/// <summary>
/// Computes the intergrated probability density.
/// </summary>
public float Norm()
{
GridSpec gridSpec = GridSpec;
int sx = gridSpec.SizeX;
int sy = gridSpec.SizeY;
int sz = gridSpec.SizeZ;
float[] norm = new float[sz];
TdseUtils.Misc.ForLoop(0, sz, z =>
{
float xySum = 0.0f;
for (int y = 0; y < sy; y++)
{
float[] dataZY = m_data[z][y];
for (int x = 0; x < sx; x++)
{
xySum += dataZY[x];
}
}
norm[z] = xySum;
}, true);
float normTot = 0.0f;
for (int z = 0; z < sz; z++)
{
normTot += norm[z];
}
normTot *= (m_latticeSpacing * m_latticeSpacing * m_latticeSpacing);
return(normTot);
}
/// <summary>
/// Writes a set of densities to a file, in VTK format.
/// </summary>
public static void SaveToVtkFile(ProbabilityDensity[] probs, string fileSpec)
{
using (FileStream fileStream = File.Create(fileSpec))
{
using (BinaryWriter bw = new BinaryWriter(fileStream))
{
GridSpec gridSpec = probs[0].GridSpec;
int sx = gridSpec.SizeX;
int sy = gridSpec.SizeY;
int sz = gridSpec.SizeZ;
string nl = Environment.NewLine;
// Write the header
bw.Write(Encoding.ASCII.GetBytes("# vtk DataFile Version 3.0" + nl));
bw.Write(Encoding.ASCII.GetBytes("Probability3D2P " + "spacing: " + probs[0].LatticeSpacing.ToString() + nl));
bw.Write(Encoding.ASCII.GetBytes("BINARY" + nl));
bw.Write(Encoding.ASCII.GetBytes("DATASET STRUCTURED_POINTS" + nl));
bw.Write(Encoding.ASCII.GetBytes("DIMENSIONS " + sx + " " + sy + " " + sz + nl));
bw.Write(Encoding.ASCII.GetBytes("ORIGIN 0 0 0" + nl));
bw.Write(Encoding.ASCII.GetBytes("SPACING 1 1 1" + nl));
bw.Write(Encoding.ASCII.GetBytes("POINT_DATA " + sx * sy * sz + nl));
for (int i = 0; i < probs.Length; i++)
{
probs[i].ToVtkStream(bw, "prob_" + i.ToString());
}
}
}
}
/// <summary>
/// Creates a Gaussian wavepacket with given properties.
/// </summary>
public static WaveFunction CreateGaussianWavePacket(
GridSpec gridSpec, float latticeSpacing, bool originAtLatticeCenter, float mass,
Vec3 packetCenter, Vec3 packetWidth, Vec3 avgMomentum, bool multiThread = true)
{
WaveFunction wf = new WaveFunction(gridSpec, latticeSpacing);
int sx = gridSpec.SizeX;
int sy = gridSpec.SizeY;
int sz = gridSpec.SizeZ;
float[][][] wfData = wf.Data;
Complex I = Complex.I;
float rootPi = (float)Math.Sqrt(Math.PI);
float sigmaXSq = packetWidth.X * packetWidth.X;
float sigmaYSq = packetWidth.Y * packetWidth.Y;
float sigmaZSq = packetWidth.Z * packetWidth.Z;
float norm = (float)Math.Sqrt(1.0 / (rootPi * packetWidth.X * rootPi * packetWidth.Y * rootPi * packetWidth.Z));
int halfGridSizeX = (sx - 1) / 2;
int halfGridSizeY = (sy - 1) / 2;
int halfGridSizeZ = (sz - 1) / 2;
TdseUtils.Misc.ForLoop(0, sz, (z) =>
{
float zf = (originAtLatticeCenter) ? (z - halfGridSizeZ) * latticeSpacing : (z * latticeSpacing);
Complex expArgZ = I * zf * avgMomentum.Z - (zf - packetCenter.Z) * (zf - packetCenter.Z) / (2 * sigmaZSq);
for (int y = 0; y < sy; y++)
{
float yf = (originAtLatticeCenter) ? (y - halfGridSizeY) * latticeSpacing : (y * latticeSpacing);
Complex expArgZY = expArgZ + I * yf * avgMomentum.Y - (yf - packetCenter.Y) * (yf - packetCenter.Y) / (2 * sigmaYSq);
float[] wfDataZY = wf.Data[z][y];
for (int x = 0; x < sx; x++)
{
float xf = (originAtLatticeCenter) ? (x - halfGridSizeX) * latticeSpacing : (x * latticeSpacing);
Complex expArgZYX = expArgZY + I * xf * avgMomentum.X - (xf - packetCenter.X) * (xf - packetCenter.X) / (2 * sigmaXSq);
Complex wfVal = norm * Complex.Exp(expArgZYX);
wfDataZY[2 * x] = wfVal.Re;
wfDataZY[2 * x + 1] = wfVal.Im;
}
}
}, multiThread);
wf.Normalize();
return(wf);
}
/// <summary>
/// Writes the density values to a stream, in vtk format.
