/// <summary>Computes M*x and stores the result in y. Does not automatically read result from device memory</summary>
/// <param name="M">Sparse matrix</param>
/// <param name="x">Vector to be multiplied</param>
/// <param name="y">Result</param>
public void Multiply(CLImgSparseMatrix M, CLImgVector x, CLImgVector y)
{
if (x.Length != M.MatrixDimension || y.Length != M.MatrixDimension)
{
throw new Exception("M, x and y dimensions not compatible");
}
if (CLCalc.CLAcceleration == CLCalc.CLAccelerationType.UsingCL)
{
CLNonZeroElemsPerRow.WriteToDevice(new int[] { M.NonZeroElemsPerRow });
CLCalc.Program.MemoryObject[] args = new CLCalc.Program.MemoryObject[] { M.CLMatrixData, M.CLColumns, x.CLVector, y.CLVector, CLNonZeroElemsPerRow };
//Ideally matrix dimension should be a multiple of 4, but OK if it's not
kernelSparseMatrixVecMult.Execute(args, 1 + ((M.MatrixDimension - 1) >> 2));
}
else
{
y.VectorData = MultiplyNoCL(M, x);
}
}
/// <summary>Computes product of sparse matrix M and vector x</summary>
/// <param name="M">Sparse matrix</param>
/// <param name="x">Vector to be multiplied</param>
public float[] MultiplyNoCL(CLImgSparseMatrix M, CLImgVector x)
{
if (x.Length != M.MatrixDimension)
{
throw new Exception("M and x dimensions not compatible");
}
float[] resp = new float[x.Length];
for (int i = 0; i < M.MatrixDimension; i++)
{
for (int j = 0; j < M.NonZeroElemsPerRow; j++)
{
if (M.Columns[j + M.NonZeroElemsPerRow * i] >= 0)
{
resp[i] += M.MatrixData[j + M.NonZeroElemsPerRow * i] * x.VectorData[M.Columns[j + M.NonZeroElemsPerRow * i]];
}
}
}
return(resp);
}
/// <summary>Solves linear system Mx = b using conjugate gradient method. Doesn't try to improve the solution obtained.</summary>
/// <param name="M">Matrix M</param>
/// <param name="b">Vector b</param>
/// <param name="tol">Error tolerance</param>
public void LinSolveCLStep(CLImgSparseMatrix M, CLImgVector b, float tol)
{
int n = b.Length;
int nBy4 = 1 + ((n - 1) >> 2);
if (lambda == null)
{
lambda = new float[1];
CLlambda = new CLCalc.Program.Variable(lambda);
}
if (r == null || r.Length != n)
{
r = new CLImgVector(n);
p = new CLImgVector(n);
x = new CLImgVector(n);
Ap = new CLImgVector(n);
temp = new CLImgVector(n);
}
if (temp == null)
{
temp = new CLImgVector(n);
}
float alpha, beta, RDotROld, RDotR;
//Initialization
Multiply(M, x, Ap);
CLCalc.Program.MemoryObject[] args = new CLCalc.Program.MemoryObject[] { b.CLVector, Ap.CLVector, r.CLVector, p.CLVector };
kernelInitRP.Execute(args, nBy4);
//Loop
int count = 0;
RDotR = DotProduct(r, r);
while ((RDotR > tol) && (count < n * MAXITER))
{
RDotROld = RDotR;
//if ((count & 0x0080) == 0)
//{
// Multiply(M, x, Ap);
// args = new CLCalc.Program.MemoryObject[] { b.CLVector, Ap.CLVector, r.CLVector, p.CLVector };
// kernelInitRP.Execute(args, nBy4);
//}
Multiply(M, p, Ap);
alpha = RDotROld / DotProduct(Ap, p);
//Update x
kernelCopyToTemp.Execute(new CLCalc.Program.MemoryObject[] { x.CLVector, temp.CLVector }, nBy4);
lambda[0] = alpha; CLlambda.WriteToDevice(lambda);
kernelMultiplyAdd.Execute(new CLCalc.Program.MemoryObject[] { CLlambda, p.CLVector, temp.CLVector, x.CLVector }, nBy4);
//Update r
kernelCopyToTemp.Execute(new CLCalc.Program.MemoryObject[] { r.CLVector, temp.CLVector }, nBy4);
lambda[0] = -alpha; CLlambda.WriteToDevice(lambda);
kernelMultiplyAdd.Execute(new CLCalc.Program.MemoryObject[] { CLlambda, Ap.CLVector, temp.CLVector, r.CLVector }, nBy4);
RDotR = DotProduct(r, r);
