linear-algebra/backends/openblas

API baseline for Luna-Flow/linear-algebra/backends/openblas in the current 0.4.7 repository state.

Purpose

backends/openblas provides owned native-only matrix and vector backend wrappers. Matrix multiplication delegates to OpenBLAS GEMM, while vector and matrix-vector helpers delegate to the matching BLAS kernels.

This package is separate from @immut.Matrix. There is no runtime backend selector in immut; backend choice is now expressed by the concrete matrix type you use and the compilation target you build for.

Platform Constraint

• Supported target: native
• Unsupported targets: js, wasm, wasm-gc
• Current repository link configuration searches both /opt/homebrew/opt/openblas/include and /opt/homebrew/opt/openblas/lib for Homebrew on macOS, and /usr/include/x86_64-linux-gnu/openblas-pthread, /usr/include/openblas, /usr/lib/x86_64-linux-gnu/openblas-pthread, and /usr/lib/x86_64-linux-gnu for the default Ubuntu OpenBLAS package layout

BLASInnerType

BLASInnerType is a backend-local trait implemented only for Float and Double.

It owns the scalar-specific pieces required by the backend:

• tolerance() returns the comparison tolerance used by backend tests and result checks.
• dot(length, left, right) dispatches to cblas_sdot or cblas_ddot.
• scal(length, alpha, data) dispatches to cblas_sscal or cblas_dscal.
• axpy(length, alpha, x, y) dispatches to cblas_saxpy or cblas_daxpy.
• gemm(m, n, k, left, right) dispatches matrix multiplication to the matching OpenBLAS kernel: cblas_sgemm for Float and cblas_dgemm for Double.
• gemv(row, col, matrix, vector) dispatches matrix-vector multiplication to cblas_sgemv or cblas_dgemv.

BlasMatrix[T] and BlasVector[T] public construction and conversion APIs require T : BLASInnerType, so the backend does not expose a half-open “constructible for any T but only operable for some T” surface.

BlasVector[T]

Owned native vector wrapper for the OpenBLAS backend.

Constructors, Conversions, And Accessors

• BlasVector::from_immut(inner : @immut.Vector[T]) -> BlasVector[T]
• BlasVector::from_default(inner : @default.ImmutableDenseVector[T]) -> BlasVector[T]
• BlasVector::from_array(data : Array[T]) -> BlasVector[T]
• BlasVector::make(length : Int, value : T) -> BlasVector[T]
• to_immut(self) -> @immut.Vector[T]
• to_default(self) -> @default.ImmutableDenseVector[T]
• to_array(self) -> Array[T]
• length(self) -> Int
• op_get(self, index : Int) -> T

Trait Coverage

BlasVector[T] currently implements:

• @algebra.VectorShape
• @algebra.AdditiveVector
• Add, Neg, Sub
• Show

It does not implement @algebra.VecMulVector. BLAS-style scale, dot, and axpy are exposed as backend methods rather than new structure traits.

Backend Methods

• BlasVector::scale(self, scalar : T) -> BlasVector[T]
• BlasVector::dot(self, other : BlasVector[T]) -> T
• BlasVector::axpy(self, alpha : T, other : BlasVector[T]) -> BlasVector[T]

BlasMatrix[T]

///|
test "BlasMatrix stores shape and values" {
  let matrix = @openblas.BlasMatrix::from_2d_array([[1.0F, 2.0F], [3.0F, 4.0F]])
  inspect(matrix.row(), content="2")
  inspect(matrix.col(), content="2")
}

BlasMatrix[T] is the owned concrete backend matrix type for this package. Internally it stores:

• row : Int
• col : Int
• a contiguous FixedArray[T] buffer

The public mental model stays row-major. Layout details needed by OpenBLAS stay inside the backend implementation.

Constructors And Conversions

• BlasMatrix::from_immut(inner : @immut.Matrix[T]) -> BlasMatrix[T]
• BlasMatrix::from_default(inner : @default.ImmutableDenseMatrix[T]) -> BlasMatrix[T]
• BlasMatrix::from_2d_array(data : Array[Array[T]]) -> BlasMatrix[T]
• BlasMatrix::new(row : Int, col : Int, value : T) -> BlasMatrix[T]
• to_immut(self) -> @immut.Matrix[T]
• to_default(self) -> @default.ImmutableDenseMatrix[T]
• to_2d_array(self) -> Array[Array[T]]

Accessors

• row(self) -> Int
• col(self) -> Int
• to_array(self) -> Array[T]

Backend Methods

• BlasMatrix::matvec(self, vector : BlasVector[T]) -> BlasVector[T] multiplies the matrix by an OpenBLAS backend vector through GEMV.

Trait Implementations

BlasMatrix[T] currently implements:

• @algebra.MatrixShape
• @algebra.TransposeMatrix
• @algebra.AdditiveMatrix
• @algebra.MatMulMatrix
• Add, Neg, Sub, Mul
• Show

Behavior is split intentionally:

• Mul uses OpenBLAS GEMM through BLASInnerType::gemm.
• matvec uses OpenBLAS GEMV through BLASInnerType::gemv.
• shape, transpose, +, -, and unary - are implemented locally in MoonBit inside this backend package.

Boundary

This package exposes an owned trait-compatible backend wrapper. It does not:

• add a runtime backend enum
• retrofit traits directly onto third-party OpenBLAS binding types
• expose raw OpenBLAS handle types in the public API