public Nghiem LapJacobi(double dkDung)
{
var mt = MT.Copy();
if (mt.M != mt.N)
{
throw new Exception("Không phải ma trận vuông");
}
if (!mt.isMaTranCheoTroi)
{
throw new Exception("Không phải ma trận chéo trội");
}
var a = new MaTran(mt.M, mt.N);
var b = new MaTran(mt.M, 1);
for (int i = 0; i < a.M; i++)
{
for (int j = 0; j < a.N; j++)
{
if (j == i)
{
a[i, j] = 0;
continue;
}
a[i, j] = -mt[i, j] / mt[i, i];
}
b[i, 0] = mt.MTGhep[i, 0] / mt[i, i];
}
var cstt = Function.ChuSoTinTuong(dkDung);
dkDung = dkDung - 0.5 * Math.Pow(10, -cstt);
double cvc = a.ChuanVoCung;
var x = new Nghiem(Status.NghiemDuyNhat, mt.M);
var x0 = x.Copy();
var x1 = a * x0 + b;
var soPhepLap = Math.Ceiling(
Math.Log(dkDung * (1 - cvc) / (x1 - x0).ChuanVoCung)
/
Math.Log(cvc)
);
for (int i = 0; i < soPhepLap; i++)
{
x = new Nghiem(a * x1 + b);
x1 = x.Copy();
}
for (int i = 0; i < x.M; i++)
{
x[i, 0] = Math.Round(x[i, 0], cstt);
}
return(x);
}
public new Nghiem Copy()
{
var n = new Nghiem(status, M);
for (int i = 0; i < M; i++)
{
for (int j = 0; j < N; j++)
{
n[i, j] = this[i, j];
}
if (status == Status.VoSoNghiem)
{
n.Loai[i] = Loai[i];
}
}
return(n);
}
public Nghiem BaDuongCheo()
{
var n = MT.N;
var alpha = Function.KhoiTaoList(n+1);
var beta = Function.KhoiTaoList(n+1);
alpha[1] = bdcB(0)/bdcC(0);
beta[1] = MT.MTGhep[0, 0];
for (int i = 1; i < n-1; i++)
{
alpha[i + 1] = bdcB(i) / (bdcC(i) - alpha[i] * bdcA(i));
beta[i + 1] = (bdcA(i) * beta[i] + MT.MTGhep[i, 0]) / (bdcC(i) - alpha[i] * bdcA(i));
}
var nghiem = new Nghiem(Status.NghiemDuyNhat, n);
nghiem[n-1,0] = (bdcA(n-1) * beta[n-1] + MT.MTGhep[n-1, 0]) / (bdcC(n-1));
for (int i = n-2; i >= 0; i--)
{
nghiem[i, 0] = alpha[i + 1] * nghiem[i + 1, 0] + beta[i + 1];
}
return nghiem;
}
public Nghiem BaDuongCheo()
{
var n = MT.N;
var alpha = Function.KhoiTaoList(n + 1);
var beta = Function.KhoiTaoList(n + 1);
alpha[1] = bdcB(0) / bdcC(0);
beta[1] = MT.MTGhep[0, 0];
for (int i = 1; i < n - 1; i++)
{
alpha[i + 1] = bdcB(i) / (bdcC(i) - alpha[i] * bdcA(i));
beta[i + 1] = (bdcA(i) * beta[i] + MT.MTGhep[i, 0]) / (bdcC(i) - alpha[i] * bdcA(i));
}
var nghiem = new Nghiem(Status.NghiemDuyNhat, n);
nghiem[n - 1, 0] = (bdcA(n - 1) * beta[n - 1] + MT.MTGhep[n - 1, 0]) / (bdcC(n - 1));
for (int i = n - 2; i >= 0; i--)
{
nghiem[i, 0] = alpha[i + 1] * nghiem[i + 1, 0] + beta[i + 1];
}
return(nghiem);
}
public Nghiem Gauss()
{
var mt = MT.DuaVeMaTranBacThang();
var sdk0 = mt.SoDongKhacKhong;
var sdk0A = mt.SoDongKhacKhongA;
Nghiem nghiem;
if (sdk0 > sdk0A)
{
// Vo nghiem
nghiem = new Nghiem(0, 0);
return nghiem;
}
if (sdk0 == sdk0A && sdk0 == mt.N)
{
// Co nghiem duy nhat
nghiem = new Nghiem(Status.NghiemDuyNhat, sdk0);
