{ "cells": [ { "cell_type": "code", "execution_count": 20, "metadata": { "execution": { "iopub.execute_input": "2024-01-05T15:04:47.670882Z", "iopub.status.busy": "2024-01-05T15:04:47.669914Z", "iopub.status.idle": "2024-01-05T15:04:47.695946Z", "shell.execute_reply": "2024-01-05T15:04:47.693955Z", "shell.execute_reply.started": "2024-01-05T15:04:47.670803Z" }, "tags": [] }, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "%run ../../common_functions/import_all.py\n", "\n", "from scipy import optimize\n", "from scipy.integrate import quad, odeint\n", "from scipy.interpolate import interp1d\n", "from scipy.signal import detrend\n", "from scipy.spatial import distance\n", "from matplotlib.legend_handler import HandlerLine2D\n", "\n", "from functools import partial \n", "from ipywidgets import interact\n", "\n", "from common_functions.setup_notebook import set_css_style, setup_matplotlib, config_ipython\n", "config_ipython()\n", "setup_matplotlib()\n", "set_css_style()\n", "\n", "dataset = '../../datasets/oldfaithful.txt'" ] }, { "cell_type": "markdown", "metadata": { "tags": [] }, "source": [ "# Scientific Python: Numpy and Scipy, and some more\n", "\n", "Some high-level notes to these two libraries, not intended to be comprehensive, plus some function divertissements.\n", "\n", "[**Numpy**](#Numpy)\n", "* [Arrays and Matrices](#Arrays-and-Matrices)\n", "* [Linear Algebra](#Some-linear-Algebra)\n", "* [Playing with Polynomials](#Playing-with-polynomials)\n", "* [Various](#Numpy-various)\n", " \n", "---\n", "\n", "[**Scipy**](#Scipy)\n", "* [Using `optimize`: fit and solve equations](#Using-optimize)\n", "* [The `stats` module: statistical computation](#The-stats-module)\n", "* [The `interpolate` module: ](#The-interpolate-module)\n", "* [Integrate](#The-integrate-module)\n", "* [Signal and noise](#The-signal-module)\n", "* [Mathematical distances](#Mathematical-distances)\n", "\n", "*Note: some of the stuff presented here comes from the Scipy lectures http://www.scipy-lectures.org/index.html*\n", "\n", "--- \n", "\n", "[**Divertissements with functions**](#Divertissements-with-functions)\n", "\n", "Using the `interact` widget to visualise how a function can change with parameters." ] }, { "cell_type": "markdown", "metadata": { "jp-MarkdownHeadingCollapsed": true, "tags": [] }, "source": [ "## Numpy\n", "\n", "\"Num\" stands for \"numerical\", this is a library devoted to numerical computation and it's a building block of many other projects." ] }, { "cell_type": "markdown", "metadata": { "jp-MarkdownHeadingCollapsed": true, "tags": [] }, "source": [ "### Arrays and Matrices\n", "\n", "These objects constitute the basic blocks for manipulation" ] }, { "cell_type": "markdown", "metadata": { "jp-MarkdownHeadingCollapsed": true, "tags": [] }, "source": [ "#### Attributes, slicing reshaping/resizing/flattening" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "* A vector\n", " Dimension 1 and shape (5,): [1 2 3 4 5]\n", " Slice of vector: [3 4]\n", " Slice of vector with step: [2 4]\n", " Slice with newaxis on column: [[1]\n", " [2]\n", " [3]\n", " [4]\n", " [5]]\n", " Slice with newaxis on row: [[1 2 3 4 5]]\n" ] } ], "source": [ "# NOTE: np.array is function to create an ndarray (n-dimensional array), ndarray not to be used to create\n", "\n", "# Vector: an array\n", "\n", "print('* A vector')\n", "vec = np.array([1, 2, 3, 4, 5]) \n", "print(' Dimension %d and shape %s: %s' %(vec.ndim, vec.shape, vec))\n", "print(' Slice of vector: ', vec[2:4])\n", "print(' Slice of vector with step: ', vec[1:4:2])\n", "print(' Slice with newaxis on column: ', vec[:, np.newaxis])\n", "print(' Slice with newaxis on row: ', vec[np.newaxis, :])" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "execution": { "iopub.execute_input": "2024-01-05T14:24:46.935973Z", "iopub.status.busy": "2024-01-05T14:24:46.934618Z", "iopub.status.idle": "2024-01-05T14:24:46.953686Z", "shell.execute_reply": "2024-01-05T14:24:46.952184Z", "shell.execute_reply.started": "2024-01-05T14:24:46.935889Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "* A