math
Special functions of mathematical physics
Calling Sequence
import pyTMD.math
P = pyTMD.math.legendre(2, x, m=0)
- pyTMD.math.polynomial_sum(coefficients: list | ndarray, t: ndarray)[source]
Calculates the sum of a polynomial function using Horner’s method [24]
- Parameters:
- coefficients: list or np.ndarray
leading coefficient of polynomials of increasing order
- t: np.ndarray
delta time in units for a given astronomical longitudes calculation
- pyTMD.math.normalize_angle(theta: float | ndarray, circle: float = 360.0)[source]
Normalize an angle to a single rotation
- Parameters:
- theta: float or np.ndarray
Angle to normalize
- circle: float, default 360.0
Circle of the angle
- pyTMD.math.rotate(theta: float | ndarray, axis: str = 'x')[source]
Rotate a 3-dimensional matrix about a given axis
- Parameters:
- theta: float or np.ndarray
Angle of rotation in radians
- axis: str, default ‘x’
Axis of rotation (
'x','y', or'z')
- pyTMD.math.aliasing(f: float, fs: float) float[source]
Calculate the aliasing frequency of a signal
- Parameters:
- f: float
Frequency of the signal
- fs: float
Sampling frequency of the signal
- Returns:
- fa: float
Aliasing frequency of the signal
- pyTMD.math.legendre(l: int, x: ndarray, m: int = 0)[source]
Computes associated Legendre functions for a particular degree and order [23, 35]
- Parameters:
- l: int
degree of the Legendre polynomials (0 to 3)
- x: np.ndarray
elements ranging from -1 to 1
Typically
cos(theta), wherethetais the colatitude in radians- m: int, default 0
order of the Legendre polynomials (0 to
l)
- Returns:
- Plm: np.ndarray
Legendre polynomials of degree
land orderm
- pyTMD.math.assoc_legendre(lmax, x)[source]
Computes fully-normalized associated Legendre Polynomials using a standard forward-column method [11] [23]
- Parameters:
- lmax: int
maximum degree and order of Legendre polynomials
- x: np.ndarray
elements ranging from -1 to 1
Typically
cos(theta), wherethetais the colatitude in radians
- Returns:
- Plm: np.ndarray
fully-normalized Legendre polynomials
- pyTMD.math.sph_harm(l: int, theta: ndarray, phi: ndarray, m: int = 0)[source]
Computes the spherical harmonics for a particular degree and order [23, 35]
- Parameters:
- l: int
degree of the spherical harmonics (0 to 3)
- theta: np.ndarray
colatitude in radians
- phi: np.ndarray
longitude in radians
- m: int, default 0
order of the spherical harmonics (0 to
l)
- Returns:
- Ylm: np.ndarray
complex spherical harmonics of degree
land orderm