scipy.special.agm¶
- scipy.special.agm(a, b) = <ufunc 'agm'>¶
Compute the arithmetic-geometric mean of a and b.
Start with a_0 = a and b_0 = b and iteratively compute:
a_{n+1} = (a_n + b_n)/2 b_{n+1} = sqrt(a_n*b_n)
a_n and b_n converge to the same limit as n increases; their common limit is agm(a, b).
- Parameters
- a, barray_like
Real values only. If the values are both negative, the result is negative. If one value is negative and the other is positive, nan is returned.
- Returns
- float
The arithmetic-geometric mean of a and b.
Examples
>>> from scipy.special import agm >>> a, b = 24.0, 6.0 >>> agm(a, b) 13.458171481725614
Compare that result to the iteration:
>>> while a != b: ... a, b = (a + b)/2, np.sqrt(a*b) ... print("a = %19.16f b=%19.16f" % (a, b)) ... a = 15.0000000000000000 b=12.0000000000000000 a = 13.5000000000000000 b=13.4164078649987388 a = 13.4582039324993694 b=13.4581390309909850 a = 13.4581714817451772 b=13.4581714817060547 a = 13.4581714817256159 b=13.4581714817256159
When array-like arguments are given, broadcasting applies:
>>> a = np.array([[1.5], [3], [6]]) # a has shape (3, 1). >>> b = np.array([6, 12, 24, 48]) # b has shape (4,). >>> agm(a, b) array([[ 3.36454287, 5.42363427, 9.05798751, 15.53650756], [ 4.37037309, 6.72908574, 10.84726853, 18.11597502], [ 6. , 8.74074619, 13.45817148, 21.69453707]])