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scipy.optimize.

# diagbroyden

scipy.optimize.diagbroyden(F, xin, iter=None, alpha=None, verbose=False, maxiter=None, f_tol=None, f_rtol=None, x_tol=None, x_rtol=None, tol_norm=None, line_search='armijo', callback=None, **kw)

  Find a root of a function, using diagonal Broyden Jacobian approximation.

  The Jacobian approximation is derived from previous iterations, by retaining only the diagonal of Broyden matrices.

  Warning

  This algorithm may be useful for specific problems, but whether it will work may depend strongly on the problem.

  Parameters:
    F function(x) -> f

      > Function whose root to find; should take and return an array-like object.

      xinarray_like

        Initial guess for the solution

    alpha float, optional

      Initial guess for the Jacobian is (-1/alpha).

    iter int, optional

      > Number of iterations to make. If omitted (default), make as many as required to meet tolerances.

      verbosebool, optional

        Print status to stdout on every iteration.

      maxiterint, optional

        Maximum number of iterations to make. If more are needed to meet convergence, `NoConvergence` is raised.

      f_tolfloat, optional

        Absolute tolerance (in max-norm) for the residual. If omitted, default is 6e-6.

      f_rtolfloat, optional

        Relative tolerance for the residual. If omitted, not used.

      x_tolfloat, optional

        Absolute minimum step size, as determined from the Jacobian approximation. If the step size is smaller than this, optimization is terminated as successful. If omitted, not used.

      x_rtolfloat, optional

        Relative minimum step size. If omitted, not used.

      tol_normfunction(vector) -> scalar, optional

        Norm to use in convergence check. Default is the maximum norm.

      line_search{None, ‘armijo’ (default), ‘wolfe’}, optional

        Which type of a line search to use to determine the step size in the direction given by the Jacobian approximation. Defaults to ‘armijo’.

      callbackfunction, optional

        Optional callback function. It is called on every iteration as `callback(x, f)` where x is the current solution and f the corresponding residual.

  Returns:
    sol ndarray

      An array (of similar array type as x0) containing the final solution.

  Raises:
    NoConvergence

      When a solution was not found.

  See also

  `root`

    Interface to root finding algorithms for multivariate functions. See `method='diagbroyden'` in particular.

  Examples

  The following functions define a system of nonlinear equations

      >>> def fun(x):
      ...     return [x[0]  + 0.5 * (x[0] - x[1])**3 - 1.0,
      ...             0.5 * (x[1] - x[0])**3 + x[1]]

  A solution can be obtained as follows.

      >>> from scipy import optimize
      >>> sol = optimize.diagbroyden(fun, [0, 0])
      >>> sol
      array([0.84116403, 0.15883384])