.. _docs-meteoinfolab-numeric-linalg-cholesky: *********************** Cholesky decomposition *********************** .. currentmodule:: numeric.linalg .. function:: cholesky(a) 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. Only ``L`` is actually returned. ``Parameters`` a : (M, M) array_like Hermitian (symmetric if all elements are real), positive-definite input matrix. ``Returns`` L : (M, M) array_like Upper or lower-triangular Cholesky factor of ``a``. Returns a matrix object if ``a`` is a matrix object. Examples:: a1 = array([[25,15,-5],[15,18,0],[-5,0,11]]) r1 = np.linalg.cholesky(a1) print r1 a2 = array([[18,22,54,42],[22,70,86,62],[54,86,174,134],[42,62,134,106]]) r2 = np.linalg.cholesky(a2) print r2 Result:: >>> run script... array([[5.0, 0.0, 0.0] [3.0, 3.0, 0.0] [-1.0, 1.0, 3.0]]) array([[4.242640687119285, 0.0, 0.0, 0.0] [5.185449728701349, 6.565905201197403, 0.0, 0.0] [12.727922061357857, 3.0460384954008553, 1.6497422479090682, 0.0] [9.899494936611667, 1.624553864213788, 1.8497110052313714, 1.3926212476455935]])