#!/usr/bin/env python
# coding: utf-8

import numpy as np
import mpmath
from scipy import stats
from scipy import spatial # for QHull

mpmath.mp.dps = 325 # to cover anything that double-presigion float can handle

# maximum radius, where norm.pdf() wasn't zero
# -38.575500173381374935388521407730877399444580.....
# don't ask me what the magic python use to distinguish
# digits after double precision
max_R_ever = 37

#č jako sůl potřebujem statefull třidu,
#č která by schovávala vnitřní implementaciju,
#č která by nabízela jednotné rozhraní pro ostatní kód WellMet
#č a byla by přiměřeně kompatibilní s ConvexHull ze scipy.spatial
#č Ze scipy bych viděl podporu atributů .points, .npoints, .equations
#č Určitě bych chtěl funkce .update() a .is_outside(sample)
#č Atribute .space by ukazoval, v jakém prostoru konvexní obál je vytvořen
# GBall, BrickHull, DirectHull, CompleteHull and QHull has been implemented


def calculate_brick_complement_probability(mins, maxs):
    "For Gaussian space"
    #č na začátku nastavíme obyčejnou 1
    #č v cyklu bude nasobit delkami 
    #č podle jednotlivých souřadnic
    #č a typ se změní na mpf (hodně přesná aritmetika)
    volume = 1
    
    # ncdf() do not support matrix input
    for xmin, xmax in zip(mins, maxs):
        volume *= mpmath.ncdf(xmax) - mpmath.ncdf(xmin)
    
    # print test
#    if len(mins) == 2:
#        min_x, min_y = mins
#        max_x, max_y = maxs
#        test_volume = 0
#        test_volume += np.sum(stats.norm.cdf(mins)) 
#        test_volume += np.sum(stats.norm.sf(maxs))
#        test_volume -= stats.norm.cdf(min_x) * stats.norm.cdf(min_y)
#        test_volume -= stats.norm.cdf(min_x) * stats.norm.sf(max_y)
#        test_volume -= stats.norm.sf(max_x) * stats.norm.cdf(min_y)
#        test_volume -= stats.norm.sf(max_x) * stats.norm.sf(max_y)
#        print("test_volume:", test_volume)  
        
    return float(1-volume)
    
# inspired by 
# https://math.stackexchange.com/questions/192610/how-to-build-a-orthogonal-basis-from-a-vector/979013
# most interesting from there:
# """Pick a vector. WLOG, you chose $(x_1,x_2,x_3,x_4)$. 
# Now write it as a quaternion: $$x_1+ix_2+jx_3+kx_4$$ 
# Then, since multiplication by $i,j,k$ 
# rotates this vector $90^0$ across the various axes of our 4D space,
# the following three vectors make your initial choice of vector into an orthonormal basis: 
# $$i(x_1+ix_2+jx_3+kx_4)=ix_1-x_2+kx_3-jx_4\mapsto (-x_2,x_1,-x_4,x_3)$$ 
# $$j(x_1+ix_2+jx_3+kx_4)=jx_1-kx_2-x_3+ix_4\mapsto (-x_3,x_4,x_1,-x_2)$$
# $$k(x_1+ix_2+jx_3+kx_4)=kx_1+jx_2-ix_3-x_4\mapsto (-x_4,-x_3,x_2,x_1)$$"""
def get_orth_basis(vector):
    dim = len(vector)
    if dim == 2:
        x, y = vector
        return np.array([[x, y],[-y, x]])
    elif dim == 4:
        x_1, x_2, x_3, x_4 = vector
        return np.array([
            [x_1, x_2, x_3, x_4],
            [-x_2, x_1, -x_4, x_3],
            [-x_3, x_4, x_1, -x_2],
            [-x_4, -x_3, x_2, x_1]])
    else:
        random_basis = np.random.random((dim, dim))
        #č QR rozklad jede po sloupcich
        random_basis[:,0] = vector
        #č co jsem viděl, numpy matici Q normalizuje
        #č a první sloupec zůstavá (skoro) tím samým, co byl před tím
        Q, __R = np.linalg.qr(random_basis)
        # yep. Numpy sometimes inverts sign of the first Q matrix vector
        Q[:,0] = vector
        return Q.T
    
