minimize関数を使いたい(jupyter)

Question

前提・実現したいこと

minimize関数を使いたい(jupyter)
どこが悪いのでしょうか？
よろしくお願いいたします。

発生している問題・エラーメッセージ

<ipython-input-2-c4d8c494bf74> in model(x, w)
      3 
      4 def model(x,w):
----> 5     y = w[0]*x + w[1]
      6     return y
      7 

can't multiply sequence by non-int of type 'numpy.float64'

該当のソースコード

import numpy as np
from scipy.optimize import minimize

X=[1,2,3,4,5]
T=[7,9,11,13,15]

def model(x,w):
    y = w[0]*x + w[1]
    return y

def mse_model(w,x,t):
    y = model(x,w)
    mse = np.mean((y-t)**2)
    return mse

def fit_model(w_init,x,t):
    res1 = minimize(mse_model,w_init,args=(x,t),method="powell")
    return res1.x

W_init = [4,10]
W = fit_model(W_init,X,T)
print(W)

試したこと

補足情報（FW/ツールのバージョンなど）

return res1.x の .xを付ける理由も分からないです。もしご存じの方いたら教えてください。

Answer 1

分からないときは、ドキュメント文字列を読みましょう。

from scipy.optimize import minimize
print(minimize.__doc__)

英語で表示されるので、英語が不得意ならGoogle翻訳などで翻訳して読んでください。
長いので全ては載せることができませんが、以下のようなものが表示されます。

>>> print(minimize.__doc__)
Minimization of scalar function of one or more variables.

    Parameters
    ----------
    fun : callable
        The objective function to be minimized.

            ``fun(x, *args) -> float``

        where ``x`` is an 1-D array with shape (n,) and ``args``
        is a tuple of the fixed parameters needed to completely
        specify the function.
    x0 : ndarray, shape (n,)
        Initial guess. Array of real elements of size (n,),
        where 'n' is the number of independent variables.
    args : tuple, optional
        Extra arguments passed to the objective function and its
        derivatives (`fun`, `jac` and `hess` functions).
    method : str or callable, optional
        Type of solver.  Should be one of

            - 'Nelder-Mead' :ref:`(see here) <optimize.minimize-neldermead>`
            - 'Powell'      :ref:`(see here) <optimize.minimize-powell>`
            - 'CG'          :ref:`(see here) <optimize.minimize-cg>`
            - 'BFGS'        :ref:`(see here) <optimize.minimize-bfgs>`
            - 'Newton-CG'   :ref:`(see here) <optimize.minimize-newtoncg>`
            - 'L-BFGS-B'    :ref:`(see here) <optimize.minimize-lbfgsb>`
            - 'TNC'         :ref:`(see here) <optimize.minimize-tnc>`
            - 'COBYLA'      :ref:`(see here) <optimize.minimize-cobyla>`
            - 'SLSQP'       :ref:`(see here) <optimize.minimize-slsqp>`
            - 'trust-constr':ref:`(see here) <optimize.minimize-trustconstr>`
            - 'dogleg'      :ref:`(see here) <optimize.minimize-dogleg>`
            - 'trust-ncg'   :ref:`(see here) <optimize.minimize-trustncg>`
            - 'trust-exact' :ref:`(see here) <optimize.minimize-trustexact>`
            - 'trust-krylov' :ref:`(see here) <optimize.minimize-trustkrylov>`
            - custom - a callable object (added in version 0.14.0),
              see below for description.

        If not given, chosen to be one of ``BFGS``, ``L-BFGS-B``, ``SLSQP``,
        depending if the problem has constraints or bounds.
    jac : {callable,  '2-point', '3-point', 'cs', bool}, optional
        Method for computing the gradient vector. Only for CG, BFGS,
        Newton-CG, L-BFGS-B, TNC, SLSQP, dogleg, trust-ncg, trust-krylov,
        trust-exact and trust-constr.
        If it is a callable, it should be a function that returns the gradient
        vector:

            ``jac(x, *args) -> array_like, shape (n,)``

        where ``x`` is an array with shape (n,) and ``args`` is a tuple with
        the fixed parameters. If `jac` is a Boolean and is True, `fun` is
        assumed to return and objective and gradient as an ``(f, g)`` tuple.
        Methods 'Newton-CG', 'trust-ncg', 'dogleg', 'trust-exact', and
        'trust-krylov' require that either a callable be supplied, or that
        `fun` return the objective and gradient.
        If None or False, the gradient will be estimated using 2-point finite
        difference estimation with an absolute step size.
        Alternatively, the keywords  {'2-point', '3-point', 'cs'} can be used
        to select a finite difference scheme for numerical estimation of the
        gradient with a relative step size. These finite difference schemes
        obey any specified `bounds`.
    hess : {callable, '2-point', '3-point', 'cs', HessianUpdateStrategy}, optional
        Method for computing the Hessian matrix. Only for Newton-CG, dogleg,
        trust-ncg,  trust-krylov, trust-exact and trust-constr. If it is
        callable, it should return the  Hessian matrix:

