{
"cells": [
{
"cell_type": "markdown",
"source": [
"# Variational problems\n",
"\n",
"*You are seeing the\n",
"notebook output generated by\n",
"[Literate.jl](https://github.com/fredrikekre/Literate.jl) from the\n",
"[Julia source file](https://github.com/JuliaOptimalTransport/OptimalTransport.jl/blob/master/examples/variational/script.jl).\n",
"The rendered HTML can be viewed [in the docs](https://juliaoptimaltransport.github.io/OptimalTransport.jl/dev/examples/variational/).*"
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"In this example, we will numerically simulate an entropy-regularised Wasserstein gradient flow\n",
"approximating the Fokker-Planck and porous medium equations.\n",
"\n",
"The connection between Wasserstein gradient flows and (non)-linear PDEs is due to Jordan, Kinderlehrer and Otto [^JKO98], and\n",
"an easy-to-read overview of the topic is provided in Section 9.3 [^PC19]\n",
"\n",
"[^JKO98]: Jordan, Richard, David Kinderlehrer, and Felix Otto. \"The variational formulation of the Fokker--Planck equation.\" SIAM journal on mathematical analysis 29.1 (1998): 1-17.\n",
"[^PC19]: Peyré, Gabriel, and Marco Cuturi. \"Computational optimal transport: With applications to data science.\" Foundations and Trends® in Machine Learning 11.5-6 (2019): 355-607.\n",
"\n",
"## Fokker-Planck equation as a $W_2$ gradient flow\n",
"For a potential function $\\Psi$ and noise level $\\sigma^2$, the Fokker-Planck equation (FPE) is\n",
"$$\n",
"\\partial_t \\rho_t = \\nabla \\cdot (\\rho_t \\nabla \\Psi) + \\frac{\\sigma^2}{2} \\Delta \\rho_t,\n",
"$$\n",
"and we take no-flux (Neumann) boundary conditions.\n",
"\n",
"This describes the evolution of a massless particle undergoing both diffusion (with diffusivity $\\sigma^2$) and drift (along potential $\\Psi$) according to the stochastic differential equation\n",
"$$\n",
"dX_t = -\\nabla \\Psi(X_t) dt + \\sigma dB_t.\n",
"$$\n",
"The result of Jordan, Kinderlehrer and Otto (commonly referred to as the JKO theorem) states that\n",
"$\\rho_t$ evolves following the 2-Wasserstein gradient flow of the Gibbs free energy functional\n",
"$$\n",
" F(\\rho) = \\int \\Psi d\\rho + \\int \\log(\\rho) d\\rho.\n",
"$$\n",
"\n",
"## Implicit schemes for gradient flows\n",
"In an Euclidean space, the gradient flow of a functional $F$ is simply the solution of an ordinary differential equation\n",
"$$\n",
" \\dfrac{dx(t)}{dt} = -\\nabla F(x(t)).\n",
"$$\n",
"Of course, there is a requirement that $F$ is smooth. A more general formulation of a gradient flow that allows\n",
"$F$ to be non-smooth is the implicit scheme\n",
"$$\n",
" x_{t+\\tau} = \\operatorname{argmin}_x \\frac{1}{2} \\| x - x_t \\|_2^2 + \\tau F(x).\n",
"$$\n",
"As the timestep $\\tau$ shrinks, $x_t$ becomes a better and better approximation to the gradient flow of $F$.\n",
"\n",
"## Wasserstein gradient flow\n",
"In the context of the JKO theorem, we seek $\\rho_t$ that is the gradient flow of $F$ with\n",
"respect to the 2-Wasserstein distance. This can be achieved by choosing the $W_2$ metric in the implicit step:\n",
"$$\n",
" \\rho_{t + \\tau} = \\operatorname{argmin}_{\\rho} d_{W_2}^2(\\rho_{t}, \\rho) + \\tau F(\\rho).\n",
"$$\n",
"Finally, a numerical scheme for computing this gradient flow can be developed by using the entropic regularisation\n",
"of optimal transport on a discretised domain\n",
"$$\n",
" \\rho_{t + \\tau} = \\operatorname{argmin}_{\\rho} \\operatorname{OT}_\\varepsilon(\\rho_{t}, \\rho) + \\tau F(\\rho),\n",
"$$\n",
"where\n",
"$$\n",
" \\operatorname{OT}_\\varepsilon(\\alpha, \\beta) = \\min_{\\gamma \\in \\Pi(\\alpha, \\beta)} \\sum_{i,j} \\frac{1}{2} \\| x_i - x_j \\|_2^2 \\gamma_{ij} + \\varepsilon \\sum_{i, j} \\gamma_{ij} \\log(\\gamma_{ij}).\n",
"$$\n",
"Each step of this problem is a minimisation problem with respect to $\\rho$.\n",
"Since we use entropic optimal transport which is differentiable, this can be solved using gradient-based methods."
