

Definition at line 231 of file polynomial.cc.

## ◆ operator-=()

 Polynomial< double > & Polynomials::Polynomial< double >::operator-= ( const Polynomial< double > & p )
inherited

Subtract a second polynomial.

Definition at line 237 of file polynomial.cc.

## ◆ operator==()

 bool Polynomials::Polynomial< double >::operator== ( const Polynomial< double > & p ) const
inherited

Test for equality of two polynomials.

Definition at line 243 of file polynomial.cc.

## ◆ print()

 void Polynomials::Polynomial< double >::print ( std::ostream & out ) const
inherited

Print coefficients.

Definition at line 249 of file polynomial.cc.

## ◆ serialize()

 void Polynomials::Polynomial< double >::serialize ( Archive & ar, const unsigned int version )
inlineinherited

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 258 of file polynomial.h.

## ◆ memory_consumption()

 std::size_t Polynomials::Polynomial< double >::memory_consumption
virtualinherited

Return an estimate (in bytes) for the memory consumption of this object.

Definition at line 264 of file polynomial.cc.

## ◆ multiply()

 void Polynomials::Polynomial< double >::multiply ( std::vector< double > & coefficients, const double factor )
staticprotectedinherited

Multiply polynomial by a factor.

Definition at line 284 of file polynomial.cc.

## ◆ transform_into_standard_form()

 void Polynomials::Polynomial< double >::transform_into_standard_form
protectedinherited

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 292 of file polynomial.cc.

## ◆ subscribe()

 void Subscriptor::subscribe ( std::atomic< bool > *const validity, const std::string & identifier = "" ) const
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 136 of file subscriptor.cc.

## ◆ unsubscribe()

 void Subscriptor::unsubscribe ( std::atomic< bool > *const validity, const std::string & identifier = "" ) const
inherited

Unsubscribes a user from the object.

Note
The identifier and the validity pointer must be the same as the one supplied to subscribe().

Definition at line 156 of file subscriptor.cc.

## ◆ n_subscriptions()

 unsigned int Subscriptor::n_subscriptions ( ) const
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 300 of file subscriptor.h.

## ◆ list_subscribers() [1/2]

template<typename StreamType >
 void Subscriptor::list_subscribers ( StreamType & stream ) const
inlineinherited

List the subscribers to the input stream.

Definition at line 317 of file subscriptor.h.

## ◆ list_subscribers() [2/2]

 void Subscriptor::list_subscribers ( ) const
inherited

List the subscribers to deallog.

Definition at line 204 of file subscriptor.cc.

## ◆ check_no_subscribers()

 void Subscriptor::check_no_subscribers ( ) const
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.

Note
Since this function is just a consistency check it does nothing in release mode.
If this function is called when there is an uncaught exception then, rather than aborting, this function prints an error message to the standard error stream and returns.

Definition at line 53 of file subscriptor.cc.

## ◆ coefficients

 std::vector Polynomials::Polynomial< double >::coefficients
protectedinherited

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 302 of file polynomial.h.

## ◆ in_lagrange_product_form

 bool Polynomials::Polynomial< double >::in_lagrange_product_form
protectedinherited

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 308 of file polynomial.h.

## ◆ lagrange_support_points

 std::vector Polynomials::Polynomial< double >::lagrange_support_points
protectedinherited

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 314 of file polynomial.h.

## ◆ lagrange_weight

 double Polynomials::Polynomial< double >::lagrange_weight
protectedinherited

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 320 of file polynomial.h.

## ◆ counter

 std::atomic Subscriptor::counter
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 219 of file subscriptor.h.

## ◆ counter_map

 std::map Subscriptor::counter_map
mutableprivateinherited

In this map, we count subscriptions for each different identification string supplied to subscribe().

Definition at line 225 of file subscriptor.h.

## ◆ validity_pointers

 std::vector *> Subscriptor::validity_pointers
mutableprivateinherited

In this vector, we store pointers to the validity bool in the SmartPointer objects that subscribe to this class.

Definition at line 241 of file subscriptor.h.

## ◆ object_info

 const std::type_info* Subscriptor::object_info
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 249 of file subscriptor.h.

## ◆ mutex

 std::mutex Subscriptor::mutex
staticprivateinherited

A mutex used to ensure data consistency when printing out the list of subscribers.

Definition at line 271 of file subscriptor.h.

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