sparseqr 1.4.1

Python wrapper for SuiteSparseQR

Python wrapper for SuiteSparseQR

This module wraps the SuiteSparseQR decomposition function for use with SciPy. This is Matlab's sparse [Q,R,E] = qr(). For some reason, no one ever wrapped that function of SuiteSparseQR for Python.

Also wrapped are the SuiteSparseQR solvers for A x = b for the cases with sparse A and dense or sparse b. This is especially useful for solving sparse overdetermined linear systems in the least-squares sense. Here A is of size m-by-n and b is m-by-k (storing k different right-hand side vectors, each considered separately).

Usage

import numpy
import scipy.sparse.linalg
import sparseqr

# QR decompose a sparse matrix M such that  Q R = M E
#
M = scipy.sparse.rand( 10, 10, density = 0.1 )
Q, R, E, rank = sparseqr.qr( M )
print( "Should be approximately zero:", abs( Q*R - M*sparseqr.permutation_vector_to_matrix(E) ).sum() ) 

# Solve many linear systems "M x = b for b in columns(B)"
#
B = scipy.sparse.rand( 10, 5, density = 0.1 )  # many RHS, sparse (could also have just one RHS with shape (10,))
x = sparseqr.solve( M, B, tolerance = 0 )

# Solve an overdetermined linear system  A x = b  in the least-squares sense
#
# The same routine also works for the usual non-overdetermined case.
#
A = scipy.sparse.rand( 20, 10, density = 0.1 )  # 20 equations, 10 unknowns
b = numpy.random.random(20)  # one RHS, dense, but could also have many (in shape (20,k))
x = sparseqr.solve( A, b, tolerance = 0 )
## Call `rz()`:
sparseqr.rz( A, b, tolerance = 0 )

# Solve a linear system  M x = B  via QR decomposition
#
# This approach is slow due to the explicit construction of Q, but may be
# useful if a large number of systems need to be solved with the same M.
#
M = scipy.sparse.rand( 10, 10, density = 0.1 )
Q, R, E, rank = sparseqr.qr( M )
r = rank  # r could be min(M.shape) if M is full-rank

# The system is only solvable if the lower part of Q.T @ B is all zero:
print( "System is solvable if this is zero (unlikely for a random matrix):", abs( (( Q.tocsc()[:,r:] ).T ).dot( B ) ).sum() )

# Systems with large non-square matrices can benefit from "economy" decomposition.
M = scipy.sparse.rand( 20, 5, density=0.1 )
B = scipy.sparse.rand( 20, 5, density = 0.1 )
Q, R, E, rank = sparseqr.qr( M )
print("Q shape (should be 20x20):", Q.shape)
print("R shape (should be 20x5):", R.shape)
Q, R, E, rank = sparseqr.qr( M, economy=True )
print("Q shape (should be 20x5):", Q.shape)
print("R shape (should be 5x5):", R.shape)


R = R.tocsr()[:r,:r] #for best performance, spsolve_triangular() wants the Matrix to be in CSR format.
Q = Q.tocsc()[:,:r] # Use CSC format for fast indexing of columns.
QB = (Q.T).dot(B).todense()  # spsolve_triangular() need the RHS in array format.
result = scipy.sparse.linalg.spsolve_triangular(R, QB, lower=False)

# Recover a solution (as a dense array):
x = numpy.zeros( ( M.shape[1], B.shape[1] ), dtype = result.dtype )
x[:r] = result
x[E] = x.copy()

# Recover a solution (as a sparse matrix):
x = scipy.sparse.vstack( ( result, scipy.sparse.coo_matrix( ( M.shape[1] - rank, B.shape[1] ), dtype = result.dtype ) ) )
x.row = E[ x.row ]

Installation

Before installing this module, you must first install SuiteSparseQR. You can do that via conda (conda install suitesparse) or your system's package manager (macOS: brew install suitesparse; debian/ubuntu linux: apt-get install libsuitesparse-dev).

Now you are ready to install this module.

Via pip

From PyPI:

pip install sparseqr

From GitHub:

pip install git+https://github.com/yig/PySPQR.git

Directly

Copy the three sparseqr/*.py files next to your source code, or leave them in their directory and call it as a module.

Deploy

1. Change the version in:

   sparseqr/__init__.py
   pyproject.toml
   

2. Update CHANGELOG.md

3. Run:

   flit publish --format sdist
   

We don't publish binary wheels, because it must be compiled against suite-sparse as a system dependency. We could publish a none-any wheel, which would cause compilation to happen the first time the module is imported rather than when it is installed. Is there a point to that?

Known issues

pip uninstall sparseqr won't remove the generated libraries. It will list them with a warning.

Tested on

• Python 3.9, 3.13.

• Conda and not conda.

• macOS, Ubuntu Linux, and Linux Mint.

  PYTHONPATH='.:$PYTHONPATH' python3 test/test.py

Dependencies

These are installed via pip:

• SciPy/NumPy
• cffi

These must be installed manually:

• SuiteSparseQR (macOS: brew install suitesparse; debian/ubuntu linux: apt-get install libsuitesparse-dev)

License

Public Domain CC0