{ "cells": [ { "cell_type": "markdown", "id": "78d9f07d-6323-41d1-8461-431208741334", "metadata": {}, "source": [ "# 2025-09-26 Householder QR\n", "\n", "* Right vs left-looking algorithms\n", "\n", "* Elementary reflectors\n", "\n", "* Householder QR" ] }, { "cell_type": "code", "execution_count": 1, "id": "416b8a20-581d-491a-9a89-fa41f9a8be9e", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "vander (generic function with 2 methods)" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "using LinearAlgebra\n", "using Plots\n", "using Polynomials\n", "default(lw=4, ms=5, legendfontsize=12, xtickfontsize=12, ytickfontsize=12)\n", "\n", "# Here's our Vandermonde matrix again\n", "function vander(x, k=nothing)\n", " if isnothing(k)\n", " k = length(x)\n", " end\n", " m = length(x)\n", " V = ones(m, k)\n", " for j in 2:k\n", " V[:, j] = V[:, j-1] .* x\n", " end\n", " V\n", "end" ] }, { "cell_type": "markdown", "id": "3f61baf9-cc81-48ec-a6b7-7a1283fe8d40", "metadata": {}, "source": [ "## Gram-Schmidt orthogonalization\n", "\n", "Suppose we're given some vectors and want to find an orthogonal basis for their span.\n", "\n", "$$ A = \\begin{split} \\Bigg[ a_1 \\Bigg| a_2 \\Bigg] = \\Bigg[ q_1 \\Bigg| q_2 \\Bigg] \\begin{bmatrix} r_{11} & r_{12} \\\\ 0 & r_{22} \\end{bmatrix} \\end{split} = Q R$$" ] }, { "cell_type": "code", "execution_count": 2, "id": "4a398107-2466-46b3-9d1e-64b7872115c9", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "gram_schmidt_naive (generic function with 1 method)" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Let's form Q and R by making each column orthonormal to all previous columns\n", "function gram_schmidt_naive(A)\n", " m, n = size(A)\n", " Q = zeros(m, n) # Orthonormal basis\n", " R = zeros(n, n) # Upper triangular\n", " for j in 1:n\n", " v = A[:, j] # current column to normalize\n", " for k in 1:j-1\n", " # We do a projection against the previous columns of Q. Why?\n", " r = Q[:, k]' * v \n", " v -= Q[:, k] * r\n", " R[k, j] = r # What is this factor?\n", " end\n", " # Normalize and store our final v\n", " R[j, j] = norm(v)\n", " Q[:, j] = v / R[j, j]\n", " end\n", " Q, R\n", "end" ] }, { "cell_type": "markdown", "id": "fa730048-22e3-4821-93fe-f027b7f35280", "metadata": {}, "source": [ "## A variant with more parallelism\n", "\n", "$$ q_2 q_2^T \\left( q_1 q_1^T v \\right) = q_2 \\left( q_2^T q_1 \\right) q_1^T v = 0 $$" ] }, { "cell_type": "code", "execution_count": 3, "id": "9bbafdfc-0a29-4ed6-b386-f33f71712abf", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "gram_schmidt_classical (generic function with 1 method)" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Let's form Q and R by making each column orthonormal to all previous columns\n", "function gram_schmidt_classical(A)\n", " m, n = size(A)\n", " # Same setup as our naive version\n", " Q = zeros(m, n)\n", " R = zeros(n, n)\n", " for j in 1:n\n", " v = A[: ,j]\n", " # Here we make the current column othogonal to all previous\n", " R[1:j-1, j] = Q[:, 1:j-1]' * v\n", " v -= Q[:, 1:j-1] * R[1:j-1, j]\n", " # And normalize our result\n", " R[j, j] = norm(v)\n", " Q[:, j] = v / norm(v)\n", " end\n", " Q, R\n", "end" ] }, { "cell_type": "markdown", "id": "0aadf500-d274-46e7-8d35-3670a0c1776e", "metadata": {}, "source": [ "## Right-looking modified Gram-Schmidt\n", "\n", "There are inherent data dependencies in this process.