public Fraction GetPolyNewtonDiff2Err(Fraction fr, int poryadok, int row = 1)
{
if (poryadok >= this.NRow - row - 1)
{
poryadok = this.NRow - row - 1;
if (poryadok >= 5)
{
poryadok = 5;
}
if (poryadok >= this.NCol - row - 2)
{
poryadok = this.NCol - row - 2;
}
}
Fraction rez = new Fraction();
if (isRavnom())
{
Fraction q = new Fraction();
Fraction l = new Fraction();
Fraction h = new Fraction();
h = this.matr.A[1, 0].CopyFr;
q = this.matr.A[2, 0].CopyFr;
h = q - h;
q = this.matr.A[row, 0].CopyFr;
q = (fr - q) / h;
switch (poryadok)
{
case 1:
l = this.matr.A[row, 3].CopyFr;
rez = h.Invert().Power(2) * l;
break;
case 2:
l = this.matr.A[row, 4].CopyFr;
rez = h.Invert().Power(2) * l * (q - 1);
break;
case 3:
l = this.matr.A[row, 5].CopyFr;
rez = h.Invert().Power(2) * l * (6 * q.Power(2) - 18 * q + 11) / 12;
break;
case 4:
l = this.matr.A[row, 6].CopyFr; //возможна ошибка
rez = h.Invert().Power(2) * l * (2 * q.Power(3) - 12 * q.Power(2) + 21 * q - 10) / 12;
break;
case 5:
l = this.matr.A[row, 7].CopyFr; //возможна ошибка
rez = h.Invert().Power(2) * l * GetPolyNewtonDiff1Val(fr, poryadok, row) / 720; //доделать
break;
default:
MessageBox.Show("Максимальный поддерживаемый порядок = 5!");
break;
}
}
return(rez);
}
public string GetPolyNewton(int poryadok, int row = 1)
{
string str = this.txtBxs[row, 1].Text;
string proizv = "";
Fraction m = new Fraction();
Fraction l = new Fraction();
Fraction k = new Fraction();
if (isRavnom())
{
Fraction h = new Fraction();
m = this.matr.A[1, 0].CopyFr;
k = this.matr.A[2, 0].CopyFr;
h = k - m;
if (poryadok >= this.NRow - row - 1)
{
poryadok = this.NRow - row - 1;
}
for (int i = 1; i <= poryadok; i++)
{
m.FractTxt = "" + MyFuncs.factorial(i);
m *= h.Power(i);
l = this.matr.A[row, i + 1].CopyFr;
l /= m;
//str += "+" + l.FractTxt;
str += (l < 0?"":"+") + l.FractTxt;
proizv = "";
for (int j = 1; j < i + 1; j++)
{
//proizv += "(" + this.txtBxs[0, 0].Text + "-" + this.txtBxs[j + row - 1, 0].Text + ")";
proizv += '\x00D7' + (this.txtBxs[j + row - 1, 0].Text == "0" ? "" :"(") + this.txtBxs[0, 0].Text + (this.txtBxs[j + row - 1, 0].Text == "0"?"": "-" + this.txtBxs[j + row - 1, 0].Text + ")");
}
str += proizv;
}
}
else
{
if (poryadok >= this.NRow - row - 1)
{
poryadok = this.NRow - row - 1;
}
for (int i = 1; i <= poryadok; i++)
{
l = this.matr.A[row, i + 1].CopyFr;
str += (l < 0 ? "" : "+") + l.FractTxt;
proizv = "";
for (int j = 1; j < i + 1; j++)
{
proizv += '\x00D7' + (this.txtBxs[j + row - 1, 0].Text == "0" ? "" : "(") + this.txtBxs[0, 0].Text + (this.txtBxs[j + row - 1, 0].Text == "0" ? "" : "-" + this.txtBxs[j + row - 1, 0].Text + ")");
}
str += proizv;
}
}
return(str);
}
public Fraction GetPolyNewtonVal(Fraction fr, int poryadok, int row = 1)
{
Fraction rez = new Fraction();
rez = this.matr.A[row, 1].CopyFr;
Fraction m = new Fraction(1, 1);
Fraction n = new Fraction(1, 1);
Fraction l = new Fraction(1, 1);
Fraction k = new Fraction(1, 1);
if (poryadok >= this.NRow - row - 1)
{
poryadok = this.NRow - row - 1;
}
if (isRavnom())
{
Fraction h = new Fraction();
m = this.matr.A[1, 0].CopyFr;
k = this.matr.A[2, 0].CopyFr;
h = k - m;
for (int i = 1; i <= poryadok; i++)
{
m.FractTxt = "" + MyFuncs.factorial(i);
m *= h.Power(i);
l = this.matr.A[row, i + 1].CopyFr;
l /= m;
n.FractTxt = "1";
for (int j = 1; j < i + 1; j++)
{
k = this.matr.A[j + row - 1, 0].CopyFr;
n *= (fr - k);
}
rez += l * n;
}
}
else
{
for (int i = 1; i <= poryadok; i++)
{
l = this.matr.A[row, i + 1].CopyFr;
n.FractTxt = "1";
for (int j = 1; j < i + 1; j++)
{
k = this.matr.A[j + row - 1, 0].CopyFr;
n *= (fr - k);
}
rez += l * n;
}
}
return(rez);
}
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);
}