public float[][] Fit(float[][] X)
{
int exaggerationLength = (int)(MaxEpochs * ExaggerationRatio);
gpu = new GpuDevice();
cc = gpu.CreateConstantBuffer <TsneMapConstants>(0);
int N = X.Length;
cc.c.columns = X[0].Length;
cc.c.N = N;
cc.c.outDim = OutDim;
cc.c.metricType = MetricType;
#region Initialize Y
Buffer Y2Buf = null;
Buffer Y3Buf = null;
Buffer Y3StagingBuf = null;
Buffer Y2StagingBuf = null;
Buffer v2Buf = null;
Buffer v3Buf = null;
if (cc.c.outDim <= 2)
{
Y2Buf = gpu.CreateBufferRW(N, 8, 3);
Y2StagingBuf = gpu.CreateStagingBuffer(Y2Buf);
v2Buf = gpu.CreateBufferRW(N, 2 * 8, 5);
}
else
{
Y3Buf = gpu.CreateBufferRW(N, 12, 4);
Y3StagingBuf = gpu.CreateStagingBuffer(Y3Buf);
v3Buf = gpu.CreateBufferRW(N, 2 * 12, 6);
}
float rang = 0.05f;
Random rGenerator = new Random(435243);
if (cc.c.outDim <= 2)
{
using (var ws = gpu.NewWriteStream(v2Buf)) {
for (int row = 0; row < N; row++)
{
ws.Write <float>(0, 1, 0, 1);
}
}
using (var ws = gpu.NewWriteStream(Y2Buf)) {
for (int row = 0; row < N; row++)
{
for (int col = 0; col < cc.c.outDim; col++)
{
ws.Write((float)(rang * rGenerator.NextDouble() - rang / 2));
}
if (cc.c.outDim == 1)
{
ws.Write(0.0f);
}
}
}
}
else
{
using (var ws = gpu.NewWriteStream(v3Buf)) {
for (int row = 0; row < N; row++)
{
ws.Write <float>(0, 1, 0, 1, 0, 1);
}
}
using (var ws = gpu.NewWriteStream(Y3Buf)) {
for (int row = 0; row < N; row++)
{
for (int col = 0; col < cc.c.outDim; col++)
{
ws.Write((float)(rang * rGenerator.NextDouble() - rang / 2));
}
}
}
}
#endregion
#region Upload data table and initialize the distance matrix
// Used to aggregate values created by parallel threads.
// the size of of groupMaxBuf must be large enoght to hold a float value for each thread started in parallel.
// Notice: gpu.Run(k) will start k*GROUP_SIZE threads.
int gpSize = Math.Max(GpuGroupSize, MaxGroupNumber * GroupSize);
gpSize = Math.Max(gpSize, MaxGroupNumberHyp * GroupSizeHyp);
groupMaxBuf = gpu.CreateBufferRW(gpSize, 4, 7);
resultBuf = gpu.CreateBufferRW(3, 4, 2); // to receive the total changes.
resultStaging = gpu.CreateStagingBuffer(resultBuf);
tableBuf = gpu.CreateBufferRO(N * cc.c.columns, 4, 0);
if (MetricType == 1)
{
NormalizeTable(X);
}
gpu.WriteMarix(tableBuf, X, true);
const int MinCpuDimension = 100; // minimal dimension to trigger CPU caching.
const int MaxDimension = 64; // maximal dimension (table columns) for fast EuclideanNoCache shader. Must be the same as MAX_DIMENSION.
const int MaxDimensionS = 32; // maximal dimension (table columns) for fast EuclideanNoCache shader. Must be the same as MAX_DIMENSIONs.
