/*! portfolio-allocation - v0.0.10 (2020-09-14), Roman Rubsamen <roman.rubsamen@gmail.com> */
var PortfolioAllocation=PortfolioAllocation||{};PortfolioAllocation=function(y){function k(t){var r={getCorrelationMatrix:function(t){for(var r=_(this.nbRows,this.nbColumns,t),n=0;n<r.nbRows;++n){for(var o=Math.sqrt(this.data[n*this.nbColumns+n]),i=0;i<n;++i)r.data[n*r.nbColumns+i]=r.data[i*this.nbColumns+n];for(i=n+(r.data[n*r.nbColumns+i]=1);i<r.nbColumns;++i){var e=Math.sqrt(this.data[i*this.nbColumns+i]);r.data[n*r.nbColumns+i]=this.data[n*this.nbColumns+i]/(o*e)}}return r},getVariances:function(t){return this.diagonal(t)},getStandardDeviations:function(t){return this.diagonal(t).elemMap(function(t,r,n){return Math.sqrt(n)},t)},standardizedGeneralizedVariance:function(){var t=this.determinant();if(t<0)throw new Error("covariance matrix is not positive semi-definite");return Math.pow(t,1/this.nbRows)}};for(var n in r)t[n]=r[n]}function it(t){function o(t){var r=Object.prototype.toString.call(t);return"[object Array]"===r||"[object Int8Array]"===r||"[object Uint8Array]"===r||"[object Uint8ClampedArray]"===r||"[object Int16Array]"===r||"[object Uint16Array]"===r||"[object Int32Array]"===r||"[object Uint32Array]"===r||"[object Float32Array]"===r||"[object Float64Array]"===r}if(!(this instanceof it))return new it(t);var i=this;if(o(t)&&o(t[0]))return function(t){i=_(t.length,t[0].length);for(var r=0;r<i.nbRows;++r){if(!o(t[r]))throw new Error("unsupported input type");if(t[r].length!==i.nbColumns)throw new Error("unsupported input type");for(var n=0;n<i.nbColumns;++n)i.data[r*i.nbColumns+n]=t[r][n]}return i}(t);if(o(t))return function(t){i=_(t.length,1);for(var r=0;r<i.nbRows;++r)i.data[r*i.nbColumns]=t[r];return i}(t);if(t instanceof it)return function(t){i=_(t.nbRows,t.nbColumns);for(var r=t.nbRows*t.nbColumns,n=0;n<r;++n)i.data[n]=t.data[n];return i}(t);throw new Error("unsupported input type")}function _(t,r,n){var o;if(void 0===n)(o=Object.create(it.prototype)).nbRows=t,o.nbColumns=r,o.data="function"==typeof Float64Array?new Float64Array(o.nbRows*o.nbColumns):new Array(o.nbRows*o.nbColumns);else{if(!(n instanceof it))throw new Error("provided output must be a matrix");if(n.nbRows!==t||n.nbColumns!==r)throw new Error("provided output matrix size does not match expected matrix size: ("+n.nbRows+","+n.nbColumns+") v.s. 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Array(t.length),o=0,i="function"==typeof Uint32Array?new Uint32Array(t.length):new Array(t.length),e=0,a=0;a<t.length;++a)t[a]>r?(i[e]=a,++e):(n[o]=a,++o);for(t=t.slice(0);0<o&&0<e;){a=n[--o];var s=i[--e];this.prob[a]=t.length*t[a],t[this.alias[a]=s]=t[s]+(t[a]-r),t[s]>r?(i[e]=s,++e):(n[o]=s,++o)}for(;0<o;)--o,this.prob[n[o]]=1;for(;0<e;)--e,this.prob[i[e]]=1;this.sample=function(){var t=Math.random()*this.prob.length,r=Math.floor(t);return t-r<=this.prob[r]?r:this.alias[r]}}function o(t,r,n){this.n=t,this.k=r,this.reuseOutputArray=n,this.firstcall=!0,this.mtc=!1,this.r="function"==typeof Uint32Array?new Uint32Array(r):new Array(r),this.t=this.n,this.h=0,this.next=function(){if(!this.firstcall&&!this.mtc)return-1;if(this.firstcall){this.firstcall=!1,this.r[0]=this.n;for(var t=1;t<=this.k-1;++t)this.r[t]=0}else 1<this.t&&(this.h=0),++this.h,this.t=this.r[this.h-1],this.r[this.h-1]=0,this.r[0]=this.t-1,++this.r[this.h];return 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t=1;t<=this.h;++t)this.a[this.k+t-this.h-1]=this.m2+t;return this.mtc=this.a[0]!=this.endval,this.useArrayCopy?this.a.slice(0):this.a}}function C(t,r,n){function d(){for(var t=Math.random();0===t;)t=Math.random();return t}this.n=t,this.k=r,this.useArrayCopy=n,this.a="function"==typeof Uint32Array?new Uint32Array(r):new Array(r),this.N,this.nn,this.idx_a,this.selected_record,this.method_a=function(){for(var t=this.N-this.nn;2<=this.nn;){for(var r=d(),n=0,o=t/this.N;r<o;)++n,--t,--this.N,o=o*t/this.N;this.selected_record+=n+1,this.a[this.idx_a++]=this.selected_record,--this.N,--this.nn}(n=Math.floor(this.N*d()))===this.N&&(n=this.N-1),this.selected_record+=n+1,this.a[this.idx_a++]=this.selected_record},this.method_d=function(){for(var t=1/this.nn,r=Math.pow(d(),t),n=1-this.nn+this.N,o=13*this.nn;1<this.nn&&o<this.N;){for(var i,e,a=1/(-1+this.nn);;){for(;i=this.N*(1-r),!((e=Math.floor(i))<n);)r=Math.pow(d(),t);var s=d(),u=Math.pow(s*this.N/n,a);if((r=u*(-i/this.N+1)*(n/(-e+n)))<=1)break;var l,f,h=1,m=-1+this.N;f=-1+this.nn>e?(l=-this.nn+this.N,-e+this.N):(l=-1-e+this.N,n);for(var c=-1+this.N;f<=c;--c)h=h*m/l,--m,--l;if(this.N/(-i+this.N)>=u*Math.pow(h,a)){r=Math.pow(d(),a);break}r=Math.pow(d(),t)}this.selected_record+=e+1,this.a[this.idx_a++]=this.selected_record,this.N=-e+(-1+this.N),--this.nn,t=a,n=-e+n,o+=-13}1<this.nn?this.method_a():((e=Math.floor(this.N*r))===this.N&&(e=this.N-1),this.selected_record+=e+1,this.a[this.idx_a++]=this.selected_record)},this.next=function(){for(var t=0;t<this.k;++t)this.a[t]=0;return this.N=this.n,this.nn=this.k,this.idx_a=0,this.selected_record=0,this.method_d(),this.useArrayCopy?this.a.slice(0):this.a}}function g(t){this.n=t,this.firstcall=!0,this.mtc=!1,this.iin="function"==typeof Uint32Array?new Uint32Array(t):new Array(t),this.ncard=0,this.next=function(){var t=[];if(!this.firstcall&&!this.mtc)return-1;if(this.firstcall){this.firstcall=!1;for(var 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o=t;n||(o=t.slice(0).sort(function(t,r){return t-r}));var i=r*(t.length-1),e=Math.floor(i);return e==i?o[e]:o[e]+(o[e+1]-o[e])*(i-e)}function M(t,r,n,o){if(this.n=t,this.x="function"==typeof Float64Array?new Float64Array(t):new Array(t),this.reuseOutputArray=o,this.l=r,!this.l){this.l="function"==typeof Float64Array?new Float64Array(this.n):new Array(this.n);for(var i=0;i<this.n;++i)this.l[i]=0}if(this.u=n,!this.u){this.u="function"==typeof Float64Array?new Float64Array(this.n):new Array(this.n);for(i=0;i<this.n;++i)this.u[i]=1}for(i=0;i<this.n;++i)if(this.l[i]>this.u[i])throw new Error("empty box detected: lower bound strictly greater than upper bound");this.sample=function(){for(var t=0;t<this.n;++t)this.x[t]=Math.random()*(this.u[t]-this.l[t])+this.l[t];return this.reuseOutputArray?this.x:this.x.slice(0)}}function W(t,r){r=r||function(t,r){return t-r};for(var n=t.length,o=t[0],i=0,e=1;e<n;++e)0<r(t[e],o)&&(o=t[e],i=e);return[o,i]}function B(t,r,n){n=n||function(t,r){return t-r};var 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i=t*(t<0?1-r/2:1+r);i===t&&(i=0<o*r?t+o*r:t+o),i===1/0&&(i=+n);var e=t+(i-t)/2;t<e&&e<i&&(i=e);var a=(i+t)/2;return t<a&&a<i&&(i=a),0===i?-0:i}function A(t,r){var n=0,o=Math.abs(t),i=Math.abs(r);return n=i<o?(n=r/t,o*Math.sqrt(1+n*n)):0!=r?(n=t/r,i*Math.sqrt(1+n*n)):0}function I(t){for(var r,n=t.length,o=0,i=0;i<n;++i)o+=t[i];r=o/n;var e=0;for(i=0;i<n;++i)e+=t[i]-r;return(o+e)/n}function n(t){for(var r=t.length,n=I(t),o=0,i=0,e=0;e<r;++e){var a=t[e]-n;o+=a*a,i+=a}return(o-i*i/r)/r}function d(t){return Math.sqrt(function(t){var r=t.length;return n(t)*r/(r-1)}(t))}function w(t){var r=t,n=0,o=t,i=t*t,e=1;if(t<-8)return 0;if(8<t)return 1;for(;r!=n;)r=(n=r)+(o*=i/(e+=2));return.5+r*Math.exp(-.5*i-.9189385332046728)}function b(t,r){null==t&&(t=0),null==r&&(r=1);for(var n=Math.random();0===n;)n=Math.random();return t+r*function(t){if(t<=0||1<=t){if(0==t)return-1/0;if(1==t)return 1/0;throw"The probality p must be bigger than 0 and smaller than 1"}var r,n=t-.5;if(Math.abs(n)<=.425){r=n*(((((((2509.0809287301227*(o=.180625-n*n)+33430.57558358813)*o+67265.7709270087)*o+45921.95393154987)*o+13731.69376550946)*o+1971.5909503065513)*o+133.14166789178438)*o+3.3871328727963665)/(((((((5226.495278852854*o+28729.085735721943)*o+39307.89580009271)*o+21213.794301586597)*o+5394.196021424751)*o+687.1870074920579)*o+42.31333070160091)*o+1)}else{var o;if(o=n<0?t:1-t,(o=Math.sqrt(-Math.log(o)))<=5)r=(((((((.0007745450142783414*(o-=1.6)+.022723844989269184)*o+.2417807251774506)*o+1.2704582524523684)*o+3.6478483247632045)*o+5.769497221460691)*o+4.630337846156546)*o+1.4234371107496835)/(((((((1.0507500716444169e-9*o+.0005475938084995345)*o+.015198666563616457)*o+.14810397642748008)*o+.6897673349851)*o+1.6763848301838038)*o+2.053191626637759)*o+1);else 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p[i-1]=0,p}(t,r,a,e,o),u=r,l=t(u),f=l.f_x,h=l.f_x_context,m=u,c=f,d=0;d<o;++d)for(var w=0;w<i;++w){var p=v(u.slice(),a),b=p.xx,y=t(b,{x_c:u,f_x_c:f,f_x_c_context:h,x_c_updatedIndexes:p.x_updated_indexes}),g=y.f_x,x=y.f_x_context;g-f<s[d]&&(u=b,f=g,h=x),g<c&&(c=g,m=b)}return[m,c]}function L(t,r,n,o){void 0===o&&(o={});var i=o.maxIter;void 0===i&&(i=45);var e=o.eps;void 0===e&&(e=1e-6);var a=o.outputInterval;void 0===a&&(a=!1);var s,u,l=t(r),f=t(n);if(n<=r)throw new Error("bracketing interval lower bound "+r+" greater than bracketing interval upper bound "+n);if(0==l)return a?