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linalg

linalg#

Linear algebra routines with broadcasting and complex value support.

This module exists because support for broadcasting and complex values is spotty in the NumPy and CuPy libraries.

tike.linalg.cov(x)[source]#

Compute the covariance of x with observations along axis -2.

tike.linalg.hermitian(x)[source]#

Compute the conjugate transpose of x along last two dimensions.

tike.linalg.inner(x, y, axis=None, keepdims=False)[source]#

Return the complex inner product; the order of the operands matters.

tike.linalg.lstsq(a, b, weights=None)[source]#

Return the least-squares solution for a @ x = b.

This implementation, unlike cp.linalg.lstsq, allows a stack of matricies to be processed simultaneously. The input sizes of the matricies are as follows:

a (…, M, N) b (…, M, K) x (…, N, K)

Optionally include weights (…, M) for weighted-least-squares if the errors are uncorrelated.

…seealso:: numpy/numpy#8720

cupy/cupy#3062

tike.linalg.mnorm(x, axis=None, keepdims=False)[source]#

Return the vector 2-norm of x but replace sum with mean.

tike.linalg.norm(x, axis=None, keepdims=False)[source]#

Return the vector 2-norm of x along given axis.

tike.linalg.orthogonalize_gs(x, axis=-1, N=None)[source]#

Gram-schmidt orthogonalization for complex arrays.

Parameters

  • x ((..., D) array) – containing dimensions to be orthogonalized.

  • axis (Union[int, Tuple[int, ...]]) – The axis/axes to be orthogonalized. By default only the last axis is orthogonalized. If axis is a tuple, then the number of orthogonal vectors is the length of the last dimension not included in axis. The other dimensions are broadcast.

  • N (Optional[int]) – The axis along which to orthogonalize. Other dimensions are broadcast.

tike.linalg.pca_eig(data, k)[source]#

Return k principal components via Eigen decomposition.

Parameters

  • data ((..., N, D) array) – N observations of a D dimensional space.

  • k (int) – The number of principle components.

Returns

  • S ((…, k) array) – The singular values corresponding to the current principal components sorted largest to smallest.

  • U ((…, D, k) array) – The current best principal components of the population.

Return type

Tuple[numpy.typing.NDArray, numpy.typing.NDArray]

tike.linalg.projection(a, b, axis=None)[source]#

Return complex vector projection of a onto b for along given axis.

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