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"## Problem setup"
],
"metadata": {}
},
{
"outputs": [],
"cell_type": "code",
"source": [
"using OptimalTransport\n",
"using Distances\n",
"using LogExpFunctions\n",
"using Optim\n",
"using Plots\n",
"using StatsBase\n",
"using ReverseDiff\n",
"\n",
"using LinearAlgebra\n",
"using Logging"
],
"metadata": {},
"execution_count": 1
},
{
"cell_type": "markdown",
"source": [
"Here, we set up the computational domain that we work on - we discretize the interval $[-1, 1]$.\n",
"The natural boundary conditions to use will be Neumann (zero flux), see e.g. [^Santam2017]\n",
"\n",
"[^Santam2017]: Santambrogio, Filippo. \"{Euclidean, metric, and Wasserstein} gradient flows: an overview.\" Bulletin of Mathematical Sciences 7.1 (2017): 87-154."
],
"metadata": {}
},
{
"outputs": [],
"cell_type": "code",
"source": [
"support = range(-1, 1; length=64)\n",
"C = pairwise(SqEuclidean(), support');"
],
"metadata": {},
"execution_count": 2
},
{
"cell_type": "markdown",
"source": [
"Now we set up various functionals that we will use.\n",
"\n",
"We define the generalised entropy (Equation (4.4) of [^Peyre2015]) as follows. For $m = 1$ this is just the \"regular\" entropy, and $m = 2$ this is squared $L_2$.\n",
"\n",
"[^Peyre2015]: Peyré, Gabriel. \"Entropic approximation of Wasserstein gradient flows.\" SIAM Journal on Imaging Sciences 8.4 (2015): 2323-2351."
],
"metadata": {}
},
{
"outputs": [],
"cell_type": "code",
"source": [
"function E(ρ; m=1)\n",
" if m == 1\n",
" return sum(xlogx.(ρ)) - sum(ρ)\n",
" elseif m > 1\n",
" return dot(ρ, @. (ρ^(m - 1) - m) / (m - 1))\n",
" end\n",
"end;"
],
"metadata": {},
"execution_count": 3
},
{
"cell_type": "markdown",
"source": [
"Now define $\\psi(x)$ to be a potential energy function that has two potential wells at $x = ± 0.5$."
],
"metadata": {}
},
{
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "Plot{Plots.GRBackend() n=1}",
"image/png": 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",
"text/html": [
"\n",
"\n"
],
"image/svg+xml": [
"\n",
"\n"
]
},
"metadata": {},
"execution_count": 4
}
],
"cell_type": "code",
"source": [
"ψ(x) = 10 * (x - 0.5)^2 * (x + 0.5)^2;\n",
"plot(support, ψ.(support); color=\"black\", label=\"Scalar potential\")"
],
"metadata": {},
"execution_count": 4
},
{
"cell_type": "markdown",
"source": [
"Having defined $\\psi$, this induces a potential energy functional $\\Psi$ on probability distributions $\\rho$:\n",
"$$\n",
" \\Psi(\\rho) = \\int \\psi(x) \\rho(x) dx = \\langle \\psi, \\rho \\rangle .\n",
"$$"
],
"metadata": {}
},
{
"outputs": [],
"cell_type": "code",
"source": [
"Ψ = ψ.(support);"
],
"metadata": {},
"execution_count": 5
},
{
"cell_type": "markdown",
"source": [
"Define the time step $\\tau$ and entropic regularisation level $\\varepsilon$, and form the associated Gibbs kernel $K = e^{-C/\\varepsilon}$."
],
"metadata": {}
},
{
"outputs": [],
"cell_type": "code",
"source": [
"τ = 0.05\n",
"ε = 0.01\n",
"K = @. exp(-C / ε);"
],
"metadata": {},
"execution_count": 6
},
{
"cell_type": "markdown",
"source": [
"We define the (non-smooth) initial condition $\\rho_0$ in terms of step functions."
