From 9982dd0fee67e907fb6fadefd47ccf3c5e13c50a Mon Sep 17 00:00:00 2001 From: hiwamoto Date: Wed, 1 Nov 2023 17:41:41 +0900 Subject: [PATCH] Add tutorial of limitation --- doc/common/img/limitation_beta_max.pdf | Bin 0 -> 28121 bytes doc/common/img/limitation_beta_max.png | Bin 0 -> 27412 bytes doc/common/img/limitation_beta_min.pdf | Bin 0 -> 68638 bytes doc/common/img/limitation_beta_min.png | Bin 0 -> 67183 bytes doc/ja/source/tutorial/index.rst | 2 + doc/ja/source/tutorial/limitation.rst | 192 +++++++++++++++++++++++++ 6 files changed, 194 insertions(+) create mode 100644 doc/common/img/limitation_beta_max.pdf create mode 100644 doc/common/img/limitation_beta_max.png create mode 100644 doc/common/img/limitation_beta_min.pdf create mode 100644 doc/common/img/limitation_beta_min.png create mode 100644 doc/ja/source/tutorial/limitation.rst diff --git a/doc/common/img/limitation_beta_max.pdf b/doc/common/img/limitation_beta_max.pdf new file mode 100644 index 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a/doc/ja/source/tutorial/index.rst b/doc/ja/source/tutorial/index.rst index 133470a5..8b3ebded 100644 --- a/doc/ja/source/tutorial/index.rst +++ b/doc/ja/source/tutorial/index.rst @@ -38,6 +38,7 @@ TRHEPDでは原子座標を与えた場合に、回折データがシミュレ の5つのアルゴリズムが用意されています。 本チュートリアルでは、最初に順問題プログラム ``sim_trhepd_rheed`` の実行方法、 その後に ``minsearch`` , ``mapper_mpi``, ``bayes``, ``exchange``, ``pamc`` の実行方法について順に説明します。 +また、制約式を用いて探索範囲を制限出来る ``[runner.limitation]`` セクションを使用した実行方法も説明しています。 最後に、自分で順問題ソルバーを定義する簡単な例について説明します。 .. toctree:: @@ -48,6 +49,7 @@ TRHEPDでは原子座標を与えた場合に、回折データがシミュレ mpi bayes exchange + limitation pamc solver_simple diff --git a/doc/ja/source/tutorial/limitation.rst b/doc/ja/source/tutorial/limitation.rst new file mode 100644 index 00000000..dd53f3be --- /dev/null +++ b/doc/ja/source/tutorial/limitation.rst @@ -0,0 +1,192 @@ +制約式を適用したレプリカ交換モンテカルロ法による探索 +========================================================================== + +ここでは、 ``[runner.limitation]`` セクションに設定できる制約式機能のチュートリアルを示します。 +例として、レプリカ交換モンテカルロ法を、Himmelblauを対象に探索する計算に制約式を適用します。 + +サンプルファイルの場所 +~~~~~~~~~~~~~~~~~~~~~~~~ + +サンプルファイルは ``sample/analytical/limitation`` にあります。 +フォルダには以下のファイルが格納されています。 + +- ``ref.txt`` + + 計算が正しく実行されたか確認するためのファイル(本チュートリアルを行うことで得られる ``best_result.txt`` の回答)。 + +- ``input.toml`` + + メインプログラムの入力ファイル。 + +- ``do.sh`` + + 本チュートリアルを一括計算するために準備されたスクリプト + +以下、これらのファイルについて説明したあと、実際の計算結果を紹介します。 + +入力ファイルの説明 +~~~~~~~~~~~~~~~~~~~ + +メインプログラム用の入力ファイル ``input.toml`` について説明します。 +``input.toml`` の詳細については入力ファイルに記載されています。 +以下は、サンプルファイルにある ``input.toml`` の中身になります。 + +.. code-block:: + + [base] + dimension = 2 + output_dir = "output" + + [algorithm] + name = "exchange" + seed = 12345 + + [algorithm.param] + max_list = [6.0, 6.0] + min_list = [-6.0, -6.0] + unit_list = [0.3, 0.3] + + [algorithm.exchange] + Tmin = 1.0 + Tmax = 100000.0 + numsteps = 10000 + numsteps_exchange = 100 + + [solver] + name = "analytical" + function_name = "himmelblau" + + [runner] + [runner.limitation] + co_a = [[1, -1],[1, 1]] + co_b = [[0], [-1]] + +ここではこの入力ファイルを簡単に説明します。 +詳細は入力ファイルのレファレンスを参照してください。 + +``[base]`` セクションはメインプログラム全体のパラメータです。 +``dimension`` は最適化したい変数の個数で、今の場合は2つの変数の最適化を行うので、``2`` を指定します。 + +``[algorithm]`` セクションは用いる探索アルゴリズムを設定します。 +交換モンテカルロ法を用いる場合には、 ``name`` に ``"exchange"`` を指定します。 +``label_list`` は、``value_0x`` (x=1,2) を出力する際につけるラベル名のリストです。 +``seed`` は擬似乱数生成器に与える種です。 + +``[algorithm.param]`` サブセクションは、最適化したいパラメータの範囲などを指定します。 +``min_list`` は最小値、 ``max_list`` は最大値を示します。 + +``[algorithm.exchange]`` サブセクションは、交換モンテカルロ法のハイパーパラメータを指定します。 + +- ``numstep`` はモンテカルロ更新の回数です。 +- ``numsteps_exchange`` で指定した回数のモンテカルロ更新の後に、温度交換を試みます。 +- ``Tmin``, ``Tmax`` はそれぞれ温度の下限・上限です。 +- ``Tlogspace`` が ``true`` の場合、温度を対数空間で等分割します。このオプションはデフォルト値が ``true`` であるため、今回の ``input.toml`` に指定は無いですが、 ``true`` になっています。 + +``[solver]`` セクションではメインプログラムの内部で使用するソルバーを指定します。 +今回は ``analytical`` ソルバーを指定しています。 ``analytical`` ソルバーは ``function_name`` パラメータを用いて関数を設定します。 +今回はHimmelblau 関数を指定しています。 +``analytical`` ソルバーに関してはチュートリアル「順問題ソルバーの追加」を参照してください。 + +``[runner]`` セクションは ``[runner.limitation]`` サブセクションを持ち、この中に制約式を設定します。 +現在、制約式は :math:`N` 次元のパラメータ :math:`x` 、 :math:`M` 行 :math:`N` 列の行列 :math:`A` 、 +:math:`M` 次元の縦ベクトル :math:`b` から定義される :math:`Ax+b>0` の制約式が利用可能です。 +パラメータとしては、以下の項目が設定可能です。 + +- ``co_a`` は行列 :math:`A` を設定します。 +- ``co_b`` は縦ベクトル :math:`b` を設定します。 + +パラメータの詳しい設定方法はマニュアル内「入力ファイル」項の「 [``limitation``] セクション」を参照してください。 +今回は + +.. math:: + + x_{1} − x_{2} > 0\\ + x_{1} + x_{2} − 1 > 0 + +の制約式を課して実行しています。 + +計算実行 +~~~~~~~~~~~~ + +最初にサンプルファイルが置いてあるフォルダへ移動します(以下、本ソフトウェアをダウンロードしたディレクトリ直下にいることを仮定します). + +.. code-block:: + + cd sample/analytical/limitation + +そのあとに、メインプログラムを実行します(計算時間は通常のPCで20秒程度で終わります)。 + +.. code-block:: + + mpiexec -np 10 python3 ../../../src/py2dmat_main.py input.toml | tee log.txt + +ここではプロセス数10のMPI並列を用いた計算を行っています。 +(Open MPI を用いる場合で、使えるコア数よりも要求プロセス数の方が多い時には、 +``mpiexec`` コマンドに ``--oversubscribed`` オプションを追加してください。) +実行すると、 ``output`` フォルダが生成され、その中に各ランクのフォルダが作成されます。 +更にその中には、各モンテカルロステップで評価したパラメータおよび目的関数の値を記した ``trial.txt`` ファイルと、 +実際に採択されたパラメータを記した ``result.txt`` ファイルが作成されます。 +ともに書式は同じで、最初の2列がステップ数とプロセス内のwalker 番号、次が温度、3列目が目的関数の値、4列目以降がパラメータです。 +以下は、 ``output/0/result.txt`` ファイルの冒頭部分です。 + +.. code-block:: + + # step walker T fx x1 x2 + 0 0 1.0 187.94429125133564 5.155393113805774 -2.203493345018569 + 1 0 1.0 148.23606736778044 4.9995614992887525 -2.370212436322816 + 2 0 1.0 148.23606736778044 4.9995614992887525 -2.370212436322816 + 3 0 1.0 148.23606736778044 4.9995614992887525 -2.370212436322816 + +最後に、 ``output/best_result.txt`` に、目的関数が最小となったパラメータとそれを得たランク、モンテカルロステップの情報が書き込まれます。 + +.. code-block:: + + nprocs = 10 + rank = 2 + step = 4523 + walker = 0 + fx = 0.00010188398524402734 + x1 = 3.584944906595298 + x2 = -1.8506985826548874 + +なお、一括計算するスクリプトとして ``do.sh`` を用意しています。 +``do.sh`` では ``best_result.txt`` と ``ref.txt`` の差分も比較しています。 +以下、説明は割愛しますが、その中身を掲載します。 + +.. code-block:: + + #!/bin/bash + mpiexec -np 10 --oversubscribe python3 ../../../src/py2dmat_main.py input.toml + + echo diff output/best_result.txt ref.txt + res=0 + diff output/best_result.txt ref.txt || res=$? + if [ $res -eq 0 ]; then + echo TEST PASS + true + else + echo TEST FAILED: best_result.txt and ref.txt differ + false + fi + +計算結果の可視化 +~~~~~~~~~~~~~~~~~~~ + +``result.txt`` を図示して、制約式を満たした座標のみを探索しているかを確認します。 +今回の場合は、以下のコマンドを打つことで2次元パラメータ空間の図が ``<実行日>_histogram`` フォルダ内に作成されます。 +生成されるヒストグラムは、burn-in期間として最初の1000ステップ分の探索を捨てたデータを使用しています。 + +.. code-block:: + + python3 hist2d_limitation_sample.py -p 10 -i input.toml -b 0.1 + +作成された図には2本の直線 :math:`x_{1} − x_{2} = 0, x_{1} + x_{2} − 1 = 0` と +探索結果(事後確率分布のヒストグラム)を図示しています。 +図を見ると :math:`x_{1} − x_{2} > 0, x_{1} + x_{2} − 1 > 0` の範囲のみ探索をしていることが確認できます。 +以下に図の一部を掲載します。 + +.. figure:: ../../../common/img/limitation_beta_min.* + +.. figure:: ../../../common/img/limitation_beta_max.* + + サンプルされたパラメータと確率分布。横軸は ``value_01 (x1)`` , 縦軸は ``value_02 (x2)`` を表す。