計算物理学 Rubin H. Landau , Manuel Jos´e P´aez Mej´ia
https://www.amazon.co.jp/dp/product/4254130864/
http://www.physics.orst.edu/`rubin/CPbook/PROGS
Computational Physics problem solving with computers 2nd Contents(目次)
https://www.researchgate.net/publication/204752438_Computational_Physics_Problem_Solving_with_Computers_2nd
実行
３分類。
1)PythonCodes
2)HPCodes
3)Animations
2) HPCodes
7 モンテカルロ法の応用
7.10 手法：フォンノイマンの棄却法 pond.c
# cd /home/cp/HCPcodes
# clang pond.c -o pond
pond.c:19:1: warning: type specifier missing, defaults to 'int' [-Wimplicit-int]
main() {
^
1 warning generated.
# ./pond
data stored in pond.dat
# cat pond.dat
1 4.000000
2 4.000000
...
998 3.130261
999 3.131131
1000 3.132000
19 ハイパフォーマンス・コンピューティング：プロファイリングとチューニング
高効率計算：横顔と調律
19.3 チューニング前のプログラム tune.f
19.5 基本的な最適化 tune1.f
19.6 ベクトルチューニング tune2.f
19.7 RISC上でのベクトルコード tune3.f
19.8 スーパースカラーチューニング tune4.f
# cd /home/cp/HPCodes
# gfortran tune1.f -o tune1
# gfortran tune2.f -o tune2
# gfortran tune3.f95 -o tune3
# gfortran tune4.f95 -o tune4
# ./tune1
1 1.00000 0.30350 1.00000
2 0.92179 0.05728 0.95690
3 0.91720 0.01562 0.96664
4 0.91691 0.00402 0.96348
5 0.91688 0.00116 0.96414
6 0.91688 0.00031 0.96391
7 0.91688 0.00009 0.96397
8 0.91688 0.00002 0.96395
9 0.91688 0.00001 0.96395
10 0.91688 0.00000 0.96395
11 0.91688 0.00000 0.96395
# ./tune2
1 1.00000 0.30350 1.00000
2 0.92179 0.05728 0.95690
3 0.91720 0.01562 0.96664
4 0.91691 0.00402 0.96348
5 0.91688 0.00116 0.96414
6 0.91688 0.00031 0.96391
7 0.91688 0.00009 0.96397
8 0.91688 0.00002 0.96395
9 0.91688 0.00001 0.96395
10 0.91688 0.00000 0.96395
11 0.91688 0.00000 0.96395
# ./tune3
1 1.00000 0.30350 1.00000
2 0.92179 0.05728 0.95690
3 0.91720 0.01562 0.96664
4 0.91691 0.00402 0.96348
5 0.91688 0.00116 0.96414
6 0.91688 0.00031 0.96391
7 0.91688 0.00009 0.96397
8 0.91688 0.00002 0.96395
9 0.91688 0.00001 0.96395
10 0.91688 0.00000 0.96395
11 0.91688 0.00000 0.96395
# ./tune4
1 1.30000 0.43195 1.00000
2 0.25846 0.25262 0.91802
3 0.91078 0.12232 0.98690
4 0.60074 0.07103 0.96267
5 0.78326 0.03775 0.97875
6 0.68699 0.02114 0.97091
7 0.74112 0.01151 0.97550
8 0.71171 0.00637 0.97306
9 0.72800 0.00349 0.97443
10 0.71908 0.00192 0.97368
11 0.72400 0.00106 0.97409
12 0.72129 0.00058 0.97387
13 0.72278 0.00032 0.97399
14 0.72196 0.00018 0.97393
15 0.72241 0.00010 0.97396
25 静電ポテンシャル
25.6 格子上の解 laplace.c(.f)
# cd /home/cp/HPCodes
# gcc laplace.c -o laplacec
# ./laplacec
data stored in laplace.dat
# cp laplace.dat laplacec.dat
# gfortran laplace.f -o laplacef
# ./laplacef
Note: The following floating-point exceptions are signalling: IEEE_DENORMAL
STOP data saved in laplace.dat
# cp laplace.dat laplacef.dat
# cat laplacec.dat
100.000000
0.000000
...
