tensor_methods

Tensor Methods for DS and SC
git clone git://popovic.xyz/tensor_methods.git
Log | Files | Refs

commit c13af253d98b1c574a64e07a35a94426c4702673
parent c360f99714ace66de0b281ecc98a66a8fa7a693b
Author: miksa234 <milutin@popovic.xyz>
Date:   Sun, 24 Oct 2021 21:14:13 +0200

small fix

Diffstat:
Dconfig | 11-----------
Dsesh1/src/.ipynb_checkpoints/main-checkpoint.ipynb | 1000-------------------------------------------------------------------------------
Dsesh1/src/main.ipynb | 1000-------------------------------------------------------------------------------
3 files changed, 0 insertions(+), 2011 deletions(-)

diff --git a/config b/config @@ -1,11 +0,0 @@ -[core] - repositoryformatversion = 0 - filemode = true - bare = false - logallrefupdates = true -[remote "origin"] - url = repos:/srv/up/tensor_methods.git - fetch = +refs/heads/*:refs/remotes/origin/* -[branch "master"] - remote = origin - merge = refs/heads/master diff --git a/sesh1/src/.ipynb_checkpoints/main-checkpoint.ipynb b/sesh1/src/.ipynb_checkpoints/main-checkpoint.ipynb @@ -1,1000 +0,0 @@ -{ - "cells": [ - { - "cell_type": "code", - "execution_count": 22, - "id": "6d0b3f7d", - "metadata": {}, - "outputs": [], - "source": [ - "using LinearAlgebra\n", - "using Plots\n", - "using Permutations\n", - "using Maxvol\n", - "using TSVD\n", - "using LaTeXStrings" - ] - }, - { - "cell_type": "markdown", - "id": "6cf390f0", - "metadata": {}, - "source": [ - "# Definitions" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "id": "25790e7e", - "metadata": {}, - "outputs": [], - "source": [ - "f(x::Number, y::Number) = 1/(1 + x^2 + y^2);\n", - "g(x::Number, y::Number) = sqrt(x^2 + y^2)*(1 + 1/2*cos(15x + 22y));\n", - "\n", - "n = 901;\n", - "t = [(2*(i-1)/(n-1) - 1) for i in 1:n];\n", - "A = [f(t_i, t_j) for t_i in t, t_j in t];\n", - "B = [g(t_i, t_j) for t_i in t, t_j in t];" - ] - }, - { - "cell_type": "markdown", - "id": "05616300", - "metadata": {}, - "source": [ - "# Exercise 1: Matrix Approximation by TSVD" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "id": "d0bd6885", - "metadata": {}, - "outputs": [], - "source": [ - "function get_errors_tsvd(M ,k)\n", - " U, s, V = tsvd(M, k)\n", - " M_hat = U * Diagonal(s) * transpose(V)\n", - " dM = M_hat - M\n", - " return [norm(dM), norm(dM, Inf)]\n", - "end;\n", - "\n", - "function sort_out_values(M, x, error_function)\n", - " errors = [error_function(M, i) for i in x] \n", - " y_f = [i[1] for i in errors]\n", - " y_m = [i[2] for i in errors]\n", - " return y_f, y_m\n", - "end;" - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "id": "843d0342", - "metadata": {}, - "outputs": [], - "source": [ - "x_a = collect(1:rank(A))\n", - "x_b = collect(1:rank(B))\n", - "y_a_tsvd_f, y_a_tsvd_m = sort_out_values(A, x_a, get_errors_tsvd);\n", - "y_b_tsvd_f, y_b_tsvd_m = sort_out_values(B, x_b, get_errors_tsvd);" - ] - }, - { - "cell_type": "code", - "execution_count": 31, - "id": "5abfb6ad", - "metadata": {}, - "outputs": [], - "source": [ - "x_a_l = log.(x_a); x_b_l = log.