\n", "\n", "$$\n", "\\begin{split} \\Bigg[ q_1 \\Bigg| q_2 \\Bigg| q_3 \\Bigg| q_4 \\Bigg| q_5 \\Bigg]\n", "\\begin{bmatrix} r_{11} & r_{12} & r_{13} & r_{14} & r_{15} \\\\\n", " & r_{22} & r_{23} & r_{24} & r_{25} \\\\\n", " & & r_{33} & r_{34} & r_{35} \\\\\n", " & & & r_{44} & r_{45} \\\\\n", " & & & & r_{55}\n", "\\end{bmatrix}\n", "\\end{split}\n", "$$" ] }, { "cell_type": "code", "execution_count": 4, "id": "30ebe8e0-08c9-4903-9fdf-f6f779961a07", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "gram_schmidt_modified (generic function with 1 method)" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "function gram_schmidt_modified(A)\n", " m, n = size(A)\n", " Q = copy(A)\n", " R = zeros(n, n)\n", " for j in 1:n\n", " # First we normalize our column\n", " R[j, j] = norm(Q[:, j])\n", " Q[:, j] /= R[j, j]\n", " # Then we make all following columns orthogonal to the current\n", " R[j, j+1:end] = Q[:, j]' * Q[:, j+1:end]\n", " Q[:, j+1:end] -= Q[:, j] * R[j, j+1:end]'\n", " end\n", " Q, R\n", "end" ] }, { "cell_type": "markdown", "id": "4f930e65-68b0-4db7-9191-6375a702ff4e", "metadata": {}, "source": [ "## Classical vs modified\n", "\n", "Classical\n", "\n", "* Really unstable, orthogonality error size of $1 \\gg \\epsilon_\\text{machine}$\n", "\n", "* Don't need to know all the vectors in advance\n", "\n", "Modified\n", "\n", "* Needs to be right-looking for efficiency\n", "\n", "* Less unstable, but orthogonality error $10^{-9} \\gg \\epsilon_\\text{machine}$" ] }, { "cell_type": "markdown", "id": "6f3cdeab-10b9-4f41-a553-a16e0ea898db", "metadata": {}, "source": [ "## Householder QR\n", "\n", "Gram-Schmidt constructed a triangular matrix $R$ to orthogonalize $A$ into $Q$.\n", "Each step was a projector, which is a rank-deficient operation.\n", "Householder uses orthogonal transformations (reflectors) to triangularize.\n", "\n", "$$ \\underbrace{Q_{n} \\dotsb Q_1}_{Q^T} A = R $$\n", "\n", "The structure of the algorithm is\n", "\n", "$$ \\begin{split} \\underbrace{\\begin{bmatrix} * & * & * \\\\ * & * & * \\\\ * & * & * \\\\ * & * & * \\\\ * & * & * \\\\ \\end{bmatrix}}_{A} \\to\n", "\\underbrace{\\begin{bmatrix} * & * & * \\\\ 0 & * & * \\\\ 0 & * & * \\\\ 0 & * & * \\\\ 0 & * & * \\\\ \\end{bmatrix}}_{Q_1 A} \\to\n", "\\underbrace{\\begin{bmatrix} * & * & * \\\\ 0 & * & * \\\\ 0 & 0 & * \\\\ 0 & 0 & * \\\\ 0 & 0 & * \\\\ \\end{bmatrix}}_{Q_2 Q_1 A} \\to\n", "\\underbrace{\\begin{bmatrix} * & * & * \\\\ 0 & * & * \\\\ 0 & 0 & * \\\\ 0 & 0 & 0 \\\\ 0 & 0 & 0 \\\\ \\end{bmatrix}}_{Q_3 Q_2 Q_1 A}\n", "\\end{split} $$" ] }, { "attachments": { "2a2f64ce-2c1d-4a6f-9004-ac8d5ca980b6.png": { "image/png": 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" } }, "cell_type": "markdown", "id": "ef56d932-7d7d-424c-b55d-448bd741eccd", "metadata": {}, "source": [ "### Constructing the $Q_j$\n", "\n", "$$ \\underbrace{Q_n \\dotsb Q_1}_{Q^T} A = R $$\n", "\n", "Each of our $Q_j$ will have the form\n", "\n", "$$ \\begin{split}Q_j = \\begin{bmatrix} I_j & 0 \\\\ 0 & F \\end{bmatrix}\\end{split} $$\n", "\n", "where $F$ is a \"reflection\" that achieves\n", "\n", "$$ \\begin{split} F x = \\begin{bmatrix} \\lVert x \\rVert \\\\ 0 \\\\ 0 \\\\ \\vdots \\end{bmatrix} \\end{split} $$\n", "\n", "where $x$ is the column of $R$ from the diagonal down.\n", "This transformation is a reflection across a plane with normal $v = F x - x = \\left\\lvert \\left\\lvert x \\right\\rvert \\right\\rvert e_1 - x$.