100.000000
49.927579
30.090184
20.722835
..
100.000000
69.620142
49.710342
37.238386
source code
https://physics.oregonstate.edu/~landaur/Books/CPbook/Codes/index.html
次の３分類
Python Codes
https://physics.oregonstate.edu/~landaur/Books/CPbook/Codes/PythonCodes/
High Performance Computing (HPC) Codes
https://physics.oregonstate.edu/~landaur/Books/CPbook/Codes/HPCodes/
Animations
https://physics.oregonstate.edu/~landaur/Books/CPbook/Codes/Animations/
Contents 3rd edition
Preface ii 1. ComputationalScienceBasics1 1
1.1 Software Needed to Use This eBook 1
1.2 Using The Features of This eBook 4
1.3 Computational Physics and Computational Science 7
1.4 Viewing the Subjects to be Covered 8
1.5 Making Computers Obey; Languages (Theory) 11
1.6 Programming Warmup 14
1.7 Computer Number Representations (Theory) 21
1.8 Problem: Summing Series 29
2. Errors&UncertaintiesinComputations2 32
2.1 Types of Errors (Theory) 32
2.2 Errors in Spherical Bessel Functions (Problem) 37
2.3 Experimental Error Investigation (Problem) 40
3. VisualizationTools3 45
3.1 Data Visualization (General) 46
3.2 Python Matplotlib, Visual (VPython) Packages 46
3.3 Using Packages in Python Programs 47
3.4 Matplotlib for 2-D Graphs in Python 48
3.5 2-D Plots with Visual (VPython) 54
3.6 Animations with Visual (VPython) 56
3.7 Gnuplot: Reliable 2-D and 3-D Plots 57
3.8 Texturing and 3-D Imaging 65
3.9 Grace/ACE: Superb 2-D Graphs for Unix/Linux 65
4. PythonObject-OrientedPrograms:Impedance&Batons4 71
4.1 Unit I. Basic Objects: Complex Impedance 71
4.2 Complex Numbers (Math) 72
4.3 Resistance Becomes Impedance (Theory) 73
4.4 Abstract Data Structures, Objects (CS) 74
4.5 Python’s Built-in Complex Number Type 80
4.6 Complex Currents (Solution) 80
4.7 OOP Worked Examples 81
4.8 Subclasses and Class Inheritance 85
4.9 Unit II. Advanced Objects: Baton Projectiles⊙ 85
4.10 Trajectory of a Thrown Baton (Problem) 86
4.11 OOP Design Concepts (CS) 88
4.12 Multiple Classes and Multiple Inheritances 89
4.13 Multiple Inheritances, Classes in One File 92
4.14 Multiple Inheritance, Separate Files 93
4.15 OOP Example: Superposition of Motions 101
4.16 Newton’s Laws of Motion (Theory) 101
4.17 OOP Class Structure (Method) 102
4.18 Python Implementation 102
5. MonteCarloSimulations(Nonthermal)5 104
5.1 Unit I. Deterministic Randomness 104
5.2 Random Sequences (Theory) 104
5.3 Unit II. Monte Carlo Applications 109
5.4 A Random Walk (Problem) 109
5.5 Radioactive Decay (Problem) 112
5.6 Decay Implementation and Visualization 115
6. Integration6 116
6.1 Integrating a Spectrum (Problem) 116
6.2 Quadrature as Box Counting (Math) 116
6.3 Experimentation 125
6.4 Higher-Order Rules (Algorithm) 125
6.5 Monte Carlo Integration by Stone Throwing 126
6.6 High-Dimensional Integration (Problem) 128
6.7 Integrating Rapidly Varying Functions (Problem) 129
6.8 Nonuniform Assessment ⊙ 132
7. Differentiation&Searching7 135
7.1 Unit I. Numerical Differentiation 135
7.2 Forward Difference (Algorithm) 136
7.3 Central Difference (Algorithm) 136
7.4 Extrapolated Difference (Method) 137
7.5 Error Analysis (Assessment) 138
7.6 Second Derivatives (Problem) 139
7.7 Unit II. Trial-and-Error Searching 140
7.8 Quantum States in a Square Well (Problem) 140
7.9 Trial-and-Error Roots via Bisection Algorithm 140
7.10 Newton–Raphson Searching (Improved Algorithm) 142
8. MatrixEquationSolutions;DataFitting8 146
8.1 Unit I. Systems of Equations, Matrix Computing 146
8.2 Two Masses on a String 147