if (N <= CacheLimit)
{
cachingMode = CachingMode.OnGpu;
}
else
{
if ((cc.c.columns > MinCpuDimension) && ((double)N * N * 4) < ((double)MaxCpuCacheSize * 1024.0 * 1024.0))
{
cachingMode = CachingMode.OnCpu;
}
else
{
if (cc.c.columns < MaxDimensionS)
{
cachingMode = CachingMode.OnFlySmS;
}
else if (cc.c.columns < MaxDimension)
{
cachingMode = CachingMode.OnFlySm;
}
else
{
cachingMode = CachingMode.OnFly;
}
}
}
#endregion
cc.c.targetH = (float)Math.Log(PerplexityRatio * N);
if (cachingMode == CachingMode.OnGpu)
{
CalculateP();
}
else if (cachingMode == CachingMode.OnCpu)
{
InitializePCpu();
}
else // (cachingMode == CachingMode.OnFly[Sm,SmS])
{
InitializeP();
}
using (var sd = gpu.LoadShader("TsneDx.CalculateSumQ.cso")) {
gpu.SetShader(sd);
cc.c.groupNumber = 256;
for (int i = 0; i < N; i += cc.c.groupNumber)
{
cc.c.blockIdx = i;
cc.Upload();
gpu.Run(cc.c.groupNumber);
}
cc.c.blockIdx = -1;
cc.Upload();
gpu.Run();
}
var sdNames = new Dictionary <CachingMode, string>()
{
{ CachingMode.OnGpu, "TsneDx.OneStep.cso" },
{ CachingMode.OnCpu, "TsneDx.OneStepCpuCache.cso" },
{ CachingMode.OnFly, "TsneDx.OneStepNoCache.cso" },
{ CachingMode.OnFlySm, "TsneDx.FastStep.cso" },
{ CachingMode.OnFlySmS, "TsneDx.FastStepS.cso" },
};
ComputeShader csOneStep = gpu.LoadShader(sdNames[cachingMode]);
ComputeShader csSumUp = gpu.LoadShader("TsneDx.OneStepSumUp.cso");
int stepCounter = 0;
while (true)
{
if (stepCounter < exaggerationLength)
{
if (ExaggerationSmoothen)
{
int len = (int)(0.9 * MaxEpochs);
if (stepCounter < len)
{
double t = (double)stepCounter / len;
t = Math.Sqrt(Math.Sqrt(t));
cc.c.PFactor = (float)((1 - t) * ExaggerationFactor + t);
}
else
{
cc.c.PFactor = 1.0f;
}
}
else
{
cc.c.PFactor = (float)ExaggerationFactor;
}
}
else
{
cc.c.PFactor = 1.0f;
}
gpu.SetShader(csOneStep);
if (cachingMode == CachingMode.OnGpu)
{
cc.c.groupNumber = MaxGroupNumber;
// Notice: cc.c.groupNumber*GroupSize must fit into groupMax[].
for (int bIdx = 0; bIdx < N; bIdx += cc.c.groupNumber * GroupSize)
{
cc.c.blockIdx = bIdx;
cc.Upload();
gpu.Run(cc.c.groupNumber);
}
cc.c.groupNumber = MaxGroupNumber * GroupSize;
}
else if (cachingMode == CachingMode.OnCpu)
{
int bSize = MaxGroupNumberHyp * GroupSizeHyp;
cc.c.groupNumber = MaxGroupNumberHyp;
for (int bIdx = 0; bIdx < N; bIdx += bSize)
{
gpu.WriteArray(cpuP, bIdx, Math.Min(N, bIdx + bSize), P2Buf);
cc.c.blockIdx = bIdx;
cc.Upload();
gpu.Run(cc.c.groupNumber);
}
cc.c.groupNumber = Math.Min(N, bSize);
}
else if ((cachingMode == CachingMode.OnFlySm) || (cachingMode == CachingMode.OnFlySmS))
{
const int GrSize = 64; // This value must match that of GR_SIZE in TsneMap.hlsl.
cc.c.groupNumber = MaxGroupNumber;
for (int bIdx = 0; bIdx < N; bIdx += cc.c.groupNumber * GrSize)
{
cc.c.blockIdx = bIdx;
cc.Upload();
gpu.Run(cc.c.groupNumber);
}
cc.c.groupNumber = cc.c.groupNumber * GrSize;
}
else // cachingMode==CachingMode.OnFly
{
cc.c.groupNumber = 128;
for (int bIdx = 0; bIdx < N; bIdx += cc.c.groupNumber)
{
cc.c.blockIdx = bIdx;
cc.Upload();
gpu.Run(cc.c.groupNumber);
}
}
//Notice: cc.c.groupNumber must be number of partial sumQ_next, which add up to sumQ for the next step.
