function [x,w]=knots_gaussian_leja(n)

% [x,w] = knots_gaussian_leja(n)
%
% DEPRECATED!! This function has been replaced by KNOTS_NORMAL_LEJA in release 22.2 and will disappear in future releases
%
%
% returns the collocation points (x) and the weights (w) 
% for the weighted Leja sequence for integration 
% w.r.t to the weight function 
%
% rho(x)=1/sqrt(2*pi)*exp(-x^2/2) 
%
% i.e. the density of a gaussian random variable 
% with mean 0 and standard deviation 1.
%
% Knots and weights have been precomputed (up to 150) following the work
% 
% A. Narayan, J. Jakeman, "Adaptive Leja sparse grid constructions for stochastic collocation and high-dimensional approximation"
% SIAM Journal on Scientific Computing,  Vol. 36, No. 6, pp. A2952–A2983, 2014
%
% an error is raised if more than 150 points are requested.
%
% knots are sorted increasingly before returning (weights are returned in the corresponding order)

%----------------------------------------------------
% Sparse Grid Matlab Kit
% Copyright (c) 2009-2023 L. Tamellini, F. Nobile, B. Sprungk
% See LICENSE.txt for license
%----------------------------------------------------

error('SparseGKit:RenamedFunction',['knots_gaussian_leja has been replaced by knots_normal_leja in release 22.2, '...
    'which takes as input also the mean and the standard deviation of the normal (Gaussian) pdf '  ...
    'to allow for integration w.r.t. general normal densities (and not only w.r.t. the standard Gaussian). '...
    'This message will disappear in future releases of the sparse-grid-matlab-kit.'])

if n>150
   error('SparseGKit:OutOfTable',strcat('this number of points is not available:',num2str(n)))

else
    
    % load points and weights
    % SS = load('GaussianLejaPrecomputedKnotsAndWeights90.mat');
    % x = SS.X(1:n);
    % w = SS.W(1:n,n);

    %[X,W] = get_GaussianLejaPrecomputedKnotsAndWeights90;
    [X,W] = get_GaussianLejaPrecomputedKnotsAndWeights150;
    x = X(1:n);
    w = W(1:n,n);
    
    
    % sort knots increasingly and weights accordingly. Weights need to be row vectors
    [x,sorter]=sort(x);
    w=w(sorter)';

end

end


function [X,W] = get_GaussianLejaPrecomputedKnotsAndWeights90()


X = [0.0000000000000000e+00  -1.4142135698899674e+00   1.7634954606551199e+00  -2.7172574860819614e+00   3.0327562054451591e+00   8.2779559487910315e-01  -3.9576676419989196e+00   4.2949619906389991e+00  -4.9609862274765382e+00  -7.3030308526500465e-01   5.3675997712939996e+00  -5.9509559830609993e+00   2.4251469127784575e+00   6.3935177408000001e+00  -2.1394800099619991e+00  -6.9441467744259988e+00   3.7147090166999988e+00   7.4128451145034902e+00  -3.3947284984004922e+00  -7.8986994213039976e+00   8.2675322128533111e+00   1.2558396376999998e+00  -5.4447580241609996e+00   4.8821990268550799e+00  -8.8799928198800000e+00   9.1872387432990905e+00  -3.7412293280599185e-01  -9.6984413686851294e+00   6.8721436193959988e+00  -4.4306250244000003e+00   1.0117637822499876e+01  -7.4118085202000001e+00   5.8491911170000002e+00  -1.0631852065919999e+01  -1.7727689940220008e+00   1.0972729438500004e+01   2.1105998384820173e+00  -1.1423072749099680e+01   8.7249821236000003e+00  -6.4401496045814097e+00   1.1847676796300370e+01  -8.4470564716609982e+00   4.2495324739999463e-01  -1.2292419068100001e+01   1.2591402304092000e+01   3.3964234700995708e+00  -3.0667181918609989e+00   9.6771589325044189e+00  -1.3051321240400418e+01  -1.0140189810291998e+01   1.3388913475961999e+01   7.7921447640040498e+00  -1.3804202567700001e+01   4.5855965609489999e+00  -4.6970424443958931e+00   1.4139472396934899e+01  -9.2823121051998481e+00   1.1375194155790432e+01  -1.4552659097626458e+01  -1.0732454285525419e+00  -1.1829740724749412e+01   1.4899705704100001e+01   6.1225606345959989e+00  -6.6867078066005901e+00   1.0530958224909000e+01  -1.5341672088761539e+01   2.7258644519059989e+00   1.5648376945700001e+01  -1.1013504297380008e+01  -2.4324589885775216e+00   1.2977943745937999e+01  -1.6078021480200000e+01   7.1449802626987307e+00  -1.3415306341130998e+01   1.6415532402099998e+01  -5.6937186243386497e+00   1.4856568294000003e+00  -1.6826055633975038e+01   1.4501997379199999e+01  -8.1703562911119985e+00   1.7178489265601002e+01  -1.4929123110508980e+01   9.4240374296664200e+00  -3.6847063106173712e+00   1.2200789360323711e+01  -1.7614084157410442e+01   4.0064500705495902e+00   1.7905157531005088e+01  -1.2642778138965218e+01   2.1197572351972926e-01];