for (int i = sdk0 - 1; i >= 0; i--)
{
nghiem[i, 0] = mt.MTGhep[i, 0];
for (int j = 0; j < mt.N; j++)
{
if (mt[i, j] == 0 || j == i)
{
continue;
}
nghiem[i, 0] -= mt[i, j] * nghiem[j, 0];
}
nghiem[i, 0] /= mt[i, i];
}
return nghiem;
}
if (sdk0 == sdk0A && sdk0 < mt.N)
{
// Co vo so nghiem
nghiem = new Nghiem(Status.VoSoNghiem, mt.N);
int dongChon = 0;
for (int i = 0; i < mt.N; i++)
{
if (mt[dongChon, i] != 0)
{
nghiem.Loai[i] = LoaiNghiem.PhuThuoc;
for (int j = dongChon; j < mt.N; j++)
{
if (j == i)
{
continue;
}
nghiem[i, j] = -mt[dongChon, j] / mt[dongChon, i];
}
nghiem[i, mt.N] = mt.MTGhep[dongChon, 0] / mt[dongChon, i];
dongChon++;
if (dongChon > mt.M - 1)
{
break;
}
}
}
return nghiem;
}
return new Nghiem(0, 0);
}
public Nghiem LapJacobi(double dkDung)
{
var mt = MT.Copy();
if (mt.M != mt.N)
{
throw new Exception("Không phải ma trận vuông");
}
if (!mt.isMaTranCheoTroi)
{
throw new Exception("Không phải ma trận chéo trội");
}
var a = new MaTran(mt.M, mt.N);
var b = new MaTran(mt.M, 1);
for (int i = 0; i < a.M; i++)
{
for (int j = 0; j < a.N; j++)
{
if (j == i)
{
a[i, j] = 0;
continue;
}
a[i, j] = -mt[i, j] / mt[i, i];
}
b[i, 0] = mt.MTGhep[i, 0] / mt[i, i];
}
var cstt = Function.ChuSoTinTuong(dkDung);
dkDung = dkDung - 0.5 * Math.Pow(10, -cstt);
double cvc = a.ChuanVoCung;
var x = new Nghiem(Status.NghiemDuyNhat, mt.M);
var x0 = x.Copy();
var x1 = a * x0 + b;
var soPhepLap = Math.Ceiling(
Math.Log(dkDung * (1 - cvc) / (x1 - x0).ChuanVoCung)
/
Math.Log(cvc)
);
for (int i = 0; i < soPhepLap; i++)
{
x = new Nghiem(a * x1 + b);
x1 = x.Copy();
}
for (int i = 0; i < x.M; i++)
{
x[i, 0] = Math.Round(x[i, 0], cstt);
}
return x;
}
public Nghiem GaussJordan()
{
var mt = MT.Copy();
int i = 0, j = 0;
var luuHang = new Dictionary<int, int>();
for (int m = 0; m < mt.M; m++)
{
mt.TimPhanTuTroi(luuHang, ref i, ref j);
if (mt[i, j] == 0)
{
break;
}
luuHang[i] = j;
for (int k = 0; k < mt.M; k++)
{
if (k == i)
{
continue;
}
mt.BienDoiTrenHang(k, i, (ref double ak, ref double ai) =>
{
ak = ak - ai * mt[k, j] / mt[i, j];
});
}
}
// Biện luận
var sdk0 = mt.SoDongKhacKhong;
var sdk0A = mt.SoDongKhacKhongA;
Nghiem nghiem;
if (sdk0 > sdk0A)
{
// Vo nghiem
nghiem = new Nghiem(0, 0);
return nghiem;
}
if (sdk0 == sdk0A && sdk0 == mt.N)
{
// Co nghiem duy nhat
nghiem = new Nghiem(Status.NghiemDuyNhat, sdk0);
foreach (KeyValuePair<int, int> item in luuHang)
{
nghiem[item.Value, 0] = mt.MTGhep[item.Key, 0] / mt[item.Key, item.Value];
}
return nghiem;
}
if (sdk0 == sdk0A && sdk0 < mt.N)
{
// Co vo so nghiem
nghiem = new Nghiem(Status.VoSoNghiem, mt.N);
foreach (KeyValuePair<int, int> item in luuHang)
{
nghiem.Loai[item.Value] = LoaiNghiem.PhuThuoc;
for (int k = 0; k < mt.N; k++)
