public Fraction determinant()
{
QuadMatr m = new QuadMatr(this.NCol);
Array.Copy(this.A, m.A, this.A.Length);
int n = this.NCol;
Fraction fr1, fr2;
Fraction d = new Fraction(1, 1);
double sumRow = 0, sumCol = 0;
for (int i = 0; i < n; i++)
{
for (int j = 0; j < n; j++)
{
if (m.A[i, j] == 0)
{
sumRow = 0;
sumCol = 0;
for (int p = 0; p < n; p++)
{
sumCol += Math.Abs(m.A[i, p].ToDouble());
sumRow += Math.Abs(m.A[p, j].ToDouble());
}
if (sumCol == 0 || sumRow == 0)
{
return(new Fraction());
}
}
}
}
for (int shag = 0; shag < n - 1; shag++)
{
for (int i = shag; i < n; i++)
{
if (m.A[i, shag] != 0)
{
if (m.A[shag, shag] == 0)
{
this.swapRows(shag, i);
}
else
{
for (int j = 0; j < n; j++)
{
if (i != j && m.A[j, shag] != 0 && j >= shag)
{
if (j < i)
{
fr1 = m.A[i, shag];
fr2 = m.A[j, shag];
m.multRows(j, i, fr1 / fr2);
}
else
{
fr1 = m.A[j, shag];
fr2 = m.A[i, shag];
m.multRows(i, j, fr1 / fr2);
}
}
}
}
}
}
}
for (int i = 0; i < n; i++)
{
d *= m.A[i, i];
}
return(d);
}
public QuadMatr TransformMatr(int type)
{
if (this.determinant() == 0)
{
throw new Exception("Определитель матрицы равен нулю, обратная матрица не существует!");
}
else
{
Fraction m = new Fraction();
int n = this.NCol;
QuadMatr e = new QuadMatr(n);
QuadMatr x = new QuadMatr(n);
QuadMatr y = new QuadMatr(n);
QuadMatr b = new QuadMatr(n);
QuadMatr c = new QuadMatr(n);
e.setEMatr();
for (int j = 0; j < n; j++)
{
for (int i = j; i < n; i++)
{
for (int g = 0; g <= j - 1; g++)
{
m += b.A[i, g] * c.A[g, j];
}
b.A[i, j] = this.A[i, j] - m;
m.FractTxt = "0";
for (int g = 0; g <= j - 1; g++)
{
m += b.A[j, g] * c.A[g, i];
}
c.A[j, i] = (this.A[j, i] - m) / b.A[j, j];
m.FractTxt = "0";
}
}
for (int i = 0; i < n; i++)
{
for (int j = 0; j < n; j++)
{
for (int g = 0; g <= j - 1; g++)
{
m += b.A[j, g] * y.A[g, i];
}
y.A[j, i] = (e.A[j, i] - m) / b.A[j, j];
m.FractTxt = "0";
}
}
for (int i = 0; i < n; i++)
{
for (int j = n - 1; j >= 0; j--)
{
for (int g = 0; g < n - j - 1; g++)
{
m += c.A[j, n - g - 1] * x.A[n - g - 1, i];
}
x.A[j, i] = y.A[j, i] - m;
m.FractTxt = "0";
}
}
switch (type)
{
case 1:
return(x);
case 2:
return(b);
default:
return(c);
}
}
}
public QuadMatr getFrobeniusMatr()
{
int n = this.NCol;
QuadMatr mFr = new QuadMatr(n);
QuadMatr e = new QuadMatr(n);
QuadMatr m1 = new QuadMatr(n);
Array.Copy(this.A, mFr.A, this.A.Length);
for (int g = 0; g < n - 1; g++)
{
Fraction d = new Fraction();
for (int i = 0; i <= n - g - 2; i++)
{
d += mFr.A[n - g - 1, i];
}
if (d == 0)
{
QuadMatr b = new QuadMatr(n - g - 1);
for (int i = 0; i < n - g - 1; i++)
{
for (int j = 0; j < n - g - 1; j++)
{
b.A[i, j] = mFr.A[i, j];
}
}
b = b.getFrobeniusMatr();
for (int i = 0; i < n - g - 1; i++)
{
for (int j = 0; j < n - g - 1; j++)
{
mFr.A[i, j] = b.A[i, j];
mFr.A[i, j].Color = Color.FromRgb(127, 251, 189);
}
}
for (int i = n - g - 1; i < n; i++)
{
for (int j = n - g - 1; j < n; j++)
{
mFr.A[i, j].Color = Color.FromRgb(127, 251, 189);
}
}
return(mFr);
