Численные методы интегрирования — различия между версиями

  1 //Метод Монте-Карло
  2 
  3 window.addEventListener("load", program_code, false);
  4 function program_code() {
  5 
  6 	var ctx = canvas_example.getContext("2d");
  7 	var w = canvas_example.width;
  8 	var h = canvas_example.height;
  9 
 10 	ctx.translate(w/2, h/2);
 11 
 12 	var x = [];
 13 	var y = [];
 14 	var min = 1000;
 15 	var max = -1000;
 16 	var n = 0;
 17 	var points;
 18 	var cur_points;
 19 	var ok = 0;
 20 	var a;
 21 	var b ;
 22 	var scalex, scaley;
 23 	var dx;
 24 	var dy;
 25 	var func;
 26 	var time = 5000;
 27 	var dt;
 28 	var flag = false;
 29 
 30 
 31 	var result;
 32 
 33 
 34 
 35 	//функция
 36 	function f(x){
 37 		return (eval(func));
 38 	}
 39 
 40 	function search(){
 41 
 42 		func = document.getElementById("fun").value;
 43 
 44 		for (var i = a; i < b; i+=0.001){
 45 
 46 			//максимум
 47 			if (f(i) > max){
 48 				max = f(i);
 49 			}
 50 
 51 			//минимум
 52 			if (f(i) < min){
 53 				min = f(i);
 54 			}
 55 		}
 56 
 57 		//масштаб
 58     scaley = 100/(Math.abs(max) + Math.abs(min));
 59 
 60 		if (Math.abs(b) >= Math.abs(a)){
 61 			scalex = 250/b * 0.9;
 62 		}
 63 
 64 		if (Math.abs(b) < Math.abs(a)){
 65 			scalex = 250/Math.abs(a) * 0.9;
 66 		}
 67 
 68     //сдвиг
 69 		dx = (b + a)/2;
 70 		dy = (max + min)/2;
 71 
 72 		//точки
 73 		//points = 100;
 74 	}
 75 
 76 	function calculation(){
 77 
 78 		cur_points++;
 79 
 80 		//положительная функция
 81 		if (min * max >= 0 && min >= 0 && n < points){
 82 			x[n] = Math.random() * (b - a) + a;
 83 			y[n] = Math.random() * (max - 0) + 0;
 84 
 85 			if (y[n] < f(x[n])){
 86 				ok++;
 87 			}
 88 
 89 
 90 			result = (ok / cur_points) * (b - a) * max;
 91 			n++;
 92 
 93 		}
 94 
 95 		//отрицательная функция
 96 		if (min * max >= 0 && max <= 0 && n < points){
 97 			x[n] = Math.random() * (b - a) + a;
 98 			y[n] = Math.random() * (min - 0) + 0;
 99 
100 			if (y[n] > f(x[n])){
101 				ok++;
102 			}
103 
104 			result = -(ok/cur_points) * (b - a) * (-min);
105  			n++;
106 		}
107 
108 		//знакопеременные функции
109 		if (min * max < 0 && n < points){
110 
111 			x[n] = Math.random() * (b - a) + a;
112 			y[n] = Math.random() * (max - min) + min;
113 
114 
115 			if (y[n] > 0 && f(x[n]) > 0 && y[n] < f(x[n])){
116 				ok++;
117 			}
118 
119 			if (y[n] < 0 && f(x[n]) < 0 && y[n] > f(x[n])){
120 				ok--;
121 			}
122 
123 			result = (ok/cur_points) * (b - a) * (max - min);
124 			n++;
125 		}
126 	}
127 
128 	function draw(){
129 		//оси
130 		ctx.beginPath();
131 		ctx.moveTo(0 - dx * scalex, -h/2);
132 		ctx.lineTo(0 - dx * scalex, h/2);
133 		ctx.moveTo(w/2 , dy * scaley);
134 		ctx.lineTo(-w/2 , dy * scaley);
135 		ctx.stroke();
136 
137 		ctx.font = '10px Arial';
138 		ctx.strokeText('1', (1 - dx) * scalex, (-0.1 + dy) * scaley);
139 		ctx.strokeText('1', (0.1 -dx) * scalex, (-1 + dy) * scaley);
140 
141 
142 		//кривая
143 		ctx.beginPath();
144 		for (var i = a; i < b; i+=0.01){
145 			ctx.moveTo((i - dx) * scalex, (-f(i) + dy) * scaley);
146 			ctx.lineTo((i+0.01 - dx) * scalex, (-f(i+0.01) + dy) * scaley);
147 		}
148 