],
"metadata": {}
},
{
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "Plot{Plots.GRBackend() n=1}",
"image/png": 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",
"text/html": [
"\n",
"\n"
],
"image/svg+xml": [
"\n",
"\n"
]
},
"metadata": {},
"execution_count": 7
}
],
"cell_type": "code",
"source": [
"H(x) = x > 0\n",
"ρ0 = @. H(support + 0.25) - H(support - 0.25)\n",
"ρ0 = ρ0 / sum(ρ0)\n",
"plot(support, ρ0; label=\"Initial condition ρ0\", color=\"blue\")"
],
"metadata": {},
"execution_count": 7
},
{
"cell_type": "markdown",
"source": [
"`G_fpe` is the objective function for the implicit step scheme\n",
"$$\n",
"G_\\mathrm{fpe}(\\rho) = \\operatorname{OT}_\\varepsilon(\\rho_{t}, \\rho) + \\tau F(\\rho),\n",
"$$\n",
"and we seek to minimise in $\\rho$."
],
"metadata": {}
},
{
"outputs": [],
"cell_type": "code",
"source": [
"function G_fpe(ρ, ρ0, τ, ε, C)\n",
" return sinkhorn2(ρ, ρ0, C, ε; regularization=true, maxiter=250) + τ * (dot(Ψ, ρ) + E(ρ))\n",
"end;"
],
"metadata": {},
"execution_count": 8
},
{
"cell_type": "markdown",
"source": [
"`step` solves the implicit step problem to produce $\\rho_{t + \\tau}$ from $\\rho_t$."
],
"metadata": {}
},
{
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "step (generic function with 1 method)"
},
"metadata": {},
"execution_count": 9
}
],
"cell_type": "code",
"source": [
"function step(ρ0, τ, ε, C, G)\n",
" # only print error messages\n",
" obj = u -> G(softmax(u), ρ0, τ, ε, C)\n",
" opt = with_logger(SimpleLogger(stderr, Logging.Error)) do\n",
" optimize(\n",
" obj,\n",
" ones(size(ρ0)),\n",
" LBFGS(),\n",
" Optim.Options(; iterations=50, g_tol=1e-6);\n",
" autodiff=:forward,\n",
" )\n",
" end\n",
" return softmax(Optim.minimizer(opt))\n",
"end"
],
"metadata": {},
"execution_count": 9
},
{
"cell_type": "markdown",
"source": [
"Now we simulate `N = 10` iterates of the gradient flow and plot the result."
],
"metadata": {}
},
{
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[ Info: 2\n",
"[ Info: 3\n",
"[ Info: 4\n",
"[ Info: 5\n",
"[ Info: 6\n",
"[ Info: 7\n",
"[ Info: 8\n",
"[ Info: 9\n",
"[ Info: 10\n"
]
},
{
"output_type": "execute_result",
"data": {
"text/plain": "Plot{Plots.GRBackend() n=10}",
"image/png": 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",
"text/html": [
"\n",
"\n"
],
"image/svg+xml": [
"\n",
"\n"
]
},
"metadata": {},
"execution_count": 10
}
],
"cell_type": "code",
"source": [
"N = 10\n",
"ρ = similar(ρ0, size(ρ0, 1), N)\n",
"ρ[:, 1] = ρ0\n",
"for i in 2:N\n",
" @info i\n",
" ρ[:, i] = step(ρ[:, i - 1], τ, ε, C, G_fpe)\n",
"end\n",
"colors = range(colorant\"red\"; stop=colorant\"blue\", length=N)\n",
"plot(\n",
" support,\n",
" ρ;\n",
" title=raw\"$F(\\rho) = \\langle \\psi, \\rho \\rangle + \\langle \\rho, \\log(\\rho) \\rangle$\",\n",
" palette=colors,\n",
" legend=nothing,\n",
")"
],
"metadata": {},
"execution_count": 10
},
{
"cell_type": "markdown",
"source": [
"## Porous medium equation\n",
"\n",
"The porous medium equation (PME) is the nonlinear PDE\n",
"$$\n",
"\\partial_t \\rho = \\nabla \\cdot (\\rho \\nabla \\Psi) + \\Delta \\rho^m,\n",
"$$\n",
"again with Neumann boundary conditions. The value of $m$ in the PME corresponds to picking $m$ in the generalised entropy functional.\n",
"Now, we will solve the PME with $m = 2$ as a Wasserstein gradient flow."
