spleaf.cov.Cov

class spleaf.cov.Cov(t, **kwargs)

Covariance matrix class.

The covariance is modeled as the sum of different components (or terms), which split into two categories: noise terms and kernel terms (gaussian processes). See the API reference for a list of available terms.

Each component is provided in **kwargs, where the key is user-defined and is used to refer to the term parameters.

The covariance matrix is represented internally as a S+LEAF matrix (see spleaf.Spleaf).

Parameters:

t(n,) ndarray

Time of the measurements. This array must be in increasing order.

**kwargs

Components of the covariance matrix.

Attributes:

t(n,) ndarray

See parameters.

nint

Number of measurements.

dt(n-1,) ndarray

time between two measurements.

paramlist,

List of all covariance parameters.

termdict,

Dictionary of all covariance terms.

noisedict,

Dictionary of noise terms.

kerneldict,

Dictionary of kernel terms.

r, A, U, V, phi, offsetrow, b, F, D, W, G

S+LEAF representation of the covariance matrix (see spleaf.Spleaf).

Methods

chi2(y)	Compute \(\chi^2 = y^T C^{-1} y\) for a given vector of residuals \(y\).
chi2_grad(*args, **kwargs)	Compute the gradient of the \(\chi^2\) (chi2()) with respect to the residuals and to the initial parameters (see grad_param()).
cholesky_back()	Backward propagation of the gradient for the Cholesky decomposition.
conditional(y, t2[, calc_cov, kernel])	Conditional mean and covariance of the kernel part, or a subset of kernel terms, at new times \(t_2\), knowning the observed values \(y\).
conditional_derivative(y, t2[, calc_cov, kernel])	Conditional mean and covariance of the derivative of the kernel part, or a subset of kernel terms, at new times \(t_2\), knowning the observed values \(y\).
dotL(x[, copy])	Compute \(y = L x\).
dotLT(x[, copy])	Compute \(y = L^T x\).
dotLT_back(grad_y)	Backward propagation of the gradient for dotLT().
dotL_back(grad_y)	Backward propagation of the gradient for dotL().
eval(dt[, kernel])	Direct evaluation of the kernel part at lag \(\delta t\).
expand()	Expand the matrix as a full (n x n) matrix.
expandInv()	Expand the inverse of the matrix as a full (n x n) matrix.
expandInvL()	Expand \(L^{-1}\) as a full (n x n) matrix.
expandL()	Expand \(L\) as a full (n x n) matrix.
get_param([param])	Get the values of the parameters.
grad_param([param])	Gradient of a function with respect to the parameters, after a call to cholesky_back().
init_grad()	Initialize (or reinitialize) the backward propagation of the gradient.
logdet()	Compute the (natural) logarithm of the determinant of the matrix.
loglike(y)	Compute the (natural) logarithm of the likelihood for a given vector of residuals \(y\).
loglike_grad(*args, **kwargs)	Compute the gradient of the log-likelihood (loglike()) with respect to the residuals and to the initial parameters (see grad_param()).
sample([nreal])	Generate random samples from the covariance matrix.
self_conditional(y[, calc_cov, kernel])	Conditional mean and covariance of the kernel part, or a subset of kernel terms, knowning the observed values \(y\).
self_conditional_derivative(y[, calc_cov, ...])	Conditional mean and covariance of the derivative of the kernel part, or a subset of kernel terms, knowning the observed values \(y\).
set_param(value[, param])	Set the values of the parameters.
solveL(y[, copy])	Solve for \(x = L^{-1} y\).
solveLT(y[, copy])	Solve for \(x = L^{-T} y\).
solveLT_back(grad_x)	Backward propagation of the gradient for solveLT().
solveL_back(grad_x)	Backward propagation of the gradient for solveL().
sqD()	Compute the square-root of D.