ExaModels
ExaModels.ExaModels — ModuleExaModelsAn algebraic modeling and automatic differentiation tool in Julia Language, specialized for SIMD abstraction of nonlinear programs.
For more information, please visit https://github.com/exanauts/ExaModels.jl
ExaModels.AdjointNode1 — TypeAdjointNode1{F, T, I}A node with one child for first-order forward pass tree
Fields:
x::T: function valuey::T: first-order sensitivityinner::I: children
ExaModels.AdjointNode2 — TypeAdjointNode2{F, T, I1, I2}A node with two children for first-order forward pass tree
Fields:
x::T: function valuey1::T: first-order sensitivity w.r.t. first argumenty2::T: first-order sensitivity w.r.t. second argumentinner1::I1: children #1inner2::I2: children #2
ExaModels.AdjointNodeSource — TypeAdjointNodeSource{VT}A source of AdjointNode. adjoint_node_source[i] returns an AdjointNodeVar at index i.
Fields:
inner::VT: variable vector
ExaModels.AdjointNodeVar — TypeAdjointNodeVar{I, T}A variable node for first-order forward pass tree
Fields:
i::I: indexx::T: value
ExaModels.AdjointNull — TypeNullA null node
ExaModels.Compressor — TypeCompressor{I}Data structure for the sparse index
Fields:
inner::I: stores the sparse index as a tuple form
ExaModels.ExaCore — TypeExaCore([array_eltype::Type; backend = backend, minimize = true])
Returns an intermediate data object ExaCore, which later can be used for creating ExaModel
Example
julia> using ExaModels
+API Manual · ExaModels.jl ExaModels
ExaModels.ExaModels — ModuleExaModels
An algebraic modeling and automatic differentiation tool in Julia Language, specialized for SIMD abstraction of nonlinear programs.
For more information, please visit https://github.com/exanauts/ExaModels.jl
sourceExaModels.AdjointNode1 — TypeAdjointNode1{F, T, I}
A node with one child for first-order forward pass tree
Fields:
x::T: function valuey::T: first-order sensitivityinner::I: children
sourceExaModels.AdjointNode2 — TypeAdjointNode2{F, T, I1, I2}
A node with two children for first-order forward pass tree
Fields:
x::T: function valuey1::T: first-order sensitivity w.r.t. first argumenty2::T: first-order sensitivity w.r.t. second argumentinner1::I1: children #1inner2::I2: children #2
sourceExaModels.AdjointNodeSource — TypeAdjointNodeSource{VT}
A source of AdjointNode. adjoint_node_source[i] returns an AdjointNodeVar at index i.
Fields:
inner::VT: variable vector
sourceExaModels.AdjointNodeVar — TypeAdjointNodeVar{I, T}
A variable node for first-order forward pass tree
Fields:
i::I: indexx::T: value
sourceExaModels.AdjointNull — TypeNull
A null node
sourceExaModels.Compressor — TypeCompressor{I}
Data structure for the sparse index
Fields:
inner::I: stores the sparse index as a tuple form
sourceExaModels.ExaCore — TypeExaCore([array_eltype::Type; backend = backend, minimize = true])
Returns an intermediate data object ExaCore, which later can be used for creating ExaModel
Example
julia> using ExaModels
julia> c = ExaCore()
An ExaCore
@@ -31,7 +31,7 @@
Backend: ......................... CUDA.CUDAKernels.CUDABackend
number of objective patterns: .... 0
- number of constraint patterns: ... 0
sourceExaModels.ExaModel — MethodExaModel(core)
Returns an ExaModel object, which can be solved by nonlinear optimization solvers within JuliaSmoothOptimizer ecosystem, such as NLPModelsIpopt or MadNLP.
Example
julia> using ExaModels
+ number of constraint patterns: ... 0
sourceExaModels.ExaModel — MethodExaModel(core)
Returns an ExaModel object, which can be solved by nonlinear optimization solvers within JuliaSmoothOptimizer ecosystem, such as NLPModelsIpopt or MadNLP.
