import autograd.numpy as np
import math
import scipy.optimize
from scipy.odr import ODR, Model, RealData
from scipy.linalg import cholesky
from scipy.stats import norm
import pyerrors as pe
import pytest

np.random.seed(0)


def test_fit_lin():
    x = [0, 2]
    y = [pe.pseudo_Obs(0, 0.1, 'ensemble'),
         pe.pseudo_Obs(2, 0.1, 'ensemble')]

    res = pe.fits.fit_lin(x, y)

    assert res[0] == y[0]
    assert res[1] == (y[1] - y[0]) / (x[1] - x[0])

    x = y = [pe.pseudo_Obs(0, 0.1, 'ensemble'),
         pe.pseudo_Obs(2, 0.1, 'ensemble')]

    res = pe.fits.fit_lin(x, y)

    m = (y[1] - y[0]) / (x[1] - x[0])
    assert res[0] == y[1] - x[1] * m
    assert res[1] == m


def test_least_squares():
    dim = 10 + int(30 * np.random.rand())
    x = np.arange(dim)
    y = 2 * np.exp(-0.06 * x) + np.random.normal(0.0, 0.15, dim)
    yerr = 0.1 + 0.1 * np.random.rand(dim)

    oy = []
    for i, item in enumerate(x):
        oy.append(pe.pseudo_Obs(y[i], yerr[i], str(i)))

    def f(x, a, b):
        return a * np.exp(-b * x)

    popt, pcov = scipy.optimize.curve_fit(f, x, y, sigma=[o.dvalue for o in oy], absolute_sigma=True)

    def func(a, x):
        y = a[0] * np.exp(-a[1] * x)
        return y

    out = pe.least_squares(x, oy, func, expected_chisquare=True, resplot=True, qqplot=True)
    beta = out.fit_parameters

    str(out)
    repr(out)
    len(out)

    for i in range(2):
        beta[i].gamma_method(S=1.0)
        assert math.isclose(beta[i].value, popt[i], abs_tol=1e-5)
        assert math.isclose(pcov[i, i], beta[i].dvalue ** 2, abs_tol=1e-3)
    assert math.isclose(pe.covariance(beta[0], beta[1]), pcov[0, 1], abs_tol=1e-3)

    chi2_pyerrors = np.sum(((f(x, *[o.value for o in beta]) - y) / yerr) ** 2) / (len(x) - 2)
    chi2_scipy = np.sum(((f(x, *popt) - y) / yerr) ** 2) / (len(x) - 2)
    assert math.isclose(chi2_pyerrors, chi2_scipy, abs_tol=1e-10)

    out = pe.least_squares(x, oy, func, const_par=[beta[1]])
    assert((out.fit_parameters[0] - beta[0]).is_zero())
    assert((out.fit_parameters[1] - beta[1]).is_zero())

    oyc = []
    for i, item in enumerate(x):
        oyc.append(pe.cov_Obs(y[i], yerr[i]**2, 'cov' + str(i)))

    outc = pe.least_squares(x, oyc, func)
    betac = outc.fit_parameters

    for i in range(2):
        betac[i].gamma_method(S=1.0)
        assert math.isclose(betac[i].value, popt[i], abs_tol=1e-5)
        assert math.isclose(pcov[i, i], betac[i].dvalue ** 2, abs_tol=1e-3)
    assert math.isclose(pe.covariance(betac[0], betac[1]), pcov[0, 1], abs_tol=1e-3)


def test_correlated_fit():
    num_samples = 400
    N = 10

    x = norm.rvs(size=(N, num_samples))

    r = np.zeros((N, N))
    for i in range(N):
        for j in range(N):
            r[i, j] = np.exp(-0.8 * np.fabs(i - j))

    errl = np.sqrt([3.4, 2.5, 3.6, 2.8, 4.2, 4.7, 4.9, 5.1, 3.2, 4.2])
    for i in range(N):
        for j in range(N):
            r[i, j] *= errl[i] * errl[j]

    c = cholesky(r, lower=True)
    y = np.dot(c, x)
    x = np.arange(N)
    for linear in [True, False]:
        data = []
        for i in range(N):
            if linear:
                data.append(pe.Obs([[i + 1 + o for o in y[i]]], ['ens']))
            else:
                data.append(pe.Obs([[np.exp(-(i + 1)) + np.exp(-(i + 1)) * o for o in y[i]]], ['ens']))

