API reference¶

The API reference is generated from the source code with Doxygen and is available here:

Modules · Files · Classes · Functions

Overview of the code¶

Ensign's headers provide data structures and operations for dynamical low-rank (DLR) and interpolatory low-rank methods, along with general-purpose numerical utilities. Below is an overview of the code structure.

Fundamental data types¶

• generic/storage.hpp defines multi_array<T, d>, a contiguous, column-major dense array with number of dimensions determined at compile time. Arrays can reside in host (CPU) or device (GPU) memory, and can reserve extra capacity to allow for fast rank adaptive schemes.
• lr/lr.hpp defines lr2<T>, the matrix low-rank representation \(f = X S V^T\). The basis matrices X and V and the small coefficient matrix S represent a large matrix without storing the full f. lr2 uses the same host/device storage choice as multi_array.
• generic/common.hpp provides shared definitions such as Index (ptrdiff_t) and stloc (the host/device location selector).

Building dynamical low-rank schemes¶

• generic/matrix.hpp provides dense matrix and vector operations, matrix-vector products, transposes, SVD, QR, symmetric diagonalization, and an LU solver. Matrix::blas_ops selects CPU or optional GPU execution.
• lr/coefficients.hpp defines coeff and integrate for weighted integrals of basis functions, producing the small coefficient matrices needed in the DLR K, S, and L steps.
• lr/lr.hpp provides higher-level operations on lr2 representations: initialization, weighted orthogonalization, addition, multiplication, truncation, inner products and norms.
• generic/kernels.hpp declares the CUDA kernels used for GPU-side elementwise operations and numerical updates. These are low-level building blocks that are available alongside the higher-level matrix and low-rank operations.

Binary tree tensor networks¶

• generic/tree.hpp defines the binary-tree tensor structure: internal nodes hold coefficient tensors that connect their two children, while external (leaf) nodes hold basis matrices. Each node also stores its incoming rank and coefficient matrix.
• generic/tensor.hpp supplies the supporting tensor operations, including matricization, tensorization, and orthogonalization.

Interpolatory low-rank schemes¶

lr/interpolatory.hpp provides DEIM-style sampling and reconstruction operations for interpolatory low-rank representations. deim_ext selects sample points, and colloquation_to_lr constructs low-rank factors from sampled matrix entries.

Other utilities¶