[r,r+e]:r;if(0==f)return a?[n-e,n]:n;if(0<l*f)throw new Error("interval ["+r+","+n+"] is not a bracketing interval");u=l<=0?n-(s=r):r-(s=n);for(var h=0;;){if(-1!==i&&i<h)throw new Error("maximum number of iterations reached: "+i);++h;var m=s+(u/=2),c=t(m);if(c<=0&&(s=m),Math.abs(u)<=e||0==c)return a?[Math.max(r,s-e/2),Math.min(n,s+e/2)]:s}}function O(r,t,n,i,o,e){function a(t){return r(t)+n(t)}function s(t,r,n){var o=it.axpby(1,r,-t,n);return[o,it.copy(i(o,t))]}void 0===e&&(e={});for(var u,l,f,h,m,c,d,w,p,v,b,y,g,x,C,R,E=e.eps||1e-4,M=e.maxIter||1e4,A=e.maxLine||100,P=e.beta||.5,z=e.alphaMin||1e-10,k=e.alphaMax||1e10,_=e.restartPeriod||1e3,I=o.nbRows,V=1e-12,F=.5,O=z,T=it.zeros(I,1),S=it.zeros(I,1),N=it.zeros(I,1),W=it.zeros(I,1),q=it.zeros(I,1),B=!0,L=0;;){if(-1!==M&&M<L)throw new Error("maximum number of iterations reached: "+M);++L%_==0&&(o=m,B=!0),!0===B&&(u=0,f=l=1,h=null,new it(c=new it(m=new it(o))),d=it.zeros(I,1),T=it.copy(t(m),T),S=it.copy(T,S),N=it.copy(S,N),w=it.zeros(I,1),W=it.copy(m,W),q=it.copy(T,q),B=!1);for(var U=O,D=s(U,W,q),G=D[0],H=D[1],j=0;a(H)>(p=U,v=H,y=q,x=void 0,g=r(b=W),x=it.xmy(v,b),C=x.vectorNorm("two"),R=n(v),g+it.vectorDotProduct(x,y)+1/(2*p)*C*C+R+V);){if(-1!==A&&A<j)throw new Error("maximum number of line searches reached: "+A+" at iteration: "+L);++j,U*=P,f/=P,l=(1+Math.sqrt(1+4*f*u*u))/2,G=(D=s(U,W=it.axpby(1,c,(u-1)/l,d,W),q=it.axpby(1,S,(u-1)/l,w,q)))[0],H=D[1]}T=it.copy(t(m=H),T);var Y=it.xmy(m,c),K=it.xmy(T,S),Z=it.vectorDotProduct(Y,Y),J=Math.max(it.vectorDotProduct(K,K),V),Q=it.vectorDotProduct(Y,K);if(Q<=V)mu_kp_0=k;else{var X=Math.max(z,Math.min(Z/Q,k)),$=Math.max(z,Math.min(Q/J,k));$/X<=F?(mu_kp_0=$,F*=.9):(mu_kp_0=X,F*=1.1)}h=U/mu_kp_0;var tt=(1+Math.sqrt(1+4*h*l*l))/2,rt=it.axpby(1,m,(l-1)/tt,Y),nt=it.axpby(1,T,(l-1)/tt,K),ot=it.axpby(1/U,G,-1/U,m);if(it.xpy(T,ot).vectorNorm("infinity")<=E)break;V<=it.vectorDotProduct(it.xmy(W,m),Y)&&(o=m,B=!0),O=mu_kp_0,c,c=m,d=Y,N=it.copy(S,N),S=it.copy(T,S),w=K,W=it.copy(rt,W),q=it.copy(nt,q),f=h,u=l,l=tt}return[m,a(m)]}function U(a,s,u,t,l,f,r){function n(t,r){return t instanceof Array?(t.length=r,t):t instanceof Float64Array||t instanceof Int32Array?t.subarray(0,r):void 0}function o(t){for(var r=v-t*b+y,n=new p.iterator,o=n.next();0!=o;){var i,e=o-1;t<=w[e]?i=f.data[e]:w[e]<=t&&t<=d[e]?i=(s.data[e]-t*u.data[e])/a.data[e]:d[e]<=t&&(i=l.data[e]),r+=u.data[e]*i,o=n.next()}return r}void 0===r&&(r={});var i=r.eps||1e-16,e=r.outputLagrangeMultiplier;if(!(a instanceof it&&a.isVector()))throw new Error("first input must be a vector");if(!(s instanceof it&&s.isVector()))throw new Error("second input must be a vector");if(!(u instanceof it&&u.isVector()))throw new Error("third input must be a vector");if(!(l instanceof it&&l.isVector()))throw new Error("fifth input must be a vector");if(!(f instanceof it&&f.isVector()))throw new Error("sixth input must be a vector");if(a.nbRows!==s.nbRows)throw new Error("first and second inputs number of rows do not match: "+a.nbRows+"-"+s.nbRows);if(a.nbRows!==u.nbRows)throw new Error("first and third inputs number of rows do not match: "+a.nbRows+"-"+u.nbRows);if(a.nbRows!==l.nbRows)throw new Error("first and fifth inputs number of rows do not match: "+a.nbRows+"-"+l.nbRows);if(a.nbRows!==f.nbRows)throw new Error("first and sixth inputs number of rows do not match: "+a.nbRows+"-"+f.nbRows);for(var h=u.nbRows,m=Math.abs(t),c="function"==typeof Float64Array?new Float64Array(2*h):new Array(2*h),d="function"==typeof Float64Array?new Float64Array(h):new Array(h),w="function"==typeof Float64Array?new Float64Array(h):new Array(h),p=(new nt).setRange(1,h),v=0,b=0,y=0,g=1/0,x=-1/0,C=0,R=0;C<h;++C){if(l.data[C]>f.data[C])throw new Error("infeasible problem detected");if(u.data[C]<=0)throw new Error("negative element detected in b");if(a.data[C]<=0)throw new Error("negative element detected in d");var E=(s.data[C]-l.data[C]*a.data[C])/u.data[C];d[C]=E,c[R++]=E;var M=(s.data[C]-f.data[C]*a.data[C])/u.data[C];w[C]=M,x<E&&(x=E),(c[R++]=M)<g&&(g=M)}var A=o(g),P=o(x);if(A<t||t<P)throw new Error("infeasible problem detected");var z=null;if(Math.abs(A-t)<=i*m)z=g;else if(Math.abs(A-t)<=i*m)z=x;else{for(var k=g,_=x;0!=c.length;){var I=Math.ceil(c.length/2),V=B(c,I),F=o(V);if(Math.abs(F-t)<=i*m){z=V;break}if(t<F){k=V;for(R=0,C=I;C<c.length;++C)c[R++]=c[C];c=n(c,R)}else F<t&&(_=V,c=n(c,I-1));for(var O=new p.iterator,T=O.next();0!=T;){var S=!1;if(d[C=T-1]<=k&&(y+=u.data[C]*l.data[C],S=!0),_<=w[C]&&(y+=u.data[C]*f.data[C],S=!0),w[C]<=k&&_<=d[C]){var N=u.data[C]/a.data[C];v+=s.data[C]*N,b+=u.data[C]*N,S=!0}!0===S&&p.unset(C+1),T=O.next()}}0==c.length&&(z=(v+y-t)/b)}var W=function(){for(var t=it.zeros(h,1),r=0;r<h;++r){var n;z<=w[r]?n=f.data[r]:w[r]<=z&&z<=d[r]?n=(s.data[r]-z*u.data[r])/a.data[r]:d[r]<=z&&(n=l.data[r]),t.data[r]=n}return t}(),q=.5*it.vectorDotProduct(W,it.elementwiseProduct(W,a))-it.vectorDotProduct(s,W);return!0===e?[W,q,z]:[W,q]}function T(t,r,n,o,i,e,s){void 0===s&&(s={});var u=s.eps;null==u&&(u=1e-4);var l=s.maxIter;null==l&&(l=1e4);var f=s.antiCycling;null==f&&(f=!1);var h=s.x0;if(!(t instanceof it&&t.isSquare()))throw new Error("first input must be a square matrix");if(!(r instanceof it&&r.isVector()))throw new Error("second input must be a vector");if(!(n instanceof it&&n.isVector()))throw new Error("third input must be a vector");if(!(i instanceof it&&i.isVector()))throw new Error("fifth input must be a vector");if(!(e instanceof it&&e.isVector()))throw new Error("sixth input must be a vector");if(t.nbRows!==r.nbRows)throw new Error("first and second inputs number of rows do not match: "+t.nbRows+"-"+a.nbRows);if(t.nbRows!==n.nbRows)throw new Error("first and third inputs number of rows do not match: "+t.nbRows+"-"+n.nbRows);if(t.nbRows!==i.nbRows)throw new Error("first and fifth inputs number of rows do not match: "+t.nbRows+"-"+i.nbRows);if(t.nbRows!==e.nbRows)throw new Error("first and sixth inputs number of rows do not match: "+t.nbRows+"-"+e.nbRows);var m,c=t.nbRows;if(null==h){var d=it.fill(c,1,function(t,r){return o/c*1/n.data[t-1]});m=U(it.ones(c,1),d,n,o,i,e)[0]}else m=new it(h);for(var w=it.xpy(it.xy(t,m),r),p=1==f?new q(c,void 0,!0):void 0,v=0;;){if(-1!==l&&l<=v)throw new Error("maximum number of iterations reached: "+l);++v;var b,y=-1,g=-1/0,x=-1,C=1/0;1==f&&(b=p.next());for(var R=0;R<c;++R){var E=R;1==f&&(E=b[R]-1),F_i=w.data[E]/n.data[E],i.data[E]<m.data[E]&&m.data[E]<e.data[E]?(F_i>g&&(g=F_i,y=E),F_i<C&&(C=F_i,x=E)):m.data[E]==i.data[E]?F_i<C&&(C=F_i,x=E):m.data[E]==e.data[E]&&F_i>g&&(g=F_i,y=E)}if(g-C<=u)break;E=x,R=y;var M,A=(i.data[E]-m.data[E])*n.data[E],P=(m.data[R]-e.data[R])*n.data[R],z=P<=A?A:P,k=(e.data[E]-m.data[E])*n.data[E],_=(m.data[R]-i.data[R])*n.data[R],I=k<=_?k:_,V=C-g,F=t.data[E*t.nbColumns+E]/(n.data[E]*n.data[E])+t.data[R*t.nbColumns+R]/(n.data[R]*n.data[R])-2*t.data[E*t.nbColumns+R]/(n.data[E]*n.data[R]);if(0<F)I<(M=-V/F)?M=I:M<z&&(M=z);else{if(0!=F)throw new Error("internal error: the input matrix might not be positive semi-definite");M=0<V?z:I}var O=m.data[E],T=m.data[R],S=M/n.data[E],N=-M/n.data[R];m.data[E]+=S,m.data[R]+=N,M==z&&(z==A&&(m.data[E]=i.data[E],S=m.data[E]-O),z==P&&(m.data[R]=e.data[R],N=m.data[R]-T)),M==I&&(I==k&&(m.data[E]=e.data[E],S=m.data[E]-O),I==_&&(m.data[R]=i.data[R],N=m.data[R]-T));for(var W=0;W<c;++W)w.data[W]=w.data[W]+t.data[W*t.nbColumns+E]*S+t.data[W*t.nbColumns+R]*N}return[m,.5*it.vectorDotProduct(m,it.xy(t,m))+it.vectorDotProduct(r,m)]}function ot(n,t,r){var o=(n=new it(n)).nbRows;t=t?new it(t):it.zeros(o,1),r=r?new it(r):it.ones(o,1);G(o,t.toArray(),r.toArray());for(var i="function"==typeof Uint32Array?new Uint32Array(o):new Array(o),e=0;e<o;++e)i[e]=e+1;i.sort(function(t,r){return n.getValue(t,1)-n.getValue(r,1)});for(var a=new it(t),s=1-a.sum(),u=-1,l=0;l<o&&!