{"action":"created","comment":{"url":"https://api.github.com/repos/JuliaDiffEq/DiffEqParamEstim.jl/pulls/comments/107526970","pull_request_review_id":28505801,"id":107526970,"diff_hunk":"@@ -0,0 +1,99 @@\n+export two_stage_method\n+\n+# Step - 1\n+function decide_kernel(kernel)\n+    if kernel == \"Epanechnikov\"\n+        return Epanechnikov_kernel\n+    elseif kernel == \"Uniform\"\n+        return Uniform_kernel\n+    else\n+        return Triangular_kernel\n+    end\n+end\n+function Epanechnikov_kernel(t)\n+    if abs(t) > 1\n+        return 0\n+    else\n+        return 0.75*(1-t^2)\n+    end\n+end\n+\n+function Uniform_kernel(t)\n+    if abs(t) > 1\n+        return 0\n+    else\n+        return 0.5\n+    end\n+end\n+\n+function Triangular_kernel(t)\n+    if abs(t) > 1\n+        return 0\n+    else\n+        return (1-abs(t))\n+    end\n+end\n+\n+\n+function construct_t1(t,tpoints)\n+    T1 = []\n+    for i in 1:length(tpoints)\n+        push!(T1,[1 tpoints[i]-t])\n+    end\n+    foldl(vcat,T1)\n+    #print(T1)\n+end\n+function construct_t2(t,tpoints)\n+    T2 = []\n+    for i in 1:length(tpoints)\n+        push!(T2,[1 tpoints[i]-t (tpoints[i]-t)^2])\n+    end\n+    foldl(vcat,T2)\n+end\n+function construct_w(t,tpoints,h,kernel_function)\n+    n = length(tpoints)\n+    W = zeros(n)\n+    for i in 1:n\n+        W[i] = kernel_function((tpoints[i]-t)/h)/h\n+    end\n+    diagm(W)\n+end\n+\n+\n+function two_stage_method(prob::DEProblem,tpoints,data,kernel=\"Epanechnikov\";kwargs...)\n+    f = prob.f\n+    n = length(tpoints)\n+    h = (n^(-1/5))*(n^(-3/35))*((log(n))^(-1/16))\n+    estimated_solution = zeros(n,size(data)[2])\n+    estimated_derivative = zeros(n,size(data)[2])\n+    kernel_function = decide_kernel(kernel)\n+    e1 = [1;0]\n+    e2 = [0;1;0]\n+\n+    for i in 1:n\n+        T1 = construct_t1(tpoints[i],tpoints)\n+        T2 = construct_t2(tpoints[i],tpoints)\n+        W = construct_w(tpoints[i],tpoints,h,kernel_function)\n+        estimated_solution[i,:] = e1'*inv(T1'*W*T1)*T1'*W*data\n+        estimated_derivative[i,:] = e2'*inv(T2'*W*T2)T2'*W*data\n+    end\n+\n+    \n+    # Step - 2\n+    cost_function = function (p)\n+        ff = (t,u,du) -> prob.f(t,u,p,du)","path":"src/two_stage_method.jl","position":84,"original_position":84,"commit_id":"45817bb80f674e92d5a6002cde4e889f744ec7a0","original_commit_id":"45817bb80f674e92d5a6002cde4e889f744ec7a0","user":{"login":"ChrisRackauckas","id":1814174,"avatar_url":"https://avatars1.githubusercontent.com/u/1814174?v=3","gravatar_id":"","url":"https://api.github.com/users/ChrisRackauckas","html_url":"https://github.com/ChrisRackauckas","followers_url":"https://api.github.com/users/ChrisRackauckas/followers","following_url":"https://api.github.com/users/ChrisRackauckas/following{/other_user}","gists_url":"https://api.github.com/users/ChrisRackauckas/gists{/gist_id}","starred_url":"https://api.github.com/users/ChrisRackauckas/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/ChrisRackauckas/subscriptions","organizations_url":"https://api.github.com/users/ChrisRackauckas/orgs","repos_url":"https://api.github.com/users/ChrisRackauckas/repos","events_url":"https://api.github.com/users/ChrisRackauckas/events{/privacy}","received_events_url":"https://api.github.com/users/ChrisRackauckas/received_events","type":"User","site_admin":false},"body":"that's good","created_at":"2017-03-22T20:44:04Z","updated_at":"2017-03-22T20:44:04Z","html_url":"https://github.com/JuliaDiffEq/DiffEqParamEstim.jl/pull/6#discussion_r107526970","pull_request_url":"https://api.github.com/repos/JuliaDiffEq/DiffEqParamEstim.jl/pulls/6","_links":{"self":{"href":"https://api.github.com/repos/JuliaDiffEq/DiffEqParamEstim.jl/pulls/comments/107526970"},"html":{"href":"https://github.com/JuliaDiffEq/DiffEqParamEstim.jl/pull/6#discussion_r107526970"},"pull_request":{"href":"https://api.github.com/repos/JuliaDiffEq/DiffEqParamEstim.jl/pulls/6"}}},"pull_request":{"url":"https://api.github.com/repos/JuliaDiffEq/DiffEqParamEstim.jl/pulls/6","id":109378839,"html_url":"https://github.com/JuliaDiffEq/DiffEqParamEstim.jl/pull/6","diff_url":"https://github.com/JuliaDiffEq/DiffEqParamEstim.jl/pull/6.diff","patch_url":"https://github.com/JuliaDiffEq/DiffEqParamEstim.jl/pull/6.patch","issue_url":"https://api.github.com/repos/JuliaDiffEq/DiffEqParamEstim.jl/issues/6","number":6,"state":"open","locked":false,"title":"[WIP]: Two-stage