• plotcsv1.py
  Plot a single graph from (x, y1, y2, ...) data in a CSV file.
  What you learn: Graph plot using the matplotlib module, read data from a CSV file using the csv module.
  Usage: python plotcsv1.py csv_file_path
  How to use: download plotcsv1.py and data.csv, run 'python plotcsv1.py data.csv'.
• plotcsv_mult.py
  Plot tile-arrayed graphs from (x, y1, y2, ...) data in a CSV file.
  What you learn: Graph plot using the matplotlib module, read data from a CSV file using the csv module.
  Usage: python plotcsv_mult.py csv_file_path
  How to use: download plotcsv_mult.py and diff_order.csv , run 'python plotcsv_mult.py diff_order.csv'.
• plot_realtimeupdate.py
  An example of dynamic graph where graph is updated real-time.
  What you learn: Real-time update of graph using matplotlib.
  Usage: python plot_realtimeupdate.py
  How to use: download plot_realtimeupdate.py'.

講義予定日
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講義内容
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講義資料
Lecture materials

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Level *: Roundoff error from summing up small values (compare different precisions):  
   It compares the roundoff errors for different precision floating point types using ndarray of numpy module.
   Program: download sum_error.py (Source code) or sum_error-plt.py (Source code)
   Algorisms / Python modules: numpy
   Usage: python sum_error.py
   Output: to display and sum_error.csv
   What you learn: for, if, write to csv, numpy ndarray with specified FP precision

Level *: Roundoff error from summing up small values:  
   Show roundoff errors for given increment h and iteration number n.
   Program: download sum.py (Source code)
   Algorisms / Python modules: none
   Usage: python sum.py h n
   Ex: python sum.py 0.1 20
      Add 0.1 incrementally for 20 times and show each result.
   Output: to display
   What you learn: nothing new

Level *: Information buried:  
   Show the result of exp(-40) by Taylor expansion to show the  error of information buried.
   Program: download information_buried.py (Source code)
   Algorisms / Python modules: none
   Usage: python information_buried.py
   Output: to display
   What you learn: nothing new

Level *: Effect of different approximations on numerical differentiation: 
   It compares the differentiation errors for two- to seven-point difference approximations.
   Program: Download diff_order.py ( Source code)
   Algorisms / Python modules: none
   Usage: python diff_order.py
   Output: to display, diff_order.csv, and graph
   Visualization: implemented in the python script
   What you learn: how to plot graph using matplotlib 

Level *: Effect of different approximations on numerical differentiation with random noise data: 
   It compares the differentiation errors for two- to seven-point difference approximations.
   Program: download diff_order_noise.py (Source code)
   Algorisms / Python modules: two- to seven-point difference approximations
   Usage: python diff_order_noise.py
   Output: to display, diff_order_noise.csv, and graph
   What you learn: random functions in random module

Level ***:  Richardson extrapolation differentiation: 
   Program: download diff_richardson.py (Source code)
   Algorisms / Python modules: Richardson extrapolation
   Usage: python diff_richardson.py
   Output: to display.
   What you learn: for ~ break 　
 

python programs: Numerical integration
Level **:  Effect of different approximations on numerical integration: 
   It compares the integration errors for different approximations
   Program: download integ_order.py (Source code)
   Algorisms / Python modules: Rieman sum, trapezoid method, Simpson method, Bode method
   Usage: python integ_order.py
   Output: to display and integ_order.csv
   What you learn:  

Level ***: Numerical integration by Gauss-Legendre formula: 
   Program: download integ_gauss_legendre.py (Source code)
   Algorisms / Python modules: Gauss-Legendre formula
   Usage: python integ_gauss_legendre.py
   Output: to display.
   What you learn:  

Level ***:  Numerical integration by Romberg formula: 
   Download integ_romberg.py and run 'python integ_romberg.py'.
     Output: to display.
     What you learn:  

Level ****:  Numerical integration by variable conversion type formula: I.M.T. formula: 
   Download integ_imt.py and integ_gauss_legendre.py and run 'python integ_imt.py'.
     Output: to display.
     What you learn: use users' module (integ_gauss_legendre.py)