],
"metadata": {}
},
{
"outputs": [],
"cell_type": "code",
"source": [
"function G_pme(ρ, ρ0, τ, ε, C)\n",
" return sinkhorn2(ρ, ρ0, C, ε; regularization=true, maxiter=250) +\n",
" τ * (dot(Ψ, ρ) + E(ρ; m=2))\n",
"end;"
],
"metadata": {},
"execution_count": 11
},
{
"cell_type": "markdown",
"source": [
"set up as previously"
],
"metadata": {}
},
{
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "Plot{Plots.GRBackend() n=10}",
"image/png": 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",
"text/html": [
"\n",
"\n"
],
"image/svg+xml": [
"\n",
"\n"
]
},
"metadata": {},
"execution_count": 12
}
],
"cell_type": "code",
"source": [
"N = 10\n",
"ρ = similar(ρ0, size(ρ0, 1), N)\n",
"ρ[:, 1] = ρ0\n",
"for i in 2:N\n",
" ρ[:, i] = step(ρ[:, i - 1], τ, ε, C, G_pme)\n",
"end\n",
"plot(\n",
" support,\n",
" ρ;\n",
" title=raw\"$F(\\rho) = \\langle \\psi, \\rho \\rangle + \\langle \\rho, \\rho - 1\\rangle$\",\n",
" palette=colors,\n",
" legend=nothing,\n",
")"
],
"metadata": {},
"execution_count": 12
},
{
"cell_type": "markdown",
"source": [
"## Exploiting duality\n",
"\n",
"The previous examples solved the minimisation problem for the implicit gradient flow step directly, involving automatic differentiation through the Sinkhorn iterations used to compute $\\operatorname{OT}_\\varepsilon(\\rho_t, \\rho)$ each time a gradient needs to be evaluated.\n",
"While this is straightforward to implement, it is computationally costly.\n",
"An alternative approach for convex variational problems is to proceed via the [dual problem](https://en.wikipedia.org/wiki/Duality_(optimization)).\n",
"The benefit of proceeding via the dual problem is that the part of the dual minimisation problem corresponding to the (entropy-regularised) optimal transport loss is typically available in closed form. This is in contrast to the primal problem, where evaluation of the objective and its gradients requires potentially many Sinkhorn iterations.\n",
"\n",
"Consider a general convex and unconstrained problem. Under (usually satisfied) conditions for strong duality to hold, we have\n",
"$$\n",
"\\begin{aligned}\n",
"&\\min_{\\rho} \\operatorname{OT}_{\\varepsilon}(\\rho_0, \\rho) + \\mathcal{F}(\\rho) \\\\\n",
"&= \\min_{\\rho} \\sup_{u}\\left[\\langle \\rho, u \\rangle - \\operatorname{OT}^*_{\\varepsilon}(\\rho_0, u)\\right] + \\mathcal{F}(\\rho) \\\\\n",
"&= \\sup_{u} \\min_{\\rho} \\langle \\rho, u \\rangle - \\operatorname{OT}^*_{\\varepsilon}(\\rho_0, u) + \\mathcal{F}(\\rho) \\\\\n",
"&= \\sup_{u} - \\operatorname{OT}^*_{\\varepsilon}(\\rho_0, u) + \\min_{\\rho} \\langle \\rho, u \\rangle + \\mathcal{F}(\\rho) \\\\\n",
"&= \\sup_{u} - \\operatorname{OT}^*_{\\varepsilon}(\\rho_0, u) - \\sup_{\\rho} \\langle \\rho, -u \\rangle - \\mathcal{F}(\\rho) \\\\\n",
"&= \\sup_{u} - \\operatorname{OT}^*_{\\varepsilon}(\\rho_0, u) - \\mathcal{F}^*(-u).\n",
"\\end{aligned}\n",
"$$\n",
"Thus, the dual problem is\n",
"$$\n",
"\\min_{u} \\operatorname{OT}^*_{\\varepsilon}(\\rho_0, u) + \\mathcal{F}^*(-u).\n",
"$$\n",
"\n",
"The upshot here is that $u \\mapsto \\operatorname{OT}^*_{\\varepsilon}(\\rho_0, u)$ and its gradient is available in closed form. This is a known result in the literature [^CP18].\n",
"\n",