/// </summary>
private void ToVtkStream(BinaryWriter bw, string name)
{
GridSpec gridSpec = GridSpec;
int sx = gridSpec.SizeX;
int sy = gridSpec.SizeY;
int sz = gridSpec.SizeZ;
string nl = Environment.NewLine;
unsafe
{
// For performance, we keep a temporary float value with pointers to its bytes
float floatVal = 0.0f;
byte *floatBytes0 = (byte *)(&floatVal);
byte *floatBytes1 = floatBytes0 + 1;
byte *floatBytes2 = floatBytes0 + 2;
byte *floatBytes3 = floatBytes0 + 3;
bw.Write(Encoding.ASCII.GetBytes("SCALARS " + name + " float" + nl));
bw.Write(Encoding.ASCII.GetBytes("LOOKUP_TABLE default" + nl));
byte[] bytePlane = new byte[sx * sy * 4];
for (int z = 0; z < sz; z++)
{
int n = 0;
for (int y = 0; y < sy; y++)
{
float[] dataZY = m_data[z][y];
for (int x = 0; x < sx; x++)
{
floatVal = dataZY[x];
bytePlane[n] = *floatBytes3; // Reverse the bytes, since VTK wants big-endian data
bytePlane[n + 1] = *floatBytes2;
bytePlane[n + 2] = *floatBytes1;
bytePlane[n + 3] = *floatBytes0;
n += 4;
}
}
bw.Write(bytePlane);
}
}
}
/// <summary>
/// Constructor.
/// </summary>
public WaveFunction(GridSpec gridSpec, float latticeSpacing)
{
m_data = TdseUtils.Misc.Allocate3DArray(gridSpec.SizeZ, gridSpec.SizeY, 2 * gridSpec.SizeX);
m_latticeSpacing = latticeSpacing;
}
/// <summary>
/// Constructor.
/// </summary>
public ProbabilityDensity(GridSpec gridSpec, float latticeSpacing)
{
m_data = TdseUtils.Misc.Allocate3DArray(gridSpec.SizeZ, gridSpec.SizeY, gridSpec.SizeX);
m_latticeSpacing = latticeSpacing;
}
/// <summary>
/// Compares two GridSpecs by value.
/// </summary>
public bool ValueEquals(GridSpec that)
{
return((this.SizeX == that.SizeX) && (this.SizeY == that.SizeY) && (this.SizeZ == that.SizeZ));
}
/// <summary>
/// Copy constructor.
/// </summary>
public GridSpec(GridSpec src)
{
SizeX = src.SizeX;
SizeY = src.SizeY;
SizeZ = src.SizeZ;
}
/// <summary>
/// Evolves the wavefunction by a single time step
/// </summary>
private void EvolveByOneTimeStep(VisscherWf wf, float[][][] V)
{
GridSpec wfGrid = wf.GridSpec;
int sx = wfGrid.SizeX;
int sy = wfGrid.SizeY;
int sz = wfGrid.SizeZ;
int sxm1 = sx - 1;
int sym1 = sy - 1;
int szm1 = sz - 1;
float keFactor = (1.0f / 12.0f) / (2 * m_reducedMass * wf.LatticeSpacing * wf.LatticeSpacing);
// Compute the next real part in terms of the current imaginary part
TdseUtils.Misc.ForLoop(0, sz, z =>
{
int zp = (z < szm1) ? z + 1 : 0;
int zpp = (zp < szm1) ? zp + 1 : 0;
int zm = (z > 0) ? z - 1 : szm1;
int zmm = (zm > 0) ? zm - 1 : szm1;
for (int y = 0; y < sy; y++)
{
int yp = (y < sym1) ? y + 1 : 0;
int ypp = (yp < sym1) ? yp + 1 : 0;
int ym = (y > 0) ? y - 1 : sym1;
int ymm = (ym > 0) ? ym - 1 : sym1;
