{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Gaussian elimination\n", "\n", "This Julia notebook allows us to interactively visualize the process of Gaussian elimination.\n", "\n", "Recall that the process of [Gaussian elimination](https://en.wikipedia.org/wiki/Gaussian_elimination) involves subtracting rows to turn a matrix $A$ into an [upper triangular matrix](https://en.wikipedia.org/wiki/Triangular_matrix) $U$. Often we *augment* the matrix with an additional column, representing the right-hand side $b$ of a system of equations $Ax=b$ that we want to solve: by doing the same row operations to both $A$ and $b$, we arrive at an equivalent equation $Ux=c$ that is easy to solve by *backsubstitution* (solving for one variable at a time, working from the last row to the top row).\n", "\n", "For example, suppose we are solving:\n", "\n", "$$\n", "Ax = \n", "\\begin{pmatrix}\n", "1 & 3 & 1 \\\\\n", "1 & 1 & -1 \\\\\n", "3 & 11 & 6 \n", "\\end{pmatrix} x = \n", "\\begin{pmatrix}\n", "9 \\\\\n", "1 \\\\\n", "35\n", "\\end{pmatrix} = b\n", "$$\n", "\n", "We would perform the following elimination process.\n", "\n", "$$\n", "\\left[\\begin{array}{rrr|r}\n", "\\boxed{1} & 3 & 1 & 9 \\\\\n", "1 & 1 & -1 & 1 \\\\\n", "3 & 11 & 6 & 35\n", "\\end{array}\\right]\\to\n", "\\left[\\begin{array}{rrr|r}\n", "\\boxed{1} & 3 & 1 & 9 \\\\\n", "0 & \\boxed{-2} & -2 & -8 \\\\\n", "0 & 2 & 3 & 8\n", "\\end{array}\\right]\\to\n", "\\left[\\begin{array}{rrr|r}\n", "\\boxed{1} & 3 & 1 & 9 \\\\\n", "0 & \\boxed{-2} & -2 & -8 \\\\\n", "0 & 0 & \\boxed{1} & 0\n", "\\end{array}\\right]\n", "$$\n", "\n", "The boxed values are known as the **pivots**. Now we do **backsubstitution**, working from the bottom up. The last row is a single equation in a single unknown:\n", "\n", "$$\n", "1 x_3 = 0 \\implies x_3 = 0 .\n", "$$\n", "\n", "Now that we know $x_3$, the second row gives:\n", "\n", "$$\n", "-2x_2 - 2x_3 = -8 \\implies -2x_2 - 0 = -8 \\implies x_2 = 4 .\n", "$$\n", "\n", "Finally, now that we know $x_2$ and $x_3$, the first row gives:\n", "\n", "$$\n", "1 x_1 + 3 x_2 + 1x_3 = 9 \\implies x_1 + 12 + 0 = 9 \\implies x_1 = -3.\n", "$$\n", "\n", "It is much more fun to let the computer do the arithmetic than to crunch through it ourselves on the blackboard, but usually the computer does things *too* quickly (and it often does some re-ordering of the rows that makes it harder to follow what is going on). For example, in Julia, we can solve the above system of equations by simply:" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "3×3 Matrix{Int64}:\n", " 1 3 1\n", " 1 1 -1\n", " 3 11 6" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A = [1 3 1\n", " 1 1 -1\n", " 3 11 6]" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "3-element Vector{Int64}:\n", " 9\n", " 1\n", " 35" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "b = [9, 1, 35]" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "3-element Vector{Float64}:\n", " -3.0\n", " 4.0\n", " -0.0" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x = A \\ b # solves Ax = b by (essentially) Gaussian elimination" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "3-element Vector{Float64}:\n", " -3.0\n", " 4.0\n", " 0.0" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A^-1 * b" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## What's next?