Lec03S.ipynb

{"nbformat":4,"nbformat_minor":0,"metadata":{"kernelspec":{"display_name":"Python 3","language":"python","name":"python3"},"language_info":{"codemirror_mode":{"name":"ipython","version":3},"file_extension":".py","mimetype":"text/x-python","name":"python","nbconvert_exporter":"python","pygments_lexer":"ipython3","version":"3.6.4"},"colab":{"name":"Lec03S.ipynb","provenance":[],"collapsed_sections":["Atwth9_Au1tK"]}},"cells":[{"cell_type":"markdown","metadata":{"id":"HJIL_suvu1s7"},"source":["# Day 3 (Vector and matrix operation, and statistical processing)\n","\n","## Content \n","\n","* mathematical module\n","* numpy module\n","* Vector and matrix operation\n","* Statistical processing\n","\n","## Library `math`\n","- It has the fixed value $\\pi$ and functions `sin`, `cos`, `tan`, `exp`, `log` etc.\n","- Please see the following example."]},{"cell_type":"code","metadata":{"id":"MgNtCYZDu1s7"},"source":["import math\n","\n","print(math.pi)\n","print(math.sin(math.pi * 0.5))\n","et = math.exp(2.0)\n","print(et)\n","print(math.log(et))\n"],"execution_count":null,"outputs":[]},{"cell_type":"markdown","metadata":{"id":"OXEjiBqru1tH"},"source":["### Practice\n","- Try to use such functions."]},{"cell_type":"code","metadata":{"id":"o6i0gjkXu1tI","executionInfo":{"status":"ok","timestamp":1606286968878,"user_tz":-540,"elapsed":792,"user":{"displayName":"Yamashita Yukihiko","photoUrl":"","userId":"17969210254483143968"}}},"source":["# Make a program: Use math library"],"execution_count":1,"outputs":[]},{"cell_type":"markdown","metadata":{"id":"Atwth9_Au1tK"},"source":["## Bisection method\n","\n","### Assumption\n","- Assume that $f(x)$ is monotone increasing function.\n","- We solve $f(x) = 0$.\n","- For initial values $a$ and $b$, we have $f(a) < 0$ and $f(b) > 0$.\n","- The precision of answer is $\\varepsilon$.\n","### Algorithm\n","0. $x = (a + b) / 2$\n","0. If $b - a < \\varepsilon$, stop the algorithrm and $x$ is answer.\n","0. If $f(x) > 0$, let $b = x$.\n","0. If $f(x) < 0$, let $a = x$.\n","0. If $f(x) = 0$, stop the algorithrm and $x$ is answer.\n","0. Go to 1. \n","\n","\n","### Practice\n","- Solve the following by bisection method.\n","$$\n","\\sin(x) + x - 1 = 0\n","$$\n","- The lower initila value is 0 and the upper initial value $\\pi / 2$.\n","- $\\varepsilon = 10^{-6}$"]},{"cell_type":"markdown","metadata":{"id":"SnLfoUA2u1tK"},"source":["## Practice of using mathematical description by Markdown\n","- Functions, fraction, subscription, superscription, sum, integral, large parenthesis. \n","- In line."]},{"cell_type":"code","metadata":{"id":"clVLmOUDu1tL"},"source":["# Make a program: bisection method\n","import math\n"],"execution_count":null,"outputs":[]},{"cell_type":"markdown","metadata":{"id":"6jiG2scYu1tT"},"source":["# Vector and matrix calculation\n","\n","## Vector and matrix operation\n","\n","* <font color=\"blue\">{Major part of numerical analysis is the calculation of linear algebra.}</font>\n","  * Structure analysis and Fluid analysis\n","  * Electromagnetic analysis and circuit analysis\n","  * Statistical processing and image processing.\n","* Recent computers are designed to accelerate vector operations.\n","  * Vector processor (Super computer)\n","  * Operations for vector processing in CPU.   \n","  SIMD: Single instruction multiple data\n","     * SSE: Streaming Single instruction multiple data Extensions\n","     * AVX: Advanced Vector eXtensions\n","  * GPU (Graphics Processing Unit)\n","* Expressions of vector and matrix in Python.\n"," * 1-dimensional array : vector\n"," * 2-dimensional array : matrix\n"," * $n$-dimensional array ($n \\leq 2$) : tensor\n","* In order to accelerate the calculation, the amount of program for the matrix multiplication become longer and longer.   \n","<font color=\"orange\">$\\Rightarrow$ Use libraries.  \n"," * BLAS (Basic Linear Algebra Subprograms) \n"," * LAPACK (Linner Algebra Package)\n","\n","## Library `numpy`\n","- ndarray (array of numpy) is similar to list.\n","- Calulation of np.array is faster than them.\n","- `dtype` should be set if it is not `int`. Mix of type is not allowed."]},{"cell_type":"code","metadata":{"id":"4aakd9ENu1tT"},"source":["import numpy as np\n","\n","v1 = np.array([1, 2, 3, 4, 5], dtype='float64')\n","v2 = np.array([2, -1, 3, 3, -2], dtype = 'float64')\n","m1 = np.array([[5, 3, -1, 4, 5],[1, 4, 5, 3, 2],[-1, 0, 5, 2, 2]], dtype='float64')\n","m2 = np.array([[1, 3, -2],[1, -2, 5]], dtype='float64')\n","print(v1)\n","print(m1)\n","\n","# Size\n","print(\"v1.size = {0}\".format(v1.size))\n","print(\"m1.size = {0}\".format(m1.size))\n","\n","# Len\n","print(\"len(v1) = {0}\".format(len(v1)))\n","print(\"len(m1) = {0}\".format(len(m1)))\n","\n","# Shape\n","print(\"v1.shape = {0}\".format(v1.shape))\n","print(\"m1.shape = {0}\".format(m1.shape))\n","\n","(rowM1, colM1) = m1.shape\n","\n","print(\"Number of rows of m1 = {0}\".format(rowM1))\n","print(\"Number of columns of m1 = {0}\".format(colM1))\n","\n","# An element\n","print(\"v1[2] = {0}\".format(v1[2]))\n","print(\"m1[1,2] = {0}\".format(m1[1,2]))\n","\n","# Extract elements\n","print(\"m1[0:2,1:3] = {0}\".format(m1[0:2,1:3]))\n","\n","# Make zero matrix\n","print(\"np.zeros(2) = {0}\".format(np.zeros(2)))\n","print(\"np.zeros((2, 3)) = {0}\".format(np.zeros((2, 3))))\n","\n","# Make a matrix with all elements 1\n","print(\"np.ones(2) = {0}\".format(np.ones(2)))\n","print(\"np.ones((2, 3)) = {0}\".format(np.ones((2, 3))))\n"],"execution_count":null,"outputs":[]},{"cell_type":"markdown","metadata":{"id":"zbKxQGA-u1tW"},"source":["### Practice\n","- Calculate the innerproduct of `v1` and `v2` by using `for` sentence.\n","- Calculate the product of `m1` and `v1` by using `for` sentence.\n","- Calculate the product of `m1` and `m2` by using `for` sentence."]},{"cell_type":"code","metadata":{"id":"qaT2Ho2Fu1tW"},"source":["# Make a program\n","# Inner product\n","\n","# Multiplicastion of a matrix and a vector\n","\n","# Multiplicastion of a matrix and a matrix\n"],"execution_count":null,"outputs":[]},{"cell_type":"markdown","metadata":{"id":"EJzJ6AdFu1tb"},"source":["### dot product\n","- Inner product and matrix multiplication can be done easily."]},{"cell_type":"code","metadata":{"id":"5wO2jWvcu1tc"},"source":["print(np.dot(v1, v2))\n","print(v1.dot(v2))\n","print(v1)"],"execution_count":null,"outputs":[]},{"cell_type":"markdown","metadata":{"id":"v8XAc8Ywu1th"},"source":["### Practice\n","- Try dot product for matrix and vector multiplication.\n","- Try dot product for matrix and matrix multiplication."]},{"cell_type":"code","metadata":{"id":"J889RRV7u1ti"},"source":["# Make a program: Use dot product\n"],"execution_count":null,"outputs":[]},{"cell_type":"markdown","metadata":{"id":"QFbBUO25u1tk"},"source":["### Practice\n","- Make functions to do selection sort in both ascending and descending orders for given data in ndarray."]},{"cell_type":"code","metadata":{"id":"W1pXHbocu1tl"},"source":["# Make a program sort ascending/descending orders\n","import numpy as np\n","\n","#def sortSelectAscend(ar):\n","\n","#def sortSelectDescend(ar):\n","                \n","ar1 = np.array([10, -2, 13, 42, 35, 23, -23, 12, 12])\n","print(ar1)\n","sortSelectAscend(ar1)\n","print(ar1)\n","sortSelectDescend(ar1)\n","print(ar1)"],"execution_count":null,"outputs":[]},{"cell_type":"markdown","metadata":{"id":"CxvMZL1Tu1tn"},"source":["## Statistics\n","### Practice\n","- Calulate mean, variance, standard deviation, and median for given data in `ndarray` by using `for` sentence.\n","- Median : If the number of data $N$ is odd, the $(N+1)/2$-th largest data. If it is even, the average of $N$-th and $(N+1)$-th largest data."]