        
        
#ё рельса
#č nepodařílo se mi nějak rozumně zobecnit pro libovolný prostor
#č takže Gauss
#č (každá třida implementuje zvlášť)

def shot(hull, ns, use_MC=False):
    if hull.space == 'G':
        to_fire = np.nanargmax(hull.b)
        r = -hull.b[to_fire]
        a = hull.A[to_fire]
        
        if use_MC:
            fire_from = stats.norm.sf(r)
            t = np.linspace(fire_from, 0, ns, endpoint=False)
            t = stats.norm.isf(t)
        else:
            if r < max_R_ever:
                R = max_R_ever
            else:
                R = r + 10
            t = np.linspace(r, R, ns, endpoint=True)
            
        fire_G = t.reshape(-1,1) @ a.reshape(1,-1)
        return hull.sample.f_model.new_sample(fire_G, space='G')


def fire(hull, ns, use_MC=False):
    if hull.space == 'G':
        to_fire = np.nanargmax(hull.b)
        r = -hull.b[to_fire]
        a = hull.A[to_fire]
        
        orth_nodes_T = np.random.randn(len(a), ns) # len(a) == ndim
        orth_basis = get_orth_basis(a)
        
        if use_MC:
            fire_from = stats.norm.sf(r)
            t = np.linspace(fire_from, 0, ns, endpoint=False)
            orth_nodes_T[0] = stats.norm.isf(t)
        else:
            if r < max_R_ever:
                R = max_R_ever
            else:
                R = r + 10
            orth_nodes_T[0] = np.linspace(r, R, ns, endpoint=True)
            
        fire_G = (orth_basis.T @ orth_nodes_T).T
        return hull.sample.f_model.new_sample(fire_G, space='G')

#
# Common orth functions for DirectHull, CompleteHull and QHull
#

# (even private function can be shared :D )
def _orth_helper(hull):
    # supposed hull.space == 'G'
    hull._update()
    to_fire = np.nanargmax(hull.b)
    a = hull.A[to_fire]
    
    orth_basis = get_orth_basis(a)
    
    #č musí tam bejt G coordinates
    A = orth_basis @ hull.points.T
    bp = np.nanmax(A, axis=1)
    bm = np.nanmin(A, axis=1)
    
    return orth_basis, bp, bm
    
    
def get_orth_outside(hull):
    if hull.space == 'G' :
        # hull._update() will perform _orth_helper()
        A, bp, bm = hull._orth_helper()
        return calculate_brick_complement_probability(bm, bp)
    else:
        #č když prostor není G, můžeme sice něco odvodit od s-ball 
        #č ale nechť se s tím pará GHull, vrátíme nulu.
        return 0

def get_orth_equations(hull):
    # hull._update() will perform _orth_helper()
    direct_plan, bp, bm = hull._orth_helper()

    A = np.vstack((-direct_plan, direct_plan))
    b = np.concatenate((bm, -bp))
    return np.hstack((A,b[:,None]))     


#
# Common 2FORM functions for DirectHull, CompleteHull and QHull
#

# (even private function can be shared :D )
def _2FORM_helper(hull):
    # supposed hull.space == 'G'
    hull._update()
    to_fire = np.nanargmax(hull.b)
    a = hull.A[to_fire]
    
