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.