\n", "\n", "The basic Gaussian-elimination process is essentially the same as what you learned in 8th–9th grade algebra. Where do we go from here? There are several directions we would like to pursue in 18.06:\n", "\n", "* Zooming out and understanding this process *algebraically*: we want to think of elimination steps in terms of matrix operations (matrix products), and this will eventually lead us to viewing elimination as a *factorization* of the matrix A: the **LU factorization**. This factorization is key to how Gaussian elimination is *actually used* in large problems, and it helps us *understand* A by breaking it into simpler matrices.\n", "\n", "* What happens if you encounter a zero pivot?\n", " - At the simplest hand-calculation level, you just swap rows *if you can*, as reviewed below. But in practical numerical calculations something more interesting happens — it turns out that you need to swap rows even if the pivots are nonzero! This eventually leads us to a \"PA = LU\" factorization, which is critical if you actually want to *use* Gaussian elimination in real life.\n", " - If you *can't* swap rows to get rid of a zero pivot, then the matrix is *singular*. In high school, you typically just give up if the matrix is singular, but it turns out that there are lots of things to say about this case.\n", " \n", "* How does this process scale? It is good to understand what happens for $n \\times n$ matrices. Is Gaussian elimination practical on a computer for $n = 1000$? What about $n = 10^6$?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Row swaps\n", "\n", "Occasionally, we may encounter a zero in the pivot position. Sometimes this means that the equations are **singular** (may have no solutions) — we will talk more about this later. However, as long as there is a nonzero value *below* the pivot, we can fix the problem by **swapping rows** (which just corresponds to re-ordering the equations).\n", "\n", "For example:\n", "\n", "\n", "$$\n", "\\left[\\begin{array}{rrr|r}\n", "\\boxed{1} & 3 & 1 & 9 \\\\\n", "1 & 3 & -1 & 1 \\\\\n", "3 & 11 & 6 & 35\n", "\\end{array}\\right]\\to\n", "\\left[\\begin{array}{rrr|r}\n", "\\boxed{1} & 3 & 1 & 9 \\\\\n", "0 & 0 & -2 & -8 \\\\\n", "0 & 2 & 3 & 8\n", "\\end{array}\\right]\\to\n", "\\left[\\begin{array}{rrr|r}\n", "\\boxed{1} & 3 & 1 & 9 \\\\\n", "0 & \\boxed{2} & 3 & 8 \\\\\n", "0 & 0 & \\boxed{-2} & -8\n", "\\end{array}\\right]\n", "$$\n", "\n", "where in the second step we swapped the second and third rows to get a nonzero pivot in the second row.\n", "\n", "At this point we can again solve bottom-up by backsubstitution:\n", "\n", "$$\n", "-2x_3 = 8 \\implies x_3 = 4 \\\\\n", "2x_2 + 3x_3 = 8 = 2x_2 + 12 \\implies x_2 = -2 \\\\\n", "x_1 + 3x_2 + x_3 = 9 = x_1 -6 + 4 \\implies x_3 = 11\n", "$$\n", "\n", "Of course, the computer can get the answer much more quickly and easily:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "3-element Vector{Float64}:\n", " 11.000000000000005\n", " -2.0000000000000013\n", " 4.0" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "[ 1 3 1\n", " 1 3 -1\n", " 3 11 6 ] \\\n", "[9\n", " 1\n", " 35]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## “Big” matrices on the computer\n", "\n", "Of course, the computer can solve *much bigger problems* easily. It can solve 1000 equations in 1000 unknowns in a fraction of a second — nowadays, that is no longer considered a \"big\" system of equations." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1000×1000 Matrix{Float64}:\n", " 0.754693 0.560733 0.910327 … 0.611877 0.292508 0.72601\n", " 0.351665 0.369858 0.871103 0.25676 0.0405945 0.726211\n", " 0.763593 0.464121 0.390283 0.604981 0.147775 0.72878\n", " 0.453561 0.147726 0.600355 0.178248 0.914899 0.757964\n", " 0.247388 0.981658 0.410212 0.817523 0.826953 0.440147\n", " 0.633554 0.862141 0.688732 … 0.264323 0.497675 0.514361\n", " 0.133259 0.527097 0.376906 0.965998 0.945114 0.884697\n", " 0.711564 0.423059 0.870123 0.823831 0.272452 0.92002\n", " 0.564027 0.638453 0.530519 0.900897 0.0810425 0.0930512\n", " 0.214856 0.290041 0.819278 0.90219 0.552371 0.553739\n", " 0.903851 0.897284 0.759832 … 0.208446 0.173989 0.0596702\n", " 0.104133 0.113186 0.0797224 0.250324 0.604153 0.41286\n", " 0.235456 0.590892 0.789271 0.973052 0.294701 0.143293\n", " ⋮ ⋱ \n", " 0.215499 0.188321 0.975163 0.957026 0.871916 0.828928\n", " 0.967067 0.591485 0.632038 0.010651 0.100226 0.991383\n", " 0.119558 0.460483 0.199182 … 0.261509 0.324492 0.965666\n", " 0.607541 0.628893 0.434687 0.263299 0.525989 0.577185\n", " 0.230643 0.298218 0.603661 0.184217 0.13649 0.918041\n", " 0.976573 0.985378 0.0157184 0.842938 0.745338 0.0950755\n", " 0.461015 0.438604 0.308731 0.139264 0.478038 0.482712\n", " 0.732309 0.0759328 0.585691 … 0.638138 0.604144 0.850571\n", " 0.636802 0.322266 0.469396 0.578963 0.205645 0.172984\n", " 0.414916 0.494336 0.807718 0.320688 0.657784 0.982512\n", " 0.293371 0.493783 0.74403 0.799018 0.264314 0.186339\n", " 0.104612 0.662899 0.301098 0.698438 0.609498 0.937989" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Ahuge = rand(1000,1000)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1000-element Vector{Float64}:\n", " 0.11648951400817487\n", " 0.638398291445165\n", " 0.8298021277628341\n", " 0.6578245083268514\n", " 0.2992909571326191\n", " 0.04434321426269938\n", " 0.2273049093293089\n", " 0.9208209561794793\n", " 0.508792941046068\n", " 0.6918189711915684\n", " 0.6824429390834486\n", " 0.914443078331818\n", " 0.2796681550890874\n", " ⋮\n", " 0.9260513170733145\n", " 0.9305175378530915\n", " 0.019844020048994104\n", " 0.5146618522657653\n", " 0.9889596344281131\n", " 0.7890502663051733\n", " 0.7176160909676175\n", " 0.33518616859067674\n", " 0.6782977395680323\n", " 0.6828375702950923\n", " 0.6045951621057377\n", " 0.9432704795434865" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "bhuge = rand(1000)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1000-element Vector{Float64}:\n", " -0.40242365163345395\n", " -1.2575603935803086\n", " 1.3767709589169037\n", " 0.020777542800422127\n", " -0.43224063490856907\n", " 0.07846278754888261\n", " -1.2788481293898533\n", " -0.23363827638256934\n", " 1.1367178501838064\n", " -0.6419266345464728\n", " 1.16574989194809\n", " -1.0109259917168187\n", " -0.2547952187241332\n", " ⋮\n", " 0.17760057480194702\n", " -0.026736570616518872\n", " 1.7923137060044423\n", " -0.9918298946342873\n", " -1.0221141312210762\n", " 0.4426412052246268\n", " -0.13777635985018952\n", " -0.4722031299540175\n", " -0.14595252778895984\n", " -0.37017438393408275\n", " 0.88508351548458\n", " -0.1397370446925542" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Ahuge \\ bhuge" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " 0.016476 seconds (4 allocations: 7.645 MiB)\n", " 0.017585 seconds (4 allocations: 7.645 MiB)\n", " 0.014655 seconds (4 allocations: 7.645 MiB)\n" ] } ], "source": [ "@time Ahuge \\ bhuge;\n", "@time Ahuge \\ bhuge;\n", "@time Ahuge \\ bhuge;" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If we want to see the matrix $U$ from above, we use the fact (covered soon in 18.06) that Gaussian elimination is really \"LU\" factorization, performed by the function `lufact` in the built-in `LinearAlgebra` package. By default, however, \"serious\" computer implementations of this process automatically re-order the rows to reduce the effect of roundoff errors, so we need to pass an extra option that tells Julia not to do this. (You should *not* normally do this, except for learning exercises.)" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "using LinearAlgebra" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "3×4 Matrix{Float64}:\n", " 1.0 3.0 1.0 9.0\n", " 0.0 -2.0 -2.0 -8.0\n", " 0.0 0.0 1.0 0.0" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# LU factorization (Gaussian elimination) of the augumented matrix [A b], \n", "# passing the NoPivot() option to prevent row re-ordering\n", "F = lu([A b], NoPivot()) # a \"factorization\" object storing both L and U\n", "F.U # just show U" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "However, it would be nice to show the individual steps of this process. This requires some programming." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Code to interactively visualize Gaussian elimination\n", "\n", "The following is some slightly tricky code that lets us visualize the process of Gaussian elimination in Julia. It takes advantage of the [Interact](https://github.com/JuliaGizmos/Interact.jl) package in Julia, which allows us to easily create interactive displays using sliders, pushbuttons, and other widgets.\n", "\n", "Implementing this is **not really a beginner exercise** for new Julia programmers, though it is fairly straightforward for people who are used to Julia. It involves defining our own type to control display, our own implementation of Gaussian elimination that allows us to stop partway through, and using the Interact package to create interactive widgets.\n", "\n", "You can skip this part if you aren't ready for the programming details." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "naive_gauss" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "\"\"\"\n", " naive_gauss(A, [step])\n", "\n", "Given a matrix `A`, performs Gaussian elimination to convert\n", "`A` into an upper-triangular matrix `U`.\n", "\n", "This implementation is \"naive\" because it *never re-orders the rows*.\n", "(It will obviously fail if a zero pivot is encountered.)\n", "\n", "If the optional `step` argument is supplied, only performs `step`\n", "steps of Gaussian elimination.\n", "\n", "Returns `(U, row, col, factor)`, where `row` and `col` are the\n", "row and column of the last step performed, while `factor`\n", "is the last factor multiplying the pivot row.\n", "\"\"\"\n", "function naive_gauss(A, step=typemax(Int))\n", " m = size(A,1) # number of rows\n", " factor = A[1,1]/A[1,1]\n", " step ≤ 0 && return (A, 1, 1, factor)\n", " U = copyto!(similar(A, typeof(factor)), A)\n", " for j = 1:m # loop over m columns\n", " for i = j+1:m # loop over rows below the pivot row j\n", " # subtract a multiple of the pivot row (j)\n", " # from the current row (i) to cancel U[i,j] = Uᵢⱼ:\n", " factor = -U[i,j]/U[j,j]\n", " U[i,:] = U[i,:] + U[j,:] * factor\n", " step -= 1\n", " step ≤ 0 && return (U, i, j, factor)\n", " end\n", " end\n", " return U, m, m, factor\n", "end" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For display purposes on the 18.06 github page, we can't use interactive sliders, so I just use the following code to switch to non-interactively output each of the \"steps\" of the animation.\n", "\n", "To go back to interactive sliders, change `import Interact` to `using Interact` below:" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "application/vnd.webio.node+json": { "children": [], "instanceArgs": { "namespace": "html", "tag": "div" }, "nodeType": "DOM", "props": {}, "type": "node" }, "text/html": [ "
