pfPySpectra

pfPySpectra offers the Python interface to the C++ Spectra library by pybind11, faster than sicpy in some ways.

Eigensolvers

pfPySpecta offers two general interfaces to Spectra: eigensolver and eigensolverh. For general(dense&sparse) and symmetric(dense&sparse) matrices respectively.These two functions would invoke the most suitable method based on the information provided by the user

Usage

import numpy as np
import scipy.sparse as s
from pfpyspectra import eigensolver, eigensolverh

# matrix size
size = 100

# number of eigenpairs to compute
nvalues = 2

# Create random matrix
xs = np.random.normal(size=size ** 2).reshape(size, size)
new_xs=sp.rand(size, size, density=0.1, format='csc')

# Create symmetric matrix
mat = xs + xs.T
new_mat = new_xs + new_xs.T

# Compute two eigenpairs selecting the eigenvalues with
# largest magnitude (default).
eigenvalues, eigenvectors = eigensolver(xs, nvalues)
sprse_eigenvalues, sprse_eigenvectors = eigensolver(new_xs, nvalues)
# Compute two eigenpairs selecting the eigenvalues with
# largest algebraic value
selection_rule = "LargestAlge"
symm_eigenvalues, symm_eigenvectors = eigensolverh(
  mat, nvalues, selection_rule)
sprse_symm_eigenvalues, sprse_symm_eigenvectors = eigensolverh(
  mat, nvalues, selection_rule)

Note: The available selection_rules to compute a portion of the spectrum are:

• LargestMagn
• LargestReal
• LargestImag
• LargestAlge
• SmallestMagn
• SmallestReal
• SmallestImag
• SmallestAlge
• BothEnds

Eigensolvers Dense Interface

You can also call directly the dense interface. You would need to import the following module:

import numpy as np
from pfpyspectra import spectra_dense_interface

The following functions are available in the spectra_dense_interface:

• general_eigensolver(
   mat: np.ndarray, eigenpairs: int, basis_size: int, selection_rule: str)
   -> (np.ndarray, np.ndarray)

• general_real_shift_eigensolver(
  mat: np.ndarray, eigenpairs: int, basis_size: int, shift: float, selection_rule: str)
  -> (np.ndarray, np.ndarray)

• general_complex_shift_eigensolver(
    mat: np.ndarray, eigenpairs: int, basis_size: int,
    shift_real: float, shift_imag: float, selection_rule: str)
    -> (np.ndarray, np.ndarray)

• symmetric_eigensolver(
    mat: np.ndarray, eigenpairs: int, basis_size: int, selection_rule: str)
    -> (np.ndarray, np.ndarray)

• symmetric_shift_eigensolver(
    mat: np.ndarray, eigenpairs: int, basis_size: int, shift: float, selection_rule: str)
    -> (np.ndarray, np.ndarray)

• symmetric_generalized_shift_eigensolver(
    mat_A: np.ndarray, mat_B: np.ndarray, eigenpairs: int, basis_size: int, shift: float,
    selection_rule: str)
    -> (np.ndarray, np.ndarray)

Eigensolvers Sparse Interface

You can also call directly the sparse interface. You would need to import the following module:

import scipy as sp
from pfpyspectra import spectra_sparse_interface

The following functions are available in the spectra_sparse_interface:

• sparse_general_eigensolver(
   mat: sp.spmatrix, eigenpairs: int, basis_size: int, selection_rule: str)
   -> (np.ndarray, np.ndarray)

• sparse_general_real_shift_eigensolver(
  mat: sp.spmatrix, eigenpairs: int, basis_size: int, shift: float, selection_rule: str)
  -> (np.ndarray, np.ndarray)

• sparse_general_complex_shift_eigensolver(
    mat: sp.spmatrix, eigenpairs: int, basis_size: int,
    shift_real: float, shift_imag: float, selection_rule: str)
    -> (np.ndarray, np.ndarray)

• sparse_symmetric_eigensolver(
    mat: sp.spmatrix, eigenpairs: int, basis_size: int, selection_rule: str)
    -> (np.ndarray, np.ndarray)

• sparse_symmetric_shift_eigensolver(
    mat: sp.spmatrix, eigenpairs: int, basis_size: int, shift: float, selection_rule: str)
    -> (np.ndarray, np.ndarray)

• sparse_symmetric_generalized_shift_eigensolver(
    mat_A: sp.spmatrix, mat_B: sp.spmatrix, eigenpairs: int, basis_size: int, shift: float,
    selection_rule: str)
    -> (np.ndarray, np.ndarray)

Example

import numpy as np
from pfpyspectra import spectra_dense_interface

size = 100
nvalues = 2 # eigenpairs to compute
search_space = nvalues * 2 # size of the search space
shift = 1.0

# Create random matrix
xs = np.random.normal(size=size ** 2).reshape(size, size)

# Create symmetric matrix
mat = xs + xs.T

# Compute two eigenpairs selecting the eigenvalues with
# largest algebraic value
selection_rule = "LargestAlge"
symm_eigenvalues, symm_eigenvectors = \
  spectra_dense_interface.symmetric_eigensolver(
  mat, nvalues, search_space, selection_rule)

Note: All functions return a tuple whith the resulting eigenvalues and eigenvectors. For more examples, please see the directory: pfpyspectra/tests/

Installation

To install pyspectra, do:

  git clone [email protected]:PerfXLab/spectra4py.git
  cd pyspectra
  bash ./install.sh

Test

Run tests (including coverage) with:

  pytest tests/test_dense_pyspectra.py
  pytest tests/test_sparse_pyspectra.py
  pytest tests/test_pyspectra.py
  # also you can just `pytest tests`

Help: If you don't pass them all, don't worry, try a few more times.
I think that's because of the random parameter problem, It will not affect the use, can you help me?

License

No. Just for fun!
Thanks :
pyspectra,
C++ Spectra library