Example
julia> using ExaModels
julia> c = ExaCore(); # create an ExaCore object
@@ -58,7 +58,7 @@
julia> result = ipopt(m; print_level=0) # solve the problem
"Execution stats: first-order stationary"
-
sourceExaModels.Node1 — TypeNode1{F, I}
A node with one child for symbolic expression tree
Fields:
inner::I: children
sourceExaModels.Node2 — TypeNode2{F, I1, I2}
A node with two children for symbolic expression tree
Fields:
inner1::I1: children #1inner2::I2: children #2
sourceExaModels.Null — TypeNull
A null node
sourceExaModels.ParIndexed — TypeParIndexed{I, J}
A parameterized data node
Fields:
inner::I: parameter for the data
sourceExaModels.ParSource — TypeParSource
A source of parameterized data
sourceExaModels.SIMDFunction — TypeSIMDFunction(gen::Base.Generator, o0 = 0, o1 = 0, o2 = 0)
Returns a SIMDFunction using the gen.
Arguments:
gen: an iterable function specified in Base.Generator formato0: offset for the function evaluationo1: offset for the derivative evalutiono2: offset for the second-order derivative evalution
sourceExaModels.SecondAdjointNode1 — TypeSecondAdjointNode1{F, T, I}
A node with one child for second-order forward pass tree
Fields:
x::T: function valuey::T: first-order sensitivityh::T: second-order sensitivityinner::I: DESCRIPTION
sourceExaModels.SecondAdjointNode2 — TypeSecondAdjointNode2{F, T, I1, I2}
A node with one child for second-order forward pass tree
Fields:
x::T: function valuey1::T: first-order sensitivity w.r.t. first argumenty2::T: first-order sensitivity w.r.t. first argumenth11::T: second-order sensitivity w.r.t. first argumenth12::T: second-order sensitivity w.r.t. first and second argumenth22::T: second-order sensitivity w.r.t. second argumentinner1::I1: children #1inner2::I2: children #2
sourceExaModels.SecondAdjointNodeSource — TypeSecondAdjointNodeSource{VT}
A source of AdjointNode. adjoint_node_source[i] returns an AdjointNodeVar at index i.
Fields:
inner::VT: variable vector
sourceExaModels.SecondAdjointNodeVar — TypeSecondAdjointNodeVar{I, T}
A variable node for first-order forward pass tree
Fields:
i::I: indexx::T: value
sourceExaModels.SecondAdjointNull — TypeNull
A null node
sourceExaModels.Var — TypeVar{I}
A variable node for symbolic expression tree
Fields:
i::I: (parameterized) index
sourceExaModels.VarSource — TypeVarSource
A source of variable nodes
sourceExaModels.WrapperNLPModel — MethodWrapperNLPModel(VT, m)
Returns a WrapperModel{T,VT} wrapping m <: AbstractNLPModel{T}
sourceExaModels.WrapperNLPModel — MethodWrapperNLPModel(m)
Returns a WrapperModel{Float64,Vector{64}} wrapping m
sourceExaModels.constraint — Methodconstraint(core, n; start = 0, lcon = 0, ucon = 0)
Adds empty constraints of dimension n, so that later the terms can be added with constraint!.
sourceExaModels.constraint — Methodconstraint(core, generator; start = 0, lcon = 0, ucon = 0)
Adds constraints specified by a generator to core, and returns an Constraint object.
Keyword Arguments
start: The initial guess of the solution. Can either be Number, AbstractArray, or Generator.lcon : The constraint lower bound. Can either be Number, AbstractArray, or Generator.ucon : The constraint upper bound. Can either be Number, AbstractArray, or Generator.
Example
julia> using ExaModels
+
sourceExaModels.Node1 — TypeNode1{F, I}
A node with one child for symbolic expression tree
Fields:
inner::I: children
sourceExaModels.Node2 — TypeNode2{F, I1, I2}
A node with two children for symbolic expression tree
Fields:
inner1::I1: children #1inner2::I2: children #2
sourceExaModels.Null — TypeNull
A null node
sourceExaModels.ParIndexed — TypeParIndexed{I, J}
A parameterized data node
Fields:
inner::I: parameter for the data
sourceExaModels.ParSource — TypeParSource
A source of parameterized data
sourceExaModels.SIMDFunction — TypeSIMDFunction(gen::Base.Generator, o0 = 0, o1 = 0, o2 = 0)
Returns a SIMDFunction using the gen.
