diff --git a/.github/dependabot.yml b/.github/dependabot.yml new file mode 100644 index 0000000..7e6c742 --- /dev/null +++ b/.github/dependabot.yml @@ -0,0 +1,14 @@ +version: 2 +updates: + # Maintain dependencies for GitHub Actions + - package-ecosystem: "github-actions" + directory: "/" + schedule: + interval: "weekly" + day: "friday" + + - package-ecosystem: "uv" + directory: "/" + schedule: + interval: "weekly" + day: "friday" diff --git a/.github/workflows/code_style.yml b/.github/workflows/code_style.yml new file mode 100644 index 0000000..cc0fdde --- /dev/null +++ b/.github/workflows/code_style.yml @@ -0,0 +1,36 @@ +name: Lint and Format + +on: + push: + branches: [ main ] + + pull_request: + branches: [ main ] + paths: [ '**/*.py' ] + + workflow_dispatch: + +concurrency: + group: ${{ github.workflow }}/${{ github.ref }} + cancel-in-progress: true + +jobs: + python-format: + name: Ruff Lint and Format + runs-on: ubuntu-latest + + steps: + - name: Checkout Repository + uses: actions/checkout@v6 + + - name: Setup Ruff + uses: astral-sh/ruff-action@v3 + with: + args: --version + + - name: Enforce Lint + run: ruff check . + + - name: Enforce Format + run: | + ruff format --diff . diff --git a/.github/workflows/code_test.yml b/.github/workflows/code_test.yml new file mode 100644 index 0000000..1dd8d3b --- /dev/null +++ b/.github/workflows/code_test.yml @@ -0,0 +1,96 @@ +name: Code Test + +on: + push: + branches: [ main ] + + pull_request: + branches: [ main ] + + workflow_dispatch: + workflow_call: + outputs: + artifact_name: + value: ${{ jobs.fresh_build.outputs.artifact_name }} + artifact_run_id: + value: ${{ jobs.fresh_build.outputs.run_id }} + +concurrency: + group: ${{ github.workflow }}-${{ github.ref }} + cancel-in-progress: true + +jobs: + + setup: + runs-on: ubuntu-latest + + steps: + - name: Fetch Supported Python + id: fetch-versions + run: | + versions=$(curl -fsSL https://endoflife.date/api/v1/products/python/ \ + | jq '[ .result.releases[] | select(.isEol == false) | .label ]') + + echo "supported_versions=$(echo $versions |jq -c '.')" >> $GITHUB_OUTPUT + echo "bound_versions=$(echo $versions |jq -c '[.[0],.[-1]]')" >> $GITHUB_OUTPUT + + outputs: + supported_versions: ${{ steps.fetch-versions.outputs.supported_versions }} + bound_versions: ${{ steps.fetch-versions.outputs.bound_versions }} + + fresh_build: + uses: ./.github/workflows/dist_build.yml + + testing: + runs-on: ${{ matrix.os }} + + permissions: + id-token: write # for working of oidc of codecov + + strategy: + matrix: + os: [ ubuntu-latest ] + py-version: ${{ fromJson(needs.setup.outputs.supported_versions) }} + include: + - os: windows-latest + py-version: ${{ fromJson(needs.setup.outputs.bound_versions)[0] }} + - os: windows-latest + py-version: ${{ fromJson(needs.setup.outputs.bound_versions)[1] }} + - os: macos-latest + py-version: ${{ fromJson(needs.setup.outputs.bound_versions)[0] }} + - os: macos-latest + py-version: ${{ fromJson(needs.setup.outputs.bound_versions)[1] }} + + needs: + - fresh_build + - setup + + steps: + - uses: actions/checkout@v6 + + - name: Download Build Artifacts + uses: actions/download-artifact@v7 + with: + name: ${{ needs.fresh_build.outputs.artifact_name }} + run-id: ${{ needs.fresh_build.outputs.run_id }} + path: ./dist + + - uses: astral-sh/setup-uv@v7 + with: + python-version: ${{ matrix.py-version }} + + - name: Install Packages + shell: bash + run: | + uv sync --no-dev --group test + uv pip install -v ./dist/*.whl + + - name: Run Tests + run: uv run --no-sync pytest -v -n auto --cov --cov-report=xml + + - name: Upload coverage to Codecov + uses: codecov/codecov-action@v5 + with: + fail_ci_if_error: true + use_oidc: true + verbose: true diff --git a/.github/workflows/dist_build.yml b/.github/workflows/dist_build.yml new file mode 100644 index 0000000..05c6dd6 --- /dev/null +++ b/.github/workflows/dist_build.yml @@ -0,0 +1,40 @@ +name: Build Distribution + +on: + workflow_call: + outputs: + artifact_name: + value: ${{ jobs.build.outputs.artifact_name }} + run_id: + value: ${{ github.run_id }} + +jobs: + build: + runs-on: ubuntu-latest + + steps: + - uses: actions/checkout@v6 + with: + fetch-depth: 0 + + - name: Setup uv + uses: astral-sh/setup-uv@v7 + + - name: Build distribution + run: uv build -v --clear . + + - name: Set Artifact Name + id: artifact-name + run: | + echo "artifact_name=${{ github.run_id }}[${{ github.run_attempt }}]--build-artifacts" \ + | tee -a $GITHUB_OUTPUT + + - name: Upload Build Artifacts + uses: actions/upload-artifact@v6 + with: + name: ${{ steps.artifact-name.outputs.artifact_name }} + path: dist + if-no-files-found: error + + outputs: + artifact_name: ${{ steps.artifact-name.outputs.artifact_name }} diff --git a/.github/workflows/docs_build.yml b/.github/workflows/docs_build.yml new file mode 100644 index 0000000..0eb291c --- /dev/null +++ b/.github/workflows/docs_build.yml @@ -0,0 +1,52 @@ +name: Build Documentation +permissions: + pages: write + id-token: write + +on: + pull_request: + branches: [ main ] + workflow_call: + inputs: &build-docs-inputs + deploy: + type: boolean + required: false + default: false + + workflow_dispatch: + inputs: *build-docs-inputs + +concurrency: + group: docs-build + +jobs: + + build: + runs-on: ubuntu-latest + + steps: + - uses: actions/checkout@v6 + + - name: Setup uv + uses: astral-sh/setup-uv@v7 + + - name: Build Documentation + run: uv run --no-dev --group docs mkdocs build --clean --strict + + - name: Set Artifact Name + id: artifact-name + run: | + echo "artifact_name=${{ github.run_id }}[${{ github.run_attempt }}]--docs-artifacts" \ + | tee -a $GITHUB_OUTPUT + + - name: Upload Pages Artifacts + uses: actions/upload-pages-artifact@v4 + with: + name: ${{ steps.artifact-name.outputs.artifact_name }} + path: site/ + + - name: Deploy to GitHub Pages + if: ${{ inputs.deploy }} + uses: actions/deploy-pages@v4 + with: + artifact_name: ${{ steps.artifact-name.outputs.artifact_name }} diff --git a/.github/workflows/publish_dist.yml b/.github/workflows/publish_dist.yml new file mode 100644 index 0000000..b40e2f7 --- /dev/null +++ b/.github/workflows/publish_dist.yml @@ -0,0 +1,56 @@ +name: Publish to PyPI + +on: + release: + types: [published] + +permissions: + id-token: write + +concurrency: + group: ${{ github.workflow }} + +jobs: + testing: + uses: ./.github/workflows/code_test.yml + + publish-to-pypi: + runs-on: ubuntu-latest + + environment: + name: pypi + + needs: testing + + steps: + + - &download_dist + name: Download Distributions + uses: actions/download-artifact@v7 + with: + name: ${{ needs.testing.outputs.artifact_name }} + run-id: ${{ needs.testing.outputs.artifact_run_id }} + path: ./dist + + - name: Publish to PyPI + uses: pypa/gh-action-pypi-publish@release/v1 + with: + verbose: true + + - name: Smoke Test on PyPI + shell: bash + run: | + sleep 60 + pip install -v --index-url https://pypi.org/simple/ sparse_grid + python -c "import sparse_grid;print(sparse_grid.