The simplex optimizer does not require gradients.
505577
def opt(self, x_init, f_fp=None, f=None, fp=None):
        

        statuses = ['Converged', 'Maximum number of function evaluations made', 'Maximum number of iterations reached']

        opt_dict = {}
        if self.xtol is not None:
            opt_dict['xtol'] = self.xtol
        if self.ftol is not None:
            opt_dict['ftol'] = self.ftol
        if self.gtol is not None:
            print("WARNING: simplex doesn't have an gtol arg, so I'm going to ignore it")

        opt_result = optimize.fmin(f, x_init, (), disp=self.messages,
                   maxfun=self.max_f_eval, full_output=True, **opt_dict)

        self.x_opt = opt_result[0]
        self.f_opt = opt_result[1]
        self.funct_eval = opt_result[3]
        self.status = statuses[opt_result[4]]
        self.trace = None
697645
function constrainedMDSGradient(x, fxprime, distances, constraints) {
        var loss = 0, i;
        for (i = 0; i < fxprime.length; ++i) {
            fxprime[i] = 0;
        }

        for (i = 0; i < distances.length; ++i) {
            var xi = x[2 * i], yi = x[2 * i + 1];
            for (var j = i + 1; j < distances.length; ++j) {
                var xj = x[2 * j], yj = x[2 * j + 1],
                    dij = distances[i][j],
                    constraint = constraints[i][j];

                var squaredDistance = (xj - xi) * (xj - xi) + (yj - yi) * (yj - yi),
                    distance$$1 = Math.sqrt(squaredDistance),
                    delta = squaredDistance - dij * dij;

                if (((constraint > 0) && (distance$$1 <= dij)) ||
                    ((constraint < 0) && (distance$$1 >= dij))) {
                    continue;
                }

                loss += 2 * delta * delta;

                fxprime[2*i]     += 4 * delta * (xi - xj);
                fxprime[2*i + 1] += 4 * delta * (yi - yj);

                fxprime[2*j]     += 4 * delta * (xj - xi);
                fxprime[2*j + 1] += 4 * delta * (yj - yi);
            }
        }
        return loss;
    }
17299
def spm(x, model, y=None, n_samples=None, dx_min=-0.1,
        dx_max=0.1, n_dxs=5, dy_min=-0.1, dy_max=0.1, n_dys=5,
        angle_min=-30, angle_max=30, n_angles=31, black_border_size=0):
  
  if y is None:
    preds = model.get_probs(x)
    # Using model predictions as ground truth to avoid label leaking
    preds_max = reduce_max(preds, 1, keepdims=True)
    y = tf.to_float(tf.equal(preds, preds_max))
    y = tf.stop_gradient(y)
    del preds
  y = y / reduce_sum(y, 1, keepdims=True)

  # Define the range of transformations
  dxs = np.linspace(dx_min, dx_max, n_dxs)
  dys = np.linspace(dy_min, dy_max, n_dys)
  angles = np.linspace(angle_min, angle_max, n_angles)

  if n_samples is None:
    import itertools
    transforms = list(itertools.product(*[dxs, dys, angles]))
  else:
    sampled_dxs = np.random.choice(dxs, n_samples)
    sampled_dys = np.random.choice(dys, n_samples)
    sampled_angles = np.random.choice(angles, n_samples)
    transforms = zip(sampled_dxs, sampled_dys, sampled_angles)
  transformed_ims = parallel_apply_transformations(
      x, transforms, black_border_size)

  def _compute_xent(x):
    preds = model.get_logits(x)
    return tf.nn.softmax_cross_entropy_with_logits_v2(
        labels=y, logits=preds)

  all_xents = tf.map_fn(
      _compute_xent,
      transformed_ims,
      parallel_iterations=1)  # Must be 1 to avoid keras race conditions

  # Return the adv_x with worst accuracy

  # all_xents is n_total_samples x batch_size (SB)
  all_xents = tf.stack(all_xents)  # SB

  # We want the worst case sample, with the largest xent_loss
  worst_sample_idx = tf.argmax(all_xents, axis=0)  # B

  batch_size = tf.shape(x)[0]
  keys = tf.stack([
      tf.range(batch_size, dtype=tf.int32),
      tf.cast(worst_sample_idx, tf.int32)
  ], axis=1)
  transformed_ims_bshwc = tf.einsum('sbhwc->bshwc', transformed_ims)
  after_lookup = tf.gather_nd(transformed_ims_bshwc, keys)  # BHWC
  return after_lookup
151499
def optimize_no(self):
        ''' 
        '''
        self.optimization = 0
        self.relax = False
        self.gc_sections = False
        self.ffunction_sections = False
        self.fdata_sections = False
        self.fno_inline_small_functions = False
421358
def opt(self, x_init, f_fp=None, f=None, fp=None):
        