    #č musí tam bejt G coordinates
    # we'll get 1D npoints-sized negative b array
    x = a @ hull.points.T
    # here x == _b array has another meaning than hull.b
    # where in hull.b we search for least distanced hyperplane
    # here, in x, we search for a valid b_backward hyperplane offset
    # It can be seen as transformation of the ED to 1D a-projection.
    # There evidently exist min(x) and max(x)
    # such that every single x value lies inside (between)
    # max(x) (forward) value should be corresponding to r, to -hull.b
    # So, we need to find min(x) (backward) value
    # x_forward == max(x) == -b == r == max(a @ points.T) == -max(hull.b) == min(-hull.b)
    # x_backward == min(x) == max(-a @ points.T)
    x_forward = np.max(x)
    x_backward = np.min(x)
    #print(-np.max(hull.b), x_forward) 
    return x_backward, x_forward, a


def get_2FORM_outside(hull):
    if hull.space == 'G':
        # hull._update() will perform _FORM_helper()
        x_backward, x_forward, __a = hull._2FORM_helper()
        return stats.norm.cdf(x_backward) + stats.norm.sf(x_forward)
    else:
        #č když prostor není G, můžeme sice něco odvodit od s-ball 
        #č ale nechť se s tím pará GHull, vrátíme nulu.
        return 0
            
def get_2FORM_equations(hull):
    # hull._update() will perform _2FORM_helper()
    x_backward, x_forward, a = hull._2FORM_helper()
    A = np.vstack((-a, a))
    b = np.array([[x_backward],[-x_forward]])
    return np.hstack((A,b))  
    

#č jistě musíme mít nějaký zbytečný kus kódu
#č třida jen pro formu, jen tak na hračku
#č když tečíčky jsou dále jak nejvzdálenější vzorek (bod),
#č tak řekneme, že jsou totálně mimo!
class GBall:
    def __init__(hull, sample):
        hull.sample = sample
        hull.space = 'G' #оӵ малы? Кинлы со кулэ?
    
    @property
    def points(hull):
        return hull.sample.G
        
    @property
    def npoints(hull):
        return len(hull.sample)
        
    @property
    def nsimplex(hull):
        return 1
        
    #def update(hull): pass
    
    def is_inside(hull, nodes):
        R2_hull = np.nanmax(np.sum(np.square(hull.sample.G), axis=1))
        
        R2_nodes = np.sum(np.square(nodes.G), axis=1)
        return R2_nodes < R2_hull 

    def is_outside(hull, nodes): 
        return ~hull.is_inside(nodes)
        
    def get_R(hull):
        return np.sqrt(np.nanmax(np.sum(np.square(hull.sample.G), axis=1)))
        
    def get_r(hull): 
        # zero at best, 
        # on the safe side, between -R and 0
        #r2_hull = np.nanmin(np.sum(np.square(hull.sample.G), axis=1))
        #return -np.sqrt(r2_hull)
        
        #č když na get_r nahlížím z hlediska toho,
        #č že r vymezuje mezikruží, kde nejsme jistí
        #č inside-outside,
        #č tak zde get_r vždy musí vracet prostě R
        return hull.get_R()
        
    def get_orth_outside(hull):
        x = np.full(hull.sample.nvar, hull.get_r())
        return calculate_brick_complement_probability(-x, x)
        
     
    def get_2FORM_outside(hull):
        return 2*stats.norm.sf(hull.get_r())
        
     
    def fire(hull, *args, **kwargs):
        pass
    
    def shot(hull, *args, **kwargs):
        pass
        


#č vyhejbám slovu Box, ať nevnáším ještě víc zmatku v označení
class BrickHull: #č nebo BoundingBrick
    def __init__(hull, sample, space='G'):
        hull.sample = sample
        hull.space = space
        
        
        hull._npoints = 0
        #č miny a maxy obsahují minima a maxima 
        #č podel jednotlivých souřadnic (proměnných)
        #č sincerely yours, Captain Obvious.
        hull.mins = np.full(hull.sample.nvar, np.inf)
        hull.maxs = np.full(hull.sample.nvar, -np.inf)
    
    def _update(hull):
        if hull._npoints < hull.npoints:
            hull.mins = np.nanmin(hull.points, axis=0)
            hull.maxs = np.nanmax(hull.points, axis=0)
            hull._npoints = hull.npoints
        
        
    def is_inside(hull, nodes):
        hull._update()
        x = getattr(nodes, hull.space)
        more = np.all(x < hull.maxs, axis=1)
        less = np.all(x > hull.mins, axis=1)
        
        return np.all((more, less), axis=0) #np.all(np.array((more, less)), axis=0)
        
    def is_outside(hull, nodes): 
        return ~hull.is_inside(nodes)
        
    def get_design_points(hull):
        hull._update()
        #sample_model = -hull.A * hull.b.reshape(-1,1)
        sample_model = np.vstack((np.diag(hull.maxs), np.diag(hull.mins)))
        return hull.sample.f_model.new_sample(sample_model, space=hull.space)
        