        [o.gamma_method() for o in data]

        if linear:
            def fitf(p, x):
                return p[1] + p[0] * x
        else:
            def fitf(p, x):
                return p[1] * np.exp(-p[0] * x)

        fitp = pe.least_squares(x, data, fitf, expected_chisquare=True)

        fitpc = pe.least_squares(x, data, fitf, correlated_fit=True)
        for i in range(2):
            diff = fitp[i] - fitpc[i]
            diff.gamma_method()
            assert(diff.is_zero_within_error(sigma=5))


def test_total_least_squares():
    dim = 10 + int(30 * np.random.rand())
    x = np.arange(dim) + np.random.normal(0.0, 0.15, dim)
    xerr = 0.1 + 0.1 * np.random.rand(dim)
    y = 2 * np.exp(-0.06 * x) + np.random.normal(0.0, 0.15, dim)
    yerr = 0.1 + 0.1 * np.random.rand(dim)

    ox = []
    for i, item in enumerate(x):
        ox.append(pe.pseudo_Obs(x[i], xerr[i], str(i)))

    oy = []
    for i, item in enumerate(x):
        oy.append(pe.pseudo_Obs(y[i], yerr[i], str(i)))

    def f(x, a, b):
        return a * np.exp(-b * x)

    def func(a, x):
        y = a[0] * np.exp(-a[1] * x)
        return y

    data = RealData([o.value for o in ox], [o.value for o in oy], sx=[o.dvalue for o in ox], sy=[o.dvalue for o in oy])
    model = Model(func)
    odr = ODR(data, model, [0, 0], partol=np.finfo(np.float64).eps)
    odr.set_job(fit_type=0, deriv=1)
    output = odr.run()

    out = pe.total_least_squares(ox, oy, func, expected_chisquare=True)
    beta = out.fit_parameters

    str(out)
    repr(out)
    len(out)

    for i in range(2):
        beta[i].gamma_method(S=1.0)
        assert math.isclose(beta[i].value, output.beta[i], rel_tol=1e-5)
        assert math.isclose(output.cov_beta[i, i], beta[i].dvalue ** 2, rel_tol=2.5e-1), str(output.cov_beta[i, i]) + ' ' + str(beta[i].dvalue ** 2)
    assert math.isclose(pe.covariance(beta[0], beta[1]), output.cov_beta[0, 1], rel_tol=2.5e-1)

    out = pe.total_least_squares(ox, oy, func, const_par=[beta[1]])

    diff = out.fit_parameters[0] - beta[0]
    assert(diff / beta[0] < 1e-3 * beta[0].dvalue)
    assert((out.fit_parameters[1] - beta[1]).is_zero())

    oxc = []
    for i, item in enumerate(x):
        oxc.append(pe.cov_Obs(x[i], xerr[i]**2, 'covx' + str(i)))

    oyc = []
    for i, item in enumerate(x):
        oyc.append(pe.cov_Obs(y[i], yerr[i]**2, 'covy' + str(i)))

    outc = pe.total_least_squares(oxc, oyc, func)
    betac = outc.fit_parameters

    for i in range(2):
        betac[i].gamma_method(S=1.0)
        assert math.isclose(betac[i].value, output.beta[i], rel_tol=1e-3)
        assert math.isclose(output.cov_beta[i, i], betac[i].dvalue ** 2, rel_tol=2.5e-1), str(output.cov_beta[i, i]) + ' ' + str(betac[i].dvalue ** 2)
    assert math.isclose(pe.covariance(betac[0], betac[1]), output.cov_beta[0, 1], rel_tol=2.5e-1)

    outc = pe.total_least_squares(oxc, oyc, func, const_par=[betac[1]])

    diffc = outc.fit_parameters[0] - betac[0]
    assert(diffc / betac[0] < 1e-3 * betac[0].dvalue)
    assert((outc.fit_parameters[1] - betac[1]).is_zero())