matrix\n", " This is an ndarray of dimension 2 and shape (3, 4):\n", " [[1 2 3 0]\n", " [2 3 4 1]\n", " [4 0 1 0]]\n", " It contains 12 elements (size)\n", " Its element on row 2, col 3 is 4\n", " A slice of it is (second column) [2 3 0]\n" ] } ], "source": [ "# Matrix, a 2D array\n", "\n", "print('* A matrix')\n", "mat = np.array([[1,2,3, 0], [2,3,4, 1], [4, 0, 1, 0]])\n", "print(' This is an ndarray of dimension %d and shape %s:\\n %s' %(mat.ndim, mat.shape, mat))\n", "print(' It contains %d elements (size)' %mat.size)\n", "print(' Its element on row 2, col 3 is %d' %mat[1,2])\n", "print(' A slice of it is (second column)', mat[:,1])" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "* Reshaping and resizing ['t_red']\n", " Original vector: [0 1 2 3 4 5]\n", " Reshaping vector to shape (2, 3) (change shape, return reshaped ndarray): \n" ] }, { "data": { "text/plain": [ "array([[0, 1, 2],\n", " [3, 4, 5]])" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" }, { "name": "stdout", "output_type": "stream", "text": [ " Resizing vector to shape (2, 2) (change shape and size, do in place and return None): \n" ] }, { "data": { "text/plain": [ "array([0, 1, 2, 3, 4, 5])" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" }, { "name": "stdout", "output_type": "stream", "text": [ " Original matrix: [[1 2 3 0]\n", " [2 3 4 1]\n", " [4 0 1 0]]\n", " Flattened matrix: [1 2 3 0 2 3 4 1 4 0 1 0]\n" ] } ], "source": [ "# Reshaping, resizing and flattening\n", "\n", "print('* Reshaping and resizing', ['t_red'])\n", "a = np.arange(6)\n", "print(' Original vector: ', a)\n", "print(' Reshaping vector to shape (2, 3) (change shape, return reshaped ndarray): ')\n", "a.reshape((2, 3))\n", "print(' Resizing vector to shape (2, 2) (change shape and size, do in place and return None): ')\n", "a\n", "print(' Original matrix: ', mat)\n", "print(' Flattened matrix: ', mat.ravel())" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "* Matrices of zeros and ones ['t_red']\n" ] }, { "data": { "text/plain": [ "array([[0., 0., 0., 0.],\n", " [0., 0., 0., 0.],\n", " [0., 0., 0., 0.]])" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "array([[1., 1., 1., 1., 1.]])" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Matrices of zeros and ones\n", "\n", "print('* Matrices of zeros and ones', ['t_red'])\n", "np.zeros((3, 4))\n", "np.ones((1, 5))" ] }, { "cell_type": "markdown", "metadata": { "jp-MarkdownHeadingCollapsed": true, "tags": [] }, "source": [ "#### Operations on arrays/matrices" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "* Vectors and matrices to use\n", " vector v is [1 2 3]\n", " Matrix A is\n", "[[1 2 0]\n", " [2 3 4]]\n", " Matrix B is\n", "[[0 1]\n", " [2 0]\n", " [1 1]]\n", " Matrix C is\n", "[[3 5 1]\n", " [0 0 2]]\n" ] } ], "source": [ "# Setting the vars to use\n", "\n", "print('* Vectors and matrices to use')\n", "v = np.array([1, 2, 3])\n", "A = np.array([[1,2, 0], [2,3,4]])\n", "B = np.array([[0, 1], [2, 0], [1, 1]])\n", "C = np.array([[3, 5, 1], [0, 0, 2]])\n", "print(' vector v is', v)\n", "print(' Matrix A is')\n", "print(A)\n", "print(' Matrix B is')\n", "print(B)\n", "print(' Matrix C is')\n", "print(C)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "* Matrix and transpose\n", " Transpose of A is\n", " [[1 2]\n", " [2 3]\n", " [0 4]]\n" ] } ], "source": [ "# matrix transpose\n", "\n", "print('* Matrix and transpose')\n", "print(' Transpose of A is\\n', A.T)" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "* Properties of matrix elements\n", " Sum, mean, std of elements: 12 2.0 1.2909944487358056\n", " Sum of A on axis 0: [3 5 4]\n", " Sum of A on axis 1: [3 9]\n" ] } ], "source": [ "# Some Matrix properties of elements\n", "\n", "print('* Properties of matrix elements')\n", "print(' Sum, mean, std of elements: ', A.sum(), A.mean(), A.std())\n", "print(' Sum of A on axis 0: ', A.sum(axis=0))\n", "print(' Sum of A on axis 1: ', A.sum(axis=1))" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "* Matrix product\n", " Product A * B is\n", "[[ 4 1]\n", " [10 6]]\n" ] } ], "source": [ "# Product of