Dense Solver — NVMathNet.Solver

DenseSolver (static)

Stateless helpers for cuSOLVER dense operations.

Member	Description
Task SolveAsync(DeviceBuffer<float> a, b, int n, int nrhs = 1, ...)	Single-precision LU solve: A*X = B. A is overwritten with LU factors; B with solution.
Task SolveAsync(DeviceBuffer<double> a, b, int n, int nrhs = 1, ...)	Double-precision LU solve.
Task CholeskyAsync(DeviceBuffer<float> a, int n, bool upper = false, ...)	Single-precision Cholesky factorisation of SPD matrix.
Task CholeskyAsync(DeviceBuffer<double> a, int n, bool upper = false, ...)	Double-precision Cholesky factorisation.
Task SvdAsync(DeviceBuffer<float> a, s, u, vt, int m, n, ...)	Single-precision SVD: A = U·diag(S)·VT.
Task SvdAsync(DeviceBuffer<double> a, s, u, vt, int m, n, ...)	Double-precision SVD.
Task EigAsync(DeviceBuffer<float> a, w, int n, bool computeVectors = true, upper = false, ...)	Single-precision symmetric eigenvalue decomposition.
Task EigAsync(DeviceBuffer<double> a, w, int n, ...)	Double-precision symmetric eigenvalue decomposition.
Task<int> LuFactorAsync<T>(DeviceBuffer<T> a, DeviceBuffer<int> ipiv, int m, int n, ...)	LU with partial pivoting P·A = L·U in place. Returns 0, or a positive value if U(i,i) is exactly zero (singular).
Task LuSolveAsync<T>(DeviceBuffer<T> a, DeviceBuffer<int> ipiv, DeviceBuffer<T> b, int n, int nrhs = 1, bool transpose = false, ...)	Solves op(A)·X = B from an LU factorisation.
Task QrAsync<T>(DeviceBuffer<T> a, DeviceBuffer<T> tau, int m, int n, ...)	QR factorisation in place (R in the upper triangle, reflectors below and in tau).
Task QrFormQAsync<T>(DeviceBuffer<T> a, DeviceBuffer<T> tau, int m, int n, ...)	Overwrites a with the explicit m×n orthonormal Q (m ≥ n).
Task LeastSquaresAsync<T>(DeviceBuffer<T> a, DeviceBuffer<T> b, int m, int n, int nrhs = 1, ...)	Solves min ‖A·X − B‖ by QR (m ≥ n, full column rank). The first n rows of each column of b hold the solution.
Task<int[]> CholeskyBatchedAsync<T>(DeviceBuffer<T> a, int n, int batchCount, bool upper = false, ...)	Cholesky of a packed batch of SPD matrices; returns a per-matrix status (positive = not positive definite).

The <T> methods accept float or double. All overloads check cuSOLVER's devInfo: the older Solve, Cholesky, Svd and Eig overloads throw InvalidOperationException for a singular matrix, a matrix that is not positive definite, or a failure to converge. The <T> factorisation methods report singularity through their return value instead. | Task<int[]> LuFactorBatchedAsync<T>(DeviceBuffer<T> a, DeviceBuffer<int> ipiv, int n, int batchCount, ...) | Batched LU (cuBLAS getrfBatched) of packed n×n matrices; returns a per-matrix status (positive = singular). ipiv holds batchCount·n entries. | | Task LuSolveBatchedAsync<T>(DeviceBuffer<T> a, DeviceBuffer<int> ipiv, DeviceBuffer<T> b, int n, int nrhs, int batchCount, bool transpose = false, ...) | Batched solve from the factors; b holds batchCount·n·nrhs values. | | Task<int[]> SvdBatchedAsync<T>(DeviceBuffer<T> a, s, u, v, int m, int n, int batchCount, bool computeVectors = true, ...) | Batched Jacobi SVD (cuSOLVER gesvdjBatched) of packed m×n matrices, m, n ≤ 32. Returns V (not Vᵀ), s sorted descending, a is destroyed. u/v may be null when computeVectors is false. Returns a per-matrix convergence status. |

Complex (double precision) variants

System.Numerics.Complex (= cuDoubleComplex) overloads are available for LuFactorAsync, LuSolveAsync (with transpose and conjugate), QrAsync, QrFormQAsync, LeastSquaresAsync and CholeskyAsync (Hermitian positive definite), plus HermitianEigAsync(DeviceBuffer<Complex> a, DeviceBuffer<double> w, int n, bool computeVectors = true, bool upper = false, ...) for Hermitian eigenproblems (real eigenvalues, ascending). Also available for Complex: SvdAsync (A = U·diag(S)·Vᴴ; returns Vᴴ; requires m ≥ n), CholeskyBatchedAsync, LuFactorBatchedAsync/LuSolveBatchedAsync (with transpose and conjugate) and SvdBatchedAsync (Jacobi, m, n ≤ 32, returns V, not Vᴴ). .NET has no single-precision complex type, so complex64 is not offered.