\n", "

The WebIO Jupyter extension was not detected. See the\n", "\n", " WebIO Jupyter integration documentation\n", "\n", "for more information.\n", "

\n" ], "text/plain": [ "WebIO._IJuliaInit()" ] }, "metadata": { "application/vnd.webio.node+json": { "kernelId": "a047c49e-3ec7-4b3d-bfa2-571929d498c5" } }, "output_type": "display_data" }, { "data": { "text/plain": [ "slider (generic function with 1 method)" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import Interact # change to \"using Interact\" to make interactive\n", "\n", "# non-interactive replacements for Interact features\n", "if !isdefined(Main, :slider)\n", " # non-interactive replacement for Interact.@manipulate\n", " macro manipulate(expr)\n", " return Expr(:for, esc(expr.args[1]), :(display($(esc(expr.args[2])))))\n", " end\n", " slider(r; kws...) = r\n", "end" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "visualize_gauss (generic function with 1 method)" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "\n", "# For display, I only want to show 3 decimal places of floating-point values,\n", "# but I want to show integers and similar types exactly, so I define a little\n", "# function to do this rounding\n", "shorten(x::AbstractFloat) = round(x, digits=3)\n", "shorten(x) = x # leave non floating-point values as-is\n", "\n", "# create an interactive widget to visualize the Gaussian-elimination process for the matrix A.\n", "function visualize_gauss(A)\n", " m = size(A, 1)\n", " @manipulate for step in slider(1:(m*(m-1))÷2, value=1, label=\"gauss step\")\n", " Uprev, = naive_gauss(A, step-1)\n", " U, row, col, factor = naive_gauss(A, step)\n", " pivot = U[col,col]\n", " Interact.vbox(\n", " Interact.node(:pre, \"Gaussian elimination for column $col with pivot $pivot: add $(shorten(factor)) * (row $col) to (row $row)\"),\n", " Interact.hbox(shorten.(Uprev),\n", " Interact.hskip(1*Interact.em), \"⟶\", Interact.hskip(1*Interact.em),\n", " shorten.(U)\n", " )(Interact.alignitems(:center))\n", " )(Interact.alignitems(:center))\n", " end\n", "end" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Gaussian elimination examples\n", "\n", "Now, let's use this machinery to interact with some examples, starting with our $3 \\times 3$ matrix from above:" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "application/vnd.webio.node+json": { "children": [ { "children": [ "Gaussian elimination for column 1 with pivot 1.0: add -1.0 * (row 1) to (row 2)" ], "instanceArgs": { "namespace": "html", "tag": "pre" }, "nodeType": "DOM", "props": {}, "type": "node" }, { "children": [ { "children": [], "instanceArgs": { "namespace": "html", "tag": "div" }, "nodeType": "DOM", "props": { "setInnerHtml": "
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5×5 Matrix{Float64}:\n  -3.0    5.0    5.0    3.0   -7.0\n   0.0    0.0   13.0   -5.0  -13.0\n NaN    NaN    -Inf    Inf    Inf\n NaN    NaN    NaN    NaN    NaN\n NaN    NaN    NaN    NaN    NaN
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5×5 Matrix{Float64}:\n  -3.0    5.0    5.0    3.0   -7.0\n   0.0    0.0   13.0   -5.0  -13.0\n NaN    NaN    -Inf    Inf    Inf\n NaN    NaN    NaN    NaN    NaN\n NaN    NaN    NaN    NaN    NaN
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5×5 Matrix{Int64}:\n -8   4  -6  -1   8\n  3  -5   8  -8  -6\n  8   2   8   2  -8\n -6  -2   6   4  -8\n -3   5   5   3  -7
