Implement prototype for torch based fermionic library.

.github/workflows/CI.yml

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+name: CI
+
+on: [push, pull_request]
+
+jobs:
+  CI:
+
+    runs-on: ubuntu-latest
+    strategy:
+      fail-fast: false
+      matrix:
+        include:
+          - python-version: "3.10"
+            pytorch-version: "1.11"
+          - python-version: "3.10"
+            pytorch-version: "1.12"
+          - python-version: "3.10"
+            pytorch-version: "1.13"
+          - python-version: "3.10"
+            pytorch-version: "2.0"
+          - python-version: "3.10"
+            pytorch-version: "2.1"
+
+          - python-version: "3.11"
+            pytorch-version: "1.13"
+          - python-version: "3.11"
+            pytorch-version: "2.0"
+          - python-version: "3.11"
+            pytorch-version: "2.1"
+
+    steps:
+      - uses: actions/checkout@v4
+      - name: Set up Python ${{ matrix.python-version }}
+        uses: actions/setup-python@v4
+        with:
+          python-version: ${{ matrix.python-version }}
+      - name: Install requirements
+        run: |
+          pip install pylint mypy pytest pytest-cov
+          pip install torch==${{ matrix.pytorch-version }}+cpu --index-url https://download.pytorch.org/whl/cpu
+          pip install multimethod
+      - name: Run pylint
+        run: pylint tat
+        working-directory: ${{ github.workspace }}
+      - name: Run mypy
+        run: mypy tat
+        working-directory: ${{ github.workspace }}
+      - name: Run pytest
+        run: pytest
+        working-directory: ${{ github.workspace }}

.gitignore

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+.coverage
+__pycache__
+env

README.md

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+# TAT
+
+A Fermionic tensor library based on pytorch.
+
+---
+
+Some function not implemented or defined.
+- identity
+- exponential
+- conjugate
+- svd
+- qr

pyproject.toml

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+[project]
+name = "tat"
+version = "0.4.0"
+authors = [
+  {email = "[email protected]", name = "Hao Zhang"}
+]
+description = "A Fermionic tensor library based on pytorch."
+readme = "README.md"
+requires-python = ">=3.10"
+license = {text = "GPL-3.0-or-later"}
+dependencies = [
+  "multimethod",
+  "torch",
+]
+
+[tool.pylint]
+max-line-length = 120
+generated-members = "torch.*"
+
+[tool.yapf]
+based_on_style = "google"
+column_limit = 120
+
+[tool.mypy]
+check_untyped_defs = true
+disallow_untyped_defs = true
+
+[tool.pytest.ini_options]
+pythonpath = "."
+testpaths = ["tests",]
+addopts = "--cov=tat"

tat/__init__.py

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+"""
+The tat is a Fermionic tensor library based on pytorch.
+"""
+
+from .edge import Edge
+from .tensor import Tensor

tat/_utility.py

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+"""
+Some internal utility used by tat.
+"""
+
+import torch
+
+# pylint: disable=missing-function-docstring
+# pylint: disable=no-else-return
+
+
+def unsqueeze(tensor: torch.Tensor, index: int, rank: int) -> torch.Tensor:
+    return tensor.reshape([-1 if i == index else 1 for i in range(rank)])
+
+
+def neg_symmetry(tensor: torch.Tensor) -> torch.Tensor:
+    if tensor.dtype is torch.bool:
+        return tensor
+    else:
+        return -tensor
+
+
+def add_symmetry(tensor_1: torch.Tensor, tensor_2: torch.Tensor) -> torch.Tensor:
+    if tensor_1.dtype is torch.bool:
+        return torch.logical_xor(tensor_1, tensor_2)
+    else:
+        return torch.add(tensor_1, tensor_2)
+
+
+def zero_symmetry(tensor: torch.Tensor) -> torch.Tensor:
+    # pylint: disable=singleton-comparison
+    if tensor.dtype is torch.bool:
+        return tensor == False
+    else:
+        return tensor == 0
+
+
+def parity(tensor: torch.Tensor) -> torch.Tensor:
+    if tensor.dtype is torch.bool:
+        return tensor
+    else:
+        return tensor % 2 != 0