8.3 Classes of Matrix Problems (Maths) 150
8.4 Numerical Python and Python Matrix Library 155
8.5 Unit II. Data Fitting 162
8.6 Fitting Exponential Decay (Problem) 167
8.7 Least-Squares Fitting (Method) 170
9. DifferentialEquationApplications9 178
9.1 Unit I. Free Nonlinear Oscillations 178
9.2 Nonlinear Oscillators (Models) 179
9.3 Types of Differential Equations (Math) 180
9.4 Dynamic Form for ODEs (Theory) 181
9.5 ODE Algorithms 183
9.6 Solution for Nonlinear Oscillations (Assessment) 191
9.7 Extensions: Nonlinear Resonances, Beats, Friction 192
9.8 Extension: Time-Dependent Forces 194
9.9 Unit II. Binding A Quantum Particle 194
9.10 Theory: Quantum Eigenvalue Problem 195
9.11 Algorithm: Eigenvalues via ODE Solver + Search 196
9.12 Explorations 202
9.13 Unit III. Scattering, Projectiles & Orbits 203
9.14 Problem 1: Classical Chaotic Scattering 203
9.15 Problem 2: Balls Falling Out of the Sky 206
9.16 Theory: Projectile Motion with Drag 207
9.17 Problem 3: Planetary Motion 208
10.Fourier Analysis: Signals and Filters 10 211
10.1 Unit I. Fourier Analysis of Nonlinear Oscillations 211
10.2 Fourier Series (Math) 212
10.3 Exercise: Summation of Fourier Series 214
10.4 Fourier Transforms (Theory) 215
10.5 Unit II. Filtering Noisy Signals 223
10.6 Noise Reduction via Autocorrelation (Theory) 224
10.7 Filtering with Transforms (Theory) 227
10.8 Unit III. Fast Fourier Transform Algorithm (FFT) ⊙ 231
10.9 FFT Implementation 234
10.10 FFT Assessment 234
11.Wavelet Analysis & Data Compression 11 238
11.1 Unit I. Wavelet Basics 238
11.2 Wave Packets and Uncertainty Principle (Theory) 240
11.3 Short-Time Fourier Transforms (Math) 241
11.4 The Wavelet Transform 242
11.5 Unit II. Discrete Wavelet Transforms, MRA⊙ 246
12.Discrete & Continuous Nonlinear Dynamics 12 259
12.1 Unit I. Bug Population Dynamics (Discrete) 259
12.2 The Logistic Map (Model) 259
12.3 Properties of Nonlinear Maps (Theory) 260
12.4 Mapping Implementation 262
12.5 Bifurcation Diagram 263
12.6 Logistic Map Random Numbers (Exploration)· 265
12.7 Other Maps (Exploration) 266
12.8 Signals of Chaos: Lyapunov Coefficients ⊙ 266
12.9 Unit I Quiz 268
12.10 Unit II. Pendulums Become Chaotic 270
12.11 Chaotic Pendulum ODE 270
12.12 Visualization: Phase Space Orbits 273
12.13 Exploration: Bifurcations of Chaotic Pendulums 279
12.14 Alternate Problem: The Double Pendulum 280
12.15 Assessment: Fourier/Wavelet Analysis of Chaos 282
12.16 Exploration: Alternate Phase Space Plots 283
12.17 Further Explorations 283
12.18 Unit III. Coupled Predator–Prey Models ⊙ 284
12.19 Lotka–Volterra Model 285
13.Fractals & Statistical Growth 13 290
13.1 Fractional Dimension (Math) 290
13.2 The Sierpin ́ski Gasket (Problem 1) 291
13.3 Beautiful Plants (Problem 2) 293
13.4 Ballistic Deposition (Problem 3) 296
13.5 Length of British Coastline (Problem 4) 298
13.6 Correlated Growth, Forests, Films (Problem 5) 301
13.7 Globular Cluster (Problem 6) 301
13.8 Fractals in Bifurcation Plot (Problem 7) 305
13.9 Fractals from Cellular Automata 305
13.10 Perlin Noise Adds Realism ⊙ 307
13.11 Quiz 311
14.HPC Hardware, Tuning, Parallel Computing 14 312
14.1 Unit I. High-Performance Computers (CS) 312
14.2 Memory Hierarchy 313
14.3 The Central Processing Unit 316
14.4 CPU Design: Reduced Instruction Set Computer 316
14.5 CPU Design: Multiple-Core Processors 317
14.6 CPU Design: Vector Processor 318
14.7 Unit II. Parallel Computing 319
14.8 Parallel Semantics (Theory) 319