"[^CP18]: Cuturi, Marco, and Gabriel Peyré. “Semi-Dual Regularized Optimal Transport.” ArXiv: Learning, 2018.\n",
"\n",
"The formulas we state below are lifted from statements in [^Z21].\n",
"\n",
"[^Z21]: Zhang, Stephen Y. “A Unified Framework for Non-Negative Matrix and Tensor Factorisations with a Smoothed Wasserstein Loss.” ArXiv: Machine Learning, 2021.\n",
"\n",
"$$\n",
"\\begin{aligned}\n",
"\\operatorname{OT}^*_{\\varepsilon}(\\rho_0, u) &= -\\varepsilon \\left\\langle \\rho_0, \\log\\left( \\dfrac{\\rho_0}{K e^{u/\\varepsilon}} \\right) - 1\\right\\rangle, \\\\\n",
"\\nabla_u \\operatorname{OT}^*_{\\varepsilon}(\\rho_0, u) &= K^\\top \\left( \\dfrac{\\rho_0}{K e^{u/\\varepsilon}} \\right) \\odot e^{u/\\varepsilon}.\n",
"\\end{aligned}\n",
"$$\n",
"At optimality, we can recover the primal optimal point $\\rho^\\star$ from the dual optimal point $u^\\star$ following the formula\n",
"$$\n",
"\\rho^\\star = e^{u^\\star/\\varepsilon} \\odot K^\\top \\dfrac{\\rho_0}{K e^{u^\\star/\\varepsilon}}.\n",
"$$\n",
"\n",
"When $\\mathcal{F}^*(\\cdot)$ is also available in closed form (this is not always the case), the dual problem has a closed form objective and can generally be solved much more efficiently than the primal problem.\n",
"\n",
"In the setting of the Fokker-Planck and porous medium equations, the function $\\mathcal{F}$ can be identified with\n",
"\n",
"$$\n",
"\\mathcal{F}(\\rho) = \\tau \\left[ \\langle \\psi, \\rho \\rangle + E_m(\\rho) \\right].\n",
"$$\n",
"\n",
"A straightforward computation shows that\n",
"$$\n",
"\\mathcal{F}^*(u) = \\tau E_m^*\\left( \\frac{u}{\\tau}-\\psi \\right),\n",
"$$\n",
"where\n",
"$$\n",
" E_m^*(u) = \\begin{cases}\n",
" \\langle e^u, \\mathbf{1} \\rangle, & m = 1 \\\\\n",
" \\sum_i \\left[ \\left( u_i + \\frac{m}{m-1} \\right) \\left( \\frac{m-1}{m} u_i + 1 \\right)^{\\frac{1}{m-1}} - \\frac{1}{m-1} \\left( \\frac{m-1}{m} u_i + 1 \\right)^{\\frac{m}{m-1}} \\right], & m > 1.\n",
" \\end{cases}\n",
"$$\n",
"In particular, for $m = 2$ we have a simpler formula\n",
"$$\n",
"E_2^*(u) = \\left\\| \\frac{u}{2} + 1 \\right\\|_2^2\n",
"$$\n",
"\n",
"We now implement $E_m^*$ for $m = 1, 2$."
],
"metadata": {}
},
{
"outputs": [],
"cell_type": "code",
"source": [
"E_dual(u, m::Val{1}) = sum(exp.(u))\n",
"function E_dual(u, m::Val{2})\n",
" return dot(u / 2 .+ 1, u / 2 .+ 1)\n",
"end;"
],
"metadata": {},
"execution_count": 13
},
{
"cell_type": "markdown",
"source": [
"So, the dual problem we are dealing with reads\n",
"$$\n",
"\\min_{u} \\operatorname{OT}^*_{\\varepsilon}(\\rho_0, u) + \\tau E_m^*\\left( \\frac{-u}{\\tau}-\\psi \\right),\n",
"$$\n",
"and we can thus set up `G_dual_fpe`, the dual objective."
],
"metadata": {}
},
{
"outputs": [],
"cell_type": "code",
"source": [
"function G_dual_fpe(u, ρ0, τ, ε, K)\n",
" return OptimalTransport.Dual.ot_entropic_semidual(ρ0, u, ε, K) +\n",
" τ * E_dual(-u / τ - Ψ, Val(1))\n",
"end;"
],
"metadata": {},
"execution_count": 14
},
{
"cell_type": "markdown",
"source": [
"Now we set up `step` as previously, except this time we need to convert from the optimal dual variable $u^\\star$ to the primal variable $\\rho^\\star$. In the code, this is handled by `getprimal_ot_entropic_semidual`. We use `ReverseDiff` in this problem."
