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Строка 1: |
| − | ==Описание==
| + | {{#widget:Iframe |url=http://tm.spbstu.ru/htmlets/Durnev_AA/home.html |width=1550 |height=1500 |border=0 }} |
| − | | |
| − | Визуализация различных численных методов
| |
| − | | |
| − | Исполнитель: [[Дурнев_Андрей|Дурнев Андрей]]
| |
| − | | |
| − | Группа 13632/1 Кафедра Теоретической механики
| |
| − | | |
| − | Файл:[[http://tm.spbstu.ru/htmlets/Durnev_AA/Kursovaya.docx]]
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| − | | |
| − | {{#widget:Iframe |url=http://tm.spbstu.ru/htmlets/Durnev_AA/home.html |width=1000 |height=1000 |border=0 }} | |
| − | | |
| − | ==Код программы==
| |
| − | <div class="mw-collapsible mw-collapsed">
| |
| − | '''Текст программы на языке JavaScript:''' <div class="mw-collapsible-content">
| |
| − | <syntaxhighlight lang="javascript" line start="1" enclose="div">
| |
| − | | |
| − | //Метод Монте-Карло
| |
| − | | |
| − | window.addEventListener("load", program_code, false);
| |
| − | function program_code() {
| |
| − | | |
| − | var ctx = canvas_example.getContext("2d");
| |
| − | var w = canvas_example.width;
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| − | var h = canvas_example.height;
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| − | | |
| − | ctx.translate(w/2, h/2);
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| − | | |
| − | var x = [];
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| − | var y = [];
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| − | var min = 1000;
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| − | var max = -1000;
| |
| − | var n = 0;
| |
| − | var points;
| |
| − | var cur_points;
| |
| − | var ok = 0;
| |
| − | var a;
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| − | var b ;
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| − | var scalex, scaley;
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| − | var dx;
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| − | var dy;
| |
| − | var func;
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| − | var time = 5000;
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| − | var dt;
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| − | var flag = false;
| |
| − | | |
| − | | |
| − | var result;
| |
| − | | |
| − | | |
| − | | |
| − | //функция
| |
| − | function f(x){
| |
| − | return (eval(func));
| |
| − | }
| |
| − | | |
| − | function search(){
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| − | | |
| − | func = document.getElementById("fun").value;
| |
| − | | |
| − | for (var i = a; i < b; i+=0.001){
| |
| − | | |
| − | //максимум
| |
| − | if (f(i) > max){
| |
| − | max = f(i);
| |
| − | }
| |
| − | | |
| − | //минимум
| |
| − | if (f(i) < min){
| |
| − | min = f(i);
| |
| − | }
| |
| − | }
| |
| − | | |
| − | //масштаб
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| − | scaley = 100/(Math.abs(max) + Math.abs(min));
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| − | | |
| − | if (Math.abs(b) >= Math.abs(a)){
| |
| − | scalex = 250/b * 0.9;
| |
| − | }
| |
| − | | |
| − | if (Math.abs(b) < Math.abs(a)){
| |
| − | scalex = 250/Math.abs(a) * 0.9;
| |
| − | }
| |
| − | | |
| − | //сдвиг
| |
| − | dx = (b + a)/2;
| |
| − | dy = (max + min)/2;
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| − | | |
| − | //точки
| |
| − | //points = 100;
| |
| − | }
| |
| − | | |
| − | function calculation(){