float[] V_z_y = V[z][y];
float[] wfR_z_y = wf.RealPart[z][y];
float[] wfI_z_y = wf.ImagPartP[z][y];
float[] wfI_z_ym = wf.ImagPartP[z][ym];
float[] wfI_z_yp = wf.ImagPartP[z][yp];
float[] wfI_z_ymm = wf.ImagPartP[z][ymm];
float[] wfI_z_ypp = wf.ImagPartP[z][ypp];
float[] wfI_zm_y = wf.ImagPartP[zm][y];
float[] wfI_zp_y = wf.ImagPartP[zp][y];
float[] wfI_zmm_y = wf.ImagPartP[zmm][y];
float[] wfI_zpp_y = wf.ImagPartP[zpp][y];
for (int x = 0; x < sx; x++)
{
int xp = (x < sxm1) ? x + 1 : 0;
int xpp = (xp < sxm1) ? xp + 1 : 0;
int xm = (x > 0) ? x - 1 : sxm1;
int xmm = (xm > 0) ? xm - 1 : sxm1;
// Discretization of the 2nd derivative
float ke = keFactor * (
90.0f * wfI_z_y[x] -
16.0f * (wfI_zm_y[x] + wfI_zp_y[x] + wfI_z_yp[x] + wfI_z_ym[x] + wfI_z_y[xm] + wfI_z_y[xp]) +
(wfI_zmm_y[x] + wfI_zpp_y[x] + wfI_z_ypp[x] + wfI_z_ymm[x] + wfI_z_y[xmm] + wfI_z_y[xpp])
);
float pe = V_z_y[x] * wfI_z_y[x];
wfR_z_y[x] += m_deltaT * (ke + pe);
}
}
}, m_multiThread);
// Swap prev and post imaginary parts
float[][][] temp = wf.ImagPartM;
wf.ImagPartM = wf.ImagPartP;
wf.ImagPartP = temp;
// Compute the next imaginary part in terms of the current real part
TdseUtils.Misc.ForLoop(0, sz, z =>
{
int zp = (z < szm1) ? z + 1 : 0;
int zpp = (zp < szm1) ? zp + 1 : 0;
int zm = (z > 0) ? z - 1 : szm1;
int zmm = (zm > 0) ? zm - 1 : szm1;
for (int y = 0; y < sy; y++)
{
int yp = (y < sym1) ? y + 1 : 0;
int ypp = (yp < sym1) ? yp + 1 : 0;
int ym = (y > 0) ? y - 1 : sym1;
int ymm = (ym > 0) ? ym - 1 : sym1;
float[] V_z_y = V[z][y];
float[] wfIM_z_y = wf.ImagPartM[z][y];
float[] wfIP_z_y = wf.ImagPartP[z][y];
float[] wfR_z_y = wf.RealPart[z][y];
float[] wfR_z_ym = wf.RealPart[z][ym];
float[] wfR_z_yp = wf.RealPart[z][yp];
float[] wfR_z_ymm = wf.RealPart[z][ymm];
float[] wfR_z_ypp = wf.RealPart[z][ypp];
float[] wfR_zm_y = wf.RealPart[zm][y];
float[] wfR_zp_y = wf.RealPart[zp][y];
float[] wfR_zmm_y = wf.RealPart[zmm][y];
float[] wfR_zpp_y = wf.RealPart[zpp][y];
for (int x = 0; x < sx; x++)
{
int xp = (x < sxm1) ? x + 1 : 0;
int xpp = (xp < sxm1) ? xp + 1 : 0;
int xm = (x > 0) ? x - 1 : sxm1;
int xmm = (xm > 0) ? xm - 1 : sxm1;
// Discretization of the 2nd derivative
float ke = keFactor * (
90.0f * wfR_z_y[x] -
16.0f * (wfR_zm_y[x] + wfR_zp_y[x] + wfR_z_yp[x] + wfR_z_ym[x] + wfR_z_y[xm] + wfR_z_y[xp]) +
(wfR_zmm_y[x] + wfR_zpp_y[x] + wfR_z_ypp[x] + wfR_z_ymm[x] + wfR_z_y[xmm] + wfR_z_y[xpp])
);
float pe = V_z_y[x] * wfR_z_y[x];
wfIP_z_y[x] = wfIM_z_y[x] - m_deltaT * (ke + pe);
}
}
}, m_multiThread);
// Optionally perform damping to suppress reflection and transmission at the borders.
if ((m_dampingBorderWidth > 0) && (m_dampingFactor > 0.0f))
{
ApplyDamping(wf);
}
}