From 38fad3ba5bc690092dcd0d74961a29912b1c050c Mon Sep 17 00:00:00 2001 From: Tuomas Koskela Date: Wed, 17 Mar 2021 14:49:56 +0000 Subject: [PATCH] Implement optimal particle filter from Alex (#133) MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit * Add functions for Alex optimal filter * Rewrite functions with rho_bar a vector and R21,R12 matrices * sample_height_proposal passes preliminary tests * sample_height_proposal passes preliminary tests * Add validation against Alex code * Add performance benchmarks * Shift grid indices so that both station and grid indexing starts at 1. Shift indices when initialising StationVectors from st.st_ij of Sample_Optimal_Height_Proposal.jl * Add get_log_weights function * Add comments, fix bugs change i to iprt for correct behaviour in get_log_weights! interpolate variables in function calls that are timed with @btime * Apply suggestions from code review Add dots and in-place operations Co-authored-by: Mosè Giordano * matrices.K*KH is a real matrix product * Use mul! to do multiplication in-place * Remove duplicate call * Minimal allocations reduction * Add get_stations and set_particles! to the interface * Reorder data structures for compatibility. Remove unit tests (will move to runtests.jl) * Integrate Optimal Filter to ParticleDA - Added unit tests and validation tests - Made changes to model interface to expose fields needed by optimal filter - Added a OptimalFilter type for dispatching - No implementation of run_particle_filter yet * Apply suggestions from code review Co-authored-by: Mosè Giordano * Draft implementation * Changes suggested by review Changing rand(rng,nd) to randn(rng) causes validation test to fail unless it's done on both sides. Unclear why. * Implementation according to comment on 5 Feb in #136 * Add compat entry for FFTW * Change to a more sensible test height field * Make grid size nx (not nx+1) on both ParticleDA and OptimalFilter. Something goes wrong. * Correct dx,dy in covariance calculations. tests pass. * Fix bugs * Apply suggestions from code review Co-authored-by: Mosè Giordano * Apply suggestions from code review In two parts because I didn't realize github doesn't automatically load a large diff even when there are comments. Co-authored-by: Mosè Giordano * Define model grid as storing values at the nodes (instead of cell faces) The only change required is defining dx as L_x/(nx-1) instead of L_x/nx In my opinion this is more consistent with the way we define the stations Makes it easier (or perhaps even possible) to integrate with the optimal filter Also fixed a bug in write_stations that created an Int dataset on the hdf5 file for the coordinate (float) value Reference data and some tests had to be updated * Pass grid parameters instead of using model_params * Fix bugs * Minor improvements - Parametric types in init_filter - Comments - Indentations * Fix arguments to init_*line_matrices * Use sigma and lambda from model params instead of redefining them in filter. * update notebook with animation and parameters * Point out bootstrap filter in example * add FFTW to benchmark environment * Pass filter type to run_particle_filter and use it to dispatch (#155) * Pass filter type to run_particle_filter and use it to dispatch appropriate functions * Update to simpler syntax * Update benchmarks and the benchmark environment Co-authored-by: Mosè Giordano * Split get_grid_size into three functions (#157) * Split get_grid_size into three functions that return NTuples * Remove extra parenthesis * Clarify function names * Changes suggested by review - Define Grid in OptimalFilter - Annotate argument types - Fix runtests.jl - Fix docstrings * Add integration test with optimal filter * Add input file for the test * Precompute FFTW plan (#159) * Precompute FFTW plan * Support in-place and out-of-place FFTs * Reduce duplication in `normalized_2d_fft!` methods * Force A to be hermitian to avoid roundoff errors Co-authored-by: Mosè Giordano * Throw error if matrix is not approximately Hermitian * clean up * Pass RNG directly to the filter instead of the model Also, use the RNG also in the `resample!` function. * Reduce allocations in `sample_height_proposal!` (#162) Co-authored-by: Mosè Giordano Co-authored-by: Mosè Giordano --- .github/workflows/benchmark.yml | 2 +- Project.toml | 5 + benchmark/Manifest.toml | 43 +- benchmark/Project.toml | 2 + benchmark/benchmarks.jl | 17 +- docs/src/index.md | 4 +- extra/Plot_tdac_output.ipynb | 105 +++- src/OptimalFilter.jl | 412 +++++++++++++ src/ParticleDA.jl | 181 ++++-- src/params.jl | 3 + test/Project.toml | 3 +- test/model/model.jl | 43 +- test/optimal_filter_test_1.yaml | 10 + test/optimal_filter_validation.jl | 900 ++++++++++++++++++++++++++++ test/optimal_filter_validation.yaml | 14 + test/reference_data.h5 | Bin 1086144 -> 1333016 bytes test/runtests.jl | 161 ++++- test/update_reference_data.jl | 9 +- 18 files changed, 1801 insertions(+), 113 deletions(-) create mode 100644 src/OptimalFilter.jl create mode 100644 test/optimal_filter_test_1.yaml create mode 100644 test/optimal_filter_validation.jl create mode 100644 test/optimal_filter_validation.yaml diff --git a/.github/workflows/benchmark.yml b/.github/workflows/benchmark.yml index 816b71f1..22ace1b1 100644 --- a/.github/workflows/benchmark.yml +++ b/.github/workflows/benchmark.yml @@ -28,7 +28,7 @@ jobs: env = Dict( "JULIA_NUM_THREADS" => "2", ), - ) + ), ) - name: Print judgement shell: julia --color=yes {0} diff --git a/Project.toml b/Project.toml index 7c56205b..6be5c994 100644 --- a/Project.toml +++ b/Project.toml @@ -5,9 +5,13 @@ version = "0.1.0" [deps] Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f" +FFTW = "7a1cc6ca-52ef-59f5-83cd-3a7055c09341" +Future = "9fa8497b-333b-5362-9e8d-4d0656e87820" HDF5 = "f67ccb44-e63f-5c2f-98bd-6dc0ccc4ba2f" LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e" MPI = "da04e1cc-30fd-572f-bb4f-1f8673147195" +Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c" +SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf" Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2" TimerOutputs = "a759f4b9-e2f1-59dc-863e-4aeb61b1ea8f" YAML = "ddb6d928-2868-570f-bddf-ab3f9cf99eb6" @@ -18,4 +22,5 @@ HDF5 = "0.14, 0.15" MPI = "0.16" TimerOutputs = "0.5" YAML = "0.4" +FFTW = "1" julia = "1.5" diff --git a/benchmark/Manifest.toml b/benchmark/Manifest.toml index 568fde15..eb925c8b 100644 --- a/benchmark/Manifest.toml +++ b/benchmark/Manifest.toml @@ -2,15 +2,14 @@ [[AbstractFFTs]] deps = ["LinearAlgebra"] -git-tree-sha1 = "8ed9de2f1b1a9b1dee48582ad477c6e67b83eb2c" +git-tree-sha1 = "485ee0867925449198280d4af84bdb46a2a404d0" uuid = "621f4979-c628-5d54-868e-fcf4e3e8185c" -version = "1.0.0" +version = "1.0.1" [[AbstractTrees]] -deps = ["Markdown"] -git-tree-sha1 = "33e450545eaf7699da1a6e755f9ea65f14077a45" +git-tree-sha1 = "03e0550477d86222521d254b741d470ba17ea0b5" uuid = "1520ce14-60c1-5f80-bbc7-55ef81b5835c" -version = "0.3.3" +version = "0.3.4" [[ArgTools]] uuid = "0dad84c5-d112-42e6-8d28-ef12dabb789f" @@ -110,9 +109,9 @@ uuid = "8ba89e20-285c-5b6f-9357-94700520ee1b" [[Distributions]] deps = ["FillArrays", "LinearAlgebra", "PDMats", "Printf", "QuadGK", "Random", "SparseArrays", "SpecialFunctions", "Statistics", "StatsBase", "StatsFuns"] -git-tree-sha1 = "0fc424e725eaec6ea3e9fa8df773bee18a1ab503" +git-tree-sha1 = "e64debe8cd174cc52d7dd617ebc5492c6f8b698c" uuid = "31c24e10-a181-5473-b8eb-7969acd0382f" -version = "0.24.14" +version = "0.24.15" [[DocStringExtensions]] deps = ["LibGit2", "Markdown", "Pkg", "Test"] @@ -144,9 +143,9 @@ version = "0.4.7" [[FillArrays]] deps = ["LinearAlgebra", "Random", "SparseArrays"] -git-tree-sha1 = "4705cc4e212c3c978c60b1b18118ec49b4d731fd" +git-tree-sha1 = "dd4ab4257c257532003eb9836eea07473fcc732e" uuid = "1a297f60-69ca-5386-bcde-b61e274b549b" -version = "0.11.5" +version = "0.11.6" [[Future]] deps = ["Random"] @@ -338,25 +337,25 @@ uuid = "bac558e1-5e72-5ebc-8fee-abe8a469f55d" version = "1.4.0" [[PDMats]] -deps = ["LinearAlgebra", "SparseArrays", "SuiteSparse", "Test"] -git-tree-sha1 = "95a4038d1011dfdbde7cecd2ad0ac411e53ab1bc" +deps = ["LinearAlgebra", "SparseArrays", "SuiteSparse"] +git-tree-sha1 = "f82a0e71f222199de8e9eb9a09977bd0767d52a0" uuid = "90014a1f-27ba-587c-ab20-58faa44d9150" -version = "0.10.1" +version = "0.11.0" [[Parsers]] deps = ["Dates"] -git-tree-sha1 = "50c9a9ed8c714945e01cd53a21007ed3865ed714" +git-tree-sha1 = "223a825cccef2228f3fdbf2ecc7ca93363059073" uuid = "69de0a69-1ddd-5017-9359-2bf0b02dc9f0" -version = "1.0.15" +version = "1.0.16" [[ParticleDA]] -deps = ["Distributions", "HDF5", "LinearAlgebra", "MPI", "Statistics", "TimerOutputs", "YAML"] +deps = ["Distributions", "FFTW", "Future", "HDF5", "LinearAlgebra", "MPI", "Random", "SparseArrays", "Statistics", "TimerOutputs", "YAML"] path = ".." uuid = "61cd1fb4-f4c4-4bc8-80c6-ea5639a6ca2e" version = "0.1.0" [[Pkg]] -deps = ["Artifacts", "Dates", "Downloads", "LibGit2", "Libdl", "Logging", "Markdown", "Printf", "REPL", "Random", "SHA", "Serialization", "TOML", "Tar", "UUIDs"] +deps = ["Artifacts", "Dates", "Downloads", "LibGit2", "Libdl", "Logging", "Markdown", "Printf", "REPL", "Random", "SHA", "Serialization", "TOML", "Tar", "UUIDs", "p7zip_jll"] uuid = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f" [[PkgBenchmark]] @@ -401,9 +400,9 @@ version = "1.0.0" [[Requires]] deps = ["UUIDs"] -git-tree-sha1 = "cfbac6c1ed70c002ec6361e7fd334f02820d6419" +git-tree-sha1 = "4036a3bd08ac7e968e27c203d45f5fff15020621" uuid = "ae029012-a4dd-5104-9daa-d747884805df" -version = "1.1.2" +version = "1.1.3" [[Rmath]] deps = ["Random", "Rmath_jll"] @@ -510,9 +509,9 @@ uuid = "8dfed614-e22c-5e08-85e1-65c5234f0b40" [[TimerOutputs]] deps = ["Printf"] -git-tree-sha1 = "3318281dd4121ecf9713ce1383b9ace7d7476fdd" +git-tree-sha1 = "32cdbe6cd2d214c25a0b88f985c9e0092877c236" uuid = "a759f4b9-e2f1-59dc-863e-4aeb61b1ea8f" -version = "0.5.7" +version = "0.5.8" [[URIs]] git-tree-sha1 = "7855809b88d7b16e9b029afd17880930626f54a2" @@ -556,3 +555,7 @@ version = "1.0.18+1" [[nghttp2_jll]] deps = ["Artifacts", "Libdl"] uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d" + +[[p7zip_jll]] +deps = ["Artifacts", "Libdl"] +uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0" diff --git a/benchmark/Project.toml b/benchmark/Project.toml index 5597b883..77745169 100644 --- a/benchmark/Project.toml +++ b/benchmark/Project.toml @@ -3,6 +3,7 @@ BenchmarkCI = "20533458-34a3-403d-a444-e18f38190b5b" BenchmarkTools = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf" DelimitedFiles = "8bb1440f-4735-579b-a4ab-409b98df4dab" Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f" +FFTW = "7a1cc6ca-52ef-59f5-83cd-3a7055c09341" Future = "9fa8497b-333b-5362-9e8d-4d0656e87820" GaussianRandomFields = "e4b2fa32-6e09-5554-b718-106ed5adafe9" HDF5 = "f67ccb44-e63f-5c2f-98bd-6dc0ccc4ba2f" @@ -15,6 +16,7 @@ StableRNGs = "860ef19b-820b-49d6-a774-d7a799459cd3" [compat] BenchmarkCI = "0.1" BenchmarkTools = "0.5" +FFTW = "1" GaussianRandomFields = "2.1.1" MPI = "0.16" PkgBenchmark = "0.2.10" diff --git a/benchmark/benchmarks.jl b/benchmark/benchmarks.jl index b5a7e483..f208cd6e 100644 --- a/benchmark/benchmarks.jl +++ b/benchmark/benchmarks.jl @@ -1,6 +1,9 @@ using BenchmarkTools using ParticleDA using MPI +using Random +using Future +using Base.Threads include(joinpath(joinpath(@__DIR__, "..", "test"), "model", "model.jl")) using .Model @@ -15,6 +18,7 @@ const my_size = MPI.Comm_size(MPI.COMM_WORLD) SUITE["base"] = BenchmarkGroup() SUITE["BootstrapFilter"] = BenchmarkGroup() +SUITE["OptimalFilter"] = BenchmarkGroup() const params = Dict( "filter" => Dict( @@ -34,8 +38,12 @@ const params = Dict( ) const nprt_per_rank = Int(params["filter"]["nprt"] / my_size) -const model_data = Model.init(params["model"]["llw2d"], nprt_per_rank, my_rank) -const bootstrap_filter_data = ParticleDA.init_filter(ParticleDA.get_params(ParticleDA.FilterParameters, params["filter"]), model_data, nprt_per_rank, Float64) +const rng = let + m = Random.default_rng() + [m; accumulate(Future.randjump, fill(big(10)^20, nthreads()-1), init=m)] +end +const model_data = Model.init(params["model"]["llw2d"], nprt_per_rank, my_rank, rng) +const bootstrap_filter_data = ParticleDA.init_filter(ParticleDA.get_params(ParticleDA.FilterParameters, params["filter"]), model_data, nprt_per_rank, rng, Float64, BootstrapFilter()) const filter_params = ParticleDA.get_params(ParticleDA.FilterParameters, params["filter"]) SUITE["base"]["get_particles"] = @benchmarkable ParticleDA.get_particles($(model_data)) @@ -48,5 +56,8 @@ SUITE["base"]["normalized_exp!"] = @benchmarkable ParticleDA.normalized_exp!(wei SUITE["base"]["resample!"] = @benchmarkable ParticleDA.resample!(resampling_indices, weights) setup=(resampling_indices = Vector{Int}(undef, filter_params.nprt); weights = rand(filter_params.nprt)) # SUITE["base"]["copy_states!"] = @benchmarkable ParticleDA.copy_states!($(ParticleDA.get_particles(model_data)), $(bootstrap_filter_data.copy_buffer), $(bootstrap_filter_data.resampling_indices), $(my_rank), $(nprt_per_rank)) -SUITE["BootstrapFilter"]["init_filter"] = @benchmarkable ParticleDA.init_filter($(filter_params), $(model_data), $(nprt_per_rank), Float64) +SUITE["BootstrapFilter"]["init_filter"] = @benchmarkable ParticleDA.init_filter($(filter_params), $(model_data), $(nprt_per_rank), $(rng), Float64, $(BootstrapFilter())) SUITE["BootstrapFilter"]["run_particle_filter"] = @benchmarkable ParticleDA.run_particle_filter($(Model.init), $(params), $(BootstrapFilter())) seconds=30 setup=(cd(mktempdir())) + +SUITE["OptimalFilter"]["init_filter"] = @benchmarkable ParticleDA.init_filter($(filter_params), $(model_data), $(nprt_per_rank), $(rng), Float64, $(OptimalFilter())) +SUITE["OptimalFilter"]["run_particle_filter"] = @benchmarkable ParticleDA.run_particle_filter($(Model.init), $(params), $(OptimalFilter())) seconds=30 setup=(cd(mktempdir())) diff --git a/docs/src/index.md b/docs/src/index.md index ac83c58a..f0416cad 100644 --- a/docs/src/index.md +++ b/docs/src/index.md @@ -99,7 +99,7 @@ The particle filter parameters are saved in the following data structure: ParticleDA.FilterParameters ``` -## Example: tsunami modelling +## Example: tsunami modelling with the bootstrap filter A full example of a model interfacing `ParticleDA` is available in `test/model/model.jl`. This model represents a tsunami and is partly based on @@ -124,7 +124,7 @@ Pkg.instantiate() include(module_src) using .Model -# Run the particle filter using the `init` file defined in the `Model` module +# Run the particle filter using the `init` file defined in the `Model` module. run_particle_filter(Model.init, input_file, BootstrapFilter()) ``` diff --git a/extra/Plot_tdac_output.ipynb b/extra/Plot_tdac_output.ipynb index c2a37731..3c1c2f4f 100644 --- a/extra/Plot_tdac_output.ipynb +++ b/extra/Plot_tdac_output.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "code", - "execution_count": 2, + "execution_count": null, "metadata": {}, "outputs": [], "source": [ @@ -21,21 +21,11 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": null, "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "The following datasets found in file ../tdac.h5 : ['data_avg', 'data_syn', 'data_var', 'grid', 'params', 'stations', 'timer', 'weights']\n", - "The following timestamps found: ['t0', 't1', 't10', 't11', 't12', 't13', 't14', 't15', 't16', 't17', 't18', 't19', 't2', 't20', 't3', 't4', 't5', 't6', 't7', 't8', 't9']\n", - "The following fields found: ['height', 'vx', 'vy']\n" - ] - } - ], - "source": [ - "filename = \"../tdac.h5\"\n", + "outputs": [], + "source": [ + "filename = \"../particle_da.h5\"\n", "fh = h5py.File(filename,'r')\n", "print(\"The following datasets found in file\",filename,\":\",list(fh))\n", "if \"data_syn\" in list(fh): print(\"The following timestamps found: \", list(fh[\"data_syn\"]))\n", @@ -103,7 +93,9 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "scrolled": false + }, "outputs": [], "source": [ "plt.rcParams[\"figure.figsize\"] = (18,6)\n", @@ -128,7 +120,7 @@ " a.scatter(x_st, y_st, color = 'r', marker = '*')\n", " a.set_xlabel(f\"x [{y.units:~}]\")\n", " a.set_ylabel(f\"y [{x.units:~}]\")\n", - " plt.colorbar(im,ax=a)" + " fig.colorbar(im,ax=a)" ] }, { @@ -178,6 +170,83 @@ "plt.xlabel('Time step')\n", "plt.ylabel('Estimated Sample Size (1 / sum(weight^2))');" ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Animation" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "from matplotlib import animation\n", + "\n", + "plt.rcParams[\"figure.figsize\"] = (18,6)\n", + "\n", + "n_contours = 100\n", + "\n", + "fig, ax = plt.subplots(1,3)\n", + "ax[0].set_title(f\"True {field_desc.lower()} [{z_t.units:~}]\")\n", + "ax[1].set_title(f\"Assimilated {field_desc.lower()} [{z_avg.units:~}]\")\n", + "ax[2].set_title(f\"Std of assimilated {field_desc.lower()} [{z_std.units:~}]\")\n", + "\n", + "cb = []\n", + "\n", + "def animate(i):\n", + " \n", + " for a in ax:\n", + " for c in a.collections:\n", + " c.remove()\n", + " \n", + " timestamp = f\"t{i}\"\n", + " z_t = fh[\"data_syn\"][timestamp][field][()] * ureg(field_unit)\n", + " z_avg = fh[\"data_avg\"][timestamp][field][()] * ureg(field_unit)\n", + " z_var = fh[\"data_var\"][timestamp][field][()] * ureg(var_unit)\n", + " z_std = np.sqrt(z_var)\n", + " \n", + " zmax = max(np.max(z_t), np.max(z_avg)).magnitude\n", + " zmin = min(np.min(z_t), np.min(z_avg)).magnitude\n", + " levels = np.linspace(zmin, zmax, n_contours) \n", + " \n", + " i1 = ax[0].contourf(x,y,z_t,levels)\n", + " i2 = ax[1].contourf(x,y,z_avg,levels)\n", + " i3 = ax[2].contourf(x,y,z_std,n_contours)\n", + " \n", + " images = [i1, i2, i3]\n", + " \n", + " for a,im in zip(ax,images):\n", + " a.scatter(x_st, y_st, color = 'r', marker = '*')\n", + " a.set_xlabel(f\"x [{y.units:~}]\")\n", + " a.set_ylabel(f\"y [{x.units:~}]\")\n", + " #if len(cb) < 3:\n", + " # cb.append(plt.colorbar(im, ax=a))\n", + " #else:\n", + " # for c in cb:\n", + " # c.update_normal(im)\n", + " \n", + " return images\n", + " \n", + "anim = animation.FuncAnimation(fig, animate, frames=50)\n", + "anim.save(\"animation.mp4\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "for key in fh[\"params\"].attrs:\n", + " try:\n", + " print(key, ':', fh[\"params\"].attrs[key])\n", + " except TypeError:\n", + " print(key, ':', 'N/A')" + ] } ], "metadata": { @@ -196,7 +265,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.7.7" + "version": "3.8.7" } }, "nbformat": 4, diff --git a/src/OptimalFilter.jl b/src/OptimalFilter.jl new file mode 100644 index 00000000..de540674 --- /dev/null +++ b/src/OptimalFilter.jl @@ -0,0 +1,412 @@ +using FFTW +using LinearAlgebra +using SparseArrays +using Random +using Distributions + +struct OfflineMatrices{T<:AbstractArray, S<:AbstractArray, U<:AbstractArray} + + rho_bar::S + R12::T + R21_bar::T + R22::T # Covariance between observation stations + R22_inv::T # Inverse of R22 + R12_invR22::T + Lambda::S + K::U + L::T + mu20::T + + buf1::T + buf2::T + +end + + +struct OnlineMatrices{T<:AbstractVector, S<:AbstractArray, U<:AbstractArray} + + z1_bar::T + z2::T + + Z1::S + Z2::S + + samples::U + mean::U + +end + +struct Grid{T} + nx::Int + ny::Int + dx::T + dy::T + x_length::T + y_length::T +end + +# Covariance function r(x,y), equation 1 in Dietrich and Newsam 96 +function covariance(x::T, y::T, noise_params::NamedTuple) where T + + return noise_params.sigma^2 * exp(-(abs(x) + abs(y))/(2 * noise_params.lambda)) + +end + +# Extended covariance function /bar r(x,y), equation 8 of Dietrich and Newsam 96 +function extended_covariance(x::T, y::T, grid::Grid, noise_params::NamedTuple) where T + + if 0 <= x <= grid.x_length + x_ext = x + elseif grid.x_length <= x <= 2 * grid.x_length + x_ext = 2 * grid.x_length - x + else + @error "value of x is out of bounds" + end + + if 0 <= y <= grid.y_length + y_ext = y + elseif grid.y_length <= y <= 2 * grid.y_length + y_ext = 2 * grid.y_length - y + else + @error "value of y is out of bounds" + end + + return covariance(x_ext, y_ext, noise_params) + +end + +# Covariance between observations and the extended grid /bar R_21, from equation 11 in Dietrich & Newsam 96 +function covariance_stations_extended_grid!(cov::AbstractMatrix{T}, grid::Grid, grid_ext::Grid, stations::NamedTuple, noise_params::NamedTuple) where T + + xid = 1:grid_ext.nx + yid = 1:grid_ext.ny + + c = CartesianIndices((xid, yid))[:] + + @assert size(cov) == (stations.nst, length(c)) + + for (i,ist,jst) in zip(1:stations.nst, stations.ist, stations.jst) + cov[i,:] .= extended_covariance.(abs.(getindex.(c, 1) .- ist) .* grid_ext.dx, + abs.(getindex.(c, 2) .- jst) .* grid_ext.dy, + (grid,), (noise_params,)) + end + +end + +# Covariance between stations and the original grid R_21, from equations 3-4 in Dietrich & Newsam 96 +function covariance_grid_stations!