/// <summary>
/// Do symbolic factorization for current type.
/// </summary>
protected virtual int DoSymbolic()
{
int n = matrix.ColumnCount;
int nrhs = 1;
int error = 0;
var iparm = options.iparm;
var h = new List <GCHandle>();
try
{
var a = InteropHelper.Pin(matrix.Values, h);
var ia = InteropHelper.Pin(matrix.ColumnPointers, h);
var ja = InteropHelper.Pin(matrix.RowIndices, h);
// Reordering and Symbolic Factorization. This step also allocates
// all memory that is necessary for the factorization.
int phase = 11;
NativeMethods.pardiso(pt, ref maxfct, ref mnum, ref mtype, ref phase,
ref n, a, ia, ja, perm, ref nrhs, iparm, ref msglvl,
IntPtr.Zero, IntPtr.Zero, out error);
}
finally
{
InteropHelper.Free(h);
}
return(error);
}
/// <summary>
/// Solves a system of linear equations, Ax = b.
/// </summary>
/// <param name="input">Right hand side vector b.</param>
/// <param name="result">Solution vector x.</param>
public void Solve(T[] input, T[] result)
{
if (!factorized)
{
Factorize();
}
var handles = new List <GCHandle>();
try
{
var h_b = InteropHelper.Pin(input, handles);
var h_x = InteropHelper.Pin(result, handles);
int rows = input.Length;
int columns = result.Length;
Cuda.CopyToDevice(d_b, h_b, sizeT * rows);
// Solve A*x = b.
Check(Solve(rows, columns));
Cuda.CopyToHost(h_x, d_x, sizeT * columns);
}
finally
{
InteropHelper.Free(handles);
}
}
protected void Dispose(bool disposing)
{
if (pt != null && pt.Any(p => p != IntPtr.Zero))
{
int n = matrix.ColumnCount;
int nrhs = 1;
int error = 0;
var iparm = options.iparm;
var h = new List <GCHandle>();
try
{
var ia = InteropHelper.Pin(matrix.ColumnPointers, h);
var ja = InteropHelper.Pin(matrix.RowIndices, h);
// Release internal memory.
int phase = -1;
NativeMethods.pardiso(pt, ref maxfct, ref mnum, ref mtype, ref phase,
ref n, IntPtr.Zero, ia, ja, null, ref nrhs, iparm, ref msglvl,
IntPtr.Zero, IntPtr.Zero, out error);
}
finally
{
InteropHelper.Free(h);
}
pt = null;
}
}
protected virtual int DoNumeric()
{
if (qr == IntPtr.Zero)
{
throw new Exception("A call to DoNumeric() must be preceeded by DoSymbolic().");
}
var h = new List <GCHandle>();
try
{
var A = CreateSparse(matrix, h);
double tol = Constants.SPQR_DEFAULT_TOL;
int status = NativeMethods.SuiteSparseQR_C_numeric(tol, ref A, qr, ref common);
if (common.status != Constants.CHOLMOD_OK)
{
throw new CholmodException(common.status);
}
return(status);
}
finally
{
InteropHelper.Free(h);
}
}
/// <summary>
/// Solve multiple systems of linear equations.
/// </summary>
/// <param name="sys">The system to solve.</param>
/// <param name="input">Right hand side B</param>
/// <param name="result">Solution matrix X.</param>
protected virtual int DoSolve(CholmodSolve sys, DenseColumnMajorStorage <T> input, DenseColumnMajorStorage <T> result)
{
var h = new List <GCHandle>();
try
{
var B = CreateDense(input, h);
var ptr = NativeMethods.cholmod_solve((int)sys, ref L, ref B, ref common);
if (common.status != Constants.CHOLMOD_OK)
{
throw new CholmodException(common.status);
}
var X = (CholmodDense)Marshal.PtrToStructure(ptr, typeof(CholmodDense));
CopyDense(X, result);
NativeMethods.cholmod_free_dense(ref ptr, ref common);
return(1);
}
finally
{
InteropHelper.Free(h);
}
}
/// <summary>
/// Solve the standard eigenvalue problem in shift-invert mode.