}
else if (mFr.A[n - g - 1, n - g - 2] == 0)
{
mFr.swapCols(n - g - 1, n - g - 2);
mFr.swapRows(n - g - 1, n - g - 2);
}
e.setEMatr();
for (int i = 0; i < n; i++)
{
e.A[n - g - 2, i].FractTxt = mFr.A[n - g - 1, i].FractTxt;
}
if (e.determinant() != 0)
{
mFr = (e * mFr * e.TransformMatr(1));
}
else
{
mFr = (e * mFr * e.TransformMatr(1));
}
}
return(mFr);
}
public Fraction GetPolyNewtonDiff2Val(Fraction fr, int poryadok, int row = 1)
{
if (poryadok >= this.NRow - row - 1)
{
poryadok = this.NRow - row - 1;
if (poryadok >= 5)
{
poryadok = 5;
}
}
Fraction rez = new Fraction();
if (isRavnom())
{
Fraction m = new Fraction();
Fraction q = new Fraction();
Fraction k = new Fraction();
Fraction l1 = new Fraction();
Fraction l2 = new Fraction();
Fraction l3 = new Fraction();
Fraction l4 = new Fraction();
Fraction l5 = new Fraction();
Fraction h = new Fraction();
m = this.matr.A[1, 0].CopyFr;
k = this.matr.A[2, 0].CopyFr;
h = k - m;
k = this.matr.A[row, 0].CopyFr;
q = (fr - k) / h;
switch (poryadok)
{
case 1:
l1 = this.matr.A[row, 2].CopyFr;
rez = l1;
break;
case 2:
l1 = this.matr.A[row, 2].CopyFr;
l2 = this.matr.A[row, 3].CopyFr;
rez = h.Invert() * (l1 + l2 * (q * 2 - 1) / MyFuncs.factorial(2));
break;
case 3:
l1 = this.matr.A[row, 2].CopyFr;
l2 = this.matr.A[row, 3].CopyFr;
l3 = this.matr.A[row, 4].CopyFr;
rez = h.Invert().Power(2) * (l2 + l3 * (q - 1));
break;
case 4:
l1 = this.matr.A[row, 2].CopyFr;
l2 = this.matr.A[row, 3].CopyFr;
l3 = this.matr.A[row, 4].CopyFr;
l4 = this.matr.A[row, 5].CopyFr;
rez = h.Invert().Power(2) * (l2 + l3 * (q - 1) + l4 * (6 * q.Power(2) - 18 * q + 11) / 12);
break;
case 5:
l1 = this.matr.A[row, 2].CopyFr;
l2 = this.matr.A[row, 3].CopyFr;
l3 = this.matr.A[row, 4].CopyFr;
l4 = this.matr.A[row, 5].CopyFr;
l5 = this.matr.A[row, 6].CopyFr;
rez = h.Invert().Power(2) * (l2 + l3 * (q - 1) + l4 * (6 * q.Power(2) - 18 * q + 11) / 12 + l5 * (2 * q.Power(3) - 12 * q.Power(2) + 21 * q - 10) / 12);
break;
default:
MessageBox.Show("Максимальный поддерживаемый порядок = 5!");
break;
}
}
return(rez);
}
public Fraction GetPolyNewtonDiff1Val(Fraction fr, int poryadok, int row = 1)
{
if (poryadok >= this.NRow - row - 1)
{
poryadok = this.NRow - row - 1;
if (poryadok >= 5)
{
poryadok = 5;
}
}
Fraction rez = new Fraction();
if (isRavnom())
{
Fraction q = new Fraction();
Fraction l1 = new Fraction();
Fraction l2 = new Fraction();
Fraction l3 = new Fraction();
Fraction l4 = new Fraction();
Fraction l5 = new Fraction();
Fraction h = new Fraction();
q = this.matr.A[1, 0].CopyFr;
h = this.matr.A[2, 0].CopyFr;
h -= q;
q = this.matr.A[row, 0].CopyFr;
q = (fr - q) / h;
switch (poryadok)
{
case 1:
l1 = this.matr.A[row, 2].CopyFr;
rez = h.Invert() * (l1);
break;
case 2:
l1 = this.matr.A[row, 2].CopyFr;
l2 = this.matr.A[row, 3].CopyFr;
rez = h.Invert() * (l1 + l2 * (2 * q - 1) / 2);
break;
case 3:
l1 = this.matr.A[row, 2].CopyFr;
l2 = this.matr.A[row, 3].CopyFr;
l3 = this.matr.A[row, 4].CopyFr;