__version__)" + + publish_docs: + needs: publish-to-pypi + + permissions: + pages: write + id-token: write + + uses: ./.github/workflows/docs_build.yml + with: + deploy: true diff --git a/.python-version b/.python-version new file mode 100644 index 0000000..c8cfe39 --- /dev/null +++ b/.python-version @@ -0,0 +1 @@ +3.10 diff --git a/docs/api/grid.md b/docs/api/grid.md new file mode 100644 index 0000000..25d8989 --- /dev/null +++ b/docs/api/grid.md @@ -0,0 +1,3 @@ +# sparse_grid.grid + +::: sparse_grid.grid diff --git a/docs/api/index.md b/docs/api/index.md new file mode 100644 index 0000000..1378785 --- /dev/null +++ b/docs/api/index.md @@ -0,0 +1,10 @@ +# API Reference + +API documentation is generated with `mkdocstrings` from module docstrings and +signatures. + +Use the pages in this section for module-level details: + +- `sparse_grid.grid` +- `sparse_grid.point` +- `sparse_grid.utils` diff --git a/docs/api/point.md b/docs/api/point.md new file mode 100644 index 0000000..be037ef --- /dev/null +++ b/docs/api/point.md @@ -0,0 +1,3 @@ +# sparse_grid.point + +::: sparse_grid.point diff --git a/docs/api/utils.md b/docs/api/utils.md new file mode 100644 index 0000000..b706eed --- /dev/null +++ b/docs/api/utils.md @@ -0,0 +1,3 @@ +# sparse_grid.utils + +::: sparse_grid.utils diff --git a/docs/getting-started.md b/docs/getting-started.md new file mode 100644 index 0000000..b2a0f9d --- /dev/null +++ b/docs/getting-started.md @@ -0,0 +1,44 @@ +# Getting Started + +## Installation + +```bash +pip install sparse_grid +``` + +## Create a sparse grid + +```python +from sparse_grid import SparseGrid + +sg = SparseGrid(dim=3, level=3) +sg.generate_points() +print(len(sg.indices)) +``` + +## Assign nodal values + +Populate nodal values (`fv`) at each sparse-grid point. + +```python +for index in sg.indices: + pos = sg.g_p[tuple(index)].pos + value = 1.0 + for coord in pos: + value *= 4.0 * coord * (1.0 - coord) + sg.g_p[tuple(index)].fv = value +``` + +## Convert to hierarchical values + +```python +sg.nodal_2_hier() +``` + +## Evaluate the sparse-grid interpolant + +```python +x = [0.2, 0.4, 0.8] +y = sg.eval_funct(x) +print(y) +``` diff --git a/docs/index.md b/docs/index.md new file mode 100644 index 0000000..1ecf370 --- /dev/null +++ b/docs/index.md @@ -0,0 +1,35 @@ +# sparse_grid + +`sparse_grid` is a compact Python implementation of regular sparse grids over +box domains. + +It provides: + +- sparse-grid index and point generation, +- nodal-to-hierarchical coefficient conversion, +- fast function evaluation using hierarchical basis functions. + +## Documentation map + +- **Getting Started**: installation and first working example. +- **User Guide**: core workflow and key data structures. +- **API Reference**: auto-generated module docs via `mkdocstrings`. + +## Quick example + +```python +from sparse_grid import SparseGrid + +sg = SparseGrid(dim=2, level=3) +sg.generate_points() + +for index in sg.indices: + pos = sg.g_p[tuple(index)].pos + sg.g_p[tuple(index)].fv = ( + 4.0 * pos[0] * (1.0 - pos[0]) * 4.0 * pos[1] * (1.0 - pos[1]) + ) + +sg.nodal_2_hier() +value = sg.eval_funct([0.25, 0.75]) +print(value) +``` diff --git a/docs/user-guide.md b/docs/user-guide.md new file mode 100644 index 0000000..63170d5 --- /dev/null +++ b/docs/user-guide.md @@ -0,0 +1,28 @@ +# User Guide + +## Core workflow + +1. Build a `SparseGrid(dim, level)`. +2. Generate points with `generate_points()`. +3. Set nodal values in each point's `fv`. +4. Convert nodal values using `nodal_2_hier()`. +5. Evaluate with `eval_funct(x)`. + +## Main objects + +- `SparseGrid` + - Manages sparse-grid structure and transforms. +- `GridPoint` + - Stores