    outc = pe.total_least_squares(oxc, oy, func)
    betac = outc.fit_parameters

    for i in range(2):
        betac[i].gamma_method(S=1.0)
        assert math.isclose(betac[i].value, output.beta[i], rel_tol=1e-3)
        assert math.isclose(output.cov_beta[i, i], betac[i].dvalue ** 2, rel_tol=2.5e-1), str(output.cov_beta[i, i]) + ' ' + str(betac[i].dvalue ** 2)
    assert math.isclose(pe.covariance(betac[0], betac[1]), output.cov_beta[0, 1], rel_tol=2.5e-1)

    outc = pe.total_least_squares(oxc, oy, func, const_par=[betac[1]])

    diffc = outc.fit_parameters[0] - betac[0]
    assert(diffc / betac[0] < 1e-3 * betac[0].dvalue)
    assert((outc.fit_parameters[1] - betac[1]).is_zero())


def test_odr_derivatives():
    x = []
    y = []
    x_err = 0.01
    y_err = 0.01

    for n in np.arange(1, 9, 2):
        loc_xvalue = n + np.random.normal(0.0, x_err)
        x.append(pe.pseudo_Obs(loc_xvalue, x_err, str(n)))
        y.append(pe.pseudo_Obs((lambda x: x ** 2 - 1)(loc_xvalue) +
                               np.random.normal(0.0, y_err), y_err, str(n)))

        def func(a, x):
            return a[0] + a[1] * x ** 2
    out = pe.total_least_squares(x, y, func)
    fit1 = out.fit_parameters

    tfit = fit_general(x, y, func, base_step=0.1, step_ratio=1.1, num_steps=20)
    assert np.abs(np.max(np.array(list(fit1[1].deltas.values()))
                  - np.array(list(tfit[1].deltas.values())))) < 10e-8


def test_r_value_persistence():
    def f(a, x):
        return a[0] + a[1] * x

    a = pe.pseudo_Obs(1.1, .1, 'a')
    assert np.isclose(a.value, a.r_values['a'])

    a_2 = a ** 2
    assert np.isclose(a_2.value, a_2.r_values['a'])

    b = pe.pseudo_Obs(2.1, .2, 'b')

    y = [a, b]
    [o.gamma_method() for o in y]

    fitp = pe.fits.least_squares([1, 2], y, f)

    assert np.isclose(fitp[0].value, fitp[0].r_values['a'])
    assert np.isclose(fitp[0].value, fitp[0].r_values['b'])
    assert np.isclose(fitp[1].value, fitp[1].r_values['a'])
    assert np.isclose(fitp[1].value, fitp[1].r_values['b'])

    fitp = pe.fits.total_least_squares(y, y, f)

    assert np.isclose(fitp[0].value, fitp[0].r_values['a'])
    assert np.isclose(fitp[0].value, fitp[0].r_values['b'])
    assert np.isclose(fitp[1].value, fitp[1].r_values['a'])
    assert np.isclose(fitp[1].value, fitp[1].r_values['b'])

    fitp = pe.fits.least_squares([1, 2], y, f, priors=y)

    assert np.isclose(fitp[0].value, fitp[0].r_values['a'])
    assert np.isclose(fitp[0].value, fitp[0].r_values['b'])
    assert np.isclose(fitp[1].value, fitp[1].r_values['a'])
    assert np.isclose(fitp[1].value, fitp[1].r_values['b'])


def test_prior_fit():
    def f(a, x):
        return a[0] + a[1] * x

    a = pe.pseudo_Obs(0.0, 0.1, 'a')
    b = pe.pseudo_Obs(1.0, 0.2, 'a')

    y = [a, b]
    with pytest.raises(Exception):
        fitp = pe.fits.least_squares([0, 1], 1 * np.array(y), f, priors=['0.0(8)', '1.0(8)'])