14.9 Distributed Memory Programming 321
14.10 Parallel Performance 322
14.11 Parallelization Strategy 324
14.12 Practical Aspects of MIMD Message Passing 325
14.13 Example of a Supercomputer: IBM Blue Gene/L 327
14.14 Towards Exascale Computing via Multinode-Multicore-GPU Com-
puters 329
14.15 Unit III. HPC Program Optimization 331
14.16 Programming for the Data Cache (Method) 340
14.17 Practical Tips for Multicore, GPU Programming 342
15.Thermodynamic Simulations, Quantum Path Integration 15 345
15.1 Unit I. Magnets via the Metropolis Algorithm 345
15.2 An Ising Chain (Model) 345
15.3 Statistical Mechanics (Theory) 347
15.4 Metropolis Algorithm 348
15.5 Unit II. Magnets via Wang–Landau Sampling ⊙ 354
15.6 Wang–Landau Sampling 356
15.7 Unit III. Feynman Path Integrals ⊙ 361
15.8 Feynman’s Space-Time Propagation (Theory) 361
15.9 Exploration: Quantum Bouncer’s Paths ⊙ 370
16.Simulating Matter with Molecular Dynamics 16 374
16.1 Molecular Dynamics (Theory) 374
16.2 Verlet and Velocity-Verlet Algorithms 380
16.3 1-D Implementation and Exercise 381
16.4 Trajectory Analysis 384
16.5 Quiz 384
17.PDEs for Electrostatics & Heat Flow 17 386
17.1 PDE Generalities 386
17.2 Unit I. Electrostatic Potentials 387
17.3 Fourier Series Solution of a PDE 388
17.4 Solution: Finite-Difference Method 391
17.5 Assessment via Surface Plot 394
17.6 Alternate Capacitor Problems 395
17.7 Implementation and Assessment 397
17.8 Electric Field Visualization (Exploration) 398
17.9 Laplace Quiz 398
17.10 Unit II. Finite-Element Method ⊙ 399
17.11 Electric Field from Charge Density (Problem) 399
17.12 Analytic Solution 400
17.13 Finite-Element (Not Difference) Methods 400
17.14 FEM Implementation and Exercises 404
17.15 Exploration 406
17.16 Unit III. Heat Flow via Time-Steps (Leapfrogs) 406
17.17 The Parabolic Heat Equation (Theory) 407
17.18 Assessment and Visualization 412
17.19 Improved Heat Flow: Crank–Nicolson Method 413
18.PDE Waves: String, Quantum Packet, E&M 18 418
18.1 Unit I. Vibrating String 418
18.2 The Hyperbolic Wave Equation (Theory) 418
18.3 Waves with Friction (Extension) 424
18.4 Waves for Variable Tension and Density (Extension) 425
18.5 Unit II. Quantum Wave Packets 429
18.6 Time-Dependent Schro ̈dinger Equation (Theory) 429
18.7 Algorithm for the 2-D Schro ̈dinger Equation 433
18.8 Unit III. E&M Waves, Finite-Difference t Domain ⊙ 435
18.9 Maxwell’s Equations 435
18.10 FDTD Algorithm 436
19.Solitons & Computational Fluid Dynamics 19 443
19.1 Unit I. Advection, Shocks, Russell’s Soliton 443
19.2 Theory: Continuity and Advection Equations 444
19.3 Theory: Shock Waves via Burgers’ Equation 445
19.4 Including Dispersion 448
19.5 Shallow-Water Solitons; the KdeV Equation 449
19.6 Unit II. River Hydrodynamics 453
19.7 Hydrodynamics, the Navier–Stokes Equation (Theory) 453
19.8 2-D Flow over a Beam 459
19.9 Theory: Vorticity Form of Navier–Stokes Equation 459
20.Integral Equations in Quantum Mechanics 20 468
20.1 Unit I. Bound States of Nonlocal Potentials 468
20.2 Momentum-Space Schro ̈dinger Equation (Theory) 469
20.3 Unit II. Nonlocal Potential Scattering ⊙ 473
20.4 Lippmann–Schwinger Equation (Theory) 473
A. Glossary A 479
B. Installing Python, Matplotlib, NumPy B 485
C. Software Directories E 486
D. Compression via DWT with Thresholding F 489
D.1 More on Thresholding 491
D.2 Wavelet Implementation and Assessment 492
Bibliography 493
Index 503
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docker
上記ソースコードをdocker上で利用できるようにした.