point coordinates (`pos`), nodal value (`fv`), and hierarchical value (`hv`). + +## Data layout + +- `indices`: list of interleaved indices `[l_1, p_1, ..., l_d, p_d]`. +- `g_p`: dictionary keyed by index tuple, value is `GridPoint`. +- `domain`: tuple of intervals per dimension, default `[0, 1]^d`. + +## Typical usage notes + +- Always call `generate_points()` before filling values. +- Always call `nodal_2_hier()` before `eval_funct()`. +- Use consistent dimension between `x` and the grid `dim`. diff --git a/mkdocs.yml b/mkdocs.yml new file mode 100644 index 0000000..93d69b0 --- /dev/null +++ b/mkdocs.yml @@ -0,0 +1,35 @@ +site_name: sparse_grid +site_description: A Python Sparse Grid Package +site_url: https://eggzec.github.io/sparse_grid/ +repo_url: https://github.com/eggzec/sparse_grid +repo_name: eggzec/sparse_grid + +theme: + name: material + +nav: + - Home: index.md + - Getting Started: getting-started.md + - User Guide: user-guide.md + - API Reference: + - Overview: api/index.md + - SparseGrid: api/grid.md + - GridPoint: api/point.md + - Utilities: api/utils.md + +plugins: + - search + - mkdocstrings: + handlers: + python: + options: + show_source: false + show_signature_annotations: true + merge_init_into_class: true + show_root_heading: true + show_root_toc_entry: false + +markdown_extensions: + - admonition + - pymdownx.superfences + - pymdownx.highlight diff --git a/pyproject.toml b/pyproject.toml new file mode 100644 index 0000000..e4ae102 --- /dev/null +++ b/pyproject.toml @@ -0,0 +1,126 @@ +[build-system] +requires = ["hatchling >= 1.26", "hatch-vcs"] +build-backend = "hatchling.build" + +[project] +name = "sparse_grid" +dynamic = ["version"] +description = "A Python Sparse Grid Package" +authors = [ + { name = "John Burkardt", email = "jvb25@pitt.edu" }, +] +maintainers = [ + { name = "Saud Zahir", email = "m.saud.zahir@gmail.com" }, + { name = "M Laraib Ali", email = "laraibg786@outlook.com" } +] +readme = "README.md" +license = "BSD-3-Clause" +keywords = [ + "sparse grids", "python", +] +classifiers = [ + "Development Status :: 5 - Production/Stable", + "Intended Audience :: Science/Research", + "Intended Audience :: Developers", + "License :: OSI Approved :: BSD License", + "Programming Language :: Python", + "Programming Language :: Python :: 3", + "Programming Language :: Python :: 3.10", + "Programming Language :: Python :: 3.11", + "Programming Language :: Python :: 3.12", + "Programming Language :: Python :: 3.13", + "Programming Language :: Python :: 3.14", + "Programming Language :: Python :: 3 :: Only", + "Topic :: Software Development", + "Topic :: Scientific/Engineering", + "Operating System :: OS Independent", + "Operating System :: Microsoft :: Windows", + "Operating System :: POSIX", + "Operating System :: Unix", + "Operating System :: MacOS", +] +dependencies = [] +requires-python = ">=3.10" + +[project.urls] +homepage = "https://eggzec.github.io/sparse_grid/" +documentation = "https://eggzec.github.io/sparse_grid/" +source = "https://github.com/eggzec/sparse_grid" +# TODO: provide changelog URL from docs +releasenotes = "https://github.com/eggzec/sparse_grid/releases/latest" +issues = "https://github.com/eggzec/sparse_grid/issues" + +[dependency-groups] +dev = [ + {include-group = "docs"}, + {include-group = "lint"}, + {include-group = "test"} +] +docs = [ + "mkdocs>=1.6.1", + "mkdocs-material>=9.7.1", + "mkdocstrings[python]>=0.30.1", + "mkdocs-minify-plugin>=0.8.0", + "pymdown-extensions>=10.15", +] +lint = [ + "ruff==0.15.