    # shortcut for Ghull
    # valid only if space==G
    def get_r(hull):
        if hull.space=='G':
            hull._update()
            return np.min((-hull.mins, hull.maxs))
        else:
            return 0
        
    @property
    def points(hull):
        return getattr(hull.sample, hull.space)
        
    @property
    def npoints(hull):
        return len(hull.sample)
        
    @property
    def nsimplex(hull):
        return hull.sample.nvar*2
        
    @property
    def A(hull):
        hull._update()
        #č žádná optimizace, ale kdo tu funkci bude spouštět?
        diag = np.diag(np.ones(hull.sample.nvar))
        return np.vstack((diag, -diag))
        
    @property
    def b(hull):
        hull._update()
        return np.concatenate((hull.maxs, -hull.mins))
        
    @property
    def equations(hull):
        hull._update()
        #č žádná optimizace, ale kdo tu funkci bude spouštět?
        diag = np.diag(np.ones(hull.sample.nvar))
        
        A = np.vstack((diag, -diag))
        b = np.concatenate((-hull.maxs, hull.mins))
        return np.hstack((A,b[:,None]))
        
        
    def get_orth_outside(hull):
        if hull.space == 'G':
            hull._update()
            return calculate_brick_complement_probability(hull.mins, hull.maxs)
        else:
            #č když prostor není G, můžeme sice něco odvodit od s-ball 
            #č ale nechť se s tím pará GHull, vrátíme nulu.
            return 0
            
    def get_orth_equations(hull):
        return hull.equations
        
        
    def _2FORM_helper(hull):
        hull._update()
        #č je to úplně zbýtečně trapit se nejakejma argama
        #č poďme na to globálně!
        #č (doufám, že nvar*2 výpočtů cdf() nikomu neublíží... )
        #min_arg = np.nanargmin(hull.mins)
        #max_arg = np.nanargmax(hull.maxs)
        cdfs = stats.norm.cdf(hull.mins)
        sfs = stats.norm.sf(hull.maxs)
        #č _update() počítá nanmin a nanmax
        #č takže nemusíme se bat nějakého hnusu v číslech
        pfs = cdfs + sfs
        i = np.argmax(pfs) # number of variable
        # we'll return 2FORM estimation 
        # and corresponding number of variable
        return pfs[i], i
        
        
    def get_2FORM_outside(hull):
        if hull.space == 'G':
            # hull._update() will perform _FORM_helper()
            p_out, __i = hull._2FORM_helper()
            return p_out
        else:
            #č když prostor není G, můžeme sice něco odvodit od s-ball 
            #č ale nechť se s tím pará GHull, vrátíme nulu.
            return 0
            
        
    def get_2FORM_equations(hull):
        __p_out, i = hull._2FORM_helper()
        equations = np.zeros((2,hull.sample.nvar+1))
        equations[0, i] = 1
        equations[0, -1] = -hull.maxs[i]
        equations[1, i] = -1
        equations[1, -1] = hull.mins[i]
        return equations
        
    def shot(hull, *args, **kwargs):
        pass
        
        # add use_MC to the function signature
        # but remain unimplemented for now
        #č ten fire je hrozný. Výhodit U prostor 
        #č (jsou tam nepřesné cdf transformace)
        #č po úpravě přídat hull._update() na začátku.
    def fire(hull, ns, use_MC=False): # boom
        sample_U = hull.sample.U
        
        U_mins = np.nanmin(sample_U, axis=0)
        U_maxs = np.nanmax(sample_U, axis=0)
        
