easygsvd

A pure-Python, friendly interface to the generalized singular value decomposition (GSVD).

easygsvd is built on NumPy/SciPy and provides:

• A simple function gsvd(A, L) for dense GSVD of a matrix pair $(A, L)$.
• A GSVDResult object exposing the core GSVD factors (Uhat, Vhat, X, Y, c, s, etc.).
• Convenience methods for:
  • orthogonal projectors onto col(A), ker(A), col(L), ker(L), etc.
  • oblique projectors associated with the pair (A, L).
  • A-weighted and L-weighted oblique pseudoinverses.
• An incremental API for appending columns to (A, L) and updating the GSVD efficiently.

See the documentation for more details.

Note: This implementation assumes the stacked matrix np.vstack([A, L]) has full column rank. If this condition is violated (initially or after appending columns), a LinAlgError is raised.

---

Installation

pip install easygsvd

Example usage

import numpy as np
from easygsvd import gsvd

# Sizes of test matrices
M = 200
K = 195
N = 100

# Draw random test matrices with standard Gaussian entries
A = np.random.normal(size=(M, N))
L = np.random.normal(size=(K, N))

# Compute the economic GSVD of (A, L)
gsvd_result = gsvd(A, L, full_matrices=False)

# Compute the economic GSVD of (A, L)
gsvd_result_full = gsvd(A, L, full_matrices=True)
gsvd_full = gsvd(A, L, tol=1e-12, full_matrices=True)