/// </summary>
public override IEigenSolverResult SolveStandard(int k, Complex sigma, Spectrum job = Spectrum.LargestMagnitude)
{
if (!CheckSquare(A))
{
throw new InvalidOperationException("Cannot solve eigenvalue problem with non-square matrix.");
}
if (!Job.Validate(symmetric, job))
{
throw new ArgumentException("Invalid job for given eigenvalue problem.", "job");
}
var result = new ArpackResult(k, size, ComputeEigenVectors);
var handles = new List <GCHandle>();
var a = GetMatrix(A, handles);
var e = result.GetEigenvalueStorage(handles);
int conv = NativeMethods.ar_zi_ns_shift(GetJob(job), k, ArnoldiCount, Iterations,
Tolerance, sigma, ref a, ref e);
result.IterationsTaken = e.iterations;
result.ArnoldiCount = e.ncv;
result.ConvergedEigenValues = conv;
result.ErrorCode = e.info;
InteropHelper.Free(handles);
return(result);
}
/// <summary>
/// Do symbolic and numeric factorization for current type.
/// </summary>
protected virtual int DoFactorize()
{
int n = matrix.ColumnCount;
int nrhs = 1;
int error = 0;
var iparm = options.iparm;
var h = new List <GCHandle>();
try
{
var a = InteropHelper.Pin(matrix.Values, h);
var ia = InteropHelper.Pin(matrix.ColumnPointers, h);
var ja = InteropHelper.Pin(matrix.RowIndices, h);
// Analysis and numerical factorization.
int phase = 12;
NativeMethods.pardiso(pt, ref maxfct, ref mnum, ref mtype, ref phase,
ref n, a, ia, ja, perm, ref nrhs, iparm, ref msglvl,
IntPtr.Zero, IntPtr.Zero, out error);
}
finally
{
InteropHelper.Free(h);
}
return(error);
}
/// <summary>
/// Solve the generalized eigenvalue problem in user-defined shift-invert mode.
/// </summary>
public IEigenSolverResult SolveGeneralized(int k, double sigma, ShiftMode mode, Spectrum job = Spectrum.LargestMagnitude)
{
if (!symmetric && !(mode == ShiftMode.None || mode == ShiftMode.Regular))
{
throw new InvalidOperationException("This mode is only available for symmetric eigenvalue problems.");
}
if (!CheckSquare(A))
{
throw new InvalidOperationException("Cannot solve eigenvalue problem with non-square matrix.");
}
if (!Job.Validate(symmetric, job))
{
throw new ArgumentException("Invalid job for symmetric eigenvalue problem.", "job");
}
var result = new ArpackResult(k, size, ComputeEigenVectors, symmetric);
var handles = new List <GCHandle>();
var a = GetMatrix(A, handles);
var b = GetMatrix(B, handles);
var e = result.GetEigenvalueStorage(handles);
int conv = 0;
if (symmetric)
{
char m = 'S';
if (mode == ShiftMode.Buckling)
{
m = 'B';
}
else if (mode == ShiftMode.Cayley)
{
m = 'C';
}
conv = NativeMethods.ar_di_sg_shift(GetJob(job), m, k, ArnoldiCount, Iterations,
Tolerance, sigma, ref a, ref b, ref e);
}
else
{
conv = NativeMethods.ar_di_ng_shift(GetJob(job), k, ArnoldiCount, Iterations,
Tolerance, sigma, ref a, ref b, ref e);
}
result.IterationsTaken = e.iterations;
result.ArnoldiCount = e.ncv;
result.ConvergedEigenValues = conv;
result.ErrorCode = e.info;
InteropHelper.Free(handles);
return(result);
}
private MetisStatus Partition(int nparts, int[] part, MetisOptions options, bool kway)
{
int objval = 0;
if (part == null || part.Length < this.nvtxs)
{
return(MetisStatus.ERROR_INPUT);
}
var handles = new List <GCHandle>();
// Pin array data.
