# CHOLESKY

The CHOLESKY node is based on a numpy or scipy function. The description of that function is as follows: Cholesky decomposition. Return the Cholesky decomposition, "L * L.H", of the square matrix "a", where "L" is lower-triangular and .H is the conjugate transpose operator (which is the ordinary transpose if "a" is real-valued). "a" must be Hermitian (symmetric if real-valued) and positive-definite. No checking is performed to verify whether "a" is Hermitian or not. In addition, only the lower-triangular and diagonal elements of "a" are used. Only "L" is actually returned. Params: a : (..., M, M) array_like Hermitian (symmetric if all elements are real), positive-definite input matrix. Returns: out : DataContainer type 'ordered pair', 'scalar', or 'matrix'
Python Code
from flojoy import flojoy, Matrix, Scalar
import numpy as np

import numpy.linalg

@flojoy
def CHOLESKY(
default: Matrix,
) -> Matrix | Scalar:
"""The CHOLESKY node is based on a numpy or scipy function.

The description of that function is as follows:

Cholesky decomposition.

Return the Cholesky decomposition, "L * L.H", of the square matrix "a", where "L" is lower-triangular and .H is the conjugate transpose operator (which is the ordinary transpose if "a" is real-valued).

"a" must be Hermitian (symmetric if real-valued) and positive-definite. No checking is performed to verify whether "a" is Hermitian or not.

In addition, only the lower-triangular and diagonal elements of "a" are used. Only "L" is actually returned.

Parameters
----------
a : (..., M, M) array_like
Hermitian (symmetric if all elements are real), positive-definite input matrix.

Returns
-------
DataContainer
type 'ordered pair', 'scalar', or 'matrix'
"""

result = numpy.linalg.cholesky(
a=default.m,
)

if isinstance(result, np.ndarray):
result = Matrix(m=result)
else:
assert isinstance(
result, np.number | float | int
), f"Expected np.number, float or int for result, got {type(result)}"
result = Scalar(c=float(result))

return result


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