rez = h.Invert() * (l1 + l2 * (2 * q - 1) / 2 + l3 * (3 * q.Power(2) - 6 * q + 2) / 6);
break;
case 4:
l1 = this.matr.A[row, 2].CopyFr;
l2 = this.matr.A[row, 3].CopyFr;
l3 = this.matr.A[row, 4].CopyFr;
l4 = this.matr.A[row, 5].CopyFr;
rez = h.Invert() * (l1 + l2 * (2 * q - 1) / 2 + l3 * (3 * q.Power(2) - 6 * q + 2) / 6 + l4 * (2 * q.Power(3) - 9 * q.Power(2) + 11 * q - 3) / 12);
break;
case 5:
l1 = this.matr.A[row, 2].CopyFr;
l2 = this.matr.A[row, 3].CopyFr;
l3 = this.matr.A[row, 4].CopyFr;
l4 = this.matr.A[row, 5].CopyFr;
l5 = this.matr.A[row, 6].CopyFr;
rez = h.Invert() * (l1 + l2 * (2 * q - 1) / 2 + l3 * (3 * q.Power(2) - 6 * q + 2) / 6 + l4 * (2 * q.Power(3) - 9 * q.Power(2) + 11 * q - 3) / 12 + l5 * (5 * q.Power(4) - 40 * q.Power(3) + 105 * q.Power(2) - 100 * q + 24) / 120);
break;
default:
MessageBox.Show("Максимальный поддерживаемый порядок = 5!");
break;
}
}
return(rez);
}
public void DrawIntegr(ref Grid gr, Fraction a, Fraction b, int res = 100)
{
int por = this.NCol - 2;
int row = 1;
Fraction xfrMin = new Fraction();
Fraction yfrMin = new Fraction();
Fraction xfrMax = new Fraction();
Fraction yfrMax = new Fraction();
//Fraction xfr0 = new Fraction((int)((gr.Width - 20) / 2), 1);
//Fraction yfr0 = new Fraction((int)((gr.Height - 20) / 2), 1);
xfrMin = this.matr.A[1, 0].CopyFr;
//yfrMin.FractTxt = this.txtBxs[1, 1].Text;
//double yMin = yfrMin.ToDouble();
Fraction h = new Fraction();
xfrMax = this.matr.A[this.NRow - 1, 0].CopyFr;
//double xMax = xfrMax.ToDouble();
yfrMax = this.matr.A[this.NRow - 1, 1].CopyFr;
yfrMin = this.matr.A[1, 1].CopyFr;
for (Fraction i = xfrMin; i <= xfrMax; i += (xfrMax - xfrMin) / 50)
{
if (GetPolyNewtonVal(i, por, row) >= yfrMax)
{
yfrMax = GetPolyNewtonVal(i, por, row);
}
}
for (Fraction i = xfrMin; i <= xfrMax; i += (xfrMax - xfrMin) / 50)
{
if (GetPolyNewtonVal(i, por, row) < yfrMin)
{
yfrMin = GetPolyNewtonVal(i, por, row);
}
}
CoordAxis axis = new CoordAxis(ref gr, xfrMin.ToDouble(), xfrMax.ToDouble(), yfrMin.ToDouble(), yfrMax.ToDouble(), 10);
//Fraction yMult = new Fraction((int)((gr.Height - 20) * 1000), 1000);
h = (b - a) / res;
PointCollection pc = new PointCollection();
for (Fraction i = a; i <= b; i += h)
{
//pc.Add(new System.Windows.Point((xfr0 + i*xMult).ToDouble(), (yfr0 - GetPolyNewtonVal(i, por, row)*yMult).ToDouble()));
pc.Add(axis.ConvertCoord(i.ToDouble(), GetPolyNewtonVal(i, por, row).ToDouble()));
}
//double wdt = gr.Width - 20;
//double hgt = gr.Height - 20;
PointCollection pgPt = new PointCollection();
pgPt.Add(axis.ConvertCoord(a.ToDouble(), 0));
foreach (Point pt in pc)
{
pgPt.Add(pt);
}
pgPt.Add(axis.ConvertCoord(b.ToDouble(), 0));
Polygon pg = new Polygon();
pg.Points = pgPt;
pg.Fill = Brushes.Pink;
gr.Children.Add(pg);
}
public void DrawPolynom(ref Grid gr, int por, Fraction x, int row = 1, int res = 100)
{
Fraction xfrMin = new Fraction();
Fraction yfrMin = new Fraction();
Fraction xfrMax = new Fraction();