\n", "\n", "![image.png](attachment:2a2f64ce-2c1d-4a6f-9004-ac8d5ca980b6.png)\n", "\n", "The reflection, as depicted above by Trefethen and Bau (1999) can be written as $F = I - 2 \\frac{v v^T}{v^T v}$." ] }, { "cell_type": "markdown", "id": "2a412308-4221-41f4-8d8f-1ffe067810c7", "metadata": {}, "source": [ "### Reflection" ] }, { "cell_type": "code", "execution_count": 6, "id": "96e7c559-d3ef-4f59-9361-38ed7382e684", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "4×4 Matrix{Float64}:\n", " 2.10041 1.5861 1.92938 1.9544\n", " -6.71674e-17 0.832466 0.493814 -0.0422542\n", " 3.98231e-17 -0.0690713 0.505746 0.218325\n", " -3.4793e-17 0.507456 1.58059 -0.303831" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Let's make any symmetric matrix\n", "A = rand(4, 4); A += A'\n", "\n", "# Now let's build v = |x| e_1 - x\n", "v = copy(A[:,1])\n", "v[1] -= norm(v)\n", "v = normalize(v) # v /= norm(v)\n", "\n", "# And build F to clear the first column of A below the diagonal\n", "F = I - 2 * v * v'\n", "B = F * A\n", "display(B)" ] }, { "cell_type": "code", "execution_count": 7, "id": "e2e822c5-9cff-4a3e-a1f5-233735ba0c75", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "4×4 Matrix{Float64}:\n", " 2.10041 1.5861 1.92938 1.9544\n", " -6.71674e-17 0.977385 1.2055 -0.209166\n", " 3.98231e-17 0.0 0.844947 0.138772\n", " -3.4793e-17 5.55112e-17 -0.911459 0.280636" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Now let's keep going with column 2\n", "v = copy(B[2:end, 2]) # Note - starting at 2, not the full column\n", "v[1] -= norm(v);\n", "v = normalize(v)\n", "\n", "# Build and apply F to clear the second column of B\n", "F = I - 2 * v * v'\n", "B[2:end, 2:end] = F * B[2:end, 2:end]\n", "display(B)" ] }, { "cell_type": "markdown", "id": "a4be15ae-6b5e-47e2-91e4-ef5ac2e5e668", "metadata": {}, "source": [ "## Householder algorithm" ] }, { "cell_type": "code", "execution_count": 8, "id": "f961e141-46ba-48cc-bc3a-8dbad62be5f8", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "qr_householder_naive (generic function with 1 method)" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "function qr_householder_naive(A)\n", " m, n = size(A)\n", " R = copy(A)\n", " V = [] # list of reflectors\n", " for j in 1:n\n", " # Build v for the current column\n", " v = copy(R[j:end, j])\n", " v[1] -= norm(v)\n", " v = normalize(v)\n", " # Build and apply F\n", " R[j:end,j:end] -= 2 * v * (v' * R[j:end,j:end])\n", " # Keep track of the reflectors\n", " push!(V, v)\n", " end\n", " V, R\n", "end" ] }, { "cell_type": "code", "execution_count": 9, "id": "50028360-181c-4cdb-a79d-b7ec8ae80b99", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "4×4 Matrix{Float64}:\n", " -2.0 0.0 -1.11111 0.0\n", " 0.0 1.49071 1.38778e-17 1.3582\n", " 0.0 0.0 0.888889 9.71445e-17\n", " 0.0 0.0 0.0 0.397523" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Let's pick on Vandermonde again\n", "m = 4\n", "x = LinRange(-1, 1, m)\n", "A = vander(x, m)\n", "\n", "# Factorize and check R\n", "V, R = qr_householder_naive(A)\n", "_, R = qr(A)\n", "display(R)" ] }, { "cell_type": "markdown", "id": "350292a3-7b70-4a0a-99d6-bd803ef9f00e", "metadata": {}, "source": [ "## But what about $Q$?" ] }, { "cell_type": "code", "execution_count": 10, "id": "c2f45f14-8f6a-4d6f-89ec-840138b64350", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "reflectors_to_dense (generic function with 1 method)" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Here's a functino to apply the reflectors V to a vector x\n", "function reflectors_mult(V, x)\n", " y = copy(x)\n", " for v in reverse(V)\n", " n = length(v) - 1\n", " # This is applying F as we did to form R\n", " y[end-n:end] -= 2 * v * (v' * y[end-n:end])\n", " end\n", " y\n", "end\n", "\n", "# Create a dense matrix Q from reflectors V\n", "function reflectors_to_dense(V)\n", " m = length(V[1])\n", " Q = diagm(ones(m))\n", " # Apply the reflectors to the identity matrix to build