gpu.SetShader(csSumUp);
cc.Upload();
gpu.Run();
currentVariation = gpu.ReadRange <float>(resultStaging, resultBuf, 3)[2] / N;
cc.c.mom = (float)((stepCounter < (MaxEpochs * momentumSwitch)) ? momentum : finalMomentum);
stepCounter++;
if (stepCounter % 10 == 0)
{
Console.Write('.');
}
if (stepCounter % 500 == 0)
{
Console.WriteLine();
}
if ((stepCounter >= MaxEpochs) || ((stepCounter >= (2 + exaggerationLength)) && (currentVariation < stopVariation)))
{
break;
}
}
Console.WriteLine();
float[][] Y = new float[N][];
using (var rs = gpu.NewReadStream((cc.c.outDim == 3) ? Y3StagingBuf : Y2StagingBuf, (cc.c.outDim == 3) ? Y3Buf : Y2Buf)) {
int outVDim = (cc.c.outDim == 3) ? 3 : 2;
for (int row = 0; row < N; row++)
{
Y[row] = rs.ReadRange <float>(outVDim);
}
}
if (cc.c.outDim == 1)
{
for (int i = 0; i < N; i++)
{
Y[i] = new float[] { Y[i][0] }
}
}
;
TsneDx.SafeDispose(csSumUp, csOneStep, PBuf, P2Buf, distanceBuf, tableBuf, resultBuf,
resultStaging, groupMaxBuf, Y3Buf, Y3StagingBuf, v3Buf, Y2Buf, Y2StagingBuf, v2Buf, cc, gpu);
return(AutoNormalize ? PcaNormalize.DoNormalize(Y) : Y);
}
// 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);
}
void InitializePCpu()
{
int N = cc.c.N;
const float DistanceScale = 100.0f;
const float eps = 2.22e-16f;
int bandSize = Math.Min(N, MaxGroupNumberHyp * GroupSizeHyp);
PBuf = gpu.CreateBufferRW(bandSize * N, 4, 1);
P2Buf = gpu.CreateBufferDynamic(bandSize * N, 4, 7); // dynamic buffer for fast uploading. Linked to Pcpu[] on HLSL.
int blockSize = 128; // Calculate so many rows per dispatch.
cpuP = new float[N][];
for (int i = 0; i < N; i++)
{
cpuP[i] = new float[N];
}
using (var distanceBuf = gpu.CreateBufferRW(blockSize * N, 4, 0))
using (var stagingBuf = gpu.CreateStagingBuffer(distanceBuf))
using (var sd = gpu.LoadShader("TsneDx.PartialDistance2.cso")) {
gpu.SetShader(sd);
for (int iBlock = 0; iBlock < N; iBlock += blockSize)
{
cc.c.blockIdx = iBlock;
cc.Upload();
gpu.Run(blockSize);
int iBlock2 = Math.Min(iBlock + blockSize, N);
int blockLen = (iBlock2 * (iBlock2 - 1) - iBlock * (iBlock - 1)) / 2;
float[] ret = gpu.ReadRange <float>(stagingBuf, distanceBuf, blockLen);
int idx = 0;
for (int row = iBlock; row < iBlock2; row++)
{
Array.Copy(ret, idx, cpuP[row], 0, row);
idx += row;
}
}
}
double distanceFactor = double.MinValue;
MT.For(1, N, i => {
float maxV = cpuP[i].Max();
lock (this)
distanceFactor = Math.Max(distanceFactor, maxV);
});
if (distanceFactor == 0)
{
throw new System.Exception("Distance metric degenerated: all components are zero.");
}
// Scale the distance to managable range [0, 100.0] to avoid degredation
// with exp function.
distanceFactor = DistanceScale / distanceFactor;
MT.For(1, N, i => {
for (int j = 0; j < i; j++)
{
cpuP[i][j] = (float)(cpuP[i][j] * distanceFactor);
}
});
MT.For(0, N, i => {
for (int j = 0; j < i; j++)
{
cpuP[j][i] = cpuP[i][j];
}
cpuP[i][i] = 0;
});
int bSize = MaxGroupNumberHyp * GroupSizeHyp;
using (var sd = gpu.LoadShader("TsneDx.Dist2Affinity.cso"))
using (var stagingBuf = gpu.CreateStagingBuffer(PBuf)) {
gpu.SetShader(sd);
for (int iBlock = 0; iBlock < N; iBlock += bSize)
{
cc.c.blockIdx = iBlock;
cc.Upload();
int iBlock2 = Math.Min(N, iBlock + bSize);
using (var ws = gpu.NewWriteStream(PBuf))
for (int row = iBlock; row < iBlock2; row++)
{
ws.WriteRange(cpuP[row]);
}
gpu.Run(MaxGroupNumberHyp);
using (var rs = gpu.NewReadStream(stagingBuf, PBuf))
for (int row = iBlock; row < iBlock2; row++)
{
rs.ReadRange(cpuP[row], 0, N);
}
}
}
double sum = 0;
MT.For(0, N, i => {
double sum2 = 0.0;
for (int j = i + 1; j < N; j++)
{
cpuP[i][j] += cpuP[j][i];
sum2 += cpuP[i][j];
}
lock (this)
sum += sum2;
});
if (sum == 0)
{
throw new System.Exception("Perplexity too small!");
}
sum *= 2;
MT.For(0, N, i => {
for (int j = i + 1; j < N; j++)
{
cpuP[i][j] = (float)Math.Max(cpuP[i][j] / sum, eps);
cpuP[j][i] = cpuP[i][j];
}
cpuP[i][i] = 1.0f;
});
}