*", +] +test = [ + "pytest>=8.3.5", + "pytest-cov>=7.0.0", + "pytest-xdist>=3.6.1", +] + +[tool.hatch.version] +source = "vcs" + +[tool.ruff] +line-length = 80 +indent-width = 4 +preview = true + +# Output serialization format for violations. The default serialization +# format is "full" [env: RUFF_OUTPUT_FORMAT=] [possible values: +# concise, full, json, json-lines, junit, grouped, github, gitlab, +# pylint, rdjson, azure, sarif] +output-format = "grouped" + +[tool.ruff.lint] +isort.lines-after-imports = 2 +isort.split-on-trailing-comma = false + +select = [ + "ANN", # flake8-annotations (required strict type annotations for public functions) + "S", # flake8-bandit (checks basic security issues in code) + "BLE", # flake8-blind-except (checks the except blocks that do not specify exception) + "FBT", # flake8-boolean-trap (ensure that boolean args can be used with kw only) + "E", # pycodestyle errors (PEP 8 style guide violations) + "W", # pycodestyle warnings (e.g., extra spaces, indentation issues) + "DOC", # pydoclint issues (e.g., extra or missing return, yield, warnings) + "A", # flake8-buitins (check variable and function names to not shadow builtins) + "N", # Naming convention checks (e.g., PEP 8 variable and function names) + "F", # Pyflakes errors (e.g., unused imports, undefined variables) + "I", # isort (Ensures imports are sorted properly) + "B", # flake8-bugbear (Detects likely bugs and bad practices) + "TID", # flake8-tidy-imports (Checks for banned or misplaced imports) + "UP", # pyupgrade (Automatically updates old Python syntax) + "YTT", # flake8-2020 (Detects outdated Python 2/3 compatibility issues) + "FLY", # flynt (Converts old-style string formatting to f-strings) + "PIE", # flake8-pie + "PL", # pylint + "RUF", # Ruff-specific rules (Additional optimizations and best practices) +] + +ignore = [] + +[tool.ruff.lint.per-file-ignores] +"**/__init__.py" = ["RUF067"] +"tests/*.py" = [] + +[tool.ruff.format] +docstring-code-format = true +skip-magic-trailing-comma = true + +[tool.pytest.ini_options] +addopts = "--doctest-modules" diff --git a/sparse_grid/__init__.py b/sparse_grid/__init__.py new file mode 100644 index 0000000..a9074ad --- /dev/null +++ b/sparse_grid/__init__.py @@ -0,0 +1,11 @@ +from importlib.metadata import PackageNotFoundError, version + +from .grid import SparseGrid + + +try: + __version__ = version(__name__) +except PackageNotFoundError: + __version__ = "unknown" + +__all__ = ["SparseGrid"] diff --git a/sparse_grid/grid.py b/sparse_grid/grid.py new file mode 100644 index 0000000..ae113b6 --- /dev/null +++ b/sparse_grid/grid.py @@ -0,0 +1,208 @@ +"""Sparse-grid container and algorithms.""" + +from __future__ import annotations + +import copy +import math + +from .point import GridPoint +from .utils import cross, eval_basis_1d + + +EVEN_DIVISOR = 2 + + +class SparseGrid: + """Regular sparse grid over a box domain. + + A grid is defined by: + - `dim`: number of dimensions, + - `level`: sparse-grid level, + - `indices`: generated hierarchical indices, + - `g_p`: map from index tuple to `GridPoint`. + """ + + def __init__(self, dim: int = 1, level: int = 1) -> None: + self.dim = dim + self.level = level + self.g_p: dict[tuple[int, ...], GridPoint] = {} + self.indices: list[list[int]] = [] + self.domain = ((0.0, 1.0),) * dim + self.action = self.eval_action + + def print_grid(self) -> None: + """Print the currently active hierarchical subspace index.""" + print(self.h_space) + + def eval_action(self) -> None: + """Accumulate contribution of the current