(x_b);\n", - "p1 = plot(x_a_l, y_a_tsvd_f, title=\"A: frb-error\", lw=2, xlabel=L\"ln(r)\\;\\;[\\;]\", ylabel=L\"||\\tilde{M} -M||\\;\\;[\\;]\", label=\"\");\n", - "p2 = plot(x_a_l, y_a_tsvd_m, title=\"A: max-error\", lw=2, xlabel=L\"ln(r)\\;\\;[\\;]\", ylabel=L\"||\\tilde{M} -M||\\;\\;[\\;]\", label=\"\");\n", - "p3 = plot(x_b_l, y_b_tsvd_f, title=\"B: frb-error\", lw=2, xlabel=L\"ln(r)\\;\\;[\\;]\", ylabel=L\"||\\tilde{M} -M||\\;\\;[\\;]\", label=\"\");\n", - "p4 = plot(x_b_l, y_b_tsvd_m, title=\"B: max-error\", lw=2, xlabel=L\"ln(r)\\;\\;[\\;]\", ylabel=L\"||\\tilde{M} -M||\\;\\;[\\;]\", label=\"\");\n", - "savefig(plot(p1, p2, p3, p4, layout=(2, 2), titlefontsize=10, xlabelfontsize=7, ylabelfontsize=5, dpi=300), \"svd-err.png\")\n" - ] - }, - { - "cell_type": "markdown", - "id": "775466ab", - "metadata": {}, - "source": [ - "# Exercise 2: Matrix approx. by LU without pivoting" - ] - }, - { - "cell_type": "code", - "execution_count": 29, - "id": "6949a352", - "metadata": {}, - "outputs": [], - "source": [ - "## EXERCISE 2\n", - "function M_cross_lu_err(M, r, pivot=Val(true))\n", - " M_mk = copy(M[:, 1:r]);\n", - " C = copy(M_mk);\n", - " piv, ntimes = maxvol!(C);\n", - " F = lu(M_mk[piv, :], pivot, check=false)\n", - " M_mk[piv, :] = F.P * F.L * F.U ;\n", - " return M - C*M[piv, :], piv\n", - "end\n", - "\n", - "function cross_lu_error(M, x, pivot) \n", - " y_frb = [norm(M_cross_lu_err(M, i,pivot)[1]) for i in x]\n", - " y_max = [norm(M_cross_lu_err(M, i,pivot)[1], Inf) for i in x]\n", - " return y_frb, y_max\n", - "end;" - ] - 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xlabel=L\"ln(r)\\;\\;[\\;]\", ylabel=L\"||\\tilde{M} -M||\\;\\;[\\;]\", label=\"\");\n", - "p4 = plot(x_b_l, y_err_B_max_p, title=\"B: max-error\", lw=2, xlabel=L\"ln(r)\\;\\;[\\;]\", ylabel=L\"||\\tilde{M} -M||\\;\\;[\\;]\", label=\"\");\n", - "savefig(plot(p1, p2, p3, p4, layout=(2, 2), titlefontsize=10, xlabelfontsize=7, ylabelfontsize=5, dpi=300), \"lu-p-err.png\")\n", - "plot(p1, p2, p3, p4, layout=(2,2))" - ] - }, - { - "cell_type": "markdown", - "id": "ce999320", - "metadata": {}, - "source": [ - "# Exercise 4: graph restrictions by LU vizualization" - ] - }, - { - "cell_type": "code", - "execution_count": 41, - "id": "ef510fcd", - "metadata": {}, - "outputs": [], - "source": [ - "r_b = [1, 2, 3, 4, 5, 10, 15, 20 ,30 , 40]\n", - "r_a = [1, 2, 3, 4, 5]\n", - "P_A_s = [M_cross_lu_err(A, i, Val(true))[2] for i in r_a]\n", - "P_B_s = [M_cross_lu_err(B, i, Val(true))[2] for i in r_b]\n", - "t_red = t[1:3:n];" - ] - }, - { - "cell_type": "code", - "execution_count": 71, - "id": "5d127a82", - "metadata": { - "scrolled": true - }, - "outputs": [], - "source": [ - "s_1 = surface(t_red, t_red, f, colorbar=false);\n", - "c_1 = contour(t_red, t_red, f, colorbar=false);\n", - "#s_2 = surface(t_red, t_red, g, colorbar=false);\n", - "#c_2 = contour(t_red, t_red, g, colorbar=false);\n", - "for (i, r) in enumerate(r_a)\n", - " p = plot(s_1, c_1, layout=(1, 2), titlefontsize=10, xlabelfontsize=7, ylabelfontsize=5, dpi=300,\n", - " title=\"f(x, y) at r=$r\", size=(600, 300))\n", - "\n", - " hline!(p[1], [0], t[P_A_s[i]], color=:red, opacity=0.5, label=\"\", lw=2)\n", - " hline!(p[2], [0], t[P_A_s[i]], color=:red, opacity=0.5, label=\"\", lw=2)\n", - " #hline!(p[1], [1], t[P_B_s[i]], color=:red, opacity=0.5, label=\"\", lw=2)\n", - " #hline!(p[2], [1], t[P_B_s[i]], color=:red, opacity=0.5, label=\"\", lw=2)\n", - " savefig(p, \"rc-a-$r.png\")\n", - "end" - ] - }, - { - "cell_type": "code", - "execution_count": 73, - "id": "62ea33aa", - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "\"f\"" - ] - }, - "execution_count": 73, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "c0fd51b6", - "metadata": {}, - "outputs": [], - "source": [] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "f8872b26", - "metadata": {}, - "outputs": [], - "source": [] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "70500acf", - "metadata": {}, - "outputs": [], - "source": [] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "50a8f94c", - "metadata": {}, - "outputs": [], - "source": [] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "1de4ad3a", - "metadata": {}, - "outputs": [], - "source": [] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "2e2189ca", - "metadata": {}, - "outputs": [], - "source": [] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "62ff18cd", - "metadata": {}, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Julia 