Fraction yfrMax = new Fraction();
xfrMin = this.matr.A[1, 0].CopyFr;
yfrMin = this.matr.A[1, 1].CopyFr;
//double yMin = yfrMin.ToDouble();
Fraction h = new Fraction();
xfrMax = this.matr.A[this.NRow - 1, 0].CopyFr;
//double xMax = xfrMax.ToDouble();
yfrMax = this.matr.A[this.NRow - 1, 1].CopyFr;
for (Fraction i = xfrMin; i <= xfrMax; i += (xfrMax - xfrMin) / res)
{
if (GetPolyNewtonVal(i, por, row) >= yfrMax)
{
yfrMax = GetPolyNewtonVal(i, por, row);
}
}
for (Fraction i = xfrMin; i <= xfrMax; i += (xfrMax - xfrMin) / res)
{
if (GetPolyNewtonVal(i, por, row) < yfrMin)
{
yfrMin = GetPolyNewtonVal(i, por, row);
}
}
CoordAxis axis = new CoordAxis(ref gr, xfrMin.ToDouble(), xfrMax.ToDouble(), yfrMin.ToDouble(), yfrMax.ToDouble(), 10);
axis.DrawAxis();
//Fraction xMult = new Fraction((int)((gr.Width - 20)*1000), 1000);
//xMult /= xfrMax*2;
//Fraction yMult = new Fraction((int)((gr.Height - 20)*1000), 1000);
//yMult /= yfrMax*2;
h = (xfrMax - xfrMin) / res;
Polyline pl = new Polyline();
Ellipse el = new Ellipse();
el.HorizontalAlignment = HorizontalAlignment.Left;
el.VerticalAlignment = VerticalAlignment.Top;
el.Width = 8;
el.Height = 8;
Point valXY = axis.ConvertCoord(x.ToDouble(), (GetPolyNewtonVal(x, por, row).ToDouble()));
System.Windows.Thickness th = new System.Windows.Thickness(valXY.X - el.Width / 2, valXY.Y - el.Height / 2, 0, 0);
el.Margin = th;
el.Stroke = Brushes.Red;
el.Fill = Brushes.Red;
PointCollection pc = new PointCollection();
for (Fraction i = xfrMin; i <= xfrMax; i += h)
{
//pc.Add(new System.Windows.Point((xfr0 + i*xMult).ToDouble(), (yfr0 - GetPolyNewtonVal(i, por, row)*yMult).ToDouble()));
pc.Add(axis.ConvertCoord(i.ToDouble(), GetPolyNewtonVal(i, por, row).ToDouble()));
}
pl.Points = pc;
pl.Stroke = Brushes.Blue;
pl.StrokeThickness = 4;
double wdt = gr.Width - 20;
double hgt = gr.Height - 20;
Line xVal = new Line();
//xVal.X1 = (xfr0 + x * xMult).ToDouble();
xVal.X1 = axis.ConvertCoord(x.ToDouble(), GetPolyNewtonVal(x, por, row).ToDouble()).X;
xVal.Y1 = axis.ConvertCoord(x.ToDouble(), GetPolyNewtonVal(x, por, row).ToDouble()).Y;
xVal.X2 = xVal.X1;
xVal.Y2 = axis.crossAxis.Y;
xVal.Stroke = Brushes.Red;
xVal.StrokeDashArray = new DoubleCollection()
{
8, 4
};
Line yVal = new Line();
yVal.X1 = axis.ConvertCoord(x.ToDouble(), GetPolyNewtonVal(x, por, row).ToDouble()).X;
yVal.Y1 = axis.ConvertCoord(x.ToDouble(), GetPolyNewtonVal(x, por, row).ToDouble()).Y;
yVal.X2 = axis.crossAxis.X;
yVal.Y2 = yVal.Y1;
yVal.Stroke = Brushes.Red;
yVal.StrokeDashArray = new DoubleCollection()
{
8, 4
};
gr.Children.Add(pl);
gr.Children.Add(xVal);
gr.Children.Add(yVal);
TextBox valX = new TextBox();
valX.Text = "" + x.ToDouble();
valX.Width = 100;
valX.Height = 25;
valX.HorizontalAlignment = HorizontalAlignment.Left;
valX.VerticalAlignment = VerticalAlignment.Top;
TextBox valY = new TextBox();
valY.Text = "" + GetPolyNewtonVal(x, por, row).ToDouble();
valY.Width = 200;