(cov::AbstractMatrix{T}, grid::Grid, stations::NamedTuple, noise_params::NamedTuple) where T + + xid = 1:grid.nx + yid = 1:grid.ny + + c = CartesianIndices((xid, yid))[:] + + @assert size(cov) == (length(c), stations.nst) + + for (i,ist,jst) in zip(1:stations.nst, stations.ist, stations.jst) + cov[:,i] .= extended_covariance.(abs.(getindex.(c, 1) .- ist) .* grid.dx, + abs.(getindex.(c, 2) .- jst) .* grid.dy, + (grid,), (noise_params,)) + end + +end + +# Covariance between observations R_22, from equationd 3-4 in in Dietrich & Newsam 96 +# TODO: Ask Alex why we add sigma^2 on the diagonal +function covariance_stations!(cov::AbstractMatrix{T}, grid::Grid, stations::NamedTuple, noise_params::NamedTuple, std::T) where T + + cov .= covariance.(abs.(stations.ist .- stations.ist') .* grid.dx, + abs.(stations.jst' .- stations.jst) .* grid.dy, + (noise_params,)) .+ I(stations.nst) .* std.^2 + +end + +# First column vector rho_bar of covariance matrix among pairs of points of the extended grid R11_bar, +# from Dietrich & Newsam 96 described in text between equations 11 and 12 +function first_column_covariance_grid!(rho::AbstractVector{T}, grid::Grid, grid_ext::Grid, noise_params::NamedTuple) where T + + xid = 1:grid_ext.nx + yid = 1:grid_ext.ny + + c = CartesianIndices((xid, yid))[:] + + rho .= extended_covariance.((getindex.(c, 1) .- 1) .* grid_ext.dx, + (getindex.(c, 2) .- 1) .* grid_ext.dy, + (grid,), (noise_params,)) + + +end + +# Normalized two-dimension discrete Fourier transofrm normalized by sqrt(n1_bar). +# Operates on the 2d data stored as a matrix. +# The argument `f` lets you switch between forward transform (`f=identity`) and +# inverse transform (`f=inv`). +# From Dietrich & Newsam 96 in text following equation 12 +function normalized_2d_fft!(transformed_array::AbstractMatrix{<:Complex}, array::AbstractMatrix{S}, fft_plan::FFTW.FFTWPlan, fft_plan!::FFTW.FFTWPlan, grid_ext, f=identity) where {S} + + normalization_factor = f(sqrt(grid_ext.nx * grid_ext.ny)) + if pointer(transformed_array) == pointer(array) + mul!(transformed_array, f(fft_plan!), array) + else + mul!(transformed_array, f(fft_plan), array) + end + transformed_array ./= normalization_factor + +end + +# Normalized two-dimension discrete Fourier transofrm normalized by sqrt(n1_bar). +# Operates on the 2d data stored as a vector. +# The argument `f` lets you switch between forward transform (`f=identity`) and +# inverse transform (`f=inv`). +# From Dietrich & Newsam 96 in text following equation 12 +function normalized_2d_fft!(transformed_vector::AbstractVector{<:Complex}, vector::AbstractVector{S}, fft_plan::FFTW.FFTWPlan, fft_plan!::FFTW.FFTWPlan, grid_ext, f=identity) where {S} + + normalization_factor = f(sqrt(grid_ext.nx * grid_ext.ny)) + tmp_array = complex(reshape(vector, grid_ext.nx, grid_ext.ny)) + mul!(tmp_array, f(fft_plan!), tmp_array) + transformed_vector .= @view(tmp_array[:]) ./ normalization_factor + +end + +# Decomposition of R11, equation 12 of Deitrich and Newsam +function WΛWH_decomposition!(transformed_array::AbstractMatrix{T}, + array::AbstractMatrix{T}, + offline_matrices::OfflineMatrices, + grid::Grid, + grid_ext::Grid, + fft_plan::FFTW.FFTWPlan, + fft_plan!::FFTW.FFTWPlan, + ) where T + + @assert size(array) == (grid.nx, grid.ny) + + extended_array = zeros(ComplexF64, grid_ext.nx, grid_ext.ny) + + extended_array[1:grid.nx, 1:grid.ny] .= array + + normalized_2d_fft!(extended_array, extended_array, fft_plan, fft_plan!, grid_ext) + + # Here we do an element-wise multiplication of the extended_array with the vector Lambda. This is identical to + # Diagonal(Lambda) * extended_array[:], but avoids flattening and reshaping extended_array. + normalized_2d_fft!(extended_array, reshape(offline_matrices.Lambda, grid_ext.nx, grid_ext.ny).*extended_array, fft_plan, fft_plan!, grid_ext, inv) + + transformed_array .= real.(@view(extended_array[1:grid.nx, 1:grid.ny])) + +end + +# Get a vector of values of field at positions of [stations.ist, stations.jst] +function get_values_at_stations(field::AbstractMatrix{T}, stations) where T + + values = zeros(T, length(stations.ist)) + + for (num,(i,j)) in enumerate(zip(stations.ist, stations.jst)) + values[num] = field[i,j] + end + + return values + +end + +# Allocate and compute matrices that do not depend on time-dependent variables (height and observations). +function init_offline_matrices(grid::Grid, + grid_ext::Grid, + stations::NamedTuple, + noise_params::NamedTuple, + obs_noise_std::T, + fft_plan::FFTW.FFTWPlan, + fft_plan!::FFTW.FFTWPlan, + F::Type, + ) where T + + n1 = grid.nx * grid.ny # number of elements in original grid + n1_bar = grid_ext.nx * grid_ext.ny # number of elements in extended grid + + C = complex(F) + + matrices = OfflineMatrices(Vector{F}(undef, n1_bar), #rho_bar + Matrix{F}(undef, n1, stations.nst), #R12 + Matrix{F}(undef, stations.nst, n1_bar), #R21_bar + Matrix{F}(undef, stations.nst, stations.nst), #R22 + Matrix{F}(undef, stations.nst, stations.nst), #R22_inv + Matrix{F}(undef, n1, stations.nst), #R12_invR22 + Vector{F}(undef, n1_bar), #Lambda (diagonal elements) + Matrix{C}(undef, stations.nst, n1_bar), #K + Matrix{F}(undef, stations.nst, stations.nst), #L + Matrix{F}(undef, stations.nst, stations.nst), #mu20 + + Matrix{F}(undef, grid.nx, grid.ny), #buf1 + Matrix{F}(undef, grid.nx, grid.ny) #buf2 + ) + + first_column_covariance_grid!(matrices.rho_bar, grid, grid_ext, noise_params) + covariance_grid_stations!(matrices.R12, grid, stations, noise_params) + covariance_stations_extended_grid!(matrices.R21_bar, grid, grid_ext, stations, noise_params) + covariance_stations!(matrices.R22, grid, stations, noise_params, obs_noise_std) + matrices.R22_inv .= inv(matrices.R22) + matrices.R12_invR22 .= matrices.R12 * matrices.R22_inv + + fourier_coeffs = Vector{C}(undef, n1_bar) + normalized_2d_fft!(fourier_coeffs, matrices.rho_bar, fft_plan, fft_plan!, grid_ext, inv) + matrices.Lambda .= sqrt(n1_bar) .* real.(fourier_coeffs) + + WHbar_R12 = Matrix{C}(undef, n1_bar, stations.nst) + for i in 1:stations.nst + normalized_2d_fft!(@view(WHbar_R12[:,i]), @view(matrices.R21_bar[i,:]), fft_plan, fft_plan!, grid_ext) + end + KH = Diagonal(matrices.Lambda)^(-1/2)*WHbar_R12 + matrices.K .= KH' + + A = real.(matrices.R22 .- matrices.K*KH) + + if A ≈ Hermitian(A) + matrices.L .= cholesky(Hermitian(A)).L + else + error("R22 - K*KH is not hermitian! Increasing the grid size may help. See Dietrich and Newsam '96 for details.") + end + + matrices.mu20 .= obs_noise_std^(-2) .* (matrices.R22 .- I(stations.nst) .* obs_noise_std^2) + + return matrices + +end + +# Allocate memory for matrices that will be updated during the time stepping loop. +function init_online_matrices(grid::Grid, grid_ext::Grid, stations::NamedTuple, filter_params, T::Type) + + n1 = grid.nx * grid.ny # number of elements in original grid + n1_bar = grid_ext.nx * grid_ext.ny # number of elements in extended grid + + C = complex(T) + + matrices = OnlineMatrices(Vector{C}(undef, n1_bar), + Vector{C}(undef, stations.nst), + Matrix{C}(undef, grid.nx, grid.ny), + Matrix{C}(undef, grid.nx, grid.ny), + Array{T}(undef, grid.nx, grid.ny, filter_params.nprt), + Array{T}(undef, grid.nx, grid.ny, filter_params.nprt) + ) + + return matrices + + +end + +# Calculate the mean for the optimal proposal of the height +function calculate_mean_height!(mean::AbstractArray{T,3}, + height::AbstractArray{T,3}, + offline_matrices::OfflineMatrices, + observations::AbstractVector{T}, + stations::NamedTuple, + grid::Grid, + grid_ext::Grid, + fft_plan::FFTW.FFTWPlan, + fft_plan!::FFTW.FFTWPlan, + filter_params, + obs_noise_std::T, + ) where T + + # The arguments for the WΛWH decompositions are matrices that only have nonzero values + # at the indices of the stations. Store them as sparse arrays to save space. + mu21 = sparse(stations.ist, stations.jst, + offline_matrices.R22_inv * (offline_matrices.mu20 * observations), + grid.nx, grid.ny) + mu22 = obs_noise_std^(-2) * sparse(stations.ist, stations.jst, observations, grid.nx, grid.ny) + + # Compute WΛWH decompositions, results are dense matrices, store them in buffers + # These correspond to mu21 and mu22 in Alex's code + WΛWH_decomposition!(offline_matrices.buf1, mu21, offline_matrices, grid, grid_ext, fft_plan, fft_plan!) + WΛWH_decomposition!(offline_matrices.buf2, mu22, offline_matrices, grid, grid_ext, fft_plan, fft_plan!) + + # Compute the difference of the decomposition results, store in offline_matrices.buf1 + # This corresponds to mu2 in Alex's code. + # TODO: Check if WΛWH is linear and you could swap the order + offline_matrices.buf2 .-= offline_matrices.buf1 + + mu10 = Vector{T}(undef, stations.nst) + + # Loop over particles + for iprt = 1:filter_params.nprt + + mul!(mu10, offline_matrices.R22_inv, get_values_at_stations(@view(height[:,:,iprt]), stations)) + mu10_sparse = sparse(stations.ist, stations.jst, mu10, grid.nx, grid.ny) + + # Compute decomposition of height values at stations times the inverse covariance matrix + # The argument corresponds to mu10 and the outcome to mu11 in Alex's code + WΛWH_decomposition!(offline_matrices.buf1, mu10_sparse, offline_matrices, grid, grid_ext, fft_plan, fft_plan!) + + # Compute the mean for the ith particle using mu2 and mu11 + # Skip storing the temporary mu1 in Alex's code + mean[:,:,iprt] .= @view(height[:,:,iprt]) .- offline_matrices.buf1 .+ offline_matrices.buf2 + + end + +end + +function sample_height_proposal!(height::AbstractArray{T,3}, + offline_matrices::OfflineMatrices, + online_matrices::OnlineMatrices, + observations::AbstractVector{T}, + stations::NamedTuple, + grid::Grid, + grid_ext::Grid, + fft_plan::FFTW.FFTWPlan, + fft_plan!::FFTW.FFTWPlan, + filter_params, + rng::Random.AbstractRNG, + obs_noise_std::T, + ) where T + + @assert iseven(filter_params.nprt) "Number of particles must be even" + + calculate_mean_height!(online_matrices.mean, height, offline_matrices, observations, stations, grid, grid_ext, fft_plan, fft_plan!, filter_params, obs_noise_std) + + i_n1 = LinearIndices((grid.nx, grid.ny)) + i_n1_bar = LinearIndices((grid_ext.nx, grid_ext.ny)) + + e1 = Vector{ComplexF64}(undef, grid_ext.nx * grid_ext.ny) + e2 = Vector{ComplexF64}(undef, stations.nst) + + for iprt in 1:2:filter_params.nprt + + @. e1 = complex(randn(rng), randn(rng)) + @. e2 = complex(randn(rng), randn(rng)) + + # This gives the vector z1_bar + normalized_2d_fft!(online_matrices.z1_bar, Diagonal(offline_matrices.Lambda)^(1/2) * e1, fft_plan, fft_plan!, grid_ext, inv) + + # This is the vector z2 + mul!(online_matrices.z2, offline_matrices.K, e1) + mul!