17#ifndef dealii_simplex_barycentric_polynomials_h
18#define dealii_simplex_barycentric_polynomials_h
80template <
int dim,
typename Number =
double>
93 const Number coefficient);
108 print(std::ostream &out)
const;
125 template <
typename Number2>
132 template <
typename Number2>
139 template <
typename Number2>
146 template <
typename Number2>
178 derivative(
const unsigned int coordinate)
const;
271 std::vector<double> & values,
333 name()
const override;
338 virtual std::unique_ptr<ScalarPolynomialsBase<dim>>
339 clone()
const override;
354template <
int dim,
typename Number1,
typename Number2>
358 return bp * Number1(a);
364template <
int dim,
typename Number1,
typename Number2>
368 return bp + Number1(a);
374template <
int dim,
typename Number1,
typename Number2>
378 return bp - Number1(a);
384template <
int dim,
typename Number>
395template <
int dim,
typename Number>
399 for (
unsigned int d = 0; d < dim + 1; ++d)
401 coefficients.reinit(extents);
408template <
int dim,
typename Number>
411 const Number coefficient)
414 for (
unsigned int d = 0; d < dim + 1; ++d)
415 extents[d] = powers[d] + 1;
416 coefficients.reinit(extents);
418 coefficients(powers) = coefficient;
423template <
int dim,
typename Number>
435template <
int dim,
typename Number>
439 const auto &coeffs = this->coefficients;
440 auto first = index_to_indices(0, coeffs.size());
441 bool print_plus =
false;
442 if (coeffs(
first) != Number())
444 out << coeffs(
first);
447 for (std::size_t i = 1; i < coeffs.n_elements(); ++i)
449 const auto indices = index_to_indices(i, coeffs.size());
450 if (coeffs(indices) == Number())
454 out << coeffs(indices);
455 for (
unsigned int d = 0; d < dim + 1; ++d)
458 out <<
" * t" << d <<
'^' << indices[d];
469template <
int dim,
typename Number>
473 auto deg = coefficients.size();
474 for (
unsigned int d = 0; d < dim + 1; ++d)
481template <
int dim,
typename Number>
485 return *
this * Number(-1);
490template <
int dim,
typename Number>
491template <
typename Number2>
503template <
int dim,
typename Number>
504template <
typename Number2>
513template <
int dim,
typename Number>
514template <
typename Number2>
524 for (std::size_t i = 0; i < result.
coefficients.n_elements(); ++i)
526 const auto index = index_to_indices(i, result.
coefficients.size());
535template <
int dim,
typename Number>
536template <
typename Number2>
541 return *
this * (Number(1) / Number(a));
546template <
int dim,
typename Number>
552 for (
unsigned int d = 0; d < dim + 1; ++d)
560 for (std::size_t i = 0; i < in.n_elements(); ++i)
562 const auto index = index_to_indices(i, in.size());
567 add_coefficients(this->coefficients);
574template <
int dim,
typename Number>
579 return *
this + (-augend);
584template <
int dim,
typename Number>
590 for (
unsigned int d = 0; d < dim + 1; ++d)
592 deg[d] = multiplicand.
degrees()[d] + degrees()[d];
597 const auto &coef_1 = this->coefficients;
601 for (std::size_t i1 = 0; i1 < coef_1.n_elements(); ++i1)
603 const auto index_1 = index_to_indices(i1, coef_1.size());
604 for (std::size_t i2 = 0; i2 < coef_2.n_elements(); ++i2)
606 const auto index_2 = index_to_indices(i2, coef_2.size());
609 for (
unsigned int d = 0; d < dim + 1; ++d)
610 index_out[d] = index_1[d] + index_2[d];
611 coef_out(index_out) += coef_1(index_1) * coef_2(index_2);
620template <
int dim,
typename Number>
623 const unsigned int coordinate)
const
627 if (degrees()[coordinate] == 0)
630 auto deg = degrees();
631 deg[coordinate] -= 1;
633 std::numeric_limits<Number>::max());
634 const auto & coeffs_in = coefficients;
636 for (std::size_t i = 0; i < coeffs_out.n_elements(); ++i)
638 const auto out_index = index_to_indices(i, coeffs_out.size());
639 auto input_index = out_index;
640 input_index[coordinate] += 1;
642 coeffs_out(out_index) = coeffs_in(input_index) * input_index[coordinate];
650template <
int dim,
typename Number>
653 const unsigned int coordinate)
const
656 return -barycentric_derivative(0) + barycentric_derivative(coordinate + 1);
661template <
int dim,
typename Number>
671 std::array<Number, dim + 1> b_point;
673 for (
unsigned int d = 0; d < dim; ++d)
675 b_point[0] -= point[d];