| |
| − | | |
| − | cur_points++;
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| − | | |
| − | //положительная функция
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| − | if (min * max >= 0 && min >= 0 && n < points){
| |
| − | x[n] = Math.random() * (b - a) + a;
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| − | y[n] = Math.random() * (max - 0) + 0;
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| − | | |
| − | if (y[n] < f(x[n])){
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| − | ok++;
| |
| − | }
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| − | | |
| − | | |
| − | result = (ok / cur_points) * (b - a) * max;
| |
| − | n++;
| |
| − | | |
| − | }
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| − | | |
| − | //отрицательная функция
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| − | if (min * max >= 0 && max <= 0 && n < points){
| |
| − | x[n] = Math.random() * (b - a) + a;
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| − | y[n] = Math.random() * (min - 0) + 0;
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| − | | |
| − | if (y[n] > f(x[n])){
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| − | ok++;
| |
| − | }
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| − | | |
| − | result = -(ok/cur_points) * (b - a) * (-min);
| |
| − | n++;
| |
| − | }
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| − | | |
| − | //знакопеременные функции
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| − | if (min * max < 0 && n < points){
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| − | | |
| − | x[n] = Math.random() * (b - a) + a;
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| − | y[n] = Math.random() * (max - min) + min;
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| − | | |
| − | | |
| − | if (y[n] > 0 && f(x[n]) > 0 && y[n] < f(x[n])){
| |
| − | ok++;
| |
| − | }
| |
| − | | |
| − | if (y[n] < 0 && f(x[n]) < 0 && y[n] > f(x[n])){
| |
| − | ok--;
| |
| − | }
| |
| − | | |
| − | result = (ok/cur_points) * (b - a) * (max - min);
| |
| − | n++;
| |
| − | }
| |
| − | }
| |
| − | | |
| − | function draw(){
| |
| − | //оси
| |
| − | ctx.beginPath();
| |
| − | ctx.moveTo(0 - dx * scalex, -h/2);
| |
| − | ctx.lineTo(0 - dx * scalex, h/2);
| |
| − | ctx.moveTo(w/2 , dy * scaley);
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| − | ctx.lineTo(-w/2 , dy * scaley);
| |
| − | ctx.stroke();
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| − | | |
| − | ctx.font = '10px Arial';
| |
| − | ctx.strokeText('1', (1 - dx) * scalex, (-0.1 + dy) * scaley);
| |
| − | ctx.strokeText('1', (0.1 -dx) * scalex, (-1 + dy) * scaley);
| |
| − | | |
| − | | |
| − | //кривая
| |
| − | ctx.beginPath();
| |
| − | for (var i = a; i < b; i+=0.01){
| |
| − | ctx.moveTo((i - dx) * scalex, (-f(i) + dy) * scaley);
| |
| − | ctx.lineTo((i+0.01 - dx) * scalex, (-f(i+0.01) + dy) * scaley);
| |
| − | }
| |
| − | | |
| − | ctx.stroke();
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| − | | |
| − | | |
| − | //точки
| |
| − | ctx.fillStyle = 'red';
| |
| − | ctx.beginPath();
| |
| − | ctx.arc((x[n-1] - dx) * scalex, (-y[n-1] + dy) * scaley, 1, 0, 2 * Math.PI);
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| − | ctx.fill();
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| − | | |
| − | }
| |
| − | | |
| − | function control(){
| |
| − | calculation();
| |
| − | draw();
| |