(online_matrices.z2, offline_matrices.L, e2, 1, 1) + + # Restrict z1_bar to Omega1 and reshape into an array + online_matrices.Z1 .= online_matrices.z1_bar[i_n1_bar[1:grid.nx,1:grid.nx]] + # Multiply z2 with R12*R22^-1 and reshape the result into an array + online_matrices.Z2 .= (offline_matrices.R12_invR22 * online_matrices.z2)[i_n1] + + online_matrices.samples[:,:,iprt ] .= @view(online_matrices.mean[:,:,iprt ]) .+ real.(online_matrices.Z1 .- online_matrices.Z2) + online_matrices.samples[:,:,iprt + 1] .= @view(online_matrices.mean[:,:,iprt + 1]) .+ imag.(online_matrices.Z1 .- online_matrices.Z2) + + end + +end + +function get_log_weights!(log_weights::AbstractVector{T}, + obs::AbstractVector{T}, + obs_model::AbstractMatrix{T}, + matrices::OfflineMatrices) where T + + #TODO: Is this just the same as get_log_weights! in ParticleDA with R22_inv as cov_obs? + # DONE: No, ParticleDA.get_log_weights! fails with + # ERROR: PosDefException: matrix is not Hermitian; Cholesky factorization failed. + + nprt = size(obs_model,2) + + for iprt in 1:nprt + + log_weights[iprt] = -0.5 * (obs - obs_model[:,iprt])' * matrices.R22_inv * (obs - obs_model[:,iprt]) + + end + + #Normalization is done in a separate function due to parallelism optimisation + +end diff --git a/src/ParticleDA.jl b/src/ParticleDA.jl index b2e39cb3..ab3e9b1f 100644 --- a/src/ParticleDA.jl +++ b/src/ParticleDA.jl @@ -1,12 +1,15 @@ module ParticleDA +using Random using Distributions, Statistics, MPI, Base.Threads, YAML, HDF5 using TimerOutputs +import Future -export run_particle_filter, BootstrapFilter +export run_particle_filter, BootstrapFilter, OptimalFilter include("params.jl") include("io.jl") +include("OptimalFilter.jl") using .Default_params @@ -15,9 +18,21 @@ using .Default_params """ ParticleDA.get_grid_size(model_data) -> NTuple{N, Int} where N -Return a tuple with the size of the data. +Return a tuple with the dimensions (number of nodes) of the grid. """ function get_grid_size end +""" + ParticleDA.get_grid_domain_size(model_data) -> NTuple{N, float} where N + +Return a tuple with the dimensions (metres) of the grid domain. +""" +function get_grid_domain_size end +""" + ParticleDA.get_grid_cell_size(model_data) -> NTuple{N, float} where N + +Return a tuple with the dimensions (metres) of a grid cell. +""" +function get_grid_cell_size end """ ParticleDA.get_n_state_var(model_data) -> Int @@ -26,6 +41,20 @@ Return the number of state variables. """ function get_n_state_var end +""" + ParticleDa.get_obs_noise_std(model_data) -> Float + +Return standard deviation of observation noise. Required for optimal filter only. +""" +function get_obs_noise_std end + +""" + ParticleDa.get_model_noise(model_data) -> NamedTuple({:sigma, :lambda, :nu},Tuple{Float, Float, Float}) + +Return standard deviation of observation noise. Required for optimal filter only. +""" +function get_model_noise_params end + """ ParticleDA.get_particle(model_data) -> particles @@ -34,6 +63,14 @@ user with the above signature, specifying the type of `model_data`. """ function get_particles end +""" + ParticleDA.set_particles!(model_data, particles) + +Overwrite particle state in model_data with the vector particles. This method is intended to be extended by the +user with the above signature, specifying the type of `model_data`. +""" +function set_particles! end + """ ParticleDA.get_truth(model_data) -> truth_observations @@ -42,6 +79,16 @@ by the user with the above signature, specifying the type of `model_data`. """ function get_truth end +""" + ParticleDA.get_stations(model_data) -> NamedTuple({:nst,:ist,:jst},Tuple{Int, Array{Float,1}, Array{Float,1}}) + +Return a named tuple with number of stations and their coordinates (nst,ist,jst) of the +points of observation. This method is intended to be extended by the user with the above signature, +specifying the type of `model_data`. +Required for optimal filter only. +""" +function get_stations end + """ ParticleDA.update_truth!(model_data, nprt_per_rank::Int) -> truth_observations @@ -93,6 +140,23 @@ signature, specifying the type of `model_data`. """ function write_snapshot end +""" + ParticleFilter + +Abstract type for the particle filter to use. Currently used subtypes are: +* [`BootstrapFilter`](@ref) +* [`OptimalFilter`](@ref) +""" +abstract type ParticleFilter end +""" + BootstrapFilter() + +Instantiate the singleton type `BootstrapFilter`. This can be used as argument +of [`run_particle_filter`](@ref) to select the bootstrap filter. +""" +struct BootstrapFilter <: ParticleFilter end +struct OptimalFilter <: ParticleFilter end + # Get weights for particles by evaluating the probability of the observations predicted by the model # from independent normal pdfs for each observation. function get_log_weights!(weight::AbstractVector{T}, @@ -133,7 +197,7 @@ function normalized_exp!(weight::AbstractVector) end # Resample particles from given weights using Stochastic Universal Sampling -function resample!(resampled_indices::AbstractVector{Int}, weight::AbstractVector{T}) where T +function resample!(resampled_indices::AbstractVector{Int}, weight::AbstractVector{T}, rng::Random.AbstractRNG=Random.default_rng()) where T nprt = length(weight) nprt_inv = 1.0 / nprt @@ -142,7 +206,7 @@ function resample!(resampled_indices::AbstractVector{Int}, weight::AbstractVecto #TODO: Do we need to sort state by weight here? weight_cdf = cumsum(weight) - u0 = nprt_inv * rand(T) + u0 = nprt_inv * rand(rng, T) # Note: To parallelise this loop, updates to k and u have to be atomic. # TODO: search for better parallel implementations @@ -258,7 +322,7 @@ function copy_states!(particles::AbstractArray{T,4}, end # Initialize arrays used by the filter -function init_filter(filter_params::FilterParameters, model_data, nprt_per_rank::Int, T::Type) +function init_filter(filter_params::FilterParameters, model_data, nprt_per_rank::Int, ::Vector{<:Random.AbstractRNG}, T::Type, ::BootstrapFilter) if MPI.Comm_rank(MPI.COMM_WORLD) == filter_params.master_rank weights = Vector{T}(undef, filter_params.nprt) @@ -278,36 +342,74 @@ function init_filter(filter_params::FilterParameters, model_data, nprt_per_rank: # Memory buffer used during copy of the states copy_buffer = Array{T, length(size) + 2}(undef, size..., n_state_var, nprt_per_rank) - return FilterData(weights, resampling_indices, statistics, avg_arr, var_arr, copy_buffer) + return (;weights, resampling_indices, statistics, avg_arr, var_arr, copy_buffer) end -struct FilterData{T, S, U, V, X} +# Initialize arrays used by the filter +function init_filter(filter_params::FilterParameters, model_data, nprt_per_rank::Int, rng::Vector{<:Random.AbstractRNG}, T::Type, ::OptimalFilter) + + filter_data = init_filter(filter_params, model_data, nprt_per_rank, rng, T, BootstrapFilter()) + + stations = get_stations(model_data) + size = get_grid_size(model_data) + domain_size = get_grid_domain_size(model_data) + cell_size = get_grid_cell_size(model_data) + + grid = Grid(size...,cell_size...,domain_size...) + grid_ext = Grid((grid.nx-1)*2, (grid.ny-1)*2, grid.dx, grid.dy, (grid.x_length-grid.dx)*2, (grid.y_length-grid.dy)*2) + + model_noise_params = get_model_noise_params(model_data) + obs_noise_std = get_obs_noise_std(model_data) + # Precompute two FFT plans, one in-place and the other out-of-place + C = complex(T) + tmp_array = Matrix{C}(undef, grid_ext.nx, grid_ext.ny) + fft_plan, fft_plan! = FFTW.plan_fft(tmp_array), FFTW.plan_fft!(tmp_array) - weights::T - resampling_indices::U - statistics::S - avg_arr::V - var_arr::V - copy_buffer::X + offline_matrices = init_offline_matrices(grid, grid_ext, stations, model_noise_params, obs_noise_std, fft_plan, fft_plan!, T) + online_matrices = init_online_matrices(grid, grid_ext, stations, filter_params, T) + return (; filter_data..., offline_matrices, online_matrices, stations, grid, grid_ext, rng, obs_noise_std, fft_plan, fft_plan!) end -""" - ParticleFilter +function update_particle_proposal!(model_data, filter_data, filter_params, truth_observations, nprt_per_rank, filter_type::BootstrapFilter) -Abstract type for the particle filter to use. Currently used subtypes are: -* [`BootstrapFilter`](@ref) -""" -abstract type ParticleFilter end -""" - BootstrapFilter() + update_particle_noise!(model_data, nprt_per_rank) -Instantiate the singleton type `BootstrapFilter`. This can be used as argument -of [`run_particle_filter`](@ref) to select the bootstrap filter. -""" -struct BootstrapFilter <: ParticleFilter end +end + +function update_particle_proposal!(model_data, filter_data, filter_params, truth_observations, nprt_per_rank, filter_type::OptimalFilter) + + # Optimal Filter: After updating the particle dynamics, we apply the "optimal proposal" in + # sample_height_proposal!() to the first state variable (height). We apply + # a sample from the gaussian random field in update_particle_noise!() to the other + # state variables (velocity). + + particles = get_particles(model_data) + + # Apply optimal proposal, the result will be in offline_matrices.samples + sample_height_proposal!(@view(particles[:,:,1,:]), + filter_data.offline_matrices, + filter_data.online_matrices, + truth_observations, + filter_data.stations, + filter_data.grid, + filter_data.grid_ext, + filter_data.fft_plan, + filter_data.fft_plan!, + filter_params, + filter_data.rng[threadid()], + filter_data.obs_noise_std) + + # Add noise from the standard gaussian random field to all state variables in model_data + update_particle_noise!(model_data, nprt_per_rank) -function run_particle_filter(init, filter_params::FilterParameters, model_params_dict::Dict, ::BootstrapFilter) + # Overwrite the height state variable with the samples of the optimal proposal + particles[:,:,1,:] .= filter_data.online_matrices.samples + set_particles!(model_data, particles) + +end + +function run_particle_filter(init, filter_params::FilterParameters, model_params_dict::Dict, filter_type; rng::Union{Random.AbstractRNG,Nothing}=nothing) if !MPI.Initialized() MPI.Init() @@ -326,11 +428,22 @@ function run_particle_filter(init, filter_params::FilterParameters, model_params end timer = TimerOutput() + nprt_per_rank = Int(filter_params.nprt / MPI.Comm_size(MPI.COMM_WORLD)) + + _rng = let + m = if isnothing(rng) + Random.MersenneTwister(filter_params.random_seed + my_rank) + else + rng + end + [m; accumulate(Future.randjump, fill(big(10)^20, nthreads()-1), init=m)] + end + # Do memory allocations - @timeit_debug timer "Model initialization" model_data = init(model_params_dict, nprt_per_rank, my_rank) + @timeit_debug timer "Model initialization" model_data = init(model_params_dict, nprt_per_rank, my_rank, _rng) # TODO: put the body of this block in a function - @timeit_debug timer "Filter initialization" filter_data = init_filter(filter_params, model_data, nprt_per_rank, Float64) + @timeit_debug timer "Filter initialization" filter_data = init_filter(filter_params, model_data, nprt_per_rank, _rng, Float64, filter_type) @timeit_debug timer "get_particles" particles = get_particles(model_data) @timeit_debug timer "Mean and Var" get_mean_and_var!