matrices\n", "\n", "print('* Matrix product')\n", "print(' Product A * B is')\n", "print(np.dot(A, B))" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "* Multiplication and sum with scalar (v and A)\n", " 2 * v: [2 4 6]\n", " 2 * A: [[2 4 0]\n", " [4 6 8]]\n", " v + 1: [2 3 4]\n", " A + 1: [[2 3 1]\n", " [3 4 5]]\n" ] } ], "source": [ "# scalar * vector; scalar * matrix\n", "\n", "print('* Multiplication and sum with scalar (v and A)')\n", "print(' 2 * v: ', 2 * v)\n", "print(' 2 * A: ', 2 * A)\n", "print(' v + 1: ', v + 1)\n", "print(' A + 1: ', A + 1)" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "* Arithmetics with matrices\n", " Summing A and C\n", "[[4 7 1]\n", " [2 3 6]]\n", " Subtracting C from A\n", "[[-2 -3 -1]\n", " [ 2 3 2]]\n" ] } ], "source": [ "# Matrix arithmetics\n", "\n", "print('* Arithmetics with matrices')\n", "print(' Summing A and C')\n", "print(A + C)\n", "print(' Subtracting C from A')\n", "print(A - C)" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "* Sorting matrix\n", " Sorting A: [[0 1 2]\n", " [2 3 4]]\n", " Sorting A on axis 0 [[1 2 0]\n", " [2 3 4]]\n", " Sorting A on axis 1 [[0 1 2]\n", " [2 3 4]]\n" ] } ], "source": [ "# sorting a matrix\n", "\n", "print('* Sorting matrix')\n", "A_copy = A.copy()\n", "A.sort()\n", "print(' Sorting A: ', A)\n", "A = A_copy.copy()\n", "A.sort(axis=0)\n", "print(' Sorting A on axis 0', A)\n", "A = A_copy.copy()\n", "A.sort(axis=1)\n", "print(' Sorting A on axis 1', A)" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "* Randomly shuffling array:\n", "[3 2 1]\n" ] } ], "source": [ "# array shuffling at random\n", "\n", "print('* Randomly shuffling array:')\n", "np.random.shuffle(v) # shuffles and returns None\n", "print(v)" ] }, { "cell_type": "markdown", "metadata": { "jp-MarkdownHeadingCollapsed": true, "tags": [] }, "source": [ "### Some linear Algebra" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "# set the vars to use\n", "\n", "v = np.array([1, 2, 1, 1])\n", "A = np.array([[1, 2, 3], [0, 1, 0], [0, 2, 1]])" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "* Determinant, trace, inverse, norm\n", " Determinant of matrix A: 1.0\n", " Trace of matrix A: 3\n", " Inverse of matrix A: [[ 1. 4. -3.]\n", " [ 0. 1. 0.]\n", " [-0. -2. 1.]]\n", " Norm of vector v and of matrix A: 2.6457513110645907 4.47213595499958\n" ] } ], "source": [ "# determinant & co\n", "\n", "print('* Determinant, trace, inverse, norm')\n", "print(' Determinant of matrix A: ', np.linalg.det(A))\n", "print(' Trace of matrix A:', np.trace(A))\n", "print(' Inverse of matrix A: ', np.linalg.inv(A))\n", "print(' Norm of vector v and of matrix A:', np.linalg.norm(v), np.linalg.norm(A))" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "* Eigenvalues/Eigenvectors\n", " Eigenvalues and eigenvectors of matrix A: (array([1., 1., 1.]), array([[ 1.00000000e+00, -1.00000000e+00, 1.00000000e+00],\n", " [ 0.00000000e+00, 0.00000000e+00, 8.21730110e-33],\n", " [ 0.00000000e+00, 7.40148683e-17, -7.40148683e-17]]))\n" ] } ], "source": [ "# eigenthings\n", "\n", "print('* Eigenvalues/Eigenvectors')\n", "print(' Eigenvalues and eigenvectors of matrix A:', np.linalg.eig(A))" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "* Single Value Decomposition\n", " SVD of matrix A: (array([[ 0.86349489, 0.47752005, -0.16233045],\n", " [ 0.15573818, -0.55857386, -0.81470293],\n", " [ 0.47971053, -0.67821077, 0.55669378]]), array([4.27194722, 1.3109472 , 0.17856195]), array([[ 0.20213145, 0.66530528, 0.71868753],\n", " [ 0.36425575, -0.73226084, 0.57542317],\n", " [-0.9090988 , -0.14547494, 0.39035422]]))\n" ] } ], "source": [ "# SVD\n", "\n", "print('* Single Value Decomposition')\n", "print(' SVD of matrix A:', np.linalg.svd(A))" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "* Linear systems\n", " Solving linear system Ax = b: [ 0.4 -0.2]\n", " Least Square solution for Ax = b: (array([ 0.4, -0.2]), array([], dtype=float64), 2, array([3.61803399, 1.38196601]))\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/Users/martina/Desktop/Mallzee/repos/plantation/venv/lib/python3.7/site-packages/ipykernel_launcher.py:7: FutureWarning: `rcond` parameter will change to the default of machine precision times ``max(M, N)`` where M and N are the input matrix dimensions.