private void btnFrobMatr_Click(object sender, RoutedEventArgs e)
{
myM1.MatrWrite();
myM1.Redraw();
if (myM1.NCol == myM1.NRow)
{
try
{
Matr m = myM1.matr.toQuadMatr().getFrobeniusMatr();
RezWnd = new RezWindow();
RezWnd.Owner = this;
RezWnd.Title = "Матрица Фробениуса";
myMRez = new MyMatr(ref RezWnd.MatrRezGrid, ref m, 5);
myMRez.isDouble = (bool)isDbl.IsChecked;
myMRez.Redraw();
RezWnd.btnCopyTo1.Click += btnCopyTo1_Click;
RezWnd.btnCopyTo2.Click += btnCopyTo2_Click;
RezWnd.ShowDialog();
myMRez = null;
}
catch (Exception ex)
{
MessageBox.Show(ex.Message);
}
}
else
{
MessageBox.Show("Матрица должна быть квадратной");
}
}
public Table(ref Grid g, ref Matr m, int sp, string zapoln = "") : base(ref g, ref m, sp, zapoln)
{
for (int i = 0; i < this.NCol; i++)
{
this.txtBxs[0, i].IsEnabled = false;
this.txtBxs[0, i].Background = br;
if (i == 0 || i == 1)
{
for (int j = 1; j < this.NRow; j++)
{
this.txtBxs[j, i].Background = brc;
}
}
switch (i)
{
case 0:
this.txtBxs[0, i].Text = "X";
break;
case 1:
this.txtBxs[0, i].Text = "Y";
break;
case 2:
this.txtBxs[0, i].Text = '\u2206' + "Y";
break;
default:
this.txtBxs[0, i].Text = '\u2206' + "" + (i - 1) + "Y";
break;
}
}
}
private void btnMult_Click(object sender, RoutedEventArgs e)
{
myM1.MatrWrite();
myM1.Redraw();
myM2.MatrWrite();
myM2.Redraw();
try
{
Matr m = myM1.MyMatrToMatr() * myM2.MyMatrToMatr();
RezWnd = new RezWindow();
RezWnd.Owner = this;
RezWnd.Title = "Произведение матриц";
myMRez = new MyMatr(ref RezWnd.MatrRezGrid, ref m, 5);
myMRez.isDouble = (bool)isDbl.IsChecked;
myMRez.Redraw();
RezWnd.btnCopyTo1.Click += btnCopyTo1_Click;
RezWnd.btnCopyTo2.Click += btnCopyTo2_Click;
RezWnd.ShowDialog();
myMRez = null;
}
catch (Exception ex)
{
MessageBox.Show(ex.Message);
}
}
private void SystUr_Orto_Click(object sender, RoutedEventArgs e)
{
myM1.MatrWrite();
myM2.MatrWrite();
SystUrav sr = new SystUrav((QuadMatr)myM1.matr, myM2.MyMatrToMatr());
Matr r = sr.OrtoRoots();
}
public MyMatr(ref Grid g, ref Matr m, int sp, string zapoln = "")
{
g.Children.Clear();
this.zapoln = zapoln;
this.g = g;
this.matr = m;
this.nRow = m.NRow;
this.nCol = m.NCol;
this.sp = sp;
double hMar, vMar, bW, bH;
bW = (g.Width - (nCol + 1) * sp) / nCol;
bH = (g.Height - (nRow + 1) * sp) / nRow;
if (bH > bW)
{
bH = bW;
}
else
{
bW = bH;
}
hMar = (g.Width - sp * (nCol + 1) - bW * nCol) / 2;
vMar = (g.Height - sp * (nRow + 1) - bH * nRow) / 2;
txtBxs = new TextBox[nRow, nCol];
for (int i = 1; i <= nRow; i++)
{
for (int j = 1; j <= nCol; j++)
{
TextBox txtBx = new TextBox();
txtBx.LostFocus += new RoutedEventHandler(TextBox_LostFocus);
txtBx.GotFocus += new RoutedEventHandler(TextBox_GotFocus);
txtBxs[i - 1, j - 1] = txtBx;
