Map Factory#
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namespace MapFactory#
Namespace containing factory methods for constructing triangular maps and map components.
Example usage:
// First, set options defining the paramterization MapOptions options; options.basisType = BasisTypes::ProbabilistHermite; // Optional. Default = BasisTypes::ProbabilistHermite options.posFuncType = PosFuncTypes::SoftPlus; // Optional. Default = PosFuncTypes::SoftPlus options.quadType = QuadTypes::AdaptiveSimpson; // Optional. Default = QuadTypes::AdaptiveSimpson options.quadAbsTol = 1e-6; // Optional. Default = 1e-6 options.quadRelTol = 1e-6; // Optional. Default = 1e-6 options.quadMaxSub = 10; // Optional. Default = 30 options.contDeriv = true; // Optional. Default = true options.nugget = 1e-4; // Optional. Default = 0.0 // Create a triangular map with these options unsigned int inDim = 4; unsigned int outDim = 3; unsigned int totalOrder = 3; auto map = MapFactory::CreateTriangular<Kokkos::HostSpace>(inDim, outDim, totalOrder, options);
Functions
- Parameters:
mset – The multiindex set specifying which terms should be used in the multivariate expansion.
Creates a square triangular map that is an identity in all but one output dimension.
Constructs a “Single entry” map, which is an identity for all but one output dimension. The active output dimension is defined by a given component.
Given a dimension \(d\), an active index \(i\), and a real-valued map \(f:\mathbb{R}^d\rightarrow\mathbb{R}\), this function creates a map \(T:\mathbb{R}^d\rightarrow\mathbb{R}^d\) such that \(T_j(x) = x_j\) for all \(j\neq i\) and \(T_i(x) = f(x)\).
- Parameters:
dim – The dimension of the map.
activeInd – The index of the component to be non-identity.
comp – The component placed the activeInd.
dim – The dimension of the mapping
activeInd – Which output dimension is “active”, i.e., not identity
comp – The component that will be used for the active output dimension.
Constructs a triangular map with MonotoneComponents for each block. A total order multiindex set is used to define the MonotoneComponent.
For more control over the individual components, consider constructing components with MapFactory::CreateComponent function and then manually constructing and instance of the TriangularMap class.
- Parameters:
inputDim – The dimension of the input to this map. Will be the number of inputs passed to the last component of the triangular map.
outputDim – The output dimension of the map. Note that this must be less than or equal to the input dimension.
totalOrder – The total order used to define the parameterization of each MonotoneComponent.
options – Additional options that will be passed on to CreateComponent to construct each MonotoneComponent.
Constructs a (generally) non-monotone multivariate expansion.
- Parameters:
outputDim – The output dimension of the expansion. Each output will be defined by the same multiindex set but will have different coefficients.
mset – The multiindex set specifying which terms should be used in the multivariate expansion.
options – Options specifying the 1d basis functions used in the parameterization.
Create a RectifiedMultivariateExpansion using sigmoids.
Using the parameters described in
opts, this function creates a “rectified multivariate expansion” object that uses a collection of sigmoid functions to map the input space to the output space. The pertinent options areopts.basisType: The type of basis function to use in the expansion for the first \(d-1\) inputsopts.posFuncType: The type of positive function to use in the rectified basis MultivariateExpansionWorkeropts.edgeWidth: The width of the “edge terms” on the last input Sigmoid1dopts.sigmoidType: The type of sigmoid function to use in the expansion Sigmoid1d
This is only creating a scalar-valued function; to create a map, use
TriangularMapfunction.- Template Parameters:
MemorySpace –
- Parameters:
inputDim – Dimension of the input space to component
offDiagOrder – Maximum value of sum(alpha_{1:n-1}) when alpha_n=0. i.e., the total order of terms in the multiindex set that only contain nonzero values for off diagonal inputs.
crossOrder – Maximum value of sum(alpha_{1:n-1}) terms when alpha_n>0. This parameter controls the complexity of interactions between off-diagonal components and the diagonal component.
centers – Set of centers of the sigmoids. Should be length \(2 + (k_1 + k_2 + ... + k_L)\) where \(L\) is the maximum order of the map component in the last input.
opts –
- Returns:
std::shared_ptr<ConditionalMapBase<MemorySpace>>
Same as other CreateSigmoidComponent function, but offDiagOrder and crossOrder are both set to the value of totalOrder.
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template<typename MemorySpace>
struct CompFactoryImpl# - #include <MapFactory.h>
This struct is used to map the options to functions that can create a map component with types corresponding to the options.
