![]() Or even biaxial stripes: y = rand.uniform(low=-0.01, high=0. Y += rand.uniform(low=-1, high=1, size=I) Predictably, this performs much better for data that have stripe patterns, as in y = rand.uniform(low=-0.01, high=0.01, size=(I, T)) In order to solve systems of equations in three variables, known as three-by-three systems, the primary tool we will be using is called Gaussian elimination, named after the prolific German mathematician Karl Friedrich Gauss. Using row operations, get the entry in row 2, column 2 to be 1. Solving Systems of Three Equations in Three Variables. Using row operations, get zeros in column 1 below the 1. Using row operations get the entry in row 1, column 1 to be 1. Write the augmented matrix for the system of equations. ![]() The Jacobian will happily point toward a minimum, and where that minimum might be local, that might be OK for your purposes. Solve a system of equations using matrices. Gamma_est, eta_est = factors_from_flat(result.x) Result = minimize(fun=scalar_cost, x0=x0, jac=jacobian) X0 = np.full(I*J + J*T, 1/np.sqrt(I*J*T))Įrr = check_grad(func=scalar_cost, grad=jacobian, x0=x0) Y = rand.uniform(low=-1, high=1, size=(I, T))ĭef factors_from_flat(params: np.ndarray) -> tuple:ĭef matrix_cost(gamma: np.ndarray, eta: np.ndarray) -> np.ndarray:ĭef scalar_cost(params: np.ndarray) -> float:ĭef jacobian(params: np.ndarray) -> float: ![]() The following doesn't produce a very good fit, but that may be because your problem is highly over-determined: import numpy as npįrom scipy.optimize import minimize, check_gradįrom numpy.random._generator import default_rng Recognize that your "sum of a series of products" is really just a matrix product.
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