{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "ChEn-3170: Computational Methods in Chemical Engineering Spring 2020 UMass Lowell; Prof. V. F. de Almeida **12Feb20**\n", "\n", "# Laboratory Work 05 (18Feb20)\n", "$\n", " \\newcommand{\\Amtrx}{\\boldsymbol{\\mathsf{A}}}\n", " \\newcommand{\\Bmtrx}{\\boldsymbol{\\mathsf{B}}}\n", " \\newcommand{\\Cmtrx}{\\boldsymbol{\\mathsf{C}}}\n", " \\newcommand{\\Mmtrx}{\\boldsymbol{\\mathsf{M}}}\n", " \\newcommand{\\Imtrx}{\\boldsymbol{\\mathsf{I}}}\n", " \\newcommand{\\Pmtrx}{\\boldsymbol{\\mathsf{P}}}\n", " \\newcommand{\\Lmtrx}{\\boldsymbol{\\mathsf{L}}}\n", " \\newcommand{\\Umtrx}{\\boldsymbol{\\mathsf{U}}}\n", " \\newcommand{\\xvec}{\\boldsymbol{\\mathsf{x}}}\n", " \\newcommand{\\yvec}{\\boldsymbol{\\mathsf{y}}}\n", " \\newcommand{\\zvec}{\\boldsymbol{\\mathsf{z}}}\n", " \\newcommand{\\avec}{\\boldsymbol{\\mathsf{a}}}\n", " \\newcommand{\\bvec}{\\boldsymbol{\\mathsf{b}}}\n", " \\newcommand{\\cvec}{\\boldsymbol{\\mathsf{c}}}\n", " \\newcommand{\\rvec}{\\boldsymbol{\\mathsf{r}}}\n", " \\newcommand{\\norm}[1]{\\bigl\\lVert{#1}\\bigr\\rVert}\n", " \\DeclareMathOperator{\\rank}{rank}\n", " \\DeclareMathOperator{\\abs}{abs}\n", "$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Name: `your name`" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Rubric for each assignment: \n", "\n", "| Context | Points |\n", "| ----------------------- | ------- |\n", "| Precision of the answer | 80% |\n", "| Answer Markdown readability | 10% |\n", "| Code readability | 10% |\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Guidance:\n", " + \n", " Save your work frequently to a file locally to your computer.\n", " \n", " + \n", " Before submitting, `Kernel` -> `Restart & Run All`, to verify your notebook runs correctly.\n", " \n", " + \n", " Save your file again.\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "---\n", "### Table of Contents\n", "* [Assignment 1 (35pts) ](#a1): $\\Lmtrx$ forward solve.\n", " - [1.1)](#a11) Code the forward solve in a `Python` function.\n", " - [1.2)](#a12) Verify your forward solve code against `NumPy` (provide your own test).\n", " - [1.3)](#a13) Test your forward solve code with a given matrix and right side vector.\n", "* [Assignment 2 (35pts) ](#a2): $\\Umtrx$ forward solve.\n", " - [2.1)](#a21) Code the backward solve in a `Python` function.\n", " - [2.2)](#a22) Verify your backward solve code against `NumPy` (provide your own test).\n", " - [2.3)](#a23) Test your backward solve code with a given matrix and right side vector.\n", "* [Assignment 3 (30pts)](#a3) $\\Lmtrx\\Umtrx$ factorization code and $\\Lmtrx\\Umtrx\\xvec = \\bvec$ solution.\n", " - [3.1)](#a31) Code the LU factorization in a `Python` function and test against a given matrix.\n", " - [3.2)](#a32) Verify your factorization code against `NumPy`.\n", " - [3.3)](#a33) Test your $\\Lmtrx\\Umtrx\\,\\xvec = \\bvec$ solution with a given matrix and right side vector.\n", " ---" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Assignment 1 (35 pts): For each item below respond in a separate notebook cell." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " \n", "1.1) Program a solution algorithm, as a `Python` function, for a system of equations with a lower triangular matrix of coefficients $\\Lmtrx\\,\\xvec=\\bvec$ (suggestion: use a test matrix and right side vector of *variable size* to test your code). The algorithm for solving $\\Lmtrx\\,\\xvec=\\bvec$ is as follows: \n", "\\begin{equation*}\n", " x_i = \\Bigl(b_i - \\sum\\limits_{j=1}^{i-1} L_{i,j}\\,x_j \\Bigr)\\,L^{-1}_{i,i} \\ \\ \\forall \\ \\ i=1,\\ldots,m\n", "\\end{equation*}\n", "for $i$ and $j$ with offset 1. Recall that `NumPy` and `Python` have offset 0 for their sequence data types. Provide an output example for $\\Lmtrx$, $\\bvec$, and $\\xvec$. \n", "" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "code_folding": [] }, "outputs": [], "source": [ "'''1.1) Forward solve function'''\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "'''1.1) Test L x = b'''\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " 1.2) Using the `numpy.linalg.solve()` function solve the same system, $\\Lmtrx\\,\\yvec = \\bvec$, print $\\yvec$, and compute the norm of the\n", "difference of the solutions, i.e., $\\norm{\\xvec-\\yvec}$.\n", " " ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "||x_vec - y_vec|| = 5.330084e-12\n" ] } ], "source": [ "'''1.2) Compare solutions'''\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "1.3) Import the following image URL: \n", " \n", " + https://raw.githubusercontent.com/dpploy/chen-3170/master/notebooks/images/cermet.png\n", "\n", "as a matrix $\\Amtrx$ (need internet connection) and extract from it a lower triangular matrix of the same dimensions, show the image, and solve for a right side vector $\\bvec$ with all ones as elements (*i.e.* $b_i = 1\\ \\forall \\ i=1,\\ldots,m$), using **your** forward solve function. Compute the difference of your solution to the solution using `numpy.linalg.solve()` function and show the norm of the difference.\n", "" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "'''1.3) A matrix and its L part'''\n" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "||x_vec - y_vec|| = 1.950040e-13\n" ] } ], "source": [ "'''1.3) Solve L y = b for b equal to a vector of ones'''\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Assignment 2 (35 pts): For each item below respond in a separate notebook cell." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "2.1) Program a solution algorithm, as a `Python` function, for a system of equations with an upper triangular matrix of coefficients $\\Umtrx\\,\\xvec=\\bvec$ (suggestion: use a test matrix and right side vector of *variable size* to test your code). The algorithm for solving $\\Umtrx\\,\\xvec=\\bvec$ is as follows: \n", "\\begin{equation*}\n", "x_i = \\Bigl(b_i - \\sum\\limits_{j=i+1}^{m} U_{i,j}\\,x_j \\Bigr)\\,U^{-1}_{i,i} \\ \\ \\forall \\ \\ i=m,\\ldots,1\n", "\\end{equation*}\n", "for $i$ and $j$ with offset 1. Recall that `NumPy` and `Python` have offset 0 for their sequence data types. Provide an output example for $\\Umtrx$, $\\bvec$, and $\\xvec$.\n", "" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "code_folding": [] }, "outputs": [], "source": [ "'''2.1) Backward solve function'''\n", " " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "'''2.1) Example U x = b'''\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "2.2) Using the `numpy.linalg.solve()` function solve the same system, $\\Umtrx\\,\\yvec = \\bvec$, print $\\yvec$, and compute the norm of the difference of the solutions, i.e., $\\norm{\\xvec-\\yvec}$.\n", "" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "||x_vec - y_vec|| = 2.009718e-14\n" ] } ], "source": [ "'''2.2) Compare solutions'''\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "2.3) Extract from $\\Amtrx$ an upper triangular matrix of the same dimensions, show the image, and solve for a right side vector $\\bvec$ with all ones as elements (i.e. $b_i = 1\\ \\forall \\ i=1,\\ldots,m$), using your backward solve function. Compute the difference of your solution to the solution using the `numpy.linalg.solve()` function and show the norm of the difference.