Q\n", " for j in 1:m\n", " Q[:, j] = reflectors_mult(V, Q[:,j])\n", " end\n", " Q\n", "end" ] }, { "cell_type": "code", "execution_count": 11, "id": "3bc268f0-476d-44c5-be04-57d370c05670", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "norm(Q' * Q - I) = 4.043305005028868e-15\n", "norm(Q * R - A) = 7.653110366995408e-15\n" ] } ], "source": [ "# Again with Vandermonde as our example\n", "m = 20\n", "x = LinRange(-1, 1, m)\n", "A = vander(x, m)\n", "\n", "# Factorize\n", "V, R = qr_householder_naive(A)\n", "Q = reflectors_to_dense(V)\n", "\n", "# And check\n", "@show norm(Q' * Q - I)\n", "@show norm(Q * R - A);" ] }, { "cell_type": "markdown", "id": "d6904d73-1c16-48ef-9935-2c6005d052ff", "metadata": {}, "source": [ "The columns of Q retain orthogonality!\n", "This is better than we saw from our right looking $QR$ last time." ] }, { "cell_type": "markdown", "id": "0be4bd14-44ec-446a-9cf9-a5a7bdc1649e", "metadata": {}, "source": [ "### An edge case" ] }, { "cell_type": "code", "execution_count": 12, "id": "ae8470ac-ad17-4942-a2ee-b64f9128761a", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(Any[[NaN, NaN], [NaN]], [NaN NaN; NaN NaN])" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Should be trivial, since A == I\n", "A = [1 0; 0 1.]\n", "# But this result is not good\n", "V, R = qr_householder_naive(A)" ] }, { "attachments": { "ad70bdf4-86a2-4197-b4c7-4c9f531818a1.png": { "image/png": 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" } }, "cell_type": "markdown", "id": "c9227d6e-5cd3-4c5f-b4b8-c8780083170b", "metadata": {}, "source": [ "We have the lines\n", "\n", "```julia\n", " v = copy(R[j:end, j])\n", " v[1] -= norm(v)\n", " v = normalize(v)\n", "```\n", "\n", "What happens when $R$ is already upper triangular?\n", "\n", "![image2.png](attachment:ad70bdf4-86a2-4197-b4c7-4c9f531818a1.png)" ] }, { "cell_type": "markdown", "id": "b799493e-42c3-4647-bf8c-6f1762bd8885", "metadata": {}, "source": [ "## Improved Householder QR\n", "\n", "Let's fix that problem by selecting the reflector that moves $x$ the larger distance." ] }, { "cell_type": "code", "execution_count": 13, "id": "2aa557bc-f347-491b-8964-6eae627a296d", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "qr_householder (generic function with 1 method)" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "function qr_householder(A)\n", " m, n = size(A)\n", " R = copy(A)\n", " V = [] # list of reflectors\n", " for j in 1:n\n", " # Build v for the current column\n", " v = copy(R[j:end, j])\n", " v[1] += sign(v[1]) * norm(v) # Here's the fix!\n", " v = normalize(v)\n", " # Build and apply F\n", " R[j:end, j:end] -= 2 * v * (v' * R[j:end,j:end])\n", " # Keep track of the reflectors\n", " push!(V, v)\n", " end\n", " V, R\n", "end" ] }, { "cell_type": "code", "execution_count": 14, "id": "7b1e5f57-b811-4adb-aea0-aa5cd3327c68", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(Any[[1.0, 0.0], [1.0]], [-1.0 0.0; 0.0 -1.0])" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Now this works as expected\n", "A = [1 0; 0 1.]\n", "V, R = qr_householder(A)" ] }, { "cell_type": "code", "execution_count": 15, "id": "3b1a2abe-d852-4a55-81b9-122006217eae", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "tau = [2.0, 2.0]\n", "V1 = [[1.0, -4.999999999e-11], [1.0]]\n", "R =\n" ] }, { "data": { "text/plain": [ "2×2 Matrix{Float64}:\n", " -1.0 2.0e-10\n", " 0.0 -1.0" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# And with a more robust test\n", "A = [2 -1; -1 2] * 1e-10\n", "A += [1 0; 0 1]\n", "\n", "V, R = qr_householder(A)\n", "tau = [2*v[1]^2 for v