fix(Tensor & UniTensor): support rank-zero tensors and zero extents

[ianmccul]

Summary

This PR adds proper rank-0 Tensor and UniTensor. Resolves #1016. It also adds proper support for tensors that have extent zero (such as an empty vector), following NumPy and PyTorch, and basically every other tensor library out there. Resolves #1040.

Historically Cytnx represented several scalar results as rank-1 tensors with shape {1}. That makes shape metadata ambiguous: a one-leg length-1 tensor is not the same object as a scalar. This PR starts separating those cases by treating an empty shape () as the scalar tensor shape, while preserving ordinary shape {1} as a rank-1 tensor.

This adds more code than I was expecting, but of the net lines added, +942 are tests/pytests, and the rest is hardening, replacing the old rank-1-size-1 scalar hacks with explicit rank-0 behavior, and about about 93 added cytnx_error_msg checks, 55 added tests, and hardened many existing tests.

The biggest user-visible change in Python is that contractions over all legs of a tensor (including inner products etc) now return a proper rank-0 tensor, so e.g. the example DMRG code needs

-        return psivec, energy[0].item()
+        return psivec, energy.item()

I think that's an improvement: previously the energy was a rank-1 tensor.

Also added Tensor and UniTensor helpers .is_void(), .is_scalar(), and .is_empty(). The old model was not able to distinguish properly genuinely empty tensors from rank-0 tensors where shape is empty, and was not able to distinguish a rank-1 size-1 tensor from a genuine scalar.

UniTensor had no canonical way to store its symmetry data. Functions that needed the symmetry data would typically get it from _bonds[0].syms(), which of course doesn't exist for a rank-0 UniTensor. The symmetry data is now held by UniTensor itself. To avoid too much code churn, existing behavior of setting the symmetry data from _bonds[0].syms() is still supported as a fallback, but retrieving the symmetry data should be done via this->syms().

This should be regarded as a breaking change for Tensor file I/O. Previous Cytnx cannot distinguish a genuine rank-1 size-1 tensor from a scalar-like tensor that should have been rank 0. Loading old Tensor files remains supported, but old shape {1} is preserved as rank-1 rather than auto-converted to rank 0. Tensors saved in the new version are not loadable by old Cytnx because old Cytnx would choke on a genuine rank-0 Tensor. The Tensor file magic number has changed so new Tensor files loaded by old Cytnx will fail early.

The SVD-style return values now follow a consistent rank-zero convention.

• Svd / Gesvd on Tensor return Tensor objects, and Svd / Gesvd on UniTensor return UniTensor objects: the singular values S remain a diagonal object in the same API family as U and vT, with block/symmetric SVD preserving the singular-value bond structure. Truncated SVD routines keep the existing homogeneous vector return type, so the optional return_err object is also a Tensor for Tensor APIs and a UniTensor for UniTensor APIs.
• return_err == 0 appends nothing.
• return_err == 1 appends a scalar rank-0 object containing the largest actually discarded singular value, or scalar zero if nothing was discarded. (I think this is a little inconsistent in the sense that it does not distinguish the case of discarding nothing at all vs discarding actual zero singular values. I'd favor returning some sentinel like -1 in the case where truely nothing was discarded.)
• return_err > 1 appends a rank-1 vector containing all actually discarded singular values in descending order; if nothing was discarded, this is a tensor with shape {0}. For block/symmetric truncation, “discarded” means after the real truncation decision, including exact-degeneracy enlargement and min_blockdim, so the error return reports values that were actually removed.

The core API now has a clean distinction: is_void() means uninitialized, is_scalar() means rank zero with one value, and is_empty() means initialized with logical size() == 0 (i.e. it has rank > 0 but at least one extent is zero).

