MVProductMatrix¶

MVProductMatrix is a 3‑D tensor encoding one product matrix per blade of an a_mask subspace. It is the return type of product_matrix and is used internally by the solver pipeline.

from pytanga.matrix import MVProductMatrix

Construction¶

MVProductMatrix is created by the product_matrix function:

from pytanga.matrix.product import product_matrix

M = product_matrix(A, a_mask=a_mask, b_mask=b_mask, c_mask=c_mask)
# M is an MVProductMatrix; shape (|a_mask|, |c_mask|, |b_mask|)

Each slice M.data[i, :, :] is the (|c_mask| × |b_mask|) product matrix for multivector i of the A‑subspace.

Data shape¶

The 3‑D tensor has axes:

Axis	Dimension	Mask	Meaning
0	`\|a_mask\|`	`a_mask`	Which multivector of the A‑subspace
1 (middle)	`\|c_mask\|`	`c_mask`	Output blade rows
2 (last)	`\|b_mask\|`	`b_mask`	Unknown X blades (columns)

Properties¶

Property	Type	Description
`data`	`np.ndarray`	3‑D array of shape `(n_mvs, \\|c_mask\\|, \\|b_mask\\|)`
`a_mask`	`BladeMask`	First axis — A‑subspace
`b_mask`	`BladeMask`	Last axis — subspace of unknown X
`c_mask`	`BladeMask`	Middle axis — output subspace
`n_mvs`	`int`	Number of multivectors encoded (= `\\|a_mask\\|`)
`shape`	`tuple`	`data.shape`
`product`	`EProduct`	`GP`, `IP`, or `OP`
`left`	`bool`	`True` = A ∘ X, `False` = X ∘ A
`left_inv`	`EInv`	Involution on left operand
`right_inv`	`EInv`	Involution on right operand
`algebra`	`Algebra`	From `b_mask`

Matrix multiplication pattern¶

A standard numpy matrix product with a single‑column MVMatrix contracts the last axis and broadcasts over the first:

from pytanga.matrix.product import product_matrix
from pytanga.matrix.convert import to_matrix

M = product_matrix(A, a_mask=..., b_mask=b_mask, c_mask=c_mask)
V = to_matrix(X, mask=b_mask)                    # shape (|b|, 1)

result = np.matmul(M.data, V.data)               # → (|a_mask|, |c_mask|, 1)
result = result.squeeze(-1).T                    # → (|c_mask|, |a_mask|)
# Each column of result is A_i ∘ X for one MV of a_mask

For a single MV, |a_mask| == 1 and M.data[0] is the familiar 2‑D product matrix.

Examples¶

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

alg = BasisE3()
full = BladeMask.full(alg)
vectors = BladeMask(alg, grades=[1])

A = alg({"e1": 2.0, "e2": -3.0})

# Product matrix for one MV
M = product_matrix(A, a_mask=BladeMask(A),
                   b_mask=vectors, c_mask=full)
# M.data[0] is (8×3)

# Outer product
M_op = product_matrix(A, a_mask=BladeMask(A),
                      b_mask=full, c_mask=full, product='op')

# Batch: product matrices for a list of MVs
points = [RndMV(full, [(-1.0, 1.0)] * len(full))(np.random.default_rng(i)) for i in range(5)]
M_arr = product_matrix(points, b_mask=full, c_mask=full)
# M_arr.data.shape == (5, 8, 8)