Arguments:
gen: an iterable function specified in Base.Generator formato0: offset for the function evaluationo1: offset for the derivative evalutiono2: offset for the second-order derivative evalution
sourceExaModels.SecondAdjointNode1 — TypeSecondAdjointNode1{F, T, I}
A node with one child for second-order forward pass tree
Fields:
x::T: function valuey::T: first-order sensitivityh::T: second-order sensitivityinner::I: DESCRIPTION
sourceExaModels.SecondAdjointNode2 — TypeSecondAdjointNode2{F, T, I1, I2}
A node with one child for second-order forward pass tree
Fields:
x::T: function valuey1::T: first-order sensitivity w.r.t. first argumenty2::T: first-order sensitivity w.r.t. first argumenth11::T: second-order sensitivity w.r.t. first argumenth12::T: second-order sensitivity w.r.t. first and second argumenth22::T: second-order sensitivity w.r.t. second argumentinner1::I1: children #1inner2::I2: children #2
sourceExaModels.SecondAdjointNodeSource — TypeSecondAdjointNodeSource{VT}
A source of AdjointNode. adjoint_node_source[i] returns an AdjointNodeVar at index i.
Fields:
inner::VT: variable vector
sourceExaModels.SecondAdjointNodeVar — TypeSecondAdjointNodeVar{I, T}
A variable node for first-order forward pass tree
Fields:
i::I: indexx::T: value
sourceExaModels.SecondAdjointNull — TypeNull
A null node
sourceExaModels.Var — TypeVar{I}
A variable node for symbolic expression tree
Fields:
i::I: (parameterized) index
sourceExaModels.VarSource — TypeVarSource
A source of variable nodes
sourceExaModels.WrapperNLPModel — MethodWrapperNLPModel(VT, m)
Returns a WrapperModel{T,VT} wrapping m <: AbstractNLPModel{T}
sourceExaModels.WrapperNLPModel — MethodWrapperNLPModel(m)
Returns a WrapperModel{Float64,Vector{64}} wrapping m
sourceExaModels.constraint — Methodconstraint(core, n; start = 0, lcon = 0, ucon = 0)
Adds empty constraints of dimension n, so that later the terms can be added with constraint!.
sourceExaModels.constraint — Methodconstraint(core, generator; start = 0, lcon = 0, ucon = 0)
Adds constraints specified by a generator to core, and returns an Constraint object.
Keyword Arguments
start: The initial guess of the solution. Can either be Number, AbstractArray, or Generator.lcon : The constraint lower bound. Can either be Number, AbstractArray, or Generator.ucon : The constraint upper bound. Can either be Number, AbstractArray, or Generator.
Example
julia> using ExaModels
julia> c = ExaCore();
@@ -70,7 +70,7 @@
s.t. (...)
g♭ ≤ [g(x,p)]_{p ∈ P} ≤ g♯
- where |P| = 9
sourceExaModels.constraint — Methodconstraint(core, expr [, pars]; start = 0, lcon = 0, ucon = 0)
Adds constraints specified by a expr and pars to core, and returns an Constraint object.