txtBx.Name = g.Name + "_txtBx" + i + "_" + j;
if (this.isDouble)
{
txtBx.Text = "" + matr.A[i - 1, j - 1].ToDouble();
}
else
{
txtBx.Text = matr.A[i - 1, j - 1].FractTxt;
}
txtBx.Width = bW;
txtBx.Height = bH;
txtBx.VerticalAlignment = VerticalAlignment.Top;
txtBx.HorizontalAlignment = HorizontalAlignment.Left;
txtBx.TextAlignment = TextAlignment.Center;
txtBx.VerticalContentAlignment = VerticalAlignment.Center;
txtBx.TextWrapping = TextWrapping.Wrap;
txtBx.FontSize = txtBx.Height / FontMult;
Thickness myTh = new Thickness();
myTh.Left = hMar + sp * j + txtBx.Width * (j - 1);
myTh.Top = vMar + sp * i + txtBx.Height * (i - 1);
txtBx.Margin = myTh;
g.Children.Add(txtBx);
}
}
}
public PriblWindow()
{
InitializeComponent();
tblMatr = new Matr(int.Parse(tblRows.Text) + 1, int.Parse(tblRows.Text) + 1);
tabl = new Table(ref GrdFunc, ref tblMatr, 2);
tblIspRow.maxVal = tabl.NRow - 1;
Poryadok.maxVal = tabl.NCol - 2;
myWeb.NavigateToString("<h1>Test</h1>");
txtPolynom.Text = MyFuncs.diffUr("y(1)=(2/x)*y+x", new Fraction(), new Fraction(1, 1), new Fraction(1, 20), new Fraction(3, 2)).FractTxt;
}
private void SwapMatr_Click(object sender, RoutedEventArgs e)
{
myM1.MatrWrite();
myM2.MatrWrite();
Matr ms = myM1.matr;
myM1.matr = myM2.matr;
myM2.matr = ms;
myM1.Redraw();
myM2.Redraw();
}
public Matr GetGaussRootsMatr()
{
Matr x = new Matr(this.nUr, 1);
Matr rt = GaussRoots();
for (int i = 0; i < this.nUr; i++)
{
x.A[i, 0] = rt.A[i + 1, 0].CopyFr;
}
return(x);
}
public Matr GaussRoots()
{
//начало
Matr x = new Matr(this.nUr + 1, 3);
//этап 1
Fraction m = new Fraction();
for (int shag = 0; shag < this.nUr - 1; shag++)
{
for (int i = shag + 1; i < this.nUr; i++)
{
m = this.a.A[i, shag] / this.a.A[shag, shag];
for (int j = 0; j < this.nUr; j++)
{
this.a.A[i, j] = this.a.A[i, j] - m * this.a.A[shag, j];
}
this.b.A[i, 0] = this.b.A[i, 0] - m * this.b.A[shag, 0];
}
}
//этап 2
m.FractTxt = "0";
x.A[this.nUr, 0] = this.b.A[this.nUr - 1, 0] / this.a.A[this.nUr - 1, this.nUr - 1];
for (int i = 0; i <= this.nUr - 1; i++)
{
for (int j = 0; j < i; j++)
{
m += this.a.A[this.nUr - i - 1, this.nUr - j - 1] * x.A[this.nUr - j, 0];
}
x.A[this.nUr - i, 0] = (this.b.A[this.nUr - i - 1, 0] - m) / this.a.A[this.nUr - i - 1, this.nUr - i - 1];
m.FractTxt = "0";
}
//этап 3
for (int i = 0; i < this.nUr; i++)
{
m.FractTxt = "0";
for (int k = 0; k < this.nUr; k++)
{
m += this.a.A[i, k] * x.A[k + 1, 0];
}
x.A[i + 1, 1] = m - this.b.A[i, 0];
if (x.A[i + 1, 1] == 0 || Abs(x.A[i + 1, 1].ToDouble()) < 0.001)
{
x.A[i + 1, 2].FractTxt = "1";
}
else
{
x.A[i + 1, 2].FractTxt = "0";
}
}
return(x);
}
public Matr MyMatrToMatr()
{
Matr m = new Matr(this.NRow, this.nCol);
for (int i = 0; i < this.NRow; i++)
{