Level ****:  Numerical integration by variable conversion type formula:  Double Exponential function formula: 
   Download integ_doubleexp.py and run 'python integ_doubleexp.py'.
     Output: to display.
     What you learn:  

Level **: Effect of different h and approximations on numerical integration
   It compares the integration errors for Rieman, trapezoid, Simpson, and Bode methods with different h
   Program: download integ_order_h.py (Source code)
   Algorisms / Python modules: numerical integration (Rieman sum, trapezoid formula, Simpson formula, Bode formula)
   Usage: python integ_order_h.py xmin xmax nhscan func_type
                    func_type: [lorentz|gauss|exp]
                    nhscan: Number of division for the integration range is 2^nhscan (default: 18)
   Ex: python integ_order_h.py 0 1 18 gauss
              Check accuracy is improved in order of Rieman sum, trapezoid, Simpson and Bode formula for usual cases
        python integ_order_h.py -1 1 18 gauss
              Check Rieman sum is equal to trapezoid formula for symmetric integration
        python integ_order_h.py -5 5 12 gauss
              Check Rieman/trapezoid formula are better than the Simpson and Bode forumula 
   Output: to display and graph
   Visualization: implemented in the python script
   What you learn:  

Level **: Calculate Debye function
   Plot Debye function with given Debye temperature and temprature range
   Program: download debye_function.py (Source code)
　Show usage: python debye_function.py
　Usage: python debye_function.py Debye_T Tmin Tmax Tstep
　Ex.: python debye_funciton.py 300 0 500 10
　　　Debye temperature 300K, temperature range 0 - 500 K, 10 K step

Level **: Calculate electron density in metal based on the free electron model
   It calculate the electron density in metal using the density of states function N(E) and the Fermi-Dirac distribution function f(E) by integrating N(E)f(e). Different integration functions in scipy, integrate.quad() and integrate.romberg() are compared. 
   Program: download N-integration-metal.py  (Source code)
   Algorisms / Python modules: Numerical integration (adaptive integration scipy.integrate.quad(), Romberg integration scipy.integrate.romberg()) 
   Usage: python N-integration-metal.py T EF
   Ex.: python N-integration-metal.py 300 5.0
        　At 300K, EF = 5.0 eV, integrate with the specified relative accuration of 10^-8 for integrate.quad() function. Compare the execution time for 300 cycles integrations.
　　　　　Integration range (1): E = 0 ~ E_F + 6k_BT
　　　　　Integration range (2): E = 0 ~ E_F - 6k_BT
　　　　　Integration range (3): E = E_F - 6k_BT ~ E_F + 6k_BT
　　　　　　　Integration range (1) = Integration range (1) ＋ Integration range (2)
　

python programs: Solve a first-order differential equation
Level ***: Euler and Heun formula: 
   Solve differential equation, dx(t) / dt = -x²
   Program: download diffeq_euler_heun.py (Source code)
   Algorisms / Python modules: Euler formula and Heun formula
   Usage: python diffeq_euler_heun.py x0 dt nt
   Output: to display, diffeq_euler_heun.csv, and graph
   Visualization: implemented in the python script
   What you learn:  

  Simpson formula: 
   Download diffeq_simpson.py and run 'python diffeq_simpson.py'.
     Output: to display.
     What you learn:  

  Three-stage third-order Runge-Kutta formula: 
   Download diffeq_rungekutta.py and run 'python diffeq_rungekutta.py'.
     Output: to display.
     What you learn:  

  Four-stage fourth-order Runge-Kutta formula: 
   Download diffeq_rungekutta4.py and run 'python diffeq_rungekutta4.py'.
     Output: to display.
     What you learn:  

python programs: Solve a second-order differential equation
  Euler formula: 
   Download diffeq2nd_euler.py and run 'python diffeq2nd_euler.py'.
     Output: to display and diffeq2nd_euler.csv.
     Visualization: download plotcsv1.py and run 'python plotcsv1.py diffeq2nd_euler.csv'.
     What you learn:  

  Heun formula: 
   Download diffeq2nd_heun.py and run 'python diffeq2nd_heun.py'.
     Output: to display and diffeq2nd_heun.csv.
     Visualization: download plotcsv1.py and run 'python plotcsv1.py diffeq2nd_heun.csv'.
     What you learn:  