var p_part = InteropHelper.Pin(part, handles);
var p_xadj = InteropHelper.Pin(xadj, handles);
var p_adjncy = InteropHelper.Pin(adjncy, handles);
var p_vwgt = InteropHelper.Pin(vwgt, handles);
var p_ewgt = InteropHelper.Pin(adjwgt, handles);
var p_vsize = InteropHelper.Pin(vsize, handles);
var p_opts = options == null ? IntPtr.Zero : InteropHelper.Pin(options.raw, handles);
int l_nv = nvtxs;
int l_nw = ncon;
int status = 0;
try
{
if (kway)
{
status = NativeMethods.PartGraphKway(ref l_nv, ref l_nw, p_xadj, p_adjncy,
p_vwgt, p_vsize, p_ewgt, ref nparts, IntPtr.Zero, IntPtr.Zero,
p_opts, ref objval, p_part);
}
else
{
status = NativeMethods.PartGraphRecursive(ref l_nv, ref l_nw, p_xadj, p_adjncy,
p_vwgt, p_vsize, p_ewgt, ref nparts, IntPtr.Zero, IntPtr.Zero,
p_opts, ref objval, p_part);
}
}
catch (Exception)
{
throw;
}
finally
{
InteropHelper.Free(handles);
}
return((MetisStatus)status);
}
/// <inheritdoc />
public override FeastResult <double> SolveGeneralized(int m0, double emin, double emax, DenseColumnMajorStorage <double> subspace)
{
// TODO: check subspace matrix dimensions.
char uplo = 'F'; // Full matrix.
int n = A.RowCount;
double epsout; // Relative error on the trace.
int loop; // Number of refinement loops.
int m = m0; // Total number of eigenvalues found in the interval.
int info;
var E = new double[m0]; // Eigenvalues
var R = new double[m0]; // Residual
var X = subspace.Values; // Eigenvectors
var fpm = this.Options.fpm;
var h = new List <GCHandle>();
try
{
Increment(A);
Increment(B);
var a = InteropHelper.Pin(A.Values, h);
var ia = InteropHelper.Pin(A.ColumnPointers, h);
var ja = InteropHelper.Pin(A.RowIndices, h);
var b = InteropHelper.Pin(B.Values, h);
var ib = InteropHelper.Pin(B.ColumnPointers, h);
var jb = InteropHelper.Pin(B.RowIndices, h);
var pe = InteropHelper.Pin(E, h);
var px = InteropHelper.Pin(X, h);
var pr = InteropHelper.Pin(R, h);
NativeMethods.dfeast_scsrgv(ref uplo, ref n, a, ia, ja, b, ib, jb, fpm, out epsout, out loop, ref emin, ref emax, ref m0, pe, px, out m, pr, out info);
Decrement(A);
Decrement(B);
return(new FeastResult(info, m0, n, loop, epsout, m, E, subspace, R));
}
finally
{
InteropHelper.Free(h);
}
}
/// <summary>
/// Special case solving the standard real generalized eigenvalue problem with complex shift.
/// </summary>
/// <param name="k">The number of eigenvalues to compute.</param>
/// <param name="sigma_r">The real part of the complex shift.</param>
/// <param name="sigma_i">The imaginary part of the complex shift.</param>
/// <param name="part">Part to apply ('R' for real, 'I' for imaginary).</param>
/// <param name="job">The part of the spectrum to compute.</param>
/// <returns>The number of converged eigenvalues.</returns>
public IEigenSolverResult SolveGeneralized(int k, double sigma_r, double sigma_i, char part, Spectrum job = Spectrum.LargestMagnitude)
{
if (symmetric)
{
throw new InvalidOperationException("Complex shift doesn't apply to real symmetric eigenvalue problems.");
}
if (!CheckSquare(A))
{
throw new InvalidOperationException("Cannot solve eigenvalue problem with non-square matrix.");
}
if (!Job.ValidateGeneral(job))
{
throw new ArgumentException("Invalid job for non-symmetric eigenvalue problem.", "job");
}
part = char.ToUpperInvariant(part);
if (part != 'R' && part != 'I')
{
throw new ArgumentException("Invalid part specified for complex shift.", "part");
}
var result = new ArpackResult(k, size, ComputeEigenVectors, symmetric);
var handles = new List <GCHandle>();
var a = GetMatrix(A, handles);
var b = GetMatrix(B, handles);
var e = result.GetEigenvalueStorage(handles);
int conv = 0;
conv = NativeMethods.ar_di_ng_shift_cx(GetJob(job),
k, ArnoldiCount, Iterations, Tolerance,
part, sigma_r, sigma_i, ref a, ref b, ref e);
result.IterationsTaken = e.iterations;
result.ArnoldiCount = e.ncv;
result.ConvergedEigenValues = conv;
result.ErrorCode = e.info;
InteropHelper.Free(handles);
return(result);
}
protected virtual void Dispose(bool disposing)
{
if (disposing)
{
InteropHelper.Free(handles);
}
if (Lp != IntPtr.Zero)
{
NativeMethods.cholmod_free_factor(ref Lp, ref common);
NativeMethods.cholmod_finish(ref common);
L = default(CholmodFactor);
}
}
public override void Solve(double[] input, double[] result)
{
if (!factorized && DoFactorize() != 0)
{
throw new Exception(); // TODO: exception
}
var n = matrix.RowCount;
var h = new List <GCHandle>();
var b = InteropHelper.Pin(input, h);
var x = InteropHelper.Pin(result, h);
var t = InteropHelper.Pin(w, h);
try
{
// x = b(p)
if (NativeMethods.cs_di_ipvec(N.pinv, b, t, n) == 0)
{
return;
}
// x = L\x
if (NativeMethods.cs_di_lsolve(N.L, t) == 0)
{
return;
}
// x = U\x
if (NativeMethods.cs_di_usolve(N.U, t) == 0)
{
return;
}
// b(q) = x
if (NativeMethods.cs_di_pvec(S.q, t, x, n) == 0)
{
return;
}
}
finally
{
InteropHelper.Free(h);
}
}
/// <summary>
/// Compute singular values and the partial singular value decomposition.
