Public Member Functions | |
template<class Pol > | |
PolynomialSpace (const std::vector< Pol > &pols) | |
template<class STREAM > | |
void | output_indices (STREAM &out) const |
void | set_numbering (const std::vector< unsigned int > &renumber) |
void | compute (const Point< dim > &unit_point, std::vector< double > &values, std::vector< Tensor< 1, dim > > &grads, std::vector< Tensor< 2, dim > > &grad_grads) const |
double | compute_value (const unsigned int i, const Point< dim > &p) const |
Tensor< 1, dim > | compute_grad (const unsigned int i, const Point< dim > &p) const |
Tensor< 2, dim > | compute_grad_grad (const unsigned int i, const Point< dim > &p) const |
unsigned int | n () const |
unsigned int | degree () const |
template<> | |
void | compute_index (const unsigned int n, unsigned int(&index)[1]) const |
template<> | |
void | compute_index (const unsigned int n, unsigned int(&index)[2]) const |
template<> | |
void | compute_index (const unsigned int n, unsigned int(&index)[3]) const |
Static Public Member Functions | |
static unsigned int | compute_n_pols (const unsigned int n) |
Protected Member Functions | |
void | compute_index (const unsigned int n, unsigned int(&index)[dim]) const |
Private Attributes | |
const std::vector < Polynomials::Polynomial < double > > | polynomials |
const unsigned int | n_pols |
std::vector< unsigned int > | index_map |
std::vector< unsigned int > | index_map_inverse |
Representation of the space of polynomials of degree at most n in higher dimensions.
Given a vector of n one-dimensional polynomials P0 to Pn, where Pi has degree i, this class generates all dim-dimensional polynomials of the form Pijk(x,y,z) = Pi(x)Pj(y)Pk(z), where the sum of i, j and k is less than or equal n.
The output_indices() function prints the ordering of the polynomials, i.e. for each dim-dimensional polynomial in the polynomial space it gives the indices i,j,k of the one-dimensional polynomials in x,y and z direction. The ordering of the dim-dimensional polynomials can be changed by using the set_numbering() function.
The standard ordering of polynomials is that indices for the first space dimension vasry fastest and the last space dimension is slowest. In particular, if we take for simplicity the vector of monomials x0, x1, x2,..., xn, we get
PolynomialSpace< dim >::PolynomialSpace | ( | const std::vector< Pol > & | pols | ) | [inline] |
Constructor. pols
is a vector of pointers to one-dimensional polynomials and will be copied into a private member variable. The static type of the template argument pols
needs to be convertible to Polynomials::Polynomial<double>, i.e. should usually be a derived class of Polynomials::Polynomial<double>.
References PolynomialSpace< dim >::index_map, PolynomialSpace< dim >::index_map_inverse, and PolynomialSpace< dim >::n_pols.
void PolynomialSpace< dim >::output_indices | ( | STREAM & | out | ) | const [inline] |
Prints the list of the indices to out
.
References PolynomialSpace< dim >::compute_index(), and PolynomialSpace< dim >::n_pols.
void PolynomialSpace< dim >::set_numbering | ( | const std::vector< unsigned int > & | renumber | ) |
Sets the ordering of the polynomials. Requires renumber.size()==n()
. Stores a copy of renumber
.
void PolynomialSpace< dim >::compute | ( | const Point< dim > & | unit_point, | |
std::vector< double > & | values, | |||
std::vector< Tensor< 1, dim > > & | grads, | |||
std::vector< Tensor< 2, dim > > & | grad_grads | |||
) | const |
Computes the value and the first and second derivatives of each polynomial at unit_point
.
The size of the vectors must either be equal 0 or equal n(). In the first case, the function will not compute these values, i.e. you indicate what you want to have computed by resizing those vectors which you want filled.
If you need values or derivatives of all polynomials then use this function, rather than using any of the compute_value(), compute_grad() or compute_grad_grad() functions, see below, in a loop over all polynomials.
double PolynomialSpace< dim >::compute_value | ( | const unsigned int | i, | |
const Point< dim > & | p | |||
) | const |
Computes the value of the i
th polynomial at unit_point
.
Consider using compute() instead.
Tensor<1,dim> PolynomialSpace< dim >::compute_grad | ( | const unsigned int | i, | |
const Point< dim > & | p | |||
) | const |
Computes the gradient of the i
th polynomial at unit_point
.
Consider using compute() instead.
Tensor<2,dim> PolynomialSpace< dim >::compute_grad_grad | ( | const unsigned int | i, | |
const Point< dim > & | p | |||
) | const |
Computes the second derivative (grad_grad) of the i
th polynomial at unit_point
.
Consider using compute() instead.
unsigned int PolynomialSpace< dim >::n | ( | ) | const [inline] |
Return the number of polynomials spanning the space represented by this class. Here, if N
is the number of one-dimensional polynomials given, then the result of this function is N in 1d, N(N+1)/2 in 2d, and N(N+1)(N+2)/6 in 3d.
References PolynomialSpace< dim >::n_pols.
unsigned int PolynomialSpace< dim >::degree | ( | ) | const [inline] |
Degree of the space. This is by definition the number of polynomials given to the constructor, NOT the maximal degree of a polynomial in this vector. The latter value is never checked and therefore left to the application.
References PolynomialSpace< dim >::polynomials.
static unsigned int PolynomialSpace< dim >::compute_n_pols | ( | const unsigned int | n | ) | [static] |
Static function used in the constructor to compute the number of polynomials.
void PolynomialSpace< dim >::compute_index | ( | const unsigned int | n, | |
unsigned int(&) | index[dim] | |||
) | const [protected] |
Compute numbers in x, y and z direction. Given an index n
in the d-dimensional polynomial space, compute the indices i,j,k such that pn(x,y,z) = pi(x)pj(y)pk(z).
Referenced by PolynomialSpace< dim >::output_indices().
void PolynomialSpace< 1 >::compute_index | ( | const unsigned int | n, | |
unsigned int(&) | index[1] | |||
) | const [inline] |
void PolynomialSpace< 2 >::compute_index | ( | const unsigned int | n, | |
unsigned int(&) | index[2] | |||
) | const [inline] |
void PolynomialSpace< 3 >::compute_index | ( | const unsigned int | n, | |
unsigned int(&) | index[3] | |||
) | const [inline] |
const std::vector<Polynomials::Polynomial<double> > PolynomialSpace< dim >::polynomials [private] |
Copy of the vector pols
of polynomials given to the constructor.
Referenced by PolynomialSpace< dim >::degree().
const unsigned int PolynomialSpace< dim >::n_pols [private] |
Store the precomputed value which the n()
function returns.
Referenced by PolynomialSpace< dim >::n(), PolynomialSpace< dim >::output_indices(), and PolynomialSpace< dim >::PolynomialSpace().
std::vector<unsigned int> PolynomialSpace< dim >::index_map [private] |
Index map for reordering the polynomials.
Referenced by PolynomialSpace< dim >::PolynomialSpace().
std::vector<unsigned int> PolynomialSpace< dim >::index_map_inverse [private] |
Index map for reordering the polynomials.
Referenced by PolynomialSpace< dim >::PolynomialSpace().