(Math.abs(s)<=1e-16);++l){u=i[l];var f=a.getValue(u,1);s>=r.getValue(u,1)-f?(a.setValue(u,1,r.getValue(u,1)),s-=r.getValue(u,1)-f):(a.setValue(u,1,f+s),s=0)}return[a.toArray(),it.vectorDotProduct(n,a)]}function S(t,r,n){var o=t.length;G(o,r,n);for(var i=0,e=0;e<o;++e){var a=0;r&&(a=r[e]);var s=1;n&&(s=n[e]);var u=t[e];if(u<a||s<u)return Number.POSITIVE_INFINITY;i+=u}return 1e-12<Math.abs(i-1)?Number.POSITIVE_INFINITY:0}function D(t,r,n){for(var o=0,i=0,e=0;e<t;++e){var a=0;r&&(a=r[e]);var s=1;if(n&&(s=n[e]),s<a)throw new Error("infeasible problem detected: lower bound strictly greater than upper bound");if(a<0)throw new Error("incorrect problem detected: lower bound strictly lower than 0");if(1<s)throw new Error("incorrect problem detected: upper bound strictly greater than 1");o+=a,i+=s}if(1<o)throw new Error("infeasible problem detected: the restricted simplex is empty");return[o,i]}function G(t,r,n){for(var o=0,i=0,e=0;e<t;++e){var a=0;r&&(a=r[e]);var s=1;if(n&&(s=n[e]),s<a)throw new Error("infeasible problem detected: lower bound strictly greater than upper bound");if(a<0)throw new Error("incorrect problem detected: lower bound strictly lower than 0");if(1<s)throw new Error("incorrect problem detected: upper bound strictly greater than 1");o+=a,i+=s}if(1<o||i<1)throw new Error("infeasible problem detected: the restricted simplex is empty");return[o,i]}function H(t,r,n){var o=t.length;G(o,r,n);for(var i=it.ones(o,1),e=new it(t),a=it.ones(o,1),s=r?new it(r):it.zeros(o,1),u=n?new it(n):it.ones(o,1),l=U(i,e,a,1,s,u),f=l[0].toArray();S(f,r,n)==Number.POSITIVE_INFINITY;)f=(l=U(i,e=new it(f),a,1,s,u))[0].toArray();return f}function Y(t,r,n){this.n=t,this.k=r,this.reuseOutputArray=n,this.x="function"==typeof Float64Array?new Float64Array(t):new Array(t),this.compositionIterator=new o(r,t,!0),this.sample=function(){var t=this.compositionIterator.next();if(-1==t)return-1;for(var r=0;r<this.n;++r)this.x[r]=t[r]/this.k;return this.reuseOutputArray?this.x:this.x.slice(0)}}function K(l,t,r,n){if(this.n=l,this.x="function"==typeof Float64Array?new Float64Array(l):new Array(l),this.u="function"==typeof Float64Array?new Float64Array(l-1):new Array(l-1),this.randomGenerator=function(t){for(var r=0;r<this.n;++r)t[r]=Math.random()},n){if("function"!=typeof n)throw new Error("the random number generator must be a function");this.randomGenerator=n}if(t&&(this.lowerBounds=t,!r)){this.upperBounds="function"==typeof Float64Array?new Float64Array(l):new Array(l);for(var o=0;o<this.n;++o)this.upperBounds[o]=1}if(r&&(this.upperBounds=r,!t)){this.lowerBounds="function"==typeof Float64Array?new Float64Array(l):new Array(l);for(o=0;o<this.n;++o)this.lowerBounds[o]=0}if(this.lowerBounds||this.upperBounds){var i=G(l,this.lowerBounds,this.upperBounds);if(this.sumLowerBounds=i[0],this.sumUpperBounds=i[1],1==this.sumLowerBounds||1==this.sumUpperBounds);else{var e=0,a=0;for(o=0;o<this.n;++o){var s=this.lowerBounds[o],u=this.upperBounds[o],f=Math.max(s,u+1-this.sumUpperBounds),h=Math.min(u,s+1-this.sumLowerBounds);e+=this.lowerBounds[o]=f,a+=this.upperBounds[o]=h}this.sumLowerBounds=e,this.sumUpperBounds=a,this.upperStarBounds="function"==typeof Float64Array?new Float64Array(l):new Array(l),this.runningSumUpperStarBounds="function"==typeof Float64Array?new Float64Array(l):new Array(l);var m=0;for(o=0;o<this.n;++o)this.upperStarBounds[o]=(this.upperBounds[o]-this.lowerBounds[o])/(1-this.sumLowerBounds),m+=this.upperStarBounds[o],this.runningSumUpperStarBounds[o]=m}}this.sample_no_bounds=function(){for(var t=0,r=0;r<this.n;++r){var n=1-Math.random(),o=Math.log(n);t+=this.x[r]=o}for(r=0;r<this.n;++r)this.x[r]=this.x[r]/t;return this.x.slice(0)},this.sample_binding_bounds=function(){var t=null;if(1==this.sumLowerBounds)t=this.lowerBounds;else{if(1!=this.sumUpperBounds)throw new Error("internal error");t=this.upperBounds}for(var r=0;r<this.n;++r)this.x[r]=t[r];return this.x.slice(0)},this.sample_with_bounds=function(){this.randomGenerator(this.u);for(var t=this.u,r=1,n=l;2<=n;--n){if(Math.abs(r)<=1e-14){for(var o=n;1<=o;--o)this.x[o-1]=0;break}var i=t[n-2],e=Math.max(0,1-this.runningSumUpperStarBounds[n-2]/r),a=Math.min(1,this.upperStarBounds[n-1]/r),s=r*(1-Math.pow(i*Math.pow(1-a,n-1)+(1-i)*Math.pow(1-e,n-1),1/(n-1)));r-=this.x[n-1]=s}1==n&&(this.x[0]=r);for(var u=0;u<this.n;++u)this.x[u]=(1-this.sumLowerBounds)*this.x[u]+this.lowerBounds[u];return this.x.slice(0)},this.lowerBounds||this.upperBounds?1==this.sumLowerBounds||1==this.sumUpperBounds?this.sample=this.sample_binding_bounds:this.sample=this.sample_with_bounds:this.sample=this.sample_no_bounds}function Z(t,r,n){if(e.call(this,t,r,n),this.cornerPortfolios=function(t,n,r,o,i,e){var a=1e-8;function w(t){this.STATUS_UNDEF=-1,this.STATUS_IN=0,this.STATUS_LOW=1,this.STATUS_UP=2,this.nbAssets=t,this.varIn=new nt,this.varIn.resize(t),this.varLow=new nt,this.varLow.resize(t),this.varUp=new nt,this.varUp.resize(t),this.setIn=function(t){this.varIn.set(t),this.varLow.unset(t),this.varUp.unset(t)},this.setOnLowerBound=function(t){this.varLow.set(t),this.varIn.unset(t),this.varUp.unset(t)},this.setOnUpperBound=function(t){this.varUp.set(t),this.varIn.unset(t),this.varLow.unset(t)},this.isIn=function(t){return this.varIn.get(t)},this.isOnLowerBound=function(t){return this.varLow.get(t)},this.isOnUpperBound=function(t){return this.varUp.get(t)},this.isOut=function(t){return this.varLow.get(t)||this.varUp.get(t)},this.getInIndexes=function(){return this.varIn.toArray()},this.getOutIndexes=function(){return this.varLow.toArray().concat(this.varUp.toArray())}}function s(n,t,r,o,i){for(var e=t.nbRows,a="function"==typeof Uint32Array?new Uint32Array(e):new Array(e),s=0;s<e;++s)a[s]=s+1;a.sort(function(t,r){return n.getValue(r,1)-n.getValue(t,1)});for(var u,l=!0,f=1;f<e;++f)if(n.getValue(a[f],1)==n.getValue(a[f-1],1)){l=!1;break}1==l?u=new it(ot(n.elemMap(function(t,r,n){return-n}),r,o)[0]):u=new et(n,t,{optimizationMethodParams:{antiCyclingGsmo:!0,maximumRiskToleranceValueOnlyGsmo:!0,maxIterGsmo:-1},constraints:{minWeights:r,maxWeights:o}}).getHighestReturnPortfolio();var h=0,m=0,c=0,d=new w(e);for(f=1;f<=e;++f)Math.abs(u.getValue(f,1)-r.getValue(f,1))<=i?(d.setOnLowerBound(f),++m):Math.abs(u.getValue(f,1)-o.getValue(f,1))<=i&&o.getValue(f,1)<1-i?(d.setOnUpperBound(f),++c):(d.setIn(f),++h);return{weights:u,variablesStatusManager:d,nbAssetsLow:m,nbAssetsIn:h,nbAssetsUp:c}}void 0===e&&(e={constraints:{}});void 0===e.optimizationMethodParams&&(e.optimizationMethodParams={});var u=e.optimizationMethodParams.maxIterCriticalLine;null==u&&(u=1e3);var l=n.nbColumns,f=r,h=o,m=[],c=it.ones(1,l),d=c.nbRows,p=it.ones(1,1),v=it.fill(l,l+d,function(t,r){return r<=l?n.data[(t-1)*n.nbColumns+(r-1)]:c.data[(r-l-1)*c.nbColumns+(t-1)]}),b=s(t,n,f,h,i),y=b.weights,g=b.variablesStatusManager;{if(b.nbAssetsLow==l||b.nbAssetsUp==l){var x=new it(y);return m.push([x,0]),m}if(0==b.nbAssetsIn){var C=h.elemMap(function(t,r,n){return Math.min(n+1e-8,1)}),R=s(t,n,f,C,i);if(g=R.variablesStatusManager,0==R.nbAssetsIn)throw new Error("internal error: impossible to determine the IN variables associated to the maximum return portfolio")}}var E=0;for(;;){if(-1!