geometric_kernels.lab_extras

Custom extensions for LAB.

Package Contents

geometric_kernels.lab_extras.complex_conj(x)

Return complex conjugate.

Parameters:

x (lab.Numeric) – Array of any backend.

geometric_kernels.lab_extras.complex_like(reference)

Return complex dtype of a backend based on the reference.

Parameters:

reference (lab.Numeric) – Array of any backend.

geometric_kernels.lab_extras.cosh(x)

Compute hyperbolic cosine using the formula

\[\textrm{cosh}(x) = \frac{\exp(x) + \exp(-x)}{2}.\]

Parameters:

x (lab.Numeric) – Array of any backend.

Return type:

lab.Numeric

geometric_kernels.lab_extras.create_complex(real, imag)

Return a complex number with the given real and imaginary parts.

Parameters:

• real (lab.Numeric) – Array of any backend, real part of the complex number.

• imag (lab.Numeric) – Array of any backend, imaginary part of the complex number.

geometric_kernels.lab_extras.cumsum(a, axis=None)

Return cumulative sum (optionally along axis).

Parameters:

• a (lab.Numeric) – Array of any backend.

• axis – As in numpy.cumsum.

geometric_kernels.lab_extras.degree(a)

Given an adjacency matrix a, return a diagonal matrix with the col-sums of a as main diagonal - this is the degree matrix representing the number of nodes each node is connected to.

Parameters:

a – Array of any backend or scipy.sparse array.

geometric_kernels.lab_extras.dtype_double(reference)

Return double dtype of a backend based on the reference.

Parameters:

reference (lab.RandomState) – A random state to infer the backend from.

geometric_kernels.lab_extras.dtype_integer(reference)

Return int dtype of a backend based on the reference.

Parameters:

reference (lab.RandomState) – A random state to infer the backend from.

geometric_kernels.lab_extras.eigenpairs(L, k)

Obtain the eigenpairs that correspond to the k lowest eigenvalues of a symmetric positive semi-definite matrix L.

Parameters:

• a – Array of any backend or scipy.sparse array.

• k (int) – The number of eigenpairs to compute.

geometric_kernels.lab_extras.eigvalsh(x)

Compute the eigenvalues of a Hermitian or real symmetric matrix x.

Parameters:

x (lab.Numeric) – Array of any backend.

geometric_kernels.lab_extras.float_like(reference)

Return the type of the reference if it is a floating point type. Otherwise return double dtype of a backend based on the reference.

Parameters:

reference (lab.Numeric) – Array of any backend.

geometric_kernels.lab_extras.from_numpy(_, b)

Converts the array b to a tensor of the same backend as _.

Parameters:

• _ (lab.Numeric) – Array of any backend used to determine the backend.

• b (plum.Union[beartype.typing.List, lab.Numeric]) – Array of any backend or list to be converted to the backend of _.

geometric_kernels.lab_extras.get_random_state(key)

Return the random state of a random generator.

Parameters:

key (lab.RandomState) – The random generator.

geometric_kernels.lab_extras.int_like(reference)

Return the type of the reference if it is integer type. Otherwise return int32 dtype of a backend based on the reference.

Parameters:

reference (lab.Numeric) – Array of any backend.

geometric_kernels.lab_extras.is_complex(reference)

Return True if reference of complex dtype.

Parameters:

reference (lab.Numeric) – Array of any backend.

geometric_kernels.lab_extras.logspace(start, stop, num=50)

Return numbers spaced evenly on a log scale.

Parameters:

• start (lab.Numeric) – Array of any backend, as in numpy.logspace.

• stop (lab.Numeric) – Array of any backend, as in numpy.logspace.

• num (int) – As in numpy.logspace.

geometric_kernels.lab_extras.qr(x, mode='reduced')

Return a QR decomposition of a matrix x.

Parameters:

• x (lab.Numeric) – Array of any backend.

• mode – As in numpy.linalg.qr.

geometric_kernels.lab_extras.reciprocal_no_nan(x)

Return element-wise reciprocal (1/x). Whenever x = 0 puts 1/x = 0.

Parameters:

x (plum.Union[lab.Numeric, scipy.sparse.spmatrix]) – Array of any backend or scipy.sparse.spmatrix.

geometric_kernels.lab_extras.restore_random_state(key, state)

Set the random state of a random generator. Return the new random generator with state state.

Parameters:

• key (lab.RandomState) – The random generator.

• state – The new random state of the random generator.

geometric_kernels.lab_extras.set_value(a, index, value)

Set a[index] = value. This operation is not done in place and a new array is returned.

Parameters:

• a – Array of any backend or scipy.sparse array.

• index (int) – The index.

• value (float) – The value to set at the given index.

geometric_kernels.lab_extras.sinh(x)

Compute hyperbolic sine using the formula

\[\textrm{sinh}(x) = \frac{\exp(x) - \exp(-x)}{2}.\]

Parameters:

x (lab.Numeric) – Array of any backend.

Return type:

lab.Numeric

geometric_kernels.lab_extras.slogdet(x)

Return the sign and log-determinant of a matrix x.

Parameters:

x (lab.Numeric) – Array of any backend.

geometric_kernels.lab_extras.take_along_axis(a, index, axis=0)

Gathers elements of a along axis at index locations.

Parameters:

• a (lab.Numeric) – Array of any backend, as in numpy.take_along_axis.

• index (lab.Numeric) – Array of any backend, as in numpy.take_along_axis.

• axis (int) – As in numpy.take_along_axis.

geometric_kernels.lab_extras.trapz(y, x, dx=1.0, axis=-1)

Integrate along the given axis using the trapezoidal rule.

Parameters:

• y (lab.Numeric) – Array of any backend, as in numpy.trapz.

• x (lab.Numeric) – Array of any backend, as in numpy.trapz.

• dx (lab.Numeric) – Array of any backend, as in numpy.trapz.

• axis (int) – As in numpy.trapz.