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Tensorium_lib

Tensorium_lib is a C++17 scientific computing library focused on high-performance CPU kernels and numerical relativity workflows.

Current scope

  • Core dense linear algebra and tensor containers (Vector, Matrix, Tensor) with aligned storage and SIMD paths.
  • Numerical relativity stack centered on BSSN_Grid (single-grid, vacuum BSSN/Z4c style evolution).
  • Test and visualization tooling for long moving-puncture runs.
  • Optional R&D compiler plugins (LLVM/Clang/MLIR).

Domain coherence (what is production vs experimental)

Area Status Notes
Core/Vector.hpp usable SIMD + aligned storage, covered by Tests/core/VectorTests.cpp.
Core/Matrix.hpp usable Dense ops + GEMM path + inverse/solve utilities, covered by Tests/core/MatrixTests.cpp.
Core/Tensor.hpp usable with caution Generic rank support, contraction/product utilities; still evolving.
Physics/DiffGeometry/BSSN_Grid active core Main NR implementation used by current tests and runs.
Physics/DiffGeometry/BSSN legacy/experimental Historical pointwise layer, not the main runtime path.
Backend/MPI foundational Domain decomposition and halo exchange utilities exist, not yet integrated end-to-end in BSSN_Grid runtime.
Backend/CUDA scaffold CUDA structures exist; NR kernels are currently CPU/OpenMP.
Plugins/ (LLVM/MLIR) R&D Optional compiler tooling, not required for physics runs.

Repository map

includes/Tensorium/Core/                          # Vector/Matrix/Tensor + solvers + derivatives
includes/Tensorium/Backend/SIMD/                 # ISA traits (SSE/AVX/AVX2/AVX512/NEON)
includes/Tensorium/Backend/OpenMP/               # OpenMP compatibility helpers
includes/Tensorium/Backend/MPI/                  # Cartesian decomposition + halo exchange building blocks
includes/Tensorium/Physics/DiffGeometry/BSSN_Grid/  # Main numerical relativity implementation
Tests/core/                                      # Core numerical tests
Tests/bssn/                                      # NR validation/stability tests and CSV exporters
Plugins/                                         # Optional LLVM/Clang/MLIR experiments

Build

Requirements

  • CMake >= 3.22
  • C++17 compiler (Clang recommended)
  • OpenMP runtime
  • Optional: MPI, CUDA toolkit, OpenBLAS/BLAS (or Accelerate on macOS), pybind11, NumPy

Configure and compile

cmake -S . -B build \
  -DCMAKE_BUILD_TYPE=Release \
  -DBUILD_TESTS=ON \
  -DBUILD_PYBIND=OFF \
  -DBUILD_PLUGINS=OFF
cmake --build build -j

If you need the Python extension from CMake:

cmake -S . -B build \
  -DCMAKE_BUILD_TYPE=Release \
  -DBUILD_TESTS=OFF \
  -DBUILD_PYBIND=ON \
  -DBUILD_PLUGINS=OFF
cmake --build build -j --target tensorium

Useful options

Option Default Description
BUILD_TESTS ON Build test executables in Tests/.
BUILD_PYBIND OFF Build Python bindings.
BUILD_PLUGINS ON Build LLVM/Clang plugins. Disable if you only need runtime/library code.
USE_MPI OFF Link MPI and enable MPI compile definitions.
USE_CUDA OFF Enable CUDA language/backend pieces.
AVX2 / AVX512 OFF Force stronger x86 codegen flags when desired.
TENSORIUM_BSSN_PROFILE_KERNELS OFF BSSN kernel timers.
TENSORIUM_BSSN_VALIDATE_TILDE_GAMMA_SYMBOLS OFF Extra BSSN consistency validation.

Running tests

ctest --test-dir build --output-on-failure

Common filters:

ctest --test-dir build -R core
ctest --test-dir build -R bssn
./build/Tests/TensoriumTests --list

Python bindings

Python bindings expose core vector/matrix/tensor algebra and selected differential-geometry helpers.

Prerequisites

  • python3
  • python3 -m pip
  • Python packages: setuptools, wheel, cmake, numpy, pybind11

Install prerequisites:

python3 -m pip install --upgrade pip setuptools wheel cmake numpy pybind11

Build and install (editable)

python3 -m pip install -e .