  Verlet formula: 
   Download diffeq2nd_verlet.py and run 'python diffeq2nd_verlet.py'.
     Output: to display and diffeq2nd_verlet.csv.
     Visualization: download plotcsv1.py and run 'python plotcsv1.py diffeq2nd_verlet.csv'.
     What you learn:  

python programs: Solve simultaneous second-order differential equations (連立2次微分方程式)
  Euler formula: 
   Download diffeq2nd_2d_euler.py and run 'python diffeq2nd_2d_euler.py'.
     Output: to display and diffeq2nd_2d_euler.csv.
     Visualization: download plotcsv1.py and run 'python plotcsv1.py diffeq2nd_2d_euler.csv'.
     What you learn: function that returns two values  

  Verlet formula: 
   Download diffeq2nd_2d_verlet.py and run 'python diffeq2nd_2d_verlet.py'.
     Output: to display and diffeq2nd_2d_verlet.csv.
     Visualization: download plotcsv1.py and run 'python plotcsv1.py diffeq2nd_2d_verlet.csv'.
     What you learn:

Level ******: Planet simulator: 
  Simulate motions of the planets in the solar system by the Euler or the Verlet formula
   Program: download diffeq2nd_planet.py (Source code)
   Input file(s): Planets database planet_db.csv
   Algorisms / Python modules: Euler formula and Heun formula
   Usage: python diffeq2nd_planet.py solver dt nt fplot
                    solver: 'Euler' or 'Verlet'
                    dt: time step in day
                    nt: number of steps
                    fplot: flag to plot graph (1: default) or not to plot (0)
   Ex: python diffeq2nd_planet.py Euler 0.5 5000 1
   Output: to display, diffeq2nd_planet_euler.csv and diffeq2nd_planet_euler_conservation.csv, and graph
   Visualization: integrated
   What you learn: realtime update of graph using matplotlib, min(), max(), sys.arg to change the solver
　

Level ***: Convolution with Gauss function:
   Program: convolution.py (Source code)
   Input file(s): dos.csv
   Usage: python convolution.py
   Output: to display, convolution.csv, and graph
   Visualization: integrated.  
              Or download plotcsv1.py and run, e.g., 'python plotcsv1.py convolution.csv'.
     What you learn:  

Level *****: Convolution/Deconvolution with Gauss function:
   Deconvolution by scipy.signal.deconvolve(), fft, the Jacobi method, and the Gauss-Seidel method.
   Program:  deconvolution.py (Source code)       
   Input file(s): pes.csv
   Show usage: python deconvolution.py
   Output: to display and graph
   Visualization: integrated
   What you learn: scipy.signal.convolve() and scipy.signal.deconvolve().
        Deconvolution using FFT and iFFT.
   More details:
         Show usage: python deconvolution.py
           usage for convolve() and fft: 
                python deconvolution.py file mode convmode smoothmode xmin xmax Wa Grange kzero klin
                   mode = [convolve|fft]
                   convmode = ['|full|same], effective only for mode = 'convolve'
                   smoothmode = combination of [convolve|extend|average]
          ex.: python deconvolution.py SnSe-DOS.csv convolve same convolve+extend -4.5 2.0 0.12 2.0 1 5
                Deconvolute using scipy.signal.deconvolve() after extending the raw data with zeros and linear filter.
                The x range is from -4.5 to 2.0.
                Gaussian filter has the width of 12 and the 2.0 times of the width will be used.
                Note that the filter elements should have somewhat large values e.g. > 0.01 for scipy.signal.deconvolve()
          ex.: python deconvolution.py SnSe-DOS.csv fft full convolve+extend -4.5 2.0 0.12 2.0 5 5
                Deconvolute using fft-based deconvoluation after extending the raw data with zeros and linear filter.
                The x range is from -4.5 to 2.0.
                Gaussian filter has the width of 12 and the 2.0 times of the width will be used.
           usage for the Jacobi/Gauss-Seidel mehods:
                  python deconvolution.py file mode xmin xmax Wa dump nmaxiter eps nsmooth zeroc
                      mode = [gs|jacobi] 
                      gs=Gauss-Seidel method jacobi=Jacobi method
                       zeroc = [0|1] zero correction after a Jacobi/Gauss-Seidel cycle
         ex.: python deconvolution.py pes.csv gs -6.0 2.0 0.12 1.0 300 1.0e-4 15 0