Changes

• Allow Tensor to be initialized with an empty shape, allocating one storage element.
• Add Tensor::is_scalar(), true for initialized rank-0 tensors only.
• Add Tensor::is_void() and expose it to Python, replacing uses of shape.empty() as an initialized/non-void proxy.
• Support rank-0 scalar access through item(), at({}), get({}), and set({}, ...).
• Keep .item() as a size-one element extractor, NumPy-style: shape (), {1}, and {1,1} all work if storage size is one.
• Make fully indexed Tensor::get(...) return a rank-0 Tensor rather than shape {1}.
• Expose Tensor.is_scalar() and Tensor.is_void() to Python, also the UniTensor versions.
• Make Python len(tensor) raise for rank-0 tensors, matching NumPy rank-0 array behavior.
• Add rank-0 Python indexing support for tensor[()] and dense unitensor[()].
• Update Tensor save/load to use a versioned Tensor header, keep loading legacy Tensor files, and avoid empty-vector data access for rank-0 metadata.
• Preserve singleton broadcasting for ordinary Tensor: shape {}, {1}, {1,1}, and other one-element shapes can broadcast in binary arithmetic and assignment. Tensor::is_scalar() remains a structural query that is true only for rank 0. UniTensor broadcasting remains restricted to true rank-0 scalars because singleton bonds can carry symmetry information.
• Reject void tensor arithmetic before dtype promotion/dispatch, so void tensors do not fall into scalar-broadcast setup.
• Apply the same initialized-Tensor precondition to every raw scalar and Scalar overload of Add, Sub, Mul, Div, and Mod, in both operand orders, so Void inputs fail with a controlled operation-level error.
• Add a narrow helper for out-of-place binary scalar-broadcast output initialization. This can go away in a later arithmetic-kernel refactor.
• Make dense no-bond UniTensor use a rank-0 backing block.
• Normalize loaded dense no-bond UniTensor blocks to rank 0 when the stored block has one element.
• Make scalar-valued reductions such as Norm() and Vectordot() return rank-0 tensors.
• Make Block/Fermionic Norm() return rank-0 Tensor results as well.
• Preserve Block/Fermionic rank-0 full-trace results instead of converting out-of-place Trace() to DenseUniTensor.
• Store Block/Fermionic symmetry metadata separately, so rank-0 Block/Fermionic UniTensors do not need a fake public bond just to answer syms().
• Add a constructor path for initializing the symmetry data of a Block/Fermionic UniTensor. If symmetry data is not supplied, it is inferred from the first added Bond.
• Fix existing full-trace behavior for BlockUniTensor::Trace_ and BlockFermionicUniTensor::Trace_: after tracing the last two bonds, the old code could leave _bonds empty while syms() still indexed _bonds[0].
• Make Sort return rank-0 scalar tensors unchanged before reading the last shape dimension.
• Make Matmul_dg reject rank-0 operands before reading matrix dimensions from shape().back() / shape()[0].
• Update Tensor::append to distinguish void tensors from rank-0 tensors, reject rank-0 lhs append, and allow rank-0 rhs append as a scalar element.
• Breaking change: DirectSum now throws for rank-0 tensors. The direct sum of scalars is not well defined here; previous behavior treated scalars as rank-1 size-1 tensors and returned a rank-1 size-2 tensor.
• Drive-by bug fix in Kron the lhs_pad_left branch prepends ones to rhs’s shape and assigns that to the lhs padded shape. That can make the lhs padded product larger than lhs storage.
• Drive-by bug fix in diagonal permute() resized the block vector and then left every block Void, so it manufactured bad blocks. permute_nosignflip() in Fermionic has the same diagonal branch bug.
• Fixed lots of bugs exposed by tests and other code assuming that a scalar tensor could be accessed using [0] and similar. This ought to produce an exception on accessing an axis beyond the rank of the tensor, but in many cases (e.g. Tensordot) would silently read invalid memory if you supply it invalid axes to contract over.
• Bug fix in _from_numpy that does not handle rank-0 numpy arrays.
• Drive-by fixes to add UInt16 and Int16 to _from_numpy and numpy functions.
• Some minor code cleanups in the touched code.
• Fixed cuQuantum terr init now uses S.dtype() (real) instead of in.dtype() (possibly complex) (a real dtype bug for complex-input truncated SVD) and skips allocation when return_err == 0.
• Drive-by (unintended) bug fix in the free linalg::Norm(UniTensor) function, that would silently return Double on input Float tensors (differently to the member function UniTensor::Norm and differently to Tensor). This was via initializing the variable to accumulate the block norms vla zeros(1), which defaults to Double. Fixed by removing the free function and forwarding to the member function.
• Update the Tensor and UniTensor guides to document rank-0 construction, zero extents, Void/empty/scalar queries, item() on size-one tensors, and the distinction between Tensor singleton broadcasting and symmetry-carrying UniTensors.

Notes

I removed the int overloads of the C++ generators zeros() and ones(), and changed the array versions to take std::initializer_list. The problem with the int overload is that zeros({}), to create a rank-0 tensor of zeros, would instead call the int overload and end up as zeros(0). Now, to make a rank-1 tensor you need to write zeros({N}). This is not a problem in Python, which continues to have zeros(N) and zeros([]) versions, since Python can distinguish [] and 0. This affects a lot of tests that construct rank-1 tensors. There are quite a few of these that look suspicious, eg zeros(3 * 4 * 5).reshape({3,4,5}).astype(Types.Double).to(Device.cuda) in a GPU test, and was presumably intended to be the equivalent zeros({3,4,5}, Types.Double, Device.cuda), which has always worked. I fixed all of the ones I saw, and added some more tests of the generators.

