// Reduce give matrix to top PC components.
public float[][] DoPca(float[][] A, int eigenCount)
{
GpuDevice gpu = new GpuDevice();
var cc = gpu.CreateConstBuffer <PcaConstants>(0);
bool transposing = (A.Length > A[0].Length);
cc.c.eigenCount = eigenCount;
cc.c.rows = transposing ? A[0].Length : A.Length;
cc.c.columns = (!transposing) ? A[0].Length : A.Length;
var resultBuf = gpu.CreateBufferRW(3, 4, 1); // to receive the total changes.
var resultStaging = gpu.CreateStagingBuffer(resultBuf);
Buffer tableBuf = gpu.CreateBufferRO(cc.c.rows * cc.c.columns, 4, 0);
double[] colMean = new double[A[0].Length];
Parallel.For(0, A[0].Length, col => {
colMean[col] = 0.0;
for (int row = 0; row < A.Length; row++)
{
colMean[col] += A[row][col];
}
colMean[col] /= A.Length;
});
using (var ds = gpu.NewWriteStream(tableBuf)) {
float[] buf = new float[cc.c.rows * cc.c.columns];
if (transposing)
{
Parallel.For(0, cc.c.columns, col => {
int offset = col * cc.c.rows;
for (int row = 0; row < cc.c.rows; row++)
{
buf[offset + row] = (float)(A[col][row] - colMean[row]);
}
});
}
else
{
Parallel.For(0, cc.c.columns, col => {
int offset = col * cc.c.rows;
for (int row = 0; row < cc.c.rows; row++)
{
buf[offset + row] = (float)(A[row][col] - colMean[col]);
}
});
}
ds.WriteRange(buf);
}
cc.c.covFactor = transposing ? 1.0f / (cc.c.columns - 1) : 1.0f / (cc.c.rows - 1);
Buffer covBuf = gpu.CreateBufferRW(cc.c.rows * cc.c.rows, 4, 0);
using (var shader = gpu.LoadShader("TsneDx.PcaCreateCovMatrix.cso")) {
gpu.SetShader(shader);
cc.c.groupNumber = 256;
for (int iBlock = 0; iBlock < cc.c.rows; iBlock += cc.c.groupNumber)
{
cc.c.iBlock = iBlock;
cc.Upload();
gpu.Run(cc.c.groupNumber);
}
}
var eVectorBuf = gpu.CreateBufferRW(cc.c.rows, 4, 2);
var eVectorStaging = gpu.CreateStagingBuffer(eVectorBuf);
var eVector2Buf = gpu.CreateBufferRW(cc.c.rows, 4, 3);
var sdInit = gpu.LoadShader("TsneDx.PcaInitIteration.cso");
var sdStep = gpu.LoadShader("TsneDx.PcaIterateOneStep.cso");
var sdNorm = gpu.LoadShader("TsneDx.PcaCalculateNormal.cso");
var sdAdjCov = gpu.LoadShader("TsneDx.PcaAdjustCovMatrix.cso");
gpu.SetShader(sdInit);
cc.c.eigenIdx = 0;
cc.Upload();
gpu.Run();
float preEigen = 1e30f;
float newEigen = 0;
float[][] eVectors = new float[eigenCount][];
double[] eValues = new double[eigenCount];
for (int eigenIdx = 0; eigenIdx < eigenCount; eigenIdx++)
{
cc.c.groupNumber = 256;
cc.Upload();
for (int repeat = 0; repeat < MAX_ITERATION; repeat++)
{
gpu.SetShader(sdStep);
gpu.Run(cc.c.groupNumber);
gpu.SetShader(sdNorm);
gpu.Run(1);
newEigen = gpu.ReadFloat(resultStaging, resultBuf);
double delta = Math.Abs((newEigen - preEigen) / preEigen);
if (delta < epsilon)
{
break;
}
preEigen = newEigen;
}
eValues[eigenIdx] = (double)newEigen;
// Eigenvector with extrem small eigenvalue (i.e. 0.0) will be ignored and stop the calculation.
if (Math.Abs(eValues[eigenIdx] / eValues[0]) < stopEpsilon)
{
Array.Resize(ref eValues, eigenIdx);
Array.Resize(ref eVectors, eigenIdx);
break;
}
eVectors[eigenIdx] = new float[cc.c.rows];
Array.Copy(gpu.ReadRange <float>(eVectorStaging, eVectorBuf, cc.c.rows), eVectors[eigenIdx], cc.c.rows);
if (eigenIdx == (eigenCount - 1))
{
break;
}
// Adjust the covariance matrix.