| − | result1.innerHTML = Math.round(result * 100)/100;
| |
| − | }
| |
| − | | |
| − | knopka.onclick = function(){
| |
| − | | |
| − | if (flag){
| |
| − | location.reload();
| |
| − | }
| |
| − | | |
| − | flag = true;
| |
| − | knopka.value = 'Очистить';
| |
| − | cur_points = 0;
| |
| − | points = parseFloat(document.getElementById("qual").value);
| |
| − | dt = time/points;
| |
| − | console.log(dt)
| |
| − | a = parseFloat(document.getElementById("a1").value);
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| − | b = parseFloat(document.getElementById("b1").value);
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| − | search();
| |
| − | var name = setInterval(control, dt);
| |
| − | }
| |
| − | | |
| − | | |
| − | if (n == points){
| |
| − | clearInterval(name);
| |
| − | console.log('a');
| |
| − | }
| |
| − | }
| |
| − | | |
| − | //Метод трапеций
| |
| − | window.addEventListener("load", program_code, false);
| |
| − | function program_code() {
| |
| − | | |
| − | var ctx = canvas_example.getContext("2d");
| |
| − | var w = canvas_example.width;
| |
| − | var h = canvas_example.height;
| |
| − | | |
| − | var flag = false;
| |
| − | var a;
| |
| − | var b;
| |
| − | var func;
| |
| − | var max = -100000;
| |
| − | var min = 100000;
| |
| − | var scale, scale1, scale2;
| |
| − | var x = [];
| |
| − | var y = [];
| |
| − | var result = 0;
| |
| − | | |
| − | ctx.translate(w/2, h/2);
| |
| − | | |
| − | //функция
| |
| − | function f(x){
| |
| − | return (eval(func));
| |
| − | }
| |
| − | | |
| − | function input(){
| |
| − | | |
| − | a = parseFloat(document.getElementById("a1").value);
| |
| − | b = parseFloat(document.getElementById("b1").value);
| |
| − | func = document.getElementById("fun").value;
| |
| − | number = parseFloat(document.getElementById('qual').value);
| |
| − | | |
| − | //минимум и максимум
| |
| − | for (var i = a; i < b; i+=0.001){
| |
| − | | |
| − | //максимум
| |
| − | if (f(i) > max){
| |
| − | max = f(i);
| |
| − | }
| |
| − | | |
| − | //минимум
| |
| − | if (f(i) < min){
| |
| − | min = f(i);
| |
| − | }
| |
| − | }
| |
| − | | |
| − | //масштаб
| |
| − | scaley = 100/(Math.abs(max) + Math.abs(min));
| |
| − | | |
| − | if (Math.abs(b) >= Math.abs(a)){
| |
| − | scalex = 250/b * 0.9;
| |
| − | }
| |
| − | | |
| − | if (Math.abs(b) < Math.abs(a)){
| |
| − | scalex = 250/Math.abs(a) * 0.9;
| |
| − | }
| |
| − | | |
| − | //сдвиг
| |
| − | dx = (b + a)/2;
| |
| − | dy = (max + min)/2;
| |
| − | dt = (b - a)/number;
| |
| − | | |
| − | //разбиение
| |
| − | for (var i = a; i < b + 1/2 * dt; i += dt){
| |
| − | x.push(i);
| |
| − | y.push(f(i));
| |
| − | }
| |
| − | }
| |
| − | | |
| − | function calculation(){
| |
| − | for (var i = 0; i < number; i++){
| |
| − | | |
| − | if (f(x[i]) >= 0 && f(x[i+1]) >= 0){
| |
| − | result += (x[i + 1] - x[i]) * (Math.abs(y[i]) + Math.abs(y[i + 1])) * 0.5;
| |
| − | }
| |
| − | | |
| − | if (f(x[i]) < 0 && f(x[i+1]) < 0){
| |
| − | result -= (x[i + 1] - x[i]) * (Math.abs(y[i]) + Math.abs(y[i + 1])) * 0.5;
| |
| − | }
| |
| − | | |
| − | else{
| |
| − | result += 0;
| |
| − | }
| |
| − | | |
| − | }
| |
| − | }
| |
| − | | |
| − | function draw(){
| |
| − | | |
| − | //оси
| |
| − | ctx.beginPath();
| |
| − | ctx.moveTo(0 - dx * scalex, -h/2);
| |
| − | ctx.lineTo(0 - dx * scalex, h/2);
| |
| − | ctx.moveTo(w/2 , 0 + dy * scaley);
| |
| − | ctx.lineTo(-w/2 , 0 + dy * scaley);
| |
| − | ctx.stroke();
| |
| − | | |
