geope.jax.logm

geope.jax.logm.roots_legendre(n, max_n=10)

Compute roots and weights for Gauss-Legendre quadrature.

JAX implementation compatible with JIT compilation.

Parameters:

Name	Type	Description	Default
n	int	Quadrature order.	required
max_n	int	Maximum number of roots to compute. Output arrays will have this size; entries beyond n are zero.	10

Returns:

Type	Description
tuple[Array, Array]	A tuple (nodes, weights) of arrays of length max_n.

Note

For inputs of 10000 and more, results may include NaNs due to precision errors.

References

W. H. Press et al., Numerical Recipes in FORTRAN (1992), section 4.5, page 152.

geope.jax.logm.sqrtm(A, blocksize=1)

Compute the matrix square root.

JAX implementation of scipy.linalg.sqrtm.

Parameters:

Name	Type	Description	Default
A	Union	Array of shape (N, N).	required
blocksize	int	Not supported in JAX; always uses blocksize=1.	1

Returns:

Type	Description
Array	An array of shape (N, N) containing the matrix square root.

Raises:

Type	Description
NotImplementedError	If blocksize > 1.

References

Björck, Å., & Hammarling, S. (1983). "A Schur method for the square root of a matrix". Linear Algebra and its Applications, 52, 127–140.

geope.jax.logm.logm(A, key)

Compute the matrix logarithm.

JAX implementation of scipy.linalg.logm using the improved inverse scaling-and-squaring method.

Parameters:

Name	Type	Description	Default
A	Union	Array of shape (N, N).	required
key	Union	JAX PRNG key for internal norm estimation.	required

Returns:

Type	Description
Array	An array of shape (N, N) containing the matrix logarithm.

References

Al-Mohy, A. H., & Higham, N. J. (2012). "Improved Inverse Scaling and Squaring Algorithms for the Matrix Logarithm". SIAM J. Sci. Comput., 34(4), C152–C169.

geope.jax.logm.rsf2csf(T, Z, check_finite=True)

Convert real Schur form to complex Schur form.

JAX implementation of scipy.linalg.rsf2csf.

Parameters:

Name	Type	Description	Default
T	Union	Array of shape (N, N) containing the real Schur form.	required
Z	Union	Array of shape (N, N) containing the corresponding Schur transformation matrix.	required
check_finite	bool	Unused by JAX (present for API compatibility).	True

Returns:

Type	Description
Array	A tuple (T, Z) of the same shape, containing the complex
Array	Schur form and its transformation matrix.

Raises:

Type	Description
ValueError	If T or Z is not square, or if their sizes do not match.