beta = RDotR / RDotROld;
//Update p
kernelCopyToTemp.Execute(new CLCalc.Program.MemoryObject[] { p.CLVector, temp.CLVector }, nBy4);
lambda[0] = beta; CLlambda.WriteToDevice(lambda);
kernelMultiplyAdd.Execute(new CLCalc.Program.MemoryObject[] { CLlambda, temp.CLVector, r.CLVector, p.CLVector }, nBy4);
count++;
}
}
/// <summary>Solves linear system Mx = b using conjugate gradient method. Writes variables to Device memory. Improves solution if accuracy is low.</summary>
/// <param name="M">Matrix M</param>
/// <param name="b">Vector b</param>
/// <param name="tol">Error tolerance</param>
public float[] LinSolveCL(CLImgSparseMatrix M, CLImgVector b, float tol)
{
if (b.Length != M.MatrixDimension)
{
throw new Exception("M and x dimensions not compatible");
}
int n = b.Length;
tol = Math.Abs(tol);
//Writes M to device memory
M.WriteToDevice();
//Backs up b data
float[] bbkp = new float[n];
for (int i = 0; i < n; i++)
{
bbkp[i] = b.VectorData[i];
}
//Residue variables
double ResidueSumSquares = 1E100;
double resAnt = 1E200;
double[] dblResidues = new double[n];
float[] Solution = new float[n];
while (ResidueSumSquares > tol && Math.Abs(resAnt - ResidueSumSquares) >= tol && resAnt > ResidueSumSquares)
{
//Check if solution is not improving anymore
resAnt = ResidueSumSquares;
b.WriteToDevice();
LinSolveCLStep(M, b, tol);
//Solution
x.ReadFromDevice();
if (ResidueSumSquares == tol * 2)
{
//Copies solution
for (int i = 0; i < n; i++)
{
Solution[i] = x.VectorData[i];
}
}
else
{
//Improves solution
for (int i = 0; i < n; i++)
{
Solution[i] -= x.VectorData[i];
x.VectorData[i] = Solution[i];
}
}
//Compute residue sum of squares and improves solution
dblResidues = ExactMultiply(M, x);
ResidueSumSquares = 0;
for (int i = 0; i < n; i++)
{
//Computes residues
dblResidues[i] = dblResidues[i] - (double)bbkp[i];
ResidueSumSquares += dblResidues[i] * dblResidues[i];
b.VectorData[i] = (float)dblResidues[i];
}
}
//Restores b data
for (int i = 0; i < n; i++)
{
b.VectorData[i] = bbkp[i];
}
return(Solution);
}
/// <summary>Solves linear system Mx = b using conjugate gradient method</summary>
/// <param name="M">Matrix M</param>
/// <param name="b">Vector b</param>
/// <param name="tol">Error tolerance</param>
public float[] LinSolveNoCL(CLImgSparseMatrix M, CLImgVector b, float tol)
{
if (b.Length != M.MatrixDimension)
{
throw new Exception("M and x dimensions not compatible");
}
int n = b.Length;
if (r == null || r.Length != n)
{
r = new CLImgVector(n);
p = new CLImgVector(n);
x = new CLImgVector(n);
Ap = new CLImgVector(n);
}
float alpha, beta, RDotROld, RDotR;
//Initialization
Ap.VectorData = MultiplyNoCL(M, x);
for (int i = 0; i < n; i++)
{
r.VectorData[i] = b.VectorData[i] - Ap.VectorData[i];
p.VectorData[i] = r.VectorData[i];
}
//Loop
int count = 0;
RDotR = DotProductNoCL(r, r);
while ((RDotR > tol) && (count < n * MAXITER))
{
RDotROld = RDotR;
Ap.VectorData = MultiplyNoCL(M, p);
alpha = RDotROld / DotProductNoCL(Ap, p);
for (int i = 0; i < n; i++)
{
x.VectorData[i] += alpha * p.VectorData[i];
r.VectorData[i] -= alpha * Ap.VectorData[i];
}
RDotR = DotProductNoCL(r, r);
beta = RDotR / RDotROld;
for (int i = 0; i < n; i++)
{
p.VectorData[i] = r.VectorData[i] + beta * p.VectorData[i];
}
count++;
}
float[] resp = new float[n];
for (int i = 0; i < n; i++)
{
resp[i] = x.VectorData[i];
}
return(resp);
}
/// <summary>Computes product of sparse matrix M and vector x</summary>
/// <param name="M">Sparse matrix</param>