/// </summary>
/// <param name="k">The number of singular values to compute.</param>
/// <param name="normal">Use normal equation to compute (squared) singular values.</param>
/// <param name="job">The part of the spectrum to compute.</param>
/// <returns>The number of converged singular values.</returns>
/// <remarks>
/// If <paramref name="normal"/> is true, the normal equation <c>(A'*A)*v = sigma*v</c>
/// is considered, where A is an m-by-n real matrix. This formulation is appropriate
/// when m >= n. The roles of A and A' must be reversed in the case that m < n.
///
/// The eigenvalues returned are the squared singular values of A. If requested, the
/// returned eigenvectors correspond to the right singular vectors, if <c>A = U*S*V'</c>.
/// The left singular vectors can be computed from the equation <c>A*v - sigma*u = 0</c>.
///
/// If <paramref name="normal"/> is false, the symmetric system <c>[0 A; A' 0]</c> is
/// considered (size m + n), where A is an m-by-n real matrix.
///
/// This problem can be used to obtain the decomposition <c>A = U*S*V'</c>. The positive
/// eigenvalues of this problem are the singular values of A (the eigenvalues come in
/// pairs, the negative eigenvalues have the same magnitude of the positive ones and
/// can be discarded). The columns of U can be extracted from the first m components
/// of the eigenvectors y, while the columns of V can be extracted from the remaining
/// n components.
/// </remarks>
public IEigenSolverResult SingularValues(int k, bool normal, Spectrum job = Spectrum.LargestMagnitude)
{
if (!Job.ValidateSymmetric(job))
{
throw new ArgumentException("Invalid job for singular value decomposition.", "job");
}
int m = A.RowCount;
int n = A.ColumnCount;
if (normal && m < n)
{
throw new InvalidOperationException("Number of columns must not be smaller than number of rows (use transposed matrix).");
}
int size = normal ? n : m + n;
var result = new ArpackResult(k, size, ComputeEigenVectors, true);
var handles = new List <GCHandle>();
var a = GetMatrix(A, handles);
var e = result.GetEigenvalueStorage(handles);
int conv = 0;
if (normal)
{
conv = NativeMethods.ar_di_svd_nrm(GetJob(job),
k, ArnoldiCount, Iterations, Tolerance, ref a, ref e);
}
else
{
conv = NativeMethods.ar_di_svd(GetJob(job),
k, ArnoldiCount, Iterations, Tolerance, ref a, ref e);
}
result.IterationsTaken = e.iterations;
result.ArnoldiCount = e.ncv;
result.ConvergedEigenValues = conv;
result.ErrorCode = e.info;
InteropHelper.Free(handles);
return(result);
}
public override void Solve(Complex[] input, Complex[] result)
{
if (!factorized && DoFactorize() != 0)
{
throw new Exception(); // TODO: exception
}
var n = matrix.RowCount;
var h = new List <GCHandle>();
var b = InteropHelper.Pin(input, h);
var x = InteropHelper.Pin(result, h);
var t = InteropHelper.Pin(w, h);
try
{
// x = P*b
if (NativeMethods.cs_ci_ipvec(S.pinv, b, t, n) == 0)
{
return;
}
// x = L\x
if (NativeMethods.cs_ci_lsolve(N.L, t) == 0)
{
return;
}
// x = L'\x
if (NativeMethods.cs_ci_ltsolve(N.L, t) == 0)
{
return;
}
// b = P'*x
if (NativeMethods.cs_ci_pvec(S.pinv, t, x, n) == 0)
{
return;
}
}
finally
{
InteropHelper.Free(h);
}
}
protected virtual void Dispose(bool disposing)
{
if (disposing)
{
InteropHelper.Free(handles);
}
if (L.Store != IntPtr.Zero)
{
NativeMethods.Destroy_SuperNode_Matrix(ref L);
L.Store = IntPtr.Zero;