hierarchical subspace.""" + basis = copy.deepcopy(self.eval_per_dim[0][self.h_space[0] - 1][0]) + value = self.eval_per_dim[0][self.h_space[0] - 1][1] + for i in range(1, self.dim): + value *= self.eval_per_dim[i][self.h_space[i] - 1][1] + basis += self.eval_per_dim[i][self.h_space[i] - 1][0] + self.value += self.g_p[tuple(basis)].hv * value + + def eval_funct(self, x: list[float]) -> float: + """Evaluate a sparse grid function. + + Hierarchical values have to be set. + + Parameters + ---------- + x + Evaluation point in physical coordinates. + + Returns + ------- + float + Evaluated sparse-grid function value at `x`. + """ + self.value = 0.0 + self.eval_per_dim: list[list[list[list[int]] | float]] = [] + for i in range(self.dim): + self.eval_per_dim.append([]) + for j in range(1, self.level + 1): + pos = (x[i] - self.domain[i][0]) / ( + self.domain[i][1] - self.domain[i][0] + ) + basis = int(math.ceil(pos * 2 ** (j - 1)) * 2 - 1) + if basis == -1: + basis = 1 + self.eval_per_dim[i].append([[j, basis]]) + else: + self.eval_per_dim[i].append([[j, basis]]) + self.eval_per_dim[i][j - 1].append( + eval_basis_1d( + x[i], self.eval_per_dim[i][j - 1][0], self.domain[i] + ) + ) + self.action = self.eval_action + self.loop_hier_spaces() + return self.value + + def loop_hier_spaces(self) -> None: + """Iterate over all hierarchical subspaces of the sparse grid.""" + for i in range(1, self.level + 1): + self.h_space = [i] + self.loop_hier_spaces_rec(self.dim - 1, self.level - (i - 1)) + + def loop_hier_spaces_rec(self, dim: int, level: int) -> None: + """Recursively traverse hierarchical subspaces. + + Parameters + ---------- + dim + Remaining dimensions to recurse through. + level + Remaining level budget for sparse-grid admissibility. + """ + if dim > 1: + for i in range(1, level + 1): + self.h_space.append(i) + self.loop_hier_spaces_rec(dim - 1, level - (i - 1)) + self.h_space.pop() + else: + for i in range(1, level + 1): + self.h_space.append(i) + self.action() + self.h_space.pop() + + def generate_points(self) -> None: + """Generate sparse-grid indices and corresponding `GridPoint` values.""" + self.indices = self.generate_points_rec(self.dim, self.level) + for i in range(len(self.indices)): + self.g_p[tuple(self.indices[i])] = GridPoint( + self.indices[i], self.domain + ) + + def generate_points_rec( + self, dim: int, level: int, cur_level: int | None = None + ) -> list[list[int]]: + """Run over all hierarchical subspaces and add all their indices. + + Returns + ------- + list[list[int]] + All generated sparse-grid multi-indices. + """ + basis_cur = [] + if cur_level is None: + cur_level = 1 + for i in range(1, 2 ** (cur_level) + 1, 2): + basis_cur.append([cur_level, i]) + if dim == 1 and cur_level == level: + return basis_cur + if dim == 1: + basis_cur += self.generate_points_rec(dim, level, cur_level + 1) + return basis_cur + if cur_level == level: + return cross( + basis_cur, + self.generate_points_rec(dim - 1, level - cur_level + 1), + ) + return cross( + basis_cur, self.generate_points_rec(dim - 1, level - cur_level + 1) + ) + self.generate_points_rec(dim, level, cur_level + 1) + + def nodal_2_hier_1d( + self, node: list[int], i: int, j: int, dim: int + ) -> None: + """Apply one-dimensional nodal-to-hierarchical transform. + + Parameters + ---------- + node + Fixed index components from all dimensions except `dim`. + i + Level index in transformed dimension. + j + Position index in transformed dimension. + dim + Dimension currently being transformed. + """ + left = [i - 1, j // 2] + right = [i - 1, j // 2 + 1] + while left[1] % EVEN_DIVISOR == 0 and left[0] > 0: + left = [left[0] - 1, left[1] // EVEN_DIVISOR] + while right[1] % EVEN_DIVISOR == 0 and right[0] > 0: + right = [right[0] - 1, right[1] // EVEN_DIVISOR] + if len(node) > EVEN_DIVISOR: + pre_cur_dim = node[0 : 2 * dim] + post_cur_dim = node[2 * dim : len(node) + 1] + index = [*pre_cur_dim, i, j, *post_cur_dim] + left = [*pre_cur_dim, *left, *post_cur_dim] + right = [*pre_cur_dim, *right, *post_cur_dim] + elif dim == 0: + index = [i, j, *node] + left += node + right += node + else: + index = [*node, i, j] + left = [*node, *left] + right = [*node, *right] + + if left[2 * dim] == 0: + if right[2 * dim] != 0: + self.g_p[tuple(index)].hv -= 0.5 * self.g_p[tuple(right)].hv + elif right[2 * dim] == 0: + self.g_p[tuple(index)].hv -= 0.5 * self.g_p[tuple(left)].hv + else: + self.g_p[tuple(index)].hv -= 0.5 * ( + self.g_p[tuple(left)].hv + self.g_p[tuple(right)].hv + ) + + def nodal_2_hier(self) -> None: + """Convert all nodal values in the grid to hierarchical values.""" + for i in range(len(self.indices)): + self.g_p[tuple(self.indices[i])].hv = self.g_p[ + tuple(self.indices[i]) + ].fv + for d in range(self.dim): + for i in range(self.level, 0, -1): + indices = self.generate_points_rec( + self.dim - 1, self.level - i + 1 + ) + for j in range(1, 2**i + 1, 2): + for k in range(len(indices)): + self.nodal_2_hier_1d(indices[k], i, j, d) diff --git a/sparse_grid/point.py b/sparse_grid/point.py new file mode 100644 index 0000000..8037f4f --- /dev/null +++ b/sparse_grid/point.py @@ -0,0 +1,65 @@ +"""Point model used by sparse-grid containers.""" + +from __future__ import annotations + + +class GridPoint: + """Representation of a sparse-grid point. + + Stores the Cartesian position and both nodal (`fv`) and hierarchical + (`hv`) function values. + """ + + def __init__( + self, + index: list[int] | None = None, + domain: tuple[tuple[float, float], ...] | None = None, + ) -> None: + self.hv: float = 0.0 + self.fv: float = 0.0 + if index is None: + self.pos: list[float] = [] + else: + self.pos = self.point_position(index, domain) + + @staticmethod + def point_position( + index: list[int], domain: tuple[tuple[float, float], ...] | None = None + ) -> list[float]: + """Convert a level/position index into physical coordinates. + + Parameters + ---------- + index + Interleaved multi-index `[l_1, p_1, ..., l_d, p_d]`. + domain + Optional domain bounds per dimension. If omitted, `[0, 1]^d` + is assumed. + + Returns + ------- + list[float] + Point coordinates in physical space. + """ + coord = [] + if domain is None: + for i in range(len(index) // 2): + coord.append(index[2 * i + 1] / 2.0 ** index[2 * i]) + else: + for i in range(len(index) // 2): + coord.append( + (domain[i][1] - domain[i][0]) + * index[2 * i + 1] + / 2.0 ** index[2 * i] + + domain[i][0] + ) + return coord + + def print_point(self) -> None: + """Print point coordinates as a tab-separated line.""" + if not self.pos: + return + out = "" + for i in range(len(self.pos)): + out += str(self.pos[i]) + "\t" + print(out) diff --git a/sparse_grid/utils.py b/sparse_grid/utils.py new file mode 100644 index 0000000..e919ab5 --- /dev/null +++ b/sparse_grid/utils.py @@ -0,0 +1,48 @@ +"""Utility functions for sparse-grid basis and index operations.""" + +from __future__ import annotations + + +def cross(*args: list[list[int]]) -> list[list[int]]: + """Compute pairwise cross-product (concatenation) of two index lists. + + Parameters + ---------- + *args + Two index collections to