From c5fcf7179a83ef65c86c6a4a390029149e518649 Mon Sep 17 00:00:00 2001 From: Franciszek Malinka Date: Tue, 5 Oct 2021 21:49:54 +0200 Subject: Duzy commit ze smieciami --- Semestr 3/anm/pracowniaPOP/prog/program.ipynb | 7922 ------------------------- 1 file changed, 7922 deletions(-) delete mode 100644 Semestr 3/anm/pracowniaPOP/prog/program.ipynb (limited to 'Semestr 3/anm/pracowniaPOP/prog/program.ipynb') diff --git a/Semestr 3/anm/pracowniaPOP/prog/program.ipynb b/Semestr 3/anm/pracowniaPOP/prog/program.ipynb deleted file mode 100644 index f8cb21c..0000000 --- a/Semestr 3/anm/pracowniaPOP/prog/program.ipynb +++ /dev/null @@ -1,7922 +0,0 @@ -{ - "cells": [ - { - "cell_type": "code", - "execution_count": 1, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "set_cordic_iterations (generic function with 1 method)" - ] - }, - "execution_count": 1, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "include(\"program.jl\")" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "Plots.PlotlyBackend()" - ] - }, - "execution_count": 2, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "using Plots\n", - "using Random\n", - "using Distributions\n", - "\n", - "plotly()" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": {}, - "outputs": [], - "source": [ - "# Zadanie 10, Franiszek malinka, Kacper Solecki\n", - "\n", - "# instrukcja:\n", - "# Nasz program udostępnia funkcje \n", - "\n", - "# -> taylor_sin(a, b) - sinus liczby a+bi liczony za pomocą szeregu Taylora\n", - "# -> taylor_cos(a, b) - cosinus liczby a+bi liczony za pomocą szeregu Taylora\n", - "# -> taylor_sinh(x) - sinus hiperboliczny liczby x liczony za pomocą szeregu Taylora\n", - "# -> taylor_cosh(x) - cosinus hiperboliczny liczby x liczony za pomocą szeregu Taylora\n", - "# -> cordic_sin(x) - sinus (rzeczywistej) liczby x liczony za pomocą algorytmu Cordic\n", - "# -> cordic_cos(x) - cosinus (rzeczywistej) liczby x liczony za pomocą algorytmu Cordic" - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "0.9092974268256817" - ] - }, - "execution_count": 4, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "# porównianie na sin(2), cos(2)\n", - "sin(2.0)" - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "(0.9092974268256817, -0.0)" - ] - }, - "execution_count": 5, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "taylor_sin(2.0, 0.0)" - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "0.9092974280938506" - ] - }, - "execution_count": 6, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "cordic_sin(2.0)" - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "-0.4161468365471424" - ] - }, - "execution_count": 7, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "cos(2)" - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "(-0.41614683654714246, -0.0)" - ] - }, - "execution_count": 8, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "taylor_cos(2.0, 0.0)" - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "-0.4161468353122473" - ] - }, - "execution_count": 9, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "cordic_cos(2.0)" - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "-5991.431207677988 - 9240.89014825243im" - ] - }, - "execution_count": 10, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "# porównianie na sin(10 + 10i)\n", - "sin(10 + 10im)" - ] - }, - { - "cell_type": "code", - "execution_count": 11, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "(-5991.431207678, -9240.890148252452)" - ] - }, - "execution_count": 11, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "taylor_sin(10, 10)" - ] - }, - { - "cell_type": "code", - "execution_count": 12, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "rel_error (generic function with 1 method)" - ] - }, - "execution_count": 12, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "# w ten sposób liczony jest błąd względny zarówno dla liczb rzeczywistych jak i zespolonych\n", - "function rel_error(x, y)\n", - " if x == 0\n", - " return 0\n", - " end\n", - " return abs((x-y)/x)\n", - "end" - ] - }, - { - "cell_type": "code", - "execution_count": 13, - "metadata": {}, - "outputs": [], - "source": [ - "# Funkcje użyte w wykresach błędów od liczby iteracji:" - ] - }, - { - "cell_type": "code", - "execution_count": 14, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "taylor_error_of_iterations (generic function with 1 method)" - ] - }, - "execution_count": 14, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "# błąd przy liczeniu sin(100 + 100i) szeregiem Taylora przy x iteracjach\n", - "function taylor_error_of_iterations(x)\n", - " set_taylor_iterations(x)\n", - " return rel_error(sin(100+100im), taylor_sin(100, 100)[1] + taylor_sin(100, 100)[2]*im)\n", - "end" - ] - }, - { - "cell_type": "code", - "execution_count": 15, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "cordic_error_of_iterations (generic function with 1 method)" - ] - }, - "execution_count": 15, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "# błąd przy liczeniu sin(100) Cordicem przy x iteracjach\n", - "function cordic_error_of_iterations(x)\n", - " set_cordic_iterations(x)\n", - " return rel_error(sin(100), cordic_sin(100.0))\n", - "end" - ] - }, - { - "cell_type": "code", - "execution_count": 16, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "taylor_error_of_iterations2 (generic function with 1 method)" - ] - }, - "execution_count": 16, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "# błąd przy liczeniu sin(100) szeregiem Taylora przy x iteracjach\n", - "function taylor_error_of_iterations2(x)\n", - " set_taylor_iterations(x)\n", - " return rel_error(sin(100), taylor_sin(100.0, 0.0)[1])\n", - "end" - ] - }, - { - "cell_type": "code", - "execution_count": 17, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "1:20" - ] - }, - "execution_count": 17, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "X = 1:20" - ] - }, - { - "cell_type": "code", - "execution_count": 18, - "metadata": {}, - 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\n", - " \n", - "\n", - " \n", - "\n" - ] - }, - "execution_count": 34, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "# Błąd względny obliczania sinusa szeregiem Taylora na przedziale (0, 6.3)\n", - "plot(OX, res_taylor, xguide = \"x\", yguide = \"relative error\", label = \"taylor_sin\")" - ] - }, - { - "cell_type": "code", - "execution_count": 27, - "metadata": {}, - "outputs": [], - "source": [ - "# Poniżej znajdują się funkcje testujące, na podstawie których powstała Tabela 2 w sprawozdaniu" - ] - }, - { - "cell_type": "code", - "execution_count": 28, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "MersenneTwister(UInt32[0x00003039], Random.DSFMT.DSFMT_state(Int32[-870096391, 1072918504, -1812426662, 1073255081, -733866021, 1073404543, 807620846, 1073368448, 1919433844, 1072852359 … -362113007, 1073100625, -166402106, 1073460158, -1907020342, 721295190, -750225566, -1300227565, 382, 0]), [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 … 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], UInt128[0x00000000000000000000000000000000, 0x00000000000000000000000000000000, 0x00000000000000000000000000000000, 0x00000000000000000000000000000000, 0x00000000000000000000000000000000, 0x00000000000000000000000000000000, 0x00000000000000000000000000000000, 0x00000000000000000000000000000000, 0x00000000000000000000000000000000, 0x00000000000000000000000000000000 … 0x00000000000000000000000000000000, 0x00000000000000000000000000000000, 0x00000000000000000000000000000000, 0x00000000000000000000000000000000, 0x00000000000000000000000000000000, 0x00000000000000000000000000000000, 0x00000000000000000000000000000000, 0x00000000000000000000000000000000, 0x00000000000000000000000000000000, 0x00000000000000000000000000000000], 1002, 0)" - ] - }, - "execution_count": 28, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "TESTS = 100000000\n", - "\n", - "Random.seed!