MVMatrix¶

MVMatrix wraps a 2‑D numpy array with a BladeMask labelling its rows. Each column stores the coefficients of one multivector, ordered by the row_mask.

from pytanga.matrix import MVMatrix

Construction¶

import numpy as np
from pytanga import BladeMask

mask = BladeMask.full(alg)                     # 8 blades

# Single multivector — column vector
m = MVMatrix(data=np.zeros((len(mask), 1)), row_mask=mask)

# Batch of 3 multivectors
m = MVMatrix(data=np.zeros((len(mask), 3)), row_mask=mask)

Validation at construction time checks that data.ndim == 2 and data.shape[0] == len(row_mask).

Properties¶

Property	Type	Description
`data`	`np.ndarray`	Shape `(len(row_mask), n_cols)`
`row_mask`	`BladeMask`	Ordered blade IDs labelling each row
`shape`	`tuple[int, ...]`	`data.shape`
`n_cols`	`int`	Number of multivectors (columns)
`is_single`	`bool`	`True` when exactly one column
`algebra`	`Algebra`	From `row_mask`

Conversion¶

MVMatrix is created and consumed by the matrix conversion functions:

from pytanga.matrix.convert import to_matrix, from_matrix

# MV → MVMatrix
mat = to_matrix(mv, mask=full)                  # single MV → (8, 1)
mat = to_matrix([mv1, mv2, mv3], mask=full)     # list → (8, 3)

# MVMatrix → MV (or list[MV])
mv = from_matrix(mat)                           # single col → MV
mvs = from_matrix(mat)                          # multi‑col → list[MV]

Relationship to product matrices¶

Multiplying an MVProductMatrix.data with an MVMatrix performs the corresponding GA operation in matrix form:

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

M = product_matrix(A, b_mask=b_mask, c_mask=c_mask)   # MVProductMatrix
V = to_matrix(X, mask=b_mask)                          # MVMatrix

result = np.matmul(M.data, V.data)                     # (|a|, |c|, 1)
result = result.squeeze(-1).T                           # (|c|, |a|)

Examples¶

from pytanga import Algebra, BladeMask
from pytanga.basis import BasisE3
from pytanga.matrix import MVMatrix
import numpy as np

alg = BasisE3()
full = BladeMask.full(alg)

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

# Build a batch of 5 multivectors
batch = MVMatrix(data=np.random.randn(8, 5), row_mask=full)
print(batch.n_cols)                            # 5
print(batch.is_single)                         # False