pypeit.core.basis module

Module implements a set of basis functions for fitting.

pypeit.core.basis._build_basis(x, m, func)[source]

Perform initial checks of the basis function inputs.

Parameters:

  • x (array-like) – Compute the basis polynomials at these abscissa values.

  • m (int) – The number of polynomials to compute. For example, if \(m = 3\), \(P_0 (x)\), \(P_1 (x)\) and \(P_2 (x)\) will be computed. Must be \(\geq1\).

  • func (callable) – Callable function that generates the basis polynomials. E.g., scipy.special.legendre for Legendre polynomials.

Returns:

An array of shape \((N_x, m)\) with the basis polynomials.

Return type:

numpy.ndarray

Raises:

TypeError – Raised if the provided func is not callable.

pypeit.core.basis._init_basis(x, m)[source]

Initialize the basis functions.

Parameters:

  • x (array-like) – Compute the basis polynomials at these abscissa values.

  • m (int) – The number of polynomials to compute. For example, if \(m = 3\), \(P_0 (x)\), \(P_1 (x)\) and \(P_2 (x)\) will be computed. Must be \(\geq1\).

Returns:

Returns (1) the input \(x\) array explicitly converted to a numpy.ndarray and (2) a unity array with the same data type as \(x\). The returned shape of the latter is the \((N_x, m)\).

Return type:

tuple

Raises:

ValueError – Raised if the input order is not at least 1.

pypeit.core.basis.fchebyshev(x, m)[source]

Compute the first m Chebyshev polynomials.

Parameters:

  • x (array-like) – Compute the Chebyshev polynomials at these abscissa values.

  • m (int) – The number of Chebyshev polynomials to compute. For example, if \(m = 3\), \(T_0 (x)\), \(T_1 (x)\) and \(T_2 (x)\) will be computed.

Returns:

Polynomial basis functions evaluated at x.

Return type:

numpy.ndarray

pypeit.core.basis.fchebyshev_split(x, m)[source]

Compute the first m Chebyshev polynomials, but modified to allow a split in the baseline at \(x=0\). The intent is to allow a model fit where a constant term is different for positive and negative x.

Parameters:

  • x (array-like) – Compute the Chebyshev polynomials at these abscissa values.

  • m (int) – The number of Chebyshev polynomials to compute. For example, if \(m = 3\), \(T_0 (x)\), \(T_1 (x)\) and \(T_2 (x)\) will be computed.

Returns:

Polynomial basis functions evaluated at x.

Return type:

numpy.ndarray

pypeit.core.basis.flegendre(x, m)[source]

Compute the first m Legendre polynomials.

Parameters:

  • x (array-like) – Compute the Legendre polynomials at these abscissa values.

  • m (int) – The number of Legendre polynomials to compute. For example, if \(m = 3\), \(P_0 (x)\), \(P_1 (x)\) and \(P_2 (x)\) will be computed.

Returns:

Polynomial basis functions evaluated at x.

Return type:

numpy.ndarray

pypeit.core.basis.fpoly(x, m)[source]

Compute the first m simple polynomials.

Parameters:

  • x (array-like) – Compute the simple polynomials at these abscissa values.

  • m (int) – The number of simple polynomials to compute. For example, if \(m = 3\), \(x^0\), \(x^1\) and \(x^2\) will be computed.

Returns:

Polynomial basis functions evaluated at x.

Return type:

numpy.ndarray