Python optimize.bisect方法代碼示例

# 需要導入模塊: from scipy import optimize [as 別名]
# 或者: from scipy.optimize import bisect [as 別名]
def fermi_energy(ee, nelec, telec):
  """ Determine Fermi energy """
  from pyscf.nao.m_fermi_dirac import fermi_dirac_occupations
  
  d = len(ee.shape)
  if d==1 : # assuming state2energy
    fe = bisect(func1, ee.min(), ee.max(), args=(ee, nelec, telec, 2.0))
  elif d==2: # assuming spin_state2energy
    nspin = ee.shape[-2]
    assert nspin==1 or nspin==2
    fe = bisect(func1, ee.min(), ee.max(), args=(ee, nelec, telec, (3.0-nspin)))
  elif d==3: # assuming kpoint_spin_state2energy
    nspin = ee.shape[-2]
    nkpts = ee.shape[0]
    assert nspin==1 or nspin==2
    fe = bisect(func1, ee.min(), ee.max(), args=(ee, nelec, telec, (3.0-nspin)/nkpts))
  else: # how to interpret this ?
    raise RuntimeError('!impl?')

  return fe 

# 需要導入模塊: from scipy import optimize [as 別名]
# 或者: from scipy.optimize import bisect [as 別名]
def solve(self):
        try:
            lambda_star = optimize.bisect(
                self._sum_to_one_constraint,
                0,
                BISECTION_UPPER_BOUND,
                maxiter=MAXITER_BISECTION,
            )
            self.lambda_star = lambda_star
            self._x = self._lambda_solve(lambda_star)
        except Exception as e:
            if e.args[0] == "f(a) and f(b) must have different signs":
                logging.exception(
                    "Bisection failed: "
                    + str(e)
                    + ". If you are using expected returns the parameter 'c' need to be correctly scaled (see remark 1 in the paper). Otherwise please check the constraints or increase the bisection upper bound."
                )
            else:
                logging.exception("Problem not solved: " + str(e)) 

# 需要導入模塊: from scipy import optimize [as 別名]
# 或者: from scipy.optimize import bisect [as 別名]
def _dtdv_cutoff_velocity(m1, m2, chi1, chi2):
    _, dtdv2, dtdv3, dtdv4, dtdv5, dtdv6, dtdv6log, dtdv7 = _dtdv_coeffs(m1, m2, chi1, chi2)

    def dtdv_func(v):
        x = dtdv7
        x = v * x + dtdv6 + dtdv6log * 3. * numpy.log(v)
        x = v * x + dtdv5
        x = v * x + dtdv4
        x = v * x + dtdv3
        x = v * x + dtdv2
        return v * v * x + 1.

    if dtdv_func(1.0) < 0.:
        return bisect(dtdv_func, 0.05, 1.0)
    else:
        return 1.0 

# 需要導入模塊: from scipy import optimize [as 別名]
# 或者: from scipy.optimize import bisect [as 別名]
def volume_to_level(self, node, waterlevel):
        if node.current_vol > 0:
            maxelev = node.parent.elev
            if node.elev:
                minelev = node.elev
            else:
                # TODO: This bound could be a lot better
                minelev = np.nanmin(self.dem)
            target_vol = node.current_vol
            elev = optimize.bisect(self.compute_vol, minelev, maxelev,
                                   args=(node, target_vol))
            if node.name:
                mask = self.ws[node.level] == node.name
            else:
                leaves = []
                self.enumerate_leaves(node, level=node.level, stack=leaves)
                mask = np.isin(self.ws[node.level], leaves)
                boundary = list(chain.from_iterable([self.b[node.level].setdefault(pair, [])
                                                     for pair in combinations(leaves, 2)]))
                mask.flat[boundary] = True
            mask = np.flatnonzero(mask & (self.dem < elev))
            waterlevel.flat[mask] = elev
        else:
            if node.l:
                self.volume_to_level(node.l, waterlevel)
            if node.r:
                self.volume_to_level(node.r, waterlevel) 

# 需要導入模塊: from scipy import optimize [as 別名]
# 或者: from scipy.optimize import bisect [as 別名]
def _setup(self):
        super(MinValueEntropySearch, self)._setup()

        # Apply Gumbel sampling
        m = self.models[0]
        valid = self.feasible_data_index()

        # Work with feasible data
        X = self.data[0][valid, :]
        N = np.shape(X)[0]
        Xrand = RandomDesign(self.gridsize, self._domain).generate()
        fmean, fvar = m.predict_f(np.vstack((X, Xrand)))
        idx = np.argmin(fmean[:N])
        right = fmean[idx].flatten()# + 2*np.sqrt(fvar[idx]).flatten()
        left = right
        probf = lambda x: np.exp(np.sum(norm.logcdf(-(x - fmean) / np.sqrt(fvar)), axis=0))

        i = 0
        while probf(left) < 0.75:
            left = 2. ** i * np.min(fmean - 5. * np.sqrt(fvar)) + (1. - 2. ** i) * right
            i += 1

        # Binary search for 3 percentiles
        q1, med, q2 = map(lambda val: bisect(lambda x: probf(x) - val, left, right, maxiter=10000, xtol=0.01),
                          [0.25, 0.5, 0.75])
        beta = (q1 - q2) / (np.log(np.log(4. / 3.)) - np.log(np.log(4.)))
        alpha = med + beta * np.log(np.log(2.))

