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--- 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": {},
- "outputs": [],
- "source": [
- "# Przykładowe błędy w zależności od liczby iteracji\n",
- "# obrazują jak szybko zbiega metoda:"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 19,
- "metadata": {},
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- {
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- "source": [
- "# funkcje do kolejnych wykresów, pokaujących błąd względny liczenia sinusa w przedziale [0, 2pi]:\n",
- "\n",
- "function rel_error_cordic(x)\n",
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- "xs = range(0, stop = 6.3, step = 0.01)\n",
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- "res_cordic = [rel_error_cordic(x) for x in xs]\n",
- "res_taylor = [rel_error_taylor(x) for x in xs]"
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- "source": [
- "# Błąd względny obliczania sinusa Cordicem na przedziale (0, 6.3)\n",
- "plot(OX, res_cordic, xguide = \"x\", yguide = \"relative error\", label = \"cordic_sin\")"
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- "execution_count": 34,
- "metadata": {},
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- ],
- "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,
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- "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
-}
generated by cgit v1.2.3 (git 2.25.1) at 2024-11-11 12:36:17 +0000