Alternative: build extension only (no install)

python3 setup.py build_ext --inplace

Quick check

python3 - <<'PY'
import tensorium
v = tensorium.Vectord([1.0, 2.0, 3.0])
print(v)
PY

NumPy interop example:

python3 - <<'PY'
import numpy as np
import tensorium
A = tensorium.Matrixd.from_numpy(np.array([[1.0, 2.0], [3.0, 4.0]]))
print(tensorium.matrices.det(A))
PY

Current scope of Python API:

  • Vector/Vectord, Matrix/Matrixd, Tensor2d, Tensor4d
  • tns.* algebra helpers (add/sub/mul, norms, solvers, tensor contractions, etc.)
  • metric/curvature helpers (Metric, compute_christoffel, compute_riemann_tensor, Ricci utilities)
  • bssn.BSSNGrid with BSSN initial-data builders (minkowski, schwarzschild_isotropic, kerr_schild_single, Bowen-York puncture initializers)
  • explicit TwoPuncturesC init path via tensorium.bssn.binary_bowen_york_puncture_twopunctures_c_init(...)

bssn quick start:

python3 - <<'PY'
import tensorium
g = tensorium.bssn.BSSNGrid(24, 24, 24, 4, 0.25, 0.25, 0.25)
tensorium.bssn.minkowski(g)
alpha = g.alpha()
print(alpha.shape, alpha.min(), alpha.max())
PY

Field access examples:

  • g.alpha() interior values
  • g.alpha(include_halo=True) including ghost zones
  • g.beta(0) for beta^x
  • g.gamma_tilde(tensorium.bssn.XX) for \\tilde{\\gamma}_{xx}

TwoPuncturesC availability check:

python3 - <<'PY'
import tensorium
print(tensorium.bssn.has_twopunctures_c())
PY

Not yet exposed in Python:

  • full BSSN_Grid evolution runtime (RK stepper/gauge controls/diagnostics callbacks)
  • MPI/CUDA backends

Numerical relativity notes

  • The active physics path is includes/Tensorium/Physics/DiffGeometry/BSSN_Grid.
  • The moving puncture visualization/stability driver is in Tests/bssn/bowen_york_boost_stability.cpp.
  • A standalone moving-puncture executable is available at: ./build/Tests/TensoriumMovingPuncture
  • It consumes the same environment variables as the test driver (TENSORIUM_MOVING_PUNCTURE_* + OMP_*) without --test.
  • Interpolated Two-Punctures initialization requires the external TwoPunctures codebase from: https://github.com/GRTLCollaboration/TwoPunctures.git
  • In this repository, that external solver is expected through the local ../TwoPuncturesC integration (with GSL) at build time.

Standalone run example:

OMP_NUM_THREADS=24 \
OMP_PROC_BIND=spread \
OMP_PLACES=cores \
OMP_DYNAMIC=FALSE \
TENSORIUM_MOVING_PUNCTURE_USE_INTERPOLATED_INIT=1 \
TENSORIUM_MOVING_PUNCTURE_GRID_N=212 \
TENSORIUM_MOVING_PUNCTURE_BOX_LENGTH=24.0 \
TENSORIUM_MOVING_PUNCTURE_SPATIAL_ORDER=6 \
TENSORIUM_MOVING_PUNCTURE_CFL=0.11 \
TENSORIUM_MOVING_PUNCTURE_STEPS=12000 \
./build/Tests/TensoriumMovingPuncture

For nested moving-puncture FMR runs, the most useful controls are:

  • TENSORIUM_MOVING_PUNCTURE_FMR_LEVELS: number of refined levels nested inside the root grid
  • TENSORIUM_MOVING_PUNCTURE_FMR_REFINEMENT_RATIO: refinement ratio between successive levels; 2 is the intended production setting
  • TENSORIUM_MOVING_PUNCTURE_FMR_OUTER_BOX_HALF_WIDTH: physical half-width of the outermost refined box
  • TENSORIUM_MOVING_PUNCTURE_FMR_FINEST_BOX_HALF_WIDTH: physical half-width of the finest box when sizing from the center outward
  • TENSORIUM_MOVING_PUNCTURE_FMR_FINE_LEVELS_USE_PARENT_INIT=1: initialize refined levels from parent prolongation instead of a second local TwoPunctures solve
  • TENSORIUM_MOVING_PUNCTURE_FMR_MOVE_WITH_PUNCTURES=1: re-center the refined hierarchy on the tracked puncture midpoint during evolution
  • TENSORIUM_MOVING_PUNCTURE_FMR_REGRID_INTERVAL: root-step interval between regrid checks when moving boxes are enabled
  • TENSORIUM_MOVING_PUNCTURE_FMR_REGRID_THRESHOLD_CELLS: minimum midpoint drift, in finest-grid cells, before rebuilding the hierarchy
  • TENSORIUM_MOVING_PUNCTURE_TRACKER_RECENTER_ON_DRIFT=1: snap the shift-integrated puncture tracker back to the slice minima if it drifts too far
  • TENSORIUM_MOVING_PUNCTURE_TRACKER_RECENTER_CELLS: tracker drift threshold, in finest-grid cells, for that recenter

