Add Jacobi eigenvalue algorithm and eigSH via cuSOLVER#70
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…gnGen, index type fixes ## New functions ### BLAS: `gemm` Adds `gemm :: AFType a => MatProp -> MatProp -> a -> Array a -> Array a -> a -> Array a`, the general matrix multiply C = alpha * op(A) * op(B) + beta * C_prev. This is more expressive than the existing `matmul`: it supports in-place accumulation and scalar scaling, making it directly useful for iterative eigenvalue algorithms (e.g. Jacobi rotations) that accumulate orthogonal transformations in Q. Implemented via the C FFI binding `af_gemm`; scalars are passed through `Storable` alloca/poke so any `AFType` element type is supported. Three new unit tests cover identity scaling, alpha-scaling, and transposition. ### Algorithm: key-value (segmented) reductions Adds nine new functions mirroring ArrayFire's `af_*_by_key` family: `sumByKey`, `sumByKeyNaN`, `productByKey`, `productByKeyNaN`, `minByKey`, `maxByKey`, `allTrueByKey`, `anyTrueByKey`, `countByKey` Each takes a keys `Array Int` and a values `Array a`, performs the named reduction over contiguous equal-key runs along a given dimension, and returns `(Array Int, Array a)`. These are essential for sparse tensor contractions that arise in many-body quantum systems and tensor network methods (e.g. grouping indices in an MPO sweep). A new internal FFI helper `op2p2kv` handles the keys–values two-output calling convention. Because ArrayFire requires the key array to be `s32` (C int) while Haskell uses `Int` (typically `s64`), the helper casts input keys to `s32` before calling the C function and casts the output keys back to `s64`, keeping the Haskell API uniform at `Array Int`. ### Statistics: `meanVar` and `meanVarWeighted` Adds `meanVar :: AFType a => Array a -> VarBias -> Int -> (Array a, Array a)` and its weighted variant, bound to `af_meanvar`. Computing mean and variance in a single pass is both more accurate and more efficient than calling them separately, which matters for normalisation steps in quantum state tomography and Hamiltonian learning. Introduces the `VarBias` high-level type (`VarianceDefault | VarianceSample | VariancePopulation`) backed by the previously-commented-out `AFVarBias` newtype in `Internal/Defines.hsc` (now uncommented and given a `Storable` instance). `VarBias` and its conversion `fromVarBias` are exported from `ArrayFire.Types`. ### Index: `assignSeq`, `indexGen`, `assignGen`; rename `span` → `afSpan` Implements three functions that were previously stubs (`error "Not implemented"`): - `assignSeq :: Array a -> [Seq] -> Array a -> Array a` — write a source array into a sequential slice of a destination array, bound to `af_assign_seq`. - `indexGen :: Array a -> [Index] -> Array a` — generalised indexing by a list of `Index` values (sequence or array), bound to `af_index_gen`. - `assignGen :: Array a -> [Index] -> Array a -> Array a` — generalised slice assignment, bound to `af_assign_gen`. These are needed for constructing sparse interaction terms (e.g. projecting onto a subspace defined by an index set). `span` is renamed to `afSpan` to avoid shadowing `Prelude.span`, which caused silent import errors in downstream modules. ## Type corrections and bug fixes ### `Index` type redesign (`Internal/Types.hsc`) The `Index a` type (which parameterised over the array element type) is replaced by a simpler unparameterised GADT-style sum: `data Index = SeqIndex Bool Seq | ArrIndex Bool (Array Int)` This removes a phantom type parameter that was never meaningful (index arrays are always integral), and fixes the `toAFIndex` implementation which was using `unsafeForeignPtrToPtr` incorrectly — the old version passed a pointer whose lifetime was not guaranteed by `withForeignPtr`. The new version stores the raw pointer and relies on `touchForeignPtr` calls at the use site to keep the ForeignPtr alive. The `Storable` peek instance for `AFIndex` also had the `Left`/`Right` branches swapped (`isSeq == True` should produce a sequence, not an array pointer); this is fixed. ### Return types for index-returning operations `imin`, `imax`, `sortIndex`, and `topk` all return an index array. Their return types are corrected from `(Array a, Array a)` to `(Array a, Array Word32)`, matching ArrayFire's documented `u32` output for index arrays. The corresponding `op2p` helper in `FFI.hs` is generalised from `(Array a, Array a)` to `(Array a, Array b)`. ### `afBackendCpu` constant (`Internal/Defines.hsc`) Fixed: `afBackendCpu` was mistakenly bound to `AF_BACKEND_DEFAULT` instead of `AF_BACKEND_CPU`. ### `toConnectivity` (`Internal/Types.hsc`) Fixed: `AFConnectivity 8` was mapped to `Conn4` instead of `Conn8`. ### `histogram` (`Image.hs`) Removed a spurious `cast` wrapping around the `af_histogram` call; the C function already returns `u32`, so double-casting was wrong. ## FFI infrastructure ### `op1d` removed; `op1` generalised `op1d :: Array a -> (...) -> Array b` was an alias for `op1` but with the output type fixed to `Array b` (different from input). All call sites that used `op1d` (`not`, `real`, `imag`, `count`) are migrated to `op1`. `op1` itself is