Class sparseEigen

• Defined in File sparseSolver.hpp

Class Documentation

class sparseEigen

Sparse matrix eigenvalue solver using Eigen + Spectra libraries.

Solves sparse eigenvalue problems efficiently for large systems. Uses Spectra library for sparse iterative eigensolvers with shift-invert method to find eigenvalues near a target shift point.

The solver finds the eigenvector with eigenvalue having minimum absolute value (ground state), normalized so components sum to 1.

Note

Uses Spectra shift-invert which is efficient for interior eigenvalues

Note

Memory-efficient for sparse matrices with O(nnz) storage

Note

Suitable for large systems N > 5000 with low density

Note

Requires matrix to be stored in COO (coordinate) format internally

Public Functions

inline explicit sparseEigen(size_t n = 0)

Initialize sparse solver with matrix size.

Parameters:

n – Dimension of square matrix (default: 0)

inline void set(size_t i, size_t j, double value)

Add a matrix element (cumulative).

Elements are stored in triplet format until getMatrix() or solve() is called, at which point they’re compressed into CSR format.

Note

Accumulates: a(i,j) += value if element (i,j) added multiple times

Parameters:

• i – Row index

• j – Column index

• value – Value to add at (i,j)

inline auto getMatrix()

Get the compressed sparse matrix.

Converts triplet format to compressed sparse row (CSR) format.

Note

Must be called before operations if matrix was modified

Returns:

Reference to compressed Eigen sparse matrix

inline auto solve()

Solve sparse eigenvalue problem and return ground state eigenvector.

Uses Spectra GenEigsRealShiftSolver with shift-invert transform. Finds 1 eigenvalue with magnitude closest to zero (ground state).

Note

Number of Lanczos vectors used: column/2

Note

Shift point: 0 (finds eigenvalue closest to 0)

Note

Tolerance: 1e-6 for eigenvalue convergence

Throws:

std::runtime_error – If Spectra eigenvalue computation fails

Returns:

Normalized ground state eigenvector (sum = 1.0)

inline auto vectorDot(const std::vector<double> &X)

Compute sparse matrix-vector product y = H·x.

Manually iterates through sparse matrix structure for matrix-vector product.

Note

Uses manual iteration for maximum control and efficiency

Note

O(nnz) complexity where nnz is number of non-zeros

Parameters:

X – Input vector of length column

Returns:

Result vector containing H·X