        # obtain samples from y*
        mins = -np.log(-np.log(np.random.rand(self.num_samples).astype(np_float_type))) * beta + alpha
        self.samples.set_data(mins) 

# 需要導入模塊: from scipy import optimize [as 別名]
# 或者: from scipy.optimize import bisect [as 別名]
def inverse_rain_attenuation(
            self, lat, lon, d, f, el, Ap, tau=45, R001=None):
        """ Implementation of 'inverse_rain_attenuation' method for
        recommendation ITU-P R.530-16. See documentation for function
        'ITUR530.inverse_rain_attenuation'
        """
        # Step 1: Obtain the rain rate R0.01 exceeded for 0.01% of the time
        # (with an integration time of 1 min).
        if R001 is None:
            R001 = rainfall_rate(lat, lon, 0.01).value

        # Step 2: Compute the specific attenuation, gammar (dB/km) for the
        # frequency, polarization and rain rate of interest using
        # Recommendation ITU-R P.838
        gammar = rain_specific_attenuation(R001, f, el, tau).value
        _, alpha = rain_specific_attenuation_coefficients(f, el, tau).value

        # Step 3: Compute the effective path length, deff, of the link by
        # multiplying the actual path length d by a distance factor r
        r = 1 / (0.477 * d ** 0.633 * R001 ** (0.073 * alpha) *
                 f**(0.123) - 10.579 * (1 - np.exp(-0.024 * d)))
        deff = np.minimum(r, 2.5) * d

        # Step 4: An estimate of the path attenuation exceeded for 0.01% of
        # the time is given by:
        A001 = gammar * deff

        # Step 5: The attenuation exceeded for other percentages of time p in
        # the range 0.001% to 1% may be deduced from the following power law
        C0 = np.where(f >= 10, 0.12 * 0.4 * (np.log10(f / 10)**0.8), 0.12)
        C1 = (0.07**C0) * (0.12**(1 - C0))
        C2 = 0.855 * C0 + 0.546 * (1 - C0)
        C3 = 0.139 * C0 + 0.043 * (1 - C0)

        def func_bisect(p):
            return A001 * C1 * p ** (- (C2 + C3 * np.log10(p))) - Ap

        return bisect(func_bisect, 0, 100) 

# 需要導入模塊: from scipy import optimize [as 別名]
# 或者: from scipy.optimize import bisect [as 別名]
def update_parameters(self):
        # apply gumbel sampling to obtain samples from y*
        # we approximate Pr(y*^hat<y) by Gumbel(alpha,beta)
        # generate grid
        N = self.model.model.X.shape[0]

        random_design = RandomDesign(self.space)
        grid = random_design.get_samples(self.grid_size)
        fmean, fvar = self.model.model.predict(np.vstack([self.model.model.X, grid]), include_likelihood=False)
        fsd = np.sqrt(fvar)
        idx = np.argmin(fmean[:N])

        # scaling so that gumbel scale is proportional to IQ range of cdf Pr(y*<z)
        # find quantiles Pr(y*<y1)=r1 and Pr(y*<y2)=r2
        right = fmean[idx].flatten()
        left = right
        probf = lambda x: np.exp(np.sum(norm.logcdf(-(x - fmean) / fsd), axis=0))
        i = 0
        while probf(left) < 0.75:
            left = 2. ** i * np.min(fmean - 5. * fsd) + (1. - 2. ** i) * right
            i += 1
        i = 0
        while probf(right) > 0.25:
            right = -2. ** i * np.min(fmean - 5. * fsd) + (1. + 2. ** i) * fmean[idx].flatten()
            i += 1

        # Binary search for 3 percentiles
        q1, med, q2 = map(lambda val: bisect(lambda x: probf(x) - val, left, right, maxiter=10000, xtol=0.00001),
                            [0.25, 0.5, 0.75])

        # solve for gumbel params
        beta = (q1 - q2) / (np.log(np.log(4. / 3.)) - np.log(np.log(4.)))
        alpha = med + beta * np.log(np.log(2.))