},{"cell_type":"code","metadata":{"id":"p_pWd4Tnu1to","colab":{"base_uri":"https://localhost:8080/"},"executionInfo":{"status":"ok","timestamp":1606288499871,"user_tz":-540,"elapsed":614,"user":{"displayName":"Yamashita Yukihiko","photoUrl":"","userId":"17969210254483143968"}},"outputId":"5c0888c2-ab04-4b51-fe74-0e9bb9f7e0a7"},"source":["# Make a program\n","import numpy as np\n","data = np.array([10, 21, 34, 4, 15, 16, 7], dtype='float64') # The given data\n","N = len(data)\n","\n","# Mean\n","print(\"Mean: {0:.2f}\".format(mean))\n","\n","# Variace\n","print(\"Mean: Variance: {0:.2f}, Standard deviation: {1:.2f}\".format(variance, stdev))\n","\n","# Median\n","# Selection sort\n","\n","print('Median: {0:.2f}'.format(median))"],"execution_count":4,"outputs":[{"output_type":"stream","text":["Mean: 15.29\n","Mean: Variance: 86.78, Standard deviation: 9.32\n","Median: 15.00\n"],"name":"stdout"}]},{"cell_type":"markdown","metadata":{"id":"8wOolEx8u1tq"},"source":["- They can be calculated by using library of `statistics`"]},{"cell_type":"code","metadata":{"id":"SiSPR0jNu1tq","colab":{"base_uri":"https://localhost:8080/"},"executionInfo":{"status":"ok","timestamp":1606289225365,"user_tz":-540,"elapsed":644,"user":{"displayName":"Yamashita Yukihiko","photoUrl":"","userId":"17969210254483143968"}},"outputId":"a0cc91ee-24d6-4b02-9989-dcd34ed55f21"},"source":["import statistics as st\n","import numpy as np\n","\n","data     = np.array([10, 21, 34, 4, 15, 16, 7], dtype='float64')\n","mean     = st.mean(data)\n","print(\"Mean: {0:.2f}\".format(mean))\n","\n","variance = st.variance(data)\n","stdev    = st.stdev(data)\n","print(\"Mean: Variance: {0:.2f}, Standard deviation: {1:.2f}\".format(variance, stdev))\n","\n","median   = st.median(data)\n","print('Median: {0:.2f}'.format(median))\n"],"execution_count":6,"outputs":[{"output_type":"stream","text":["Mean: 15.29\n","Mean: Variance: 101.24, Standard deviation: 10.06\n","Median: 15.00\n"],"name":"stdout"}]},{"cell_type":"markdown","metadata":{"id":"Vz6517Ygu1tv"},"source":["- Program to describe a histgram of random values of a uniform distribution and print mean and standard deviation\n","- Its true values are 0.5 and $1 / \\sqrt{12}$, respectively."]},{"cell_type":"code","metadata":{"id":"Uk44K8fWu1tw","colab":{"base_uri":"https://localhost:8080/","height":282},"executionInfo":{"status":"ok","timestamp":1606290391537,"user_tz":-540,"elapsed":913,"user":{"displayName":"Yamashita Yukihiko","photoUrl":"","userId":"17969210254483143968"}},"outputId":"8daf70cb-07d5-4caf-e6e7-c688a529030b"},"source":["import numpy as np\n","import statistics as st\n","import matplotlib.pyplot as plt\n"," \n","N = 10000\n","# Generate N random values of unifrom distibution between 0 and 1\n","data = np.random.rand(N)\n"," \n","# Output graph\n","plt.hist(data)\n","\n","mean     = st.mean(data)\n","stdev    = st.stdev(data)\n","print(\"Mean: {0:.2f}, Standard deviation: {1:.2f},  1 / sqrt(12) = {2}\".format(mean, stdev, 1.0 / np.sqrt(12.0)))"],"execution_count":7,"outputs":[{"output_type":"stream","text":["Mean: 0.50, Standard deviation: 0.29,  1 / sqrt(12) = 0.2886751345948129\n"],"name":"stdout"},{"output_type":"display_data","data":{"image/png":"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\n","text/plain":["<Figure size 432x288 with 1 Axes>"]},"metadata":{"tags":[],"needs_background":"light"}}]},{"cell_type":"markdown","metadata":{"id":"n68Qpf-5u1ty"},"source":["### Practice\n","- Make random values of a uniform distribution of which mean is 0 and standard deviation is 1."]},{"cell_type":"code","metadata":{"id":"UNrMXbVPu1ty","colab":{"base_uri":"https://localhost:8080/","height":283},"executionInfo":{"status":"ok","timestamp":1602222671102,"user_tz":-540,"elapsed":2297,"user":{"displayName":"Yamashita Yukihiko","photoUrl":"","userId":"17969210254483143968"}},"outputId":"24d59a00-5adb-4bd0-a789-cc3bb0c612f8"},"source":["# Fill after 'data = '\n","import numpy as np\n","import statistics as st\n","import matplotlib.pyplot as plt\n"," \n","N = 10000\n","# Generate N random values of unifrom distibution of which mean is 0 and standard deviation is 1.