}
if (U.Store != IntPtr.Zero)
{
NativeMethods.Destroy_CompCol_Matrix(ref U);
U.Store = IntPtr.Zero;
}
}
protected virtual int DoSolve(int sys, int method, DenseColumnMajorStorage <T> input, DenseColumnMajorStorage <T> result)
{
if (!factorized)
{
DoFactorize();
}
var h = new List <GCHandle>();
try
{
var B = CreateDense(input, h);
// Y = Q'*B
var Yp = NativeMethods.SuiteSparseQR_C_qmult(method, qr, ref B, ref common);
if (Yp == IntPtr.Zero)
{
return(-1000);
}
// X = R\(E*Y)
var Xp = NativeMethods.SuiteSparseQR_C_solve(sys, qr, Yp, ref common);
if (Xp == IntPtr.Zero)
{
return(-1000);
}
var X = (CholmodDense)Marshal.PtrToStructure(Xp, typeof(CholmodDense));
CopyDense(X, result);
Cholmod.NativeMethods.cholmod_free_dense(ref Yp, ref common);
Cholmod.NativeMethods.cholmod_free_dense(ref Xp, ref common);
return(1);
}
finally
{
InteropHelper.Free(h);
}
}
/// <summary>
/// Solve system of linear equations.
/// </summary>
/// <param name="sys">The system to solve.</param>
/// <param name="input">Right-hand side b.</param>
/// <param name="result">The solution x.</param>
/// <returns></returns>
/// <remarks>
/// Parameter sys corresponds to iparm[11]:
/// sys = 0: non-transposed
/// sys = 1: conjugate transposed
/// sys = 2: transposed
/// </remarks>
protected virtual int DoSolve(int sys, DenseColumnMajorStorage <T> input, DenseColumnMajorStorage <T> result)
{
int n = matrix.ColumnCount;
// The number of right-hand sides.
int nrhs = input.ColumnCount;
if (nrhs != result.ColumnCount)
{
throw new ArgumentException("result");
}
int error = 0;
var iparm = options.iparm;
var h = new List <GCHandle>();
try
{
var a = InteropHelper.Pin(matrix.Values, h);
var ia = InteropHelper.Pin(matrix.ColumnPointers, h);
var ja = InteropHelper.Pin(matrix.RowIndices, h);
var b = InteropHelper.Pin(input.Values, h);
var x = InteropHelper.Pin(result.Values, h);
iparm[11] = sys;
// Solve system.
int phase = 33;
NativeMethods.pardiso(pt, ref maxfct, ref mnum, ref mtype, ref phase,
ref n, a, ia, ja, perm, ref nrhs, iparm, ref msglvl,
b, x, out error);
}
finally
{
InteropHelper.Free(h);
}
return(error);
}
/// <summary>
/// Solve the generalized eigenvalue problem.
/// </summary>
public override IEigenSolverResult SolveGeneralized(int k, Spectrum job = Spectrum.LargestMagnitude)
{
if (!Job.Validate(symmetric, job))
{
throw new ArgumentException("Invalid job for given eigenvalue problem.", "job");
}
if (ArnoldiCount < k)
{
ArnoldiCount = Math.Min(3 * k, A.RowCount);
}
var result = new SpectraResult(k, size, ComputeEigenVectors, symmetric);
var handles = new List <GCHandle>();
var a = GetMatrix(A, handles);
var b = GetMatrix(B, handles);
var e = result.GetEigenvalueStorage(handles);
int conv = 0;
if (symmetric)
{
conv = NativeMethods.spectra_di_sg(GetJob(job), k, ArnoldiCount,
Iterations, Tolerance, ref a, ref b, ref e);
}
else
{
throw new NotImplementedException();
//conv = NativeMethods.spectra_di_ng(GetJob(job), k, ArnoldiCount,
// Iterations, Tolerance, ref a, ref b, ref e);
}
result.IterationsTaken = e.iterations;
result.ConvergedEigenValues = conv;
result.ErrorCode = e.info;
InteropHelper.Free(handles);
return(result);
}
/// <inheritdoc />
public override ExtendedEigensolverResult <double> SolveStandard(int k0, Job job, DenseColumnMajorStorage <double> eigenvectors)
{
// TODO: check eigenvectors matrix dimensions.