149 		ctx.stroke();
150 
151 
152 		//точки
153 		ctx.fillStyle = 'red';
154 		ctx.beginPath();
155 		ctx.arc((x[n-1] - dx) * scalex, (-y[n-1] + dy) * scaley, 1, 0, 2 * Math.PI);
156 		ctx.fill();
157 
158 	}
159 
160 	function control(){
161 		calculation();
162 		draw();
163 		result1.innerHTML = Math.round(result * 100)/100;
164 	}
165 
166 	knopka.onclick = function(){
167 
168 		if (flag){
169 			location.reload();
170 		}
171 
172 		flag = true;
173 		knopka.value = 'Очистить';
174 		cur_points = 0;
175 		points = parseFloat(document.getElementById("qual").value);
176 		dt = time/points;
177 		console.log(dt)
178 		a = parseFloat(document.getElementById("a1").value);
179 		b = parseFloat(document.getElementById("b1").value);
180 		search();
181 		var name = setInterval(control, dt);
182 	}
183 
184 
185 	if (n == points){
186 		clearInterval(name);
187 		console.log('a');
188 	}
189 }
190 
191 //Метод трапеций
192 window.addEventListener("load", program_code, false);
193 function program_code() {
194 
195   var ctx = canvas_example.getContext("2d");
196 	var w = canvas_example.width;
197 	var h = canvas_example.height;
198 
199   var flag = false;
200   var a;
201   var b;
202   var func;
203   var max = -100000;
204   var min = 100000;
205   var scale, scale1, scale2;
206   var x = [];
207   var y = [];
208   var result = 0;
209 
210 	ctx.translate(w/2, h/2);
211 
212   //функция
213   function f(x){
214     return (eval(func));
215   }
216 
217   function input(){
218 
219     a = parseFloat(document.getElementById("a1").value);
220 		b = parseFloat(document.getElementById("b1").value);
221     func = document.getElementById("fun").value;
222     number = parseFloat(document.getElementById('qual').value);
223 
224     //минимум и максимум
225     for (var i = a; i < b; i+=0.001){
226 
227 			//максимум
228 			if (f(i) > max){
229 				max = f(i);
230 			}
231 
232 			//минимум
233 			if (f(i) < min){
234 				min = f(i);
235 			}
236 		}
237 
238     //масштаб
239     scaley = 100/(Math.abs(max) + Math.abs(min));
240 
241     if (Math.abs(b) >= Math.abs(a)){
242       scalex = 250/b * 0.9;
243     }
244 
245     if (Math.abs(b) < Math.abs(a)){
246       scalex = 250/Math.abs(a) * 0.9;
247     }
248 
249     //сдвиг
250     dx = (b + a)/2;
251     dy = (max + min)/2;
252     dt = (b - a)/number;
253 
254     //разбиение
255     for (var i = a; i < b + 1/2 * dt; i += dt){
256       x.push(i);
257       y.push(f(i));
258     }
259   }
260 
261   function calculation(){
262     for (var i = 0; i < number; i++){
263 
264       if (f(x[i]) >= 0 && f(x[i+1]) >= 0){
265         result += (x[i + 1] - x[i]) * (Math.abs(y[i]) + Math.abs(y[i + 1])) * 0.5;
266       }
267 
268       if (f(x[i]) < 0 && f(x[i+1]) < 0){
269         result -= (x[i + 1] - x[i]) * (Math.abs(y[i]) + Math.abs(y[i + 1])) * 0.5;
270       }
271 
272       else{
273         result += 0;
274       }
275 
276     }
277   }
278 
279   function draw(){
280 
281     //оси
282 		ctx.beginPath();
283 		ctx.moveTo(0 - dx * scalex, -h/2);
284 		ctx.lineTo(0 - dx * scalex, h/2);
285 		ctx.moveTo(w/2 , 0 + dy * scaley);
286 		ctx.lineTo(-w/2 , 0 + dy * scaley);