676 b_point[d + 1] = point[d];
680 for (std::size_t i = 0; i < coefficients.n_elements(); ++i)
682 const auto indices = index_to_indices(i, coefficients.size());
683 const auto coef = coefficients(indices);
684 if (coef == Number())
687 auto temp = Number(1);
688 for (
unsigned int d = 0; d < dim + 1; ++d)
689 temp *=
std::pow(b_point[d], indices[d]);
690 result += coef * temp;
696template <
int dim,
typename Number>
700 return coefficients.memory_consumption();
703template <
int dim,
typename Number>
706 const std::size_t & index,
712 for (
unsigned int n = 0; n < dim + 1; ++n)
714 std::size_t slice_size = 1;
715 for (
unsigned int n2 = n + 1; n2 < dim + 1; ++n2)
716 slice_size *= extent[n2];
717 result[n] = temp / slice_size;
BarycentricPolynomial< dim, Number > operator*(const Number2 &a) const
std::size_t memory_consumption() const
BarycentricPolynomial< dim, Number > operator+(const Number2 &a) const
TableIndices< dim+1 > degrees() const
Table< dim+1, Number > coefficients
BarycentricPolynomial< dim, Number > barycentric_derivative(const unsigned int coordinate) const
Number value(const Point< dim > &point) const
BarycentricPolynomial< dim, Number > operator/(const Number2 &a) const
static TableIndices< dim+1 > index_to_indices(const std::size_t &index, const TableIndices< dim+1 > &extent)
BarycentricPolynomial< dim, Number > operator-() const
void print(std::ostream &out) const
static BarycentricPolynomial< dim, Number > monomial(const unsigned int d)
BarycentricPolynomial< dim, Number > derivative(const unsigned int coordinate) const
std::array< HessianType, dim > ThirdDerivativesType
Tensor< 1, dim > compute_grad(const unsigned int i, const Point< dim > &p) const override
std::array< PolyType, dim > GradType
virtual std::size_t memory_consumption() const override
Tensor< 2, dim > compute_grad_grad(const unsigned int i, const Point< dim > &p) const override
std::array< ThirdDerivativesType, dim > FourthDerivativesType
std::vector< GradType > poly_grads
std::string name() const override
Tensor< 3, dim > compute_3rd_derivative(const unsigned int i, const Point< dim > &p) const override
Tensor< 1, dim > compute_1st_derivative(const unsigned int i, const Point< dim > &p) const override
Tensor< 2, dim > compute_2nd_derivative(const unsigned int i, const Point< dim > &p) const override
static constexpr unsigned int dimension
std::vector< PolyType > polys
void evaluate(const Point< dim > &unit_point, std::vector< double > &values, std::vector< Tensor< 1, dim > > &grads, std::vector< Tensor< 2, dim > > &grad_grads, std::vector< Tensor< 3, dim > > &third_derivatives, std::vector< Tensor< 4, dim > > &fourth_derivatives) const override
double compute_value(const unsigned int i, const Point< dim > &p) const override
const BarycentricPolynomial< dim > & operator[](const std::size_t i) const
std::vector< ThirdDerivativesType > poly_third_derivatives
std::array< GradType, dim > HessianType
virtual std::unique_ptr< ScalarPolynomialsBase< dim > > clone() const override
Tensor< 4, dim > compute_4th_derivative(const unsigned int i, const Point< dim > &p) const override
std::vector< HessianType > poly_hessians
static BarycentricPolynomials< dim > get_fe_p_basis(const unsigned int degree)
std::vector< FourthDerivativesType > poly_fourth_derivatives
virtual unsigned int degree() const
#define DEAL_II_NAMESPACE_OPEN
#define DEAL_II_NAMESPACE_CLOSE
#define Assert(cond, exc)
#define AssertIndexRange(index, range)
static ::ExceptionBase & ExcDivideByZero()
::VectorizedArray< Number, width > max(const ::VectorizedArray< Number, width > &, const ::VectorizedArray< Number, width > &)
::VectorizedArray< Number, width > pow(const ::VectorizedArray< Number, width > &, const Number p)
BarycentricPolynomial< dim, Number1 > operator-(const Number2 &a, const BarycentricPolynomial< dim, Number1 > &bp)
BarycentricPolynomial< dim, Number1 > operator+(const Number2 &a, const BarycentricPolynomial< dim, Number1 > &bp)
std::ostream & operator<<(std::ostream &out, const BarycentricPolynomial< dim, Number > &bp)
BarycentricPolynomial< dim, Number1 > operator*(const Number2 &a, const BarycentricPolynomial< dim, Number1 > &bp)