Multivariate Expansion Worker#

template<class BasisEvaluatorType, typename MemorySpace = Kokkos::HostSpace> class MultivariateExpansionWorker#

Defines a function in terms of the tensor product of unary basis functions.

Cache memory managed elsewhere
\[\begin{split} \text{cache} = \left[\begin{array}{c} \phi_1^0(x_1)\\ \phi_1^1(x_1)\\ \vdots\\ \phi_1^{p_1}\\ \phi_2^0(x_2)\\ \vdots\\ \phi_2^{p_2}(x_2)\\ \vdots \\ \phi_d^{p_d}(x_d)\\ \frac{\partial}{\partial x_d}\phi_d^0(x_d)\\ \vdots\\ \frac{\partial}{\partial x_d}\phi_d^{p_d}(x_d)\\ \frac{\partial^2}{\partial x_d^2}\phi_d^0(x_d^2)\\ \vdots\\ \frac{\partial^2}{\partial x_d^2}\phi_d^{p_d}(x_d) \end{array} \right] \end{split}\]

Template Parameters:: BasisEvaluatorType – The family of 1d basis functions to employ.

Public Types

using BasisType = BasisEvaluatorType #

using KokkosSpace = MemorySpace #

using Rectifier = typename GetRectifier<BasisEvaluatorType>::type#

Public Functions

inline MultivariateExpansionWorker()#

inline MultivariateExpansionWorker(MultiIndexSet const &multiSet, BasisEvaluatorType const &basis1d = BasisEvaluatorType())#

inline MultivariateExpansionWorker(FixedMultiIndexSet<MemorySpace> const &multiSet, BasisEvaluatorType const &basis1d = BasisEvaluatorType())#

MultivariateExpansionWorker(MultivariateExpansionWorker const &other) = default#

inline unsigned int CacheSize() const#

Returns the size of the cache needed to evaluate the expansion (in terms of number of doubles).

Returns:: unsigned int The length of the required cache vector.

inline unsigned int NumCoeffs() const#

Returns the number of coefficients in this expansion.

Returns:: unsigned int The number of terms in the multiindexset, which corresponds to the number of coefficients needed to define the expansion.

inline unsigned int InputSize() const#

Returns the dimension of inputs to this multivariate expansion.

Returns:: unsigned int The dimension of an input point.

template<typename PointType> inline void FillCache1(double *polyCache, PointType const &pt, DerivativeFlags::DerivativeType derivType) const#

Precomputes parts of the cache using all but the last component of the point, i.e., using only $x_1,x_2,\ldots,x_{d-1}$, not $x_d$.

See also

FillCache1

Template Parameters:

Parameters:

polyCache – A pointer to the start of the cache. This memory must be allocated before calling this function.
pt – The point to use when filling in the cache. Should contain $[x_1,\ldots,x_{d-1}]$. The vector itself can have more than $d-1$ components, but only the first $d-1$ will be accessed. The value of $x_d$ is passed through the xd argument.
xd – The value of $x_d$. This is passed separate from $[x_1,\ldots,x_{d-1}]$ to make integrating over the last component more efficient. A copy of the point does not need to be created.
derivType –

template<typename CoeffVecType> inline double Evaluate(const double *polyCache, CoeffVecType const &coeffs) const#

template<typename CoeffVecType> inline double DiagonalDerivative(const double *polyCache, CoeffVecType const &coeffs, unsigned int derivOrder) const#

Evaluates the derivative of the expansion wrt x_{D-1}.

Template Parameters:

CoeffVecType –

Parameters:

polyCache –
coeffs –

Returns:

double

template<typename CoeffVecType, typename GradVecType> inline double CoeffDerivative(const double *polyCache, CoeffVecType const &coeffs, GradVecType &grad) const#

Evaluates the expansion and also computes the gradient of the expansion output wrt the coefficients.

Using cached values in the “polyCache” argument and coefficients $\theta$ from the coeffs argument, this function returns the value of the expansion $f(x;\theta)$ and computes the gradient $\nabla_\theta f$ of the expansion output with respect to the coefficients $\theta$.

Template Parameters:

CoeffVecType –
GradVecType –

Parameters:

polyCache –
coeffs –
grad – A vector that will be updated with the scaled gradient. This is the vector $g$ in the expression above.
gradScale – The scaling $\alpha$ used in the expression above.

template<typename CoeffVecType, typename GradVecType> inline double InputDerivative(const double *polyCache, CoeffVecType const &coeffs, GradVecType &grad) const#

Computes the gradient $\nabla_x f(x_{1:d})$ with respect to the input $x$.

Parameters:

polyCache[in] – Cache vector that has been set up by calling both FillCache1 and FillCache2 with DerivativeFlags::Input
coeffs[in] – Vector of coefficients. Must have parentheses access operator.
grad[out] – Preallocated vector to hold the gradient.

Returns:

The value of $f(x_{1:d})$.

template<typename CoeffVecType, typename GradVecType> inline double MixedInputDerivative(const double *polyCache, CoeffVecType const &coeffs, GradVecType &grad) const#

Computes the gradient of the diagonal derivative $\nabla_x \partial_d f(x_{1:d})$ with respect to the input $x$.

Parameters:

polyCache[in] – Cache vector that has been set up by calling both FillCache1 and FillCache2 with DerivativeFlags::MixedInput
coeffs[in] – Vector of coefficients. Must have parentheses access operator.
grad[out] – Preallocated vector to hold the gradient.

Returns:

The value of $\partial_d f(x_{1:d})$.

template<typename CoeffVecType, typename GradVecType> inline double MixedCoeffDerivative(const double *cache, CoeffVecType const &coeffs, unsigned int derivOrder, GradVecType &grad) const#

Computes the gradient of the diagonal derivative $\nabla_w \partial_d f(x_1:d; w)$ with respect to the parameters.

Parameters:

polyCache[in] – Cache vector that has been set up by calling both FillCache1 and FillCache2 with DerivativeFlags::MixedCoeff
coeffs[in] – Vector of coefficients. Must have parentheses access operator.
grad[out] – Preallocated vector to hold the gradient.

Returns:

The value of $\partial_d f(x_{1:d})$.

inline FixedMultiIndexSet<MemorySpace> GetMultiIndexSet() const#

Allows access to the Fixed MultiIndex Set

Returns:: The Fixed MultiIndex Set

inline std::vector<unsigned int> NonzeroDiagonalEntries() const#