$ docker run -v /Users/administrator/Downloads/work:/home/work -p 8080:8080 -it kaizenjapan/computational-physics /bin/bash
dockerが起動したら。
# cd home
# ls
cp mkall.sh url0.txt url1.txt url2.txt url3.txt url4.txt url5.txt url6.txt url7.txt wgeturl.sh work
# cd cp
# ls
Animations HPCodes PythonCodes pythoncodes
ごめんなさい。小文字のフォルダは練習用が残ったままです。
python環境だけ で、まだfortranとCは導入(install)していない。 でなく、fortranとCも利用できるようにした。
近日中に導入予定。
python は import visualでエラー中。
javaは導入のエラーでここでは使えない。
別記事の方は使える。
計算物理学 Rubin H. Landau docker登録その２
https://qiita.com/kaizen_nagoya/items/a72a79de29a2b43b172b
java error
今日のdocker error: java E: Sub-process /usr/bin/dpkg returned an error code (1)
https://qiita.com/kaizen_nagoya/items/d0d890c6bdf455c66087
python error
今日のpython error: import visual
https://qiita.com/kaizen_nagoya/items/ae8209ba4cff4218f1e7
今日のpython error: psychopy
https://qiita.com/kaizen_nagoya/items/e47f5ee6cc522485f109
fortran error
今日のfortran error
https://qiita.com/kaizen_nagoya/items/97a95ea3bb6786c76b1f
c warning
今日のCの警告 warning: type specifier missing, defaults to 'int'
https://qiita.com/kaizen_nagoya/items/94e4080235e75194213e
bibliographyの入力作業
Google Drive OCR機能を試してみた
https://qiita.com/kaizen_nagoya/items/5ad1ada6577396601eaa
dockerへの登録作業
計算物理学 Rubin H. Landau docker内 script
https://qiita.com/kaizen_nagoya/items/799b72523826f5fc7043
登録作業でのエラーは下記。
今日のshell error : File exists
https://qiita.com/kaizen_nagoya/items/2b6223b34fb81a7b871a
Qiitaへの記事分類は下記。
Qiitaに掲載する記事の分類
https://qiita.com/kaizen_nagoya/items/7b966ae426859d7ef0d7
参考資料(reference)
docker(19) 言語処理100本ノックをdockerで。python覚えるのに最適。
https://qiita.com/kaizen_nagoya/items/7e7eb7c543e0c18438c4
プログラムちょい替え（11) Fortran 多次元配列のアクセス順序による計算時間の違い
https://qiita.com/kaizen_nagoya/items/3d657649d74fdd753bad
Cコンパイラ３種をdockerで
https://qiita.com/kaizen_nagoya/items/77184cf005490d7579e6
文書履歴(document history)
ver. 0.01 初稿 20190806
ver. 0.02 docker追記 20190807 朝
ver. 0.03 fortran導入 20190807 午前
ver. 0.04 bibliograpy記入 20190807 昼
ver. 0.05 clang導入 20190807 午後
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