==u&&u<=E)throw new Error("maximum number of iterations reached: "+u);++E;var M=g.getInIndexes(),A=g.getOutIndexes(),P=it.fill(l+d,l+d,function(t,r){return t<=l&&r<=l?g.isIn(t)?n.data[(t-1)*n.nbColumns+(r-1)]:t==r?1:0:l+1<=t&&r<=l?g.isIn(r)?c.data[(t-l-1)*c.nbColumns+(r-1)]:0:t<=l&&l+1<=r&&g.isIn(t)?c.data[(r-l-1)*c.nbColumns+(t-1)]:0}),z=it.fill(l,1,function(t,r){return g.isOnUpperBound(t)?h.data[t-1]:g.isOnLowerBound(t)?f.data[t-1]:0}),k=it.xy(c,z),_=it.fill(l+d,1,function(t,r){return t<=l?z.data[t-1]:p.data[t-l-1]-k.data[t-l-1]}),I=t.elemMap(function(t,r,n){return g.isIn(t)?n:0}),V=it.fill(l+d,1,function(t,r){return t<=l?I.data[t-1]:0});try{var F=it.luDecomposition(P),O=(F.lowerTriangular,F.upperTriangular,F.rowPermutation,F.columnPermutation,it.linsolveForwardSubstitution(F.lowerTriangular,it.xy(F.rowPermutation,_))),T=it.linsolveBackSubstitution(F.upperTriangular,O),S=it.xy(F.columnPermutation,T);O=it.linsolveForwardSubstitution(F.lowerTriangular,it.xy(F.rowPermutation,V)),T=it.linsolveBackSubstitution(F.upperTriangular,O);var N=it.xy(F.columnPermutation,T)}catch(t){throw new Error("internal error: impossible to solve the KKT system")}for(var W=it.xy(v,S),q=it.xmy(it.xy(v,N),t),B=-1,L=0,U=g.STATUS_UNDEF,D=1;D<=M.length;++D){var G=M[D-1],H=S.data[G-1],j=N.data[G-1];if(a<j){var Y=f.data[G-1];L<=(K=(Y-H)/j)&&(B=G,L=K,U=g.STATUS_LOW)}else if(j<-a){var K,Z=h.data[G-1];L<=(K=(Z-H)/j)&&(B=G,L=K,U=g.STATUS_UP)}}var J=-1,Q=0;for(D=1;D<=A.length;++D){var X=A[D-1],$=W.data[X-1],tt=q.data[X-1];if(g.isOnLowerBound(X)){if(a<tt)Q<=(rt=-$/tt)&&(J=X,Q=rt)}else{if(!g.isOnUpperBound(X))throw new Error("internal error: OUT variable neither on its lower of upper bound");var rt;tt<-a&&Q<=(rt=-$/tt)&&(J=X,Q=rt)}}lambda_e=Math.max(L,Q,0);x=it.fill(l,1,function(t,r){if(t<=l){var n=S.data[t-1]+lambda_e*N.data[t-1],o=f.data[t-1],i=h.data[t-1];return Math.max(Math.min(n,i),o)}});if(m.push([x,lambda_e]),lambda_e<a)break;Q<=L?U==g.STATUS_LOW?g.setOnLowerBound(B):g.setOnUpperBound(B):g.setIn(J)}return m}(this.mu,this.sigma,this.lowerBounds,this.upperBounds,this.epsBounds,n),0==this.cornerPortfolios.length)throw new Error("internal error: no corner portfolio could be computed")}function et(t,r,n){if(e.call(this,t,r,n),void 0===n&&(n={constraints:{}}),void 0===n.optimizationMethodParams&&(n.optimizationMethodParams={}),this.epsGsmo=n.optimizationMethodParams.epsGsmo,null==this.epsGsmo&&(this.epsGsmo=1e-6),this.maxIterationsGsmo=n.optimizationMethodParams.maxIterGsmo,null==this.maxIterationsGsmo&&(this.maxIterationsGsmo=1e4),this.antiCyclingGsmo=n.optimizationMethodParams.antiCyclingGsmo,null==this.antiCyclingGsmo&&(this.antiCyclingGsmo=!1),this.maximumRiskToleranceValueOnly=n.optimizationMethodParams.maximumRiskToleranceValueOnlyGsmo,null==this.maximumRiskToleranceValueOnly&&(this.maximumRiskToleranceValueOnly=!1),this.minimumRiskToleranceValueOnly=n.optimizationMethodParams.minimumRiskToleranceValueOnlyGsmo,null==this.minimumRiskToleranceValueOnly&&(this.minimumRiskToleranceValueOnly=!1),1==this.maximumRiskToleranceValueOnly&&1==this.minimumRiskToleranceValueOnly)throw new Error("internal error: inconsistent minimum/maximum risk tolerance values computation");if(this.cachedEfficientPortfolios=new Map,0==this.minimumRiskToleranceValueOnly){var o=function(){var t,n=this.nbAssets,r=this.mu,o=this.sigma,i=this.lowerBounds,e=this.upperBounds,a=-ot(r.elemMap(function(t,r,n){return-n}),i,e)[1],s=o,u=it.ones(n,1),l=i,f=e,h=it.fill(n,1,function(t,r){return 1/n}),m=U(it.ones(n,1),h,u,1,l,f)[0],c=0,d=32;do{if(54<++c)throw new Error("internal error: maximum number of iterations reached when searching for the efficient portfolio with maximum return");var w=it.ax(-(d*=2),r),p=T(s,w,u,1,l,f,{x0:m,antiCycling:this.antiCyclingGsmo,eps:this.epsGsmo,maxIter:this.maxIterationsGsmo});t=p[0];var v=this.computePortfolioReturn(t);this.cachedEfficientPortfolios.set(d,{weights:t,ret:v,volatility:this.computePortfolioVolatility(t)})}while(1e-12<Math.abs(v-a));return[t,d]}.call(this);this.highestRiskTolerance=o[1],this.highestRiskTolerancePortfolio=o[0],this.cachedEfficientPortfolios.set(this.highestRiskTolerance,{weights:this.highestRiskTolerancePortfolio,ret:this.getHighestReturn(),volatility:this.getHighestVolatility()})}if(0==this.maximumRiskToleranceValueOnly){var i=function(){var t,n=this.nbAssets,r=this.mu,o=this.sigma,i=this.lowerBounds,e=this.upperBounds,a=o,s=it.zeros(n,1),u=it.ones(n,1),l=i,f=e,h=it.fill(n,1,function(t,r){return 1/n}),m=U(it.ones(n,1),h,u,1,l,f)[0],c=T(a,s,u,1,l,f,{x0:m,antiCycling:this.antiCyclingGsmo,eps:this.epsGsmo,maxIter:this.maxIterationsGsmo}),d=this.computePortfolioVolatility(c[0]),w=2;do{s=it.ax(-(w/=2),r);var p=T(a,s,u,1,l,f,{x0:m,antiCycling:this.antiCyclingGsmo,eps:this.epsGsmo,maxIter:this.maxIterationsGsmo});t=p[0];var v=this.computePortfolioVolatility(t);this.cachedEfficientPortfolios.set(w,{weights:t,ret:this.computePortfolioReturn(t),volatility:v})}while(1e-12<Math.abs(v-d));return[t,w]}.call(this);this.lowestRiskTolerance=i[1],this.lowestRiskTolerancePortfolio=i[0],this.cachedEfficientPortfolios.set(this.lowestRiskTolerance,{weights:this.lowestRiskTolerancePortfolio,ret:this.getLowestReturn(),volatility:this.getLowestVolatility()})}}function J(r,n,o){this.efficientFrontier=null;try{this.efficientFrontier=new Z(r,n,o),this.efficientFrontierOptimizationMethod="critical-line"}catch(t){if("internal error: impossible to solve the KKT system"!=t.message)throw t;this.efficientFrontier=new et(r,n,o),this.efficientFrontierOptimizationMethod="gsmo"}this.epsPortfolioVolatility=this.efficientFrontier.epsPortfolioVolatility,this.epsEfficientPortfolioComputation=this.efficientFrontier.epsEfficientPortfolioComputation,this.mu=this.efficientFrontier.mu,this.sigma=this.efficientFrontier.sigma,this.nbAssets=this.efficientFrontier.mu.nbRows,this.lowerBounds=this.efficientFrontier.lowerBounds,this.upperBounds=this.efficientFrontier.upperBounds}function e(t,r,n){void 0===n&&(n={constraints:{}}),void 0===n.constraints&&(n.constraints={}),this.epsBounds=1e-14,this.epsPortfolioVolatility=1e-14,this.epsEfficientPortfolioComputation=1e-10,this.mu=new it(t),this.sigma=new it(r),this.nbAssets=this.sigma.nbRows,this.lowerBounds=null==n.constraints.minWeights?it.zeros(this.nbAssets,1):new it(n.constraints.minWeights),this.upperBounds=null==n.constraints.maxWeights?it.ones(this.nbAssets,1):new it(n.constraints.maxWeights);for(var o=1;o<=this.nbAssets;++o){var i=this.lowerBounds.getValue(o,1),e=this.upperBounds.getValue(o,1);i==e&&(this.lowerBounds.setValueAt(o,1,Math.max(0,i-this.epsBounds)),this.upperBounds.setValueAt(o,1,Math.min(1,e+this.epsBounds)))}G(this.nbAssets,this.lowerBounds.toArray(),this.upperBounds.toArray())}return y.randomCorrelationMatrix=function(t,r){return it.randomCorrelation(t,r)},y.nearestCorrelationMatrix=function(t,r){function n(t){if(!t.isSymmetric(a))throw new Error("internal error: input matrix must be symmetric");return t.unitDiagonalize()}function o(t,o){if(!t.isSymmetric(a))throw new Error("internal error: input matrix must be symmetric");var r=it.eig(t,{maxIter:-1,epsSymmetric:a}),n=r[0],i=r[1].elemMap(function(t,r,n){return Math.max(o,n)}),e=it.axty(1,it.elementwiseProduct(n,i.transpose()),n);return e=e.symmetrize({inPlace:!0})}t=new it(t);void 0===r&&(r={});var a=r.epsSymmetric;null==a&&(a=1e-12);var i=r.eps;null==i&&(i=1e-6);var e=r.maxIter;null==e&&(e=100);var s=r.minEigenvalue;if(null==s&&(s=1e-8),!t.isSymmetric(a))throw new Error("input matrix must be symmetric");for(var u=t.nbRows,l=it.copy(t),f=it.copy(t),h=it.zeros(u,u),m=Number.POSITIVE_INFINITY,c=Number.POSITIVE_INFINITY,d=Number.POSITIVE_INFINITY,w=0;;){if(-1!==e&&e<=w)throw new Error("maximum number of iterations reached: "+e);++w;var p=it.xmy(f,h),v=o(p,s),b=it.xmy(v,p),y=n(v);if(m=it.xmy(v,l).vectorNorm("infinity")/l.vectorNorm("infinity"),c=it.xmy(y,f).vectorNorm("infinity")/f.vectorNorm("infinity"),d=it.xmy(y,v).vectorNorm("infinity")/y.vectorNorm("infinity"),l=v,f=y,h=b,0==i){if(f.isCorrelationMatrix())break}else if(Math.max(m,c,d)<=i)break}if(0==i)return f;var g=l.diagonal().elemMap(function(t,r,n){return 1/Math.sqrt(n)});return it.elementwiseProduct(it.elementwiseProduct(l,g),g.transpose()).symmetrize({inPlace:!0}).unitDiagonalize({inPlace:!0})},y.repairCorrelationMatrix=function(t,r){void 0===r&&(r={});var n=r.method;void 0===n&&(n="nearest-correlation-matrix");var o=r.minEigenvalue;null==o&&(o=0);var i=r.epsNcm;null==i&&(i=1e-6);var e=r.epsCorrMat;null==e&&(e=1e-12);var a=r.shrinkageTarget;if("spectral"!=n&&"linear-shrinkage"!=n&&"nearest-correlation-matrix"!=n)throw new Error("unsupported correlation matrix repair method");if(!