Structured matrices
Project description
Structured Matrices
Structured matrices
Requirements and Installation
See the instructions here. Then simply
pip install backends-matrix
Example
>>> import lab as B
>>> from matrix import Diagonal
>>> d = Diagonal(B.rand(2, 3)) # A batch of diagonal marices
>>> d
<diagonal matrix: batch=(2,), shape=(3, 3), dtype=float64
diag=[[0.427 0.912 0.622]
[0.777 0.048 0.808]]>
>>> 2 * d
<diagonal matrix: batch=(2,), shape=(3, 3), dtype=float64
diag=[[0.854 1.824 1.243]
[1.553 0.096 1.616]]>
>>> 2 * d + 1
<Woodbury matrix: batch=(2,), shape=(3, 3), dtype=float64
diag=<diagonal matrix: batch=(2,), shape=(3, 3), dtype=float64
diag=[[0.854 1.824 1.243]
[1.553 0.096 1.616]]>
lr=<low-rank matrix: batch=(), shape=(3, 3), dtype=int64, rank=1
left=[[1]
[1]
[1]]
middle=<diagonal matrix: batch=(), shape=(1, 1), dtype=int64
diag=[1]>>>
>>> B.inv(2 * d + 1)
<Woodbury matrix: batch=(2,), shape=(3, 3), dtype=float64
diag=<diagonal matrix: batch=(2,), shape=(3, 3), dtype=float64
diag=[[ 1.171 0.548 0.804]
[ 0.644 10.386 0.619]]>
lr=<low-rank matrix: batch=(2,), shape=(3, 3), dtype=float64, rank=1
left=<dense matrix: batch=(2,), shape=(3, 1), dtype=float64
mat=[[[ 1.171]
[ 0.548]
[ 0.804]]
[[ 0.644]
[10.386]
[ 0.619]]]>
middle=<dense matrix: batch=(2,), shape=(1, 1), dtype=float64
mat=[[[-0.284]]
[[-0.079]]]>
right=<dense matrix: batch=(2,), shape=(3, 1), dtype=float64
mat=[[[ 1.171]
[ 0.548]
[ 0.804]]
[[ 0.644]
[10.386]
[ 0.619]]]>>>
>>> B.inv(B.inv(2 * d + 1))
<Woodbury matrix: batch=(2,), shape=(3, 3), dtype=float64
diag=<diagonal matrix: batch=(2,), shape=(3, 3), dtype=float64
diag=[[0.854 1.824 1.243]
[1.553 0.096 1.616]]>
lr=<low-rank matrix: batch=(2,), shape=(3, 3), dtype=float64, rank=1
left=<dense matrix: batch=(2,), shape=(3, 1), dtype=float64
mat=[[[1.]
[1.]
[1.]]
[[1.]
[1.]
[1.]]]>
middle=<dense matrix: batch=(2,), shape=(1, 1), dtype=float64
mat=[[[1.]]
[[1.]]]>
right=<dense matrix: batch=(2,), shape=(3, 1), dtype=float64
mat=[[[1.]
[1.]
[1.]]
[[1.]
[1.]
[1.]]]>>>
>>> B.inv(B.inv(2 * d + 1)) - 1
<diagonal matrix: batch=(2,), shape=(3, 3), dtype=float64
diag=[[0.854 1.824 1.243]
[1.553 0.096 1.616]]>
Matrix Types
All matrix types are subclasses of AbstractMatrix
.
The following base types are provided:
Zero
Dense
Diagonal
Constant
LowerTriangular
UpperTriangular
The following composite types are provided:
LowRank
Woodbury
Kronecker
TiledBlocks
Functions
The following functions are added to LAB.
They can be accessed with B.<function>
where import lab as B
.
shape_broadcast(*elements)
shape_batch(a, *indices)
shape_batch_broadcast(*elements)
shape_matrix(a, *indices)
shape_matrix_broadcast(*elements)
broadcast_batch_to(a, *batch)
dense(a)
fill_diag(a, diag_len)
block(*rows)
block_diag(*blocks)
matmul_diag(a, b, tr_a=False, tr_b=False)
pd_inv(a)
schur(a)
pd_schur(a)
iqf(a, b, c)
iqf_diag(a, b, c)
ratio(a, c)
root(a)
sample(a, num=1)
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