\n","# data = \n"," \n","# Output graph\n","plt.hist(data)\n","\n","mean     = st.mean(data)\n","stdev    = st.stdev(data)\n","print(\"Mean: {0:.2f}, Standard deviation: {1:.2f}\".format(mean, stdev))\n"],"execution_count":null,"outputs":[{"output_type":"stream","text":["Mean: -0.02, Standard deviation: 0.99\n"],"name":"stdout"},{"output_type":"display_data","data":{"image/png":"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\n","text/plain":["<Figure size 432x288 with 1 Axes>"]},"metadata":{"tags":[],"needs_background":"light"}}]},{"cell_type":"markdown","metadata":{"id":"CuNniUh5u1t2"},"source":["- Draw graph of a normal distribution."]},{"cell_type":"code","metadata":{"id":"Cj0qchCfu1t2","colab":{"base_uri":"https://localhost:8080/","height":283},"executionInfo":{"status":"ok","timestamp":1602222671430,"user_tz":-540,"elapsed":2574,"user":{"displayName":"Yamashita Yukihiko","photoUrl":"","userId":"17969210254483143968"}},"outputId":"0fd4d0f3-0a61-4b02-d31f-7aa61b3a883b"},"source":["# Fill after 'pdfn = '\n","import numpy as np\n","import matplotlib.pyplot as plt\n","\n","mean = 50.0\n","stdv = 10.0\n","x    = np.arange(0, 100, 0.1)\n","# pdfn = \n","plt.plot(x, pdfn)"],"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["[<matplotlib.lines.Line2D at 0x7fe8531f1908>]"]},"metadata":{"tags":[]},"execution_count":49},{"output_type":"display_data","data":{"image/png":"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\n","text/plain":["<Figure size 432x288 with 1 Axes>"]},"metadata":{"tags":[],"needs_background":"light"}}]},{"cell_type":"markdown","metadata":{"id":"gz1fHhPyu1t5"},"source":["- Draw graph of a normal distribution and a histgram of random values of normal distribution."]},{"cell_type":"code","metadata":{"id":"7u-8jaztu1t6","colab":{"base_uri":"https://localhost:8080/","height":283},"executionInfo":{"status":"ok","timestamp":1602222671967,"user_tz":-540,"elapsed":3072,"user":{"displayName":"Yamashita Yukihiko","photoUrl":"","userId":"17969210254483143968"}},"outputId":"c1f8a09e-bd02-4dbc-e9e8-1db6075c7ea7"},"source":["import numpy as np\n","import matplotlib.pyplot as plt\n","\n","mean = 50.0\n","stdv = 10.0\n","N    = 10000\n","\n","# Generate N random values of normal distibution of average mean and stardard deviation stdv\n","data = np.random.normal(mean, stdv, N)\n","\n","# Probability density function of normal distribution\n","x    = np.arange(0, 100, 0.1)\n","pdfn = np.exp(-(x - mean) * (x - mean) / (2.0 * stdv * stdv)) / (np.sqrt(2.0 * np.pi) * stdv)\n","\n","# Output graph\n","NBin = 50           # Number of bins\n","RangeBin = [20, 80] # Range of bins\n","plt.hist(data, NBin, RangeBin)\n","plt.plot(x, N * (RangeBin[1] - RangeBin[0]) / float(NBin) * pdfn)\n"],"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["[<matplotlib.lines.Line2D at 0x7fe853869cf8>]"]},"metadata":{"tags":[]},"execution_count":50},{"output_type":"display_data","data":{"image/png":"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\n","text/plain":["<Figure size 432x288 with 1 Axes>"]},"metadata":{"tags":[],"needs_background":"light"}}]},{"cell_type":"markdown","metadata":{"id":"LZRDzbT2u1t8"},"source":["### Central limit theorem\n","- Assume that $X_1,\\,X_2,\\,\\ldots,\\, X_M$ are independent random variable of identical distribution.\n","- Then, \n","$$\n","\\frac{X_1+ X_2 + \\cdots + X_M}{\\sqrt{M}}\n","$$\n","converges to a random variable of a normal distribution of which mean and standard deviation are respectively the same as those of original distribution when $M \\rightarrow \\infty$.