        rcstrings = ['','Maximum number of iterations exceeded', 'Gradient and/or function calls not changing']

        opt_dict = {}
        if self.xtol is not None:
            print("WARNING: bfgs doesn't have an xtol arg, so I'm going to ignore it")
        if self.ftol is not None:
            print("WARNING: bfgs doesn't have an ftol arg, so I'm going to ignore it")
        if self.gtol is not None:
            opt_dict['gtol'] = self.gtol

        opt_result = optimize.fmin_bfgs(f, x_init, fp, disp=self.messages,
                                            maxiter=self.max_iters, full_output=True, **opt_dict)
        self.x_opt = opt_result[0]
        self.f_opt = f_fp(self.x_opt)[0]
        self.funct_eval = opt_result[4]
        self.status = rcstrings[opt_result[6]]
531567
def optimise_newton(x, a, c, tolerance=0.001):
    
    x_new = x
    x_old = x-1 # dummy value
    while np.abs(x_new - x_old).sum() > tolerance:
        x_old = x_new
        x_new = newton_update(x_old, a, c)
    return x_new
212602
def xstep(self):
        
        """

        self.YU[:] = self.Y - self.U

        b = self.DSf + self.rho*sl.rfftn(self.YU, None, self.cri.axisN)
        if self.cri.Cd == 1:
            self.Xf[:] = sl.solvedbi_sm(self.Df, self.mu + self.rho,
                                        b, self.c, self.cri.axisM)
        else:
            self.Xf[:] = sl.solvemdbi_ism(self.Df, self.mu + self.rho, b,
                                          self.cri.axisM, self.cri.axisC)

        self.X = sl.irfftn(self.Xf, self.cri.Nv, self.cri.axisN)

        if self.opt['LinSolveCheck']:
            Dop = lambda x: sl.inner(self.Df, x, axis=self.cri.axisM)
            if self.cri.Cd == 1:
                DHop = lambda x: np.conj(self.Df) * x
            else:
                DHop = lambda x: sl.inner(np.conj(self.Df), x,
                                          axis=self.cri.axisC)
            ax = DHop(Dop(self.Xf)) + (self.mu + self.rho)*self.Xf
            self.xrrs = sl.rrs(ax, b)
        else:
            self.xrrs = None
199001
def gradients_X(self, dL_dK, X, X2, target):
        """"""
        if X2==None or X2 is X:
            dL_dKdiag = dL_dK.flat[::dL_dK.shape[0]+1]
            self.dKdiag_dX(dL_dKdiag, X, target)
64916
def smooth(x, y, weights):
    '''
    
    '''
    # Spline hard to smooth properly, therefore solfed with
    # bounded polynomal interpolation
    # ext=3: no extrapolation, but boundary value
#     return UnivariateSpline(x, y, w=weights,
#                             s=len(y)*weights.max()*100, ext=3)

#     return np.poly1d(np.polyfit(x,y,w=weights,deg=2))
    p = np.polyfit(x, y, w=weights, deg=2)
    if np.any(np.isnan(p)):
        # couldn't even do polynomial fit
        # as last option: assume constant noise
        my = np.average(y, weights=weights)
        return lambda x: my
    return lambda xint: np.poly1d(p)(np.clip(xint, x[0], x[-1]))
447503
def precompute_optimzation_S(laplacian_matrix,n_samples,relaxation_kwds):
    """"""
    relaxation_kwds.setdefault('presave',False)
    relaxation_kwds.setdefault('presave_name','pre_comp_current.npy')
    relaxation_kwds.setdefault('verbose',False)
    if relaxation_kwds['verbose']:
        print ('Pre-computing quantities Y to S conversions')
        print ('Making A and Pairs')
    A, pairs = makeA(laplacian_matrix)
    if relaxation_kwds['verbose']:
        print ('Making Rk and nbhds')
    Rk_tensor, nbk = compute_Rk(laplacian_matrix,A,n_samples)
    # TODO: not quite sure what is ATAinv? why we need this?
    ATAinv = np.linalg.pinv(A.T.dot(A).todense())
    if relaxation_kwds['verbose']:
        print ('Finish calculating pseudo inverse')
    if relaxation_kwds['presave']:
        raise NotImplementedError('Not yet implemented presave')
    return { 'RK': Rk_tensor, 'nbk': nbk,
             'ATAinv': ATAinv, 'pairs': pairs, 'A': A }
573208
public static UnconstrainedLeastSquaresSchur<DMatrixRMaj> levenbergMarquardtSchur(
			boolean robust,
			@Nullable ConfigLevenbergMarquardt config  )
	{
		if( config == null )
			config = new ConfigLevenbergMarquardt();

