Курсовик

/*
  Событийные функции
 */

//Данные по умолчанию
$(document).on('click', '#default', function(){
  $('#HDE').val('Math.cos(y) / (a + x) + k * y * y')
  $('#HDE_to').val(1)
  $('#HDE_step').val(0.1)
  $('#HDE_y0').val(0)
  $('#HDE_x0').val(0)
  $('#HDE_a').val('')
  $('#HDE_k').val('')
  $('#HDE_eps').val(0.001)
  $('#HDE_opt').prop('checked', 'checked')

  $('#opt').val('-Math.exp(-t)*Math.log(t)')
  $('#opt_from').val(0)
  $('#opt_to').val(2)
  $('#opt_eps').val(0.001)

  $('#int_point').val(6)
})

//ОДУ
$(document).on('click', '#HDE_getAnswer', function(){
  if ($('#HDE_opt').prop('checked')) {
    koef = dichotomy(
      parseFloat($('#opt_from').val()), 
      parseFloat($('#opt_to').val()),
      parseFloat($('#opt_eps').val()), 
      function(t) {
        return eval($('#opt').val())
      }
    )
    $('#HDE_a').val(koef.a)
    $('#HDE_k').val(koef.k)

    $('#opt_answer').html('<b>Точка минимума: ' + koef.a + ', ' + koef.k + '</b>')
  }

  result = autoStep(
    parseFloat($('#HDE_x0').val()),
    parseFloat($('#HDE_y0').val()),
    parseFloat($('#HDE_step').val()),
    parseFloat($('#HDE_to').val()),
    parseFloat($('#HDE_eps').val()),
    function (x, y) {
      a = parseFloat($('#HDE_a').val())
      k = parseFloat($('#HDE_k').val())
      return eval($('#HDE').val())
    }
  )

  if ($('#int_point').val()) {
    interp = []
    for (i = 0, x = parseFloat($('#HDE_x0').val()); x <= parseFloat($('#HDE_to').val()); x += parseFloat($('#HDE_step').val()), i++) {
      interp[i] = [x, LangrangianMethod(result, parseFloat($('#int_point').val()), x)]
    }
  }

  h = parseFloat($('#HDE_step').val())
  if (!isInt(Math.abs(lg(h)))) {
    h = Math.abs(Math.ceil(h))
  }
  outputArr(
    result, 
    ['x', 'y', 'h', 'm'], 
    [h, parseFloat($('#HDE_eps').val()), 5, 0], 
    '#autoStep'
  )

  plotData = result
  for (i = 0; i < plotData.length; i++) {
    delete plotData[i][2]
    delete plotData[i][3]
  }
  $.plot($('#HDE_graph'), [plotData])

  e = parseFloat($('#opt_eps').val()) / 100
  outputArr(
    koef.out, 
    ['x1', 'x2', 'f(x1)', 'f(x2)', 'a', 'b'], 
    [e, e, e/100000, e/100000, e/100, e/100], 
    '#Dichotomy'
  )

  plotData = []
  for (t = parseFloat($('#opt_from').val()); t <= parseFloat($('#opt_to').val()); t += 0.05) {
    plotData.push([t, eval($('#opt').val())])
  }
  $.plot($('#opt_graph'), [plotData])


  outputArr(
    interp,
    ['x', 'y'],
    [h, parseFloat($('#HDE_eps').val())],
    '#Langrang'
  )

  $.plot($('#int_graph'), [interp])
})

//Тестовая оптимизация
$(document).on('click', '#opt_getAnswer', function(){
  koef = dichotomy(
    parseFloat($('#opt_from').val()), 
    parseFloat($('#opt_to').val()),
    parseFloat($('#opt_eps').val()), 
    function(t) {
      return eval($('#opt').val())
    }
  )
  e = parseFloat($('#opt_eps').val()) / 100
  outputArr(
    koef.out, 
    ['x1', 'x2', 'f(x1)', 'f(x2)', 'a', 'b'], 
    [e, e, e/100000, e/100000, e/100, e/100], 
    '#Dichotomy'
  )

  plotData = []
  for (t = parseFloat($('#opt_from').val()); t <= parseFloat($('#opt_to').val()); t += 0.05) {
    plotData.push([t, eval($('#opt').val())])
  }
  $.plot($('#opt_graph'), [plotData])

  $('#opt_answer').text('Точка минимума: ' + koef.a + ', ' + koef.k)
})


/*
  Мат. методы
 */

//Optimization
function dichotomy(a, b, eps, f) {
  d = eps / 10
  out = []
  i = 0
  do {
    x1 = (a + b - d) / 2
    x2 = (a + b + d) / 2
    out[i] = [x1, x2, f(x1), f(x2), a, b]
    i++
    if ( f(x1) > f(x2) ) 
      a = x1
    else
      b = x2
  } while (b - a >= eps)
  x = (a + b) / 2
  y = f(x)
  return {
    "a": x,
    "k": y,
    "out": out
  }
}

//Interpolation
function LangrangianMethod(diff, point, p) {
  centralPoint = point == 0 ? Math.floor(diff.length / 2) : point - 1
  var X = [diff[0][0], diff[centralPoint][0], diff[diff.length - 1][0]]
  var Y = [diff[0][1], diff[centralPoint][1], diff[diff.length - 1][1]]
  L = 0
  var i, j
  for (i = 0; i <= 2; i++) {
    L1 = 1
    for (j = 0; j <= 2; j++) {
      if (i != j)
        L1 = ((p - X[j]) / (X[i] - X[j])) * L1
    }
    L += L1 * Y[i]
  }
  return L
}

//HDE
function r(x0, y0, h, m, f) {
  u = []
  y = []
  y[0] = y0
  var i
  for (i = 0; i < m; i++) {
    u[0] = f(x0, y[i])
    u[1] = f(x0 + h / 2, y[i] + h * u[0] / 2)
    u[2] = f(x0 + h / 2, y[i] + h * u[1] / 2)
    u[3] = f(x0 + h, y[i] + h * u[2])
    y[i + 1] = y[i] + (h / 6) * (u[0] + 2 * u[1] + 2 * u[2] + u[3])
    x0 += h
  }
  return y[m]
}

function autoStep(x0, y0, h0, b, Eps, fun) {
  output = []
  var h
  output[0] = [x0, y0, h0, 0]
  n = Math.ceil((b - x0) / h0) + 1
  for (i = 1; i < n; i++) {
    h = h0
    m = 1
    y = r(x0, y0, h, m, fun)
    do {
      y1 = y
      h /= 2
      x = x0
      y = y0
      m = 2 * m
      y = r(x, y, h, m, fun)
    } while (Math.abs(y - y1) >= Eps)
    x0 += h0
    y0 = y
    output[i] = [x0, y0, h, m]
  }
  return output
}


function outputArr(arr, title, eps, selector) {
  for (i = 0; i < eps.length; i++) 
    eps[i] = isInt(eps[i]) ? eps[i] : Math.abs(Math.log(parseFloat(eps[i])) / Math.log(10)).toFixed(0)

  str = '<tr>'
  for (i = 0; i < title.length; i++)
    str += '<td>' + title[i] + '</td>'
  str += '</tr>'

  for (i = 0; i < arr.length; i++) {
    str += '<tr>'
    for (j = 0; j < arr[0].length; j++)
      str += '<td>' + arr[i][j].toFixed(eps[j]) + '</td>'
    str += '</tr>'
  }
  $(selector).html(str)
}

function isInt(number) {
  return Math.floor(number) == Math.ceil(number) || number + 0.000001 > Math.ceil(number)
}

function lg(number) {
  return Math.log(parseFloat(number)) / Math.log(10)
}