tat/compat.py

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+"""
+This file implement a compat layer for legacy TAT interface.
+"""
+
+from __future__ import annotations
+import typing
+from multimethod import multimethod
+import torch
+from .edge import Edge as E
+from .tensor import Tensor as T
+
+# pylint: disable=too-few-public-methods
+# pylint: disable=too-many-instance-attributes
+
+
+class CompatSymmetry:
+    """
+    The common Symmetry namespace
+    """
+
+    def __init__(self: CompatSymmetry, fermion: tuple[bool, ...], dtypes: tuple[torch.dtype, ...]) -> None:
+        self.fermion: tuple[bool, ...] = fermion
+        self.dtypes: tuple[torch.dtype, ...] = dtypes
+
+        # pylint: disable=invalid-name
+        self.S: CompatScalar
+        self.D: CompatScalar
+        self.C: CompatScalar
+        self.Z: CompatScalar
+        self.float32: CompatScalar
+        self.float64: CompatScalar
+        self.float: CompatScalar
+        self.complex64: CompatScalar
+        self.complex128: CompatScalar
+        self.complex: CompatScalar
+
+        self.S = self.float32 = CompatScalar(self, torch.float32)
+        self.D = self.float64 = self.float = CompatScalar(self, torch.float64)
+        self.C = self.complex64 = CompatScalar(self, torch.complex64)
+        self.Z = self.complex128 = self.complex = CompatScalar(self, torch.complex128)
+
+    def _parse_segments(self: CompatSymmetry, segments: list) -> tuple[tuple[torch.Tensor, ...], int]:
+        # Segments may be [Sym] or [(Sym, Size)]
+        try:
+            # try [(Sym, Size)] first
+            return self._parse_segments_kernel(segments)
+        except TypeError:
+            # Cannot unpack is a type error, value[index] is a type error, too
+            # convert [Sym] to [(Sym, Size)]
+            return self._parse_segments_kernel([(sym, 1) for sym in segments])
+
+    def _parse_segments_kernel(self: CompatSymmetry, segments: list) -> tuple[tuple[torch.Tensor, ...], int]:
+        # [(Sym, Size)] for every element
+        dimension = sum(dim for _, dim in segments)
+        symmetry = tuple(
+            torch.tensor(
+                sum(
+                    ([self._parse_segments_get_subsymmetry(sym, index)] * dim
+                     for sym, dim in segments),
+                    [],
+                ),  # Concat all segment for this subsymmetry
+                dtype=sub_symmetry,
+            )  # Generate subsymmetry one by one
+            for index, sub_symmetry in enumerate(self.dtypes))
+        return symmetry, dimension
+
+    def _parse_segments_get_subsymmetry(self: CompatSymmetry, sym: object, index: int) -> object:
+        # Most of time, symmetry is a tuple of subsymmetry
+        # But if there is only ome subsymmetry, it could not be a tuple but subsymmetry itself.
+        # pylint: disable=no-else-return
+        if isinstance(sym, tuple):
+            return sym[index]
+        else:
+            if len(self.fermion) == 1:
+                return sym
+            else:
+                raise TypeError(f"{sym=} is not subscriptable")
+
+    @multimethod
+    def Edge(self: CompatSymmetry, dimension: int) -> E:
+        """
+        Create edge with compat interface.
+        """
+        # pylint: disable=invalid-name
+        symmetry = tuple(torch.zeros(dimension, dtype=sub_symmetry) for sub_symmetry in self.dtypes)
+        return E(fermion=self.fermion, dtypes=self.dtypes, symmetry=symmetry, dimension=dimension, arrow=False)
+
+    @Edge.register
+    def _(self: CompatSymmetry, segments: list, arrow: bool = False) -> E:
+        symmetry, dimension = self._parse_segments(segments)
+        return E(fermion=self.fermion, dtypes=self.dtypes, symmetry=symmetry, dimension=dimension, arrow=arrow)