for (int j = 0; j < this.nCol; j++)
{
m.A[i, j].FractTxt = this.txtBxs[i, j].Text;
}
}
return(m);
}
public Matr CopyMatr()
{
Matr rez = new Matr(this.nRow, this.nCol);
for (int i = 0; i < this.nRow; i++)
{
for (int j = 0; j < this.nCol; j++)
{
rez.A[i, j] = this.A[i, j].CopyFr;
}
}
return(rez);
}
public static Matr operator *(Fraction fr, Matr m1)
{
Matr rez = new Matr(m1.nRow, m1.nCol);
for (int i = 0; i < m1.nRow; i++)
{
for (int j = 0; j < m1.nCol; j++)
{
rez.A[i, j] = m1.A[i, j] * fr;
}
}
return(rez);
}
public SystUrav(QuadMatr m1, Matr m2)
{
if (m1.NRow == m1.NCol && m2.NCol == 1 && m1.NRow == m2.NRow)
{
this.a = m1.CopyMatr();
this.b = m2.CopyMatr();
this.nUr = m1.NRow;
}
else
{
throw new Exception("Неверная компоновка матриц для системы уравнений!");
}
}
public Matr InverseIterMetod(Fraction lambda, Matr x0)
{
Matr rez = new Matr(this.nRow, 1);
QuadMatr em = new QuadMatr(this.nRow);
em.setEMatr();
rez = x0.CopyMatr();
for (int i = 0; i < 2; i++)
{
SystUrav su = new SystUrav(this - lambda * em, rez);
rez = su.GetGaussRootsMatr();
}
return(rez);
}
public MatrWindow()
{
InitializeComponent();
m1 = new Matr(int.Parse(Sp1_1Txt.Text), int.Parse(Sp1_2Txt.Text));
m2 = new Matr(int.Parse(Sp2_1Txt.Text), int.Parse(Sp2_2Txt.Text));
myM1 = new MyMatr(ref Matr1Grid, ref m1, 5);
myM2 = new MyMatr(ref Matr2Grid, ref m2, 5);
myM1.isDouble = (bool)isDbl.IsChecked;
myM2.isDouble = (bool)isDbl.IsChecked;
Sp1_1Txt.Text = "" + myM1.NRow;
Sp1_2Txt.Text = "" + myM1.NCol;
Sp2_1Txt.Text = "" + myM2.NRow;
Sp2_2Txt.Text = "" + myM2.NCol;
}
public Matr OrtoRoots()
{
QuadMatr t = new QuadMatr(this.nUr);
QuadMatr r = new QuadMatr(this.nUr);
Matr rR = new Matr(1, this.nUr);
Matr rR2 = new Matr(1, this.nUr);
Matr rC = new Matr(this.nUr, 1);
Matr aC = new Matr(this.nUr, 1);
Matr aR = new Matr(this.nUr, 1);
t.setEMatr();
try
{
for (int j = 0; j < this.nUr; j++)
{
aC = Matr.CopyColMatr(this.a, j);
for (int i = 0; i < this.nUr; i++)
{
r.A[i, j] = this.a.A[i, j].CopyFr;
rR.A[0, j] = r.A[i, j].CopyFr;
rC.A[i, 0] = this.a.A[i, j].CopyFr;
}
for (int i = j + 1; i < this.nUr; i++)
{
aC = Matr.CopyColMatr(this.a, i);
for (int n = 0; n < this.nUr; n++)
{
aR.A[0, n] = aC.A[n, 0].CopyFr;
}
aC = Matr.CopyColMatr(this.a, i);
if (j == 0)
{
t.A[j, i] = (rR * aC).A[0, 0] / (rR * rC).A[0, 0];
}
else
{
}
}
}
}
catch (Exception ex)
{
System.Windows.MessageBox.Show(ex.Message);
}
return(new Matr());
}
public static Matr CopyRowMatr(Matr m, int Row)
{
if (Row <= m.nRow)
{
Matr rez = new Matr(1, m.nCol);
for (int j = 0; j < m.nCol; j++)
{
rez.A[0, j] = m.A[Row, j].CopyFr;
}
return(rez);
}
else
{
throw new Exception("Номер строки должен быть не больше количества строк матрицы!");
}
}
public static Matr CopyColMatr(Matr m, int Col)
