Dense 2D matrices (Matrix2D)

Dense 2-D matrix type with matmul, matvec and outer products backing the trainable-model kernels.

tensor2d is the minimal dense 2D matrix type the ML kernels build on — zero Python imports. It replaces the numpy 2D essentials (np.zeros, 2D np.array, A @ B, A @ x, A.T, A + B, c * A, row/column slicing) with a row-major List[Float64] store plus the core products, and complements tensor.mojo (1D Tensor1D) and linalg.mojo (solvers/decompositions).

The modules

Module	What it does
tensor2d	the dense row-major Matrix2D type — matmul, matvec, transpose, add, scale and row/column slicing over a flat List[Float64] store, with zero Python imports

Functions

Function	What it does
Matrix2D(rows, cols)	Dense row-major matrix; element (i, j) lives at data[i * cols + j]; negative dims clamp to 0.
m2_zeros(rows, cols)	rows x cols matrix of zeros.
m2_from_list(data, rows, cols)	Build from a row-major flat list; short input is zero-padded, extra values ignored.
m2_get(m, i, j)	Element at (i, j); returns 0.0 when out of range.
m2_set(m, i, j, val)	Write val at (i, j); silent no-op when out of range.
m2_matmul(a, b)	Matrix product A(m x p) @ B(p x n) -> (m x n); i-k-j loop order keeps the inner loop contiguous in both B and C.
m2_matvec(a, x)	Matrix-vector product A(m x n) @ x(n) -> list of m values.
m2_transpose(a)	A^T: (m x n) -> (n x m).
m2_add(a, b)	Element-wise A + B (same shape).
m2_scale(a, c)	Scalar multiple c * A.
m2_row(a, i)	Copy of row i as List[Float64]; empty when out of range.
m2_col(a, j)	Copy of column j as List[Float64]; empty when out of range.

Shape-mismatch policy: deterministic, never traps

Binary ops on incompatible shapes return an empty 0x0 Matrix2D (or an empty List for m2_matvec); out-of-range m2_get returns 0.0 and out-of-range m2_set is a no-op. Callers gate on rows/cols > 0 instead of catching exceptions. All loops are plain O(m·n) / O(m·p·n) passes — sub-millisecond for typical ML-kernel shapes (a 100x100x100 product is ~1e6 mul-adds); a full 10k x 10k dense product is inherently much slower and out of scope for this minimal type.

Verification

The test suite pins hand-computed values at 1e-12 absolute tolerance: [[1,2,3],[4,5,6]] @ [[7,8],[9,10],[11,12]] = [[58,64],[139,154]] and [[1,2,3],[4,5,6]] @ [2,1,3] = [13,31], plus the algebraic identities A @ I == A, (A^T)^T == A, (AB)^T == B^T A^T, and A + (-A) == zeros. Edge shapes are covered explicitly: 1x1 products, row-vector @ column-vector = [[32]], 3x1 @ 1x3 outer products, and 0x0 / negative-dimension inputs.

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