Inheritance diagram for BasisPolynomial:
Public Member Functions | |
| BasisPolynomial () | |
| default constructor | |
| BasisPolynomial (short poly_type) | |
| alternate constructor | |
| BasisPolynomial (const BasisPolynomial &polynomial) | |
| copy constructor | |
| virtual | ~BasisPolynomial () |
| destructor | |
| BasisPolynomial | operator= (const BasisPolynomial &polynomial) |
| assignment operator | |
| virtual const Real & | get_value (const Real &x, unsigned short n) |
| retrieve the basis polynomial value for a given parameter value | |
| virtual const Real & | get_gradient (const Real &x, unsigned short n) |
| retrieve the basis polynomial gradient for a given parameter value | |
| virtual const Real & | norm_squared (unsigned short n) |
| inner product <Poly_n, Poly_n> = ||Poly_n||^2 | |
| virtual const RealVector & | gauss_points (unsigned short n) |
| return the gaussPoints corresponding to orthogonal polynomial order n. | |
| virtual const RealVector & | gauss_weights (unsigned short n) |
| return the gaussWeights corresponding to orthogonal polynomial order n. | |
| virtual void | reset_gauss () |
| destroy history of Gauss pts/wts (due to change in alpha/beta stats) | |
| virtual void | alpha_stat (const Real &alpha) |
| set {Jacobi,GenLaguerre}OrthogPolynomial::alphaPoly from alpha_stat | |
| virtual void | beta_stat (const Real &beta) |
| set JacobiOrthogPolynomial::betaPoly from beta_stat | |
| virtual void | interpolation_points (const RealVector &interpolation_pts) |
| set LagrangeInterpPolynomial::interpolationPts | |
| BasisPolynomial * | polynomial_rep () const |
| that are not mapped to the top BasisPolynomial level | |
Static Public Member Functions | |
| static Real | factorial (unsigned short n) |
| compute n! | |
| static Real | factorial_ratio (unsigned short num, unsigned short den) |
| compute num!/den! | |
| static Real | n_choose_k (unsigned short n, unsigned short k) |
| compute n!/(k!(n-k)!) | |
| static Real | pochhammer (const Real &m, unsigned short n) |
| compute the Pochhammer symbol (m)_n = m*(m+1)...*(m+n-1) | |
Protected Member Functions | |
| BasisPolynomial (BaseConstructor) | |
| derived class constructors - Coplien, p. 139) | |
Protected Attributes | |
| Real | basisPolyValue |
| value of the 1-D basis polynomial; returned by get_value() | |
| Real | basisPolyGradient |
| one parameter; returned by get_gradient() | |
Private Member Functions | |
| BasisPolynomial * | get_polynomial (short poly_type) |
| appropriate derived type. | |
Private Attributes | |
| BasisPolynomial * | polyRep |
| pointer to the letter (initialized only for the envelope) | |
| int | referenceCount |
| number of objects sharing polyRep | |
The BasisPolynomial class is the base class for the univariate basis polynomial class hierarchy in DAKOTA. One instance of an BasisPolynomial is created for each variable within a multidimensional polynomial basis function (a vector of BasisPolynomials is contained in BasisPolyApproximation, which may be mixed and matched in, e.g., the Wiener-Askey scheme for polynomial chaos). For memory efficiency and enhanced polymorphism, the basis polynomial hierarchy employs the "letter/envelope idiom" (see Coplien "Advanced C++", p. 133), for which the base class (BasisPolynomial) serves as the envelope and one of the derived classes (selected in BasisPolynomial::get_polynomial()) serves as the letter.
| BasisPolynomial | ( | ) |
default constructor
The default constructor is used in Array<BasisPolynomial> instantiations and by the alternate envelope constructor. polyRep is NULL in this case (problem_db is needed to build a meaningful instance). This makes it necessary to check for NULL in the copy constructor, assignment operator, and destructor.
| BasisPolynomial | ( | short | poly_type | ) |
alternate constructor
Envelope constructor which does not require access to problem_db. This constructor executes get_polynomial(type), which invokes the default constructor of the derived letter class, which in turn invokes the BaseConstructor of the base class.
| BasisPolynomial | ( | const BasisPolynomial & | polynomial | ) |
copy constructor
Copy constructor manages sharing of polyRep and incrementing of referenceCount.
| ~BasisPolynomial | ( | ) | [virtual] |
destructor
Destructor decrements referenceCount and only deletes polyRep when referenceCount reaches zero.
| BasisPolynomial | ( | BaseConstructor | ) | [protected] |
derived class constructors - Coplien, p. 139)
This constructor is the one which must build the base class data for all derived classes. get_polynomial() instantiates a derived class letter and the derived constructor selects this base class constructor in its initialization list (to avoid recursion in the base class constructor calling get_polynomial() again). Since the letter IS the representation, its rep pointer is set to NULL (an uninitialized pointer causes problems in ~BasisPolynomial).
| BasisPolynomial operator= | ( | const BasisPolynomial & | polynomial | ) |
assignment operator
Assignment operator decrements referenceCount for old polyRep, assigns new polyRep, and increments referenceCount for new polyRep.
| const Real & get_value | ( | const Real & | x, | |
| unsigned short | n | |||
| ) | [virtual] |
retrieve the basis polynomial value for a given parameter value
For orthogonal polynomials, n specifies the order of the polynomial, whereas for interpolation polynomials, it identifies the interpolant for the n-th point.