(12345)" - ] - }, - { - "cell_type": "code", - "execution_count": 29, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "taylor_test_error_real (generic function with 3 methods)" - ] - }, - "execution_count": 29, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "# wszystkie te funkcje wyglądają bardzo podobnie\n", - "\n", - "function taylor_test_error_real(l::Float64=floatmin(), r::Float64=floatmax())\n", - " res = BigFloat(0) # suma błędów względnych\n", - " abs_res = BigFloat(0) # suma błędów bezwzględnych\n", - " maksi_rel = BigFloat(0) # max bląd względny\n", - " maksi_abs = BigFloat(0) # max bląd bezwzględny\n", - " for i = 1:TESTS\n", - " # losujemy argument z przedziału [l, r]\n", - " x = rand(Uniform(l, r))\n", - " lib_sin = sin(x)\n", - " # sprawdzanie błędu względnego z zerem nie ma sensu\n", - " if lib_sin == 0\n", - " continue\n", - " end\n", - " my_sin = taylor_sin(x, 0)\n", - " # obliczamy błąd względny względem funkcji bibliotecznej\n", - " error = rel_error(lib_sin, my_sin[1])\n", - " # obliczamy błąd bezwzględny względem funkcji bibliotecznej\n", - " abs_error = abs(my_sin[1] - lib_sin)\n", - " # aktualizujemy błędy\n", - " res += error\n", - " abs_res += abs_error\n", - " maksi_rel = max(maksi_rel, error)\n", - " maksi_abs = max(maksi_abs, abs_error)\n", - " end\n", - " return (res/TESTS, maksi_rel, abs_res/TESTS, maksi_abs)\n", - "end\n", - "\n", - "# (floatmin(), floatmax()):\n", - "# (1.887844299668514797145972383393008309519973773948872165524132116232181033410611e-15, \n", - "# 3.16719187748669057932019506480803006098767582443542778491973876953125e-08,\n", - "# 1.1794041986528804301572959036155385792454808324691839516162872314453125e-16,\n", - "# 8.8817841970012523233890533447265625e-16)\n", - "\n", - "# (-pi/2, pi/2):\n", - "# (1.471587646915289673578957365178574707202863924359834292944840261618821841693717e-15, \n", - "# 1.1848604479598457485905096801294400510329296594136394560337066650390625e-08, \n", - "# 9.765754183892570637182101557852154094518937199609354138374328613281249999999994e-17, \n", - "# 5.5511151231257827021181583404541015625e-16)\n", - "\n", - "# (0, 1):\n", - "# (8.693695902799099432701533207691913249153884601349429181102457242502623557811573e-17,\n", - "# 6.661260307992334044328275268948192015174572739102942797728701407322660088539124e-16,\n", - "# 4.293257315426284893844499634951716871000826358795166015624999999999999999999994e-17,\n", - "# 4.44089209850062616169452667236328125e-16)" - ] - }, - { - "cell_type": "code", - "execution_count": 30, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "taylor_test_error_complex (generic function with 3 methods)" - ] - }, - "execution_count": 30, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "function taylor_test_error_complex(l::Float64=-100.0, r::Float64=100.0)\n", - " res = BigFloat(0)\n", - " abs_res = BigFloat(0)\n", - " maksi_rel = BigFloat(0)\n", - " maksi_abs = BigFloat(0)\n", - " for i = 1:TESTS\n", - " x = rand(Uniform(l, r))\n", - " y = rand(Uniform(max(l, -Float64(√(BigFloat(r)*r - BigFloat(x)*x))), \n", - " Float64(√(BigFloat(r)*r - BigFloat(x)*x))))\n", - " lib_sin = sin(x + y*im)\n", - " my_sin = taylor_sin(x, y)\n", - " error = rel_error(lib_sin, my_sin[1] + my_sin[2]*im)\n", - " abs_error = abs(lib_sin - (my_sin[1] + my_sin[2]*im))\n", - " res += error\n", - " abs_res += abs_error\n", - " maksi_rel = max(maksi_rel, error)\n", - " maksi_abs = max(maksi_abs, abs_error)\n", - " end\n", - " return (res/TESTS, maksi_rel, abs_res/TESTS, maksi_abs)\n", - "end\n", - "\n", - "# (-100, 100):\n", - "# (4.932205036590292360305897845543684560590114030155004375572792447173773555907229e-15, \n", - "# 1.3111008357751143737471652583705182364137709072338111582212150096893310546875e-13, \n", - "# 1.688623533003329462861070079404255492323042928202526655997186385923664654746476e+26, \n", - "# 5.89784569029861503624382775296e+29)\n", - "\n", - "# (-2pi, 2pi):\n", - "# (4.338436856498561167962902801400526155223569336855327458414068651872587652334067e-16, \n", - "# 1.48720543982594402760972427363260419015678071019692652043886482715606689453125e-11, \n", - "# 1.364745868545483273874507699553481910023596725366415789061836204439613629002538e-14, \n", - "# 8.7095846425677781478128738959826782468909289747216462274082005023956298828125e-13)\n", - "\n", - "# (0, 1):\n", - "# (1.596935223079780368874812440778376297707878344605454825588075017177200118204992e-16, \n", - "# 1.098997011961567777204023105931451003520679665648174250236479565501213073730469e-15, \n", - "# 1.124298405324025732059699593805301650508046127888472394113736655893442950571177e-16, \n", - "# 1.110569915127177230816030746289393434073728902933275719533412484452128410339355e-15)" - ] - }, - { - "cell_type": "code", - "execution_count": 31, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "cordic_test_error (generic function with 3 