W = [1.0000000000000000e+00   1.0000000000000000e+00   5.9903113265433117e-01   6.5057249921300708e-01   6.2901525792821111e-01   5.3080478750937821e-01   4.9671360212071153e-01   5.2113826256788642e-01   4.9890639737532388e-01   3.5869490493760203e-01   3.5932831980155922e-01   3.5104402920781136e-01   3.5619456835930824e-01   3.7181590500479067e-01   3.1203023836708843e-01   3.0862216087898664e-01   3.1323003667481858e-01   3.1652991967047106e-01   3.0799958193096677e-01   3.0656408418276415e-01   3.0818996101653301e-01   3.1654615137588493e-01   3.1714135568839524e-01   3.1537328915100921e-01   3.1592239423416030e-01   3.1507324241261114e-01   3.2947738086535089e-01   3.3686043038747127e-01   3.2723513518376340e-01   3.4332692909570617e-01   3.3737662073570751e-01   3.4562968234638763e-01   3.3544983451777727e-01   3.4113605166212718e-01   3.7483189395390276e-01   3.6951197239430678e-01   3.4257291166936410e-01   3.4653502360238192e-01   3.4076094042393484e-01   3.4757993582594121e-01   3.4311587505235647e-01   3.4883990185614866e-01   2.1992492793626423e-01   2.1432021908967572e-01   2.1939865308180520e-01   2.3924781896810590e-01   2.1146695036417953e-01   2.1627722305820932e-01   2.1229437899932593e-01   2.0757558528780606e-01   2.1076531764109591e-01   2.1673002733502447e-01   2.1288795385928150e-01   2.2361500923758823e-01   2.1076494009525190e-01   2.1419225232420075e-01   2.0860466897374721e-01   2.1269047811892466e-01   2.0921361006924866e-01   1.6521729643495123e-01   1.6493674830490943e-01   1.6503921428002416e-01   1.6552947650060382e-01   1.6458211975773068e-01   1.6491891134262446e-01   1.6458778135382640e-01   1.6607168635321795e-01   1.6668535868929263e-01   1.6571970482656426e-01   1.6207710818298149e-01   1.6230835335149499e-01   1.6215236014928000e-01   1.6254669650671824e-01   1.6240194895208018e-01   1.6253672955962803e-01   1.6220469210606228e-01   1.6395819796470509e-01   1.6411497248602422e-01   1.6391870803538797e-01   1.6424732923087854e-01   1.6406516783749908e-01   1.6426948109803366e-01   1.6392937605924923e-01   1.6476241712021394e-01   1.6444573505366819e-01   1.6466873656845193e-01   1.6368641247488205e-01   1.6346281268335713e-01   1.6377074826893662e-01   1.4468935065901642e-01
   0.0000000000000000e+00  -0.0000000000000000e+00   2.2252093273210047e-01   1.6287403123193528e-01   1.7988771921706534e-01   2.0850634659067613e-01   2.2396417675447020e-01   2.1563272103245348e-01   2.2623997398494872e-01   1.5480440453964603e-01   1.5505982368233298e-01   1.5067791691197238e-01   1.5239875362862959e-01   1.5667261250805872e-01   1.0842123532559567e-01   1.0496724510206745e-01   1.0834953683050759e-01   1.1038366237011321e-01   1.0137060026355751e-01   9.9523082200090401e-02   1.0130996488901459e-01   1.0562944017873153e-01   1.0604506703881460e-01   1.0508774415034024e-01   1.0544137713950029e-01   1.0496746013518748e-01   1.0207579914274190e-01   1.0034061414986860e-01   1.0221669969221764e-01   9.7609707721452291e-02   9.9104333807832720e-02   9.6542474759752098e-02   9.9087177164207729e-02   9.7447688538639207e-02   4.9412761557699164e-02   5.6130708632046854e-02   7.6500358648242117e-02   7.3081145127242730e-02   7.7369034360673189e-02   7.0880301139562021e-02   7.4675175347359429e-02   6.8830728327457458e-02   9.9244141510628534e-02   1.0073829410316217e-01   9.9521145522114177e-02   9.6162414010345157e-02   