Linear algebra (xorbits.numpy.linalg)

The following table lists both implemented and not implemented methods. If you have need of an operation that is listed as not implemented, feel free to open an issue on the GitHub repository, or give a thumbs up to already created issues. Contributions are also welcome!

The following table is structured as follows: The first column contains the method name. The second column contains link to a description of corresponding numpy method. The third column is a flag for whether or not there is an implementation in Xorbits for the method in the left column. Y stands for yes, N stands for no, P standsfor partial (meaning some parameters may not be supported yet), and D stands for default to numpy.

The NumPy linear algebra functions rely on BLAS and LAPACK to provide efficient low level implementations of standard linear algebra algorithms. Those libraries may be provided by NumPy itself using C versions of a subset of their reference implementations but, when possible, highly optimized libraries that take advantage of specialized processor functionality are preferred. Examples of such libraries are OpenBLAS, MKL (TM), and ATLAS. Because those libraries are multithreaded and processor dependent, environmental variables and external packages such as threadpoolctl may be needed to control the number of threads or specify the processor architecture.

The SciPy library also contains a ~scipy.linalg submodule, and there is overlap in the functionality provided by the SciPy and NumPy submodules. SciPy contains functions not found in xorbits.numpy.linalg, such as functions related to LU decomposition and the Schur decomposition, multiple ways of calculating the pseudoinverse, and matrix transcendentals such as the matrix logarithm. Some functions that exist in both have augmented functionality in scipy.linalg. For example, scipy.linalg.eig can take a second matrix argument for solving generalized eigenvalue problems. Some functions in NumPy, however, have more flexible broadcasting options. For example, xorbits.numpy.linalg.solve can handle “stacked” arrays, while scipy.linalg.solve accepts only a single square array as its first argument.

Note

The term matrix as it is used on this page indicates a 2d xorbits.numpy.array object, and not a xorbits.numpy.matrix object. The latter is no longer recommended, even for linear algebra. See the matrix object documentation for more information.

The @ operator

Introduced in NumPy 1.10.0, the @ operator is preferable to other methods when computing the matrix product between 2d arrays. The xorbits.numpy.matmul() function implements the @ operator.

Matrix and vector products

xorbits.numpy	numpy	Implemented? (Y/N/P/D)	Notes for Current implementation
dot	dot	Y
linalg.multi_dot	linalg.multi_dot	Y
vdot	vdot	Y
inner	inner	Y
outer	outer	Y
matmul	matmul	Y
tensordot	tensordot	Y
einsum	einsum	Y
einsum_path	einsum_path	Y
linalg.matrix_power	linalg.matrix_power	Y
kron	kron	Y

Decompositions

xorbits.numpy	numpy	Implemented? (Y/N/P/D)	Notes for Current implementation
linalg.cholesky	linalg.cholesky	Y
linalg.qr	linalg.qr	Y
linalg.svd	linalg.svd	Y

Matrix eigenvalues

xorbits.numpy	numpy	Implemented? (Y/N/P/D)	Notes for Current implementation
linalg.eig	linalg.eig	Y
linalg.eigh	linalg.eigh	Y
linalg.eigvals	linalg.eigvals	Y
linalg.eigvalsh	linalg.eigvalsh	Y

Norms and other numbers

xorbits.numpy	numpy	Implemented? (Y/N/P/D)	Notes for Current implementation
linalg.norm	linalg.norm	Y
linalg.cond	linalg.cond	Y
linalg.det	linalg.det	Y
linalg.matrix_rank	linalg.matrix_rank	Y
linalg.slogdet	linalg.slogdet	Y
trace	trace	Y

Solving equations and inverting matrices

xorbits.numpy	numpy	Implemented? (Y/N/P/D)	Notes for Current implementation
linalg.solve	linalg.solve	Y
linalg.tensorsolve	linalg.tensorsolve	Y
linalg.lstsq	linalg.lstsq	Y
linalg.inv	linalg.inv	Y
linalg.pinv	linalg.pinv	Y
linalg.tensorinv	linalg.tensorinv	Y

Exceptions

xorbits.numpy	numpy	Implemented? (Y/N/P/D)	Notes for Current implementation
linalg.LinAlgError	linalg.LinAlgError	Y

Linear algebra on several matrices at once

Added in version 1.8.0.

Several of the linear algebra routines listed above are able to compute results for several matrices at once, if they are stacked into the same array.

This is indicated in the documentation via input parameter specifications such as a : (..., M, M) array_like. This means that if for instance given an input array a.shape == (N, M, M), it is interpreted as a “stack” of N matrices, each of size M-by-M. Similar specification applies to return values, for instance the determinant has det : (...) and will in this case return an array of shape det(a).shape == (N,). This generalizes to linear algebra operations on higher-dimensional arrays: the last 1 or 2 dimensions of a multidimensional array are interpreted as vectors or matrices, as appropriate for each operation.