void main() {
//* Initialize data to be fit. Data is quadratic plus random number.
Matrix c(3);
cout << "Curve fit data is created using the quadratic" << endl;
cout << " y(x) = c(1) + c(2)*x + c(3)*x^2" << endl;
cout << "Enter the coefficients:" << endl;
cout << "c(1) = "; cin >> c(1);
cout << "c(2) = "; cin >> c(2);
cout << "c(3) = "; cin >> c(3);
double alpha;
cout << "Enter estimated error bar: "; cin >> alpha;
int i, N = 50; // Number of data points
long seed = 1234; // Seed for random number generator
Matrix x(N), y(N), sigma(N);
for( i=1; i<=N; i++ ) {
x(i) = i; // x = [1, 2, ..., N]
y(i) = c(1) + c(2)*x(i) + c(3)*x(i)*x(i) + alpha*randn(seed);
sigma(i) = alpha; // Constant error bar
}
//* Fit the data to a straight line or a more general polynomial
cout << "Enter number of fit parameters (=2 for line): ";
int M; cin >> M;
Matrix a_fit(M), sig_a(M), yy(N); double chisqr;
if( M == 2 ) //* Linear regression (Straight line) fit
linreg( x, y, sigma, a_fit, sig_a, yy, chisqr);
else //* Polynomial fit
pollsf( x, y, sigma, M, a_fit, sig_a, yy, chisqr);
//* Print out the fit parameters, including their error bars.
cout << "Fit parameters:" << endl;
for( i=1; i<=M; i++ )
cout << " a(" << i << ") = " << a_fit(i) <<
" +/- " << sig_a(i) << endl;
cout << "Chi square = " << chisqr << "; N-M = " << N-M << endl;
//* Print out the plotting variables: x, y, sigma, yy
ofstream xOut("x.txt"), yOut("y.txt"),
sigmaOut("sigma.txt"), yyOut("yy.txt");
for( i=1; i<=N; i++ ) {
xOut << x(i) << endl;
yOut << y(i) << endl;
sigmaOut << sigma(i) << endl;
yyOut << yy(i) << endl;
}
}
void InstalledProgramsForm::on_pushButton_clicked()
{
QString xFilePath = QFileDialog::getSaveFileName(this, tr("Сохранить файл"),
mUI->CompName->text() + ".html",
tr("Файлы (*.html)"));
QFile xFile(xFilePath);
if(xFile.exists() == true) xFile.remove();
xFile.open(QFile::WriteOnly);
QTextStream xOut(&xFile);
xOut<<"<html><body><h4>"<<tr("Oтчет о программном обеспечении")<<"</h4>"
<<tr("Имя компьютера: ")
<<mUI->CompName->text()
<<"<br>"<<tr("IP-адресс: ")
<<mUI->CompIPAddress->text()<<endl;
xOut<<"<table border=1 cellpadding=5px style='border:solid; border-collapse:collapse;' >"<<endl;
xOut<<"<tr>";
xOut<<"<td>"<<tr("Имя программы");
xOut<<"<td>"<<tr("Отображаемая версия");
xOut<<"<td>"<<tr("Разработчик");
xOut<<"<td>"<<tr("Дата установки");
xOut<<"<td>"<<tr("Путь установки");
xOut<<"<td>"<<tr("Ключ в реестре");
xOut<<endl;
for(int i = 0; i < mUI->ProgramsList->rowCount(); i++)
{
xOut<<"<tr>";
xOut<<"<td>"<<mUI->ProgramsList->item(i,0)->text();
xOut<<"<td>"<<mUI->ProgramsList->item(i,1)->text();
xOut<<"<td>"<<mUI->ProgramsList->item(i,2)->text();
xOut<<"<td>"<<mUI->ProgramsList->item(i,3)->text();
xOut<<"<td>"<<mUI->ProgramsList->item(i,4)->text();
xOut<<"<td>"<<mUI->ProgramsList->item(i,5)->text();
xOut<<endl;
}
xOut<<"</table>"<<endl;
xOut<<"</body></html>";
xFile.flush();
xFile.close();
}
void main() {
//* Initialize parameters (grid spacing, time step, etc.)