sourceExaModels.drpass — Methoddrpass(d::D, y, adj)
Performs dense gradient evaluation via the reverse pass on the computation (sub)graph formed by forward pass
Arguments:
d: first-order computation (sub)graphy: result vectoradj: adjoint propagated up to the current node
sourceExaModels.gradient! — Methodgradient!(y, f, x, adj)
Performs dense gradient evalution
Arguments:
y: result vectorf: the function to be differentiated in SIMDFunction formatx: variable vectoradj: initial adjoint
sourceExaModels.grpass — Methodgrpass(d::D, comp, y, o1, cnt, adj)
Performs dsparse gradient evaluation via the reverse pass on the computation (sub)graph formed by forward pass
Arguments:
d: first-order computation (sub)graphcomp: a Compressor, which helps map counter to sparse vector indexy: result vectoro1: index offsetcnt: counteradj: adjoint propagated up to the current node
sourceExaModels.hdrpass — Methodhdrpass(t1::T1, t2::T2, comp, y1, y2, o2, cnt, adj)
Performs sparse hessian evaluation ((df1/dx)(df2/dx)' portion) via the reverse pass on the computation (sub)graph formed by second-order forward pass
Arguments:
t1: second-order computation (sub)graph regarding f1t2: second-order computation (sub)graph regarding f2comp: a Compressor, which helps map counter to sparse vector indexy1: result vector #1y2: result vector #2 (only used when evaluating sparsity)o2: index offsetcnt: counteradj: second adjoint propagated up to the current node
sourceExaModels.jrpass — Methodjrpass(d::D, comp, i, y1, y2, o1, cnt, adj)
Performs sparse jacobian evaluation via the reverse pass on the computation (sub)graph formed by forward pass
Arguments:
d: first-order computation (sub)graphcomp: a Compressor, which helps map counter to sparse vector indexi: constraint index (this is i-th constraint)y1: result vector #1y2: result vector #2 (only used when evaluating sparsity)o1: index offsetcnt: counteradj: adjoint propagated up to the current node
sourceExaModels.multipliers — Methodmultipliers(result, y)
Returns the multipliers for constraints y associated with result, obtained by solving the model.
Example
julia> using ExaModels, NLPModelsIpopt
+ where |P| = 9
sourceExaModels.constraint — Methodconstraint(core, expr [, pars]; start = 0, lcon = 0, ucon = 0)
Adds constraints specified by a expr and pars to core, and returns an Constraint object.
sourceExaModels.drpass — Methoddrpass(d::D, y, adj)
Performs dense gradient evaluation via the reverse pass on the computation (sub)graph formed by forward pass
Arguments:
d: first-order computation (sub)graphy: result vectoradj: adjoint propagated up to the current node
sourceExaModels.gradient! — Methodgradient!(y, f, x, adj)
Performs dense gradient evalution
Arguments:
y: result vectorf: the function to be differentiated in SIMDFunction formatx: variable vectoradj: initial adjoint
sourceExaModels.grpass — Methodgrpass(d::D, comp, y, o1, cnt, adj)
Performs dsparse gradient evaluation via the reverse pass on the computation (sub)graph formed by forward pass
Arguments:
d: first-order computation (sub)graphcomp: a Compressor, which helps map counter to sparse vector indexy: result vectoro1: index offsetcnt: counteradj: adjoint propagated up to the current node
sourceExaModels.hdrpass — Methodhdrpass(t1::T1, t2::T2, comp, y1, y2, o2, cnt, adj)
Performs sparse hessian evaluation ((df1/dx)(df2/dx)' portion) via the reverse pass on the computation (sub)graph formed by second-order forward pass
Arguments:
t1: second-order computation (sub)graph regarding f1t2: second-order computation (sub)graph regarding f2comp: a Compressor, which helps map counter to sparse vector indexy1: result vector #1y2: result vector #2 (only used when evaluating sparsity)o2: index offsetcnt: counteradj: second adjoint propagated up to the current node
sourceExaModels.jrpass — Methodjrpass(d::D, comp, i, y1, y2, o1, cnt, adj)
Performs sparse jacobian evaluation via the reverse pass on the computation (sub)graph formed by forward pass
Arguments:
d: first-order computation (sub)graphcomp: a Compressor, which helps map counter to sparse vector indexi: constraint index (this is i-th constraint)y1: result vector #1y2: result vector #2 (only used when evaluating sparsity)o1: index offsetcnt: counteradj: adjoint propagated up to the current node
sourceExaModels.multipliers — Methodmultipliers(result, y)
Returns the multipliers for constraints y associated with result, obtained by solving the model.
Example
julia> using ExaModels, NLPModelsIpopt
julia> c = ExaCore();
@@ -88,7 +88,7 @@
julia> val[1] ≈ 0.81933930
-true
sourceExaModels.multipliers_L — Methodmultipliers_L(result, x)
Returns the multipliers_L for variable x associated with result, obtained by solving the model.
Example
julia> using ExaModels, NLPModelsIpopt
+true
sourceExaModels.multipliers_L — Methodmultipliers_L(result, x)
Returns the multipliers_L for variable x associated with result, obtained by solving the model.