1.6.3", - "language": "julia", - "name": "julia-1.6" - }, - "language_info": { - "file_extension": ".jl", - "mimetype": "application/julia", - "name": "julia", - "version": "1.6.3" - } - }, - "nbformat": 4, - "nbformat_minor": 5 -} diff --git a/sesh1/src/main.ipynb b/sesh1/src/main.ipynb @@ -1,1000 +0,0 @@ -{ - "cells": [ - { - "cell_type": "code", - "execution_count": 22, - "id": "6d0b3f7d", - "metadata": {}, - "outputs": [], - "source": [ - "using LinearAlgebra\n", - "using Plots\n", - "using Permutations\n", - "using Maxvol\n", - "using TSVD\n", - "using LaTeXStrings" - ] - }, - { - "cell_type": "markdown", - "id": "6cf390f0", - "metadata": {}, - "source": [ - "# Definitions" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "id": "25790e7e", - "metadata": {}, - "outputs": [], - "source": [ - "f(x::Number, y::Number) = 1/(1 + x^2 + y^2);\n", - "g(x::Number, y::Number) = sqrt(x^2 + y^2)*(1 + 1/2*cos(15x + 22y));\n", - "\n", - "n = 901;\n", - "t = [(2*(i-1)/(n-1) - 1) for i in 1:n];\n", - "A = [f(t_i, t_j) for t_i in t, t_j in t];\n", - "B = [g(t_i, t_j) for t_i in t, t_j in t];" - ] - }, - { - "cell_type": "markdown", - "id": "05616300", - "metadata": {}, - "source": [ - "# Exercise 1: Matrix Approximation by TSVD" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "id": "d0bd6885", - "metadata": {}, - "outputs": [], - "source": [ - "function get_errors_tsvd(M ,k)\n", - " U, s, V = tsvd(M, k)\n", - " M_hat = U * Diagonal(s) * transpose(V)\n", - " dM = M_hat - M\n", - " return [norm(dM), norm(dM, Inf)]\n", - "end;\n", - "\n", - "function sort_out_values(M, x, error_function)\n", - " errors = [error_function(M, i) for i in x] \n", - " y_f = [i[1] for i in errors]\n", - " y_m = [i[2] for i in errors]\n", - " return y_f, y_m\n", - "end;" - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "id": "843d0342", - "metadata": {}, - "outputs": [], - "source": [ - "x_a = collect(1:rank(A))\n", - "x_b = collect(1:rank(B))\n", - "y_a_tsvd_f, y_a_tsvd_m = sort_out_values(A, x_a, get_errors_tsvd);\n", - "y_b_tsvd_f, y_b_tsvd_m = sort_out_values(B, x_b, get_errors_tsvd);" - ] - }, - { - "cell_type": "code", - "execution_count": 31, - "id": "5abfb6ad", - "metadata": {}, - "outputs": [], - "source": [ - "x_a_l = log.(x_a); x_b_l = log.(x_b);\n", - "p1 = plot(x_a_l, y_a_tsvd_f, title=\"A: frb-error\", lw=2, xlabel=L\"ln(r)\\;\\;[\\;]\", ylabel=L\"||\\tilde{M} -M||\\;\\;[\\;]\", label=\"\");\n", - "p2 = plot(x_a_l, y_a_tsvd_m, title=\"A: max-error\", lw=2, xlabel=L\"ln(r)\\;\\;[\\;]\", ylabel=L\"||\\tilde{M} -M||\\;\\;[\\;]\", label=\"\");\n", - "p3 = plot(x_b_l, y_b_tsvd_f, title=\"B: frb-error\", lw=2, xlabel=L\"ln(r)\\;\\;[\\;]\", ylabel=L\"||\\tilde{M} -M||\\;\\;[\\;]\", label=\"\");\n", - "p4 = plot(x_b_l, y_b_tsvd_m, title=\"B: max-error\", lw=2, xlabel=L\"ln(r)\\;\\;[\\;]\", ylabel=L\"||\\tilde{M} -M||\\;\\;[\\;]\", label=\"\");\n", - "savefig(plot(p1, p2, p3, p4, layout=(2, 2), titlefontsize=10, xlabelfontsize=7, ylabelfontsize=5, dpi=300), \"svd-err.png\")\n" - ] - }, - { - "cell_type": "markdown", - "id": "775466ab", - "metadata": {}, - "source": [ - "# Exercise 2: Matrix approx. by LU without pivoting" - ] - }, - { - "cell_type": "code", - "execution_count": 29, - "id": "6949a352", - "metadata": {}, - "outputs": [], - "source": [ - "## EXERCISE 2\n", - "function M_cross_lu_err(M, r, pivot=Val(true))\n", - " M_mk = copy(M[:, 1:r]);\n", - " C = copy(M_mk);\n", - " piv, ntimes = maxvol!