backends-matrix 0.2.0

Structured matrices

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.ones(3))

>>> d
<diagonal matrix: shape=3x3, data type=float64,
 diag=[1. 1. 1.]>
  
>>> 2 * d
<diagonal matrix: shape=3x3, data type=float64
 diag=[2. 2. 2.]>

>>> 2 * d + 1
<Woodbury matrix: shape=3x3, dtype=int64
 diag=<diagonal matrix: shape=3x3, dtype=float64
       diag=[2. 2. 2.]>
 lr=<low-rank matrix: shape=3x3, dtype=int64, rank=1, sign=1
     left=[[1]
           [1]
           [1]]
     middle=<diagonal matrix: shape=1x1, dtype=int64
             diag=[1]>>>
  
>>> B.inv(2 * d + 1)
<Woodbury matrix: shape=3x3, dtype=float64
 diag=<diagonal matrix: shape=3x3, dtype=float64
       diag=[0.5 0.5 0.5]>
 lr=<low-rank matrix: shape=3x3, dtype=float64, rank=1, sign=0
     left=<dense matrix: shape=3x1, dtype=float64
           mat=[[0.5]
                [0.5]
                [0.5]]>
     middle=[[-0.4]]
     right=<dense matrix: shape=3x1, dtype=float64
            mat=[[0.5]
                 [0.5]
                 [0.5]]>>>

>>> B.kron(d, 2 * d)
<Kronecker product: shape=9x9, dtype=float64
 left=<diagonal matrix: shape=3x3, dtype=float64
       diag=[1. 1. 1.]>
 right=<diagonal matrix: shape=3x3, dtype=float64
        diag=[2. 2. 2.]>>


>>> B.inv(B.kron(d, 2 * d))
<Kronecker product: shape=9x9, dtype=float64
 left=<diagonal matrix: shape=3x3, dtype=float64
       diag=[1. 1. 1.]>
 right=<diagonal matrix: shape=3x3, dtype=float64
        diag=[0.5 0.5 0.5]>>

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

Functions

The following functions are added to LAB. They can be accessed with B.<function> where import lab as B.

dense(a)
fill_diag(a, diag_len)
block(*rows)

matmul_diag(a, b, tr_a=False, tr_b=False)
iqf(a, b, c)
iqf_diag(a, b, c)
ratio(a, c)
root(a)
sample(a, num=1)