Example
julia> using ExaModels, NLPModelsIpopt
julia> c = ExaCore();
@@ -103,7 +103,7 @@
julia> val = multipliers_L(result, x);
julia> isapprox(val, fill(0, 10), atol=sqrt(eps(Float64)), rtol=Inf)
-true
sourceExaModels.multipliers_U — Methodmultipliers_U(result, x)
Returns the multipliers_U for variable x associated with result, obtained by solving the model.
Example
julia> using ExaModels, NLPModelsIpopt
+true
sourceExaModels.multipliers_U — Methodmultipliers_U(result, x)
Returns the multipliers_U for variable x associated with result, obtained by solving the model.
Example
julia> using ExaModels, NLPModelsIpopt
julia> c = ExaCore();
@@ -118,7 +118,7 @@
julia> val = multipliers_U(result, x);
julia> isapprox(val, fill(2, 10), atol=sqrt(eps(Float64)), rtol=Inf)
-true
sourceExaModels.objective — Methodobjective(core::ExaCore, generator)
Adds objective terms specified by a generator to core, and returns an Objective object. Note: it is assumed that the terms are summed.
Example
julia> using ExaModels
+true
sourceExaModels.objective — Methodobjective(core::ExaCore, generator)
Adds objective terms specified by a generator to core, and returns an Objective object. Note: it is assumed that the terms are summed.
Example
julia> using ExaModels
julia> c = ExaCore();
@@ -129,7 +129,7 @@
min (...) + ∑_{p ∈ P} f(x,p)
- where |P| = 10
sourceExaModels.objective — Methodobjective(core::ExaCore, expr [, pars])
Adds objective terms specified by a expr and pars to core, and returns an Objective object.
sourceExaModels.sgradient! — Methodsgradient!(y, f, x, adj)
Performs sparse gradient evalution
Arguments:
y: result vectorf: the function to be differentiated in SIMDFunction formatx: variable vectoradj: initial adjoint
sourceExaModels.shessian! — Methodshessian!(y1, y2, f, x, adj1, adj2)
Performs sparse jacobian evalution
Arguments:
y1: result vector #1y2: result vector #2 (only used when evaluating sparsity)f: the function to be differentiated in SIMDFunction formatx: variable vectoradj1: initial first adjointadj2: initial second adjoint
sourceExaModels.sjacobian! — Methodsjacobian!(y1, y2, f, x, adj)
Performs sparse jacobian evalution
Arguments:
y1: result vector #1y2: result vector #2 (only used when evaluating sparsity)f: the function to be differentiated in SIMDFunction formatx: variable vectoradj: initial adjoint
sourceExaModels.solution — Methodsolution(result, x)
Returns the solution for variable x associated with result, obtained by solving the model.
Example
julia> using ExaModels, NLPModelsIpopt
+ where |P| = 10
sourceExaModels.objective — Methodobjective(core::ExaCore, expr [, pars])
Adds objective terms specified by a expr and pars to core, and returns an Objective object.
sourceExaModels.sgradient! — Methodsgradient!(y, f, x, adj)
Performs sparse gradient evalution
Arguments:
y: result vectorf: the function to be differentiated in SIMDFunction formatx: variable vectoradj: initial adjoint
sourceExaModels.shessian! — Methodshessian!(y1, y2, f, x, adj1, adj2)
Performs sparse jacobian evalution
Arguments:
y1: result vector #1y2: result vector #2 (only used when evaluating sparsity)f: the function to be differentiated in SIMDFunction formatx: variable vectoradj1: initial first adjointadj2: initial second adjoint
sourceExaModels.sjacobian! — Methodsjacobian!(y1, y2, f, x, adj)
Performs sparse jacobian evalution
Arguments:
y1: result vector #1y2: result vector #2 (only used when evaluating sparsity)f: the function to be differentiated in SIMDFunction formatx: variable vectoradj: initial adjoint
sourceExaModels.solution — Methodsolution(result, x)
Returns the solution for variable x associated with result, obtained by solving the model.
