Getting Started

This page takes you from installation to a minimal working POLFED workflow.

Installation

Install from the Julia package manager:

import Pkg
Pkg.add("Polfed")

Then load the package in your session:

using Polfed

Minimal Working Example

The run below illustrates the full minimal pipeline:

  1. Build a matrix (here a real, symmetric many-body Quantum Sun Hamiltonian; see Quantum Sun (QSun)),
  2. Either construct one normalized initial state (vector input) or a normalized block of states (matrix input),
  3. Call polfed.
using Polfed
using Polfed.Models: qsun_hamiltonian
using LinearAlgebra

# Problem setup
L_loc = 12
L_grain = 2
g0 = 1.0
α = 0.5
mat = qsun_hamiltonian(L_loc, L_grain, g0, α; use_sparse=true)
howmany = 100 # howmany eigenpairs to target
target = 0.0 # What part of the spectrum to target

# Vector input -> Lanczos factorization
x0_vec = rand(size(mat, 1)); x0_vec ./= norm(x0_vec)
vals_l, vecs_l = polfed(mat, x0_vec, howmany, target)

# Matrix input -> Block Lanczos factorization
x0_mat = rand(size(mat, 1), 4)
x0_mat = Matrix(qr(x0_mat).Q)
vals_b, vecs_b = polfed(mat, x0_mat, howmany, target)

Interpretation:

  • x0_vec requests standard Lanczos.
  • x0_mat requests Block Lanczos with block size equal to column count.
  • Both entry modes are handled by the same polfed interface.

For a more detailed comparison, see Lanczos and Block Lanczos Factorization.

First Diagnostics

Reporting is the fastest way to understand runtime behavior:

vals, vecs, report = polfed(mat, x0_vec, howmany, target; produce_report=true)
display_report(report)

The report shows polynomial order, matrix multiplications, convergence, factorization details, and timing split. See Report and display_report.

This page was generated using Literate.jl.