cout << "Enter number of grid points: "; int N; cin >> N;
double L = 100; // System extends from -L/2 to L/2
double h = L/(N-1); // Grid size
double h_bar = 1; double mass = 1; // Natural units
cout << "Enter time step: "; double tau; cin >> tau;
Matrix x(N);
int i, j, k;
for( i=1; i<=N; i++ )
x(i) = h*(i-1) - L/2; // Coordinates of grid points
//* Set up the Hamiltonian operator matrix
Matrix eye(N,N), ham(N,N);
eye.set(0.0); // Set all elements to zero
for( i=1; i<=N; i++ ) // Identity matrix
eye(i,i) = 1.0;
ham.set(0.0); // Set all elements to zero
double coeff = -h_bar*h_bar/(2*mass*h*h);
for( i=2; i<=(N-1); i++ ) {
ham(i,i-1) = coeff;
ham(i,i) = -2*coeff; // Set interior rows
ham(i,i+1) = coeff;
}
// First and last rows for periodic boundary conditions
ham(1,N) = coeff; ham(1,1) = -2*coeff; ham(1,2) = coeff;
ham(N,N-1) = coeff; ham(N,N) = -2*coeff; ham(N,1) = coeff;
//* Compute the Crank-Nicolson matrix
Matrix RealA(N,N), ImagA(N,N), RealB(N,N), ImagB(N,N);
for( i=1; i<=N; i++ )
for( j=1; j<=N; j++ ) {
RealA(i,j) = eye(i,j);
ImagA(i,j) = 0.5*tau/h_bar*ham(i,j);
RealB(i,j) = eye(i,j);
ImagB(i,j) = -0.5*tau/h_bar*ham(i,j);
}
Matrix RealAi(N,N), ImagAi(N,N);
cout << "Computing matrix inverse ... " << flush;
cinv( RealA, ImagA, RealAi, ImagAi ); // Complex matrix inverse
cout << "done" << endl;
Matrix RealD(N,N), ImagD(N,N); // Crank-Nicolson matrix
for( i=1; i<=N; i++ )
for( j=1; j<=N; j++ ) {
RealD(i,j) = 0.0; // Matrix (complex) multiplication
ImagD(i,j) = 0.0;
for( k=1; k<=N; k++ ) {
RealD(i,j) += RealAi(i,k)*RealB(k,j) - ImagAi(i,k)*ImagB(k,j);
ImagD(i,j) += RealAi(i,k)*ImagB(k,j) + ImagAi(i,k)*RealB(k,j);
}
}
//* Initialize the wavefunction
const double pi = 3.141592654;
double x0 = 0; // Location of the center of the wavepacket
double velocity = 0.5; // Average velocity of the packet
double k0 = mass*velocity/h_bar; // Average wavenumber
double sigma0 = L/10; // Standard deviation of the wavefunction
double Norm_psi = 1/(sqrt(sigma0*sqrt(pi))); // Normalization
Matrix RealPsi(N), ImagPsi(N), rpi(N), ipi(N);
for( i=1; i<=N; i++ ) {
double expFactor = exp(-(x(i)-x0)*(x(i)-x0)/(2*sigma0*sigma0));
RealPsi(i) = Norm_psi * cos(k0*x(i)) * expFactor;
ImagPsi(i) = Norm_psi * sin(k0*x(i)) * expFactor;
rpi(i) = RealPsi(i); // Record initial wavefunction
ipi(i) = ImagPsi(i); // for plotting
}
//* Initialize loop and plot variables
int nStep = (int)(L/(velocity*tau)); // Particle should circle system
int nplots = 20; // Number of plots to record
double plotStep = nStep/nplots; // Iterations between plots
Matrix p_plot(N,nplots+2);
for( i=1; i<=N; i++ ) // Record initial condition
p_plot(i,1) = RealPsi(i)*RealPsi(i) + ImagPsi(i)*ImagPsi(i);
int iplot = 1;
//* Loop over desired number of steps (wave circles system once)
int iStep;
Matrix RealNewPsi(N), ImagNewPsi(N);
for( iStep=1; iStep<=nStep; iStep++ ) {
//* Compute new wave function using the Crank-Nicolson scheme
RealNewPsi.set(0.0); ImagNewPsi.set(0.0);
for( i=1; i<=N; i++ ) // Matrix multiply D*psi
for( j=1; j<=N; j++ ) {
RealNewPsi(i) += RealD(i,j)*RealPsi(j) - ImagD(i,j)*ImagPsi(j);