(C);\n", - " F = lu(M_mk[piv, :], pivot, check=false)\n", - " M_mk[piv, :] = F.P * F.L * F.U ;\n", - " return M - C*M[piv, :], piv\n", - "end\n", - "\n", - "function cross_lu_error(M, x, pivot) \n", - " y_frb = [norm(M_cross_lu_err(M, i,pivot)[1]) for i in x]\n", - " y_max = [norm(M_cross_lu_err(M, i,pivot)[1], Inf) for i in x]\n", - " return y_frb, y_max\n", - "end;" - ] - }, - { - "cell_type": 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xlabel=L\"ln(r)\\;\\;[\\;]\", ylabel=L\"||\\tilde{M} -M||\\;\\;[\\;]\", label=\"\");\n", - "p4 = plot(x_b_l, y_err_B_max_p, title=\"B: max-error\", lw=2, xlabel=L\"ln(r)\\;\\;[\\;]\", ylabel=L\"||\\tilde{M} -M||\\;\\;[\\;]\", label=\"\");\n", - "savefig(plot(p1, p2, p3, p4, layout=(2, 2), titlefontsize=10, xlabelfontsize=7, ylabelfontsize=5, dpi=300), \"lu-p-err.png\")\n", - "plot(p1, p2, p3, p4, layout=(2,2))" - ] - }, - { - "cell_type": "markdown", - "id": "ce999320", - "metadata": {}, - "source": [ - "# Exercise 4: graph restrictions by LU vizualization" - ] - }, - { - "cell_type": "code", - "execution_count": 41, - "id": "ef510fcd", - "metadata": {}, - "outputs": [], - "source": [ - "r_b = [1, 2, 3, 4, 5, 10, 15, 20 ,30 , 40]\n", - "r_a = [1, 2, 3, 4, 5]\n", - "P_A_s = [M_cross_lu_err(A, i, Val(true))[2] for i in r_a]\n", - "P_B_s = [M_cross_lu_err(B, i, Val(true))[2] for i in r_b]\n", - "t_red = t[1:3:n];" - ] - }, - { - "cell_type": "code", - "execution_count": 71, - "id": "5d127a82", - "metadata": { - "scrolled": true - }, - "outputs": [], - "source": [ - "s_1 = surface(t_red, t_red, f, colorbar=false);\n", - "c_1 = contour(t_red, t_red, f, colorbar=false);\n", - "#s_2 = surface(t_red, t_red, g, colorbar=false);\n", - "#c_2 = contour(t_red, t_red, g, colorbar=false);\n", - "for (i, r) in enumerate(r_a)\n", - " p = plot(s_1, c_1, layout=(1, 2), titlefontsize=10, xlabelfontsize=7, ylabelfontsize=5, dpi=300,\n", - " title=\"f(x, y) at r=$r\", size=(600, 300))\n", - "\n", - " hline!(p[1], [0], t[P_A_s[i]], color=:red, opacity=0.5, label=\"\", lw=2)\n", - " hline!(p[2], [0], t[P_A_s[i]], color=:red, opacity=0.5, label=\"\", lw=2)\n", - " #hline!(p[1], [1], t[P_B_s[i]], color=:red, opacity=0.5, label=\"\", lw=2)\n", - " #hline!(p[2], [1], t[P_B_s[i]], color=:red, opacity=0.5, label=\"\", lw=2)\n", - " savefig(p, \"rc-a-$r.png\")\n", - "end" - ] - }, - { - "cell_type": "code", - "execution_count": 73, - "id": "62ea33aa", - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "\"f\"" - ] - }, - "execution_count": 73, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "c0fd51b6", - "metadata": {}, - "outputs": [], - "source": [] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "f8872b26", - "metadata": {}, - "outputs": [], - "source": [] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "70500acf", - "metadata": {}, - "outputs": [], - "source": [] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "50a8f94c", - "metadata": {}, - "outputs": [], - "source": [] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "1de4ad3a", - "metadata": {}, - "outputs": [], - "source": [] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "2e2189ca", - "metadata": {}, - "outputs": [], - "source": [] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "62ff18cd", 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