gpu.SetShader(sdAdjCov);
cc.c.groupNumber = 128;
cc.Upload();
gpu.Run(cc.c.groupNumber);
// Initialize the iteration loop for the next eigen-vector.
gpu.SetShader(sdInit);
cc.c.eigenIdx = eigenIdx + 1;
cc.Upload();
gpu.Run();
//CmdSynchronize();
}
if (!transposing)
{
using (var shader = gpu.LoadShader("TsneDx.PcaTransposeEigenvectors.cso")) {
int eRows = eVectors.Length;
int eColumns = eVectors[0].Length;
Buffer eigenList1 = gpu.CreateBufferRO(eRows * eColumns, 4, 1);
double[] S = eValues.Select(x => 1.0 / Math.Sqrt(Math.Abs(x * (eVectors[0].Length - 1)))).ToArray();
float[] eVector1 = new float[eRows * eColumns];
for (int row = 0; row < eRows; row++)
{
for (int col = 0; col < eColumns; col++)
{
eVector1[row * eColumns + col] = (float)(S[row] * eVectors[row][col]);
}
}
using (var ds = gpu.NewWriteStream(eigenList1))
ds.WriteRange(eVector1);
Buffer eigenList2 = gpu.CreateBufferRW(eVectors.Length * cc.c.columns, 4, 4);
gpu.SetShader(shader);
cc.c.groupNumber = 128;
cc.c.eigenCount = eVectors.Length;
cc.Upload();
gpu.Run(cc.c.groupNumber);
float[] eVectors2 = gpu.ReadRange <float>(eigenList2, eVectors.Length * cc.c.columns);
eVectors = new float[eVectors.Length][];
for (int row = 0; row < eVectors.Length; row++)
{
eVectors[row] = new float[cc.c.columns];
}
Parallel.For(0, eVectors.Length, row => {
Array.Copy(eVectors2, row * cc.c.columns, eVectors[row], 0, cc.c.columns);
});
TsneDx.SafeDispose(eigenList1, eigenList2);
}
}
float[][] B = null;
cc.c.rows = A.Length;
cc.c.columns = A[0].Length;
cc.c.eigenCount = eVectors.Length;
cc.Upload();
if (transposing)
{
// The tableBuf on GPU is in wrong matrix order. We need to upload the tableBuf in needed order here.
TsneDx.SafeDispose(tableBuf);
tableBuf = gpu.CreateBufferRO(cc.c.rows * cc.c.columns, 4, 0);
Parallel.For(0, cc.c.rows, row => {
for (int col = 0; col < cc.c.columns; col++)
{
A[row][col] -= (float)colMean[col];
}
});
gpu.WriteMarix(tableBuf, A);
}
Buffer eigenTable = gpu.CreateBufferRO(cc.c.eigenCount * cc.c.columns, 4, 1);
gpu.WriteMarix(eigenTable, eVectors);
TsneDx.SafeDispose(resultBuf);
resultBuf = gpu.CreateBufferRW(cc.c.rows * cc.c.eigenCount, 4, 1);
using (var shader = gpu.LoadShader("TsneDx.PcaReduceMatrix.cso")) {
try {
gpu.SetShader(shader);
const int GROUP_NR = 256;
gpu.Run(GROUP_NR);
float[] buf = gpu.ReadRange <float>(resultBuf, cc.c.rows * cc.c.eigenCount);
B = new float[cc.c.rows][];
for (int row = 0; row < cc.c.rows; row++)
{
B[row] = new float[cc.c.eigenCount];
}
Parallel.For(0, cc.c.rows, row => {
Array.Copy(buf, row * cc.c.eigenCount, B[row], 0, cc.c.eigenCount);
});
} catch (SharpDX.SharpDXException ex) {
string msg = ex.Message;
Console.WriteLine("GPU operation timeouted: Please try to enlarge the TDR value");
}
}
TsneDx.SafeDispose(eigenTable, sdInit, sdStep, sdNorm, sdAdjCov, eVectorBuf,
eVectorStaging, eVector2Buf, resultBuf, resultStaging, covBuf, tableBuf, cc, gpu);
return(B);
}