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5×5 Matrix{Float64}:\n -8.0   4.0  -6.0   -1.0     8.0\n  0.0  -3.5   5.75  -8.375  -3.0\n  8.0   2.0   8.0    2.0    -8.0\n -6.0  -2.0   6.0    4.0    -8.0\n -3.0   5.0   5.0    3.0    -7.0
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5×5 Matrix{Float64}:\n -8.0   4.0  -6.0   -1.0     8.0\n  0.0  -3.5   5.75  -8.375  -3.0\n  8.0   2.0   8.0    2.0    -8.0\n -6.0  -2.0   6.0    4.0    -8.0\n -3.0   5.0   5.0    3.0    -7.0
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5×5 Matrix{Float64}:\n -8.0   4.0  -6.0   -1.0     8.0\n  0.0  -3.5   5.75  -8.375  -3.0\n  0.0   6.0   2.0    1.0     0.0\n -6.0  -2.0   6.0    4.0    -8.0\n -3.0   5.0   5.0    3.0    -7.0
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5×5 Matrix{Float64}:\n -8.0   4.0  -6.0   -1.0     8.0\n  0.0  -3.5   5.75  -8.375  -3.0\n  0.0   6.0   2.0    1.0     0.0\n -6.0  -2.0   6.0    4.0    -8.0\n -3.0   5.0   5.0    3.0    -7.0
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5×5 Matrix{Float64}:\n -8.0   4.0  -6.0   -1.0      8.0\n  0.0  -3.5   5.75  -8.375   -3.0\n  0.0   6.0   2.0    1.0      0.0\n  0.0  -5.0  10.5    4.75   -14.0\n -3.0   5.0   5.0    3.0     -7.0
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5×5 Matrix{Float64}:\n -8.0   4.0  -6.0   -1.0      8.0\n  0.0  -3.5   5.75  -8.375   -3.0\n  0.0   6.0   2.0    1.0      0.0\n  0.0  -5.0  10.5    4.75   -14.0\n -3.0   5.0   5.0    3.0     -7.0
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5×5 Matrix{Float64}:\n -8.0   4.0  -6.0   -1.0      8.0\n  0.0  -3.5   5.75  -8.375   -3.0\n  0.0   6.0   2.0    1.0      0.0\n  0.0  -5.0  10.5    4.75   -14.0\n  0.0   3.5   7.25   3.375  -10.0
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5×5 Matrix{Float64}:\n -8.0   4.0  -6.0   -1.0      8.0\n  0.0  -3.5   5.75  -8.375   -3.0\n  0.0   6.0   2.0    1.0      0.0\n  0.0  -5.0  10.5    4.75   -14.0\n  0.0   3.5   7.25   3.375  -10.0
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5×5 Matrix{Float64}:\n -8.0   4.0  -6.0     -1.0      8.0\n  0.0  -3.5   5.75    -8.375   -3.0\n  0.0   0.0  11.857  -13.357   -5.143\n  0.0  -5.0  10.5      4.75   -14.0\n  0.0   3.5   7.25     3.375  -10.0
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5×5 Matrix{Float64}:\n -8.0   4.0  -6.0     -1.0     8.0\n  0.0  -3.5   5.75    -8.375  -3.0\n  0.0   0.0  11.857  -13.357  -5.143\n  0.0   0.0   0.0     19.289  -8.723\n  0.0   0.0   0.0      9.645  -7.361
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5×5 Matrix{Float64}:\n -8.0   4.0  -6.0     -1.0     8.0\n  0.0  -3.5   5.75    -8.375  -3.0\n  0.0   0.0  11.857  -13.357  -5.143\n  0.0   0.0   0.0     19.289  -8.723\n  0.0   0.0   0.0      9.645  -7.361
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5×5 Matrix{Float64}:\n -8.0   4.0  -6.0     -1.0     8.0\n  0.0  -3.5   5.75    -8.375  -3.0\n  0.0   0.0  11.857  -13.357  -5.143\n  0.0   0.0   0.0     19.289  -8.723\n  0.0   0.0   0.0      0.0    -3.0
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0.0px, \"width\" => 1.0em) })\n", " \"⟶\"\n", " (div { style=Dict{String, Measures.Length{U, Float64} where U}(\"height\" => 0.0px, \"width\" => 1.0em) })\n", " [-8.0 4.0 … -1.0 8.0; 0.0 -3.5 … -8.375 -3.0; … ; 0.0 0.0 … 19.289 -8.723; 0.0 0.0 … 0.0 -3.0]))" ] }, "metadata": { "application/vnd.webio.node+json": { "kernelId": "a047c49e-3ec7-4b3d-bfa2-571929d498c5" } }, "output_type": "display_data" } ], "source": [ "Aok = [-8 4 -6 -1 8\n", " 3 -5 8 -8 -6\n", " 8 2 8 2 -8\n", " -6 -2 6 4 -8\n", " -3 5 5 3 -7]\n", "visualize_gauss(Aok)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## A bigger example\n", "\n", "We quickly run out of space for displaying matrices as text, but we can visualize the process for larger matrices by using images, with the PyPlot package (a wrapper around the Python Matplotlib library):" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [], "source": [ "using PyPlot" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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", 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", "text/plain": [ "Figure(PyObject