There is no version bump to the UniTensor version number introduced in #1022 - I am assuming that there is no tensor data saved using master branch in the few hours between that PR landing and this one.

AI review notes that there are a few round-trip GPU<->CPU data transfers in the scalar broadcast CUDA kernels. They are all pre-existing, improved in some cases by explicit transfer rather than relying on unified memory, but largely outside the scope of this PR. Those will be addressed by #1003.

Tests

Ran full CPU + GPU tests + pytests

[gemini-code-assist]

Code Review

This pull request introduces comprehensive support for rank-0 (scalar) Tensors and UniTensors across Cytnx, updating initialization, reshaping, indexing, serialization, and element-wise binary arithmetic operators to handle empty shapes. The review feedback highlights a critical safety issue in Cpr.cpp where bypassing the contiguity check for scalar broadcasting could lead to silent numerical corruption on non-contiguous tensors. Additionally, an improvement was suggested in Tensor.hpp to replace raw memcpy with iterator-based vector initialization for safer and cleaner code.

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Codecov Report

❌ Patch coverage is 80.91248% with 205 lines in your changes missing coverage. Please review.
✅ Project coverage is 57.29%. Comparing base (aa62024) to head (6375602).
✅ All tests successful. No failed tests found.

Files with missing lines	Patch %	Lines
src/Tensor.cpp	52.94%	32 Missing ⚠️
src/backend/StorageImplementation.cpp	48.97%	25 Missing ⚠️
src/linalg/Div.cpp	34.21%	25 Missing ⚠️
src/linalg/Sub.cpp	36.84%	24 Missing ⚠️
include/UniTensor.hpp	78.68%	13 Missing ⚠️
src/linalg/Mul.cpp	50.00%	13 Missing ⚠️
include/backend/Tensor_impl.hpp	52.38%	10 Missing ⚠️
src/linalg/Mod.cpp	79.48%	8 Missing ⚠️
src/DenseUniTensor.cpp	90.14%	7 Missing ⚠️
src/backend/Tensor_impl.cpp	83.33%	7 Missing ⚠️
... and 14 more

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #1026      +/-   ##
==========================================
+ Coverage   55.63%   57.29%   +1.65%     
==========================================
  Files         228      229       +1     
  Lines       32896    33337     +441     
  Branches       71       71              
==========================================
+ Hits        18303    19100     +797     
+ Misses      14573    14216     -357     
- Partials       20       21       +1     

Flag	Coverage Δ
cpp	57.22% <80.91%> (+1.67%)	⬆️
python	63.35% <ø> (+0.26%)	⬆️

Flags with carried forward coverage won't be shown. Click here to find out more.

Components	Coverage Δ
C++ backend	54.98% <79.41%> (+1.68%)	⬆️
Python bindings	71.99% <97.72%> (+1.63%)	⬆️
Python package	63.35% <ø> (+0.26%)	⬆️

Files with missing lines	Coverage Δ
include/Bond.hpp	93.87% <ø> (ø)
include/backend/Storage.hpp	96.64% <100.00%> (+1.38%)	⬆️
pybind/generator_py.cpp	95.52% <100.00%> (+24.09%)	⬆️
src/Accessor.cpp	56.20% <100.00%> (+2.35%)	⬆️
src/Bond.cpp	66.46% <ø> (-0.20%)	⬇️
src/Generator.cpp	91.66% <100.00%> (-0.50%)	⬇️
src/UniTensor.cpp	88.65% <100.00%> (ø)
src/algo/Concatenate.cpp	100.00% <100.00%> (ø)
src/algo/Sort.cpp	88.23% <100.00%> (+1.56%)	⬆️
src/backend/Storage.cpp	67.35% <100.00%> (+0.16%)	⬆️
... and 44 more

... and 11 files with indirect coverage changes

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[ianmccul]

/gemini review

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Code Review

This pull request introduces comprehensive support for rank-0 (scalar) Tensors and UniTensors in Cytnx, enabling proper scalar indexing, broadcast arithmetic, reductions, and trace operations, alongside an updated versioned serialization format. The review feedback identifies important safety and robustness improvements, specifically recommending checks for uninitialized tensors in element access methods to prevent undefined behavior, and adding an explicit header inclusion in tests to avoid potential compilation failures.