/// <param name="x">Vector to be multiplied</param>
public float[] MultiplyNoCL(CLImgSparseMatrix M, CLImgVector x)
{
if (x.Length != M.MatrixDimension) throw new Exception("M and x dimensions not compatible");
float[] resp = new float[x.Length];
for (int i = 0; i < M.MatrixDimension; i++)
{
for (int j = 0; j < M.NonZeroElemsPerRow; j++)
{
if (M.Columns[j + M.NonZeroElemsPerRow * i] >= 0)
resp[i] += M.MatrixData[j + M.NonZeroElemsPerRow * i] * x.VectorData[M.Columns[j + M.NonZeroElemsPerRow * i]];
}
}
return resp;
}
/// <summary>Computes M*x and stores the result in y. Does not automatically read result from device memory</summary>
/// <param name="M">Sparse matrix</param>
/// <param name="x">Vector to be multiplied</param>
/// <param name="y">Result</param>
public void Multiply(CLImgSparseMatrix M, CLImgVector x, CLImgVector y)
{
if (x.Length != M.MatrixDimension || y.Length != M.MatrixDimension) throw new Exception("M, x and y dimensions not compatible");
if (CLCalc.CLAcceleration == CLCalc.CLAccelerationType.UsingCL)
{
CLNonZeroElemsPerRow.WriteToDevice(new int[] { M.NonZeroElemsPerRow });
CLCalc.Program.MemoryObject[] args = new CLCalc.Program.MemoryObject[] { M.CLMatrixData, M.CLColumns, x.CLVector, y.CLVector, CLNonZeroElemsPerRow };
//Ideally matrix dimension should be a multiple of 4, but OK if it's not
kernelSparseMatrixVecMult.Execute(args, 1 + ((M.MatrixDimension - 1) >> 2));
}
else
{
y.VectorData = MultiplyNoCL(M, x);
}
}
/// <summary>Solves linear system Mx = b using conjugate gradient method</summary>
/// <param name="M">Matrix M</param>
/// <param name="b">Vector b</param>
/// <param name="tol">Error tolerance</param>
public float[] LinSolveNoCL(CLImgSparseMatrix M, CLImgVector b, float tol)
{
if (b.Length != M.MatrixDimension) throw new Exception("M and x dimensions not compatible");
int n = b.Length;
if (r == null || r.Length != n)
{
r = new CLImgVector(n);
p = new CLImgVector(n);
x = new CLImgVector(n);
Ap = new CLImgVector(n);
}
float alpha, beta, RDotROld, RDotR;
//Initialization
Ap.VectorData = MultiplyNoCL(M, x);
for (int i = 0; i < n; i++)
{
r.VectorData[i] = b.VectorData[i] - Ap.VectorData[i];
p.VectorData[i] = r.VectorData[i];
}
//Loop
int count = 0;
RDotR = DotProductNoCL(r, r);
while ((RDotR > tol) && (count < n * MAXITER))
{
RDotROld = RDotR;
Ap.VectorData = MultiplyNoCL(M, p);
alpha = RDotROld / DotProductNoCL(Ap, p);
for (int i = 0; i < n; i++)
{
x.VectorData[i] += alpha * p.VectorData[i];
r.VectorData[i] -= alpha * Ap.VectorData[i];
}
RDotR = DotProductNoCL(r, r);
beta = RDotR / RDotROld;
for (int i = 0; i < n; i++)
{
p.VectorData[i] = r.VectorData[i] + beta * p.VectorData[i];
}
count++;
}
float[] resp = new float[n];
for (int i = 0; i < n; i++) resp[i] = x.VectorData[i];
return resp;
}
/// <summary>Solves linear system Mx = b using conjugate gradient method. Doesn't try to improve the solution obtained.</summary>
/// <param name="M">Matrix M</param>
/// <param name="b">Vector b</param>
/// <param name="tol">Error tolerance</param>
/// <param name="x">Initial guess</param>
public void LinSolveCLStep(CLImgSparseMatrix M, CLImgVector b, float tol, ref CLImgVector x)
{
int n = b.Length;
int nBy4 = 1 + ((n - 1) >> 2);
if (lambda == null)
{
lambda = new float[1];
CLlambda = new CLCalc.Program.Variable(lambda);
}
if (r == null || r.Length != n)
{
r = new CLImgVector(n);
p = new CLImgVector(n);
//x = new CLImgVector(n);
Ap = new CLImgVector(n);