+
+    @Edge.register
+    def _(self: CompatSymmetry, segments_and_bool: tuple[list, bool]) -> E:
+        segments, arrow = segments_and_bool
+        symmetry, dimension = self._parse_segments(segments)
+        return E(fermion=self.fermion, dtypes=self.dtypes, symmetry=symmetry, dimension=dimension, arrow=arrow)
+
+
+class CompatScalar:
+    """
+    The common Scalar namespace.
+    """
+
+    def __init__(self: CompatScalar, symmetry: CompatSymmetry, dtype: torch.dtype) -> None:
+        self.symmetry: CompatSymmetry = symmetry
+        self.dtype: torch.dtype = dtype
+
+    @multimethod
+    def Tensor(self: CompatScalar, names: list[str], edges: list) -> T:
+        """
+        Create tensor with compat names and edges.
+        """
+        # pylint: disable=invalid-name
+        return T(
+            tuple(names),
+            tuple(self.symmetry.Edge(edge) for edge in edges),
+            fermion=self.symmetry.fermion,
+            dtypes=self.symmetry.dtypes,
+            dtype=self.dtype,
+        )
+
+    @Tensor.register
+    def _(self: CompatScalar) -> T:
+        result = T(
+            (),
+            (),
+            fermion=self.symmetry.fermion,
+            dtypes=self.symmetry.dtypes,
+            dtype=self.dtype,
+        )
+        result.data.reshape([-1])[0] = 1
+        return result
+
+    @Tensor.register
+    def _(
+        self: CompatScalar,
+        number: typing.Any,
+        names: list[str] | None = None,
+        edge_symmetry: list | None = None,
+        edge_arrow: list[bool] | None = None,
+    ) -> T:
+        # Create high rank tensor with only one element
+        if names is None:
+            names = []
+        if edge_symmetry is None:
+            edge_symmetry = [None for _ in names]
+        if edge_arrow is None:
+            edge_arrow = [False for _ in names]
+        result = T(
+            tuple(names),
+            tuple(
+                E(
+                    fermion=self.symmetry.fermion,
+                    dtypes=self.symmetry.dtypes,
+                    symmetry=tuple(
+                        torch.tensor([self._create_size1_get_subsymmetry(symmetry, index)], dtype=dtype)
+                        for index, dtype in enumerate(self.symmetry.dtypes)),
+                    dimension=1,
+                    arrow=arrow,
+                )
+                for symmetry, arrow in zip(edge_symmetry, edge_arrow)),
+            fermion=self.symmetry.fermion,
+            dtypes=self.symmetry.dtypes,
+            dtype=self.dtype,
+        )
+        result.data.reshape([-1])[0] = number
+        return result
+
+    def _create_size1_get_subsymmetry(self: CompatScalar, sym: object, index: int) -> object:
+        # pylint: disable=no-else-return
+        if sym is None:
+            return 0
+        elif isinstance(sym, tuple):
+            return sym[index]
+        else:
+            if len(self.symmetry.fermion) == 1:
+                return sym
+            else:
+                raise TypeError(f"{sym=} is not subscriptable")
+
+
+No: CompatSymmetry = CompatSymmetry(fermion=(), dtypes=())
+Z2: CompatSymmetry = CompatSymmetry(fermion=(False,), dtypes=(torch.bool,))
+U1: CompatSymmetry = CompatSymmetry(fermion=(False,), dtypes=(torch.int,))
+Fermi: CompatSymmetry = CompatSymmetry(fermion=(True,), dtypes=(torch.int,))
+FermiZ2: CompatSymmetry = CompatSymmetry(fermion=(True, False), dtypes=(torch.int, torch.bool))
+FermiU1: CompatSymmetry = CompatSymmetry(fermion=(True, False), dtypes=(torch.int, torch.int))
+Parity: CompatSymmetry = CompatSymmetry(fermion=(True,), dtypes=(torch.bool,))
+FermiFermi: CompatSymmetry = CompatSymmetry(fermion=(True, True), dtypes=(torch.int, torch.int))
+Normal: CompatSymmetry = No