    [o.gamma_method() for o in y]

    fitp = pe.fits.least_squares([0, 1], y, f, priors=['0.0(8)', '1.0(8)'])
    fitp = pe.fits.least_squares([0, 1], y, f, priors=y, resplot=True, qqplot=True)


def test_error_band():
    def f(a, x):
        return a[0] + a[1] * x

    a = pe.pseudo_Obs(0.0, 0.1, 'a')
    b = pe.pseudo_Obs(1.0, 0.2, 'a')

    x = [0, 1]
    y = [a, b]

    fitp = pe.fits.least_squares(x, y, f)

    with pytest.raises(Exception):
        pe.fits.error_band(x, f, fitp.fit_parameters)
    fitp.gamma_method()
    pe.fits.error_band(x, f, fitp.fit_parameters)


def fit_general(x, y, func, silent=False, **kwargs):
    """Performs a non-linear fit to y = func(x) and returns a list of Obs corresponding to the fit parameters.

    Plausibility of the results should be checked. To control the numerical differentiation
    the kwargs of numdifftools.step_generators.MaxStepGenerator can be used.

    func has to be of the form

    def func(a, x):
        y = a[0] + a[1] * x + a[2] * np.sinh(x)
        return y

    y has to be a list of Obs, the dvalues of the Obs are used as yerror for the fit.
    x can either be a list of floats in which case no xerror is assumed, or
    a list of Obs, where the dvalues of the Obs are used as xerror for the fit.

    Keyword arguments
    -----------------
    silent -- If true all output to the console is omitted (default False).
    initial_guess -- can provide an initial guess for the input parameters. Relevant for non-linear fits
                     with many parameters.
    """

    if not callable(func):
        raise TypeError('func has to be a function.')

    for i in range(10):
        try:
            func(np.arange(i), 0)
        except:
            pass
        else:
            break
    n_parms = i
    if not silent:
        print('Fit with', n_parms, 'parameters')

    global print_output, beta0
    print_output = 1
    if 'initial_guess' in kwargs:
        beta0 = kwargs.get('initial_guess')
        if len(beta0) != n_parms:
            raise Exception('Initial guess does not have the correct length.')
    else:
        beta0 = np.arange(n_parms)

    if len(x) != len(y):
        raise Exception('x and y have to have the same length')

    if all(isinstance(n, pe.Obs) for n in x):
        obs = x + y
        x_constants = None
        xerr = [o.dvalue for o in x]
        yerr = [o.dvalue for o in y]
    elif all(isinstance(n, float) or isinstance(n, int) for n in x) or isinstance(x, np.ndarray):
        obs = y
        x_constants = x
        xerr = None
        yerr = [o.dvalue for o in y]
    else:
        raise Exception('Unsupported types for x')

    def do_the_fit(obs, **kwargs):

        global print_output, beta0

        func = kwargs.get('function')
        yerr = kwargs.get('yerr')
        length = len(yerr)

        xerr = kwargs.get('xerr')

        if length == len(obs):
            assert 'x_constants' in kwargs
            data = RealData(kwargs.get('x_constants'), obs, sy=yerr)
            fit_type = 2
        elif length == len(obs) // 2:
            data = RealData(obs[:length], obs[length:], sx=xerr, sy=yerr)
            fit_type = 0
        else:
            raise Exception('x and y do not fit together.')

        model = Model(func)

        odr = ODR(data, model, beta0, partol=np.finfo(np.float64).eps)
        odr.set_job(fit_type=fit_type, deriv=1)
        output = odr.run()
        if print_output and not silent:
            print(*output.stopreason)
            print('chisquare/d.o.f.:', output.res_var)
            print_output = 0
        beta0 = output.beta
        return output.beta[kwargs.get('n')]
    res = []
    for n in range(n_parms):
        res.append(pe.derived_observable(do_the_fit, obs, function=func, xerr=xerr, yerr=yerr, x_constants=x_constants, num_grad=True, n=n, **kwargs))
    return res

import autograd.numpy as np
import math
import scipy.optimize
from scipy.odr import ODR, Model, RealData
from scipy.linalg import cholesky
from scipy.stats import norm
import pyerrors as pe
import pytest

np.random.seed(0)


def test_fit_lin():
    x = [0, 2]
    y = [pe.pseudo_Obs(0, 0.1, 'ensemble'),
         pe.pseudo_Obs(2, 0.1, 'ensemble')]