methods)" - ] - }, - "execution_count": 31, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "function cordic_test_error(l::Float64=floatmin(), r::Float64=floatmax())\n", - " res = BigFloat(0)\n", - " abs_res = BigFloat(0)\n", - " maksi_rel = BigFloat(0)\n", - " maksi_abs = BigFloat(0)\n", - " for i = 1:TESTSd\n", - " x = rand(Uniform(l, r))\n", - " lib_sin = sin(x)\n", - " my_sin = cordic_sin(x)\n", - " error = rel_error(lib_sin, my_sin)\n", - " abs_error = abs(lib_sin - my_sin)\n", - " res += error\n", - " abs_res += abs_error\n", - " if error > maksi_rel\n", - " worst_rel = x\n", - " end\n", - " maksi_rel = max(maksi_rel, error)\n", - " maksi_abs = max(maksi_abs, abs_error)\n", - " end\n", - " return (res/TESTS, maksi_rel, abs_res/TESTS, maksi_abs)\n", - "end\n", - "\n", - "# (floatmin(), floatmax()):\n", - "# (3.099880824631376815575307358441341907045753361742215192539218280437518515668677e-08, \n", - "# 0.457561153670805575988111968399607576429843902587890625, \n", - "# 2.459716652636021482355597144179802356154379561203882076370064169168472290039072e-09, \n", - "# 0.0006041780891818948617810747236944735050201416015625)\n", - "\n", - "# (-2pi, 2pi):\n", - "# (2.769658715752475495709394998775060901506630522496771093654899307916206208091117e-08, \n", - "# 0.11834204003306579566778822254491387866437435150146484375, \n", - "# 2.532059440779907667675144447194875727078638982803227008844260126352310180664052e-09,\n", - "# 0.00552917548107156875403234153054654598236083984375)\n", - "\n", - "# (0, 1):\n", - "# (4.176404604808155838824592152607760760141260709650975486490997166423577713345588e-08, \n", - "# 0.091828765031669201679420666550868190824985504150390625, \n", - "# 2.613683444981852927700279986835644064485650872597943816799670457839965820312493e-09, \n", - "# 0.00052619288922584050993691562325693666934967041015625)" - ] - }, - { - "cell_type": "code", - "execution_count": 32, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "taylor_without_reduction_test_error (generic function with 3 methods)" - ] - }, - "execution_count": 32, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "function taylor_without_reduction_test_error(l::Float64=-100.0, r::Float64=100.0)\n", - " res = BigFloat(0)\n", - " abs_res = BigFloat(0)\n", - " maksi_rel = BigFloat(0)\n", - " maksi_abs = BigFloat(0)\n", - " for i = 1:TESTS\n", - " x = rand(Uniform(l, r))\n", - " y = rand(Uniform(max(l, -Float64(√(BigFloat(r)*r - BigFloat(x)*x))), \n", - " Float64(√(BigFloat(r)*r - BigFloat(x)*x))))\n", - " lib_sin = sin(x + y*im)\n", - " my_sin = taylor_sin_no_reduction(x, y)\n", - " error = rel_error(lib_sin, my_sin[1] + my_sin[2]*im)\n", - " abs_error = abs(lib_sin - (my_sin[1] + my_sin[2]*im))\n", - " res += error\n", - " abs_res += abs_error\n", - " maksi_rel = max(maksi_rel, error)\n", - " maksi_abs = max(maksi_abs, abs_error)\n", - " end\n", - " return (res/TESTS, maksi_rel, abs_res/TESTS, maksi_abs)\n", - "end\n", - "\n", - "# (-100, 100)\n", - "# (4.774091809397734982069398193189465079787514988283523440828527859306283137571149e+23, \n", - "# 4.48814142545670189837451264e+26, \n", - "# 7.758560481134976967771949796127369173267383351574525337904198599731007318070319e+40, \n", - "# 2.20832987186165589366506156220211970162294784e+44)\n", - "\n", - "# (-2pi, 2pi)\n", - "# (0.6332711088634405192103194531076134843075526902544601426097735760298574150340518, \n", - "# 1.0, \n", - "# 23.44057586605533515691829807979128873527513778367553433852055381911453864572971, \n", - "# 267.74654227273646256435313262045383453369140625)\n", - "\n", - "# (0, 1)\n", - "# (1.589482169544726703219739509256918022523030217883325972454504856003547167066932e-16, \n", - "# 1.291897416767691567199962520855285151964115327068161054313577551511116325855255e-15, \n", - "# 1.118367257755837281340217148887719929595000777959128862241583039814976641146415e-16, \n", - "# 1.115760330918745818020084658567032229219617364690542160587938269600272178649902e-15)" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Julia 1.4.1", - "language": "julia", - "name": "julia-1.4" - }, - "language_info": { - "file_extension": ".jl", - "mimetype": "application/julia", - "name": "julia", - "version": "1.4.1" - } - }, - "nbformat": 4, - "nbformat_minor": 4 -} -- cgit v1.2.3