Low-level Solver Interface¶

This is the low-level interface to the C++ implementation of the celerite algorithm. These methods do most of the heavy lifting but most users shouldn’t need to call these directly. This interface was built using pybind11.

celerite.solver.get_kernel_value(arg0: numpy.ndarray[float64[m, 1]], arg1: numpy.ndarray[float64[m, 1]], arg2: numpy.ndarray[float64[m, 1]], arg3: numpy.ndarray[float64[m, 1]], arg4: numpy.ndarray[float64[m, 1]], arg5: numpy.ndarray[float64[m, 1]], arg6: numpy.ndarray[float]) → object¶

Get the value of the kernel for given parameters and lags

Parameters:	alpha_real (array[j_real]) – The coefficients of the real terms. beta_real (array[j_real]) – The exponents of the real terms. alpha_complex_real (array[j_complex]) – The real part of the coefficients of the complex terms. alpha_complex_imag (array[j_complex]) – The imaginary part of the coefficients of the complex terms. beta_complex_real (array[j_complex]) – The real part of the exponents of the complex terms. beta_complex_imag (array[j_complex]) – The imaginary part of the exponents of the complex terms. tau (array[n]) – The time lags where the kernel should be evaluated.
Returns:	The kernel evaluated at `tau`.
Return type:	array[n]

celerite.solver.get_psd_value(arg0: numpy.ndarray[float64[m, 1]], arg1: numpy.ndarray[float64[m, 1]], arg2: numpy.ndarray[float64[m, 1]], arg3: numpy.ndarray[float64[m, 1]], arg4: numpy.ndarray[float64[m, 1]], arg5: numpy.ndarray[float64[m, 1]], arg6: numpy.ndarray[float]) → object¶

Get the PSD of the kernel for given parameters and angular frequencies

Parameters:	alpha_real (array[j_real]) – The coefficients of the real terms. beta_real (array[j_real]) – The exponents of the real terms. alpha_complex_real (array[j_complex]) – The real part of the coefficients of the complex terms. alpha_complex_imag (array[j_complex]) – The imaginary part of the coefficients of the complex terms. beta_complex_real (array[j_complex]) – The real part of the exponents of the complex terms. beta_complex_imag (array[j_complex]) – The imaginary part of the exponents of the complex terms. omega (array[n]) – The frequencies where the PSD should be evaluated.
Returns:	The PSD evaluated at `omega`.
Return type:	array[n]

celerite.solver.check_coefficients(arg0: numpy.ndarray[float64[m, 1]], arg1: numpy.ndarray[float64[m, 1]], arg2: numpy.ndarray[float64[m, 1]], arg3: numpy.ndarray[float64[m, 1]], arg4: numpy.ndarray[float64[m, 1]], arg5: numpy.ndarray[float64[m, 1]]) → bool¶

Apply Sturm’s theorem to check if parameters yield a positive PSD

Parameters:	alpha_real (array[j_real]) – The coefficients of the real terms. beta_real (array[j_real]) – The exponents of the real terms. alpha_complex_real (array[j_complex]) – The real part of the coefficients of the complex terms. alpha_complex_imag (array[j_complex]) – The imaginary part of the coefficients of the complex terms. beta_complex_real (array[j_complex]) – The real part of the exponents of the complex terms. beta_complex_imag (array[j_complex]) – The imaginary part of the exponents of the complex terms.
Returns:	`True` if the PSD is everywhere positive.
Return type:	bool

class celerite.solver.Solver¶

A thin wrapper around the C++ BandSolver class

The class provides all of the computation power for the celerite module. The key methods are listed below but the solver.Solver.compute() method must always be called first.

compute(self: celerite.solver.Solver, arg0: numpy.ndarray[float64[m, 1]], arg1: numpy.ndarray[float64[m, 1]], arg2: numpy.ndarray[float64[m, 1]], arg3: numpy.ndarray[float64[m, 1]], arg4: numpy.ndarray[float64[m, 1]], arg5: numpy.ndarray[float64[m, 1]], arg6: numpy.ndarray[float64[m, 1]], arg7: numpy.ndarray[float64[m, 1]]) → int¶