    res = pe.fits.fit_lin(x, y)

    assert res[0] == y[0]
    assert res[1] == (y[1] - y[0]) / (x[1] - x[0])

    x = y = [pe.pseudo_Obs(0, 0.1, 'ensemble'),
         pe.pseudo_Obs(2, 0.1, 'ensemble')]

    res = pe.fits.fit_lin(x, y)

    m = (y[1] - y[0]) / (x[1] - x[0])
    assert res[0] == y[1] - x[1] * m
    assert res[1] == m


def test_least_squares():
    dim = 10 + int(30 * np.random.rand())
    x = np.arange(dim)
    y = 2 * np.exp(-0.06 * x) + np.random.normal(0.0, 0.15, dim)
    yerr = 0.1 + 0.1 * np.random.rand(dim)

    oy = []
    for i, item in enumerate(x):
        oy.append(pe.pseudo_Obs(y[i], yerr[i], str(i)))

    def f(x, a, b):
        return a * np.exp(-b * x)

    popt, pcov = scipy.optimize.curve_fit(f, x, y, sigma=[o.dvalue for o in oy], absolute_sigma=True)

    def func(a, x):
        y = a[0] * np.exp(-a[1] * x)
        return y

    out = pe.least_squares(x, oy, func, expected_chisquare=True, resplot=True, qqplot=True)
    beta = out.fit_parameters

    str(out)
    repr(out)
    len(out)

    for i in range(2):
        beta[i].gamma_method(S=1.0)
        assert math.isclose(beta[i].value, popt[i], abs_tol=1e-5)
        assert math.isclose(pcov[i, i], beta[i].dvalue ** 2, abs_tol=1e-3)
    assert math.isclose(pe.covariance(beta[0], beta[1]), pcov[0, 1], abs_tol=1e-3)

    chi2_pyerrors = np.sum(((f(x, *[o.value for o in beta]) - y) / yerr) ** 2) / (len(x) - 2)
    chi2_scipy = np.sum(((f(x, *popt) - y) / yerr) ** 2) / (len(x) - 2)
    assert math.isclose(chi2_pyerrors, chi2_scipy, abs_tol=1e-10)

    out = pe.least_squares(x, oy, func, const_par=[beta[1]])
    assert((out.fit_parameters[0] - beta[0]).is_zero())
    assert((out.fit_parameters[1] - beta[1]).is_zero())

    oyc = []
    for i, item in enumerate(x):
        oyc.append(pe.cov_Obs(y[i], yerr[i]**2, 'cov' + str(i)))

    outc = pe.least_squares(x, oyc, func)
    betac = outc.fit_parameters

    for i in range(2):
        betac[i].gamma_method(S=1.0)
        assert math.isclose(betac[i].value, popt[i], abs_tol=1e-5)
        assert math.isclose(pcov[i, i], betac[i].dvalue ** 2, abs_tol=1e-3)
    assert math.isclose(pe.covariance(betac[0], betac[1]), pcov[0, 1], abs_tol=1e-3)


def test_correlated_fit():
    num_samples = 400
    N = 10

    x = norm.rvs(size=(N, num_samples))

    r = np.zeros((N, N))
    for i in range(N):
        for j in range(N):
            r[i, j] = np.exp(-0.8 * np.fabs(i - j))

    errl = np.sqrt([3.4, 2.5, 3.6, 2.8, 4.2, 4.7, 4.9, 5.1, 3.2, 4.2])
    for i in range(N):
        for j in range(N):
            r[i, j] *= errl[i] * errl[j]

    c = cholesky(r, lower=True)
    y = np.dot(c, x)
    x = np.arange(N)
    for linear in [True, False]:
        data = []
        for i in range(N):
            if linear:
                data.append(pe.Obs([[i + 1 + o for o in y[i]]], ['ens']))
            else:
                data.append(pe.Obs([[np.exp(-(i + 1)) + np.exp(-(i + 1)) * o for o in y[i]]], ['ens']))