1.0488630107023213e-01   1.0356835847673750e-01   1.0479221223581196e-01   1.0647720978574587e-01   1.0544702675053524e-01   1.0381653502521754e-01   1.0498666837411283e-01   1.0248972582728490e-01   1.0676939039782873e-01   1.0573172385116722e-01   1.0772751244633022e-01   1.0642950559950472e-01   1.0765295352079798e-01   5.8922684080980593e-02   5.8569757903487896e-02   5.8687484761355865e-02   5.9145069881921190e-02   5.8023688738826157e-02   5.8375149155620275e-02   5.7994509067870660e-02   5.9117607545945451e-02   5.9543571272221298e-02   5.8774540117603552e-02   5.1844646031018016e-02   5.2241351485205284e-02   5.1947933305293736e-02   5.2567112475468331e-02   5.2313049983110177e-02   5.2530854331206848e-02   5.1816968655584016e-02   5.3748442045797463e-02   5.3936973910126827e-02   5.3721924102939973e-02   5.4157370965720320e-02   5.3934353757911606e-02   5.4210665757206497e-02   5.3810726482378939e-02   5.5400481328498140e-02   5.4858907823474599e-02   5.5273566038762885e-02   5.3923532578653774e-02   5.3638728442554594e-02   5.4080352835578445e-02   5.0513227377276565e-02
   0.0000000000000000e+00   0.0000000000000000e+00   1.7844793461356814e-01   1.6453763142437944e-01   1.7843909419548479e-01   1.2241025132498216e-01   1.0895626581903042e-01   1.2531028576207162e-01   1.1432829448006358e-01   9.4045369968233733e-02   9.4181833933506487e-02   9.2805046958516227e-02   9.5942468685906557e-02   1.0908246345819704e-01   8.1515655032936646e-02   8.0262464264375402e-02   8.3488197776538195e-02   8.6519384805895092e-02   8.1362525640687078e-02   8.0653109027319050e-02   8.1674470311216385e-02   6.8688784599686553e-02   6.7990116097022824e-02   7.1239081474408147e-02   7.0397239509680423e-02   7.2008339553377765e-02   6.7225248995074247e-02   6.5150808260512907e-02   6.8788832114862822e-02   6.4438310871999985e-02   6.6386600693048387e-02   6.4203705393163932e-02   6.8058390479116632e-02   6.6211584485022151e-02   6.0725259073284153e-02   6.1757311213712709e-02   9.3535172771606973e-02   8.9486430639419731e-02   9.6881443995194591e-02   9.0025529090914685e-02   9.5298649287381632e-02   8.9704997721969840e-02   4.9709952061143203e-02   4.8189285000877817e-02   4.9791572643566095e-02   6.2817472271988709e-02   5.1242530504637340e-02   5.3693359373651328e-02   5.1905658757640499e-02   5.0101407038593754e-02   5.1506021503222553e-02   5.4900938773328217e-02   5.2961873292060896e-02   6.1758792569399132e-02   5.4097335817673772e-02   5.6431940076937449e-02   5.3233469856560182e-02   5.6001399475570354e-02   5.3900575228540235e-02   4.3842909905091793e-02   4.3787096228404321e-02   4.3810217969351306e-02   4.3965602941465516e-02   4.3728006830970591e-02   4.3829463585995557e-02   4.3739996433735086e-02   4.4875618525698040e-02   4.5404905739216156e-02   4.4686990821852936e-02   4.3117071478979939e-02   4.3232408013919518e-02   4.3162294661464685e-02   4.3397615721338580e-02   4.3321272880808732e-02   4.3400914752298118e-02   4.3251111751992609e-02   3.9020856909934419e-02   3.8678524347006596e-02   3.9166416503801614e-02   3.8494522004060797e-02   3.8909574918327368e-02   3.8493229766243905e-02   3.9345834088343253e-02   3.7933457314000628e-02   3.8561093024538036e-02   3.8159346132739705e-02   4.1320449943795662e-02   4.2118601292429635e-02   4.1153962782976020e-02   3.2987317007297776e-02
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end