method","user":{"login":"Ayush-iitkgp","id":8552776,"avatar_url":"https://avatars1.githubusercontent.com/u/8552776?v=3","gravatar_id":"","url":"https://api.github.com/users/Ayush-iitkgp","html_url":"https://github.com/Ayush-iitkgp","followers_url":"https://api.github.com/users/Ayush-iitkgp/followers","following_url":"https://api.github.com/users/Ayush-iitkgp/following{/other_user}","gists_url":"https://api.github.com/users/Ayush-iitkgp/gists{/gist_id}","starred_url":"https://api.github.com/users/Ayush-iitkgp/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/Ayush-iitkgp/subscriptions","organizations_url":"https://api.github.com/users/Ayush-iitkgp/orgs","repos_url":"https://api.github.com/users/Ayush-iitkgp/repos","events_url":"https://api.github.com/users/Ayush-iitkgp/events{/privacy}","received_events_url":"https://api.github.com/users/Ayush-iitkgp/received_events","type":"User","site_admin":false},"body":"This is an attempt to implement two-stage method #4 and reorganize the source code.\r\n@ChrisRackauckas for the example:\r\n```\r\nusing DifferentialEquations\r\nusing Optim\r\ntpoints = [0.0,0.5,1.0]\r\ndata  = [1,exp(1),exp(2)]\r\npf_func = function (t,u,p)\r\n    p*u\r\n end\r\npf = ParameterizedFunction(pf_func,[2])\r\nu0 = [1.0]\r\ntspan = (0.0,1.0)\r\nprob = ODEProblem(pf,u0,tspan)\r\nresult = optimize(two_stage_method(prob,tpoints,data), -20.0, 20.0)\r\n```\r\n\r\n_**result.minimizer[1] should have been equal to 2 but it instead outputs -1.116706e+00**_\r\n\r\nAny hints where I am going wrong?\r\n\r\nUpdate - Two-stage method is not expected to converge to the actual parameter value and -1.11 is close to actual value 2. Looks like the implementation is correct.","created_at":"2017-03-07T00:09:44Z","updated_at":"2017-03-22T20:44:04Z","closed_at":null,"merged_at":null,"merge_commit_sha":"ed96360b3dac0317b288aeecf9792ca5b8356c2e","assignee":null,"assignees":[],"milestone":null,"commits_url":"https://api.github.com/repos/JuliaDiffEq/DiffEqParamEstim.jl/pulls/6/commits","review_comments_url":"https://api.github.com/repos/JuliaDiffEq/DiffEqParamEstim.jl/pulls/6/comments","review_comment_url":"https://api.github.com/repos/JuliaDiffEq/DiffEqParamEstim.jl/pulls/comments{/number}","comments_url":"https://api.github.com/repos/JuliaDiffEq/DiffEqParamEstim.jl/issues/6/comments","statuses_url":"https://api.github.com/repos/JuliaDiffEq/DiffEqParamEstim.jl/statuses/45817bb80f674e92d5a6002cde4e889f744ec7a0","head":{"label":"Ayush-iitkgp:2_stage_method","ref":"2_stage_method","sha":"45817bb80f674e92d5a6002cde4e889f744ec7a0","user":{"login":"Ayush-iitkgp","id":8552776,"avatar_url":"https://avatars1.githubusercontent.com/u/8552776?v=3","gravatar_id":"","url":"https://api.github.com/users/Ayush-iitkgp","html_url":"https://github.com/Ayush-iitkgp","followers_url":"https://api.github.com/users/Ayush-iitkgp/followers","following_url":"https://api.github.com/users/Ayush-iitkgp/following{/other_user}","gists_url":"https://api.github.com/users/Ayush-iitkgp/gists{/gist_id}","starred_url":"https://api.github.com/users/Ayush-iitkgp/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/Ayush-iitkgp/subscriptions","organizations_url":"https://api.github.com/users/Ayush-iitkgp/orgs","repos_url":"https://api.github.com/users/Ayush-iitkgp/repos","events_url":"https://api.github.com/users/Ayush-iitkgp/events{/privacy}","received_events_url":"https://api.github.com/users/Ayush-iitkgp/received_events","type":"User","site_admin":false},"repo":{"id":83908421,"name":"DiffEqParamEstim.jl","full_name":"Ayush-iitkgp/DiffEqParamEstim.jl","owner":{"login":"Ayush-iitkgp","id":8552776,"avatar_url":"https://avatars1.githubusercontent.com/u/8552776?v=3","gravatar_id":"","url":"https://api.github.com/users/Ayush-iitkgp","html_url":"https://github.com/Ayush-iitkgp","followers_url":"https://api.github.com/users/Ayush-iitkgp/followers","following_url":"https://api.github.com/users/Ayush-iitkgp/following{/other_user}","gists_url":"https://api.github.com/users/Ayush-iitkgp/gists{/gist_id}","starred_url":"https://api.github.com/users/Ayush-iitkgp/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/Ayush-iitkgp/subscriptions","organizations_url":"https://api.github.com/users/Ayush-iitkgp/orgs","repos_url":"https://api.github.com/users/Ayush-iitkgp/repos","events_url":"https://api.github.com/users/Ayush-iitkgp/events{/privacy}","received_events_url":"https://api.github.com/users/Ayush-iitkgp/received_events","type":"User","site_admin":false},"private":false,"html_url":"https://github.com/Ayush-iitkgp/DiffEqParamEstim.jl","description":"A 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