(t=new it(t)).isSymmetric(e))throw new Error("input matrix must be symmetric");if(!t.isUnitDiagonal(e))throw new Error("input matrix must be unit diagonal");if(o<0||1<o)throw new Error("lower bound on the smallest eigenvalue(s) of the correlation matrix must belong to interval [0,1]");var s,u=t.nbRows;if((d=it.eig(t,{maxIter:-1,epsSymmetric:e,sortedEigenvalues:!0}))[1].data[u-1]>=o)return t;if("spectral"==n){if(0<o)throw new Error("spectral correlation matrix repair is not compatible with a minimum eigenvalue");var l=d[0],f=d[1].elemMap(function(t,r,n){return Math.sqrt(Math.max(0,n))}),h=it.elementwiseProduct(l,f.transpose()),m=it.fill(u,1,function(t,r){return 1/h.vectorNorm("two","row",t)}),c=it.elementwiseProduct(h,m);s=(s=it.axty(1,c,c)).unitDiagonalize()}else if("linear-shrinkage"==n){if(null==a)a=it.identity(u);else{if(!(a=new it(a)).isCorrelationMatrix(e))throw new Error("shrinkage target matrix must be a correlation matrix");var d;if((d=it.eig(a,{maxIter:-1,epsSymmetric:e,sortedEigenvalues:!0}))[1].data[u-1]<o)throw new Error("smallest eigenvalue of the shrinkage target matrix strictly lower than the desired lower bound on the smallest eigenvalue(s) of the correlation matrix")}var w=t,p=a,v=L(function(t){var r=it.axpby(t,p,1-t,w);return it.eig(r,{maxIter:-1,epsSymmetric:e,sortedEigenvalues:!0})[1].data[u-1]-o},0,1,{outputInterval:!0})[1];s=(s=it.axpby(v,p,1-v,w)).symmetrize().unitDiagonalize()}else{if("nearest-correlation-matrix"!=n)throw new Error("internal error: unsupported repair method");s=y.nearestCorrelationMatrix(t,{maxIter:-1,eps:i,minEigenvalue:o})}return s},y.perturbedCorrelationMatrix=function(i,t){void 0===(t=t)&&(t={}),void 0===t.method&&(t.method="additive-noise");var r=t.epsCorrMat;null==r&&(r=1e-12);var n=t.epsNcm;null==n&&(n=1e-6);var o=t.sigma;null==o&&(o=.05);var e=t.noiseLevelMax;null==e&&(e=.01);var a=t.noiseSpaceDimension;null==a&&(a=3);var s=t.method;if("spectral-noise"!=s&&"multiplicative-noise"!=s&&"additive-noise"!=s)throw new Error("unsupported perturbation method");if(!(i=new it(i)).isCorrelationMatrix(r))throw new Error("input matrix must be symmetric, unit diagonal and positive semidefinite");var u,l=i.nbRows;if("spectral-noise"==s){var f=it.eig(i,{maxIter:-1,epsSymmetric:r,sortedEigenvalues:!0}),h=f[0],m=f[1].elemMap(function(t,r,n){return n*Math.exp(o*b(0,1))}),c=it.axty(1,it.elementwiseProduct(h,m.transpose()),h);u=(u=c.elemMap(function(t,r,n){return n/Math.sqrt(c.data[(t-1)*c.nbColumns+(t-1)]*c.data[(r-1)*c.nbColumns+(r-1)])})).symmetrize().unitDiagonalize()}else if("multiplicative-noise"==s)(u=it.fillSymmetric(l,function(t,r){return t==r?1:Math.max(-1,Math.min(1,i.data[(t-1)*i.nbColumns+(r-1)]*(1+o*b(0,1))))})).isCorrelationMatrix()||(u=y.nearestCorrelationMatrix(u,{maxIter:-1,eps:n}));else{if("additive-noise"!=s)throw new Error("internal error: unsupported perturbation method");for(var d=new P(a,!0),w=new Array(l),p=0;p<l;++p)w[p]=new it(d.sample());(u=it.fillSymmetric(l,function(t,r){if(t==r)return 1;var n=i.data[(t-1)*i.nbColumns+(r-1)],o=e*it.vectorDotProduct(w[t-1],w[r-1]);return Math.max(-1,Math.min(1,n+o))})).isCorrelationMatrix()||(u=y.nearestCorrelationMatrix(u,{maxIter:-1,eps:n}))}return u},y.covarianceMatrixFromCovarianceMatrix=function(t){return k(t=new it(t)),t},y.covarianceMatrixFromCorrelationMatrix=function(t,r,n){void 0===(n=n)&&(n={}),void 0===n.diagonalVectorType&&(n.diagonalVectorType="variances");var o=n.diagonalVectorType;if("variances"!=o&&"standard-deviations"!=o)throw new Error("unsupported diagonal vector type");t=new it(t),r=new it(r);if(t.nbRows!=r.nbRows||t.nbColumns!=r.nbRows)throw new Error("input correlation matrix dimensions not compatible with input diagonal vector dimension");var i;t.nbRows;if("variances"==o)i=r.elemMap(function(t,r,n){return Math.sqrt(n)});else{if("standard-deviations"!=o)throw new Error("internal error: unsupported diagonal vector type");i=r}var e=it.elementwiseProduct(it.elementwiseProduct(t,i),i.transpose());return k(e=e.symmetrize()),e},y.covarianceMatrix=function(i,t){void 0===(t=t)&&(t={}),void 0===t.method&&(t.method="covariance");var e=t.assumeZeroMean;null==e&&(e=!0);var r=t.regularizationMethod;if(null==r&&(r="none"),"none"!=r&&"linear-shrinkage"!=r)throw new Error("unsupported covariance matrix regularization method");var n=t.shrinkageTarget;if("linear-shrinkage"==r&&-1==["constant-variance-null-correlation","constant-variance-correlation","null-correlation","constant-correlation"].indexOf(n))throw new Error("unsupported covariance matrix shrinkage target");for(var o,a=i.length,s=i[0].length,u=0;u<a;++u)if(i[u].length!=s)throw new Error("inconsistent input matrix dimensions");if("none"==r){var l=V;0==e&&(l=F),o=_(a,a);for(u=0;u<o.nbRows;++u){for(var f=0;f<u;++f)o.data[u*o.nbColumns+f]=o.data[f*o.nbColumns+u];for(f=u;f<o.nbColumns;++f)o.data[u*o.nbColumns+f]=l(i[u],i[f])}}else{if("linear-shrinkage"!=r)throw new Error("internal error: unsupported covariance matrix regularization method");var h,m,c,d=it.fill(a,1,function(t,r){return I(i[t-1])}),w=it.fill(a,s,function(t,r){return i[t-1][r-1]-d.data[t-1]}),p=(h=1==e?it.axty(1/s,w,w).toCovarianceMatrix():it.axty(1/(s-1),w,w).toCovarianceMatrix()).getStandardDeviations(),v=h.getCorrelationMatrix();if("constant-variance-null-correlation"==n){var b=h.trace()/a;m=it.fill(a,a,function(t,r){return t==r?b:0})}else if("constant-variance-correlation"==n){var y=h.trace()/a,g=0;for(u=0;u<a-1;++u)for(f=u+1;f<a;++f)g+=h.data[u*h.nbColumns+f];g*=2/(a*(a-1)),m=it.fill(a,a,function(t,r){return t==r?y:g})}else if("null-correlation"==n)m=it.fill(a,a,function(t,r){return t==r?p.data[t-1]*p.data[t-1]:0});else if("constant-correlation"==n){for(u=c=0;u<a-1;++u)for(f=u+1;f<a;++f)c+=v.data[u*v.nbColumns+f];c*=2/(a*(a-1)),m=it.fill(a,a,function(t,r){return t==r?p.data[t-1]*p.data[t-1]:c*p.data[t-1]*p.data[r-1]})}var x,C=it.fill(a,a,function(t,r){for(var n=0,o=0;o<s;++o)n+=Math.pow((i[t-1][o]-d.data[t-1])*(i[r-1][o]-d.data[r-1])-h.data[(t-1)*h.nbColumns+(r-1)],2);return n/=1==e?s:s-1}),R=C.sum();if("constant-variance-null-correlation"==n)x=0;else if("constant-variance-correlation"==n)x=0;else if("null-correlation"==n)x=C.trace();else if("constant-correlation"==n){x=0;for(u=1;u<=a;++u)for(f=1;f<=a;++f)if(u!=f){for(var E=0,M=0;M<s;++M)E+=(Math.pow(i[u-1][M]-d.data[u-1],2)-h.data[(u-1)*h.nbColumns+(u-1)])*((i[u-1][M]-d.data[u-1])*(i[f-1][M]-d.data[f-1])-h.data[(u-1)*h.nbColumns+(f-1)]);E/=1==e?s:s-1;var A=0;for(M=0;M<s;++M)A+=(Math.pow(i[f-1][M]-d.data[f-1],2)-h.data[(f-1)*h.nbColumns+(f-1)])*((i[u-1][M]-d.data[u-1])*(i[f-1][M]-d.data[f-1])-h.data[(u-1)*h.nbColumns+(f-1)]);A/=1==e?s:s-1,x+=p.data[f-1]/p.data[u-1]*E+p.data[u-1]/p.data[f-1]*A}x*=c/2,x+=C.trace()}var P,z=(R-x)/Math.pow(it.xmy(h,m).matrixNorm("frobenius"),2);P=1==e?Math.max(0,Math.min(1,z/s)):Math.max(0,Math.min(1,z/(s-1))),o=it.axpby(P,m,1-P,h)}return k(o),o},it.prototype={constructor:it,toString:function(){for(var t=0,r=0;r<this.nbRows;++r)for(var n=0;n<this.nbColumns;++n){var o=String(this.data[r*this.nbColumns+n]).length;t<o&&(t=o)}var i=[];for(r=0;r<this.nbRows;++r){i.push("[ ");for(n=0;n<this.nbColumns;++n){var e=String(this.data[r*this.nbColumns+n]);i.push(new Array(t-e.length+1).join(" ")+e+" ")}i.push("]\n")}return i.join("")},toRowArray:function(t){t=t||function(t,r,n){return!0};for(var r=new Array(this.nbRows),n=0;n<this.nbRows;++n){r[n]=new Array(this.nbColumns);for(var o=0,i=0;i<this.nbColumns;++i){var e=this.data[n*this.nbColumns+i];t(n+1,i+1,e)&&(r[n][o++]=e)}r[n].length=o}return r},toArray:function(t){t=t||function(t,r,n){return!0};for(var r=new Array(this.nbRows*this.nbColumns),n=0,o=0;o<this.nbRows;++o)for(var i=0;i<this.nbColumns;++i){var e=this.data[o*this.nbColumns+i];t(o+1,i+1,e)&&(r[n++]=e)}return r.length=n,r},setValueAt:function(t,r,n){if(t<1||r<1||t>this.nbRows||r>this.nbColumns)throw new Error("index out of bounds when setting matrix value, ("+t+","+r+") in size ("+this.nbRows+","+this.nbColumns+")");return this.data[(t-1)*this.nbColumns+(r-1)]=n,this},setValue:function(t,r,n){return this.data[(t-1)*this.nbColumns+(r-1)]=n,this},getValueAt:function(t,r){if(t<1||r<1||t>this.nbRows||r>this.nbColumns)throw new Error("index out of bounds when getting matrix value, ("+t+","+r+") in size ("+this.nbRows+","+this.nbColumns+")");return this.data[(t-1)*this.nbColumns+(r-1)]},getValue:function(t,r){return this.data[(t-1)*this.nbColumns+(r-1)]},isSquare:function(){return this.nbRows===this.nbColumns},isSymmetric:function(t){if(null==t&&(t=0),!this.isSquare())return!1;for(var r=0;r<this.nbRows;++r)for(var n=0;n<this.nbColumns;++n)if(Math.abs(this.data[r*this.nbColumns+n]-this.data[n*this.nbColumns+r])>t)return!1;return!0},isUnitDiagonal:function(t){if(null==t&&(t=0),!this.isSquare())return!1;for(var r=this.data[0],n=0;n<this.nbRows;++n){var o=this.data[n*this.nbColumns+n];r<o&&(r=o)}return!