When TENSORIUM_MOVING_PUNCTURE_FMR_OUTER_BOX_HALF_WIDTH is set, the refined hierarchy is built geometrically toward the center. For example, LEVELS=4, RATIO=2, OUTER_BOX_HALF_WIDTH=64 produces refined half-widths close to 64 -> 32 -> 16 -> 8.

Example multilevel run:

OMP_NUM_THREADS=24 \
OMP_DYNAMIC=FALSE \
TENSORIUM_MOVING_PUNCTURE_GRID_N=192 \
TENSORIUM_MOVING_PUNCTURE_BOX_LENGTH=256.0 \
TENSORIUM_MOVING_PUNCTURE_USE_INTERPOLATED_INIT=1 \
TENSORIUM_MOVING_PUNCTURE_ENABLE_FMR=1 \
TENSORIUM_MOVING_PUNCTURE_FMR_LEVELS=4 \
TENSORIUM_MOVING_PUNCTURE_FMR_REFINEMENT_RATIO=2 \
TENSORIUM_MOVING_PUNCTURE_FMR_OUTER_BOX_HALF_WIDTH=64.0 \
TENSORIUM_MOVING_PUNCTURE_FMR_FINE_LEVELS_USE_PARENT_INIT=1 \
./build/Tests/TensoriumMovingPuncture

Example moving-box run:

OMP_NUM_THREADS=24 \
OMP_DYNAMIC=FALSE \
TENSORIUM_MOVING_PUNCTURE_GRID_N=160 \
TENSORIUM_MOVING_PUNCTURE_BOX_LENGTH=64.0 \
TENSORIUM_MOVING_PUNCTURE_USE_INTERPOLATED_INIT=1 \
TENSORIUM_MOVING_PUNCTURE_ENABLE_FMR=1 \
TENSORIUM_MOVING_PUNCTURE_FMR_LEVELS=2 \
TENSORIUM_MOVING_PUNCTURE_FMR_REFINEMENT_RATIO=2 \
TENSORIUM_MOVING_PUNCTURE_FMR_OUTER_BOX_HALF_WIDTH=20.0 \
TENSORIUM_MOVING_PUNCTURE_FMR_FINE_LEVELS_USE_PARENT_INIT=1 \
TENSORIUM_MOVING_PUNCTURE_FMR_MOVE_WITH_PUNCTURES=1 \
TENSORIUM_MOVING_PUNCTURE_FMR_REGRID_INTERVAL=16 \
TENSORIUM_MOVING_PUNCTURE_FMR_REGRID_THRESHOLD_CELLS=2.0 \
./build/Tests/TensoriumMovingPuncture

The moving-puncture slice exports now also write companion geometry metadata (slice_boxes_*.csv plus per-cell bounds in slice_*.csv) for external post-processing tools. The stock plot.py keeps its default full-slice view.

LLVM/MLIR plugins

Plugins/ contains optional compiler-side tooling (diagnostic/alignment pass, Clang pragma plugin, MLIR conversion experiments).

These plugins are not required for:

  • Vector/Matrix/Tensor runtime usage
  • BSSN/Z4c simulations
  • Standard test execution

If your goal is NR runs, keep BUILD_PLUGINS=OFF.

Documentation

About

An early-stage HPC tensor and grid-kernel library for numerical relativity, focused on a SIMD-optimized (SSE/AVX/AVX2/AVX-512/Arm NEON), parallel implementation with OpenMP of the Z4c formulation of Einstein’s equations.

Topics

python machine-learning algebra cpp hpc tensorflow optimization neon matrix linear-algebra simd high-performance-computing blas blast tensor arm64 lapack avx512 numerical-relativity blas-libraries

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