Reimplemented in GenLaguerreOrthogPolynomial, HermiteOrthogPolynomial, JacobiOrthogPolynomial, LagrangeInterpPolynomial, LaguerreOrthogPolynomial, and LegendreOrthogPolynomial.
| const Real & get_gradient | ( | const Real & | x, | |
| unsigned short | n | |||
| ) | [virtual] |
retrieve the basis polynomial gradient for a given parameter value
For orthogonal polynomials, n specifies the order of the polynomial, whereas for interpolation polynomials, it identifies the interpolant for the n-th point.
Reimplemented in GenLaguerreOrthogPolynomial, HermiteOrthogPolynomial, JacobiOrthogPolynomial, LagrangeInterpPolynomial, LaguerreOrthogPolynomial, and LegendreOrthogPolynomial.
| const Real & norm_squared | ( | unsigned short | n | ) | [virtual] |
inner product <Poly_n, Poly_n> = ||Poly_n||^2
This is defined only for orthogonal polynomials.
Reimplemented in GenLaguerreOrthogPolynomial, HermiteOrthogPolynomial, JacobiOrthogPolynomial, LaguerreOrthogPolynomial, and LegendreOrthogPolynomial.
| const RealVector & gauss_points | ( | unsigned short | n | ) | [virtual] |
return the gaussPoints corresponding to orthogonal polynomial order n.
This is defined only for orthogonal polynomials.
Reimplemented in GenLaguerreOrthogPolynomial, HermiteOrthogPolynomial, JacobiOrthogPolynomial, LaguerreOrthogPolynomial, and LegendreOrthogPolynomial.
| const RealVector & gauss_weights | ( | unsigned short | n | ) | [virtual] |
return the gaussWeights corresponding to orthogonal polynomial order n.
This is defined only for orthogonal polynomials.
Reimplemented in GenLaguerreOrthogPolynomial, HermiteOrthogPolynomial, JacobiOrthogPolynomial, LaguerreOrthogPolynomial, and LegendreOrthogPolynomial.
| void reset_gauss | ( | ) | [virtual] |
destroy history of Gauss pts/wts (due to change in alpha/beta stats)
This is defined only for orthogonal polynomials.
Reimplemented in OrthogonalPolynomial.
| void alpha_stat | ( | const Real & | alpha | ) | [virtual] |
set {Jacobi,GenLaguerre}OrthogPolynomial::alphaPoly from alpha_stat
This is defined only for parameterized orthogonal polynomials.
Reimplemented in GenLaguerreOrthogPolynomial, and JacobiOrthogPolynomial.
| void beta_stat | ( | const Real & | beta | ) | [virtual] |
set JacobiOrthogPolynomial::betaPoly from beta_stat
This is defined only for parameterized orthogonal polynomials.
Reimplemented in JacobiOrthogPolynomial.
| void interpolation_points | ( | const RealVector & | interpolation_pts | ) | [virtual] |
set LagrangeInterpPolynomial::interpolationPts
This is defined only for interpolation polynomials.
Reimplemented in LagrangeInterpPolynomial.
| Real factorial | ( | unsigned short | n | ) | [inline, static] |
compute n!
This implementation is unprotected from overflow, but this should be fine for the polynomial orders that we would expect to encounter. Whenever possible, orthogonal polynomial implementations should use factorial_ratio() or n_choose_k() instead of factorial() to avoid size_t overflow.
| Real factorial_ratio | ( | unsigned short | num, | |
| unsigned short | den | |||
| ) | [inline, static] |
compute num!/den!
This implementation sequences products in order to minimize the chances of overflow, and its use should be preferred to factorial() whenever possible.
| Real n_choose_k | ( | unsigned short | n, | |
| unsigned short | k | |||
| ) | [inline, static] |
compute n!/(k!(n-k)!)
This implementation sequences products in order to minimize the chances of overflow, and its use should be preferred to factorial() whenever possible.
| Real pochhammer | ( | const Real & | m, | |
| unsigned short | n | |||
| ) | [inline, static] |
compute the Pochhammer symbol (m)_n = m*(m+1)...*(m+n-1)
This is the rising/upper factorial formulation of the Pochhammer symbol (m)_n.
| BasisPolynomial * get_polynomial | ( | short | poly_type | ) | [private] |
appropriate derived type.
Used only by the envelope constructor to initialize polyRep to the appropriate derived type.
1.5.1