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Drake
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Represents symbolic polynomials.
A symbolic polynomial keeps a mapping from a monomial of indeterminates to its coefficient in a symbolic expression.
A polynomial p has to satisfy an invariant such that p.decision_variables() ∩ p.indeterminates() = ∅. We have CheckInvariant() method to check the invariant.
Note that arithmetic operations (+,-,*) between a Polynomial and a Variable are not provided. The problem is that Variable class has no intrinsic information if a variable is a decision variable or an indeterminate while we need this information to perform arithmetic operations over Polynomials.
#include <drake/common/symbolic_polynomial.h>
Public Types | |
| using | MapType = std::map< Monomial, Expression, internal::CompareMonomial > |
Public Member Functions | |
| Polynomial ()=default | |
| Constructs a zero polynomial. More... | |
| Polynomial (std::nullptr_t) | |
| Constructs a default value. More... | |
| Polynomial (MapType init) | |
| Constructs a polynomial from a map, Monomial → Expression. More... | |
| Polynomial (const Monomial &m) | |
Constructs a polynomial from a monomial m. More... | |
| Polynomial (const Expression &e) | |
Constructs a polynomial from an expression e. More... | |
| Polynomial (const Expression &e, const Variables &indeterminates) | |
Constructs a polynomial from an expression e by decomposing it with respect to indeterminates. More... | |
| Variables | indeterminates () const |
| Returns the indeterminates of this polynomial. More... | |
| Variables | decision_variables () const |
| Returns the decision variables of this polynomial. More... | |
| int | Degree (const Variable &v) const |
Returns the highest degree of this polynomial in a variable v. More... | |
| int | TotalDegree () const |
| Returns the total degree of this polynomial. More... | |
| const MapType & | monomial_to_coefficient_map () const |
| Returns the mapping from a Monomial to its corresponding coefficient of this polynomial. More... | |
| Expression | ToExpression () const |
| Returns an equivalent symbolic expression of this polynomial. More... | |
| Polynomial | Differentiate (const Variable &x) const |
Differentiates this polynomial with respect to the variable x. More... | |
| template<typename Derived > | |
| Eigen::Matrix< Polynomial, 1, Derived::RowsAtCompileTime > | Jacobian (const Eigen::MatrixBase< Derived > &vars) const |
Computes the Jacobian matrix J of the polynomial with respect to vars. More... | |
| double | Evaluate (const Environment &env) const |
Evaluates this polynomial under a given environment env. More... | |
| Polynomial | EvaluatePartial (const Environment &env) const |
Partially evaluates this polynomial using an environment env. More... | |
| Polynomial | EvaluatePartial (const Variable &var, double c) const |
Partially evaluates this polynomial by substituting var with c. More... | |
| Polynomial & | AddProduct (const Expression &coeff, const Monomial &m) |
Adds coeff * m to this polynomial. More... | |
| Polynomial | RemoveTermsWithSmallCoefficients (double coefficient_tol) const |
Removes the terms whose absolute value of the coefficients are smaller than or equal to coefficient_tol For example, if the polynomial is 2x² + 3xy + 10⁻⁴x - 10⁻⁵, then after calling RemoveTermsWithSmallCoefficients(1e-3), the returned polynomial becomes 2x² + 3xy. More... | |
| Polynomial & | operator+= (const Polynomial &p) |
| Polynomial & | operator+= (const Monomial &m) |
| Polynomial & | operator+= (double c) |
| Polynomial & | operator-= (const Polynomial &p) |
| Polynomial & | operator-= (const Monomial &m) |
| Polynomial & | operator-= (double c) |
| Polynomial & | operator *= (const Polynomial &p) |
| Polynomial & | operator *= (const Monomial &m) |
| Polynomial & | operator *= (double c) |
| bool | EqualTo (const Polynomial &p) const |
Returns true if this polynomial and p are structurally equal. More... | |
| bool | EqualToAfterExpansion (const Polynomial &p) const |
Returns true if this polynomial and p are equal, after expanding the coefficients. More... | |
| Formula | operator== (const Polynomial &p) const |
Returns a symbolic formula representing the condition where this polynomial and p are the same. More... | |
| Formula | operator!= (const Polynomial &p) const |
Returns a symbolic formula representing the condition where this polynomial and p are not the same. More... | |
Implements CopyConstructible, CopyAssignable, MoveConstructible, MoveAssignable | |
| Polynomial (const Polynomial &)=default | |
| Polynomial & | operator= (const Polynomial &)=default |
| Polynomial (Polynomial &&)=default | |
| Polynomial & | operator= (Polynomial &&)=default |
Friends | |
| template<class HashAlgorithm > | |
| void | hash_append (HashAlgorithm &hasher, const Polynomial &item) noexcept |
| Implements the hash_append generic hashing concept. More... | |
| using MapType = std::map<Monomial, Expression, internal::CompareMonomial> |
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default |
Constructs a zero polynomial.