{
if (Col <= m.nCol)
{
Matr rez = new Matr(m.nRow, 1);
for (int i = 0; i < m.nRow; i++)
{
rez.A[i, 0] = m.A[i, Col].CopyFr;
}
return(rez);
}
else
{
throw new Exception("Номер столбца должен быть не больше количества столбцов матрицы!");
}
}
public static Matr operator-(Matr m1, Matr m2)
{
if (m1.nCol != m2.nCol || m1.nRow != m2.nRow)
{
throw new Exception("Размерности матриц не совпадают");
}
Matr rez = new Matr(m2.nRow, m2.nCol);
for (int i = 0; i < m2.nRow; i++)
{
for (int j = 0; j < m2.nCol; j++)
{
rez.A[i, j] = m1.A[i, j] - m2.A[i, j];
}
}
return(rez);
}
private void SobstChisla_Click(object sender, RoutedEventArgs e)
{
myM1.MatrWrite();
myM2.MatrWrite();
try
{
//SystUrav s = new SystUrav(m1.MyMatrToQuadMatr(), m2.MyMatrToMatr());
QuadMatr x = myM1.matr.toQuadMatr();
Fraction fr = new Fraction();
fr.FractTxt = MyFuncs.convertToFract(lambda.Text);
Matr lbd = x.InverseIterMetod(fr, myM2.MyMatrToMatr());
}
catch (Exception ex)
{
MessageBox.Show(ex.Message);
}
}
private void SystUr_simple_Click(object sender, RoutedEventArgs e)
{
myM1.MatrWrite();
myM2.MatrWrite();
try
{
SystUrav s = new SystUrav(myM1.matr.toQuadMatr(), myM2.matr);
Fraction ep = new Fraction();
ep.FractTxt = MyFuncs.convertToFract(eps.Text);
Matr m = s.SimpleIterRoots(ep, int.Parse(SimpleIterTxt.Text));
RezWnd = new RezWindow();
RezWnd.Owner = this;
RezWnd.Title = "Корни системы уравнений";
myMRez = new MyMatr(ref RezWnd.MatrRezGrid, ref m, 5);
myMRez.isDouble = (bool)isDbl.IsChecked;
myMRez.Redraw();
RezWnd.btnCopyTo1.Visibility = Visibility.Hidden;
RezWnd.btnCopyTo2.Visibility = Visibility.Hidden;
TextBox[,] b = myMRez.GetMatrBx();
b[0, 0].Text = "корни";
b[0, 0].FontWeight = FontWeights.Bold;
b[0, 1].Text = "" + '\x03B4';
b[0, 1].FontWeight = FontWeights.Bold;
b[0, 2].Text = '\x03B4' + "(" + m.A[0, 2].FractTxt + ")";
b[0, 2].FontWeight = FontWeights.Bold;
//for (int i = 1; i < mRez.NRow; i++)
//{
// if (b[i, 2].Text == "1")
// {
// b[i, 2].Text = "верно";
// }
// else
// {
// b[i, 2].Text = "неверно";
// }
//}
RezWnd.ShowDialog();
myMRez = null;
}
catch (Exception ex)
{
MessageBox.Show(ex.Message);
}
}
private void SystUr_Click(object sender, RoutedEventArgs e)
{
myM1.MatrWrite();
myM1.Redraw();
myM2.MatrWrite();
myM2.Redraw();
try
{
SystUrav s = new SystUrav(myM1.matr.toQuadMatr(), myM2.matr);
Matr m = s.GaussRoots();
RezWnd = new RezWindow();
RezWnd.Owner = this;
RezWnd.Title = "Корни системы уравнений";
myMRez = new MyMatr(ref RezWnd.MatrRezGrid, ref m, 5);
myMRez.isDouble = (bool)isDbl.IsChecked;
myMRez.Redraw();
RezWnd.btnCopyTo1.Visibility = Visibility.Hidden;
RezWnd.btnCopyTo2.Visibility = Visibility.Hidden;
TextBox[,] b = myMRez.GetMatrBx();
b[0, 0].Text = "корни";
