Class exactSolver

• Defined in File sparseSolver.hpp

Class Documentation

class exactSolver

Exact dense matrix eigenvalue solver for small systems.

Solves the full eigenvalue problem for a dense matrix using LAPACK. Suitable for small to medium systems where memory/speed trade-off favors dense storage. Uses LAPACK’s dgeev for non-symmetric eigenvalue problems.

The solver finds the eigenvector corresponding to the eigenvalue with minimum absolute value, normalized so that components sum to 1.

Note

Eigenvector is returned as the ground state wavefunction

Note

Uses O(N^3) LAPACK algorithms - suitable for N < 5000

Public Functions

inline explicit exactSolver(size_t n = 0)

Initialize solver with matrix size.

Parameters:

n – Dimension of square matrix (default: 0)

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

Add a matrix element (cumulative, supports += operation).

Note

This method accumulates: a(i,j) += val

Parameters:

• i – Row index

• j – Column index

• val – Value to add to (i,j) element

inline std::vector<double> solve()

Solve eigenvalue problem and return ground state eigenvector.

Finds left/right eigenvector pairs and eigenvalues using non-symmetric LAPACK routines. Returns the right eigenvector corresponding to the eigenvalue with smallest absolute value, normalized to unit sum.

Note

Output is normalized: sum(components) = 1.0

Note

Modifies internal matrix during computation

Throws:

std::exception – if LAPACK eigenvalue computation fails

Returns:

Vector containing normalized ground state eigenvector components

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

Compute matrix-vector product y = H·x.

Parameters:

a – Input vector of length column

Returns:

Result vector containing H·a