(Math.abs(r-1)>t)},isCorrelationMatrix:function(t,r){if(null==t&&(t=0),null==r&&(r="boolean"),"exception"!=r&&"boolean"!=r)throw new Error("unexpected output type");try{if(!this.isSquare())throw"not square";if(!this.isSymmetric(t))throw"not symmetric";if(!this.isUnitDiagonal(t))throw"not unit diagonal";if(it.eig(this,{maxIter:-1,sortedEigenvalues:!0})[1].data[this.nbRows-1]<0)throw"not positive semi-definite";return!0}catch(t){if("exception"==r)throw new Error(t);return!1}},isCovarianceMatrix:function(t,r){if(null==t&&(t=0),null==r&&(r="boolean"),"exception"!=r&&"boolean"!=r)throw new Error("unexpected output type");try{if(!this.isSquare())throw"not square";if(!this.isSymmetric(t))throw"not symmetric";for(var n=this.data[0],o=0;o<this.nbRows;++o){var i=this.data[o*this.nbColumns+o];n<i&&(n=i)}if(n<-t)throw"not positive diagonal";if(it.eig(this,{maxIter:-1,sortedEigenvalues:!0})[1].data[this.nbRows-1]<0)throw"not positive semi-definite";return!0}catch(t){if("exception"==r)throw new Error(t);return!1}},isVector:function(){return 1===this.nbColumns},isNonNegative:function(){for(var t=0;t<this.nbRows;++t)for(var r=0;r<this.nbColumns;++r)if(this.data[t*this.nbColumns+r]<0)return!1;return!0},isPositive:function(){for(var t=0;t<this.nbRows;++t)for(var r=0;r<this.nbColumns;++r)if(this.data[t*this.nbColumns+r]<=0)return!1;return!0},isNonPositive:function(){for(var t=0;t<this.nbRows;++t)for(var r=0;r<this.nbColumns;++r)if(0<this.data[t*this.nbColumns+r])return!1;return!0},isNegative:function(){for(var t=0;t<this.nbRows;++t)for(var r=0;r<this.nbColumns;++r)if(0<=this.data[t*this.nbColumns+r])return!1;return!0},sum:function(){for(var t=0,r=0;r<this.data.length;++r)t+=this.data[r];return t},min:function(){for(var t=Number.POSITIVE_INFINITY,r=0;r<this.data.length;++r)this.data[r]<t&&(t=this.data[r]);return t},max:function(){for(var t=Number.NEGATIVE_INFINITY,r=0;r<this.data.length;++r)this.data[r]>t&&(t=this.data[r]);return t},normalize:function(t){var r=_(this.nbRows,this.nbColumns,t),n=this.sum();if(0===n)throw new Error("sum of coefficients of matrix is null");for(var o=0;o<this.data.length;++o)r.data[o]=this.data[o]/n;return r},diagonal:function(t){if(!this.isSquare())throw new Error("matrix is not square: ("+this.nbRows+","+this.nbColumns+")");for(var r=_(this.nbRows,1,t),n=0;n<this.nbRows;++n)r.data[n]=this.data[n*(this.nbColumns+1)];return r},row:function(t,r){if(t<1||t>this.nbRows)throw new Error("index out of bounds when getting matrix row, ("+t+") in size ("+this.nbRows+","+this.nbColumns+")");for(var n=_(this.nbColumns,1,r),o=0;o<this.nbColumns;++o)n.data[o]=this.data[(t-1)*this.nbColumns+o];return n},column:function(t,r){if(t<1||t>this.nbColumns)throw new Error("index out of bounds when getting matrix column, ("+t+") in size ("+this.nbRows+","+this.nbColumns+")");for(var n=_(this.nbRows,1,r),o=0;o<this.nbRows;++o)n.data[o]=this.data[o*this.nbColumns+(t-1)];return n},elemMap:function(t,r){for(var n=_(this.nbRows,this.nbColumns,r),o=0;o<n.nbRows;++o)for(var i=0;i<n.nbColumns;++i)n.data[o*n.nbColumns+i]=t(o+1,i+1,this.data[o*this.nbColumns+i]);return n},submatrix:function(t,r,n){if(!(t instanceof Array||t instanceof Uint32Array)||0==t.length)throw new Error("first parameter must be a non empty array");if(!(r instanceof Array||r instanceof Uint32Array)||0==r.length)throw new Error("second parameter must be a non empty array");for(var o=1;o<t.length;++o)if(t[o-1]>=t[o])throw new Error("first parameter must be a sorted array");for(var i=1;i<r.length;++i)if(r[i-1]>=t[i])throw new Error("second parameter must be a sorted array");var e=_(t.length,r.length,n);for(o=0;o<e.nbRows;++o){var a=t[o]-1;for(i=0;i<e.nbColumns;++i){var s=r[i]-1;e.data[o*e.nbColumns+i]=this.data[a*this.nbColumns+s]}}return e},transpose:function(t){for(var r=_(this.nbColumns,this.nbRows,t),n=0;n<r.nbRows;++n)for(var o=0;o<r.nbColumns;++o)r.data[n*r.nbColumns+o]=this.data[o*this.nbColumns+n];return r},determinant:function(){if(!this.isSquare())throw new Error("matrix is not square: ("+this.nbRows+","+this.nbColumns+")");for(var t=it.qrDecomposition(this,{qLess:!0}),r=1,n=0;n<t.data.length;n+=t.nbColumns+1)r*=t.data[n];return r},trace:function(){if(!this.isSquare())throw new Error("matrix is not square: ("+this.nbRows+","+this.nbColumns+")");for(var t=0,r=0;r<this.nbRows;++r)t+=this.data[r*this.nbColumns+r];return t},symmetrize:function(t){if(!this.isSquare())throw new Error("matrix is not square: ("+this.nbRows+","+this.nbColumns+")");var r;r=t&&t.inPlace?this:new it(this);for(var n=1;n<=r.nbRows;++n)for(var o=n+1;o<=r.nbColumns;++o){var i=(r.data[(n-1)*r.nbColumns+(o-1)]+r.data[(o-1)*r.nbColumns+(n-1)])/2;r.data[(n-1)*r.nbColumns+(o-1)]=i,r.data[(o-1)*r.nbColumns+(n-1)]=i}return r},unitDiagonalize:function(t){if(!this.isSquare())throw new Error("matrix is not square: ("+this.nbRows+","+this.nbColumns+")");var r;r=t&&t.inPlace?this:new it(this);for(var n=0;n<r.nbRows;++n)r.data[n*r.nbColumns+n]=1;return r},swapRows:function(t,r,n){if(!(1<=t&&t<=this.nbRows&&1<=r&&r<=this.nbRows))throw new Error("incorrect rows indexes: ("+t+","+r+")");var o;if(o=n&&n.inPlace?this:new it(this),t==r)return o;t-=1,r-=1;for(var i=0;i<o.nbColumns;++i){var e=o.data[t*o.nbColumns+i];o.data[t*o.nbColumns+i]=o.data[r*o.nbColumns+i],o.data[r*o.nbColumns+i]=e}return o},swapColumns:function(t,r,n){if(!(1<=t&&t<=this.nbColumns&&1<=r&&r<=this.nbColumns))throw new Error("incorrect columns indexes: ("+t+","+r+")");var o;if(o=n&&n.inPlace?this:new it(this),t==r)return o;t-=1,r-=1;for(var i=0;i<o.nbRows;++i){var e=o.data[i*o.nbColumns+t];o.data[i*o.nbColumns+t]=o.data[i*o.nbColumns+r],o.data[i*o.nbColumns+r]=e}return o},matrixNorm:function(t){if("one"==t){for(var r=0,n=0;n<this.nbColumns;++n){for(var o=0,i=0;i<this.nbRows;++i)o+=Math.abs(this.data[i*this.nbColumns+n]);r=Math.max(r,o)}return r}if("infinity"==t){var e=0;for(i=0;i<this.nbRows;++i){var a=0;for(n=0;n<this.nbColumns;++n)a+=Math.abs(this.data[i*this.nbColumns+n]);e=Math.max(e,a)}return e}if("frobenius"==t)return this.vectorNorm("two");throw new Error("unsupported matrix norm: "+t)},vectorNorm:function(t,r,n){var o,i,e,a;if(void 0===r||"matrix"==r)o=0,i=this.nbRows,e=0,a=this.nbColumns;else if("row"==r){if(void 0===n)throw new Error("undefined row index");if(n<1||n>this.nbRows)throw new Error("row index out of bounds: "+n);o=n-1,i=n,e=0,a=this.nbColumns}else if("column"==r){if(void 0===n)throw new Error("undefined row index");if(n<1||n>this.nbColumns)throw new Error("column index out of bounds: "+n);o=0,i=this.nbRows,e=n-1,a=n}else if(void 0!==r)throw new Error("unsupported matrix subset: "+r);if("one"==t){for(var s=0,u=o*this.nbColumns,l=o;l<i;++l){for(var f=u+e,h=e;h<a;++h)s+=Math.abs(this.data[f]),f++;u+=this.nbColumns}return s}if("two"==t){var m=0,c=1;for(u=o*this.nbColumns,l=o;l<i;++l){for(f=u+e,h=e;h<a;++h){var d=this.data[f],w=Math.abs(d);0!=w&&(m<w?(c=1+c*(m/d)*(m/d),m=w):c+=d/m*(d/m)),f++}u+=this.nbColumns}return m*Math.sqrt(c)}if("infinity"!=t)throw new Error("unsupported vector norm: "+t);var p=0;for(u=o*this.nbColumns,l=o;l<i;++l){for(f=u+e,h=e;h<a;++h)p=Math.max(p,Math.abs(this.data[f])),f++;u+=this.nbColumns}return p},toCovarianceMatrix:function(){return k(this),this}},it.areEqual=function(t,r,n){if(!(t instanceof it))throw new Error("a must be a matrix");if(!(r instanceof it))throw new Error("b must be a matrix");if(t.nbRows!==r.nbRows)return!1;if(t.nbColumns!