b[0, 0].FontWeight = FontWeights.Bold;
b[0, 1].Text = "невязка";
b[0, 1].FontWeight = FontWeights.Bold;
b[0, 2].Text = "верность";
b[0, 2].FontWeight = FontWeights.Bold;
for (int i = 1; i < myMRez.NRow; i++)
{
if (b[i, 2].Text == "1")
{
b[i, 2].Text = "верно";
}
else
{
b[i, 2].Text = "неверно";
}
}
RezWnd.ShowDialog();
myMRez = null;
}
catch (Exception ex)
{
MessageBox.Show(ex.Message);
}
}
public static Matr operator *(Matr m1, Matr m2)
{
if (m1.nCol == m2.nRow)
{
Matr rez = new Matr(m1.nRow, m2.nCol);
for (int i = 0; i < m1.nRow; i++)
{
for (int j = 0; j < m2.nCol; j++)
{
for (int g = 0; g < m2.nRow; g++)
{
rez.A[i, j] += m1.A[i, g] * m2.A[g, j];
}
}
}
return(rez);
}
else
{
throw new Exception("Количество столбцов матрицы1 должно быть равно количеству строк матрицы2!");
}
}
public void DrawCircles(Matr m)
{
double mult = 1;
Fraction r = new Fraction();
Fraction a = new Fraction();
for (int i = 0; i < m.NCol; i++)
{
for (int j = 0; j < m.NCol; j++)
{
if (i != j)
{
a = m.A[i, j].CopyFr;
if (a < 0)
{
a = -1 * a;
}
r += a;
}
}
a = m.A[i, i].CopyFr;
if (Math.Min((grdGraf.Width - 40) / (2 * (r + (a < 0 ? -1 * a : a))).ToDouble(), (grdGraf.Height - 40) / (2 * r).ToDouble()) <= mult || mult == 1)
{
mult = Math.Min((grdGraf.Width - 40) / (2 * (r + (a < 0 ? -1 * a : a))).ToDouble(), (grdGraf.Height - 40) / (2 * r).ToDouble());
}
r.FractTxt = "0";
a.FractTxt = "0";
}
for (int i = 0; i < m.NCol; i++)
{
for (int j = 0; j < m.NCol; j++)
{
if (i != j)
{
a = m.A[i, j].CopyFr;
if (a < 0)
{
a = -1 * a;
}
r += a;
}
}
a = m.A[i, i].CopyFr;
Ellipse el = new Ellipse();
TextBlock xVal = new TextBlock();
TextBlock rT = new TextBlock();
Line rad = new Line();
el.Stroke = Brushes.Black;
rad.Stroke = Brushes.Red;
rad.StrokeThickness = 3;
xVal.Width = 60;
el.HorizontalAlignment = HorizontalAlignment.Left;
xVal.HorizontalAlignment = HorizontalAlignment.Left;
rT.HorizontalAlignment = HorizontalAlignment.Left;
el.VerticalAlignment = VerticalAlignment.Top;
xVal.VerticalAlignment = VerticalAlignment.Top;
rT.VerticalAlignment = VerticalAlignment.Top;
el.Margin = new Thickness(grdGraf.Width / 2 - mult * r.ToDouble() + mult * a.ToDouble(), grdGraf.Height / 2 - mult * r.ToDouble(), 0, 0);
xVal.Margin = new Thickness(grdGraf.Width / 2 + mult * a.ToDouble() - xVal.Width / 2, grdGraf.Height / 2 + 10, 0, 0);
rT.Margin = new Thickness(grdGraf.Width / 2 + mult * a.ToDouble(), grdGraf.Height / 2 - mult * r.ToDouble() - 20, 0, 0);
rad.X1 = rad.X2 = grdGraf.Width / 2 + mult * a.ToDouble();
rad.Y1 = grdGraf.Height / 2;
rad.Y2 = grdGraf.Height / 2 - mult * r.ToDouble();
xVal.Text = "" + a.ToDouble();
rT.Text = "r" + (i + 1) + " = " + r.ToDouble();
xVal.TextAlignment = TextAlignment.Center;
