private static Point CoordinateDescent(FunctionWrapper function, Point x0, double h0, double epsilon)
{
var h = new Vector(new double[x0.Length]);
for (var i = 0; i < h.Length; i++)
{
h[i] = h0;
}
var xInt = x0.Clone();
Point xExt;
do
{
xExt = xInt.Clone();
for (var i = 0; i < xInt.Length; i++)
{
Program.CountThisLoop();
var x = xInt.Clone();
var y1 = x.Clone();
y1[i] += 3 * epsilon;
var y2 = x.Clone();
y2[i] -= 3 * epsilon;
var f1 = function.Eval(y1);
var f2 = function.Eval(y2);
var z = Math.Sign(f2 - f1);
h[i] = function.FindHForCoordinateDescent(xInt.Clone(), z, i, h[i], epsilon);
xInt[i] = x[i] + h[i] * z;
}
} while ((xInt - xExt).Normalize() >= epsilon);
return(xInt);
}
private void методПокоординатногоСпускуМетодомЗейделяГаусаToolStripMenuItem_Click(object sender, EventArgs e)
{
FunctionWrapper.Function firstFunction =
x => 40 * Math.Pow(x[0], 2) + 20 * x[0] * x[1] + 30 * Math.Pow(x[1], 2) - 10 * x[0] + x[1];
var firstCounter = new FunctionCallsCounter(firstFunction);
var x0ForFirstFunction = new Point(0, 2);
var firstFunctionWrapper = new FunctionWrapper(firstCounter.GetFunction(),
x => new Vector(80 * x[0] + 20 * x[1] - 10, 20 * x[0] + 60 * x[1] + 1));
var epsilon = Convert.ToDouble(comboBox1.Text);
var res = CoordinateDescent(firstFunctionWrapper, x0ForFirstFunction, h0, epsilon);
textBox1.Text = res.ToString();
textBox2.Text = firstFunctionWrapper.Eval(res).ToString();
textBox3.Text = firstCounter.Count.ToString();
textBox4.Text = _loopCounter.ToString();
}
private void методНайшвидшогоСпускуToolStripMenuItem_Click_1(object sender, EventArgs e)
{
//функцiя Розенброка
FunctionWrapper.Function RozenbrocksFunction =
x => 100 * Math.Pow(x[1] - Math.Pow(x[0], 2), 2) + Math.Pow(1 - x[0], 2);
var rozenblocksCounter = new FunctionCallsCounter(RozenbrocksFunction);
var rozenblocksFunctionWrapper = new FunctionWrapper(rozenblocksCounter.GetFunction(),
x => new Vector(400 * Math.Pow(x[0], 3) - 400 * x[0] * x[1] + 2 * x[0] - 2,
200 * x[1] - 200 * Math.Pow(x[0], 2)));
var x0ForRozenboksFunction = new Point(0, 0);
var epsilon = Convert.ToDouble(comboBox1.Text);
rozenblocksCounter.Count = 0;
_loopCounter = 0;
var res = FastestDescent(rozenblocksFunctionWrapper, x0ForRozenboksFunction, h0, epsilon);
textBox1.Text = res.ToString();
textBox2.Text = rozenblocksFunctionWrapper.Eval(res).ToString();
textBox3.Text = rozenblocksCounter.Count.ToString();
textBox4.Text = _loopCounter.ToString();
}
private void узагальненийМетодНьютонаДляПошукуДругоїФункціїToolStripMenuItem_Click(object sender, EventArgs e)
{
FunctionWrapper.Function secondFunction =
x =>
Math.Pow(x[0], 4) + 3 * Math.Pow(x[1], 4) +
Math.Sqrt(2 * Math.Pow(x[0], 2) + Math.Pow(x[1], 2) + 1) -
4 * x[0] + 6 * x[1];
var secondCounter = new FunctionCallsCounter(secondFunction);
var secondFunctionWrapper = new FunctionWrapper(secondCounter.GetFunction(),
x =>
new Vector(4 * Math.Pow(x[0], 3) + 2 * x[0] / Math.Sqrt(2 * Math.Pow(x[0], 2) + x[1] + 1) - 4,
x[1] / Math.Sqrt(2 * Math.Pow(x[0], 2) + Math.Pow(x[1], 2) + 1) + 12 * Math.Pow(x[1], 3) + 6),
x => new SquareMatrix(new double[2][]
{
new double[2]
{
2 * (6 * Math.Pow(x[0], 2) * Math.Pow(2 * Math.Pow(x[0], 2) + x[1] + 1, 1.5) + x[1] + 1) /
Math.Pow(2 * Math.Pow(x[0], 2) + x[1] + 1, 1.5),
-(x[0] / Math.Pow(Math.Pow(x[0], 2) + x[1] + 1, 1.5))
},
new double[2]
{
-(2 * x[0] * x[1] / Math.Pow(2 * Math.Pow(x[0], 2) + Math.Pow(x[1], 2) + 1, 1.5)),
(2 * Math.Pow(x[0], 2) + 1) / Math.Pow(2 * Math.Pow(x[0], 2) + Math.Pow(x[1], 2) + 1, 1.5) +
36 * Math.Pow(x[1], 2)
}
}));
var x0ForSecondFunction = new Point(1, 1);
secondCounter.Count = 0;
_loopCounter = 0;
var epsilon = Convert.ToDouble(comboBox1.Text);
var res = GeneralizedNewtonMethod(secondFunctionWrapper, x0ForSecondFunction, h0, epsilon);
textBox1.Text = res.ToString();
textBox2.Text = secondFunctionWrapper.Eval(res).ToString();
textBox3.Text = secondCounter.Count.ToString();
textBox4.Text = _loopCounter.ToString();
}