temp = new CLImgVector(n);
}
if (temp == null) temp = new CLImgVector(n);
if (x == null || x.Length != n) x = new CLImgVector(n);
float alpha, beta, RDotROld, RDotR;
//Initialization
Multiply(M, x, Ap);
CLCalc.Program.MemoryObject[] args = new CLCalc.Program.MemoryObject[] { b.CLVector, Ap.CLVector, r.CLVector, p.CLVector };
kernelInitRP.Execute(args, nBy4);
//Loop
int count = 0;
RDotR = DotProduct(r, r);
while (count<1 || ((RDotR > tol) && (count < n*MAXITER)))
{
RDotROld = RDotR;
//if ((count & 0x0080) == 0)
//{
// Multiply(M, x, Ap);
// args = new CLCalc.Program.MemoryObject[] { b.CLVector, Ap.CLVector, r.CLVector, p.CLVector };
// kernelInitRP.Execute(args, nBy4);
//}
Multiply(M, p, Ap);
alpha = RDotROld / DotProduct(Ap, p);
//Update x
kernelCopyToTemp.Execute(new CLCalc.Program.MemoryObject[] { x.CLVector, temp.CLVector }, nBy4);
lambda[0] = alpha; CLlambda.WriteToDevice(lambda);
kernelMultiplyAdd.Execute(new CLCalc.Program.MemoryObject[] { CLlambda, p.CLVector, temp.CLVector, x.CLVector }, nBy4);
//Update r
kernelCopyToTemp.Execute(new CLCalc.Program.MemoryObject[] { r.CLVector, temp.CLVector }, nBy4);
lambda[0] = -alpha; CLlambda.WriteToDevice(lambda);
kernelMultiplyAdd.Execute(new CLCalc.Program.MemoryObject[] { CLlambda, Ap.CLVector, temp.CLVector, r.CLVector }, nBy4);
RDotR = DotProduct(r, r);
beta = RDotR / RDotROld;
//Update p
kernelCopyToTemp.Execute(new CLCalc.Program.MemoryObject[] { p.CLVector, temp.CLVector }, nBy4);
lambda[0] = beta; CLlambda.WriteToDevice(lambda);
kernelMultiplyAdd.Execute(new CLCalc.Program.MemoryObject[] { CLlambda, temp.CLVector, r.CLVector, p.CLVector }, nBy4);
count++;
}
}
/// <summary>Solves linear system Mx = b using conjugate gradient method. Writes variables to Device memory. Improves solution if accuracy is low.</summary>
/// <param name="M">Matrix M</param>
/// <param name="b">Vector b</param>
/// <param name="tol">Error tolerance</param>
public float[] LinSolveCL(CLImgSparseMatrix M, CLImgVector b, float tol)
{
if (b.Length != M.MatrixDimension) throw new Exception("M and x dimensions not compatible");
int n = b.Length;
tol = Math.Abs(tol);
//Writes M to device memory
M.WriteToDevice();
////Preconditions M
//float[] preC = JacobiPrecondition(M);
////Preconditions b using M
//JacobiPrecondition(preC, b);
//Backs up b data
float[] bbkp = new float[n];
for (int i = 0; i < n; i++) bbkp[i] = b.VectorData[i];
//Residue variables
double ResidueSumSquares = 1E100;
double resAnt = 1E200;
double[] dblResidues = new double[n];
float[] Solution = new float[n];
while (ResidueSumSquares > tol && Math.Abs(resAnt - ResidueSumSquares) >= tol && resAnt > ResidueSumSquares)
{
//Check if solution is not improving anymore
resAnt = ResidueSumSquares;
b.WriteToDevice();
LinSolveCLStep(M, b, tol, ref x);
//Solution
x.ReadFromDevice();
if (ResidueSumSquares == tol * 2)
{
//Copies solution
for (int i = 0; i < n; i++)
{
Solution[i] = x.VectorData[i];
}
}
else
{
//Improves solution
for (int i = 0; i < n; i++)
{
Solution[i] -= x.VectorData[i];
x.VectorData[i] = Solution[i];
}
}
//Compute residue sum of squares and improves solution
dblResidues = ExactMultiply(M, x);
ResidueSumSquares = 0;
for (int i = 0; i < n; i++)
{
//Computes residues
dblResidues[i] = dblResidues[i] - (double)bbkp[i];
ResidueSumSquares += dblResidues[i] * dblResidues[i];
b.VectorData[i] = (float)dblResidues[i];
}
}
//Restores b data
for (int i = 0; i < n; i++) b.VectorData[i] = bbkp[i];
return Solution;
}