\n", "" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "'''2.3) A matrix and its U part'''\n" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "||x_vec - y_vec|| = 2.304705e-13\n" ] } ], "source": [ "'''2.3) Solve U y = b for b equal to a vector of ones'''\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Assignment 3 (30 pts): For each item below respond in a separate notebook cell." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "3.1) Program (in a function) a $\\Lmtrx\\,\\Umtrx$ factorization algorithm (without using pivoting) for the matrix $\\overset{(120x120)}{\\Amtrx}$ and compute the $\\Lmtrx\\,\\Umtrx$ factors. Compute the $\\max\\bigl(\\abs(\\Amtrx-\\Lmtrx\\,\\Umtrx)\\bigr)$. The factorization is obtained by elimination steps $k = 1,\\ldots,m-1$ so that \n", " \n", "\\begin{equation*}\n", " A^{(k+1)}_{i,j} = A^{(k)}_{i,j} - A^{(k)}_{k,j}\\, m_{i,k} \\quad\\quad \\forall \\quad\\quad i=k+1,\\ldots,m \\quad\\quad \\text{and} \\quad\\quad j=k+1,\\ldots,m\n", "\\end{equation*}\n", "\n", "where the multipliers $m_{i,k}$ are given by $m_{i,k} = \\frac{A^{(k)}_{i,k}}{A^{(k)}_{k,k}}$. When $k = m-1$, $A^{(m)}_{i,j}$, is upper triangular, that is, $U_{i,j} = A^{(m)}_{i,j}$ . The lower triangular matrix is obtained using the multipliers $m_{i,k}$, that is $L_{i,j} = m_{i,j} \\ \\forall \\ i>j$, $L_{i,i}=1$, and $L_{i,j}=0 \\ \\forall \\ i" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "code_folding": [], "scrolled": false }, "outputs": [], "source": [ "'''3.1) LU factorization function'''\n" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "max(abs((A - LU)) = 3.57492e-14\n" ] } ], "source": [ "'''3.1) Compute LU factors of A 120x120'''\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "3.2) Print the smallest magnitude diagonal entry of the $\\Umtrx$ factor, compute the $\\rank(\\Amtrx)$ and the $\\det(\\Amtrx)$ using the $\\Lmtrx\\,\\Umtrx$ factors.\n", "" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "min(abs(diag(U)) = 1.25385e-03\n", "my rank(A) = 120\n", "np.linalg rank(A) = 120\n", "my det(A) = -1.09249e-148\n", "np.linalg det(A) = -1.09249e-148\n" ] } ], "source": [ "'''3.2 Compute: min(diag(U)), rank(A), det(A) using the LU factors'''\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "3.3) Using your codes (Assignment 1 and 2) solve the linear system of algebraic equations $\\Amtrx\\,\\xvec=\\bvec$ for $\\bvec$ with all ones as elements (*i.e.* $b_i = 1\\ \\forall \\ i=1,\\ldots,m$). Solve the same system with `numpy.linalg.solve` and compute the norm of the solutions difference.\n", "" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "||x_vec - x_vec_gold|| = 3.26881e-10\n" ] } ], "source": [ "'''3.3 Solve A x = b for b equal to a vector of ones '''\n" ] } ], "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": "3.7.1" }, "latex_envs": { "LaTeX_envs_menu_present": true, "autoclose": false, "autocomplete": true, "bibliofile": "biblio.bib", "cite_by": "apalike", "current_citInitial": 1, "eqLabelWithNumbers": true, "eqNumInitial": 1, "hotkeys": { "equation": "Ctrl-E", "itemize": "Ctrl-I" }, "labels_anchors": false, "latex_user_defs": false, "report_style_numbering": false, "user_envs_cfg": false } }, "nbformat": 4, "nbformat_minor": 2 }