Coverage for webgeodyn/data/normPnm.py: 0%

1import numpy as np 

2 

3 

4def semiNormalisedSchmidt(lmax): 

5 """ Given the maximal degree lmax, builds an array of 

6 Schmidt semi-normalisation constants for the Legendre functions. 

7 

8 :param lmax: maximum degree 

9 :type lmax: int 

10 :return: normalisation of the Legendre functions for all l and m. 

11 :rtype: np.array 

12 """ 

13 PnmNorm = np.zeros((lmax+1, lmax+1)) 

14 for n in range(lmax+1): 

15 for m in range(lmax+1): 

16 if m > n: 

17 continue 

18 if m == 0: 

19 PnmNorm[m, n] = 1 

20 continue 

21 faclminusm = np.math.factorial(n-m) 

22 faclplusm = np.math.factorial(n+m) 

23 PnmNorm[m, n] = np.sqrt(2*faclminusm/faclplusm)*(-1)**m 

24 return PnmNorm 

25 

26 

27def noNorm(lmax): 

28 """ Returns an array of ones ('1') of appropriate dimensions to have 

29 non-normalised Legendre functions. 

30 

31 :param lmax: maximum degree 

32 :type lmax: int 

33 :return: array of ones ('1') (dim: lmax x lmax+1) 

34 :rtype: np.array 

35 """ 

36 return np.ones((lmax+1, lmax+1))