June 27, 2024

20240627LSQEquationOptimize.zip

Level **: Self-consistent method:
   Solve the I-V characteristic of a series circuit of a diode and a resister by self-consistent manner.
   Program: download equation-selfconsistent-diode.py
   Usage: python equation-selfconsistent-diode.py Vmin Vmax Vstep kmix
   Output: to display and graph
   Visualization: integrated 
   What you learn:  

Level ***: Newton-Raphson method:
   Program: download equation-newton-raphson.py (Source code)
   Usage: python equation-newton-raphson.py x0 dump tsleep
   Output: to display and graph
   Visualization:  
   What you learn:  

  Bisection method:
   Solve the Fermi level of semiconductor by bisection method.
   Download equation-bisection.py, and run 'python equation-bisection.py'.
     Output: to display.
     Visualization:  
     What you learn:  

  Brent's method:
   Solve the Fermi level of semiconductor by Brent's method.
   Download equation-brant.py, and run 'python equation-brent.py'.
     Output: to display.
     Visualization:  
     What you learn:  

Level ***: Calculation of EF for semiconductor by bisection method
   Program: download EF-bisection.py (Source code)
   Algorisms / Python modules: Bisection method
   Usage: python EF-bisection.py
   Output: to display.
   Visualization:  
   What you learn:  

Level ***: 金属のE_Fの温度依存性
   Program: download EF-T-metal.py (Source code)   
   説明：　金属のフェルミエネルギーの温度依存性を数値積分とNewton法を使って求める。
　　　　初期値として 0 K の E_F から始め、温度を上げながら、前回温度の E_F(T) を次の初期値として使うことで、
　　　　Newton法でも安定して計算できる。
  使用しているアルゴリズム： 数値積分 (多項式適合法 scipy.integrate.quad())
　　　　　　　　　　　　　　　　　　方程式の数値解法 （Newton法 scipy.optmize.newton())
  実行方法: python EF-T-metal.py 

Level ****: 半導体の統計物性の温度依存性
   Program: download EF-T-semiconductor.py (Source code)
   説明：　半導体のフェルミエネルギー、自由電子濃度、自由正孔濃度、イオン化アクセプター濃度、
           イオン化ドナー濃度の温度依存性を二分法を使って求める。非縮退近似を用い、
           ドナー・アクセプター準位の縮重は考慮していない。
　　　　　Newton法では E_F の初期値がかなり真値に近くないと発散するので、
　　　　　価電子帯上端と伝導帯下端エネルギーを初期として二分法を使う。
  使用しているアルゴリズム： 方程式の数値解法 (二分法 main()関数中に組み込み) 
  Usage: python EF-T-semiconductor.py EA NA ED ND Ec Nv Nc
  実行例: python EF-T-semiconductor.py 0.05 1.0e15 0.95 1.0e16 1.0 1.2e19 2.1e18
　　　　　Ec = 1.0 eV (= バンドギャップ)、E_A = 0.05 eV, N_A = 10¹⁵ cm^-3, E_D = 0.95 eV, N_D = 10¹⁶ cm^-3　　　 N_c = 1.2x10¹⁹ cm^-3, N_v = 2.1x10¹⁸ cm^-3 (バンドギャップを1.12 eVとすれば、ほぼ Si の物性値) 

