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Structured matrices

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Structured Matrices

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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
     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
     left=<dense matrix: shape=3x1, dtype=float64
           mat=[[0.5]
                [0.5]
                [0.5]]>
     middle=<dense matrix: shape=1x1, dtype=float64
             mat=[[-0.4]]>
     right=<dense matrix: shape=3x1, dtype=float64
            mat=[[0.5]
                 [0.5]
                 [0.5]]>>>

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

>>> B.inv(B.inv(2 * d + 1)) + 3
<Woodbury matrix: shape=3x3, dtype=float64
 diag=<diagonal matrix: shape=3x3, dtype=float64
       diag=[2. 2. 2.]>
 lr=<low-rank matrix: shape=3x3, dtype=float64, rank=1
     left=[[1.]
           [1.]
           [1.]]
     middle=[[4.]]
     right=[[1.]
            [1.]
            [1.]]>>

>>> 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)

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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