        #č min nebo max?
        if np.nanmax(U_mins) > (1-np.nanmin(U_maxs)):
            #č expandujeme se dolu
            var = np.nanargmax(U_mins)
            value = U_mins[var]
            t = np.linspace(value, 0, ns, endpoint=False)
        else:
            #č expandujeme se nahoru
            var = np.nanargmin(U_maxs)
            value = U_maxs[var]
            t = np.linspace(value, 1, ns, endpoint=False)
        
        boom = np.random.random((ns, hull.sample.nvar))
        boom[:, var] = t
        
        return hull.sample.f_model.new_sample(boom, space='U')
    

class DirectHull:
    # take some global functions
    fire = fire
    shot = shot
    _orth_helper = _orth_helper
    get_orth_outside = get_orth_outside
    get_orth_equations = get_orth_equations
    
    _2FORM_helper = _2FORM_helper
    get_2FORM_outside = get_2FORM_outside
    get_2FORM_equations = get_2FORM_equations
    
    
    def __init__(hull, sample, direct_plan, space='G'):
        hull.sample = sample
        hull.direct_plan = direct_plan
        hull.space = space
        
        hull.regen()
        
    def regen(hull):
        hull._npoints = 0
        
        hull.bp = np.full(len(hull.direct_plan), -np.inf)
        #hull.update()
    
    #č nejsem jist, jestli ten update vůbec dělat.
    #č lze navrhnout třidu aj tak, že sama bude hlídat změny.
    #č Jenomže, co kdybychom ten automatický update nechtěli?
    def _update(hull):
        if hull._npoints < hull.npoints:
            #hull.points = getattr(hull.sample, hull.space)
            new_points = hull.points[hull._npoints:]
            
            A = hull.direct_plan @ new_points.T
            new_bp = np.nanmax(A, axis=1)
            hull.bp = np.nanmax((new_bp, hull.bp), axis=0)
            
            hull._npoints = hull.npoints

    @property
    def points(hull):
        return getattr(hull.sample, hull.space)
        
    @property
    def npoints(hull):
        return len(hull.sample)
        
    @property
    def nsimplex(hull):
        return len(hull.direct_plan)
        
    @property
    def A(hull):
        return hull.direct_plan
        
    @property
    def b(hull):
        hull._update()
        return -hull.bp
        
    @property
    def equations(hull):
        return np.hstack((hull.A, hull.b[:,None]))

    def is_inside(hull, nodes):
        hull._update()
        x = getattr(nodes, hull.space)
        
        #E [normal, offset] forming the hyperplane equation of the facet (see Qhull documentation for more)
        A = hull.direct_plan
        bp = np.atleast_2d(hull.bp).T
        
        # N=ns, E - number of hyperplane equations
        ExN = A @ x.T
        higher = np.all(ExN < bp, axis=0)
        return higher
    
    def is_outside(hull, nodes): 
        return ~hull.is_inside(nodes)
        
    def get_design_points(hull):
        hull._update()
        sample_model = -hull.A * hull.b.reshape(-1,1)
        return hull.sample.f_model.new_sample(sample_model, space=hull.space)
        
    # shortcut for Ghull
    # valid only if space==G
    def get_r(hull):
        if hull.space=='G':
            hull._update()
            return np.min(hull.bp)
        else:
            return 0
    
    


class CompleteHull:
    # take some global functions
    fire = fire
    shot = shot
    _orth_helper = _orth_helper
    get_orth_outside = get_orth_outside
    get_orth_equations = get_orth_equations
    
    _2FORM_helper = _2FORM_helper
    get_2FORM_outside = get_2FORM_outside
    get_2FORM_equations = get_2FORM_equations
    
    def __init__(hull, sample, direct_plan, space='G'):
        hull.sample = sample
        hull.direct_plan = direct_plan
        hull.space = space
        
        hull.regen()
        
    def regen(hull):
        hull._npoints = 0
        hull.mins = np.full(hull.sample.nvar, np.inf)
        hull.maxs = np.full(hull.sample.nvar, -np.inf)
        
        hull.bp = np.full(len(hull.direct_plan), -np.inf)
        hull.bm = np.full(len(hull.direct_plan), np.inf)
        