\n", "To use the future default and silence this warning we advise to pass `rcond=None`, to keep using the old, explicitly pass `rcond=-1`.\n", " import sys\n" ] } ], "source": [ "# System of linear equations\n", "\n", "A = np.array([[1, 2], [3, 1]])\n", "b = np.array([0, 1])\n", "print('* Linear systems')\n", "print(' Solving linear system Ax = b:', np.linalg.solve(A, b))\n", "print(' Least Square solution for Ax = b: ', np.linalg.lstsq(A, b))" ] }, { "cell_type": "markdown", "metadata": { "jp-MarkdownHeadingCollapsed": true, "tags": [] }, "source": [ "### Playing with polynomials" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Basics" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "y = x^2 -2x + 1\n", "* Order of polynomial is 2\n", "* y(2) = 1\n", "* Roots of polynomial are [1. 1.]\n" ] } ], "source": [ "print('y = x^2 -2x + 1')\n", "y = np.poly1d([1, -2, 1])\n", "print('* Order of polynomial is ', y.order)\n", "print('* y(2) = ', y(2))\n", "print('* Roots of polynomial are ', y.roots)" ] }, { "cell_type": "markdown", "metadata": { "tags": [] }, "source": [ "#### A polynomial fit to points" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": { "image/png": { "height": 396, "width": 612 } }, "output_type": "display_data" } ], "source": [ "# Setting x's to be 50 linearly spaced points in [0, 1]\n", "x = np.linspace(0, 1, num=20)\n", "\n", "# Setting y to be a noised cosine \n", "y = np.cos(x) + 0.3*np.random.rand(20)\n", "\n", "# Fitting points (x, y) to a polynomial of deg 3\n", "fit_coeff = np.polyfit(x, y, 3)\n", "\n", "# Build the polynomial with the fitting coefficients\n", "p = np.poly1d(fit_coeff)\n", "\n", "# Considering another interval of x's and plotting original points and fitting curve\n", "x2 = np.linspace(0, 1, 200)\n", "plt.plot(x, y, 'o', x2, p(x2), '-') \n", "plt.xlabel('$x$')\n", "plt.ylabel('$y$')\n", "plt.title('A noisy cosine')\n", "plt.show();" ] }, { "cell_type": "markdown", "metadata": { "jp-MarkdownHeadingCollapsed": true, "tags": [] }, "source": [ "### Numpy various" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Loading datasets from file" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "# Load data from text file (including csv) into Numpy matrix\n", "data = np.loadtxt(dataset, \n", " delimiter=' ', \n", " skiprows=1, # skip the first 1 lines (header)\n", " usecols=(1,2) # select cols 1 (x) and 2 (y)\n", " )\n", "\n", "# If there are missing values, run this instead\n", "# data = np.genfromtxt(data_folder + filename, \n", "# delimiter=delimiter, \n", "# skip_header=1, # skip the first 1 lines (header)\n", "# usecols=features, # select which features to use\n", "# missing='?' # what missing values are mapped to\n", "# )" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Playing with NaNs" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "-inf nan\n", "[False True False]\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/usr/local/lib/python3.6/site-packages/ipykernel/__main__.py:1: RuntimeWarning: divide by zero encountered in log\n", " if __name__ == '__main__':\n", "/usr/local/lib/python3.6/site-packages/ipykernel/__main__.py:1: RuntimeWarning: invalid value encountered in log\n", " if __name__ == '__main__':\n", "/usr/local/lib/python3.6/site-packages/ipykernel/__main__.py:2: RuntimeWarning: invalid value encountered in log\n", " from ipykernel import kernelapp as app\n" ] } ], "source": [ "print(np.log(0), np.log(-1))\n", "print(np.isnan([1.,np.log(-1), 2]))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### IO Numpy data format" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": true, "jupyter": { "outputs_hidden": true } }, "outputs": [], "source": [ "data = np.ones((3, 3))\n", "\n", "# Saving and loading numpy array\n", "np.save('mat.npy', data)\n", "data_loaded = np.load('mat.npy')" ] }, { "cell_type": "markdown", "metadata": { "tags": [] }, "source": [ "## SciPy\n", "\n", "\"Sci\" stands, quite obviously, for \"scientific\": this is the library devolted to calculus, statistics and all the blocks of scientific manipulation." ] }, { "cell_type": "markdown", "metadata": { "tags": [] }, "source": [ "### Using `optimize`" ] }, { "cell_type": "markdown", "metadata": { "jp-MarkdownHeadingCollapsed": true, "tags": [] }, "source": [ "#### Finding the minimum of a function" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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vzB6fK2tqCpwIAAAAQLay55+WPlzrnbHLCkiV31m/cG1trebOnau6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"text/plain": [ "" ] }, "metadata": { "image/png": { "height": 359, "width": 598 } }, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "BFGS\n", "Optimization terminated successfully.\n", " Current function value: -7.945823\n", " Iterations: 5\n", " Function evaluations: 18\n", " Gradient evaluations: 6\n" ] }, { "data": { "text/plain": [ "array([-1.30644012])" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" }, { "name": "stdout", "output_type": "stream", "text": [ "BASINHOPPING\n" ] }, { "data": { "text/plain": [ " fun: -7.9458233756152845\n", " lowest_optimization_result: fun: -7.9458233756152845\n", " hess_inv: array([[ 0.08581276]])\n", " jac: array([ 1.19209290e-07])\n", " message: 'Optimization terminated successfully.'\n", " nfev: 15\n", " nit: 3\n", " njev: 5\n", " status: 0\n", " success: True\n", " x: array([-1.30644001])\n", " message: ['requested number of basinhopping iterations completed successfully']\n", " minimization_failures: 0\n", " nfev: 1524\n", " nit: 100\n", " njev: 508\n", " x: array([-1.30644001])" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# function definition and plot of it\n", "def f(x):\n", " return x**2 + 10*np.sin(x)\n", "\n", "x = np.arange(-10, 10, 0.1)\n", "plt.plot(x, f(x))\n", "plt.show();\n", "\n", "# Gradient Descent through BFGS (finds local min)\n", "print('BFGS')\n", "optimize.fmin_bfgs(f, 0)\n", "\n", "# Global optimizer though bashinopping (local optimizer + random sampling of starting points)\n", "print('BASINHOPPING')\n", "optimize.basinhopping(f, 0)\n", "\n", "# NOTE: there are several other optimizers available" ] }, { "cell_type": "markdown", "metadata": { "jp-MarkdownHeadingCollapsed": true, "tags": [] }, "source": [ "#### Finding roots of functions" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 0.]\n", "[-2.47948183]\n" ] } ], "source": [ "roots = []\n", "\n", "#f = x**2 + 10*np.sin(x) is the function defined above\n", "root = optimize.fsolve(f, 1) # 1 is the initial guess\n", "print(root)\n", "roots.append(root)\n", "\n", "# from plot, function has another root, so let us start from -2.5\n", "root = optimize.fsolve(f, -2.5) # 1 is the initial guess\n", "print(root)\n", "roots.append(root)" ] }, { "cell_type": "markdown", "metadata": { "jp-MarkdownHeadingCollapsed": true, "tags": [] }, "source": [ "#### Fit curve knowing the functional form, fitting the params" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "data": { "image/png": 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CXNeKiIiIiIiIKCtyZBHyXx6F7Plr2ILv4fd+/P2fB1ey9lRBAcD+B+4uy6mB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\nfYejEz96s0O7/efft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"text/plain": [ "" ] }, "metadata": { "image/png": { "height": 359, "width": 598 } }, "output_type": "display_data" } ], "source": [ "x = np.linspace(-10, 10, num=20)\n", "y = f(x) + np.random.randn(x.size)\n", "\n", "def f_to_fit(x, a, b):\n", " return a*x**2 + b*np.sin(x)\n", "\n", "guess = [2, 2]\n", "params, params_covariance = optimize.curve_fit(f_to_fit, x, y, guess)\n", "\n", "# Plotting all stuff together\n", "f_line, = plt.plot(x, f(x), label='original function')\n", "fitted_points, = plt.plot(x, f_to_fit(x, params[0], params[1]), 'o', label='points of fitted curve')\n", "original, = plt.plot(roots, f(np.array(roots)), 'x', label='roots')\n", "legend = plt.legend(handler_map={f_line: HandlerLine2D(numpoints=2)}, loc=2)\n", "plt.show();" ] }, { "cell_type": "markdown", "metadata": { "jp-MarkdownHeadingCollapsed": true, "tags": [] }, "source": [ "### The `stats` module" ] }, { "cell_type": "markdown", "metadata": { "execution": { "iopub.execute_input": "2024-01-05T14:36:19.454948Z", "iopub.status.busy": "2024-01-05T14:36:19.454451Z", "iopub.status.idle": "2024-01-05T14:36:19.463275Z", "shell.execute_reply": "2024-01-05T14:36:19.461568Z", "shell.execute_reply.started": "2024-01-05T14:36:19.454906Z" }, "jp-MarkdownHeadingCollapsed": true, "tags": [] }, "source": [ "#### Histograms and PDFs" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "data": { "image/png": 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pCLMAAAAWMBUK65O71mEWPbO+VGEI9m4Gp3R/KpTh1gAAgFxGmAUAALCAT+9O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"text/plain": [ "" ] }, "metadata": { "image/png": { "height": 359, "width": 601 } }, "output_type": "display_data" } ], "source": [ "# Build the bins separators, width 1, from -10 to 10\n", "bins_sep = np.arange(-9, 10)\n", "\n", "# Extract 1000 normally distributed points\n", "normal_points = np.random.normal(size=1000)\n", "\n", "# Histogram the points and compute the normal PDF over bins\n", "histogram = np.histogram(normal_points, bins=bins_sep, normed=True)[0]\n", "bins = 0.5*(bins_sep[1:] + bins_sep[:-1]) # to get the bins centers\n", "\n", "# Normal PDF over specified bins\n", "normal_pdf = stats.norm.pdf(bins)\n", "\n", "# Plot both things\n", "hist_line, = plt.plot(bins, histogram, 'o', label='hist norm points') \n", "pdf_line, = plt.plot(bins, normal_pdf, label='Normal PDF')\n", "legend = plt.legend(handler_map={hist_line: HandlerLine2D(numpoints=2)}, loc=2)\n", "plt.show();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Quickly compute percentiles" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "-0.0508135291078\n" ] } ], "source": [ "# 50 percentile of previously defined normal points\n", "\n", "print(stats.scoreatpercentile(normal_points, 50))" ] }, { "cell_type": "markdown", "metadata": { "tags": [] }, "source": [ "### The `interpolate` module" ] }, { "cell_type": "markdown", "metadata": { "jp-MarkdownHeadingCollapsed": true, "tags": [] }, "source": [ "#### Linear and cubic interpolation between points" ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [ { "data": { "image/png": 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AAABQHzPGAEScjCMCjYZitQJxjjKOCMi+u0r25adCjnPGTZY5qF9rtgg0afLk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QCUl5drfg4C5X0gCibijDPbw7FBUQDaQ7GXR83A0nFZ7eFYYwPUlUshjx3ttF9tUxuWlFSh4NPD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\na69Vfn6+XnzxxaCjw5xOp9avX6/NmzeHH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"text/plain": [ "" ] }, "metadata": { "image/png": { "height": 359, "width": 611 } }, "output_type": "display_data" } ], "source": [ "# Defining noisy sine wave\n", "t = np.linspace(0, 1, 10)\n", "middle_t = np.linspace(0, 1, 20)\n", "noise = (np.random.random(10)*2 - 1) * 1e-1\n", "noisy_sin = np.sin(2 * np.pi * t) + noise\n", "\n", "# Defining linear interpolation between points\n", "linear_int = interp1d(t, noisy_sin)(middle_t)\n", "\n", "# Defining cubic interpolation between points\n", "cubic_int = interp1d(t, noisy_sin, kind='cubic')(middle_t)\n", "\n", "# Plot all\n", "noisy_sin_line, = plt.plot(t, noisy_sin, label='noisy sine wave')\n", "noisy_sin_points, = plt.plot(t, noisy_sin, 'o', color='blue')\n", "linear_int_points, = plt.plot(middle_t, linear_int, 'x', label='lin int')\n", "cubic_int_points, = plt.plot(middle_t, cubic_int, 'x', label='cub int')\n", "legend = plt.legend(handler_map={hist_line: HandlerLine2D(numpoints=2)}, loc=3)\n", "plt.show();" ] }, { "cell_type": "markdown", "metadata": { "tags": [] }, "source": [ "### The `integrate` module" ] }, { "cell_type": "markdown", "metadata": { "jp-MarkdownHeadingCollapsed": true, "tags": [] }, "source": [ "#### Compute definite integral of function " ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.9999999999999999 1.1102230246251564e-14\n" ] } ], "source": [ "res, err = quad(np.sin, 