el.Width = mult * r.ToDouble() * 2;
el.Height = mult * r.ToDouble() * 2;
grdGraf.Children.Add(el);
grdGraf.Children.Add(xVal);
grdGraf.Children.Add(rad);
grdGraf.Children.Add(rT);
r.FractTxt = "0";
}
}
public Matr SimpleIterRoots(Fraction eps, long nIter = 0)
{
Matr beta = new Matr(this.b.NRow, this.b.NCol);
Matr alfa = new Matr(this.a.NRow, this.a.NCol);
Matr x = new Matr(this.b.NRow + 1, 3);
Matr x2 = new Matr(this.b.NRow, 1);
Fraction norm = new Fraction();
Fraction delta = new Fraction();
Fraction err = new Fraction();
for (int i = 0; i < this.b.NRow; i++)
{
beta.A[i, 0].FractTxt = (this.b.A[i, 0] / this.a.A[i, i]).FractTxt;
x.A[i + 1, 0].FractTxt = (this.b.A[i, 0] / this.a.A[i, i]).FractTxt;
for (int j = 0; j < this.b.NRow; j++)
{
if (i == j)
{
alfa.A[i, j].FractTxt = beta.A[i, 0].FractTxt;;
}
else
{
alfa.A[i, j].FractTxt = (-1 * this.a.A[i, j] / this.a.A[i, i]).FractTxt;
delta += alfa.A[i, j].frAbs();
}
}
if (norm == 0)
{
norm.FractTxt = delta.FractTxt;
}
else
{
if (norm < delta)
{
norm.FractTxt = delta.FractTxt;
}
}
delta.FractTxt = "0";
}
delta = eps * (1 - norm) / norm;
if (nIter == 0)
{
while (err > delta || err == 0)
{
for (int i = 0; i < this.a.NRow; i++)
{
for (int j = 0; j < this.a.NCol; j++)
{
if (i != j)
{
x2.A[i, 0] += alfa.A[i, j] * x.A[j + 1, 0];
}
else
{
x2.A[i, 0] += alfa.A[i, j];
}
}
}
///////////////////////////////////////////////////
err.FractTxt = "0";
for (int i = 0; i < this.a.NRow; i++)
{
if (err == 0)
{
err = (x2.A[i, 0] - x.A[i + 1, 0]).frAbs();
}
else
{
if (err < (x2.A[i, 0] - x.A[i + 1, 0]).frAbs())
{
err = (x2.A[i, 0] - x.A[i + 1, 0]).frAbs();
}
}
}
///////////////////////////////////////////////////
for (int i = 0; i < this.a.NRow; i++)
{
x.A[i + 1, 0].FractTxt = x2.A[i, 0].FractTxt;
x.A[i + 1, 2].FractTxt = err.FractTxt;
x2.A[i, 0].FractTxt = "0";
}
nIter++;
x.A[0, 2].FractTxt = "" + nIter;
}
}
else
{
for (int n = 0; n < nIter; n++)
{
for (int i = 0; i < this.a.NRow; i++)
{
for (int j = 0; j < this.a.NCol; j++)
{
if (i != j)
{
x2.A[i, 0] += alfa.A[i, j] * x.A[j + 1, 0];
}
else
{
x2.A[i, 0] += alfa.A[i, j];
}
}
}
///////////////////////////////////////////////////
err.FractTxt = "0";
for (int i = 0; i < this.a.NRow; i++)
{
if (err == 0)
{
err = (x2.A[i, 0] - x.A[i + 1, 0]).frAbs();
}
else
{
if (err < (x2.A[i, 0] - x.A[i + 1, 0]).frAbs())
{
err = (x2.A[i, 0] - x.A[i + 1, 0]).frAbs();
}
}
}
///////////////////////////////////////////////////
for (int i = 0; i < this.a.NRow; i++)
{
x.A[i + 1, 0].FractTxt = x2.A[i, 0].FractTxt;
x.A[i + 1, 2].FractTxt = err.FractTxt;
x2.A[i, 0].FractTxt = "0";
}
}
}
for (int i = 0; i < this.a.NRow; i++)
{
x.A[i + 1, 1].FractTxt = delta.FractTxt;
}
x.A[0, 2].FractTxt = "" + nIter;
return(x);
}