(filter_data.statistics, particles, filter_params.master_rank) @@ -357,7 +470,7 @@ function run_particle_filter(init, filter_params::FilterParameters, model_params # Parallelised with threads. @timeit_debug timer "Particle Dynamics" update_particle_dynamics!(model_data, nprt_per_rank); - @timeit_debug timer "Particle Noise" update_particle_noise!(model_data, nprt_per_rank) + @timeit_debug timer "Particle Proposal" update_particle_proposal!(model_data, filter_data, filter_params, truth_observations, nprt_per_rank, filter_type) @timeit_debug timer "Particle Observations" model_observations = get_particle_observations!(model_data, nprt_per_rank) @timeit_debug timer "Particle Weights" get_log_weights!(@view(filter_data.weights[1:nprt_per_rank]), @@ -376,7 +489,7 @@ function run_particle_filter(init, filter_params::FilterParameters, model_params filter_params.master_rank, MPI.COMM_WORLD) @timeit_debug timer "Weights" normalized_exp!(filter_data.weights) - @timeit_debug timer "Resample" resample!(filter_data.resampling_indices, filter_data.weights) + @timeit_debug timer "Resample" resample!(filter_data.resampling_indices, filter_data.weights, _rng[threadid()]) else @timeit_debug timer "MPI Gather" MPI.Gather!(filter_data.weights, @@ -477,7 +590,7 @@ Run the particle filter. `init` is the function which initialise the model, `filter_type` is the particle filter to use. See [`ParticleFilter`](@ref) for the possible values. """ -function run_particle_filter(init, path_to_input_file::String, filter_type::ParticleFilter) +function run_particle_filter(init, path_to_input_file::String, filter_type::ParticleFilter; rng::Union{Random.AbstractRNG,Nothing}=nothing) if !MPI.Initialized() MPI.Init() @@ -496,7 +609,7 @@ function run_particle_filter(init, path_to_input_file::String, filter_type::Part user_input_dict = MPI.bcast(user_input_dict, 0, MPI.COMM_WORLD) - return run_particle_filter(init, user_input_dict, filter_type) + return run_particle_filter(init, user_input_dict, filter_type; rng) end @@ -508,12 +621,12 @@ Run the particle filter. `init` is the function which initialise the model, is the particle filter to use. See [`ParticleFilter`](@ref) for the possible values. """ -function run_particle_filter(init, user_input_dict::Dict, filter_type::ParticleFilter) +function run_particle_filter(init, user_input_dict::Dict, filter_type::ParticleFilter; rng::Union{Random.AbstractRNG,Nothing}=nothing) filter_params = get_params(FilterParameters, get(user_input_dict, "filter", Dict())) model_params_dict = get(user_input_dict, "model", Dict()) - return run_particle_filter(init, filter_params, model_params_dict, filter_type) + return run_particle_filter(init, filter_params, model_params_dict, filter_type; rng) end diff --git a/src/params.jl b/src/params.jl index eb7dff33..8fb0d819 100644 --- a/src/params.jl +++ b/src/params.jl @@ -13,6 +13,7 @@ Parameters for ParticleDA run. Keyword arguments: * `output_filename::String` : Name of output file * `nprt::Int` : Number of particles for particle filter * `weight_std`: Standard deviation of the distribution of the weights +* `random_seed::Int` : Seed number for the pseudorandom number generator * `enable_timers::Bool` : Flag to control run time measurements """ Base.@kwdef struct FilterParameters{T<:AbstractFloat} @@ -28,6 +29,8 @@ Base.@kwdef struct FilterParameters{T<:AbstractFloat} weight_std::T = 1.0 + random_seed::Int = 12345 + enable_timers::Bool = false end diff --git a/test/Project.toml b/test/Project.toml index b09a4eee..2674ce31 100644 --- a/test/Project.toml +++ b/test/Project.toml @@ -1,7 +1,7 @@ [deps] DelimitedFiles = "8bb1440f-4735-579b-a4ab-409b98df4dab" Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f" -Future = "9fa8497b-333b-5362-9e8d-4d0656e87820" +FFTW = "7a1cc6ca-52ef-59f5-83cd-3a7055c09341" GaussianRandomFields = "e4b2fa32-6e09-5554-b718-106ed5adafe9" HDF5 = "f67ccb44-e63f-5c2f-98bd-6dc0ccc4ba2f" LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e" @@ -15,6 +15,7 @@ YAML = "ddb6d928-2868-570f-bddf-ab3f9cf99eb6" [compat] Distributions = "0.22, 0.23, 0.24" +FFTW = "1" GaussianRandomFields = "2.1.1" HDF5 = "0.14, 0.15" MPI = "0.16" diff --git a/test/model/model.jl b/test/model/model.jl index d6811bbf..61c4f9aa 100644 --- a/test/model/model.jl +++ b/test/model/model.jl @@ -5,7 +5,6 @@ using ParticleDA using Random, Distributions, Base.Threads, GaussianRandomFields, HDF5 using ParticleDA.Default_params using DelimitedFiles -import Future include("llw2d.jl") using .LLW2d @@ -46,7 +45,6 @@ Parameters for the model. Keyword arguments: * `sigma_initial_state::AbstractFloat` : Marginal standard deviation for Matérn covariance kernel in initial state of particles * `padding::Int` : Min padding for circulant embedding gaussian random field generator * `primes::Int`: Whether the size of the minimum circulant embedding of the covariance matrix can be written as a product of small primes (2, 3, 5 and 7). Default is `true`. -* `random_seed::Int` : Seed number for the pseudorandom number generator * `particle_initial_state::String` : Initial state of the particles before noise is added. Possible options are * "zero" : initialise height and velocity to 0 everywhere * "true" : copy the true initial state @@ -61,16 +59,14 @@ Base.@kwdef struct ModelParameters{T<:AbstractFloat} ny::Int = 200 x_length::T = 400.0e3 y_length::T = 400.0e3 - dx::T = x_length / nx - dy::T = y_length / ny + dx::T = x_length / (nx - 1) + dy::T = y_length / (ny - 1) n_state_var::Int = 3 time_step::T = 50.0 n_integration_step::Int = 50 - random_seed::Int = 12345 - station_filename::String = "" nobs::Int = 4 station_distance_x::T = 20.0e3 @@ -109,7 +105,6 @@ Base.@kwdef struct ModelParameters{T<:AbstractFloat} title_params::String = "params" obs_noise_std::T = 1.0 - end @@ -413,23 +408,29 @@ ParticleDA.get_particles(d::ModelData) = d.states.particles # TODO: we should probably get rid of `get_truth`: it is only used as return # value of `particle_filter`, we may just return the whole `model_data`. ParticleDA.get_truth(d::ModelData) = d.states.truth -ParticleDA.get_grid_size(d::ModelData) = d.model_params.nx, d.model_params.ny +ParticleDA.get_stations(d::ModelData) = (nst = d.model_params.nobs, + ist = d.stations.ist, + jst = d.stations.jst) +ParticleDA.get_obs_noise_std(d::ModelData) = d.model_params.obs_noise_std +ParticleDA.get_model_noise_params(d::ModelData) = (sigma = d.model_params.sigma, + lambda = d.model_params.lambda, + nu = d.model_params.nu) + +function ParticleDA.set_particles!(d::ModelData, particles::AbstractArray{T}) where T + + d.states.particles .= particles + +end +ParticleDA.get_grid_size(d::ModelData) = d.model_params.nx,d.model_params.ny +ParticleDA.get_grid_domain_size(d::ModelData) = d.model_params.x_length,d.model_params.y_length +ParticleDA.get_grid_cell_size(d::ModelData) = d.model_params.dx,d.model_params.dy ParticleDA.get_n_state_var(d::ModelData) = d.model_params.n_state_var -function init(model_params_dict::Dict, nprt_per_rank::Int, my_rank::Integer, _rng::Union{Random.AbstractRNG,Nothing}=nothing) +function init(model_params_dict::Dict, nprt_per_rank::Int, my_rank::Integer, rng::Vector{<:Random.AbstractRNG}) model_params = ParticleDA.get_params(ModelParameters, get(model_params_dict, "llw2d", Dict())) states, observations, stations, field_buffer = init_arrays(model_params, nprt_per_rank) - rng = let - m = if isnothing(_rng) - Random.MersenneTwister(model_params.random_seed + my_rank) - else - _rng - end - [m; accumulate(Future.randjump, fill(big(10)^20, nthreads()-1), init=m)] - end - background_grf = init_gaussian_random_field_generator(model_params) # Set up tsunami model @@ -550,9 +551,9 @@ function write_stations(output_filename, ist::AbstractVector, jst::AbstractVecto if !haskey(file, params.title_stations) group = create_group(file, params.title_stations) - for (dataset_name, index, d) in zip(("x", "y"), (ist, jst), (params.dx, params.dy)) - ds, dtype = create_dataset(group, dataset_name, index) - ds[:] = index .* d + for (dataset_name, val) in zip(("x", "y"), (ist .* params.dx, jst .* params.dy)) + ds, dtype = create_dataset(group, dataset_name, val) + ds[:] = val attributes(ds)["Description"] = "Station coordinates" attributes(ds)["Unit"] = "m" end diff --git a/test/optimal_filter_test_1.yaml b/test/optimal_filter_test_1.yaml new file mode 100644 index 00000000..77bd5384 --- /dev/null +++ b/test/optimal_filter_test_1.yaml @@ -0,0 +1,10 @@ +filter: + nprt: 4 + n_time_step: 20 + +model: + llw2d: + nx: 101 + ny: 101 + nobs: 64 + padding: 0 diff --git a/test/optimal_filter_validation.jl b/test/optimal_filter_validation.jl new file mode 100644 index 00000000..ddbf073c --- /dev/null +++ b/test/optimal_filter_validation.jl @@ -0,0 +1,900 @@ +################################### +### Last Update: 29 Oct 20 +################################### +### ''Simulation of Optimal Proposal'' +### Code follows method/notation in Dietrich & Newsam (96) +################################### + +using Distributions +using LinearAlgebra +using FFTW +using Random + +#################################################################### +#################################################################### + +Random.seed!