Matrix Operations

The pytanga.matrix submodule bridges geometric algebra multivectors with linear algebra. MVMatrix wraps a 2‑D numpy array whose rows are labelled by a BladeMask — each column stores one multivector's coefficient vector. MVProductMatrix is a 3‑D tensor encoding one product matrix per blade of a subspace, built by the product_matrix function and used internally by the equation solvers in pytanga.solver. Blade masks label every row and column, preventing mask‑mismatch bugs at every axis alignment point.

from pytanga.matrix import MVMatrix, MVProductMatrix

Reference

Topic	Guide
BladeMask — construction, membership, union/intersection, grade filtering	BladeMask
MVMatrix — row‑labelled coefficient matrix, to_matrix, from_matrix, batch support	MVMatrix
MVProductMatrix — 3‑D tensor, product_matrix, reverse/conjugate matrices	MVProductMatrix

Quick start

from pytanga import Algebra, BladeMask
from pytanga.basis import BasisE3
from pytanga.geometry import RndMV
from pytanga.matrix import MVMatrix
from pytanga.matrix.product import product_matrix
import numpy as np

alg = BasisE3()
full = BladeMask.full(alg)             # all 8 blades

# Create a column vector for one multivector
v = MVMatrix(data=np.zeros((8, 1)), row_mask=full)

# Build a product matrix for a random multivector
A = RndMV(full, [(-1.0, 1.0)] * len(full))(np.random.default_rng(42))
a_mask = BladeMask(A)
b_mask = BladeMask(alg, grades=[1])   # vector subspace

M = product_matrix(A, a_mask=a_mask, b_mask=b_mask, c_mask=a_mask)
# M.data[0] is the (|a_mask|×|b_mask|) 2‑D product matrix