string which = job == Job.Smallest ? "S" : "L";
int n = A.RowCount;
int k = 0; // Total number of eigenvalues found in the interval.
var E = new double[k0]; // Eigenvalues
var R = new double[k0]; // Residual
var X = eigenvectors.Values; // Eigenvectors
var h = new List <GCHandle>();
try
{
var pe = InteropHelper.Pin(E, h);
var px = InteropHelper.Pin(X, h);
var pr = InteropHelper.Pin(R, h);
var h_A = CreateMatrixHandle(A, h);
var desc = CreateMatrixDecriptor();
var info = NativeMethods.mkl_sparse_d_ev(new StringBuilder(which), pm, h_A, desc, k0, ref k, pe, px, pr);
//if (info != sparse_status.SUCCESS)
//{
// throw new Exception(info.ToString());
//}
return(new ExtendedEigensolverResult(info, n, k, E, eigenvectors, R));
}
finally
{
InteropHelper.Free(h);
}
}
/// <summary>
/// Computes fill reducing orderings of sparse matrices using the multilevel nested dissection algorithm.
/// </summary>
/// <param name="perm">Target array storing the fill-reducing permutaion (size nvtxs).</param>
/// <param name="iperm">Target array storing the fill-reducing inverse permutaion (size nvtxs).</param>
/// <param name="options">Partitioning options.</param>
/// <returns></returns>
public MetisStatus NestedDissection(int[] perm, int[] iperm, MetisOptions options = null)
{
if (perm.Length != nvtxs || iperm.Length != nvtxs)
{
return(MetisStatus.ERROR_INPUT);
}
var handles = new List <GCHandle>();
// Pin array data.
var p_xadj = InteropHelper.Pin(xadj, handles);
var p_adjncy = InteropHelper.Pin(adjncy, handles);
var p_vwgt = InteropHelper.Pin(vwgt, handles);
var p_opts = options == null ? IntPtr.Zero : InteropHelper.Pin(options.raw, handles);
var p_perm = InteropHelper.Pin(perm, handles);
var p_iperm = InteropHelper.Pin(iperm, handles);
int l_nv = nvtxs;
int status = 0;
try
{
status = NativeMethods.NodeND(ref l_nv, p_xadj, p_adjncy, p_vwgt, p_opts, p_perm, p_iperm);
}
catch (Exception)
{
throw;
}
finally
{
InteropHelper.Free(handles);
}
return((MetisStatus)status);
}
protected override int DoFactorize()
{
int info = 0;
var mem_usage = new mem_usage();
var stat = new SuperLUStat();
int m = A.nrow;
int n = A.ncol;
var h = new List <GCHandle>();
// Create matrix with ncol = 0 to indicate not to solve the system.
var B = CreateEmptyDense(Dtype.SLU_D, m, h);
var X = CreateEmptyDense(Dtype.SLU_D, n, h);
try
{
var o = options.Raw;
NativeMethods.StatInit(ref stat);
NativeMethods.dgssvx(ref o, ref A, perm_c, perm_r, etree, equed,
(double[])R, (double[])C, ref L, ref U,
IntPtr.Zero, 0, ref B, ref X, out rpg, out rcond, null, null,
ref glu, ref mem_usage, ref stat, out info);
NativeMethods.StatFree(ref stat);
options.Raw.Fact = Constants.FACTORED;
}
finally
{
InteropHelper.Free(h);
}
return(info);
}
protected virtual void DoFactorize()
{
var h = new List <GCHandle>();
try
{
var A = CreateSparse(matrix, h);
int ordering = (int)SpqrOrdering.Default;
double tol = Constants.SPQR_DEFAULT_TOL;
qr = NativeMethods.SuiteSparseQR_C_factorize(ordering, tol, ref A, ref common);
if (common.status != Constants.CHOLMOD_OK)
{
throw new CholmodException(common.status);
}
}
finally
{
InteropHelper.Free(h);
}
}
protected virtual void Dispose(bool disposing)
{
if (disposing)
{
InteropHelper.Free(handles);
}
// NOTE: cs_di_*free and cs_ci_*free both do the same, so there's
// no need to move this method to the derived classes.