287 		ctx.stroke();
288 
289     ctx.font = '10px Arial';
290 		ctx.strokeText('1', (1 - dx) * scalex, (-0.1 + dy) * scaley);
291 		ctx.strokeText('1', (0.1 -dx) * scalex, (-1 + dy) * scaley);
292 
293     //кривая
294     ctx.beginPath();
295     for (var i = a; i < b; i+=0.01){
296       ctx.moveTo((i - dx) * scalex, (-f(i) + dy) * scaley);
297       ctx.lineTo((i + 0.01 - dx) * scalex, (-f(i + 0.01) + dy) * scaley);
298     }
299     ctx.stroke();
300 
301 
302     ctx.strokeStyle = 'red';
303 
304     //разбиение
305     ctx.beginPath();
306     for (var i = 0; i < number + 1; i++){
307       ctx.moveTo((x[i] - dx) * scalex, dy * scaley);
308       ctx.lineTo((x[i] - dx) * scalex, (-y[i] + dy) * scaley)
309     }
310     ctx.stroke();
311 
312     ctx.beginPath();
313     for(var i = 0; i < number; i++){
314       ctx.moveTo((x[i] - dx) * scalex, (-y[i] + dy) * scaley);
315       ctx.lineTo((x[i+1] - dx) * scalex, (-y[i+1] + dy) * scaley);
316     }
317     ctx.stroke();
318 
319   }
320 
321 
322   knopka.onclick = function(){
323 
324     if (flag){
325       location.reload();
326     }
327 
328     flag = true;
329     knopka.value = 'Очистить';
330     input();
331     calculation();
332     result1.innerHTML = Math.round(result * 100)/100;
333     draw();
334   }
335 }
336 
337 
338 //Метод прямоугольников
339 window.addEventListener("load", program_code, false);
340 function program_code() {
341 
342   var ctx = canvas_example.getContext("2d");
343 	var w = canvas_example.width;
344 	var h = canvas_example.height;
345 
346   var flag = false;
347   var a;
348   var b;
349   var func;
350   var max = -100000;
351   var min = 100000;
352   var scale, scale1, scale2;
353   var x = [];
354   var y = [];
355   var result = 0;
356   var dt;
357   var dx = 0;
358   var dy = 0;
359 
360   ctx.translate(w/2, h/2);
361 
362   //функция
363   function f(x){
364     return (eval(func));
365   }
366 
367   function input(){
368 
369     a = parseFloat(document.getElementById("a1").value);
370 		b = parseFloat(document.getElementById("b1").value);
371     func = document.getElementById("fun").value;
372     var number = parseFloat(document.getElementById('qual').value);
373     dx = (b - a)/number;
374 
375     //минимум и максимум
376     for (var i = a; i < b; i+=0.001){
377 
378 			//максимум
379 			if (f(i) > max){
380 				max = f(i);
381 			}
382 
383 			//минимум
384 			if (f(i) < min){
385 				min = f(i);
386 			}
387 		}
388 
389     //масштаб
390     scaley = 100/(Math.abs(max) + Math.abs(min));
391 
392 		if (Math.abs(b) >= Math.abs(a)){
393 			scalex = 250/b * 0.9;
394 		}
395 
396 		if (Math.abs(b) < Math.abs(a)){
397 			scalex = 250/Math.abs(a) * 0.9;
398 		}
399 
400     //сдвиг
401 		dx = (b + a)/2;
402 		dy = (max + min)/2;
403     dt = (b - a)/number;
404 
405   }
406 
407   function calculation(){
408 
409     if (menu.value == 'first'){
410       console.log('a');
411       for (var i = a; i < b; i += dt){
412 
413         if (f(i) >= 0 & f(i + dt) >= 0){
414           result += Math.abs(f(i))*dt;
415         }
416 
417         if (f(i) < 0 & f(i + dt) < 0){
418           result -= Math.abs(f(i))*dt;