\n","\n","#### Various distribution of which mean is 0 and standard deviation is 1\n","- Uniform\n","- $-1$ or $+1$\n","- Triangle"]},{"cell_type":"code","metadata":{"id":"r71D2VyldzJb"},"source":["import numpy as np\n","import matplotlib.pyplot as plt\n","\n","# Unifrom\n","data = np.sqrt(12.0) * (np.random.rand(N) - 0.5)\n","#data = np.sign(np.random.rand(N) - 0.5)\n","#data = np.sqrt(18.0) * (np.sqrt(np.random.rand(N)) - 2.0/3.0)\n","\n","# Output graph\n","NBin = 50\n","RangeBin = [-4, 4]\n","plt.hist(data, NBin, RangeBin)"],"execution_count":null,"outputs":[]},{"cell_type":"markdown","metadata":{"id":"NKedO1ibd0Lm"},"source":["### Practice\n","Draw the histgram of $N$ sum of $M$ random values of various distribution of which mean is 0 and standard deviation is 1 and the graph of probability density function of the starndard normal distribution ($M = 100$ and $N = 10000$). Align hights of the two. "]},{"cell_type":"code","metadata":{"id":"KtDvVxlru1t8"},"source":["# Make a program\n","#### Central limit theorem\n","\n","import numpy as np\n","import matplotlib.pyplot as plt\n","\n","mean = 0.0\n","stdv = 1.0\n","N    = 100000\n","M    = 1\n"],"execution_count":null,"outputs":[]},{"cell_type":"markdown","metadata":{"id":"i3d-ZjJlu1uB"},"source":["## File input/output\n","\n","- `open(filePath, mode)` : to open file.\n","- `(object of io.TextIOWrapper).write()` : write data to the file.\n","- `(object of io.TextIOWrapper).readline()` : read a line\n","\n","### Google Colaboratory \n","\n","We make possible to read/write files in Google drive from programs of Google Colaboratory.\n","\n","* Click the folder icon in the left region.\n","* A list of file appears and click the folder icon with triangle (the most right of three folder icons.)\n","* A new following cell appears.\n","```\n","from google.colab import drive\n","drive.mount('/content/drive')\n","```\n","* Excute it (Ctrl-Enter) and a new window appears of which content is like.\n","'''\n","Go to this URL in a browser: (a very long URL)\n","Enter your authorization code:\n","```\n","* Click the very long URL.\n","  * Select your Google account.\n","  * Click `Allow`.\n","  * Your authorization code will appear.\n","  * Copy it by clicking the double squre icon.\n","* Paste it and type `Enter`.\n","\n","Then, `My Drive` of Google drive is mounted on `/content/drive/` of Google Colaboratory.\n","\n","* Make a folder to store data.\n","  * Go to `My Drive` of Google Drive.\n","  * Click `New`.\n","  * Select `Folder`.\n","  * Set the name of folder `APN_data`. \n","* We can use file `data1.txt` in `APN_data` as  \n","`/content/drive/My Drive/APN_data/data1.txt`  \n","from Google colaboratory."]},{"cell_type":"code","metadata":{"id":"c65yB_ZSu1uB"},"source":["# File \n","import numpy as np\n","N = 100\n","with open('/content/drive/My Drive/APN_data/data1.txt', mode='w') as fw:\n","    fw.write(str(N)+\"\\n\") # \\ = Option ¥\n","    for loop in range(0, N):\n","        n = int(1000 * np.random.rand())\n","        fw.write(str(n)+\"\\n\") # \\ = Option ¥\n","        \n","with open('/content/drive/My Drive/APN_data/data1.txt', mode='r') as fr:\n","    sVal = fr.readline()\n","    Nr   = int(sVal)\n","    data = np.zeros(Nr, dtype='int')\n","    pos  = 0\n","    sVal = fr.readline()\n","    while sVal:\n","        data[pos] = int(sVal)\n","        sVal = fr.readline()\n","        pos += 1\n","\n","print(data)"],"execution_count":null,"outputs":[]},{"cell_type":"markdown","metadata":{"id":"1Tb7-Jpru1uD"},"source":["### Practice\n","- Make a program to read file `data1.txt` in `ndarray` and sort it in both order. (Copy data to another ndarrary before sort.)\n","- And calculate its mean, variance, standard deviation, and median."]},{"cell_type":"code","metadata":{"id":"spQcuB3Su1uE"},"source":["# Make a program\n","import numpy as np\n"],"execution_count":null,"outputs":[]}]}