Example
julia> using ExaModels, NLPModelsIpopt
julia> c = ExaCore();
@@ -144,7 +144,7 @@
julia> val = solution(result, x);
julia> isapprox(val, fill(1, 10), atol=sqrt(eps(Float64)), rtol=Inf)
-true
sourceExaModels.variable — Methodvariable(core, dims...; start = 0, lvar = -Inf, uvar = Inf)
Adds variables with dimensions specified by dims to core, and returns Variable object. dims can be either Integer or UnitRange.
Keyword Arguments
start: The initial guess of the solution. Can either be Number, AbstractArray, or Generator.lvar : The variable lower bound. Can either be Number, AbstractArray, or Generator.uvar : The variable upper bound. Can either be Number, AbstractArray, or Generator.
Example
julia> using ExaModels
+true
sourceExaModels.variable — Methodvariable(core, dims...; start = 0, lvar = -Inf, uvar = Inf)
Adds variables with dimensions specified by dims to core, and returns Variable object. dims can be either Integer or UnitRange.
Keyword Arguments
start: The initial guess of the solution. Can either be Number, AbstractArray, or Generator.lvar : The variable lower bound. Can either be Number, AbstractArray, or Generator.uvar : The variable upper bound. Can either be Number, AbstractArray, or Generator.
Example
julia> using ExaModels
julia> c = ExaCore();
@@ -157,7 +157,7 @@
Variable
x ∈ R^{9 × 3}
-
sourceExaModels.@register_bivariate — Macroregister_bivariate(f, df1, df2, ddf11, ddf12, ddf22)
Register a bivariate function f to ExaModels, so that it can be used within objective and constraint expressions
Arguments:
f: functiondf1: derivative function (w.r.t. first argument)df2: derivative function (w.r.t. second argument)ddf11: second-order derivative funciton (w.r.t. first argument)ddf12: second-order derivative funciton (w.r.t. first and second argument)ddf22: second-order derivative funciton (w.r.t. second argument)
Example
julia> using ExaModels
+
sourceExaModels.@register_bivariate — Macroregister_bivariate(f, df1, df2, ddf11, ddf12, ddf22)
Register a bivariate function f to ExaModels, so that it can be used within objective and constraint expressions
Arguments:
f: functiondf1: derivative function (w.r.t. first argument)df2: derivative function (w.r.t. second argument)ddf11: second-order derivative funciton (w.r.t. first argument)ddf12: second-order derivative funciton (w.r.t. first and second argument)ddf22: second-order derivative funciton (w.r.t. second argument)
Example
julia> using ExaModels
julia> relu23(x) = (x > 0 || y > 0) ? (x + y)^3 : zero(x)
relu23 (generic function with 1 method)
@@ -177,7 +177,7 @@
julia> ddrelu2322(x) = (x > 0 || y > 0) ? 6 * (x + y) : zero(x)
ddrelu2322 (generic function with 1 method)
-julia> @register_bivariate(relu23, drelu231, drelu232, ddrelu2311, ddrelu2312, ddrelu2322)
sourceExaModels.@register_univariate — Macro@register_univariate(f, df, ddf)
Register a univariate function f to ExaModels, so that it can be used within objective and constraint expressions
Arguments:
f: functiondf: derivative functionddf: second-order derivative funciton
Example
julia> using ExaModels
+julia> @register_bivariate(relu23, drelu231, drelu232, ddrelu2311, ddrelu2312, ddrelu2322)
sourceExaModels.@register_univariate — Macro@register_univariate(f, df, ddf)
Register a univariate function f to ExaModels, so that it can be used within objective and constraint expressions
Arguments:
f: functiondf: derivative functionddf: second-order derivative funciton
Example
julia> using ExaModels
julia> relu3(x) = x > 0 ? x^3 : zero(x)
relu3 (generic function with 1 method)
@@ -188,4 +188,4 @@
julia> ddrelu3(x) = x > 0 ? 6*x : zero(x)
ddrelu3 (generic function with 1 method)
-julia> @register_univariate(relu3, drelu3, ddrelu3)
sourceSettings
This document was generated with Documenter.jl version 1.7.0 on Wednesday 6 November 2024. Using Julia version 1.9.4.