PRIMME wrapper for Python

## Project description

primme is a Python interface to PRIMME, a high-performance library for computing a few eigenvalues/eigenvectors, and singular values/vectors. PRIMME is especially optimized for large, difficult problems. Real symmetric and complex Hermitian problems, standard A x = lambda x and generalized A x = lambda B x, are supported. It can find largest, smallest, or interior singular/eigenvalues, and can use preconditioning to accelerate convergence.

The main contributors to PRIMME are James R. McCombs, Eloy Romero Alcalde, Andreas Stathopoulos and Lingfei Wu.

## Install

pip install numpy   # if numpy is not installed yet
pip install scipy   # if scipy is not installed yet
pip install future  # if using python 2
conda install mkl-devel # if using Anaconda Python distribution
pip install primme

Optionally for building the development version do:

git clone https://github.com/primme/primme
cd primme
make python_install

## Usage

The following examples compute a few eigenvalues and eigenvectors from a real symmetric matrix:

>>> import Primme, scipy.sparse
>>> A = scipy.sparse.spdiags(range(100), [0], 100, 100) # sparse diag. matrix
>>> evals, evecs = Primme.eigsh(A, 3, tol=1e-6, which='LA')
>>> evals # the three largest eigenvalues of A
array([ 99.,  98.,  97.])

>>> new_evals, new_evecs = Primme.eigsh(A, 3, tol=1e-6, which='LA', ortho=evecs)
>>> new_evals # the next three largest eigenvalues
array([ 96.,  95.,  94.])

>>> evals, evecs = primme.eigsh(A, 3, tol=1e-6, which=50.1)
>>> evals # the three closest eigenvalues to 50.1
array([ 50.,  51.,  49.])

The following examples compute a few eigenvalues and eigenvectors from a generalized Hermitian problem, without factorizing or inverting B:

>>> import Primme, scipy.sparse
>>> A = scipy.sparse.spdiags(range(100), [0], 100, 100) # sparse diag. matrix
>>> M = scipy.sparse.spdiags(np.asarray(range(99,-1,-1)), [0], 100, 100)
>>> evals, evecs = primme.eigsh(A, 3, M=M, tol=1e-6, which='SA')
>>> evals
array([1.0035e-07, 1.0204e-02, 2.0618e-02])

The following examples compute a few singular values and vectors:

>>> import Primme, scipy.sparse
>>> A = scipy.sparse.spdiags(range(1, 11), [0], 100, 10) # sparse diag. rect. matrix
>>> svecs_left, svals, svecs_right = Primme.svds(A, 3, tol=1e-6, which='SM')
>>> svals # the three smallest singular values of A
array([ 1.,  2.,  3.])

>>> A = scipy.sparse.rand(10000, 100, random_state=10)
>>> prec = scipy.sparse.spdiags(np.reciprocal(A.multiply(A).sum(axis=0)),
...           [0], 100, 100) # square diag. preconditioner
>>> svecs_left, svals, svecs_right = Primme.svds(A, 3, which=6.0, tol=1e-6,
...           precAHA=prec)
>>> ["%.5f" % x for x in svals.flat] # the three closest singular values of A to 0.5
['5.99871', '5.99057', '6.01065']

Further examples.

Documentation of eigsh and svds.

## Citing this code

• A. Stathopoulos and J. R. McCombs PRIMME: PReconditioned Iterative MultiMethod Eigensolver: Methods and software description, ACM Transaction on Mathematical Software Vol. 37, No. 2, (2010), 21:1-21:30.

• L. Wu, E. Romero and A. Stathopoulos, PRIMME_SVDS: A High-Performance Preconditioned SVD Solver for Accurate Large-Scale Computations, J. Sci. Comput., Vol. 39, No. 5, (2017), S248–S271.

## Contact Information

For reporting bugs or questions about functionality contact Andreas Stathopoulos by email, andreas at cs.wm.edu. See further information in the webpage http://www.cs.wm.edu/~andreas/software.

## Project details

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