Positive definite
Cholesky supports solves and log determinants. Sparse Cholesky adds natural or minimum-degree ordering and original-coordinate solutions.
Unified numerical engine · JDistlib 0.10.0
One linear-algebra contract from portable CPU to GPU
Use matching FP64 and FP32 dense, sparse, and factorization APIs while JDistlib owns provider discovery, device reuse, capability reporting, and checked portable fallbacks.
FP64 and FP32
Dense and sparse primitives share one shape
| Area | Released operations | Reuse support |
|---|---|---|
| Level 1 | scale, copy, swap, AXPY, dot, norm, absolute sum, absolute maximum | strided caller-owned vectors |
| Dense | GEMV/GEMM, rank updates, symmetric multiply/rank-k updates, triangular solves | offsets, leading dimensions, batching, prepared fixed operands |
| Sparse CSR | matrix-vector, matrix-dense, CSR-by-CSR, triangular solve | canonical output and prepared provider storage |
| Factorization | Cholesky, LU, LDL', pivoted QR, symmetric/generalized eigen, thin SVD | factor objects, repeated solves, determinant metadata |
Dense storage is row-major. Standard d* and s* prefixes distinguish double[] and float[] without introducing a second naming system.
Reusable decomposition results
Factor once, solve and inspect repeatedly
General systems
Partial-pivoted LU supports vector or multiple-right-side solves plus determinant sign and log-absolute-determinant metadata.
Symmetric indefinite
Pivoted LDL' retains 1x1 and 2x2 blocks for stable solves and determinant inspection.
Least squares and spectra
Pivoted QR reports numerical rank; eigen, generalized eigen, and thin SVD cover spectral and rank-deficient workflows.
Prepared operands
Avoid rebuilding or retransferring fixed matrices
try (ComputeSelection selected = ComputeBackends.select(Compute.AUTO);
PreparedDenseMatrix prepared =
selected.backend().prepareDge(a, rows, shared)) {
prepared.multiply(MatrixTranspose.NONE,
1.0, right, columns, 0.0, result);
}Prepared dense handles can retain the fixed matrix in a native CPU or CUDA/OpenCL/Vulkan provider buffer. Prepared sparse Cholesky retains symbolic analysis and accepts numeric refactorization when the authoritative CSR structure is unchanged. Batched entry points amortize dispatch for collections of independent products or factors.
Explicit capability boundary
Know which machine and implementation did the work
| Provider | Role | Installation boundary |
|---|---|---|
| Java CPU | portable deterministic reference and universal fallback | always available |
| oneMKL | native CBLAS/LAPACKE plus reusable PARDISO sparse factorization | system oneMKL runtime |
| OpenBLAS | native CBLAS/LAPACKE dense operations and factors when exported | system OpenBLAS runtime |
| CUDA | NVIDIA device kernels and resident prepared dense/CSR operands | compatible driver and NVRTC |
| OpenCL | portable GPU kernels and resident prepared dense/CSR operands | FP64-capable OpenCL implementation |
| Vulkan | SPIR-V compute kernels and resident prepared dense operands | Vulkan device with shaderFloat64 |
ComputeCapabilities reports the backend, device, memory, precision, dense/sparse acceleration, native factorization, prepared storage, reusable sparse factorization, and batching support. Execution plans separately identify portable fallback. Numerical results are tolerance-checked, but parallel reduction order means cross-hardware bit identity is not promised.
Library foundation
Ready for regression, REML, pedigree, and graphical-model packages
JDistlib now owns the low-level numerical and provider layer. A downstream package can focus on design matrices, formula handling, statistical algorithms, variance-component optimization, pedigree construction, diagnostics, and result objects. Additional primitives can be added when those real workloads expose a measured gap.