if (N.L != IntPtr.Zero)
{
cs_nfree(ref N);
N.L = IntPtr.Zero;
}
if (S.pinv != IntPtr.Zero || S.q != IntPtr.Zero)
{
cs_sfree(ref S);
S.pinv = IntPtr.Zero;
S.q = IntPtr.Zero;
}
}
protected virtual void DoSymbolic()
{
var h = new List <GCHandle>();
try
{
var A = CreateSparse(matrix, h);
int ordering = (int)SpqrOrdering.Default;
int allow_tol = 1;
qr = NativeMethods.SuiteSparseQR_C_symbolic(ordering, allow_tol, ref A, ref common);
if (common.status != Constants.CHOLMOD_OK)
{
throw new CholmodException(common.status);
}
}
finally
{
InteropHelper.Free(h);
}
}
/// <summary>
/// Initializes a new instance of the <see cref="CuSparseContext{T}"/> class.
/// </summary>
/// <param name="stream">The <see cref="CudaStream"/>.</param>
/// <param name="A">The sparse matrix.</param>
/// <param name="type">The matrix type.</param>
/// <param name="transpose">A value indicating, whether the storage should be transposed.</param>
public CuSparseContext(CudaStream stream, CompressedColumnStorage <T> A, MatrixType type, bool transpose)
{
Check(NativeMethods.cusparseCreate(ref _p));
Check(NativeMethods.cusparseSetStream(_p, stream.Pointer));
Check(NativeMethods.cusparseCreateMatDescr(ref _matDescr));
Check(NativeMethods.cusparseSetMatType(_matDescr, type));
Check(NativeMethods.cusparseSetMatIndexBase(_matDescr, IndexBase.Zero));
var sizeT = Marshal.SizeOf(typeof(T));
int rows = A.RowCount;
int nnz = A.NonZerosCount;
Cuda.Malloc(ref d_ap, sizeof(int) * (rows + 1));
Cuda.Malloc(ref d_ai, sizeof(int) * nnz);
Cuda.Malloc(ref d_ax, sizeT * nnz);
var handles = new List <GCHandle>();
try
{
// Convert storage to CSR format.
var C = transpose ? A.Transpose(true) : A;
var h_ap = InteropHelper.Pin(C.ColumnPointers, handles);
var h_ai = InteropHelper.Pin(C.RowIndices, handles);
var h_ax = InteropHelper.Pin(C.Values, handles);
Cuda.CopyToDevice(d_ap, h_ap, sizeof(int) * (rows + 1));
Cuda.CopyToDevice(d_ai, h_ai, sizeof(int) * nnz);
Cuda.CopyToDevice(d_ax, h_ax, sizeT * nnz);
}
finally
{
InteropHelper.Free(handles);
}
}
protected override int DoSolve(DenseColumnMajorStorage <double> input, DenseColumnMajorStorage <double> result)
{
int info = 0;
var mem_usage = new mem_usage();
var stat = new SuperLUStat();
int nrhs = input.ColumnCount;
var ferr = new double[nrhs];
var berr = new double[nrhs];
var h = new List <GCHandle>();
var B = CreateDense(Dtype.SLU_D, input, h);
var X = CreateDense(Dtype.SLU_D, result, h);
try
{
var o = options.Raw;
NativeMethods.StatInit(ref stat);
NativeMethods.dgssvx(ref o, ref A, perm_c, perm_r, etree, equed,
(double[])R, (double[])C, ref L, ref U,
IntPtr.Zero, 0, ref B, ref X, out rpg, out rcond, ferr, berr,
ref glu, ref mem_usage, ref stat, out info);
NativeMethods.StatFree(ref stat);
}
finally
{
InteropHelper.Free(h);
}
return(info);
}
protected override int DoFactorize()
{
var h = new List <GCHandle>();
var A = CreateSparse(matrix, h);
try
{
int order = (int)ordering;