ImagNewPsi(i) += RealD(i,j)*ImagPsi(j) + ImagD(i,j)*RealPsi(j);
}
RealPsi = RealNewPsi; // Copy new values into Psi
ImagPsi = ImagNewPsi;
//* Periodically record values for plotting
if( fmod(iStep,plotStep) < 1 ) {
iplot++;
for( i=1; i<=N; i++ )
p_plot(i,iplot) = RealPsi(i)*RealPsi(i) + ImagPsi(i)*ImagPsi(i);
cout << "Finished " << iStep << " of " << nStep << " steps" << endl;
}
}
// Record final probability density
iplot++;
for( i=1; i<=N; i++ )
p_plot(i,iplot) = RealPsi(i)*RealPsi(i) + ImagPsi(i)*ImagPsi(i);
nplots = iplot; // Actual number of plots recorded
//* Print out the plotting variables: x, rpi, ipi, p_plot
ofstream xOut("x.txt"), rpiOut("rpi.txt"), ipiOut("ipi.txt"),
p_plotOut("p_plot.txt");
for( i=1; i<=N; i++ ) {
xOut << x(i) << endl;
rpiOut << rpi(i) << endl;
ipiOut << ipi(i) << endl;
for( j=1; j<nplots; j++ )
p_plotOut << p_plot(i,j) << ", ";
p_plotOut << p_plot(i,nplots) << endl;
}
}
void main() {
//* Initialize parameters (system size, grid spacing, etc.)
double eps0 = 8.8542e-12; // Permittivity (C^2/(N m^2))
int N = 64; // Number of grid points on a side (square grid)
double L = 1; // System size
double h = L/N; // Grid spacing for periodic boundary conditions
Matrix x(N), y(N);
int i,j;
for( i=1; i<=N; i++ )
x(i) = (i-0.5)*h; // Coordinates of grid points
y = x; // Square grid
cout << "System is a square of length " << L << endl;
//* Set up charge density rho(i,j)
Matrix rho(N,N);
rho.set(0.0); // Initialize charge density to zero
cout << "Enter number of line charges: "; int M; cin >> M;
for( i=1; i<=M; i++ ) {
cout << "For charge #" << i << endl;
cout << "Enter x coordinate: "; double xc; cin >> xc;
cout << "Enter y coordinate: "; double yc; cin >> yc;
int ii = (int)(xc/h) + 1; // Place charge at nearest
int jj = (int)(yc/h) + 1; // grid point
cout << "Enter charge density: "; double q; cin >> q;
rho(ii,jj) += q/(h*h);
}
//* Compute matrix P
const double pi = 3.141592654;
Matrix cx(N), cy(N);
for( i=1; i<=N; i++ )
cx(i) = cos((2*pi/N)*(i-1));
cy = cx;
Matrix RealP(N,N), ImagP(N,N);
double numerator = -h*h/(2*eps0);
double tinyNumber = 1e-20; // Avoids division by zero
for( i=1; i<=N; i++ )
for( j=1; j<=N; j++ )
RealP(i,j) = numerator/(cx(i)+cy(j)-2+tinyNumber);
ImagP.set(0.0);
//* Compute potential using MFT method
Matrix RealR(N,N), ImagR(N,N), RealF(N,N), ImagF(N,N);
for( i=1; i<=N; i++ )
for( j=1; j<=N; j++ ) {
RealR(i,j) = rho(i,j);
ImagR(i,j) = 0.0; // Copy rho into R for input to fft2
}
fft2(RealR,ImagR); // Transform rho into wavenumber domain
// Compute phi in the wavenumber domain
for( i=1; i<=N; i++ )
for( j=1; j<=N; j++ ) {
RealF(i,j) = RealR(i,j)*RealP(i,j) - ImagR(i,j)*ImagP(i,j);
ImagF(i,j) = RealR(i,j)*ImagP(i,j) + ImagR(i,j)*RealP(i,j);
}
Matrix phi(N,N);
ifft2(RealF,ImagF); // Inv. transf. phi into the coord. domain
for( i=1; i<=N; i++ )
for( j=1; j<=N; j++ )
phi(i,j) = RealF(i,j);
//* Print out the plotting variables: x, y, phi
ofstream xOut("x.txt"), yOut("y.txt"), phiOut("phi.txt");
for( i=1; i<=N; i++ ) {
xOut << x(i) << endl;
yOut << y(i) << endl;
for( j=1; j<N; j++ )
phiOut << phi(i,j) << ", ";
phiOut << phi(i,N) << endl;
}
}