		HessianSchurComplement_DDRM hessian;

		if( robust ) {
			LinearSolverDense<DMatrixRMaj> solverA = LinearSolverFactory_DDRM.pseudoInverse(true);
			LinearSolverDense<DMatrixRMaj> solverD = LinearSolverFactory_DDRM.pseudoInverse(true);
			hessian = new HessianSchurComplement_DDRM(solverA,solverD);
		} else {
			// defaults to cholesky
			hessian = new HessianSchurComplement_DDRM();
		}

		UnconLeastSqLevenbergMarquardtSchur_F64<DMatrixRMaj> lm =
				new UnconLeastSqLevenbergMarquardtSchur_F64<>(new MatrixMath_DDRM(),hessian);
		lm.configure(config);
		return lm;
	}
1125397
def create(optimizer, max_lr, min_lr, cycles, cycle_len=1, cycle_mult=1, interpolate='linear', init_lr=0, init_iter=0):
    
    return CyclePhase(
        max_lr=max_lr,
        min_lr=min_lr,
        cycles=cycles,
        cycle_len=cycle_len,
        cycle_mult=cycle_mult,
        interpolate=interpolate,
        optimizer_factory=optimizer,
        init_lr=init_lr,
        init_iter=init_iter,
    )
1129710
def optimize(self, G, params0=None, n_times=10, verbose=False, vmax=5, perturb=1e-3, factr=1e7):
        
        # set params0 from null if params0 is None
        if params0 is None:
            if self.null is None:
                if verbose:     print(".. fitting null model")
                self.fitNull()
            if self.bgRE:
                params0 = sp.concatenate([self.null['params0_g'], self.null['params0_n']])
            else:
                params0 = self.null['params0_n']
            params_was_None = True
        else:
            params_was_None = False
        G *= sp.sqrt(self.N/(G**2).sum())
        self._gp.covar.G = G
        start = TIME.time()
        for i in range(n_times):
            if params_was_None:
                n_params = self.Cr.getNumberParams()
                _params0 = {'covar': sp.concatenate([1e-3*sp.randn(n_params), params0])}
            else:
                _params0 = {'covar': params0}
            self._gp.setParams(_params0)
            conv, info = self._gp.optimize(factr=factr, verbose=verbose)
            conv *= self.Cr.K().diagonal().max()<vmax
            conv *= self.getLMLgrad() < 0.1
            if conv or not params_was_None: break
        self.infoOpt = info
        if not conv:
            warnings.warn("not converged")
        # return value
        RV = {}
        if self.P>1:
            RV['Cr']  = self.Cr.K()
            if self.bgRE: RV['Cg']  = self.Cg.K()
            RV['Cn']  = self.Cn.K()
        RV['time']  = sp.array([TIME.time()-start])
        RV['params0'] = _params0
        RV['nit'] = sp.array([info['nit']])
        RV['funcalls'] = sp.array([info['funcalls']])
        RV['var']    = self.getVariances()
        RV['conv']  = sp.array([conv])
        RV['NLLAlt']  = sp.array([self.getNLLAlt()])
        RV['LLR']    = sp.array([self.getLLR()])
        RV['LMLgrad'] = sp.array([self.getLMLgrad()])
        return RV
827941
public static LinearSolverDense<DMatrixRMaj> general(int numRows , int numCols ) {
        if( numRows == numCols )
            return linear(numRows);
        else
            return leastSquares(numRows,numCols);
    }
434713
def optimize(self, x0, target):
        """"""
        x = x0
        for i in range(self.maxiter):
            g = self.g(x, target)
            h = self.h(x, target)
            if i == 0:
                alpha = 0
                m = g
            else:
                alpha = - np.dot(m, np.dot(h, g)) / np.dot(m, np.dot(h, m))
                m = g + np.dot(alpha, m)
            t = - np.dot(m, g) / np.dot(m, np.dot(h, m))
            delta = np.dot(t, m)
            x = x + delta
            if np.linalg.norm(delta) < self.tol:
                break
        return x
178525
def amean(x, weights=None):
    
    w_arr, x_arr = _preprocess_inputs(x, weights)
    return (w_arr*x_arr).sum(axis=0) / w_arr.sum(axis=0)
776212
def clean(self,x):
        """"""
        return x[~np.any(np.isnan(x) | np.isinf(x),axis=1)]