Diagonal Block Matrix¶

class fastmat.DiagBlocks¶

Bases: Matrix

For given \(n,m \in \mathbb{N}\) this class allows to define a block matrix \(M \in \mathbb{C}^{nm \times nm}\), where each block is a diagonal matrix \(D_{ij} \in \mathbb{C}^{m \times m}\). This obviously allows efficient storage and computations.

>>> # import the package
>>> import fastmat as fm
>>> # define the sizes
>>> n,m = 2,
>>> # define the diagonals
>>> d = np.random.randn(
>>>        n,
>>>        n,
>>>        m)
>>> # define the block
>>> # matrix diagonal-wise
>>> M = fm.DiagBlocks(d)

We have randomly drawn the defining elements \(d\) from a standard Gaussian distribution, which results in

\[\begin{split}M = \begin{bmatrix} d_{1,1,1} & & & d_{1,2,1} & & \\ & d_{1,1,2} & & & d_{1,2,2} & \\ & & d_{1,1,3} & & & d_{1,2,3} \\ d_{2,1,1} & & & d_{2,2,1} & & \\ & d_{2,1,2} & & & d_{2,2,2} & \\ & & d_{2,1,3} & & & d_{2,2,3} \\ \end{bmatrix}.\end{split}\]

__init__()¶

Initialize DiagBlocks matrix instance.

Parameters

tenDiagsnumpy.ndarray: The generating 3d-array of the flattened diagonal tensor this matrix describes. The matrix data type is determined by the data type of this array.
**optionsoptional: Additional keyworded arguments. Supports all optional arguments supported by fastmat.Matrix.