API Status & Roadmap

Current capabilities and planned features for ttglow

Overall Progress ~65% complete

Implemented

Partial

Planned

✅ Current Capabilities

tensortrain.py

Function	Description	Status
`TensorTrain`	Core class with dims, ranks, cores	Done
`.to_tensor()`	Convert to dense tensor	Done
`.random()`	Random TT with specified ranks	Done
`dot()`	Inner product of two TTs	Done
`hadamard()`	Elementwise (Hadamard) product	Done
`add()`	TT addition (rank grows: r1 + r2)	Done
`scale()`	Scalar multiplication	Done
`+, -, *, @`	Operator overloads	Done
`.shape`	Logical tensor shape (n_1, ..., n_d)	Done
`.ttshape`	TT core shapes [(r_0, n_1, r_1), ...]	Done
`.numel`	Logical element count	Done
`.ttnumel`	Actual storage size	Done
`.ndim`	Number of dimensions	Done
`.reshape()`	Reshape via merge/split of adjacent modes	Done
`.merge_modes()`	Merge adjacent modes by core contraction	Done
`.split_mode()`	Split mode into shape using SVD	Done
`.swap_adjacent()`	Swap adjacent modes i and i+1	Done
`.transpose()`	Swap any two modes	Done
`.unsqueeze()`	Insert singleton dimension	Done
`.squeeze()`	Remove singleton dimension(s)	Done
`.flatten()`	Flatten range of dimensions	Done
`cat()`	Concatenate tensors along existing dimension	Done
`stack()`	Stack tensors along new dimension	Done
`.to()`	Device/dtype conversion	Done
`.clone()`	Deep copy	Done
`.detach()`	Detach from computation graph	Done
`.from_dense()`	Convert dense tensor to TT (TT-SVD)	Done
`tt[i, j, k]`	Element access	Done
`tt[:, 2, 1:3]`	Slicing with ranges and index contraction	Done

ttmatrix.py

Function	Description	Status
`TTMatrix`	TT-matrix / MPO data structure	Done
`.to_tensor()`	Convert to dense matrix	Done
`.random()`	Random TTMatrix	Done
`.identity()`	Identity operator	Done
`matmul()`	Matrix-matrix product	Done
`apply()`	Apply TTMatrix to TensorTrain	Done
`add()`	Matrix addition	Done
`scale()`	Scalar multiplication	Done
`kron()`	Kronecker product	Done
`kronadd()`	Add operators on different sites: (H⊗I) + (I⊗H)	Done
`transpose()`	Matrix transpose	Done
`adjoint()`	Hermitian conjugate	Done
`trace()`	Matrix trace	Done
`diag()`	Extract diagonal as TensorTrain	Done
`norm()`	Frobenius norm	Done
`round()`	Rank truncation via SVD	Done
`LocatedOp / .on()`	Apply operator to specific sites	Done
`Trunc`	Truncation wrapper for rank control	Done
`Circuit`	Composable circuit builder	Done
`.shape`	Logical matrix shape (total_rows, total_cols)	Done
`.ttshape`	TT core shapes [(r_0, n_row, n_col, r_1), ...]	Done
`.numel`	Logical element count	Done
`.ttnumel`	Actual storage size	Done
`.ndim`	Number of TT sites	Done

linalg.py

Function	Description	Status
`qr()`	QR decomposition (left/right sweep)	Done
`svd()`	SVD with rank truncation	Done
`norm()`	TT norm	Done
`sum()`	Sum over dimension(s)	Done
`mean()`	Mean over dimension(s)	Done
`contract()`	Contract two TTs	Done
`tensordot()`	General tensor contraction	Done

ttcross.py

Function	Description	Status
`tt_cross()`	TT-Cross interpolation from function or dense tensor	Done
`maxvol()`	Maximal-volume submatrix selection	Done

tensor_complete.py

Function	Description	Status
`silrtc_tt()`	Tensor completion via SiLRTC-TT (nuclear norm minimization on TT-style matricizations)	Done

riemannian_complete.py

Function	Description	Status
`rgrad_tt()`	Tensor completion via Riemannian optimization on the TT manifold (ALS & gradient with line search). Scales polynomially: O(n·d·r²)	Done

Tier 0: PyTorch-like Feel In Progress

Make ttglow feel like a first-class PyTorch object with familiar APIs.

Function	Description	Status
`shape, ndim, numel`	Logical tensor metadata	Done
`ttshape, ttnumel`	TT storage metadata	Done
`reshape / view`	Merge/split adjacent modes	Done
`merge_modes`	Merge adjacent modes into one	Done
`split_mode`	Split one mode into target shape (SVD-based)	Done
`swap_adjacent`	Swap adjacent modes via SVD	Done
`transpose`	Swap any two modes (via adjacent swaps)	Done
`permute`	Arbitrary mode reordering	Planned
`unsqueeze`	Insert singleton dimension	Done
`squeeze`	Remove singleton dimension(s)	Done
`flatten`	Merge range of modes into one	Done
`cat / stack`	Concatenate along mode / stack as new mode	Done
`from_dense()`	Convert dense tensor to TT (TT-SVD)	Done
`to(device/dtype)`	Device/dtype conversion	Done
`clone, detach`	Copy and gradient control	Done

Tier 1: Reductions & Contractions Partial

Enable practical computation with daily-use operations.

Function	Description	Status
`sum(dim=...)`	Sum reduction over dimensions	Done
`mean(dim=...)`	Mean via sum + scaling	Done
`tensordot`	General tensor contraction	Done
`einsum`	Restricted einsum patterns	Planned
`outer`	Outer product	Planned

Tier 2: Elementwise Nonlinearities Planned

Support ML workflows with elementwise operations (exact or approximate).

Note: Elementwise operations may use TT-cross, sampling, or polynomial approximations with explicit rank control.

Tier 3: Advanced Indexing Planned

Widen compatibility with existing PyTorch codebases.

Function	Description	Status
`split / chunk`	Split tensor along dimension	Planned
`gather`	Gather along dimension	Planned
`slicing`	Partial slicing / fiber extraction	Done
`logsumexp`	Log-sum-exp (approximate)	Planned
`softmax`	Softmax (built from logsumexp)	Planned

Tier 4: Advanced Linear Algebra Planned

Unlock iterative solvers and matrix-free operations for large-scale problems.

Function	Description	Status
`matvec / matmul`	Matrix-free A @ x interface	Partial
`solve (CG)`	Conjugate gradient solver	Planned
`solve (GMRES)`	GMRES iterative solver	Planned
`eigsh`	Eigenvalue solver (Lanczos/DMRG-style)	Planned
`linear_operator`	LinearOperator-style interface	Planned