==r.nbColumns)return!1;for(var o=t.nbRows*t.nbColumns,i=n||0,e=0;e<o;++e)if(Math.abs(t.data[e]-r.data[e])>i)return!1;return!0},it.xpy=function(t,r,n){if(!(t instanceof it))throw new Error("first input must be a matrix");if(!(r instanceof it))throw new Error("second input must be a matrix");if(t.nbColumns!==r.nbColumns||t.nbRows!==r.nbRows)throw new Error("input matrices sizes do not match: ("+t.nbRows+","+t.nbColumns+") - ("+r.nbRows+","+r.nbColumns+")");for(var o=_(t.nbRows,t.nbColumns,n),i=t.nbRows*t.nbColumns,e=0;e<i;++e)o.data[e]=t.data[e]+r.data[e];return o},it.xmy=function(t,r,n){if(!(t instanceof it))throw new Error("first input must be a matrix");if(!(r instanceof it))throw new Error("second input must be a matrix");if(t.nbColumns!==r.nbColumns||t.nbRows!==r.nbRows)throw new Error("input matrices sizes do not match: ("+t.nbRows+","+t.nbColumns+") - ("+r.nbRows+","+r.nbColumns+")");for(var o=_(t.nbRows,t.nbColumns,n),i=t.nbRows*t.nbColumns,e=0;e<i;++e)o.data[e]=t.data[e]-r.data[e];return o},it.axpby=function(t,r,n,o,i){if(!(r instanceof it))throw new Error("first input must be a matrix");if(!(o instanceof it))throw new Error("second input must be a matrix");if(r.nbColumns!==o.nbColumns||r.nbRows!==o.nbRows)throw new Error("input matrices sizes do not match: ("+r.nbRows+","+r.nbColumns+") - ("+o.nbRows+","+o.nbColumns+")");for(var e=_(r.nbRows,r.nbColumns,i),a=r.nbRows*r.nbColumns,s=0;s<a;++s)e.data[s]=t*r.data[s]+n*o.data[s];return e},it.copy=function(t,r){if(!(t instanceof it))throw new Error("first input must be a matrix");for(var n=_(t.nbRows,t.nbColumns,r),o=t.nbRows*t.nbColumns,i=0;i<o;++i)n.data[i]=t.data[i];return n},it.elementwiseProduct=function(t,r,n){if(!(t instanceof it))throw new Error("first input must be a matrix");if(!(r instanceof it))throw new Error("second input must be a matrix");if(!(t.nbRows===r.nbRows&&t.nbColumns===r.nbColumns||r.nbRows===t.nbRows&&1===r.nbColumns||1===r.nbRows&&r.nbColumns===t.nbColumns))throw new Error("input matrices sizes do not match: ("+t.nbRows+","+t.nbColumns+") - ("+r.nbRows+","+r.nbColumns+")");var o=_(t.nbRows,t.nbColumns,n),i=t.nbRows,e=t.nbColumns;if(t.nbRows===r.nbRows&&t.nbColumns===r.nbColumns)for(var a=i*e,s=0;s<a;++s)o.data[s]=t.data[s]*r.data[s];else if(r.nbRows===t.nbRows&&1===r.nbColumns)for(var u=0,l=0;l<i;++l)for(var f=r.data[l],h=0;h<e;++h)o.data[u]=t.data[u]*f,u++;else if(1===r.nbRows&&r.nbColumns===t.nbColumns)for(u=0,l=0;l<i;++l)for(h=0;h<e;++h)o.data[u]=t.data[u]*r.data[h],u++;return o},it.xy=function(t,r,n){if(!(t instanceof it))throw new Error("first input must be a matrix");if(!(r instanceof it))throw new Error("second input must be a matrix");if(t.nbColumns!==r.nbRows)throw new Error("matrices sizes do not match: ("+t.nbRows+","+r.nbColumns+") - ("+r.nbRows+","+r.nbColumns+")");for(var o=_(t.nbRows,r.nbColumns,n),i=t.nbRows,e=t.nbColumns,a=r.nbColumns,s=0,u=0,l=0;l<i;++l){for(var f=u,h=0;h<a;++h)o.data[f]=0,f++;for(var m=0,c=0;c<e;++c){var d=t.data[s];f=u;for(h=0;h<a;++h)o.data[f]+=d*r.data[m],m++,f++;s++}u+=a}return o},it.txy=function(t,r,n){if(!(t instanceof it))throw new Error("second input must be a matrix");if(!(r instanceof it))throw new Error("third input must be a matrix");if(t.nbRows!==r.nbRows)throw new Error("matrices sizes do not match: ("+t.nbRows+","+r.nbColumns+") - ("+r.nbRows+","+r.nbColumns+")");for(var o=_(t.nbColumns,r.nbColumns,n),i=t.nbColumns,e=t.nbRows,a=r.nbColumns,s=0,u=0,l=0,f=0;f<i;++f){for(var h=t.data[s],m=d,c=0;c<a;++c)o.data[u]=h*r.data[c],u++;s++}var d=a;for(l=1;l<e;++l){for(f=u=0;f<i;++f){for(h=t.data[s],m=d,c=0;c<a;++c)o.data[u]+=h*r.data[m],u++,m++;s++}d+=a}return o},it.axy=function(t,r,n,o){if(!(r instanceof it))throw new Error("second input must be a matrix");if(!(n instanceof it))throw new Error("third input must be a matrix");if(r.nbColumns!==n.nbRows)throw new Error("matrices sizes do not match: ("+r.nbRows+","+n.nbColumns+") - ("+n.nbRows+","+n.nbColumns+")");for(var i=_(r.nbRows,n.nbColumns,o),e=r.nbRows,a=r.nbColumns,s=n.nbColumns,u=0,l=0,f=0;f<e;++f){for(var h=l,m=0;m<s;++m)i.data[h]=0,h++;for(var c=0,d=0;d<a;++d){var w=t*r.data[u];h=l;for(m=0;m<s;++m)i.data[h]+=w*n.data[c],c++,h++;u++}l+=s}return i},it.ax=function(t,r,n){if(!(r instanceof it))throw new Error("second input must be a matrix");for(var o=_(r.nbRows,r.nbColumns,n),i=r.nbRows,e=r.nbColumns,a=1;a<=i;++a)for(var s=1;s<=e;++s)o.setValue(a,s,t*r.getValue(a,s));return o},it.axty=function(t,r,n,o){if(!(r instanceof it))throw new Error("second input must be a matrix");if(!(n instanceof it))throw new Error("third input must be a matrix");if(r.nbColumns!==n.nbColumns)throw new Error("matrices sizes do not match: ("+r.nbRows+","+n.nbColumns+") - ("+n.nbRows+","+n.nbColumns+")");for(var i=_(r.nbRows,n.nbRows,o),e=0;e<r.nbRows;++e)for(var a=0;a<n.nbRows;++a){for(var s=i.data[e*i.nbColumns+a]=0;s<r.nbColumns;++s)i.data[e*i.nbColumns+a]+=r.data[e*r.nbColumns+s]*n.data[a*n.nbColumns+s];i.data[e*i.nbColumns+a]=t*i.data[e*i.nbColumns+a]}return i},it.atxy=function(t,r,n,o){if(!(r instanceof it))throw new Error("second input must be a matrix");if(!(n instanceof it))throw new Error("third input must be a matrix");if(r.nbRows!==n.nbRows)throw new Error("matrices sizes do not match: ("+r.nbRows+","+n.nbColumns+") - ("+n.nbRows+","+n.nbColumns+")");for(var i=_(r.nbColumns,n.nbColumns,o),e=0,a=0;a<r.nbColumns;++a){for(var s=t*r.data[e*r.nbColumns+a],u=0;u<n.nbColumns;++u)i.data[a*i.nbColumns+u]=0;for(u=0;u<n.nbColumns;++u)i.data[a*i.nbColumns+u]+=s*n.data[e*n.nbColumns+u]}for(e=1;e<r.nbRows;++e)for(a=0;a<r.nbColumns;++a)for(s=t*r.data[e*r.nbColumns+a],u=0;u<n.nbColumns;++u)i.data[a*i.nbColumns+u]+=s*n.data[e*n.nbColumns+u];return i},it.diagonal=function(t,r){if(!(t instanceof it&&t.isVector()))throw new Error("first input must be a vector");for(var n=t.nbRows,o=_(n,n,r),i=0;i<n;++i){for(var e=0;e<n;++e)o.data[i*n+e]=0;o.data[i*n+i]=t.data[i]}return o},it.fillSymmetric=function(t,r,n){if(t<1)throw new Error("input number of rows and columns out of bounds: "+t);for(var o=_(t,t,n),i=0;i<t;++i){for(var e=0;e<i;++e)o.data[i*t+e]=o.data[e*t+i];for(e=i;e<o.nbColumns;++e)o.data[i*t+e]=r(i+1,e+1)}return o},it.fill=function(t,r,n,o){if(t<1)throw new Error("input number of rows out of bounds: "+t);if(r<1)throw new Error("input number of columns out of bounds: "+r);for(var i=_(t,r,o),e=0;e<t;++e)for(var a=0;a<r;++a)i.data[e*r+a]=n(e+1,a+1);return i},it.zeros=function(t,r,n){for(var o=_(t,r,n),i=t*r,e=0;e<i;++e)o.data[e]=0;return o},it.ones=function(t,r){for(var n=_(t,r),o=t*r,i=0;i<o;++i)n.data[i]=1;return n},it.identity=function(t){for(var r=_(t,t),n=t*t,o=0;o<n;++o)o%(t+1)==(r.data[o]=0)&&(r.data[o]=1);return r},it.normrnd=function(t,r,n,o){for(var i=_(t,r),e=t*r,a=0;a<e;++a)i.data[a]=b(n,o);return i},it.vectorHadamardProduct=function(t,r){return it.elementwiseProduct(t,r)},it.vectorDotProduct=function(t,r){if(!t.isVector())throw new Error("first argument must be a vector");if(!r.isVector())throw new Error("second argument must be a vector");if(t.nbRows!==r.nbRows)throw new Error("Vectors sizes do not match: ("+t.nbRows+") - ("+r.nbRows+")");for(var n=0,o=t.nbRows,i=0;i<o;++i)n+=t.data[i]*r.data[i];return n},it.choleskyDecomposition=function(t,r){void 0===r&&(r={});var n=r.epsSymmetric;null==n&&(n=0);var o=r.epsSdp;null==o&&(o=1e-16*t.nbRows);var i=r.pivoting;if(null==i&&(i="none"),"none"!=i&&"complete"!=i)throw new Error("unknown pivoting");var e=r.permutationOutputForm;if(null==e&&(e="matrix"),"vector"!=e&&"matrix"!=e)throw new Error("unknown permutation output form value");if(!(t instanceof it))throw new Error("input must be a matrix");if(!t.isSymmetric(n))throw new Error("input matrix must be symmetric");var a=t.nbRows;if("none"==i)for(var s=it.zeros(a,a),u=it.zeros(a,1),l=1;l<=a;++l){for(var f=l;f<=a;++f)u.data[f-1]=t.data[(f-1)*t.nbColumns+(l-1)];for(var h=1;h<=l-1;++h)for(f=l;f<=a;++f)u.data[f-1]-=s.data[(l-1)*s.nbColumns+(h-1)]*s.data[(f-1)*s.nbColumns+(h-1)];if(u.data[l-1]<=0)throw new Error("input matrix must be positive definite");for(f=l;f<=a;++f)s.data[(f-1)*s.nbColumns+(l-1)]=u.data[f-1]/Math.sqrt(u.data[l-1])}else{if("complete"!