in V]\n", "@show tau\n", "V1 = [v ./ v[1] for v in V]\n", "@show V1\n", "println(\"R =\")\n", "display(R)" ] }, { "cell_type": "markdown", "id": "33f5f074-b442-46d8-be0c-035d3cb4edea", "metadata": {}, "source": [ "### Householder $QR$ is backward stable" ] }, { "cell_type": "code", "execution_count": 16, "id": "93c6f763-ae43-4b8b-b4a0-23b44a329f6b", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "norm(Q' * Q - I) = 5.932687575393109e-15\n", "norm(Q * R - A) = 6.6179593854314975e-15\n" ] } ], "source": [ "# Let's try to 'break' our QR with Vandermonde as before\n", "m = 40\n", "x = LinRange(-1, 1, m)\n", "A = vander(x, m)\n", "\n", "V, R = qr_householder(A)\n", "Q = reflectors_to_dense(V)\n", "@show norm(Q' * Q - I)\n", "@show norm(Q * R - A);" ] }, { "cell_type": "code", "execution_count": 19, "id": "2fb73328-fb4e-4ed3-839b-072992f63fa3", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Our QR\n", "R =\n" ] }, { "data": { "text/plain": [ "2×2 Matrix{Float64}:\n", " -1.0 0.0\n", " 0.0 -1.0" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Q = \n" ] }, { "data": { "text/plain": [ "2×2 Matrix{Float64}:\n", " -1.0 0.0\n", " 0.0 -1.0" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\n", "Julia's QR\n", "R =\n" ] }, { "data": { "text/plain": [ "2×2 Matrix{Float64}:\n", " 1.0 0.0\n", " 0.0 1.0" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Q = \n" ] }, { "data": { "text/plain": [ "2×2 Matrix{Float64}:\n", " 1.0 0.0\n", " 0.0 1.0" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# And let's compare to Julia\n", "A = [1 0; 0 1.]\n", "\n", "# Ours\n", "println(\"Our QR\")\n", "V, R = qr_householder(A)\n", "println(\"R =\")\n", "display(R)\n", "println(\"Q = \")\n", "display(reflectors_to_dense(V))\n", "\n", "# And Julia's\n", "println(\"\\nJulia's QR\")\n", "Q, R = qr(A)\n", "println(\"R =\")\n", "display(R)\n", "println(\"Q = \")\n", "display(Matrix(Q))" ] }, { "cell_type": "markdown", "id": "65dff1d0-56aa-4ad1-92d2-20090de3aa77", "metadata": {}, "source": [ "### Orthogonality is preserved" ] }, { "cell_type": "code", "execution_count": 20, "id": "7eb803ab-4c0c-4fff-82a0-549967c89301", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "norm(v) = 1.4245900685395503\n" ] }, { "data": { "image/png": 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", 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"name": "stdout", "output_type": "stream", "text": [ "norm(v) = 1.4245900685395503\n" ] }, { "data": { "image/png": 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", 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"\u001b[33m\u001b[1m└ \u001b[22m\u001b[39m\u001b[90m@ Plots ~/.julia/packages/Plots/xKhUG/src/utils.jl:106\u001b[39m\n", "\u001b[33m\u001b[1m┌ \u001b[22m\u001b[39m\u001b[33m\u001b[1mWarning: \u001b[22m\u001b[39mInvalid negative or zero value 0.0 found at series index 1 for log10 based yscale\n", "\u001b[33m\u001b[1m└ \u001b[22m\u001b[39m\u001b[90m@ Plots ~/.julia/packages/Plots/xKhUG/src/utils.jl:106\u001b[39m\n" ] }, { "data": { "image/png": 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", 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0\n", "scatter(abs.(Q[:, 1:end-1]' * v), ylims=[1e-18, 1e-15], yticks=[1e-15, 1e-16, 1e-17, 1e-18], yscale=:log10, xticks=range(1, a-1; step=2), label=\"\\$v \\\\cdot Q_{:, j}\\$\")" ] } ], "metadata": { "kernelspec": { "display_name": "Julia 1.11.6", "language": "julia", "name": "julia-1.11" }, "language_info": { "file_extension": ".jl", "mimetype": "application/julia", "name": "julia", "version": "1.11.6" } }, "nbformat": 4, "nbformat_minor": 5 }