| − | ctx.font = '10px Arial';
| |
| − | ctx.strokeText('1', (1 - dx) * scalex, (-0.1 + dy) * scaley);
| |
| − | ctx.strokeText('1', (0.1 -dx) * scalex, (-1 + dy) * scaley);
| |
| − | | |
| − | //кривая
| |
| − | ctx.beginPath();
| |
| − | for (var i = a; i < b; i+=0.01){
| |
| − | ctx.moveTo((i - dx) * scalex, (-f(i) + dy) * scaley);
| |
| − | ctx.lineTo((i + 0.01 - dx) * scalex, (-f(i + 0.01) + dy) * scaley);
| |
| − | }
| |
| − | ctx.stroke();
| |
| − | | |
| − | | |
| − | ctx.strokeStyle = 'red';
| |
| − | | |
| − | //разбиение
| |
| − | ctx.beginPath();
| |
| − | for (var i = 0; i < number + 1; i++){
| |
| − | ctx.moveTo((x[i] - dx) * scalex, dy * scaley);
| |
| − | ctx.lineTo((x[i] - dx) * scalex, (-y[i] + dy) * scaley)
| |
| − | }
| |
| − | ctx.stroke();
| |
| − | | |
| − | ctx.beginPath();
| |
| − | for(var i = 0; i < number; i++){
| |
| − | ctx.moveTo((x[i] - dx) * scalex, (-y[i] + dy) * scaley);
| |
| − | ctx.lineTo((x[i+1] - dx) * scalex, (-y[i+1] + dy) * scaley);
| |
| − | }
| |
| − | ctx.stroke();
| |
| − | | |
| − | }
| |
| − | | |
| − | | |
| − | knopka.onclick = function(){
| |
| − | | |
| − | if (flag){
| |
| − | location.reload();
| |
| − | }
| |
| − | | |
| − | flag = true;
| |
| − | knopka.value = 'Очистить';
| |
| − | input();
| |
| − | calculation();
| |
| − | result1.innerHTML = Math.round(result * 100)/100;
| |
| − | draw();
| |
| − | }
| |
| − | }
| |
| − | | |
| − | | |
| − | //Метод прямоугольников
| |
| − | window.addEventListener("load", program_code, false);
| |
| − | function program_code() {
| |
| − | | |
| − | var ctx = canvas_example.getContext("2d");
| |
| − | var w = canvas_example.width;
| |
| − | var h = canvas_example.height;
| |
| − | | |
| − | var flag = false;
| |
| − | var a;
| |
| − | var b;
| |
| − | var func;
| |
| − | var max = -100000;
| |
| − | var min = 100000;
| |
| − | var scale, scale1, scale2;
| |
| − | var x = [];
| |
| − | var y = [];
| |
| − | var result = 0;
| |
| − | var dt;
| |
| − | var dx = 0;
| |
| − | var dy = 0;
| |
| − | | |
| − | ctx.translate(w/2, h/2);
| |
| − | | |
| − | //функция
| |
| − | function f(x){
| |
| − | return (eval(func));
| |
| − | }
| |
| − | | |
| − | function input(){
| |
| − | | |
| − | a = parseFloat(document.getElementById("a1").value);
| |
| − | b = parseFloat(document.getElementById("b1").value);
| |
| − | func = document.getElementById("fun").value;
| |
| − | var number = parseFloat(document.getElementById('qual').value);
| |
| − | dx = (b - a)/number;
| |
| − | | |
| − | //минимум и максимум
| |
| − | for (var i = a; i < b; i+=0.001){
| |
| − | | |
| − | //максимум
| |
| − | if (f(i) > max){
| |
| − | max = f(i);
| |
| − | }
| |
| − | | |
| − | //минимум
| |
| − | if (f(i) < min){
| |
| − | min = f(i);
| |
| − | }
| |
| − | }
| |
| − | | |
| − | //масштаб
| |
| − | scaley = 100/(Math.abs(max) + Math.abs(min));
| |
| − | | |
| − | if (Math.abs(b) >= Math.abs(a)){
| |
| − | scalex = 250/b * 0.9;
| |
| − | }
| |
| − | | |
| − | if (Math.abs(b) < Math.abs(a)){
| |
| − | scalex = 250/Math.abs(a) * 0.9;
| |
| − | }
| |
| − | | |
| − | //сдвиг
| |
| − | dx = (b + a)/2;
| |
| − | dy = (max + min)/2;
| |
| − | dt = (b - a)/number;
| |
| − | | |
| − | }
| |
| − | | |
| − | function calculation(){
| |
| − | | |
| − | if (menu.value == 'first'){
| |
| − | console.log('a');
| |
| − | for (var i = a; i < b; i += dt){
| |
| − | | |
| − | if (f(i) >= 0 & f(i + dt) >= 0){
| |
| − | result += Math.abs(f(i))*dt;
| |