        # sample K length vector from unif([0,1])
        # return K Y* samples
        self.mins = -np.log(-np.log(np.random.rand(self.num_samples))) * beta + alpha 

# 需要導入模塊: from scipy import optimize [as 別名]
# 或者: from scipy.optimize import bisect [as 別名]
def solve_for_load_cutoff(load, energy_budget, pmin=0, pmax=None):
    lowest = min(load) - pmax - 1
    highest = max(load) + pmax + 1
    if lowest == highest:
        return lowest
    else:
        load_cutoff = optimize.bisect(residual_energy, lowest, highest, args=(load, energy_budget, pmin, pmax))
        return load_cutoff 

# 需要導入模塊: from scipy import optimize [as 別名]
# 或者: from scipy.optimize import bisect [as 別名]
def imply_volatility(self, premium):
        def objective_func(vol_guess):
            self.volatility = vol_guess
            val = self.valuation()
            return val - premium

        try:
            return optimize.bisect(objective_func, a=0.001, b=0.999, xtol=0.00005)
        except ValueError:
            raise ValueError("Unable to converge to implied volatility") 

# 需要導入模塊: from scipy import optimize [as 別名]
# 或者: from scipy.optimize import bisect [as 別名]
def tune_stud_radius(desired_force,
                     min_radius=0.0045,
                     max_radius=0.005,
                     desired_places=6,
                     side='closest',
                     **duplo_kwargs):
  """Find a stud size that gives the desired separation force."""

  @_KeepBracketingSolutions
  def func(radius):
    radius = round(radius, desired_places)  # Round radius for aesthetics (!)
    return (get_separation_force_for_radius(radius=radius, **duplo_kwargs)
            - desired_force)

  # Ensure that the min and max radii bracket the solution.
  while func(min_radius) > 0:
    min_radius = max(1e-3, min_radius - (max_radius - min_radius))
  while func(max_radius) < 0:
    max_radius += (max_radius - min_radius)

  tolerance = 10**-(desired_places)

  # Use bisection to refine the bounds on the optimal radius. Note: this assumes
  # that separation force is monotonic w.r.t. stud radius, but this isn't
  # exactly true in all cases.
  optimize.bisect(func, a=min_radius, b=max_radius, xtol=tolerance, disp=True)

  if side == 'below':
    solution = func.below
  elif side == 'above':
    solution = func.above
  else:
    solution = func.closest

  radius = round(solution.x, desired_places)
  force = get_separation_force_for_radius(radius, **duplo_kwargs)

  return radius, force 

# 需要導入模塊: from scipy import optimize [as 別名]
# 或者: from scipy.optimize import bisect [as 別名]
def meco_velocity(m1, m2, chi1, chi2):
    """
    Returns the velocity of the minimum energy cutoff for 3.5pN (2.5pN spin)

    Parameters
    ----------
    m1 : float
        First component mass in solar masses
    m2 : float
        Second component mass in solar masses
    chi1 : float
        First component dimensionless spin S_1/m_1^2 projected onto L
    chi2 : float
        Second component dimensionless spin S_2/m_2^2 projected onto L

    Returns
    -------
    v : float
        Velocity (dimensionless)
    """
    _, energy2, energy3, energy4, energy5, energy6 = \
        _energy_coeffs(m1, m2, chi1, chi2)
    def eprime(v):
        return 2. + v * v * (4.*energy2 + v * (5.*energy3 \
                + v * (6.*energy4
                + v * (7.*energy5 + 8.*energy6 * v))))
    return bisect(eprime, 0.05, 1.0) 

# 需要導入模塊: from scipy import optimize [as 別名]
# 或者: from scipy.optimize import bisect [as 別名]
def meco2(m1, m2, s1z=0, s2z=0, phase_order=-1, spin_order=-1):
    ecof = energy_coefficients(m1, m2, s1z, s2z, phase_order, spin_order)

    def test(v):
        de = 0
        for i in numpy.arange(0, len(ecof), 1):
            de += v**(i+1.0)* ecof[i] * (i + 2)

        return de

    return bisect(test, 0.001, 1.0) 

# 需要導入模塊: from scipy import optimize [as 別名]
# 或者: from scipy.optimize import bisect [as 別名]
def find_steady_state(self, a, b, method='brentq', **kwargs):
        """
        Compute the equilibrium value of capital stock (per unit effective
        labor).

        Parameters
        ----------
        a : float
            One end of the bracketing interval [a,b].
        b : float
            The other end of the bracketing interval [a,b]
        method : str (default=`brentq`)
            Method to use when computing the steady state. Supported methods
            are `bisect`, `brenth`, `brentq`, `ridder`. See `scipy.optimize`
            for more details (including references).
        kwargs : optional
            Additional keyword arguments. Keyword arguments are method specific
            see `scipy.optimize` for details.