        #hull.update()
    
    #č nejsem jist, jestli ten update vůbec dělat.
    #č lze navrhnout třidu aj tak, že sama bude hlídat změny.
    #č Jenomže, co kdybychom ten automatický update nechtěli?
    def _update(hull):
        if hull._npoints < hull.npoints:
            #hull.points = getattr(hull.sample, hull.space)
            new_points = hull.points[hull._npoints:]
            
            new_mins = np.nanmin(new_points, axis=0)
            new_maxs = np.nanmax(new_points, axis=0)
            
            hull.mins = np.nanmin((new_mins, hull.mins), axis=0)
            hull.maxs = np.nanmax((new_maxs, hull.maxs), axis=0)
            
            A = hull.direct_plan @ new_points.T
            new_bp = np.nanmax(A, axis=1)
            new_bm = np.nanmin(A, axis=1)
            
            hull.bp = np.nanmax((new_bp, hull.bp), axis=0)
            hull.bm = np.nanmin((new_bm, hull.bm), axis=0)
            
            hull._npoints = hull.npoints

    @property
    def points(hull):
        return getattr(hull.sample, hull.space)
        
    @property
    def npoints(hull):
        return len(hull.sample)
        
    @property
    def nsimplex(hull):
        return 2 * (len(hull.direct_plan) + hull.sample.nvar)
        
    @property
    def A(hull):
        hull._update()
        #č žádná optimizace, ale kdo tu funkci bude spouštět?
        diag = np.diag(np.ones(hull.sample.nvar))
        return np.vstack((diag, -diag, -hull.direct_plan, hull.direct_plan))
        
    @property
    def b(hull):
        hull._update()
        return np.concatenate((-hull.maxs, hull.mins, hull.bm, -hull.bp))
        
    @property
    def equations(hull):
        hull._update()
        #č žádná optimizace, ale kdo tu funkci bude spouštět?
        diag = np.diag(np.ones(hull.sample.nvar))
        
        A = np.vstack((diag, -diag, -hull.direct_plan, hull.direct_plan))
        b = np.concatenate((-hull.maxs, hull.mins, hull.bm, -hull.bp))
        return np.hstack((A,b[:,None]))

    def is_inside(hull, nodes):
        hull._update()
        x = getattr(nodes, hull.space)
        
        more = np.all(x < hull.maxs, axis=1)
        less = np.all(x > hull.mins, axis=1)
        
        
        #E [normal, offset] forming the hyperplane equation of the facet (see Qhull documentation for more)
        A = hull.direct_plan
        bp = np.atleast_2d(hull.bp).T
        bm = np.atleast_2d(hull.bm).T
        
        # N=ns, E - number of hyperplane equations
        ExN = A @ x.T
        higher = np.all(ExN < bp, axis=0)
        lower = np.all(ExN > bm, axis=0)
        return np.all((more, less, higher, lower), axis=0)
    
    def is_outside(hull, nodes): 
        return ~hull.is_inside(nodes)
        
    def get_design_points(hull):
        hull._update()
        sample_model = -hull.A * hull.b.reshape(-1,1)
        return hull.sample.f_model.new_sample(sample_model, space=hull.space)
        
    # shortcut for Ghull
    # valid only if space==G
    def get_r(hull):
        if hull.space=='G':
            hull._update()
            return min(-np.max(hull.mins), np.min(hull.maxs), -np.max(hull.bm), np.min(hull.bp))
        else:
            return 0
    
            

class QHull:
    # take some global function
    _orth_helper = _orth_helper
    #get_orth_outside = get_orth_outside
    get_orth_equations = get_orth_equations
    