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Apply GPU scalar host copies to typed scalar overloads

Fresh evidence beyond the earlier Tensor/Tensor CUDA scalar fix is that this helper is only used by the Tensor/Tensor arithmetic paths; typed scalar overloads such as scalar_cuda + 1.0, 1.0 + scalar_cuda, and the analogous Sub/Mul/Div/Mod/Cpr overloads still pass the rank-0 CUDA Tensor storage directly to the CUDA size-1 branches. Those branches host-read *_in[0] before launching, so a newly supported rank-0 CUDA Tensor combined with a C++/Python numeric scalar can still read the device-resident managed value without the host-copy/synchronizing path this helper provides.

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[ianmccul]

This is long-standing behavior. Size-1 operands are passed by value to kernels using _Lin[0] / _Rin[0] on the host side before launch. If that storage is actually on GPU, this relies on managed-memory host access and synchronization behavior. It is terrible thing to do, but beyond the scope of this PR. It should get fixed by #1003 .

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[ianmccul]

@codex review

[ianmccul]

/gemini review

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Code Review

This pull request introduces comprehensive support for rank-0 scalar Tensors and UniTensors across the codebase, updating backend implementations, linear algebra operations, and Python bindings to correctly handle scalar structures instead of treating them as 1-element rank-1 tensors. The review feedback highlights several violations of the repository style guide, specifically pointing out that newly introduced helper functions and utilities should be renamed from CamelCase to snake_case.

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Codex Review: Didn't find any major issues. Bravo.

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[ianmccul]

According to the repository style guide (line 48), new identifiers should use snake_case instead of CamelCase. All cases identified by Gemini have been resolved.

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Use located sign indices for scalar fermionic contracts

When a rank-0 BlockFermionicUniTensor is used as the left factor in an outer-product contraction with a non-scalar fermionic tensor, this new empty-Lidx path lets the loop run once per output/RHS block, but the sign update below still indexes this->_signflip[b]. The scalar left operand has only one sign entry, so any RHS with more than one block reads past the scalar's sign vector instead of reusing IDL[0]/IDR[0], making valid scalar-factor contractions crash or corrupt the result.

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[ianmccul]

This is pre-existing, will open a separate issue

[ianmccul]

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Code Review

This pull request introduces comprehensive support for rank-0 (scalar) Tensors and UniTensors across the Cytnx library, updating C++ implementations, Python bindings, and serialization formats. Key mathematical operations, reductions, and element-wise arithmetic have been updated to return or broadcast rank-0 tensors correctly instead of 1-element rank-1 tensors. Additionally, Block and BlockFermionic UniTensors now properly preserve symmetry metadata for rank-0 blocks. The review feedback highlights a performance optimization opportunity in the contraction loops of both BlockFermionicUniTensor and BlockUniTensor, where pre-allocating the index vectors outside the loop can prevent repeated dynamic memory allocations in a hot path.

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[ianmccul]

I think we're close to final version now.
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Code Review

This pull request introduces comprehensive support for rank-0 (scalar) Tensors and UniTensors across Dense, Block, and BlockFermionic implementations, updating various linear algebra operations and adding extensive unit tests. The review feedback highlights critical out-of-bounds read risks in Tensor_impl.cpp due to empty locator initialization, which should be corrected to {{0}}. Additionally, the feedback suggests performing is_void() checks before is_scalar() in Kron.cpp, using the is_void() and rank() helper methods for better consistency, accumulating loop results locally in Norm.cpp to avoid proxy overhead, replacing C-style casts with reinterpret_cast to adhere to the style guide, and resolving narrowing conversion warnings in iota_view usages.

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Code Review

This pull request implements comprehensive support for rank-0 scalar Tensors and UniTensors across the Cytnx library. It introduces is_scalar() and is_void() predicates, allows empty shapes {} for rank-0 representations, and updates core linear algebra operations (such as Sum, Min, Max, Norm, Det, Vectordot, and Trace) to return rank-0 scalar tensors instead of rank-1 tensors of size 1. Additionally, it updates binary arithmetic operations, in-place operators, and element access/assignment to support rank-0 scalar broadcasting and empty-tuple () indexing in both C++ and Python bindings. File serialization has also been updated with a new versioned magic number to correctly preserve rank-0 structures. There are no review comments provided, so we have no further feedback to offer.

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[ianmccul]

Latest version addressess all review items

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[yingjerkao]

Looks good to me.

[ianmccul]

currently surveying the codebase for more zero-extent edge cases.

[ianmccul]

will fix the extent-0 edge cases in a separate PR. this needs to get merged.