ComplexMatrix MatrixSqrtHermitean (const ComplexMatrix& A)
//
// Returns the matrix square root of a hermitean matrix A.
// The argument matrix is not checked for hermiticity !
//
//
{
// get the dimension information
int lo = A.Clo(),
hi = A.Chi();
// columns and rows must have the same range
if (A.Rlo() != lo || A.Rhi() != hi)
Matpack.Error(Mat::UnspecifiedError,"MatrixSqrtHermitean: hermitean matrix must be square");
Matrix z(lo,hi,lo,hi),
zr(lo,hi,lo,hi),
zi(lo,hi,lo,hi);
Vector d(lo,hi);
int i,j;
// create packed form of hermitean matrix A in matrix z
for (i = lo; i <= hi; i++) {
for (j = lo; j < i; j++) {
z[j][i]=imag(A[i][j]);
z[i][j]=real(A[i][j]);
}
z[i][i]=real(A[i][i]);
}
// diagonalize z
EigenSystemHermitean(z,d,zr,zi,false,30);
// combine real and imaginary parts of eigenvectors (zr,zi) in complex matrix
ComplexMatrix U(zr,zi);
ComplexVector dc(lo,hi);
for (i = lo; i <= hi; i++) {
if (d[i] < 0)
dc[i]=complex<double>(0,sqrt(-d[i]));
else
dc[i]=complex<double>(sqrt(d[i]),0);
}
// calculate matrix square root
U = U * Diagonal(dc) * U.Hermitean();
return U.Value();
}
int main (void)
{
MpImage image(size,size); // allocate size x size raster image
MpImage backimg; // read background image
if (back_image) {
if ( ! backimg.ReadAnyFile(back_image) )
Matpack.Error("Can't read \"%s\"",back_image);
}
// read potential matrix
ifstream pot_stream("pot");
if ( ! pot_stream) Matpack.Error("Can't open pot data file \"%s\"","pot");
pot_stream >> pot;
pot_stream.close();
for (int i = 0; i <= 175; i += 5) { // loop through frames
fprintf(stdout,"\rframe %d...",i); fflush(stdout); // what's going on
// read complex wave function
char file_name[200], pipe_name[200], output_name[200];
sprintf(file_name,"psi%d.gz",i); // generate input data file name
sprintf(pipe_name,"gunzip -c %s > psi.dat",file_name); // decompress data file
sprintf(output_name,"psi%03d.jpg",i); // generate output file name
system(pipe_name);
ifstream data_stream("psi.dat");
if ( ! data_stream) Matpack.Error("Can't open data file psi.dat");
data_stream >> psi;
data_stream.close();
unlink("psi.dat");
// consistency checks
if ( pot.Rlo() != psi.Rlo() || pot.Rhi() != psi.Rhi() ||
pot.Clo() != psi.Clo() || pot.Chi() != psi.Chi() )
Matpack.Error("non-conformant index range of potential and wave function");
Scene scene; // define scene for 3d drawing
// create surface
double u0 = psi.Clo(), u1 = psi.Chi(),
v0 = psi.Rlo(), v1 = psi.Rhi();
int nu = psi.Chi()-psi.Clo(), nv = psi.Rhi()-psi.Rlo(),
su = 0, sv = 0, periodic = 0;
ParametricSurface(scene, height_fcn, u0,u1,nu,su, v0,v1,nv,sv,
periodic, Identity, color_fcn);
scene.BoxRatios(1,z_aspect,1); // scale scene to box with x:y:z
float dist = 1.6; // distance parameter
scene.Look(Vector3D( 1.1*dist, 1.5*dist, 1.4*dist), // camera position vector
Vector3D(-1.1*dist,-1.65*dist,-1.4*dist), // look direction vector
FieldOfView(45), // field of view angle in degree
0); // "twist your head" angle in degree
scene.SetGlobalShading(Facet::Gouraud);
// shading (None, Flat, Gouraud, Phong...)
scene.SetHiddenSurface(preview ? Scene::DepthSort : Scene::TopoSort);
// edgeline drawing option (None,...)
scene.SetGlobalEdgeLines(show_grid ? Facet::Individual : None);
// Setting per-vertex coloring is the best choice to get smoothly changing
// colors on the surface. This requires Gouraud or Phong shading to be
// switched on. If you use per-facet coloring then the facet edges are still
// slightly visible ("Scene::PerFacet")
scene.SetColoring(Scene::PerVertex);
// Define ambient light, RGB color, and specular light and exponent
// If per-vertex coloring or per-facet coloring is set, then only the ambient
// light factor and the specular light factor and exponent are in effect, and
// the diffuse color is ignored (the vertex or facet color is used instead)
Material material(0.6, ColorF(1.,0.8,0.), 0.3,1.8);
scene.SetFacetMaterial(material); // set all facets to material
scene.Open(image); // direct drawing to raster image
if (back_image)
image.InsertTiled(backimg);
else
scene.SetBackground(back_color); // draw background with RGB color
scene.SetColor(edge_color); // define color for edge lines
scene.Show(); // render the surface
scene.Close(); // call always after close
image.WriteJpegFile(output_name,jpeg_quality,jpeg_smooth);// write JPEG image
// write GIF image, if you prefer that
//image.WriteGifFile(output_name); // write image as GIF
}
cout << "\nfinished" << endl;
}