            ``hess(x, *args) -> {LinearOperator, spmatrix, array}, (n, n)``

        where x is a (n,) ndarray and `args` is a tuple with the fixed
        parameters. LinearOperator and sparse matrix returns are
        allowed only for 'trust-constr' method. Alternatively, the keywords
        {'2-point', '3-point', 'cs'} select a finite difference scheme
        for numerical estimation. Or, objects implementing
        `HessianUpdateStrategy` interface can be used to approximate
        the Hessian. Available quasi-Newton methods implementing
        this interface are:

            - `BFGS`;
            - `SR1`.

        Whenever the gradient is estimated via finite-differences,
        the Hessian cannot be estimated with options
        {'2-point', '3-point', 'cs'} and needs to be
        estimated using one of the quasi-Newton strategies.
        Finite-difference options {'2-point', '3-point', 'cs'} and
        `HessianUpdateStrategy` are available only for 'trust-constr' method.
    hessp : callable, optional
        Hessian of objective function times an arbitrary vector p. Only for
        Newton-CG, trust-ncg, trust-krylov, trust-constr.
        Only one of `hessp` or `hess` needs to be given.  If `hess` is
        provided, then `hessp` will be ignored.  `hessp` must compute the
        Hessian times an arbitrary vector:

            ``hessp(x, p, *args) ->  ndarray shape (n,)``

        where x is a (n,) ndarray, p is an arbitrary vector with
        dimension (n,) and `args` is a tuple with the fixed
        parameters.
    bounds : sequence or `Bounds`, optional
        Bounds on variables for L-BFGS-B, TNC, SLSQP, Powell, and
        trust-constr methods. There are two ways to specify the bounds:

            1. Instance of `Bounds` class.
            2. Sequence of ``(min, max)`` pairs for each element in `x`. None
               is used to specify no bound.

    constraints : {Constraint, dict} or List of {Constraint, dict}, optional
        Constraints definition (only for COBYLA, SLSQP and trust-constr).

        Constraints for 'trust-constr' are defined as a single object or a
        list of objects specifying constraints to the optimization problem.
        Available constraints are:

            - `LinearConstraint`
            - `NonlinearConstraint`

        Constraints for COBYLA, SLSQP are defined as a list of dictionaries.
        Each dictionary with fields:

            type : str
                Constraint type: 'eq' for equality, 'ineq' for inequality.
            fun : callable
                The function defining the constraint.
            jac : callable, optional
                The Jacobian of `fun` (only for SLSQP).
            args : sequence, optional
                Extra arguments to be passed to the function and Jacobian.

        Equality constraint means that the constraint function result is to
        be zero whereas inequality means that it is to be non-negative.
        Note that COBYLA only supports inequality constraints.
    tol : float, optional
        Tolerance for termination. For detailed control, use solver-specific
        options.
    options : dict, optional
        A dictionary of solver options. All methods accept the following
        generic options:

            maxiter : int
                Maximum number of iterations to perform. Depending on the
                method each iteration may use several function evaluations.
            disp : bool
                Set to True to print convergence messages.

        For method-specific options, see :func:`show_options()`.
    callback : callable, optional
        Called after each iteration. For 'trust-constr' it is a callable with
        the signature:

            ``callback(xk, OptimizeResult state) -> bool``

        where ``xk`` is the current parameter vector. and ``state``
        is an `OptimizeResult` object, with the same fields
        as the ones from the return. If callback returns True
        the algorithm execution is terminated.
        For all the other methods, the signature is:

            ``callback(xk)``

        where ``xk`` is the current parameter vector.

    Returns
    -------
    res : OptimizeResult
        The optimization result represented as a ``OptimizeResult`` object.
        Important attributes are: ``x`` the solution array, ``success`` a
        Boolean flag indicating if the optimizer exited successfully and
        ``message`` which describes the cause of the termination. See
        `OptimizeResult` for a description of other attributes.

    See also
    --------
    minimize_scalar : Interface to minimization algorithms for scalar
        univariate functions
    show_options : Additional options accepted by the solvers

    Notes
    -----
    This section describes the available solvers that can be selected by the
    'method' parameter. The default method is *BFGS*.

    References
    ----------
    .. [1] Nelder, J A, and R Mead. 1965. A Simplex Method for Function

    Examples
    --------
    Let us consider the problem of minimizing the Rosenbrock function. This

Answer 2

X=[1,2,3,4,5]
T=[7,9,11,13,15]

を

X=np.array([1,2,3,4,5])
T=np.array([7,9,11,13,15])

にしたら解決しました