Crate trueno_solve 

Dense linear algebra solvers with provable contracts.

Solvers

• LU: Partial pivoting, PA = LU
• QR: Householder reflections, A = QR
• SVD: One-sided Jacobi, A = UΣV^T
• Cholesky: A = LL^T for positive definite matrices

Example

use trueno_solve::lu_factorize;

// Solve Ax = b where A = [[2, 1], [1, 3]]
let a = [2.0, 1.0, 1.0, 3.0_f32];
let lu = lu_factorize(&a, 2).unwrap();
let x = lu.solve(&[5.0, 7.0]).unwrap();
// x ≈ [1.6, 1.8]
assert!((x[0] - 1.6).abs() < 1e-5);
assert!((x[1] - 1.8).abs() < 1e-5);

Structs

CholeskyFactorization

Cholesky factorization result.

LuFactorization

LU factorization result (in-place: L and U stored in the same matrix).

QrFactorization

QR factorization result.

SvdResult

SVD result: A = U * diag(sigma) * V^T.

TrsmResult

Triangular solve result.

Enums

DiagonalType

Whether the diagonal is unit (all ones) or general.

Epilogue

Epilogue operation applied after GEMM computation.

SolverError

Errors from solver operations.

TriangularSide

Whether the triangular matrix is lower or upper.

Traits

Solver

Unified solver trait for factorization-based linear system solving.

Functions

cholesky

Cholesky factorization: A = L L^T.

f32_to_f16

Convert f32 to IEEE 754 half-precision (u16).

gemm_ex

Mixed-precision GEMM: C = α·A·B + β·C with f16 inputs, f32 accumulation.

gemm_ex_epilogue

Mixed-precision GEMM with epilogue fusion.

gemm_strided_batched

Strided batched GEMM: C_b = α·A_b·B_b + β·C_b for b = 0..batch_count.

lu_factorize

LU factorization with partial pivoting.

qr_factorize

QR factorization via Householder reflections.

svd

Compute SVD via one-sided Jacobi rotations.

symm

Symmetric matrix multiply: C = α·A·B + β·C

syr2k

Symmetric rank-2k update: C = α·A·Bᵀ + α·B·Aᵀ + β·C

syrk

Symmetric rank-k update: C = α·A·Aᵀ + β·C

trmm

Triangular matrix multiply: B = α·A·B (left side, lower triangular).

trsm

Solve AX = B where A is triangular.