        [o.gamma_method() for o in data]

        if linear:
            def fitf(p, x):
                return p[1] + p[0] * x
        else:
            def fitf(p, x):
                return p[1] * np.exp(-p[0] * x)

        fitp = pe.least_squares(x, data, fitf, expected_chisquare=True)

        fitpc = pe.least_squares(x, data, fitf, correlated_fit=True)
        for i in range(2):
            diff = fitp[i] - fitpc[i]
            diff.gamma_method()
            assert(diff.is_zero_within_error(sigma=5))


def test_total_least_squares():
    dim = 10 + int(30 * np.random.rand())
    x = np.arange(dim) + np.random.normal(0.0, 0.15, dim)
    xerr = 0.1 + 0.1 * np.random.rand(dim)
    y = 2 * np.exp(-0.06 * x) + np.random.normal(0.0, 0.15, dim)
    yerr = 0.1 + 0.1 * np.random.rand(dim)

    ox = []
    for i, item in enumerate(x):
        ox.append(pe.pseudo_Obs(x[i], xerr[i], str(i)))

    oy = []
    for i, item in enumerate(x):
        oy.append(pe.pseudo_Obs(y[i], yerr[i], str(i)))

    def f(x, a, b):
        return a * np.exp(-b * x)

    def func(a, x):
        y = a[0] * np.exp(-a[1] * x)
        return y

    data = RealData([o.value for o in ox], [o.value for o in oy], sx=[o.dvalue for o in ox], sy=[o.dvalue for o in oy])
    model = Model(func)
    odr = ODR(data, model, [0, 0], partol=np.finfo(np.float64).eps)
    odr.set_job(fit_type=0, deriv=1)
    output = odr.run()

    out = pe.total_least_squares(ox, oy, func, expected_chisquare=True)
    beta = out.fit_parameters

    str(out)
    repr(out)
    len(out)

    for i in range(2):
        beta[i].gamma_method(S=1.0)
        assert math.isclose(beta[i].value, output.beta[i], rel_tol=1e-5)
        assert math.isclose(output.cov_beta[i, i], beta[i].dvalue ** 2, rel_tol=2.5e-1), str(output.cov_beta[i, i]) + ' ' + str(beta[i].dvalue ** 2)
    assert math.isclose(pe.covariance(beta[0], beta[1]), output.cov_beta[0, 1], rel_tol=2.5e-1)

    out = pe.total_least_squares(ox, oy, func, const_par=[beta[1]])

    diff = out.fit_parameters[0] - beta[0]
    assert(diff / beta[0] < 1e-3 * beta[0].dvalue)
    assert((out.fit_parameters[1] - beta[1]).is_zero())

    oxc = []
    for i, item in enumerate(x):
        oxc.append(pe.cov_Obs(x[i], xerr[i]**2, 'covx' + str(i)))

    oyc = []
    for i, item in enumerate(x):
        oyc.append(pe.cov_Obs(y[i], yerr[i]**2, 'covy' + str(i)))

    outc = pe.total_least_squares(oxc, oyc, func)
    betac = outc.fit_parameters

    for i in range(2):
        betac[i].gamma_method(S=1.0)
        assert math.isclose(betac[i].value, output.beta[i], rel_tol=1e-3)
        assert math.isclose(output.cov_beta[i, i], betac[i].dvalue ** 2, rel_tol=2.5e-1), str(output.cov_beta[i, i]) + ' ' + str(betac[i].dvalue ** 2)
    assert math.isclose(pe.covariance(betac[0], betac[1]), output.cov_beta[0, 1], rel_tol=2.5e-1)

    outc = pe.total_least_squares(oxc, oyc, func, const_par=[betac[1]])

    diffc = outc.fit_parameters[0] - betac[0]
    assert(diffc / betac[0] < 1e-3 * betac[0].dvalue)
    assert((outc.fit_parameters[1] - betac[1]).is_zero())

    outc = pe.total_least_squares(oxc, oy, func)
    betac = outc.fit_parameters

    for i in range(2):
        betac[i].gamma_method(S=1.0)
        assert math.isclose(betac[i].value, output.beta[i], rel_tol=1e-3)
        assert math.isclose(output.cov_beta[i, i], betac[i].dvalue ** 2, rel_tol=2.5e-1), str(output.cov_beta[i, i]) + ' ' + str(betac[i].dvalue ** 2)
    assert math.isclose(pe.covariance(betac[0], betac[1]), output.cov_beta[0, 1], rel_tol=2.5e-1)