(123) + +#### Parameters for Covariance Function +struct f_th + s::Float64 + l::Float64 +end + +#### Parameters for Grid +struct f_gr + p::Int ## Number of Grid Points Along x-axis is (p+1) + q::Int ## Number of Grid Points Along y-axis is (q+1) + P::Float64 + Q::Float64 ## 2D-Field is rectangle [0,P]x[0,Q] +end + +#### Parameters for Stations +struct f_st + st_ij::Array{Int64,2} ## the position of the stations on the grid + ## i.e station positions determined using 2 co-ordinates + st_p::Array{Int64,1} ## the no of grid point occupied by each station + ## i.e station positions determined using 1 co-ordinate +end + +#################################################################### +#### Example ####################################################### + +th = f_th(1.0, 1.0) + +gr = f_gr(20, 20, 40.0, 40.0) + +################################################### +#### Example ###################################### + +p = gr.p; q = gr.q; P = gr.P; Q = gr.Q + +Dx = P/p; Dy = Q/q ## Grid Steps Along x and y Directions + +################################################### +#### Example ###################################### + +#### In real case Stations will be read from a file containing co-ordinates; +#### here, I delect position of n2 Stations at random from all grid nodes + +n2 = 3; n1 = (p+1)*(q+1) + +grid_F = fill(0,(n1,2)) + +#### the loop contructs 2-dim co-ordinates for all grid points +for j in 0:q + + for i in 0:p + + grid_F[j*(p+1)+i+1,:] = [i, j] + + end + +end +#### + +st_p = sample(1:n1,n2,replace=false) + +st_ij = grid_F[st_p,:] + +st = f_st(st_ij, st_p) + +################################################### +#### Example ###################################### + +#### I simulate some arbitrary values to be used as observations of height +#### I give an example value to the standard deviation Sobs; +#### I only consider a single time instance + +Yobs_t = rand(Normal(0,1), n2) +#### the ordering in the observations is in tandem with the ordering +#### of the stations in variable st + +Sobs = 0.01 + +################################################### +################################################### + +#### Example Specification of Covariance Function +function R(x::Float64, y::Float64, th) + + Cov = (th.s^2)*exp(-(abs(x)+abs(y))/(2.0*th.l)) + + return(Cov) + +end + +################################################### +################################################### + +#### Specification of 'Extented' Covariance Function +#### following Method/Notation in Dietrich & Newsam (96) +function bar_R(x::Float64, y::Float64, th, gr) + + P = gr.P; Q = gr.Q + + bar_Cov = 0.0 + + if ( (0<=x) & (x<=P) & (0<=y) & (y<=Q) ) + + bar_Cov = R(x, y, th) + + elseif ( (P<=x) & (x<=2*P) & (0<=y) & (y<=Q) ) + + bar_Cov = R(2*P-x, y, th) + + elseif ( (0<=x) & (x<=P) & (Q<=y) & (y<=2*Q) ) + + bar_Cov = R(x, 2*Q-y, th) + + elseif ( (P<=x) & (x<=2*P) & (Q<=y) & (y<=2*Q) ) + + bar_Cov = R(2*P-x, 2*Q-y, th) + + end + + return(bar_Cov) + +end + +################################################### +################################################### + +#### Obtain (4pq)x(1) Vector bar_rho +#### following Method/Notation in Dietrich & Newsam (96) +function f_bar_rho(th, gr) + + p = gr.p; q = gr.q; P = gr.P; Q = gr.Q + + Dx = P/p; Dy = Q/q + + bar_rho = zeros(4*p*q) + + ######### + + for j in 0:(2*q-1) + + for i in 0:(2*p-1) + + bar_rho[(j*2*p)+(i+1)] = bar_R(i*Dx, j*Dy, th, gr) + + end + + end + + ######### + + return(bar_rho) + +end + +################################################### +#### Example ###################################### + +####bar_rho = f_bar_rho(th, gr) + +################################################### +################################################### + +#### Construct W Operation on (4pq)x1 Vector V +#### W is 2D Discrete Fourier Transform +#### following Method/Notation in Dietrich & Newsam (96); +#### V is (4pq)x1; result is (4pq)x1 +function f_W(V, gr) + + p = gr.p; q = gr.q + + WV = zeros(4*p*q) + + #### Re-arrange (4pq)x(1) Vector V into an (2p)x(2q) matrix + #### by using first 2p-elements of V as 1st column, + #### next 2p-elements as 2nd column, and so on. + bar_E = reshape(V, (2*p,2*q)) + + #### Use Julia's 2D-FFT tranform + E = sqrt(4*p*q)*ifft(bar_E) + #### E is in general a Complex-Value (2p)x(2q) Matrix + + #### Re-arrange (2p)x(2q) matrix E + #### into an (4pq)x1 matrix, by using 1st column of E, + #### then 2nd column of E, and so on. + WV = reshape(E,(4*p*q)) + + return(WV) + +end + +################################################### +#### Example ###################################### + +####[bar_rho f_W(bar_rho, gr)] + +################################################### +################################################### + +#### Construct WH Operation on (4pq)x1 Vector V +#### WH is 2D Inverse Discrete Fourier Transform +#### following Method/Notation in Dietrich & Newsam (96); +#### V is (4pq)x1; result is (4pq)x1 +function f_WH(V, gr) + + p = gr.p; q = gr.q + + WHV = zeros(4*p*q) + + #### Re-arrange (4pq)x(1) Vector V into an (2p)x(2q) matrix + #### by using first 2p-elements of V as 1st column, + #### next 2p-elements as 2nd column, and so on. + E = reshape(V, (2*p,2*q)) + + #### Use Julia's 2D-IFFT tranform + bar_E = (1.0/sqrt(4*p*q))*fft(E) + #### bar_E is in general a Complex-Value (2p)x(2q) Matrix + + #### Re-arrange (2p)x(2q) matrix bar_E + #### into an (4pq)x1 matrix, by using 1st column of bar_E, + #### then 2nd column of bar_E, and so on. + WHV = reshape(bar_E,(4*p*q)) + + return(WHV) + +end + +################################################### +#### Example ###################################### + +####V = bar_rho; WV = f_W(V,gr); WHWV = f_WH(WV,gr); + +#### CHECK!! ###################################### + +####[V WV WHWV] ## Since WH*W = I, for any V, it should be V = WHWV!! + +################################################### +################################################### + +################################################### +################################################### +#### +#### Construct Covariance Matrix on Original Grid +#### following Method/Notation in Dietrich & Newsam (96) +#### This Function is Needed only for Testing!! +####function f_R11(th, gr) +#### +#### p = gr.p; q = gr.q; P = gr.P; Q = gr.Q +#### +#### Dx = P/p; Dy = Q/q; n1 = (p+1)*(q+1) +#### +#### R11 = zeros(n1, n1) +#### +#### for m in 0:q +#### +#### for l in 0:p +#### +#### for j in 0:q +#### +#### for i in 0:p +#### +#### d1 = m*(p+1)+l+1; d2 = j*(p+1)+i+1 +#### +#### R11[d1,d2] = R(abs(l*Dx-i*Dx), abs(m*Dy-j*Dy), th) +#### +#### end +#### +#### end +#### +#### end +#### +#### end +#### +#### return(R11) +#### +####end +#### +################################################### +#### Example ###################################### +#### +####R11 = f_R11(th, gr) +#### +#### Construct Covariance Matrix on Extended Grid +#### following Method/Notation in Dietrich & Newsam (96) +#### This Function is Needed only for Testing!! +####function f_bar_R11(th, gr) +#### +#### p = gr.p; q = gr.q; P = gr.P; Q = gr.Q +#### +#### Dx = P/p; Dy = Q/q; bar_n1 = 4*p*q +#### +#### bar_R11 = zeros(bar_n1, bar_n1) +#### +#### for m in 0:(2*q-1) +#### +#### for l in 0:(2*p-1) +#### +#### for j in 0:(2*q-1) +#### +#### for i in 0:(2*p-1) +#### +#### d1 = m*2*p+l+1; d2 = j*2*p+i+1 +#### +#### bar_R11[d1,d2] = bar_R(abs(l*Dx-i*Dx), abs(m*Dy-j*Dy), th, gr) +#### +#### end +#### +#### end +#### +#### end +#### +#### end +#### +#### return(bar_R11) +#### +####end +#### +################################################### +#### Example ###################################### +#### +####bar_R11 = f_bar_R11(th, gr) +#### +################################################### +################################################### + +#### Construct Covariance between Stations and Extended Grid +#### following Method/Notation in Dietrich & Newsam (96); +#### result is matrix of dimnesions n2xbar_n1 +function f_bar_R21(th, st, gr) + + st_ij = st.st_ij; n2 = size(st_ij)[1]; + ## No of Stations + + p = gr.p; q = gr.q; P = gr.P; Q = gr.Q + + Dx = P/p; Dy = Q/q + + bar_R21 = zeros(n2, 4*p*q) + + for m in 1:n2 + + for j in 0:(2*q-1) + + for i in 0:(2*p-1) + + d2 = j*2*p+i+1 + + bar_R21[m,d2] = bar_R(abs(st_ij[m,1]-i)*Dx, abs(st_ij[m,2]-j)*Dy, th, gr) + + end + + end + + end + + return(bar_R21) + +end + +################################################### +#### Example ###################################### + +####bar_R21 = f_bar_R21(th, st, gr) + +################################################### +################################################### + +#### Construct Covariance between Observations +#### following Method/Notation in Dietrich & Newsam (96); +#### result is matrix of dimnesions n2xn2 +function f_R22(th, st, Sobs, gr) + + st_ij = st.st_ij; n2 = size(st_ij)[1] + ## No of Stations + + p = gr.p; q = gr.q; P = gr.P; Q = gr.Q + + Dx = P/p; Dy = Q/q + + ############ + + R22 = zeros(n2, n2) + + for i in 1:n2 + + xi = st_ij[i,1] + yi = st_ij[i,2] + + for j in 1:n2 + + xj = st_ij[j,1] + yj = st_ij[j,2] + + R22[i,j] = R(abs(xj-xi)*Dx,abs(yj-yi)*Dy,th) + + if (i==j) + + R22[i,j] = R22[i,j] + Sobs^2 + + end + + end + + end + + return(R22) + +end + +################################################### +#### Example ###################################### + +####R22 = f_R22(th, st, Sobs, gr) + +################################################### +################################################### + +#### Construct Covariance between Original Grid & Station Positions +#### following Method/Notation in Dietrich & Newsam (96) +#### result is matrix of dimnesions n1xn2 +function f_R12(th, st, gr) + + st_ij = st.st_ij; n2 = size(st_ij)[1] + ## No of Stations + + p = gr.p; q = gr.q; P = gr.P; Q = gr.Q + + Dx = P/p; Dy = Q/q; n1 = (p+1)*(q+1) + + R12 = zeros(n1, n2) + + for m in 1:n2 + + for j in 0:q + + for i in 0:p + + d1 = j*(p+1)+i+1 + + R12[d1,m] = R(abs(st_ij[m,1]-i)*Dx, abs(st_ij[m,2]-j)*Dy, th) + + end + + end + + end + + return(R12) + +end + +################################################### +#### Example ###################################### + +####R12 = f_R12(th, st, gr) + +################################################### +################################################### +#### +#### Construct K Matrix +#### following Method/Notation in Dietrich & Newsam (96) +####function f_K(th, st, gr) +#### +#### st_ij = st.st_ij; n2 = size(st_ij)[1] +#### ## No of Stations +#### +#### p = gr.p; q = gr.q +#### +#### bar_rho = f_bar_rho(th, gr) +#### +#### Lambda = sqrt(4*p*q)*Diagonal(real.(f_W(bar_rho, gr))) +#### #### THEORY CHECKPOINT: +#### #### All values in Lambda must be POSITIVE; +#### #### OTHERWISE, the METHOD FAILS!!! +#### +#### bar_R21 = f_bar_R21(th, st, gr); bar_R12 = bar_R21' +#### +#### WHbar_R12 = zeros(Complex, 4*p*q, n2) +#### for i in 1:n2 +#### +#### WHbar_R12[:,i] = f_WH(bar_R12[:,i], gr) +#### +#### end +#### +#### KH = Lambda^(-1/2)*WHbar_R12 +#### +#### K = KH' ## this gives Cnjugate Transpose +#### +#### return(K) +#### +####end +#### +################################################### +### Example ####################################### + +#### K = f_K(th, st, gr) + +##### Check!! ##################################### + +#### sort(eigen(bar_R11).values) +#### THEORY CHECKPOINT: +#### All eigenvalues of bar_R11 must be POSITIVE; +#### OTHERWISE, the METHOD FAILS!!! + +#### A = bar_R21*inv(bar_R11)*(bar_R21)' + +#### B = real.