// ordering and symbolic analysis
var pS = NativeMethods.cs_di_sqr(order, ref A, 0);
if (pS == IntPtr.Zero)
{
return(-1);
}
S = Marshal.PtrToStructure <css>(pS);
// numeric LU factorization
var pN = NativeMethods.cs_di_lu(ref A, ref S, tol);
if (pN == IntPtr.Zero)
{
return(-1);
}
N = Marshal.PtrToStructure <csn>(pN);
}
finally
{
InteropHelper.Free(h);
}
return(0);
}
protected override int DoFactorize()
{
var h = new List <GCHandle>();
var A = CreateSparse(matrix, h);
int m = matrix.RowCount;
int n = matrix.ColumnCount;
try
{
int order = (int)ordering;
if (m >= n)
{
// ordering and symbolic analysis
var pS = NativeMethods.cs_di_sqr(order, ref A, 1);
if (pS == IntPtr.Zero)
{
return(-1);
}
S = Marshal.PtrToStructure <css>(pS);
// numeric QR factorization
var pN = NativeMethods.cs_di_qr(ref A, ref S);
if (pN == IntPtr.Zero)
{
return(-1);
}
N = Marshal.PtrToStructure <csn>(pN);
beta = new double[n];
// Copy beta values for later access.
Marshal.Copy(N.B, beta, 0, n);
}
else
{
// Ax=b is underdetermined
var pAT = NativeMethods.cs_di_transpose(ref A, 1);
AT = Marshal.PtrToStructure <cs>(pAT);
// ordering and symbolic analysis
var pS = NativeMethods.cs_di_sqr(order, ref AT, 1);
if (pS == IntPtr.Zero)
{
return(-1);
}
S = Marshal.PtrToStructure <css>(pS);
// numeric QR factorization of A'
var pN = NativeMethods.cs_di_qr(ref AT, ref S);
if (pN == IntPtr.Zero)
{
return(-1);
}
N = Marshal.PtrToStructure <csn>(pN);
beta = new double[m];
// Copy beta values for later access.
Marshal.Copy(N.B, beta, 0, m);
}
if (w.Length < S.m2)
{
// Fix workspace length, if neccessary.
w = new double[S.m2];
}
}
finally
{
InteropHelper.Free(h);
}
return(0);
}
public override void Solve(double[] input, double[] result)
{
if (!factorized && DoFactorize() != 0)
{
throw new Exception(); // TODO: exception
}
var m = matrix.RowCount;
var n = matrix.ColumnCount;
var h = new List <GCHandle>();
var b = InteropHelper.Pin(input, h);
var x = InteropHelper.Pin(result, h);
var t = InteropHelper.Pin(w, h);
try
{
// x = b(p)
if (NativeMethods.cs_di_ipvec(N.pinv, b, t, n) == 0)
{
return;
}
// x = L\x
if (NativeMethods.cs_di_lsolve(N.L, t) == 0)
{
return;
}
// x = U\x
if (NativeMethods.cs_di_ltsolve(N.U, t) == 0)
{
return;
}
// b(q) = x
if (NativeMethods.cs_di_pvec(S.q, t, x, n) == 0)
{
return;
}
}
finally
{
InteropHelper.Free(h);
}
if (m >= n)
{
// x(0:m-1) = b(p(0:m-1)
NativeMethods.cs_di_ipvec(S.pinv, b, x, m);
// apply Householder refl. to x
for (int k = 0; k < n; k++)
{
NativeMethods.cs_di_happly(N.L, k, beta[k], x);
}
// x = R\x
NativeMethods.cs_di_usolve(N.U, x);
// b(q(0:n-1)) = x(0:n-1)
NativeMethods.cs_di_ipvec(S.q, x, b, n);
}
else
{
// x(q(0:m-1)) = b(0:m-1)
NativeMethods.cs_di_pvec(S.q, b, x, m);
// x = R'\x
NativeMethods.cs_di_utsolve(N.U, x);
// apply Householder refl. to x
for (int k = m - 1; k >= 0; k--)
{
NativeMethods.cs_di_happly(N.L, k, beta[k], x);
}
// b(0:n-1) = x(p(0:n-1))
NativeMethods.cs_di_pvec(S.pinv, x, b, n);
}
}