0, np.pi/2)\n", "print(res, err)\n", "\n", "# NOTE: there are other integration methods" ] }, { "cell_type": "markdown", "metadata": { "jp-MarkdownHeadingCollapsed": true, "tags": [] }, "source": [ "#### Solve ODEs" ] }, { "cell_type": "code", "execution_count": 41, "metadata": {}, "outputs": [ { "data": { "image/png": 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AAACgZwmoyJd7ze9ssXUAAAAAPU1ARa4kJ6BKzaECAAAA2khARb4HDEoHAAAA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\nd6F349tvyW76rqy1/hYFAAAAAECWIqA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"text/plain": [ "" ] }, "metadata": { "image/png": { "height": 359, "width": 596 } }, "output_type": "display_data" } ], "source": [ "# Defining dy/dt, iteration_count is the counter for the iteration till convergence\n", "def y_dot(y, t, iteration_count):\n", " iteration_count += 1\n", " return -2 * y\n", "\n", "# Defining t, the vector of iteration count, then solve dy/dt = -2y\n", "t = np.linspace(0, 10, 100)\n", "iteration_count = np.zeros((1,), dtype=np.uint16)\n", "y_sol, infodict = odeint(y_dot, 1, t, args=(iteration_count,), full_output=True)\n", "\n", "# Plot solution y(t)\n", "plt.plot(t, y_sol)\n", "plt.plot()\n", "plt.show();\n", "\n", "# NOTE: odeint solves a system of ODEs as well\n", "# NOTE: there is no partial diff eq solver in Scipy" ] }, { "cell_type": "markdown", "metadata": { "tags": [] }, "source": [ "### The `signal` module" ] }, { "cell_type": "markdown", "metadata": { "jp-MarkdownHeadingCollapsed": true, "tags": [] }, "source": [ "#### Remove a linear trend from noisy signal" ] }, { "cell_type": "code", "execution_count": 45, "metadata": {}, "outputs": [ { "data": { "image/png": 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kOOgAJFkHqcd3APSSxIprbm52Xd+8ebMkacEC91K8yThz5oyKi/P7rcz384Cp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1Oh3BkwZUsGYCnWnrWcK/gedQmZsjVFXlGVRZsvgNBsLCubDIZUOh04ZlREHV6w9nPOQ7VZwe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\nVH9tcwzty+8k9OAHmSu1OOInLY752bWfn74wrXu2NGY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"text/plain": [ "" ] }, "metadata": { "image/png": { "height": 360, "width": 596 } }, "output_type": "display_data" } ], "source": [ "x = t + np.random.normal(size=100)\n", "plt.plot(t, x, label='original')\n", "plt.plot(t, detrend(x), label='detrended')\n", "legend = plt.legend(handler_map={hist_line: HandlerLine2D(numpoints=2)}, loc=2)\n", "plt.show();" ] }, { "cell_type": "markdown", "metadata": { "tags": [] }, "source": [ "### Mathematical distances\n", "\n", "Quick runthrough of many possible ways to compute the distance between points, as supported by SciPy." ] }, { "cell_type": "code", "execution_count": 47, "metadata": { "collapsed": true, "jupyter": { "outputs_hidden": true } }, "outputs": [], "source": [ "# Define two 1D arrays and two matrices\n", "\n", "u = np.array([1, 1, 2])\n", "v = np.array([1, 3, 1])\n", "A = np.array([[1, 2, 0], [2,3,4]])\n", "B = np.array([[0, 1, 1], [2, 0, 1]])" ] }, { "cell_type": "code", "execution_count": 50, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "* Distances between the two vectors\n", " Euclidean: 2.2360679775\n", " Cosine: 0.261451054124\n", " Manhattan: 3\n", " Minkowski with p=3: 2.08008382305\n", " Chebyshev: 2\n", " Hamming: 0.666666666667\n" ] } ], "source": [ "print('* Distances between the two vectors')\n", "print(' Euclidean:', distance.euclidean(u, v))\n", "print(' Cosine:', distance.cosine(u, v))\n", "print(' Manhattan:', distance.cityblock(u, v))\n", "print(' Minkowski with p=3:', distance.minkowski(u, v, 3))\n", "print(' Chebyshev:', distance.chebyshev(u, v))\n", "print(' Hamming:', distance.hamming(u, v))" ] }, { "cell_type": "code", "execution_count": 51, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "* Distances between each pair of rows in matrices\n", "[[ 1.73205081 2.44948974]\n", " [ 4.12310563 4.24264069]]\n" ] } ], "source": [ "print('* Distances between each pair of rows in matrices')\n", "print(distance.cdist(A, B, metric='euclidean'))\n", "# cdist is built as (numbers are row indices)\n", "# A0B0 A0B1 A0B2\n", "# A1B0 A1B1 A1B2" ] }, { "cell_type": "code", "execution_count": 53, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "* Pairwise distances between rows in matrix\n", "[ 1.41421356 2.23606798 1. ]\n" ] } ], "source": [ "print('* Pairwise distances between rows in matrix')\n", "print(distance.pdist(np.array([[0, 0], [1, 1], [1, 2]]), metric='euclidean'))\n", "# pdist is built as (numbers are row indices)\n", "# A0A1 A0A2 A1A2 # len will be N*(N-1) where N is the number of rows" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Divertissements with functions\n", "\n", "... and interaction.