combine. + + Returns + ------- + list[list[int]] + Cross-product of index lists. + """ + ans: list[list[int]] = [] + for arg in args[0]: + for arg2 in args[1]: + ans.append([*arg, *arg2]) + return ans + + +def eval_basis_1d( + x: float, basis: list[int], interval: tuple[float, float] | None = None +) -> float: + """Evaluate a one-dimensional hat basis function. + + Parameters + ---------- + x + Evaluation coordinate. + basis + Basis index as `[level, position]`. + interval + Optional physical interval. If omitted, `[0, 1]` is used. + + Returns + ------- + float + Value of 1-D hat basis at `x`. + """ + if interval is None: + return 1.0 - abs(x * 2 ** basis[0] - basis[1]) + pos = (x - interval[0]) / (interval[1] - interval[0]) + return 1.0 - abs(pos * 2 ** basis[0] - basis[1]) diff --git a/tests/test_sparse_grid_no_bound.py b/tests/test_sparse_grid_no_bound.py new file mode 100644 index 0000000..52ba9e7 --- /dev/null +++ b/tests/test_sparse_grid_no_bound.py @@ -0,0 +1,99 @@ +import unittest + +from sparse_grid import SparseGrid + + +class TestFuncTest(unittest.TestCase): + """simple test of sparse grid for sparse grid in 3d of level 3""" + + def test_sg_no_bound_3d(self) -> None: + # + # SG is a sparse grid of dimension 3 and level 3. + # Create sg.indices which stores level and position for each point. + # + sg = SparseGrid(3, 3) + # + # Determine sg.gP with the coordinates of the points + # associated with the sparse grid index set. + # + sg.generate_points() + # + # Print the points in the grid. + # + print("") + print("Coordinates of points in 3D sparse grid of level 3.") + print("") + for i in range(len(sg.indices)): + sg.g_p[tuple(sg.indices[i])].print_point() + # + # Did we compute the right number of grid points? + # + self.assertEqual(len(sg.indices), 31) + # + # Evaluate 4x(1-x)*4y(1-y)*4z(1-z) at each grid point. + # + for i in range(len(sg.indices)): + total = 1.0 + pos = sg.g_p[tuple(sg.indices[i])].pos + for j in range(len(pos)): + total *= 4.0 * pos[j] * (1.0 - pos[j]) + sg.g_p[tuple(sg.indices[i])].fv = total + # + # Convert the sparse grid from nodal to hierarchical values. + # + sg.nodal_2_hier() + # + # Does the evaluation of the sparse grid function in + # hierarchical values give the correct value gv? + # + for i in range(len(sg.indices)): + self.assertEqual( + sg.g_p[tuple(sg.indices[i])].fv, + sg.eval_funct(sg.g_p[tuple(sg.indices[i])].pos), + ) + + def test_sg_no_bound_2d(self) -> None: + # + # SG is a sparse grid of dimension 2 and level 3. + # Create sg.indices which stores level and position for each point. + # + sg = SparseGrid(2, 3) + # + # Determine sg.gP with the coordinates of the points + # associated with the sparse grid index set. + # + sg.generate_points() + # + # Print the points in the grid. + # + print("") + print("Coordinates of points in 2D sparse grid of level 3.") + print("") + for i in range(len(sg.indices)): + sg.g_p[tuple(sg.indices[i])].print_point() + # + # Did we compute the right number of grid points? + # + self.assertEqual(len(sg.indices), 17) + # + # Evaluate 4x(1-x)*4y(1-y) at each grid point. + # + for i in range(len(sg.indices)): + total = 1.0 + pos = sg.g_p[tuple(sg.indices[i])].pos + for j in range(len(pos)): + total *= 4.0 * pos[j] * (1.0 - pos[j]) + sg.g_p[tuple(sg.indices[i])].fv = total + # + # Convert to hierarchical values. + # + sg.nodal_2_hier() + # + # Does the evaluation of sparse grid function in + # hierarchical values give the correct value gv? + # + for i in 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