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", "text/plain": [ "Figure(PyObject
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", "text/plain": [ "Figure(PyObject
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", "text/plain": [ "Figure(PyObject
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", "text/plain": [ "Figure(PyObject
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", "text/plain": [ "Figure(PyObject
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", "text/plain": [ "Figure(PyObject
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", "text/plain": [ "Figure(PyObject
)" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stderr", "output_type": "stream", "text": [ "┌ Warning: `vendor()` is deprecated, use `BLAS.get_config()` and inspect the output instead\n", "│ caller = npyinitialize() at numpy.jl:67\n", "└ @ PyCall /Users/stevenj/.julia/packages/PyCall/L0fLP/src/numpy.jl:67\n" ] } ], "source": [ "m = 100\n", "Abig = randn(m,m)\n", "fig = figure()\n", "nsteps = (m*(m-1))÷2\n", "@manipulate for step in slider(0:550:nsteps, value=2, label=\"gauss step\")\n", " withfig(fig) do\n", " U, row, col = naive_gauss(Abig, step)\n", " # I had to experiment a little to find a nice way to plot this\n", " V = log10.(abs.(U) .+ 500)\n", " V[abs.(U) .< 0.001] .= 0 # color small entries black\n", " imshow(V, cmap=\"hot\", vmin=0, vmax=3)\n", " title(\"step $step: column $col, row $row\")\n", " colorbar(label=L\"\\log_{10}(|U_{i,j}| + 500)\")\n", " end\n", "end" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that it takes a *lot* more steps of Gaussian elimination for a $100 \\times 100$ matrix (4950 steps) than for a $5 \\times 5$ matrix (10 steps). Later on in 18.06, we will analyze the computational cost of Gaussian elimination and how it scales with the size of the matrix (in computer science, this is known as the [complexity](https://en.wikipedia.org/wiki/Computational_complexity_theory) of the algorithm)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Another interesting example can be found in the [Machine Learning with Gaussian Elimination notebook](https://github.com/mitmath/1806/blob/master/notes/Machine-Learning-with-Gaussian-elimination.ipynb)." ] } ], "metadata": { "@webio": { "lastCommId": "9b4f2f66effd4c52a9c59b704ece959f", "lastKernelId": "a047c49e-3ec7-4b3d-bfa2-571929d498c5" }, "anaconda-cloud": {}, "kernelspec": { "display_name": "Julia 1.7.1", "language": "julia", "name": "julia-1.7" }, "language_info": { "file_extension": ".jl", "mimetype": "application/julia", "name": "julia", "version": "1.7.1" }, "widgets": { "state": { "294167a6-1234-43dc-aef6-951949f1fac6": { "views": [ { "cell_index": 26 } ] }, "41f7367b-0ad3-43e3-bd43-c6e4a1618e8d": { "views": [ { "cell_index": 19 } ] }, "6e3620ec-4915-4734-8d3a-3332fdc63970": { "views": [ { "cell_index": 16 } ] }, "ce72699c-d8cc-4a03-902b-a490178223e5": { "views": [ { "cell_index": 17 } ] }, "db2d9825-08d3-4028-8072-1e865d1a0c4f": { "views": [ { "cell_index": 23 } ] } }, "version": "1.2.0" } }, "nbformat": 4, "nbformat_minor": 4 }