Assemble the extended matrix and perform the banded LU decomposition

Parameters:	alpha_real (array[j_real]) – The coefficients of the real terms. beta_real (array[j_real]) – The exponents of the real terms. alpha_complex_real (array[j_complex]) – The real part of the coefficients of the complex terms. alpha_complex_imag (array[j_complex]) – The imaginary part of the coefficients of the complex terms. beta_complex_real (array[j_complex]) – The real part of the exponents of the complex terms. beta_complex_imag (array[j_complex]) – The imaginary part of the exponents of the complex terms. x (array[n]) – The _sorted_ array of input coordinates. diag (array[n]) – An array that should be added to the diagonal of the matrix. This often corresponds to measurement uncertainties and in that case, `diag` should be the measurement _variance_ (i.e. sigma^2).
Returns:	`1` if the dimensions are inconsistent and `0` otherwise. No attempt is made to confirm that the matrix is positive definite. If it is not positive definite, the `solve` and `log_determinant` methods will return incorrect results.
Return type:	int

computed(self: celerite.solver.Solver) → bool¶

A flag that indicates if compute has been executed

Returns:	`True` if `solver.Solver.compute()` was previously executed successfully.
Return type:	bool

dot(self: celerite.solver.Solver, arg0: numpy.ndarray[float64[m, 1]], arg1: numpy.ndarray[float64[m, 1]], arg2: numpy.ndarray[float64[m, 1]], arg3: numpy.ndarray[float64[m, 1]], arg4: numpy.ndarray[float64[m, 1]], arg5: numpy.ndarray[float64[m, 1]], arg6: numpy.ndarray[float64[m, 1]], arg7: numpy.ndarray[float64[m, n]]) → numpy.ndarray[float64[m, n]]¶

Compute the dot product of a celerite matrix and another arbitrary matrix

This method computes A.b where A is defined by the parameters and b is an arbitrary matrix of the correct shape.

Parameters:	alpha_real (array[j_real]) – The coefficients of the real terms. beta_real (array[j_real]) – The exponents of the real terms. alpha_complex_real (array[j_complex]) – The real part of the coefficients of the complex terms. alpha_complex_imag (array[j_complex]) – The imaginary part of the coefficients of the complex terms. beta_complex_real (array[j_complex]) – The real part of the exponents of the complex terms. beta_complex_imag (array[j_complex]) – The imaginary part of the exponents of the complex terms. x (array[n]) – The _sorted_ array of input coordinates. b (array[n] or array[n, neq]) – The matrix `b` described above.
Returns:	The dot product `A.b` as described above.
Return type:	array[n] or array[n, neq]
Raises:	`ValueError` – For mismatched dimensions.

dot_solve(self: celerite.solver.Solver, arg0: numpy.ndarray[float64[m, n]]) → float¶

Solve the system b^T . A^-1 . b

A previous call to solver.Solver.compute() defines a matrix A and this method solves b^T . A^-1 . b for a vector b.

Parameters:	b (array[n]) – The right hand side of the linear system.
Returns:	The solution of `b^T . A^-1 . b`.
Return type:	float
Raises:	`ValueError` – For mismatched dimensions.

log_determinant(self: celerite.solver.Solver) → float¶

Get the log-determinant of the matrix defined by compute

Returns:	The log-determinant of the matrix defined by `solver.Solver.compute()`.
Return type:	float

solve(self: celerite.solver.Solver, arg0: numpy.ndarray[float64[m, n]]) → numpy.ndarray[float64[m, n]]¶

Solve a linear system for the matrix defined in compute

A previous call to solver.Solver.compute() defines a matrix A and this method solves for x in the matrix equation A.x = b.

Parameters:	b (array[n] or array[n, nrhs]) – The right hand side of the linear system.
Returns:	The solution of the linear system.
Return type:	array[n] or array[n, nrhs]
Raises:	`ValueError` – For mismatched dimensions.