| − | }
| |
| − | | |
| − | if (f(i) < 0 & f(i + dt) < 0){
| |
| − | result -= Math.abs(f(i))*dt;
| |
| − | }
| |
| − | | |
| − | else{
| |
| − | result += 0;
| |
| − | }
| |
| − | | |
| − | }
| |
| − | }
| |
| − | | |
| − | if (menu.value == 'second'){
| |
| − | for (var i = a + dt; i < b; i += dt){
| |
| − | if (f(i) >= 0 & f(i + dt) >= 0){
| |
| − | result += Math.abs(f(i))*dt;
| |
| − | }
| |
| − | | |
| − | if (f(i) < 0 & f(i + dt) < 0){
| |
| − | result -= Math.abs(f(i))*dt;
| |
| − | }
| |
| − | | |
| − | else{
| |
| − | result += 0;
| |
| − | }
| |
| − | }
| |
| − | }
| |
| − | | |
| − | if (menu.value == 'third'){
| |
| − | for (var i = a + dt/2 ; i < b; i += dt){
| |
| − | if (f(i) >= 0 & f(i + dt) >= 0){
| |
| − | result += Math.abs(f(i))*dt;
| |
| − | }
| |
| − | | |
| − | if (f(i) < 0 & f(i + dt) < 0){
| |
| − | result -= Math.abs(f(i))*dt;
| |
| − | }
| |
| − | | |
| − | else{
| |
| − | result += 0;
| |
| − | }
| |
| − | }
| |
| − | }
| |
| − | | |
| − | }
| |
| − | | |
| − | function draw(){
| |
| − | | |
| − | //оси
| |
| − | ctx.beginPath();
| |
| − | ctx.moveTo(0 - dx * scalex, -h/2);
| |
| − | ctx.lineTo(0 - dx * scalex, h/2);
| |
| − | ctx.moveTo(w/2 , 0 + dy * scaley);
| |
| − | ctx.lineTo(-w/2 , 0 + dy * scaley);
| |
| − | ctx.stroke();
| |
| − | | |
| − | ctx.font = '10px Arial';
| |
| − | ctx.strokeText('1', (1 - dx) * scalex, (-0.1 + dy) * scaley);
| |
| − | ctx.strokeText('1', (0.1 -dx) * scalex, (-1 + dy) * scaley);
| |
| − | | |
| − | //кривая
| |
| − | ctx.beginPath();
| |
| − | for (var i = a; i < b; i+=0.01){
| |
| − | ctx.moveTo((i - dx) * scalex, (-f(i) + dy) * scaley);
| |
| − | ctx.lineTo((i + 0.01 - dx) * scalex, (-f(i + 0.01) + dy) * scaley);
| |
| − | }
| |
| − | ctx.stroke();
| |
| − | | |
| − | ctx.strokeStyle = 'red';
| |
| − | | |
| − | if (menu.value == 'first'){
| |
| − | for (var i = a; i < b - dt/2; i += dt){
| |
| − | if(f(i) >= 0){
| |
| − | ctx.strokeRect((i - dx) * scalex, (-f(i) + dy) * scaley, dt * scalex, Math.abs(f(i)) * scaley);
| |
| − | }
| |
| − | else{
| |
| − | ctx.strokeRect((i - dx) * scalex, (dy) * scaley, dt * scalex, Math.abs(f(i)) * scaley);
| |
| − | }
| |
| − | }
| |
| − | }
| |
| − | | |
| − | if (menu.value == 'second'){
| |
| − | for (var i = a + dt; i < b + dt/2; i += dt){
| |
| − | if(f(i) >= 0){
| |
| − | ctx.strokeRect((i - dx) * scalex, (-f(i) + dy) * scaley, dt * scalex, Math.abs(f(i)) * scaley);
| |
| − | }
| |
| − | else{
| |
| − | ctx.strokeRect((i - dx) * scalex, (dy) * scaley, dt * scalex, Math.abs(f(i)) * scaley);
| |
| − | }
| |
| − | }
| |
| − | }
| |
| − | | |
| − | if (menu.value == 'third'){
| |
| − | for (var i = a + dt/2; i < b + dt/4; i += dt){
| |
| − | if(f(i) >= 0){
| |
| − | ctx.strokeRect((i - dt/2 - dx) * scalex, (-f(i) + dy) * scaley, dt * scalex, Math.abs(f(i)) * scaley);
| |
| − | }
| |
| − | else{
| |
| − | ctx.strokeRect((i - dt/2 - dx) * scalex, (dy) * scaley, dt * scalex, Math.abs(f(i)) * scaley);
| |
| − | }
| |
| − | }
| |
| − | }
| |
| − | | |
| − | }
| |
| − | | |
| − | knopka.onclick = function(){
| |
| − | | |
| − | | |
| − | if (flag){
| |
| − | location.reload();
| |
| − | }
| |
| − | | |
| − | flag = true;
| |
| − | knopka.value = 'Очистить';
| |
| − | input();
| |
| − | calculation();
| |
| − | draw();
| |
| − | result1.innerHTML = Math.round(result * 100)/100;
| |
| − | | |
| − | }
| |
| − | }
| |
| − | | |
| − | | |
| − | </syntaxhighlight>
| |
| − | | |
| − | </div>
| |