    _2FORM_helper = _2FORM_helper
    #get_2FORM_outside = get_2FORM_outside
    get_2FORM_equations = get_2FORM_equations
    
    def __init__(self, sample, space='G', incremental=True):
        self.sample = sample
        self.incremental = incremental
        self.space = space
    
    def regen(self):
        points = getattr(self.sample, self.space)
        self.convex_hull = spatial.ConvexHull(points, incremental=self.incremental)
        
    
    def __getattr__(self, attr):
        #č branime se rekurzii
        # defend against recursion
        #оӵ рекурсилы пезьдэт!
        if attr == 'convex_hull':
            #č zkusme rychle konvexní obálky sestavit
            #č a ihned ji vrátit
            self.regen()
            return self.convex_hull
        
        elif attr == 'enough_points':
            return self.sample.nvar < self.sample.nsim
            
        elif attr == 'A':
            return self.convex_hull.equations[:,:-1]
        elif attr == 'b':
            return self.convex_hull.equations[:,-1]
            
        elif attr == 'points':
            if self.enough_points:
                return self.convex_hull.points
            else:
                return getattr(self.sample, self.space)
                
        elif attr == 'npoints':
            if self.enough_points:
                return self.convex_hull.npoints
            else:
                return len(self.sample)
        
        elif attr == 'nsimplex':
            if self.enough_points:
                return self.convex_hull.nsimplex
            else:
                return 0
            
            
        #ё По всем вопросам обращайтесь 
        #ё на нашу горячую линию    
        else:
            self._update() #č dycky čerstý chleba!
            return getattr(self.convex_hull, attr)
            
    
    #č nejsem jist, jestli ten update vůbec dělat.
    #č lze navrhnout třidu aj tak, že sama bude hlídat změny.
    #č Jenomže, co kdybychom ten automatický update nechtěli?
    def _update(self):
        if self.convex_hull.npoints < self.sample.nsim:
            if self.incremental:
                points = getattr(self.sample, self.space)  
                self.convex_hull.add_points(points[self.convex_hull.npoints:])
            else:
                self.regen()
        
        
    def is_inside(self, nodes):
        if self.enough_points:
            self._update()
            x = getattr(nodes, self.space)
            
            #E [normal, offset] forming the hyperplane equation of the facet (see Qhull documentation for more)
            A = self.convex_hull.equations[:,:-1]
            b = self.convex_hull.equations[:,-1]
            
            # N=ns, E - number of hyperplane equations
            ExN = A @ x.T + np.atleast_2d(b).T
            mask = np.all(ExN < 0, axis=0)
            return mask
        else:
            return np.full(len(nodes), False)
    
    def is_outside(hull, nodes): 
        return ~hull.is_inside(nodes)
        
    def get_design_points(hull):
        hull._update()
        sample_model = -hull.A * hull.b.reshape(-1,1)
        return hull.sample.f_model.new_sample(sample_model, space=hull.space)
        
    def get_design_point(hull):
        hull._update()
        to_fire = np.nanargmax(hull.b) #č tak, pro jistotu
        sample_model = -hull.A[to_fire] * hull.b[to_fire]
        return hull.sample.f_model.new_sample(sample_model, space=hull.space)
    
        
    # shortcut for Ghull
    # valid only if space==G
    def get_r(hull):
        if hull.space=='G':
            if hull.enough_points:
                hull._update()
                b = hull.convex_hull.equations[:,-1]
                return -np.nanmax(b)
            else:
                return 0
        else:
            return 0
    
    def shot(hull, ns, use_MC=False):
        try:
            # take global function for shot()
            return shot(hull, ns, use_MC)
        except:
            pass
            
    def fire(hull, ns, use_MC=False):
        try:
            # take global function for fire()
            return fire(hull, ns, use_MC)
        except:
            pass
    
    def get_orth_outside(hull):
        try:
            return get_orth_outside(hull)
        except:
            #č asi máme problém s triangulací 
            #č odvažně vratíme jedničku
            #č neřikejte mi, že musím pěčlivějc zpracovavat chyby!
            return 1
    
    def get_2FORM_outside(hull):
        try:
            return get_2FORM_outside(hull)
        except:
            #č asi máme problém s triangulací 
            #č odvažně vratíme jedničku
            #č neřikejte mi, že musím pěčlivějc zpracovavat chyby!
            return 1