\n", "\n", "Jupyter has several wonderful widgets, like [interact](https://ipywidgets.readthedocs.io/en/latest/examples/Using%20Interact.html), which creates UI controls for you to manipulate graphics." ] }, { "cell_type": "code", "execution_count": 66, "metadata": { "execution": { "iopub.execute_input": "2024-01-05T15:36:42.458102Z", "iopub.status.busy": "2024-01-05T15:36:42.457579Z", "iopub.status.idle": "2024-01-05T15:36:42.469626Z", "shell.execute_reply": "2024-01-05T15:36:42.466500Z", "shell.execute_reply.started": "2024-01-05T15:36:42.458061Z" }, "tags": [] }, "outputs": [], "source": [ "# Define a line and a parabola parametrically\n", "\n", "def f_linear(x, a, b): \n", " \"\"\"A parametric linear function.\"\"\"\n", " return a*x + b\n", "\n", "def quad(x, a, b, c): \n", " \"\"\"A parametric quadratic function (parabola).\"\"\"\n", " return a*x**2 + b*x + c" ] }, { "cell_type": "code", "execution_count": 67, "metadata": { "execution": { "iopub.execute_input": "2024-01-05T15:36:43.947214Z", "iopub.status.busy": "2024-01-05T15:36:43.946709Z", "iopub.status.idle": "2024-01-05T15:36:43.956765Z", "shell.execute_reply": "2024-01-05T15:36:43.954332Z", "shell.execute_reply.started": "2024-01-05T15:36:43.947176Z" }, "tags": [] }, "outputs": [], "source": [ "# define a range for x\n", "\n", "x = np.linspace(-10, 10, num=50)" ] }, { "cell_type": "code", "execution_count": 88, "metadata": { "execution": { "iopub.execute_input": "2024-01-05T15:50:07.300869Z", "iopub.status.busy": "2024-01-05T15:50:07.299426Z", "iopub.status.idle": "2024-01-05T15:50:07.800271Z", "shell.execute_reply": "2024-01-05T15:50:07.798466Z", "shell.execute_reply.started": "2024-01-05T15:50:07.300817Z" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "
" ] }, "metadata": { "image/png": { "height": 378, "width": 594 } }, "output_type": "display_data" } ], "source": [ "# plot the function with some chosen params and some noisy points (value given by the function with added random noise)\n", "\n", "f = partial(f_linear, a=1,b=10) # this will behave like the called function but with chosen parameters\n", "\n", "y = [f_linear(x_, 1, 10) + np.random.randint(-10, 10) for x_ in x]\n", "plt.scatter(x, y, label='noisy points')\n", "plt.plot(x, f(x), c='b', label='f');\n", "plt.title('$x +10$');\n", "plt.legend();" ] }, { "cell_type": "code", "execution_count": 90, "metadata": { "execution": { "iopub.execute_input": "2024-01-05T15:50:57.507277Z", "iopub.status.busy": "2024-01-05T15:50:57.505658Z", "iopub.status.idle": "2024-01-05T15:50:58.049603Z", "shell.execute_reply": "2024-01-05T15:50:58.047708Z", "shell.execute_reply.started": "2024-01-05T15:50:57.507228Z" }, "tags": [] }, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "080b4ca828f7476e9e67ba3e014c3695", "version_major": 2, "version_minor": 0 }, "text/plain": [ "interactive(children=(IntSlider(value=1, description='a_', max=3, min=-1), IntSlider(value=10, description='b_…" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# now do the same but use the widget to have choseable params\n", "# the noisy points will be the same as earlier \n", "\n", "@interact(a_=1, b_=10)\n", "\n", "def plot_with_widget(a_,b_):\n", "\n", " f = partial(f_linear, a=a_,b=b_)\n", "\n", " plt.scatter(x, y, label='noisy points')\n", " plt.plot(x, f(x), c='b', label='f');\n", " plt.title('${a}x + {b}$'.format(a=a_, b=b_));\n", " plt.legend();" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.9.6" } }, "nbformat": 4, "nbformat_minor": 4 }