valY.Height = 25;
valY.HorizontalAlignment = HorizontalAlignment.Left;
valY.VerticalAlignment = VerticalAlignment.Top;
TextBox polyErr = new TextBox();
TextBox diff1 = new TextBox();
TextBox diff2 = new TextBox();
TextBox diff1Err = new TextBox();
TextBox diff2Err = new TextBox();
polyErr.Text = "погр. интерполирования равна " + GetPolyNewtonErr(x, por, row).ToDouble();
diff1.Text = "первая производная равна " + GetPolyNewtonDiff1Val(x, por, row).ToDouble();
diff1Err.Text = "ошибка первой производной " + GetPolyNewtonDiff1Err(x, por, row).ToDouble();
diff2.Text = "вторая производная равна " + GetPolyNewtonDiff2Val(x, por, row).ToDouble();
diff2Err.Text = "ошибка второй производной " + GetPolyNewtonDiff2Err(x, por, row).ToDouble();
polyErr.Width = 300;
polyErr.Height = 25;
diff1.Width = 300;
diff1.Height = 25;
diff2.Width = 300;
diff2.Height = 25;
diff1Err.Width = 300;
diff1Err.Height = 25;
diff2Err.Width = 300;
diff2Err.Height = 25;
SolidColorBrush br = new SolidColorBrush(Color.FromArgb(0, 0, 0, 0));
valY.BorderBrush = br;
valX.BorderBrush = br;
polyErr.BorderBrush = br;
diff1.BorderBrush = br;
diff2.BorderBrush = br;
diff1Err.BorderBrush = br;
diff2Err.BorderBrush = br;
valX.Background = br;
valY.Background = br;
polyErr.Background = br;
diff1.Background = br;
diff2.Background = br;
diff1Err.Background = br;
diff2Err.Background = br;
valX.HorizontalContentAlignment = System.Windows.HorizontalAlignment.Center;
diff1.HorizontalContentAlignment = System.Windows.HorizontalAlignment.Left;
diff2.HorizontalContentAlignment = System.Windows.HorizontalAlignment.Left;
polyErr.Margin = new System.Windows.Thickness(0, 0, wdt - diff1.Width, hgt - diff1.Height);
diff1.Margin = new System.Windows.Thickness(0, 0, wdt - diff1.Width, hgt - 3 * diff1.Height);
diff1Err.Margin = new System.Windows.Thickness(0, 0, wdt - diff1.Width, hgt - 5 * diff1.Height);
diff2.Margin = new System.Windows.Thickness(0, 0, wdt - diff2.Width, hgt - 7 * diff2.Height);
diff2Err.Margin = new System.Windows.Thickness(0, 0, wdt - diff2.Width, hgt - 9 * diff2.Height);
if (valXY.Y <= axis.crossAxis.Y)
{
valX.Margin = new System.Windows.Thickness(valXY.X - valX.Width / 2, axis.crossAxis.Y - valY.Height, 0, 0);
}
else
{
valX.Margin = new System.Windows.Thickness(valXY.X - valX.Width / 2, axis.crossAxis.Y + valY.Height, 0, 0);
}
if (valXY.X <= axis.crossAxis.X)
{
valY.Margin = new System.Windows.Thickness(axis.crossAxis.X - axis.bord - valY.Width, valXY.Y - valY.Height, 0, 0);
valY.TextAlignment = axis.taY;
}
else
{
valY.Margin = new System.Windows.Thickness(axis.crossAxis.X + axis.bord, valXY.Y - valY.Height, 0, 0);
//valY.HorizontalContentAlignment = System.Windows.HorizontalAlignment.Left;
valY.TextAlignment = axis.taY;
}
gr.Children.Add(el);
gr.Children.Add(valX);
gr.Children.Add(valY);
gr.Children.Add(polyErr);
gr.Children.Add(diff1);
gr.Children.Add(diff2);
gr.Children.Add(diff1Err);
gr.Children.Add(diff2Err);
}