private void TFLanctoImposto_Load(object sender, EventArgs e)
{
Utils.ShapeGrid.RestoreShape(this, dataGridDefault1);
this.Icon = Utils.ResourcesUtils.TecnoAliance_ICO;
this.pDados.set_FormatZero();
CD_Empresa.Text = this.Cd_empresa;
CD_Empresa_Leave(this, new EventArgs());
CD_Empresa.Enabled = string.IsNullOrEmpty(this.Cd_empresa);
BB_Empresa.Enabled = string.IsNullOrEmpty(this.Cd_empresa);
cd_imposto.Text = this.Cd_imposto;
cd_imposto_Leave(this, new EventArgs());
cd_imposto.Enabled = string.IsNullOrEmpty(this.Cd_imposto);
bb_imposto.Enabled = string.IsNullOrEmpty(this.Cd_imposto);
dt_lancto.Text = this.Dt_lancto;
if (!string.IsNullOrEmpty(D_c))
{
tp_lancto.SelectedIndex = D_c.Trim().ToUpper().Equals("D") ? 0 : 2;
}
this.afterBusca();
}
static void Main()
{
int n = 5;
var rnd = new Random(1);
var A = new matrix(n, n);
for (int i = 0; i < n; i++)
{
for (int j = i; j < n; j++)
{
A[i, j] = 2 * (rnd.NextDouble() - 0.5); A[j, i] = A[i, j];
}
}
WriteLine("____Assignment A____");
WriteLine("Eigenvalue Decomposition A=V*D*V^T");
A.print("Random symmetric matrix A:");
(matrix D, matrix V, int sweeps) = diag.cyclic(A);
WriteLine($"Number of sweeps={sweeps}");
matrix VTAV = V.T * A * V;
for (int i = 0; i < n; i++) // Rounding elements to avoid displaying numbers that are essentially zero
{
for (int j = 0; j < n; j++)
{
VTAV[i, j] = Round(VTAV[i, j], 6);
D[i, j] = Round(D[i, j], 6);
V[i, j] = Round(V[i, j], 6);
}
}
V.print("Matrix with eigenvectors V:");
VTAV.print("V^T*A*V (should be diagonal):");
D.print("Eigenvalues matrix D:\n");
if (D.approx(VTAV))
{
WriteLine("D=V^T*A*V, test passed");
}
else
{
WriteLine("D!=V^T*A*V, test failed");
}
Write("\n\n");
WriteLine("Quantum particle in a box");
int N = 99;
matrix H = new matrix(N, N);
for (int i = 0; i < N - 1; i++)
{
H[i, i] = 2 * Pow(N + 1, 2);
H[i, i + 1] = -1 * Pow(N + 1, 2);
H[i + 1, i] = -1 * Pow(N + 1, 2);
}
H[N - 1, N - 1] = 2 * Pow(N + 1, 2);
(matrix eig_val, matrix eig_vec, int sweeps2) = diag.cyclic(H);
for (int i = 0; i < N / 2; i++)
{
Error.WriteLine($"{i} {eig_val[i,i]} {Pow(PI*(i+1),2)}");
}
Error.WriteLine("\n\n");
for (int k = 0; k < 5; k++)
{
Error.WriteLine($"{0} {0}");
double factor = Sign(eig_vec[0, k]) / Sqrt(1.0 / (N + 1));
for (int i = 0; i < N; i++)
{
Error.WriteLine($"{(i+1.0)/(N+1.0)} {factor*eig_vec[i,k]}");
}
Error.WriteLine($"{1.0} {0}\n");
}
WriteLine("\nSee figures A_eig_vec.svg and A_eig_val.svg. We can see that our energy (eigenvalue)\ncalculation is accurate for the lowest 10-15% of the levels. The eigenfunctions\nlook as they should from the analytical result - sinusoidal oscillations.");
Write("\n\n\n");
n = 7;
rnd = new Random(1);
A = new matrix(n, n);
for (int i = 0; i < n; i++)
{
for (int j = i; j < n; j++)
{
A[i, j] = 2 * (rnd.NextDouble() - 0.5); A[j, i] = A[i, j];
}
}
WriteLine("____Assignment B____");
WriteLine("Eigenvalue Decomposition A=V*D*V^T");
A.print("Random symmetric matrix A:");
(matrix D_c, matrix V_c, int sweeps_b) = diag.cyclic(A);
WriteLine($"Number of sweeps={sweeps_b}");
(matrix D_1, int rotations_1) = diag.values(A, 1);
(matrix D_n, int rotations_n) = diag.values(A, n);
D_c.print("Eigenvalues of cyclic method:");
WriteLine($"Number of rotations: {sweeps_b*n*(n-1)/2}\n");
D_1.print("Eigenvalue of 1-value method (only first row):");
WriteLine($"Number of rotations: {rotations_1}\n");
D_n.print("Eigenvalues of value-by-value method:");
WriteLine($"Number of rotations: {rotations_n}\n");
Write("\n\n");
WriteLine("See the figures B_rot.svg and B_time.svg for a comparison in\nhow the different methods perform as a function of dimension.\nI have used the System.Diagnostics.Stopwatch to estimate times, since this\nproved easier than the POSIX time utility which was a bit tricky with my OS.\nFrom the figures we can see the O(n^3) behavior, which is explicitly\ncalculated for the times in B_time.svg.");
Write("\n\n");
WriteLine("By changing the rotation angle, we can get the highest Eigenvalues first.");
WriteLine("Eigenvalues from highest to lowest:");
vector e = diag.high_eig(A, n);
e.print("Eigenvalues:");
}