],
"metadata": {}
},
{
"outputs": [],
"cell_type": "code",
"source": [
"function step(ρ0, τ, ε, K, G)\n",
" obj = u -> G(u, ρ0, τ, ε, K)\n",
" opt = optimize(\n",
" obj,\n",
" (∇, u) -> ReverseDiff.gradient!(∇, obj, u),\n",
" zeros(size(ρ0)),\n",
" LBFGS(),\n",
" Optim.Options(; iterations=250, g_tol=1e-6),\n",
" )\n",
" return OptimalTransport.Dual.getprimal_ot_entropic_semidual(\n",
" ρ0, Optim.minimizer(opt), ε, K\n",
" )\n",
"end;"
],
"metadata": {},
"execution_count": 15
},
{
"cell_type": "markdown",
"source": [
"Now we can solve the dual problem as previously, and we note that the dual formulation is solved an order of magnitude faster than the primal formulation."
],
"metadata": {}
},
{
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "Plot{Plots.GRBackend() n=10}",
"image/png": 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",
"text/html": [
"\n",
"\n"
],
"image/svg+xml": [
"\n",
"\n"
]
},
"metadata": {},
"execution_count": 16
}
],
"cell_type": "code",
"source": [
"ρ = similar(ρ0, size(ρ0, 1), N)\n",
"ρ[:, 1] = ρ0\n",
"for i in 2:N\n",
" ρ[:, i] = step(ρ[:, i - 1], τ, ε, K, G_dual_fpe)\n",
"end\n",
"colors = range(colorant\"red\"; stop=colorant\"blue\", length=N)\n",
"plot(\n",
" support,\n",
" ρ;\n",
" title=raw\"$F(\\rho) = \\langle \\psi, \\rho \\rangle + \\langle \\rho, \\log(\\rho) \\rangle$\",\n",
" palette=colors,\n",
" legend=nothing,\n",
")"
],
"metadata": {},
"execution_count": 16
},
{
"cell_type": "markdown",
"source": [
"Setting `m = 2`, we can simulate instead the porous medium equation."
],
"metadata": {}
},
{
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[ Info: 2\n",
"[ Info: 3\n",
"[ Info: 4\n",
"[ Info: 5\n",
"[ Info: 6\n",
"[ Info: 7\n",
"[ Info: 8\n",
"[ Info: 9\n",
"[ Info: 10\n"
]
},
{
"output_type": "execute_result",
"data": {
"text/plain": "Plot{Plots.GRBackend() n=10}",
"image/png": 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",
"text/html": [
"\n",
"\n"
],
"image/svg+xml": [
"\n",
"\n"
]
},
"metadata": {},
"execution_count": 17
}
],
"cell_type": "code",
"source": [
"function G_dual_pme(u, ρ0, τ, ε, K)\n",
" return OptimalTransport.Dual.ot_entropic_semidual(ρ0, u, ε, K) +\n",
" τ * E_dual(-u / τ - Ψ, Val(2))\n",
"end\n",
"ρ = similar(ρ0, size(ρ0, 1), N)\n",
"ρ[:, 1] = ρ0\n",
"for i in 2:N\n",
" @info i\n",
" ρ[:, i] = step(ρ[:, i - 1], τ, ε, K, G_dual_pme)\n",
"end\n",
"colors = range(colorant\"red\"; stop=colorant\"blue\", length=N)\n",
"plot(\n",
" support,\n",
" ρ;\n",
" title=raw\"$F(\\rho) = \\langle \\psi, \\rho \\rangle + \\langle \\rho, \\rho - 1\\rangle$\",\n",
" palette=colors,\n",
" legend=nothing,\n",
")"
],
"metadata": {},
"execution_count": 17
},
{
"cell_type": "markdown",
"source": [
"---\n",
"\n",
"*This notebook was generated using [Literate.jl](https://github.com/fredrikekre/Literate.jl).*"
],
"metadata": {}
}
],
"nbformat_minor": 3,
"metadata": {
"language_info": {
"file_extension": ".jl",
"mimetype": "application/julia",
"name": "julia",
"version": "1.11.6"
},
"kernelspec": {
"name": "julia-1.11",
"display_name": "Julia 1.11.6",
"language": "julia"
}
},
"nbformat": 4
}