generalised from `Array a -> ... -> Array a` to `Array a -> ... -> Array b`, making `op1d` redundant. ### `mask_` added to all `unsafePerformIO` helpers Every `op*` helper in `FFI.hs` now wraps its `unsafePerformIO` block with `mask_`. Without `mask_`, an asynchronous exception arriving during the FFI call can leave the output `AFArray` pointer uninitialised, producing a segfault or a garbage `ForeignPtr` finalization. ### `af_cast` disambiguation (`Arith.hs`) `af_cast` is now qualified as `ArrayFire.Internal.Arith.af_cast` at its call site in `cast` because `FFI.hs` also imports the same C symbol (needed for `op2p2kv`), creating an ambiguous occurrence error under GHC 9.10. ## `Num` / `Floating` instance fixes (`Orphans.hs`) - `negate` is simplified from an allocate-a-zero-constant approach to `scalar (-1) \`mul\` arr`, removing a dependency on dimension information. - `Eq` checks now compare dimensions first before invoking `allTrueAll`, avoiding a broadcast-induced wrong answer when shapes differ. - `pi` now uses `realToFrac (Prelude.pi :: Double)` instead of the hard-coded literal `3.14159`, gaining full IEEE 754 double precision. - Added `NFData (Array a)` instance (shallow: evaluates the `ForeignPtr` to WHNF). ## Documentation - Haddock constructor comments added to all sum types: `Backend`, `MatProp`, `BinaryOp`, `Storage`, `InterpType`, `CSpace`, `YccStd`, `MomentType`, `CannyThreshold`, `FluxFunction`, `DiffusionEq`, `IterativeDeconvAlgo`, `InverseDeconvAlgo`, `Cell`, `ColorMap`, `MarkerType`, `MatchType`, `TopK`, `HomographyType`, and the new `VarBias`. - Fixed stale parameter documentation in `drawVectorField2d` (previously all four array parameters were labelled "is the window handle"). ## Tests - `AlgorithmSpec`: seven new tests covering all `*ByKey` functions. - `BLASSpec`: three new tests for `gemm` (identity, alpha-scaling, transpose). - `IndexSpec`: complete rewrite — `index`, `afSpan`, `lookup`, `assignSeq`, `indexGen`, `assignGen` each covered with multiple cases. - `LAPACKSpec`: variable names corrected (`s,v,d` → `l,u,piv` / `q,r,tau`); `det` test split into real and complex cases with exact expected values; `inverse`, `rank`, and `norm` tests added. - `StatisticsSpec`: `topk` index type updated to `Word32`; three new tests for `meanVar` (population, sample) and `meanVarWeighted`. - `ArraySpec`: placeholder `1+1==2` replaced with a real `Array` addition test. - `ApproxExpect`: `shouldBeApprox` rewritten to use numpy-compatible `|a-b| <= atol + rtol * max(|a|, |b|)` (rtol=1e-5, atol=1e-8) instead of the fragile scale-and-compare hack; signature now requires `Ord` and is exported cleanly. Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>
Adds two complementary paths for symmetric eigendecomposition: * `ArrayFire.Jacobi` — pure-Haskell cyclic Jacobi method that runs entirely on the GPU via ArrayFire array ops, with only 3 scalar GPU→CPU reads per active off-diagonal pair (for the rotation angle) plus one per sweep (convergence check). Works on any AF backend. * `eigSH` in `ArrayFire.LAPACK` — wraps a new C shim (`cbits/eigsh.c`) that calls `cusolverDnDsyevd` / `cusolverDnSsyevd` directly via dlopen at runtime (no link-time CUDA dependency). Gracefully returns AF_ERR_RUNTIME on non-CUDA backends. Eigenvalues returned in ascending order, matching the hmatrix `eigSH` convention. Also expands the LAPACK test suite: fixes the `qr` test (was calling `lu` by mistake), splits the determinant test into separate real and complex cases with verified imaginary parts, uncomments and corrects the inverse test, and adds rank and norm tests. New `eigSH (CUDA)` tests skip gracefully on CPU/OpenCL via `pendingWith`. Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>
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Summary
ArrayFire.Jacobi— pure-Haskell cyclic Jacobi eigenvalue method for real symmetric matrices. Runs entirely on the GPU via ArrayFire array operations; the only CPU round-trips are 3 scalar reads per active off-diagonal pair (to compute the Givens rotation angle) plus one per sweep for the convergence check. Works on any AF backend (CPU, OpenCL, CUDA).eigSHinArrayFire.LAPACK— GPU-accelerated symmetric eigendecomposition backed by a new C shim (cbits/eigsh.c) that callscusolverDnDsyevd(f64) /cusolverDnSsyevd(f32) viadlopenat runtime, so there is no link-time dependency on the CUDA toolkit. Gracefully returnsAF_ERR_RUNTIMEon CPU/OpenCL backends. Eigenvalues are returned in ascending order, matching thehmatrixeigSHconvention.LAPACK test improvements — fixes a copy-paste bug in the
qrtest (was callinglu), splits thedettest into separate real and complex cases (with verified imaginary part), uncomments and corrects theinversetest, addsrankandnormtests, and adds aeigSH (CUDA)describe block that skips gracefully viapendingWithon non-CUDA backends.Test plan
cabal testpasses on CPU backend (Jacobi tests run;eigSHtests marked pending)cabal testpasses on CUDA backend (all tests includingeigSHrun)V^T V ≈ Ifor 2×2, 3×3, 4×4, 5×5 Hilbert-like matricesV diag(λ) V^T ≈ Afor all test matriceseigSHeigenvalues confirmed ascending for 2×2 and 3×3 cases🤖 Generated with Claude Code