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default |
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explicit |
Constructs a default value.
This overload is used by Eigen when EIGEN_INITIALIZE_MATRICES_BY_ZERO is enabled.
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explicit |
Constructs a polynomial from a map, Monomial → Expression.
| Polynomial | ( | const Monomial & | m | ) |
Constructs a polynomial from a monomial m.
Note that all variables in m are considered as indeterminates.
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explicit |
Constructs a polynomial from an expression e.
Note that all variables in e are considered as indeterminates.
| std::runtime_error | if e is not a polynomial. |
| Polynomial | ( | const Expression & | e, |
| const Variables & | indeterminates | ||
| ) |
Constructs a polynomial from an expression e by decomposing it with respect to indeterminates.
e and the provided indeterminates.| std::runtime_error | if e is not a polynomial in indeterminates. |
| Polynomial & AddProduct | ( | const Expression & | coeff, |
| const Monomial & | m | ||
| ) |
Adds coeff * m to this polynomial.
| Variables decision_variables | ( | ) | const |
Returns the decision variables of this polynomial.
Returns the highest degree of this polynomial in a variable v.
| Polynomial Differentiate | ( | const Variable & | x | ) | const |
Differentiates this polynomial with respect to the variable x.
Note that a variable x can be either a decision variable or an indeterminate.
| bool EqualTo | ( | const Polynomial & | p | ) | const |
Returns true if this polynomial and p are structurally equal.
| bool EqualToAfterExpansion | ( | const Polynomial & | p | ) | const |
Returns true if this polynomial and p are equal, after expanding the coefficients.
| double Evaluate | ( | const Environment & | env | ) | const |
Evaluates this polynomial under a given environment env.
| std::out_of_range | if there is a variable in this polynomial whose assignment is not provided by env. |
| Polynomial EvaluatePartial | ( | const Environment & | env | ) | const |
Partially evaluates this polynomial using an environment env.
| std::runtime_error | if NaN is detected during evaluation. |
| Polynomial EvaluatePartial | ( | const Variable & | var, |
| double | c | ||
| ) | const |
Partially evaluates this polynomial by substituting var with c.
| std::runtime_error | if NaN is detected at any point during evaluation. |
| Variables indeterminates | ( | ) | const |
Returns the indeterminates of this polynomial.
| Eigen::Matrix<Polynomial, 1, Derived::RowsAtCompileTime> Jacobian | ( | const Eigen::MatrixBase< Derived > & | vars | ) | const |
Computes the Jacobian matrix J of the polynomial with respect to vars.
J(0,i) contains ∂f/∂vars(i).
| const Polynomial::MapType & monomial_to_coefficient_map | ( | ) | const |
Returns the mapping from a Monomial to its corresponding coefficient of this polynomial.
| Polynomial & operator *= | ( | const Polynomial & | p | ) |
| Polynomial & operator *= | ( | const Monomial & | m | ) |
| Polynomial & operator *= | ( | double | c | ) |
| Formula operator!= | ( | const Polynomial & | p | ) | const |
Returns a symbolic formula representing the condition where this polynomial and p are not the same.
| Polynomial & operator+= | ( | const Polynomial & | p | ) |
| Polynomial & operator+= | ( | const Monomial & | m | ) |
| Polynomial & operator+= | ( | double | c | ) |
| Polynomial & operator-= | ( | const Polynomial & | p | ) |
| Polynomial & operator-= | ( | const Monomial & | m | ) |
| Polynomial & operator-= | ( | double | c | ) |
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| Formula operator== | ( | const Polynomial & | p | ) | const |
Returns a symbolic formula representing the condition where this polynomial and p are the same.
| Polynomial RemoveTermsWithSmallCoefficients | ( | double | coefficient_tol | ) | const |
Removes the terms whose absolute value of the coefficients are smaller than or equal to coefficient_tol For example, if the polynomial is 2x² + 3xy + 10⁻⁴x - 10⁻⁵, then after calling RemoveTermsWithSmallCoefficients(1e-3), the returned polynomial becomes 2x² + 3xy.
| coefficient_tol | A positive scalar. |
| polynomial_cleaned | A polynomial whose terms with small coefficients are removed. |
| Expression ToExpression | ( | ) | const |
Returns an equivalent symbolic expression of this polynomial.
| int TotalDegree | ( | ) | const |
Returns the total degree of this polynomial.
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friend |
Implements the hash_append generic hashing concept.