jax.scipy.linalg.pascal#

jax.scipy.linalg.pascal(n, kind=None)[source]#

Create a Pascal matrix approximation of order n.

JAX implementation of scipy.linalg.pascal().

The elements of the Pascal matrix approximate the binomial coefficents. This implementation is not exact as JAX does not support exact factorials.

Parameters:

  • n (int) – the size of the matrix to create.

  • kind (str | None) – (optional) must be one of lower, upper, or symmetric (default).

Returns:

A Pascal matrix of shape (n, n)

Return type:

Array

Examples

>>> with jnp.printoptions(precision=3):
...   print(jax.scipy.linalg.pascal(3, kind="lower"))
...   print(jax.scipy.linalg.pascal(4, kind="upper"))
...   print(jax.scipy.linalg.pascal(5))
[[1. 0. 0.]
 [1. 1. 0.]
 [1. 2. 1.]]
[[1. 1. 1. 1.]
 [0. 1. 2. 3.]
 [0. 0. 1. 3.]
 [0. 0. 0. 1.]]
[[ 1.  1.  1.  1.  1.]
 [ 1.  2.  3.  4.  5.]
 [ 1.  3.  6. 10. 15.]
 [ 1.  4. 10. 20. 35.]
 [ 1.  5. 15. 35. 70.]]