function [X,W] = get_GaussianLejaPrecomputedKnotsAndWeights150()

    X = [0.0000000000000000e+00  -1.4142135748898197e+00   1.7634954600000108e+00  -2.7172574924973860e+00   3.0327561925000208e+00   8.2779559542107051e-01  -3.9576676564800044e+00   4.2949619713000011e+00  -4.9609862341999991e+00  -7.3030308438085823e-01   5.3675997612634099e+00  -5.9509560035030011e+00   2.4251469127200012e+00   6.3935177555790013e+00  -2.1394800128009193e+00  -6.9441467923610025e+00   3.7147090142379455e+00   7.4128451293999973e+00  -3.3947285018989986e+00  -7.8986994327219966e+00   8.2675322184999978e+00   1.2558396405000001e+00  -5.4447580410229959e+00   4.8821990143749971e+00  -8.8799928284190006e+00   9.1872387442765095e+00  -3.7412293910000249e-01  -9.6984413762607176e+00   6.8721436187999991e+00  -4.4306250405784082e+00   1.0117637822427998e+01  -7.4118085362230621e+00   5.8491911028211270e+00  -1.0631852062279998e+01  -1.7727689963000011e+00   1.0972729472599003e+01   2.1105998389000011e+00  -1.1423072778400639e+01   8.7249821217669314e+00  -6.4401496205990822e+00   1.1847676844268751e+01  -8.4470564762002684e+00   4.2495324983998950e-01  -1.2292419113580999e+01   1.2591402334323998e+01   3.3964234697395370e+00  -3.0667182072999983e+00   9.6771589258229973e+00  -1.3051321240600958e+01  -1.0140189807699999e+01   1.3388913500042140e+01   7.7921447774610009e+00  -1.3804202573099220e+01   4.5855965485619983e+00  -4.6970424614352018e+00   1.4139472409180808e+01  -9.2823121089539971e+00   1.1375194185312001e+01  -1.4552659077526458e+01  -1.0732454399990052e+00  -1.1829740751599582e+01   1.4899705707100491e+01   6.1225606343762458e+00  -6.6867078150210046e+00   1.0530958236604999e+01  -1.5341672096399998e+01   2.7258644361999989e+00   1.5648376955799879e+01  -1.1013504314200000e+01  -2.4324589925779980e+00   1.2977943766299997e+01  -1.6078021480200000e+01   7.1449802775168116e+00  -1.3415306327843000e+01   1.6415532401942546e+01  -5.6937186433619962e+00   1.4856568294599879e+00  -1.6826055631315928e+01   1.4501997397999997e+01  -8.1703563030047111e+00   1.7178489291825759e+01  -1.4929123103807997e+01   9.4240374250999501e+00  -3.6847063252999979e+00   1.2200789394400001e+01  -1.7614084157399983e+01   4.0064500610641041e+00   1.7905157506889449e+01  -1.2642778139560777e+01   2.1197572367999573e-01  -1.8303026715328997e+01   1.6013720845612941e+01  -1.0370786098435959e+01   8.0439302635238299e+00   1.8659332407918019e+01  -1.6437088235105001e+01   1.3745127352314999e+01  -7.6329926737000013e+00  -1.9061567791018000e+01   5.1478005434777607e+00   1.9337581976878131e+01  -1.4171865158047000e+01  -1.5921584416000014e+00   1.6817063570180768e+01  -1.9733252414200003e+01   1.0751236476299997e+01  -5.1969936093000006e+00   2.0041628210772704e+01  -1.7241237658278699e+01   1.0281307892603460e+00   1.5250840599499998e+01  -1.2049382894799999e+01  -2.0448220041464999e+01   6.6295978868809975e+00   2.0703319499410814e+01  -9.4822343463379983e+00  -1.5693313684780998e+01   1.8261101227631020e+01   1.1614355439284193e+01  -2.1111229118599489e+01  -4.1774002181999981e+00   2.1384051494303367e+01  -1.8669096901170299e+01   3.2140497883995054e+00   8.9343816986388980e+00  -2.1775033138215598e+01   1.7535981942443062e+01  -8.6725197108872383e+00   2.2036214148848973e+01  -5.5513941072527029e-01  -1.7949167469351998e+01   1.3181579241441998e+01  -1.3607344745261779e+01   1.9679759360147020e+01  -2.2445226777067639e+01   5.6100330980620008e+00  -6.2041645220375718e+00   2.2722885317839332e+01  -2.0080692111796999e+01   9.9181717117000012e+00  -1.1218289553800391e+01   1.8984747241925948e+01  -2.3122848534920998e+01  -2.8907992120999983e+00   2.3364507173755729e+01  -1.5135221630039149e+01   1.4699851505499996e+01  -2.1429240467275697e+01   1.9471744206141079e+00   2.1040061266021286e+01];
    
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