419         }
420 
421         else{
422           result += 0;
423         }
424 
425       }
426     }
427 
428     if (menu.value == 'second'){
429       for (var i = a + dt; i < b; i += dt){
430         if (f(i) >= 0 & f(i + dt) >= 0){
431           result += Math.abs(f(i))*dt;
432         }
433 
434         if (f(i) < 0 & f(i + dt) < 0){
435           result -= Math.abs(f(i))*dt;
436         }
437 
438         else{
439           result += 0;
440         }
441       }
442     }
443 
444     if (menu.value == 'third'){
445       for (var i = a + dt/2 ; i < b; i += dt){
446         if (f(i) >= 0 & f(i + dt) >= 0){
447           result += Math.abs(f(i))*dt;
448         }
449 
450         if (f(i) < 0 & f(i + dt) < 0){
451           result -= Math.abs(f(i))*dt;
452         }
453 
454         else{
455           result += 0;
456         }
457       }
458     }
459 
460   }
461 
462   function draw(){
463 
464     //оси
465 		ctx.beginPath();
466 		ctx.moveTo(0 - dx * scalex, -h/2);
467 		ctx.lineTo(0 - dx * scalex, h/2);
468 		ctx.moveTo(w/2 , 0 + dy * scaley);
469 		ctx.lineTo(-w/2 , 0 + dy * scaley);
470 		ctx.stroke();
471 
472     ctx.font = '10px Arial';
473 		ctx.strokeText('1', (1 - dx) * scalex, (-0.1 + dy) * scaley);
474 		ctx.strokeText('1', (0.1 -dx) * scalex, (-1 + dy) * scaley);
475 
476     //кривая
477     ctx.beginPath();
478     for (var i = a; i < b; i+=0.01){
479       ctx.moveTo((i - dx) * scalex, (-f(i) + dy) * scaley);
480       ctx.lineTo((i + 0.01 - dx) * scalex, (-f(i + 0.01) + dy) * scaley);
481     }
482     ctx.stroke();
483 
484     ctx.strokeStyle = 'red';
485 
486     if (menu.value == 'first'){
487       for (var i = a; i < b - dt/2; i += dt){
488         if(f(i) >= 0){
489           ctx.strokeRect((i - dx) * scalex, (-f(i) + dy) * scaley, dt * scalex, Math.abs(f(i)) * scaley);
490         }
491         else{
492           ctx.strokeRect((i - dx) * scalex, (dy) * scaley, dt * scalex, Math.abs(f(i)) * scaley);
493         }
494       }
495     }
496 
497     if (menu.value == 'second'){
498       for (var i = a + dt; i < b + dt/2; i += dt){
499         if(f(i) >= 0){
500           ctx.strokeRect((i - dx) * scalex, (-f(i) + dy) * scaley, dt * scalex, Math.abs(f(i)) * scaley);
501         }
502         else{
503           ctx.strokeRect((i - dx) * scalex, (dy) * scaley, dt * scalex, Math.abs(f(i)) * scaley);
504         }
505       }
506     }
507 
508     if (menu.value == 'third'){
509       for (var i = a + dt/2; i < b + dt/4; i += dt){
510         if(f(i) >= 0){
511           ctx.strokeRect((i - dt/2 - dx) * scalex, (-f(i) + dy) * scaley, dt * scalex, Math.abs(f(i)) * scaley);
512         }
513         else{
514           ctx.strokeRect((i - dt/2 - dx) * scalex, (dy) * scaley, dt * scalex, Math.abs(f(i)) * scaley);
515         }
516       }
517     }
518 
519   }
520 
521   knopka.onclick = function(){
522 
523 
524     if (flag){
525       location.reload();
526     }
527 
528     flag = true;
529     knopka.value = 'Очистить';
530     input();
531     calculation();
532     draw();
533     result1.innerHTML = Math.round(result * 100)/100;
534 
535   }
536 }