    outc = pe.total_least_squares(oxc, oy, func, const_par=[betac[1]])

    diffc = outc.fit_parameters[0] - betac[0]
    assert(diffc / betac[0] < 1e-3 * betac[0].dvalue)
    assert((outc.fit_parameters[1] - betac[1]).is_zero())


def test_odr_derivatives():
    x = []
    y = []
    x_err = 0.01
    y_err = 0.01

    for n in np.arange(1, 9, 2):
        loc_xvalue = n + np.random.normal(0.0, x_err)
        x.append(pe.pseudo_Obs(loc_xvalue, x_err, str(n)))
        y.append(pe.pseudo_Obs((lambda x: x ** 2 - 1)(loc_xvalue) +
                               np.random.normal(0.0, y_err), y_err, str(n)))

        def func(a, x):
            return a[0] + a[1] * x ** 2
    out = pe.total_least_squares(x, y, func)
    fit1 = out.fit_parameters

    tfit = fit_general(x, y, func, base_step=0.1, step_ratio=1.1, num_steps=20)
    assert np.abs(np.max(np.array(list(fit1[1].deltas.values()))
                  - np.array(list(tfit[1].deltas.values())))) < 10e-8


def test_r_value_persistence():
    def f(a, x):
        return a[0] + a[1] * x

    a = pe.pseudo_Obs(1.1, .1, 'a')
    assert np.isclose(a.value, a.r_values['a'])

    a_2 = a ** 2
    assert np.isclose(a_2.value, a_2.r_values['a'])

    b = pe.pseudo_Obs(2.1, .2, 'b')

    y = [a, b]
    [o.gamma_method() for o in y]

    fitp = pe.fits.least_squares([1, 2], y, f)

    assert np.isclose(fitp[0].value, fitp[0].r_values['a'])
    assert np.isclose(fitp[0].value, fitp[0].r_values['b'])
    assert np.isclose(fitp[1].value, fitp[1].r_values['a'])
    assert np.isclose(fitp[1].value, fitp[1].r_values['b'])

    fitp = pe.fits.total_least_squares(y, y, f)

    assert np.isclose(fitp[0].value, fitp[0].r_values['a'])
    assert np.isclose(fitp[0].value, fitp[0].r_values['b'])
    assert np.isclose(fitp[1].value, fitp[1].r_values['a'])
    assert np.isclose(fitp[1].value, fitp[1].r_values['b'])

    fitp = pe.fits.least_squares([1, 2], y, f, priors=y)

    assert np.isclose(fitp[0].value, fitp[0].r_values['a'])
    assert np.isclose(fitp[0].value, fitp[0].r_values['b'])
    assert np.isclose(fitp[1].value, fitp[1].r_values['a'])
    assert np.isclose(fitp[1].value, fitp[1].r_values['b'])


def test_prior_fit():
    def f(a, x):
        return a[0] + a[1] * x

    a = pe.pseudo_Obs(0.0, 0.1, 'a')
    b = pe.pseudo_Obs(1.0, 0.2, 'a')

    y = [a, b]
    with pytest.raises(Exception):
        fitp = pe.fits.least_squares([0, 1], 1 * np.array(y), f, priors=['0.0(8)', '1.0(8)'])

    [o.gamma_method() for o in y]

    fitp = pe.fits.least_squares([0, 1], y, f, priors=['0.0(8)', '1.0(8)'])
    fitp = pe.fits.least_squares([0, 1], y, f, priors=y, resplot=True, qqplot=True)


def test_error_band():
    def f(a, x):
        return a[0] + a[1] * x

    a = pe.pseudo_Obs(0.0, 0.1, 'a')
    b = pe.pseudo_Obs(1.0, 0.2, 'a')

    x = [0, 1]
    y = [a, b]

    fitp = pe.fits.least_squares(x, y, f)

    with pytest.raises(Exception):
        pe.fits.error_band(x, f, fitp.fit_parameters)
    fitp.gamma_method()
    pe.fits.error_band(x, f, fitp.fit_parameters)


def fit_general(x, y, func, silent=False, **kwargs):
    """Performs a non-linear fit to y = func(x) and returns a list of Obs corresponding to the fit parameters.

