r"""Minimise Augmented Lagrangian with respect to
        :math:`\mathbf{y}`.
770552
def ystep(self):
        
        """

        self.Y = self.Pcn(self.AX + self.U)
424955
def optimize(self, angles0, target):
        """"""
        def new_objective(angles):
            return self.f(angles, target)

        return scipy.optimize.minimize(
            new_objective,
            angles0,
            **self.optimizer_opt).x
675246
def lessgreater(x, y):
    
    x = BigFloat._implicit_convert(x)
    y = BigFloat._implicit_convert(y)
    return mpfr.mpfr_lessgreater_p(x, y)
1024153
def magnification(self, x, y, kwargs, diff=diff):
        
        f_xx, f_xy, f_yx, f_yy = self.hessian(x, y, kwargs, diff=diff)
        det_A = (1 - f_xx) * (1 - f_yy) - f_xy*f_yx
        return 1/det_A
360705
def _minimize_constraints_fun_summation(x):
    '''
    
    '''
    summation = sum([x[i] for i in CONSTRAINT_PARAMS_IDX])
    return CONSTRAINT_UPPERBOUND >= summation >= CONSTRAINT_LOWERBOUND
28085
def xstep(self):
        
        """

        self.YU[:] = self.Y - self.U
        self.block_sep0(self.YU)[:] += self.S
        YUf = sl.rfftn(self.YU, None, self.cri.axisN)
        b = sl.inner(np.conj(self.Zf), self.block_sep0(YUf),
                     axis=self.cri.axisK) + self.block_sep1(YUf)

        self.Xf[:] = sl.solvemdbi_ism(self.Zf, 1.0, b, self.cri.axisM,
                                      self.cri.axisK)
        self.X = sl.irfftn(self.Xf, self.cri.Nv, self.cri.axisN)
        self.xstep_check(b)
151891
def partial_derivative_scalar(self, U, V, y=0):
        """"""

        self.check_fit()

        X = np.column_stack((U, V))
        return self.partial_derivative(X, y)
1142139
def hessian_tensor_product(fun, argnum=0):
    """"""
    fun_grad = grad(fun, argnum)
    def vector_dot_grad(*args, **kwargs):
        args, vector = args[:-1], args[-1]
        return np.tensordot(fun_grad(*args, **kwargs), vector, np.ndim(vector))
    return grad(vector_dot_grad, argnum)
657239
def xstep(self):
        
        """

        self.YU[:] = self.Y - self.U
        self.block_sep0(self.YU)[:] += self.S
        Zf = sl.rfftn(self.YU, None, self.cri.axisN)
        Z0f = self.block_sep0(Zf)
        Z1f = self.block_sep1(Zf)

        DZ0f = np.conj(self.Df) * Z0f
        DZ0fBQ = sl.dot(self.B.dot(self.Q).T, DZ0f, axis=self.cri.axisC)
        Z1fQ = sl.dot(self.Q.T, Z1f, axis=self.cri.axisC)
        b = DZ0fBQ + Z1fQ

        Xh = sl.solvedbd_sm(self.gDf, (self.mu / self.rho) * self.GHGf + 1.0,
                            b, self.c, axis=self.cri.axisM)
        self.Xf[:] = sl.dot(self.Q, Xh, axis=self.cri.axisC)
        self.X = sl.irfftn(self.Xf, self.cri.Nv, self.cri.axisN)

        if self.opt['LinSolveCheck']:
            DDXf = np.conj(self.Df) *  sl.inner(self.Df, self.Xf,
                                                axis=self.cri.axisM)
            DDXfBB = sl.dot(self.B.T.dot(self.B), DDXf, axis=self.cri.axisC)
            ax = self.rho * (DDXfBB + self.Xf) + \
                 self.mu * self.GHGf * self.Xf
            b = self.rho * (sl.dot(self.B.T, DZ0f, axis=self.cri.axisC)
                            + Z1f)
            self.xrrs = sl.rrs(ax, b)
        else:
            self.xrrs = None
1267211
def xstep(self):
        
        """

        b = self.AHSf + self.rho*np.sum(
            np.conj(self.Gf)*sl.rfftn(self.Y-self.U, axes=self.axes),
            axis=self.Y.ndim-1)
        self.Xf = b / (self.AHAf + self.rho*self.GHGf)
        self.X = sl.irfftn(self.Xf, self.axsz, axes=self.axes)

        if self.opt['LinSolveCheck']:
            ax = (self.AHAf + self.rho*self.GHGf)*self.Xf
            self.xrrs = sl.rrs(ax, b)
        else:
            self.xrrs = None
1140499
def unit_vector(x):
    """"""
    y = np.array(x, dtype='float')
    return y/norm(y)
1244593
def _optimize(self, period, tmpid, use_gradient=True):
        """"""
        theta_0 = [self.y.min(), self.y.max() - self.y.min(), 0]
        result = minimize(self._chi2, theta_0, jac=bool(use_gradient),
                          bounds=[(None, None), (0, None), (None, None)],
                          args=(period, tmpid, use_gradient))
        return result.x
1327673
def ystep(self):
        
        """

        self.Y = np.asarray(sp.prox_l2(
            self.AX + self.U, (self.lmbda/self.rho)*self.Wtvna,
            axis=self.saxes), dtype=self.dtype)
316509
def ystep(self):
        
        """

        AXU = self.AX + self.U
        Y0 = (self.rho*(self.block_sep0(AXU) - self.S)) / \
             (self.W**2 + self.rho)
        Y1 = sp.prox_l1(self.block_sep1(AXU),
                        (self.lmbda / self.rho) * self.wl1)
        self.Y = self.block_cat(Y0, Y1)

        super(ConvBPDNMaskDcpl, self).ystep()
768058
def fgrad_y(self, y, return_precalc=False):
        
        d = self.d
        mpsi = self.psi

        # vectorized version
        S = (mpsi[:,1] * (y[:,:,None] + mpsi[:,2])).T
        R = np.tanh(S)
        D = 1 - (R ** 2)

        GRAD = (d + (mpsi[:,0:1][:,:,None] * mpsi[:,1:2][:,:,None] * D).sum(axis=0)).T

        if return_precalc:
            return GRAD, S, R, D

        return GRAD
226527
def ystep(self):
        """

        self.Y = np.asarray(sp.prox_l1l2(
            self.AX + self.U, (self.lmbda / self.rho) * self.wl1,
            self.mu / self.rho, axis=-1), dtype=self.dtype)
        GenericBPDN.ystep(self)
845291
def optimize(self, x0, target):
        """"""
        x = x0
        for _ in range(self.maxiter):
            delta = np.linalg.solve(self.h(x, target), -self.g(x, target))
            x = x + delta
            if np.linalg.norm(delta) < self.tol:
                break
        return x