        Returns
        -------
        x0 : float
            Zero of `f` between `a` and `b`.
        r : RootResults (present if ``full_output = True``)
            Object containing information about the convergence. In particular,
            ``r.converged`` is True if the routine converged.

        """
        if method == 'bisect':
            result = optimize.bisect(self.evaluate_k_dot, a, b, **kwargs)
        elif method == 'brenth':
            result = optimize.brenth(self.evaluate_k_dot, a, b, **kwargs)
        elif method == 'brentq':
            result = optimize.brentq(self.evaluate_k_dot, a, b, **kwargs)
        elif method == 'ridder':
            result = optimize.ridder(self.evaluate_k_dot, a, b, **kwargs)
        else:
            mesg = ("Method must be one of : 'bisect', 'brenth', 'brentq', " +
                    "or 'ridder'.")
            raise ValueError(mesg)

        return result 

# 需要導入模塊: from scipy import optimize [as 別名]
# 或者: from scipy.optimize import bisect [as 別名]
def rainfall_rate(self, lat_d, lon_d, p):
        """
        """
        if p == 0.01:
            return self.R001(lat_d, lon_d)

        lat_f = lat_d.flatten()
        lon_f = lon_d.flatten()

        Nii = np.array([[31, 28.25, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31]])

        # Step 2: For each month, determine the monthly mean surface
        # temperature
        Tii = surface_month_mean_temperature(lat_f, lon_f, self.months).value.T

        # Step 3: For each month, determine the monthly mean total rainfall
        MTii = np.array([self.Mt(lat_f, lon_f, m) for m in self.months]).T

        # Step 4: For each month, determine the monthly mean total rainfall
        tii = Tii - 273.15

        # Step 5: For each month number, calculate rii
        rii = np.where(tii >= 0, 0.5874 * np.exp(0.0883 * tii), 0.5874)

        # Step 6a For each month number, calculate the probability of rain:
        P0ii = 100 * MTii / (24 * Nii * rii)

        # Step 7b:
        rii = np.where(P0ii > 70, 100/70. * MTii / (24 * Nii), rii)
        P0ii = np.where(P0ii > 70, 70, P0ii)

        # Step 7: Calculate the annual probability of rain, P0anual
        P0anual = np.sum(Nii * P0ii, axis=-1) / 365.25

        # Step 8: Compute the rainfall rate exceeded for p
        def _ret_fcn(P0):
            if p > P0:
                return 0
            else:
                # Use a bisection method to determine
                def f_Rp(Rref):
                    P_r_ge_Rii = P0ii * stats.norm.sf(
                            (np.log(Rref) + 0.7938 - np.log(rii)) / 1.26)
                    P_r_ge_R = np.sum(Nii * P_r_ge_Rii) / 365.25
                    return 100 * (P_r_ge_R / p - 1)

                return bisect(f_Rp, 1e-10, 1000, xtol=1e-5)

        fcn = np.vectorize(_ret_fcn)
        return fcn(P0anual).reshape(lat_d.shape) 

# 需要導入模塊: from scipy import optimize [as 別名]
# 或者: from scipy.optimize import bisect [as 別名]
def find_steady_state(self, a, b, method='brentq', **kwargs):
        """
        Compute the equilibrium value of capital stock (per unit
        effective labor).

        Parameters
        ----------
        a : float
            One end of the bracketing interval [a,b].
        b : float
            The other end of the bracketing interval [a,b]
        method : str (default=`brentq`)
            Method to use when computing the steady state. Supported
            methods are `bisect`, `brenth`, `brentq`, `ridder`. See
            `scipy.optimize` for more details (including references).
        kwargs : optional
            Additional keyword arguments. Keyword arguments are method
            specific see `scipy.optimize` for details.

        Returns
        -------
        x0 : float
            Zero of `f` between `a` and `b`.
        r : RootResults (present if ``full_output = True``)
            Object containing information about the convergence. In
            particular, ``r.converged`` is True if the routine
            converged.

        """
        if method == 'bisect':
            result = optimize.bisect(self.evaluate_k_dot, a, b, **kwargs)
        elif method == 'brenth':
            result = optimize.brenth(self.evaluate_k_dot, a, b, **kwargs)
        elif method == 'brentq':
            result = optimize.brentq(self.evaluate_k_dot, a, b, **kwargs)
        elif method == 'ridder':
            result = optimize.ridder(self.evaluate_k_dot, a, b, **kwargs)
        else:
            mesg = ("Method must be one of : 'bisect', 'brenth', 'brentq', " +
                    "or 'ridder'.")
            raise ValueError(mesg)

        return result