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template<typename MemorySpace>
std::shared_ptr<ConditionalMapBase<MemorySpace>> mpart::MapFactory::CreateComponent(FixedMultiIndexSet<MemorySpace> const &mset, MapOptions options = MapOptions()) - Parameters:
mset – The multiindex set specifying which terms should be used in the multivariate expansion.
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template<typename MemorySpace>
std::shared_ptr<ConditionalMapBase<MemorySpace>> mpart::MapFactory::CreateTriangular(unsigned int inputDim, unsigned int outputDim, unsigned int totalOrder, MapOptions options = MapOptions()) Constructs a triangular map with MonotoneComponents for each block. A total order multiindex set is used to define the MonotoneComponent.
For more control over the individual components, consider constructing components with MapFactory::CreateComponent function and then manually constructing and instance of the TriangularMap class.
- Parameters:
inputDim – The dimension of the input to this map. Will be the number of inputs passed to the last component of the triangular map.
outputDim – The output dimension of the map. Note that this must be less than or equal to the input dimension.
totalOrder – The total order used to define the parameterization of each MonotoneComponent.
options – Additional options that will be passed on to CreateComponent to construct each MonotoneComponent.
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struct MapOptions#
struct to hold options used by the MapFactory methods to construct monotone components and triangular maps.
Subclassed by mpart::ATMOptions
Public Functions
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inline bool operator==(MapOptions opts2) const#
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inline virtual std::string String()#
Public Members
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BasisTypes basisType = BasisTypes::ProbabilistHermite#
The type of 1d basis function used to define the multivariate expansion.
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SigmoidTypes sigmoidType = SigmoidTypes::Logistic#
The type of sigmoid we want to use to define the diagonal of a rectified multivariate expansion
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EdgeTypes edgeType = EdgeTypes::SoftPlus#
The type of edge terms to use with sigmoids
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double edgeShape = 1.5#
The “shape” of the edge terms in a sigmoid basis (larger is “sharper” edge terms)
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SigmoidSumSizeType sigmoidBasisSumType = SigmoidSumSizeType::Linear#
How arrays of centers should be interpreted in sigmoid basis functions.
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double basisLB = -std::numeric_limits<double>::infinity()#
Linearization bounds for the 1d basis function. The basis function is linearized outside [lb,ub]
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double basisUB = std::numeric_limits<double>::infinity()#
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PosFuncTypes posFuncType = PosFuncTypes::SoftPlus#
The type of positive bijector used inside the monotonicity-guaranteeing integral formulation.
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QuadTypes quadType = QuadTypes::AdaptiveSimpson#
The type of quadrature rule to use.
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double quadAbsTol = 1e-6#
The absolute tolerance used by adaptive quadrature rules like AdaptiveSimpson and AdaptiveClenshawCurtis.
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double quadRelTol = 1e-6#
The relative tolerance used by adaptive quadrature rules like AdaptiveSimpson and AdaptiveClenshawCurtis.
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unsigned int quadMaxSub = 30#
The maximum number of subdivisions used in the adaptive quadrature rules.
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unsigned int quadMinSub = 0#
The minimum number of subdivisions used in the adaptive quadrature rules.
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unsigned int quadPts = 5#
The number of quadrature points used in fixed rules like the Clenshaw Curtis rule. Also defines the base level used in the adaptive Clenshaw-Curtis rule.
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bool contDeriv = true#
Specifies whether the derivative of the integral defining a monotone component is used or if the derivative of the quadrature-based approximation of the integral is used. See :ref:
diag_deriv_sectionfor more details. If true, the integral is differentiated directly. If false, the numerical approximation to the integral is differentiated.
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bool basisNorm = true#
If orthogonal polynomial basis functions should be normalized.
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double nugget = 0.0#
The minimum slope of the monotone component. This nugget is added to the g(df) integrand. Must be non-negative.
Public Static Attributes
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static const std::string btypes[3] = {"ProbabilistHermite", "PhysicistHermite", "HermiteFunctions"}#
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static const std::string pftypes[2] = {"Exp", "SoftPlus"}#
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static const std::string qtypes[3] = {"ClenshawCurtis", "AdaptiveSimpson", "AdaptiveClenshawCurtis"}#
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static const std::string etypes[1] = {"SoftPlus"}#
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static const std::string stypes[1] = {"Logistic"}#
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static const std::string sbstypes[2] = {"Linear", "Constant"}#
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inline bool operator==(MapOptions opts2) const#