    Plausibility of the results should be checked. To control the numerical differentiation
    the kwargs of numdifftools.step_generators.MaxStepGenerator can be used.

    func has to be of the form

    def func(a, x):
        y = a[0] + a[1] * x + a[2] * np.sinh(x)
        return y

    y has to be a list of Obs, the dvalues of the Obs are used as yerror for the fit.
    x can either be a list of floats in which case no xerror is assumed, or
    a list of Obs, where the dvalues of the Obs are used as xerror for the fit.

    Keyword arguments
    -----------------
    silent -- If true all output to the console is omitted (default False).
    initial_guess -- can provide an initial guess for the input parameters. Relevant for non-linear fits
                     with many parameters.
    """

    if not callable(func):
        raise TypeError('func has to be a function.')

    for i in range(10):
        try:
            func(np.arange(i), 0)
        except:
            pass
        else:
            break
    n_parms = i
    if not silent:
        print('Fit with', n_parms, 'parameters')

    global print_output, beta0
    print_output = 1
    if 'initial_guess' in kwargs:
        beta0 = kwargs.get('initial_guess')
        if len(beta0) != n_parms:
            raise Exception('Initial guess does not have the correct length.')
    else:
        beta0 = np.arange(n_parms)

    if len(x) != len(y):
        raise Exception('x and y have to have the same length')

    if all(isinstance(n, pe.Obs) for n in x):
        obs = x + y
        x_constants = None
        xerr = [o.dvalue for o in x]
        yerr = [o.dvalue for o in y]
    elif all(isinstance(n, float) or isinstance(n, int) for n in x) or isinstance(x, np.ndarray):
        obs = y
        x_constants = x
        xerr = None
        yerr = [o.dvalue for o in y]
    else:
        raise Exception('Unsupported types for x')

    def do_the_fit(obs, **kwargs):

        global print_output, beta0

        func = kwargs.get('function')
        yerr = kwargs.get('yerr')
        length = len(yerr)

        xerr = kwargs.get('xerr')

        if length == len(obs):
            assert 'x_constants' in kwargs
            data = RealData(kwargs.get('x_constants'), obs, sy=yerr)
            fit_type = 2
        elif length == len(obs) // 2:
            data = RealData(obs[:length], obs[length:], sx=xerr, sy=yerr)
            fit_type = 0
        else:
            raise Exception('x and y do not fit together.')

        model = Model(func)

        odr = ODR(data, model, beta0, partol=np.finfo(np.float64).eps)
        odr.set_job(fit_type=fit_type, deriv=1)
        output = odr.run()
        if print_output and not silent:
            print(*output.stopreason)
            print('chisquare/d.o.f.:', output.res_var)
            print_output = 0
        beta0 = output.beta
        return output.beta[kwargs.get('n')]
    res = []
    for n in range(n_parms):
        res.append(pe.derived_observable(do_the_fit, obs, function=func, xerr=xerr, yerr=yerr, x_constants=x_constants, num_grad=True, n=n, **kwargs))
    return res

Performs a non-linear fit to y = func(x) and returns a list of Obs corresponding to the fit parameters.      Plausibility of the results should be checked. To control the numerical differentiation     the kwargs of numdifftools.step_generators.MaxStepGenerator can be used.      func has to be of the form      def func(a, x):         y = a[0] + a[1] * x + a[2] * np.sinh(x)         return y      y has to be a list of Obs, the dvalues of the Obs are used as yerror for the fit.     x can either be a list of floats in which case no xerror is assumed, or     a list of Obs, where the dvalues of the Obs are used as xerror for the fit.      Keyword arguments     -----------------     silent -- If true all output to the console is omitted (default False).     initial_guess -- can provide an initial guess for the input parameters. Relevant for non-linear fits                      with many parameters.