Level *****: Solve multi-values equation: Calculate energy band diagram and wave functions by Kronig-Penney model
  説明： Kronig-Penneyモデルによる一次元バンド構造と波動関数
  Program: Download kronig_penney.py ( Source code)
  使用しているアルゴリズム： Find multiple solutions by direct search and secant method
  Usage: python kronig_penney.py 
  Usage1: python kronig_penney.py (graph a bwidth bpot k Emin Emax nE) 
  Usage2: python kronig_penney.py (band a bwidth bpot nG kmin kmax nk) 
  Usage3: python kronig_penney.py (wf a bwidth bpot kw iLevel xwmin xwmax nxw)
  実行例１： python kronig_penney.py graph 5.4064 0.5 10.0 0.0 0.0 9.5 51 
　　格子定数 5.4064 Å、ポテンシャル幅 0.5 Å、高さ 10.0 eVで、k = 0.0 についてのKronig-Penney方程式の
　　残差 Δ を E = 0.0 ～ 9.5 eV の範囲を51分割してプロット。Δ = 0 のEが固有エネルギー。
  実行例２： python kronig_penney.py band 5.4064 0.5 10.0 -0.5 0.5 21
　　格子定数 5.4064 Å、ポテンシャル幅 0.5 Å、高さ 10.0 eVで、k = [-0.5,0.5] の範囲を 21分割してバンド構造をプロットする。
  実行例３： python kronig_penney.py wf 5.4064 0.5 10.0 0.0 0 0.0 16.2192 101
　　格子定数 5.4064 Å、ポテンシャル幅 0.5 Å、高さ 10.0 eVで、k = 0.0 における下から 0 番目の
　　準位の波動関数をプロットする。波動関数は x = 0.0 ～ 16.2192 Å を 101 分割してプロットする。

  Two parameters Newton-Raphson method with graphical visualization of convergence process:
   Minimize a target function with two parameters by Newton-Raphson method.
   Download optimize-newton-raphson2d.py, and run, e.g., 'python optimize-newton-raphson2d.py', and  'python optimize-newton-raphson2d.py -4.0 -4.0'.
     Output: to display and graph.
     Usage:  python optimize-newton-raphson2d.py xini yini
     Visualization:  implemented in the python script
     What you learn:  

  Two parameters Steepest Descent method with graphical visualization of convergence process:
   Download optimize-steepdescent2d.py, and run, e.g., 'python optimize-steepdescent2d.py' and 'python optimize-steepdescent2d.py -4.0 -4.0'.
     Output: to display and graph.
     Usage:  python optimize-steepdescent2d.py xini yini
     Visualization:  implemented in the python script
     What you learn:  

  Two parameters Steepest Descent & Conjugate Gradient methods + Line Search methods 
with graphical visualization of convergence process:
   Minimize a target function with two parameters by the SD method and several line search methods.
   Download optimize-sd-cg2d-linesearch.py, and run, e.g., 
       'python optimize-sd-cg2d-linesearch.py'
       'python optimize-sd-cg2d-linesearch.py -4.0 -4.0'
       'python optimize-sd-cg2d-linesearch.py 2 2 sd one ellipsoid'
       'python optimize-sd-cg2d-linesearch.py 2 2 cg golden ellipsoid'
     Output: to display and graph.
     Usage:  python optimize-sd-cg2d-linesearch.py xini yini algorism lsmode functype
                    algorism: optional, [sd|cg], default = 'sd'
                    lsmode: optional, [one|simple|exact|golden|armijo], default = 'simple'
                    functype: optional, '' or 'ellipsoid', default = ''
     Visualization:  implemented in the python script
     What you learn:  

  Two parameters Marquart mehod to solve a LSQ problem:
   Download lsq-marquart2d.py, and run 'python optimize-marquart2d.py'
     Output: to display.
     Visualization:  
     What you learn:  

結晶構造関係プログラム
資料： Crystal.pdf　
* レベル★★　結晶構造・ベクトル解析基本ライブライブラリィ　tkcrystalbase.py　(プログラムコード)
　　説明： 他のpythonプログラムからimportして使用する。
* レベル★★　単位格子・逆格子描画  crystal_draw_cell.py (プログラムコード・実行結果)
    実行方法： python crystal_draw_cell.py
* レベル★★　単位格子変換・描画     crystal_convert_cell.py (プログラムコード・実行結果)
    実行方法： python crystal_convert_cell.py crystal_name conversion_mode kRatom
    実行例： python crystal_convert_cell.py FCC FCCPrim
* レベル★★　原子間距離      crystal_distance.py     (プログラムコード)
    実行方法： python crystal_distance.py
* レベル★★　Bragg角度    crystal_XRD.py    (プログラムコード)
    実行方法： python crystal_XRD.py
* レベル★★★　Madelung potentialの計算   crystal_MP_Ewald.py  ( プログラムコード)
    実行方法： python crystal_MP_Ewald.py