(K*K') + +#### Check: Must Have A=B!! + +#################################### + +#### bar_RR = [bar_R11 (bar_R21)'; bar_R21 R22] + +#### THEORY CHECKPOINT: +#### All eigenvalues of bar_RR must be POSITIVE; +#### OTHERWISE, the METHOD FAILS!!! +#### sort(eigen(bar_RR).values) + +#### Lambda = sqrt(4*p*q)*Diagonal(real.(f_W(bar_rho, gr))) + +#### [sort(eigen(bar_R11).values) sort(eigen(Lambda).values)] +#### Check: The two colums must be the same !! + +################################################### +################################################### +#### V is (n2)x1; result is (n1)x1 +function f_A1_T(V, st_p, n1) + + n2 = length(V); A1_T_V = zeros(n1) + + for i in 1:n2 + + A1_T_V[st_p[i]] = V[i] + + end + + return(A1_T_V) + +end + +################################################### +### Example ####################################### + +####V = rand(n2) + +####A1_T_V = f_A1_T(V, st_p, n1) + +################################################### +################################################### +#### U is (n1)x1; result is (n2)x1 +function f_A1(U, st_p) + + n1 = length(U); n2 = length(st_p) + + A1_U = zeros(n2) + + for i in 1:n2 + + A1_U[i] = U[st_p[i]] + + end + + return(A1_U) + +end + +################################################### +### Example ####################################### + +####U = rand(n1) + +####A1_U = f_A1(U, st_p) + +################################################### +################################################### +#### V is (n1)x1; result is (n1)x1 +function f_Sigma(V, th, gr) + + p = gr.p; q = gr.q; n1 = (p+1)*(q+1); bar_n1 = 4*p*q + + ############ + + bar_V = zeros(bar_n1) + + for j in 0:q + + bar_V[(j*2*p+1):(j*2*p+p+1)] = V[(j*(p+1)+1):((j+1)*(p+1))] + + end + + bar_rho = f_bar_rho(th, gr) + + Lambda = sqrt(bar_n1)*Diagonal(real.(f_W(bar_rho, gr))) + #### THEORY CHECKPOINT: + #### All values in Lambda must be POSITIVE; + #### OTHERWISE, the METHOD FAILS!!! + + bar_Sigma_V = f_W(Lambda*f_WH(bar_V, gr),gr) + + ############ + + Proj_Index = fill(0, n1) + + for j in 0:q + + Proj_Index[(j*(p+1)+1):((j+1)*(p+1))] = collect((j*2*p+1):(j*2*p+p+1)) + + end + + Sigma_V = bar_Sigma_V[Proj_Index] + + return(real.(Sigma_V)) + +end + +################################################### +### Example ####################################### + +####V = rand(n1); Sigma_V = f_Sigma(V, th, gr) + +####maximum(abs.(R11*V-Sigma_V)) #### difference must be 0 + +################################################### +################################################### + + +#################################################################### +#################################################################### +### ALL FUNCTIONS SO FAR ARE STAND-ALONE ONES; +### THE ONE THAT FOLLOW NEED INTEGRATION WITH TUOMAS/MOSE CODE; +### THE POSITION ASSUMED IN THE CODE THAT FOLLOWS IS THAT WE ARE +### AT TIME t-1, AND HAVE N PARTICLES, EACH OF DIMENSION 3x(n1), +### REPRESENTING THE 3-DIMENSIONAL VECTOR FIELD ON A GRID OF n1 POSITIONS, +### AT TIME t-1. +### THE FUNCTIONS THE FOLLOW APPLY A SINGLE PARTICLE FILTER STEP. +### IN PARTICULAR, THE CODE THAT FOLLOWS DOES THE FOLLOWING: +### - IT SIMULATES THE OPTIMAL PROPOSAL FOR THE HEIGHT FIELD AT TIME t. +### - IT *DOES NOT* SIMULATE THE PROPOSAL FOR THE TWO VELOCITY FIELDS. +### - FOR THE LATTER PURPOSE THE CODE MUST BE COMBINED WITH THE CODE OF +### OF TUOMAS/MOSE +################################################################### +#################################################################### + +#### Calculation of the mean for the optimal proposal for the +#### Height Field at time t; it is assumed that INTEGRATION with TUOMAS/MOSE code +#### it is assumed that INTEGRATION with TUOMAS/MOSE code will provide the +#### (N)x(n1) field FH_t which is the push-forward of all N particles at time t-1 +#### under the PDE dynamics; FH_t then considers only the (N)x(n1) matrix with +#### the values of the height field. Y_obs_t are the (n2)x1 data at time t. +#### THE RESULT IS A MATRIX (N)x(n1) +function Calculate_Mean(FH_t, th, st, Yobs_t, Sobs, gr) + + ######### Offline Calculations ######### + + p = gr.p; q = gr.q; n1 = (p+1)*(q+1) + + st_ij = st.st_ij; st_p = st.st_p + + n2 = size(st_ij)[1]; N = size(FH_t)[1] + ## No of Stations + No of Particles + + ########################## + + R22 = f_R22(th, st, Sobs, gr) + + invR22 = inv(R22) + + ########################## + + mu20 = Sobs^(-2)*(R22 - Diagonal(fill(Sobs^2,n2))) + #### (n2)x(n2) + + mu21 = f_Sigma(f_A1_T(invR22*(mu20*Yobs_t), st_p, n1), th, gr) + #### (n1)x1 + + mu22 = f_Sigma((Sobs^(-2))*f_A1_T(Yobs_t, st_p, n1), th, gr) + #### (n1)x1 + + mu2 = mu22 - mu21 + #### (n1)x1 + ########################## + + mu1 = zeros(N, n1) + + mu = zeros(N, n1) + + ##### the required mean is different for each of the N particles + for i in 1:N + + mu10 = invR22*f_A1(FH_t[i,:],st_p) + #### (n2)x1 + + mu11 = f_Sigma(f_A1_T(mu10, st_p, n1), th, gr) + #### (n1)x1 + + mu1[i,:] = FH_t[i,:] - mu11 + #### (n1)x1 + + mu[i,:] = mu1[i,:] + mu2 + #### (n1)x1 + + end + + return(mu) + +end + +################################################### +### Example ####################################### + +####N = 10; FH_t = rand(N, n1) + +####Calculate_Mean(FH_t, th, st, Yobs_t, Sobs, gr) + +################################################### +################################################### +# +# INPUT: +#### FH_t: an (N)x(n1) matrix where N is the number of particles +#### and n1 the size of the grid on the 2D-domain. +#### The i-th row of FH_t (referring to the i-th particle) +#### is the n1-dimensional Height field calculated after solving the PDE, +#### from time instance (t-1) to time t, using the i-th particle at time t-1 as initial condition. +#### th: Parameters in Covariance Function +#### st: Information about Stations +#### Yobs_t: n2-dimensional vector corresponding to the observations from the n2 stations +#### Sobs: Standard Deviation of Observations at Stations +#### gr: Parameters Specifying Regular Grid +# OUTPUT: +#### The numbers of particles N must be EVEN!! +function Sample_Height_Proposal(FH_t, th, st, Yobs_t, Sobs, gr) + + ######### Offline Calculations: ######### + ######### i.e. will be the same for 0->1, 1->2, t-1->t, etc. ######### + + st_ij = st.st_ij; st_p = st.st_p + + n2 = size(st_ij)[1]; N = size(FH_t)[1] + ## No of Stations + No of Particles + + p = gr.p; q = gr.q; P = gr.P; Q = gr.Q + + bar_n1 = 4*p*q; n1 = (p+1)*(q+1) + + Dx = P/p; Dy = Q/q + + bar_rho = f_bar_rho(th, gr) + + Lambda = sqrt(bar_n1)*Diagonal(real.(f_W(bar_rho, gr))) + #### THEORY CHECKPOINT: + #### All values in Lambda must be POSITIVE; + #### OTHERWISE, the METHOD FAILS!!! + + bar_R21 = f_bar_R21(th, st, gr); bar_R12 = bar_R21' + + WHbar_R12 = zeros(Complex, bar_n1, n2) + + for i in 1:n2 + + WHbar_R12[:,i] = f_WH(bar_R12[:,i], gr) + + end + + KH = Lambda^(-1/2)*WHbar_R12; K = KH' ## this gives Conjugate Transpose + + R22 = f_R22(th, st, Sobs, gr) + + L = cholesky(real.(R22-K*KH)).L + #### THEORY CHECKPOINT: + #### R22-K*KH must have POSITIVE EIGENVALUES, + #### i.e. all(eigen(R22-K*KH).values)>0, + #### OTHERWISE, the METHOD FAILS!!! + + R12 = f_R12(th, st, gr); + + R12_invR22 = R12*inv(R22) + + ##muZ1_C_Yobs = R12_invR22*Yobs_t + + Proj_Index = fill(0, n1) + + for j in 0:q + + Proj_Index[(j*(p+1)+1):((j+1)*(p+1))] = collect((j*2*p+1):(j*2*p+p+1)) + + end + + #### + + Samples = zeros(N,n1) + N0 = Int(N/2) ########## N must be even! + + ######################################## + ######### Online Calculations: ########## + ######### here we need info from the data at time t, or/and a separate ########## + ######### calculation for each particle. ########## + means = Calculate_Mean(FH_t, th, st, Yobs_t, Sobs, gr) + rng = Random.MersenneTwister(123) + + e1 = Vector{ComplexF64}(undef, bar_n1) + e2 = Vector{ComplexF64}(undef, n2) + + for i in 0:(N0-1) + + @. e1 = complex(randn(rng), randn(rng)) + @. e2 = complex(randn(rng), randn(rng)) + + bar_z1 = f_W(Lambda^(1/2)*e1, gr) + z2 = (K*e1) + (L*e2) + + Rbar_z = real.([bar_z1; z2]) + Ibar_z = imag.([bar_z1; z2]) + + Proj1 = [ Rbar_z[Proj_Index]; Rbar_z[(bar_n1+1):end] ] + + Proj2 = [ Ibar_z[Proj_Index]; Ibar_z[(bar_n1+1):end] ] + + ##Z1_C_Yobs_1 = muZ1_C_Yobs + Proj1[1:n1] - R12_invR22*Proj1[(n1+1):end] + Z11 = Proj1[1:n1] - R12_invR22*Proj1[(n1+1):end] + + ##Z1_C_Yobs_2 = muZ1_C_Yobs + Proj2[1:n1] - R12_invR22*Proj2[(n1+1):end] + Z12 = Proj2[1:n1] - R12_invR22*Proj2[(n1+1):end] + + ##Samples[2*i+1,:] = means[2*i+1,:] + Z1_C_Yobs_1 + Samples[2*i+1,:] = means[2*i+1,:] + Z11 + + ##Samples[2*i+2,:] = means[2*i+2,:] + Z1_C_Yobs_2 + Samples[2*i+2,:] = means[2*i+2,:] + Z12 + + end + + return(Samples) + +end + +#################################################################### +#################################################################### + + + + +################################################### +#### Example ###################################### + +N = 10; FH_t = rand(N, n1) + +Ss = Sample_Height_Proposal(FH_t, th, st, Yobs_t, Sobs, gr) + +#### + +Ss[1,st_p] - Yobs_t #### all the differences should be close to 0 if Sobs<<1 + +Ss[2,st_p] - Yobs_t #### all the differences should be close to 0 if Sobs<<1 + +Ss[3,st_p] - Yobs_t #### all the differences should be close to 0 if Sobs<<1 + +Ss[4,st_p] - Yobs_t #### all the differences should be close to 0 if Sobs<<1 + +#### + +Fs = zeros(N, q+1, p+1) + +for i in 1:N + + Fs[i,:,:] = reshape(Ss[i,:], (p+1,q+1))' + +end + +i = 2 + +#heatmap(1:size(Fs[i,:,:],2), +# 1:size(Fs[i,:,:],1), Fs[i,:,:], +# c=cgrad([:blue, :white,:red, :yellow]), +# xlabel="x-axis", ylabel="y-axis", +# title="") + + + +#####!!!!!! Need to Check if I Combine in the Correct Way +#####!!!!!! the algorithm for the Simulation of the Conditional Field +#####!!!!!! and the Use of the Mean. + +################################################### +################################################### diff --git a/test/optimal_filter_validation.yaml b/test/optimal_filter_validation.yaml new file mode 100644 index 00000000..dffedbce --- /dev/null +++ b/test/optimal_filter_validation.yaml @@ -0,0 +1,14 @@ +filter: + nprt: 2 + +model: + llw2d: + nobs: 3 + nx: 21 + ny: 21 + x_length: 40.0 + y_length: 40.0 + obs_noise_std: 0.01 + sigma: 1.0 + lambda: 1.0 + nu: 2.5 diff --git a/test/reference_data.h5 b/test/reference_data.h5 index f341b0111fb04c300f233aa25321cf98dec551b1..84cb4c39eb95bddfb0fb5130f3a8103c919febe0 100644 GIT binary patch literal 1333016 zcmeFZWmJ@1{P#CKvs62Y# zUiVq&S?hUq&N^?