{
if (k == item.Value)
{
continue;
}
nghiem[item.Value, k] = -mt[item.Key, k];
}
nghiem[item.Value, mt.N] = mt.MTGhep[item.Key, 0];
}
return nghiem;
}
return new Nghiem(0, 0);
}
public new Nghiem Copy()
{
var n = new Nghiem(status, M);
for (int i = 0; i < M; i++)
{
for (int j = 0; j < N; j++)
{
n[i, j] = this[i, j];
}
if (status == Status.VoSoNghiem)
{
n.Loai[i] = Loai[i];
}
}
return n;
}
public Nghiem GaussJordan()
{
var mt = MT.Copy();
int i = 0, j = 0;
var luuHang = new Dictionary <int, int>();
for (int m = 0; m < mt.M; m++)
{
mt.TimPhanTuTroi(luuHang, ref i, ref j);
if (mt[i, j] == 0)
{
break;
}
luuHang[i] = j;
for (int k = 0; k < mt.M; k++)
{
if (k == i)
{
continue;
}
mt.BienDoiTrenHang(k, i, (ref double ak, ref double ai) =>
{
ak = ak - ai * mt[k, j] / mt[i, j];
});
}
}
// Biện luận
var sdk0 = mt.SoDongKhacKhong;
var sdk0A = mt.SoDongKhacKhongA;
Nghiem nghiem;
if (sdk0 > sdk0A)
{
// Vo nghiem
nghiem = new Nghiem(0, 0);
return(nghiem);
}
if (sdk0 == sdk0A && sdk0 == mt.N)
{
// Co nghiem duy nhat
nghiem = new Nghiem(Status.NghiemDuyNhat, sdk0);
foreach (KeyValuePair <int, int> item in luuHang)
{
nghiem[item.Value, 0] = mt.MTGhep[item.Key, 0] / mt[item.Key, item.Value];
}
return(nghiem);
}
if (sdk0 == sdk0A && sdk0 < mt.N)
{
// Co vo so nghiem
nghiem = new Nghiem(Status.VoSoNghiem, mt.N);
foreach (KeyValuePair <int, int> item in luuHang)
{
nghiem.Loai[item.Value] = LoaiNghiem.PhuThuoc;
for (int k = 0; k < mt.N; k++)
{
if (k == item.Value)
{
continue;
}
nghiem[item.Value, k] = -mt[item.Key, k];
}
nghiem[item.Value, mt.N] = mt.MTGhep[item.Key, 0];
}
return(nghiem);
}
return(new Nghiem(0, 0));
}
public Nghiem Gauss()
{
var mt = MT.DuaVeMaTranBacThang();
var sdk0 = mt.SoDongKhacKhong;
var sdk0A = mt.SoDongKhacKhongA;
Nghiem nghiem;
if (sdk0 > sdk0A)
{
// Vo nghiem
nghiem = new Nghiem(0, 0);
return(nghiem);
}
if (sdk0 == sdk0A && sdk0 == mt.N)
{
// Co nghiem duy nhat
nghiem = new Nghiem(Status.NghiemDuyNhat, sdk0);
for (int i = sdk0 - 1; i >= 0; i--)
{
nghiem[i, 0] = mt.MTGhep[i, 0];
for (int j = 0; j < mt.N; j++)
{
if (mt[i, j] == 0 || j == i)
{
continue;
}
nghiem[i, 0] -= mt[i, j] * nghiem[j, 0];
}
nghiem[i, 0] /= mt[i, i];
}
return(nghiem);
}
if (sdk0 == sdk0A && sdk0 < mt.N)
{
// Co vo so nghiem
nghiem = new Nghiem(Status.VoSoNghiem, mt.N);
int dongChon = 0;
for (int i = 0; i < mt.N; i++)
{
if (mt[dongChon, i] != 0)
{
nghiem.Loai[i] = LoaiNghiem.PhuThuoc;
for (int j = dongChon; j < mt.N; j++)
{
if (j == i)
{
continue;
}
nghiem[i, j] = -mt[dongChon, j] / mt[dongChon, i];
}
nghiem[i, mt.N] = mt.MTGhep[dongChon, 0] / mt[dongChon, i];
dongChon++;
if (dongChon > mt.M - 1)
{
break;
}
}
}
return(nghiem);
}
return(new Nghiem(0, 0));
}