-e_n9SzV_a~_X8q zm@xcv3n&BiHo%+z!xa~Y5(oEp9n0T(n!omC2>!ic`uDz(fvW1Cw}5@%`nURjF8@C# 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@test stations.ist == [5, 5, 10, 10] - @test stations.jst == [5, 10, 5, 10] + @test stations.ist == [4, 4, 9, 9] + @test stations.jst == [4, 9, 4, 9] Model.write_stations(filter_params.output_filename, stations.ist, stations.jst, model_params) @test h5read(filter_params.output_filename, model_params.title_stations * "/x") ≈ stations.ist .* model_params.dx @test h5read(filter_params.output_filename, model_params.title_stations * "/y") ≈ stations.jst .* model_params.dy @@ -213,12 +214,12 @@ end # Test true state with standard parameters x_true,x_avg,x_var = ParticleDA.run_particle_filter(Model.init, joinpath(@__DIR__, "integration_test_1.yaml"), BootstrapFilter()) data_true = h5read(joinpath(@__DIR__, "reference_data.h5"), "integration_test_1") - @test x_true ≈ data_true + @test all(x_true .≈ data_true) # Test true state with different parameters x_true,x_avg,x_var = ParticleDA.run_particle_filter(Model.init, joinpath(@__DIR__, "integration_test_2.yaml"), BootstrapFilter()) data_true = h5read(joinpath(@__DIR__, "reference_data.h5"), "integration_test_2") - @test x_true ≈ data_true + @test all(x_true .≈ data_true) # Test particle state with ~zero noise x_true,x_avg,x_var = ParticleDA.run_particle_filter(Model.init, joinpath(@__DIR__, "integration_test_3.yaml"), BootstrapFilter()) @@ -227,18 +228,22 @@ end if Threads.nthreads() == 1 + avg_ref = h5read(joinpath(@__DIR__, "reference_data.h5"), "integration_test_4") # Test particle state with noise rng = StableRNG(123) - init_with_rng = (model_params_dict, nprt_per_rank, my_rank) -> Model.init(model_params_dict, nprt_per_rank, my_rank, rng) - x_true,x_avg,x_var = ParticleDA.run_particle_filter(init_with_rng, joinpath(@__DIR__, "integration_test_4.yaml"), BootstrapFilter()) - avg_ref = h5read(joinpath(@__DIR__, "reference_data.h5"), "integration_test_4") - @test x_avg ≈ avg_ref + x_true,x_avg,x_var = ParticleDA.run_particle_filter(Model.init, joinpath(@__DIR__, "integration_test_4.yaml"), BootstrapFilter(); rng) + @test all(x_avg .≈ avg_ref) # Test that different seed gives different result rng = StableRNG(124) - init_with_rng = (model_params_dict, nprt_per_rank, my_rank) -> Model.init(model_params_dict, nprt_per_rank, my_rank, rng) - x_true,x_avg,x_var = ParticleDA.run_particle_filter(init_with_rng, joinpath(@__DIR__, "integration_test_4.yaml"), BootstrapFilter()) - @test !(x_avg ≈ avg_ref) + x_true,x_avg,x_var = ParticleDA.run_particle_filter(Model.init, joinpath(@__DIR__, "integration_test_4.yaml"), BootstrapFilter(); rng) + @test !all(x_avg .≈ avg_ref) + + # Test optimal filter + avg_ref = h5read(joinpath(@__DIR__, "reference_data.h5"), "integration_test_6") + rng = StableRNG(123) + x_true,x_avg,x_var = ParticleDA.run_particle_filter(Model.init, joinpath(@__DIR__, "optimal_filter_test_1.yaml"), OptimalFilter(); rng) + @test all(x_avg .≈ avg_ref) end @@ -256,3 +261,137 @@ end end end end + +@testset "Optimal Filter unit tests" begin + + seed = 123 + Random.seed!(seed) + + # Use default parameters + model_params = ModelParameters() + filter_params = FilterParameters() + grid = ParticleDA.Grid(model_params.nx, + model_params.ny, + model_params.dx, + model_params.dy, + model_params.x_length, + model_params.y_length) + grid_ext = ParticleDA.Grid((grid.nx-1)*2, + (grid.ny-1)*2, + grid.dx, + grid.dy, + (grid.x_length-grid.dx)*2, + (grid.y_length-grid.dy)*2) + noise_params = (sigma = model_params.sigma, lambda = model_params.lambda, nu = model_params.nu) + + # Set station coordinates + ist = rand(1:model_params.nx, model_params.nobs) + jst = rand(1:model_params.ny, model_params.nobs) + stations = (nst = model_params.nobs, ist = ist, jst = jst) + cov_ext = ParticleDA.extended_covariance(0.0, 0.5 * grid.y_length, grid, noise_params) + @test cov_ext ≈ exp(-0.5 * model_params.y_length / (2 * noise_params.lambda)) + @test cov_ext ≈ ParticleDA.extended_covariance(2.0 * grid.x_length, 0.5 * grid.y_length, grid, noise_params) + @test cov_ext ≈ ParticleDA.extended_covariance(0.0, 1.5 * grid.y_length, grid, noise_params) + arr = rand(ComplexF64,10,10) + arr2 = zeros(ComplexF64,10,10) + arr3 = zeros(ComplexF64,10,10) + fft_plan, fft_plan! = FFTW.plan_fft(arr), FFTW.plan_fft!(arr) + ParticleDA.normalized_2d_fft!(arr2, arr, fft_plan, fft_plan!, grid_ext) + ParticleDA.normalized_2d_fft!(arr3, arr2, fft_plan, fft_plan!, grid_ext, inv) + @test arr ≈ arr3 + + cov_1 = zeros(stations.nst, grid_ext.nx * grid_ext.ny) + cov_2 = zeros(grid.nx * grid.ny, stations.nst) + cov_3 = zeros(stations.nst,stations.nst) + ParticleDA.covariance_stations_extended_grid!(cov_1,grid,grid_ext,stations,noise_params) + ParticleDA.covariance_grid_stations!(cov_2,grid,stations,noise_params) + ParticleDA.covariance_stations!(cov_3,grid,stations,noise_params,model_params.obs_noise_std) + @test all(isfinite, cov_1) + @test all(isfinite, cov_2) + @test all(isfinite, cov_3) + @test cov_3 == Symmetric(cov_3) + + height = rand(grid.nx, grid.ny, filter_params.nprt) + obs = randn(stations.nst) + tmp_array = Matrix{ComplexF64}(undef, grid_ext.nx, grid_ext.ny) + fft_plan, fft_plan! = FFTW.plan_fft(tmp_array), FFTW.plan_fft!(tmp_array) + mat_off = ParticleDA.init_offline_matrices(grid, grid_ext, stations, noise_params, model_params.obs_noise_std, fft_plan, fft_plan!, Float64) + mat_on = ParticleDA.init_online_matrices(grid, grid_ext, stations, filter_params, Float64) + @test minimum(mat_off.Lambda) > 0.0 + ParticleDA.calculate_mean_height!(mat_on.mean, height, mat_off, obs, stations, grid, grid_ext, fft_plan, fft_plan!, filter_params, model_params.obs_noise_std) + @test all(isfinite, mat_on.mean) + + rng = Random.MersenneTwister(seed) + ParticleDA.sample_height_proposal!(height, mat_off, mat_on, obs, stations, grid, grid_ext, fft_plan, fft_plan!, filter_params, rng, model_params.obs_noise_std) + @test all(isfinite, mat_on.samples) + +end + +@testset "Optimal Filter validation" begin + + seed = 123 + Random.seed!(seed) + rng = Random.MersenneTwister(seed) + + include(joinpath(@__DIR__,"optimal_filter_validation.jl")); + + params_dict = YAML.load_file(joinpath(@__DIR__, "optimal_filter_validation.yaml")) + filter_params = ParticleDA.get_params(FilterParameters, params_dict["filter"]) + model_params = ParticleDA.get_params(ModelParameters, params_dict["model"]["llw2d"]) + + grid = ParticleDA.Grid(model_params.nx, + model_params.ny, + model_params.dx, + model_params.dy, + model_params.x_length, + model_params.y_length) + grid_ext = ParticleDA.Grid((grid.nx-1)*2, + (grid.ny-1)*2, + grid.dx, + grid.dy, + (grid.x_length-grid.dx)*2, + (grid.y_length-grid.dy)*2) + + noise_params = (sigma = model_params.sigma, lambda = model_params.lambda, nu = model_params.nu) + + stations = (nst = model_params.nobs, ist = st.st_ij[:,1].+1, jst = st.st_ij[:,2].+1) + + h(x,y) = sin(x)^2 + cos(y)^2 + height = zeros(model_params.nx, model_params.ny, filter_params.nprt) + x = (1:model_params.nx) .* 2 * pi / model_params.nx + y = (1:model_params.ny) .* 4 * pi / model_params.ny + for i = 1:filter_params.nprt + height[:,:,i] .= h.(x',y) + end + + obs = zeros(model_params.nobs) + for i = 1:model_params.nobs + obs[i] = height[stations.ist[i], stations.jst[i],1] + rand() + end + + tmp_array = Matrix{ComplexF64}(undef, grid_ext.nx, grid_ext.ny) + fft_plan, fft_plan! = FFTW.plan_fft(tmp_array), FFTW.plan_fft!(tmp_array) + mat_off = ParticleDA.init_offline_matrices(grid, grid_ext, stations, noise_params, model_params.obs_noise_std, fft_plan, fft_plan!, Float64) + mat_on = ParticleDA.init_online_matrices(grid, grid_ext, stations, filter_params, Float64) + + ParticleDA.sample_height_proposal!(height, mat_off, mat_on, obs, stations, grid, grid_ext, fft_plan, fft_plan!, filter_params, rng, model_params.obs_noise_std) + + Yobs_t = copy(obs) + FH_t = copy(reshape(permutedims(height, [3 1 2]), filter_params.nprt, (model_params.nx)*(model_params.ny))) + + Mean_height = Calculate_Mean(FH_t, th, st, Yobs_t, Sobs, gr) + Samples = Sample_Height_Proposal(FH_t, th, st, Yobs_t, Sobs, gr) + + @test mat_on.mean ≈ permutedims(reshape(Mean_height, filter_params.nprt, model_params.nx, model_params.ny), [2 3 1]) + @test mat_on.samples ≈ permutedims(reshape(Samples, filter_params.nprt, model_params.nx, model_params.ny), [2 3 1]) + + # print("old mean height: ") + # @btime Mean_height = Calculate_Mean($FH_t, $th, $st, $Yobs_t, $Sobs, $gr) + # print("new mean height: ") + # @btime calculate_mean_height!($mat_on.mean, $height, $mat_off, $obs, $stations, $params) + # print("old sampling: ") + # @btime Samples = Sample_Height_Proposal($FH_t, $th, $st, $Yobs_t, $Sobs, $gr) + # print("new sampling: ") + # @btime sample_height_proposal!($height, $mat_off, $mat_on, $obs, $stations, $params, $rng) + +end diff --git a/test/update_reference_data.jl b/test/update_reference_data.jl index 39293ab9..b7b819f8 100644 --- a/test/update_reference_data.jl +++ b/test/update_reference_data.jl @@ -9,9 +9,14 @@ rm(reference_file; force=true) x_true, _, _ = ParticleDA.run_particle_filter(Model.init, joinpath(@__DIR__, "integration_test_1.yaml"), BootstrapFilter()) h5write(reference_file, "integration_test_1", x_true) + x_true, _, _ = ParticleDA.run_particle_filter(Model.init, joinpath(@__DIR__, "integration_test_2.yaml"), BootstrapFilter()) h5write(reference_file, "integration_test_2", x_true) + rng = StableRNG(123) -init_with_rng = (model_params_dict, nprt_per_rank, my_rank) -> Model.init(model_params_dict, nprt_per_rank, my_rank, rng) -_, x_avg, _ = ParticleDA.run_particle_filter(init_with_rng, joinpath(@__DIR__, "integration_test_4.yaml"), BootstrapFilter()) +_, x_avg, _ = ParticleDA.run_particle_filter(Model.init, joinpath(@__DIR__, "integration_test_4.yaml"), BootstrapFilter(); rng) h5write(reference_file, "integration_test_4", x_avg) + +rng = StableRNG(123) +_, x_avg, _ = ParticleDA.run_particle_filter(Model.init, joinpath(@__DIR__, "optimal_filter_test_1.yaml"), OptimalFilter(); rng) +h5write(reference_file, "integration_test_6", x_avg)