=i)throw new Error("internal error: unknown pivoting");u=it.zeros(a,1);var m,c=new it(t),d=it.fill(a,1,function(t,r){return t});for(h=1;h<=a;++h){l=-1;var w=Number.NEGATIVE_INFINITY;for(f=h;f<=a;++f){var p=c.data[(f-1)*c.nbColumns+(f-1)];w<p&&(l=f,w=p)}if(1==h&&(m=w),Math.abs(w)<=m*o)break;if(w<m*o)throw new Error("input matrix must be semi-definite positive");d.swapRows(h,l,{inPlace:!0}),c.swapRows(h,l,{inPlace:!0}),c.swapColumns(h,l,{inPlace:!0});for(f=h+1;f<=a;++f)u.data[f-1]=c.data[(f-1)*c.nbColumns+(h-1)];if(0==w)throw new Error("internal error: null pivot detected");for(f=h+1;f<=a;++f)c.data[(f-1)*c.nbColumns+(h-1)]/=w;for(f=h+1;f<=a;++f)for(l=h+1;l<=a;++l)c.data[(f-1)*c.nbColumns+(l-1)]-=u.data[f-1]*u.data[l-1]/w}}if("none"==i)return{lowerTriangular:s};if("complete"!=i)throw new Error("internal error: unknown pivoting");var v,b=it.fill(a,1,function(t,r){return Math.max(0,c.data[(t-1)*c.nbColumns+(t-1)])}),y=it.fill(a,a,function(t,r){return t==r?1:r<t?c.data[(t-1)*c.nbColumns+(r-1)]:0});if("vector"==e)v=d;else{if("matrix"!=e)throw new Error("internal error: unknown permutation output form value");v=it.fill(a,a,function(t,r){return t==d.data[r-1]?1:0})}return{lowerTriangular:y,diagonal:b,permutation:v}},it.luDecomposition=function(t,r){void 0===r&&(r={});var n=r.permutationsOutputForm;if(null==n&&(n="matrix"),"vector"!=n&&"matrix"!=n)throw new Error("unknown permutation output form value");if(!(t instanceof it))throw new Error("input must be a matrix");if(!t.isSquare())throw new Error("input must be square");for(var o=t.nbRows,i=it.fill(o,1,function(t,r){return t}),e=it.fill(o,1,function(t,r){return t}),a=new it(t),s=1;s<=o-1;++s){for(var u=-1,l=-1,f=-1,h=s;h<=o;++h)for(var m=s;m<=o;++m){var c=Math.abs(a.data[(h-1)*a.nbColumns+(m-1)]);f<c&&(u=h,l=m,f=c)}i.swapRows(s,u,{inPlace:!0}),a.swapRows(s,u,{inPlace:!0}),e.swapRows(s,l,{inPlace:!0}),a.swapColumns(s,l,{inPlace:!0});var d=a.data[(s-1)*a.nbColumns+(s-1)];if(0!=d)for(h=s+1;h<=o;++h){a.data[(h-1)*a.nbColumns+(s-1)]/=d;for(m=s+1;m<=o;++m)a.data[(h-1)*a.nbColumns+(m-1)]-=a.data[(h-1)*a.nbColumns+(s-1)]*a.data[(s-1)*a.nbColumns+(m-1)]}}var w,p,v=it.fill(o,o,function(t,r){return r<t?a.data[(t-1)*a.nbColumns+(r-1)]:t==r?1:0}),b=it.fill(o,o,function(t,r){return t<=r?a.data[(t-1)*a.nbColumns+(r-1)]:0});if("vector"==n)w=i,p=e;else{if("matrix"!=n)throw new Error("internal error: unknown permutation output form value");w=it.fill(o,o,function(t,r){return r==i.data[t-1]?1:0}),p=it.fill(o,o,function(t,r){return t==e.data[r-1]?1:0})}return{lowerTriangular:v,upperTriangular:b,rowPermutation:w,columnPermutation:p}},it.qrDecomposition=function(t,r){function n(t,r){var n,o,i;if(0==r)n=0<=t?1:-1,o=0,i=Math.abs(t);else if(0==t)o=(n=0)<=r?1:-1,i=Math.abs(r);else if(Math.abs(t)>Math.abs(r)){o=(e=r/t)*(n=1/(a=(0<=t?1:-1)*Math.sqrt(1+e*e))),i=t*a}else{var e,a;n=(e=t/r)*(o=1/(a=(0<=r?1:-1)*Math.sqrt(1+e*e))),i=r*a}return[n,-o,i]}void 0===r&&(r={});var o=r.qLess||!1;if(!(t instanceof it))throw new Error("first input must be a matrix");if(t.nbRows<t.nbColumns)throw new Error("matrix has more columns than rows: ("+t.nbRows+") v.s. ("+t.nbColumns+")");var i=t.nbRows,e=t.nbColumns,a=new it(t),s=null;o||(s=it.identity(i));for(var u=1;u<=e;++u)for(var l=i;u+1<=l;--l){var f=(l-2)*a.nbColumns+(u-1),h=(l-1)*a.nbColumns+(u-1),m=n(a.data[f],a.data[h]),c=m[0],d=m[1],w=m[2];a.data[f]=w,a.data[h]=0;for(var p=u+1;p<=e;++p){var v=(l-2)*a.nbColumns+(p-1),b=(l-1)*a.nbColumns+(p-1),y=a.data[v],g=a.data[b];a.data[v]=c*y-d*g,a.data[b]=d*y+c*g}if(!o)for(p=1;p<=i;++p){var x=(p-1)*s.nbColumns+(l-2),C=(p-1)*s.nbColumns+(l-1);y=s.data[x],g=s.data[C];s.data[x]=c*y-d*g,s.data[C]=d*y+c*g}}return o?a:[s,a]},it.svdDecomposition=function(t,r){void 0===r&&(r={});var n=r.eps||1e-16,o=r.maxIter||100,i=r.svdForm||"thin";if(!(t instanceof it))throw new Error("first input must be a matrix");if(t.nbRows<t.nbColumns)throw new Error("matrix has more columns than rows: "+t.nbColumns+" v.s. "+t.nbRows);for(var e=t.nbRows,a=t.nbColumns,s=new it(t),u=s.matrixNorm("frobenius"),l=it.identity(a),f=0,h="function"==typeof Float64Array?new Float64Array(a):new Array(a);;){if(++f,-1!==o&&o<f)throw new Error("maximum number of iterations reached: "+o);for(var m=1;m<=a;++m){var c=s.vectorNorm("two","column",m);h[m-1]=c*c}var d=!0;for(m=2;m<=a;++m)for(var w=1;w<=m-1;++w){for(var p=h[w-1],v=h[m-1],b=0,y=1;y<=e;++y)b+=s.data[(y-1)*s.nbColumns+(w-1)]*s.data[(y-1)*s.nbColumns+(m-1)];if(!(Math.abs(b)<=n*Math.sqrt(e*p*v))&&!(Math.sqrt(p)<=n*u||Math.sqrt(v)<=n*u)){d=!1;var g=(p-v)/(2*b),x=(0<=g?1:-1)/(Math.abs(g)+Math.sqrt(1+g*g)),C=1/Math.sqrt(1+x*x),R=C*x;for(y=1;y<=e;++y){var E=s.data[(y-1)*s.nbColumns+(w-1)],M=s.data[(y-1)*s.nbColumns+(m-1)];s.data[(y-1)*s.nbColumns+(w-1)]=C*E+R*M,s.data[(y-1)*s.nbColumns+(m-1)]=-R*E+C*M}h[w-1]+=x*b,h[m-1]-=x*b;for(y=1;y<=a;++y){E=l.data[(y-1)*l.nbColumns+(w-1)],M=l.data[(y-1)*l.nbColumns+(m-1)];l.data[(y-1)*l.nbColumns+(w-1)]=C*E+R*M,l.data[(y-1)*l.nbColumns+(m-1)]=-R*E+C*M}}}if(1==d)break}var A="function"==typeof Float64Array?new Float64Array(a):new Array(a),P="function"==typeof Uint32Array?new Uint32Array(a):new Array(a);for(m=1;m<=a;++m){var z=Math.sqrt(h[m-1]);A[m-1]=z,P[m-1]=m}P.sort(function(t,r){return A[r-1]-A[t-1]});var k=it.zeros(e,a),_=it.zeros(a,a),I=it.zeros(a,a);for(m=1;m<=a;++m){var V=P[m-1],F=A[V-1];if(0!=(_.data[(m-1)*_.nbColumns+(m-1)]=F))for(w=1;w<=e;++w)k.data[(w-1)*k.nbColumns+(m-1)]=s.data[(w-1)*s.nbColumns+(V-1)]/F;for(w=1;w<=a;++w)I.data[(w-1)*I.nbColumns+(m-1)]=l.data[(w-1)*l.nbColumns+(V-1)]}if("thin"==i)return[k,_,I];var O=it.qrDecomposition(k)[0],T=it.zeros(e,e),S=it.zeros(e,a);for(m=1;m<=a;++m){V=P[m-1],F=A[V-1];if(0!=(S.data[(m-1)*S.nbColumns+(m-1)]=F))for(w=1;w<=e;++w)T.data[(w-1)*T.nbColumns+(m-1)]=k.data[(w-1)*k.nbColumns+(m-1)];else for(w=1;w<=e;++w)T.data[(w-1)*T.nbColumns+(m-1)]=O.data[(w-1)*O.nbColumns+(m-1)]}for(m=a+1;m<=e;++m)for(w=1;w<=e;++w)T.data[(w-1)*T.nbColumns+(m-1)]=O.data[(w-1)*O.nbColumns+(m-1)];return"full"==i?[T,S,I]:void 0},it.eig=function(t,r){void 0===r&&(r={});var n=r.epsSymmetric;null==n&&(n=0);var o=r.maxIter;null==o&&(o=100);var i=r.sortedEigenvalues;if(null==i&&(i=!1),!(t instanceof it))throw new Error("input must be a matrix");if(!t.isSymmetric(n))throw new Error("input matrix must be symmetric");for(var e=t.nbRows,a=new it(t),s=it.identity(e),u=a.diagonal(),l=new it(u),f=it.zeros(e,1),h=0;;){if(++h,-1!==o&&o<h)throw new Error("maximum number of iterations reached: "+o);for(var m=0,c=1;c<=e-1;++c)for(var d=c+1;d<=e;++d)m+=Math.abs(a.data[(c-1)*a.nbColumns+(d-1)]);if(0==m)break;var w=h<4?.2*m/(e*e):0;for(c=1;c<=e-1;++c)for(d=c+1;d<=e;++d){var p=100*Math.abs(a.data[(c-1)*a.nbColumns+(d-1)]);if(4<h&&Math.abs(u.data[c-1])+p==Math.abs(u.data[c-1])&&Math.abs(u.data[d-1])+p==Math.abs(u.data[d-1]))a.data[(c-1)*a.nbColumns+(d-1)]=0;else if(Math.abs(a.data[(c-1)*a.nbColumns+(d-1)])>w){var v,b=u.data[d-1]-u.data[c-1];if(Math.abs(b)+p==Math.abs(b))v=a.data[(c-1)*a.nbColumns+(d-1)]/b;else{var y=.5*b/a.data[(c-1)*a.nbColumns+(d-1)];v=1/(Math.abs(y)+Math.sqrt(1+y*y)),y<0&&(v=-v)}var g=1/Math.sqrt(1+v*v),x=v*g,C=x/(1+g);b=v*a.data[(c-1)*a.nbColumns+(d-1)];for(f.data[c-1]-=b,f.data[d-1]+=b,u.data[c-1]-=b,u.data[d-1]+=b,a.data[(c-1)*a.nbColumns+(d-1)]=0,R=1;R<=c-1;++R){p=a.data[(R-1)*a.nbColumns+(c-1)],b=a.data[(R-1)*a.nbColumns+(d-1)];a.data[(R-1)*a.nbColumns+(c-1)]=p-x*(b+p*C),a.data[(R-1)*a.nbColumns+(d-1)]=b+x*(p-b*C)}for(R=c+1;R<=d-1;++R){p=a.data[(c-1)*a.nbColumns+(R-1)],b=a.data[(R-1)*a.nbColumns+(d-1)];a.data[(c-1)*a.nbColumns+(R-1)]=p-x*(b+p*C),a.data[(R-1)*a.nbColumns+(d-1)]=b+x*(p-b*C)}for(R=d+1;R<=e;++R){p=a.data[(c-1)*a.nbColumns+(R-1)],b=a.data[(d-1)*a.nbColumns+(R-1)];a.data[(c-1)*a.nbColumns+(R-1)]=p-x*(b+p*C),a.data[(d-1)*a.nbColumns+(R-1)]=b+x*(p-b*C)}for(var R=1;R<=e;++R){p=s.data[(R-1)*s.nbColumns+(c-1)],b=s.data[(R-1)*s.nbColumns+(d-1)];s.data[(R-1)*s.nbColumns+(c-1)]=p-x*(b+p*C),s.data[(R-1)*s.nbColumns+(d-1)]=b+x*(p-b*C)}}}for(c=1;c<=e;++c)l.data[c-1]+=f.data[c-1],u.data[c-1]=l.data[c-1],f.data[c-1]=0}var E=u,M=s;if(i){for(var A="function"==typeof Uint32Array?new Uint32Array(e):new Array(e),P=1;P<=e;++P)A[P-1]=P;A.sort(function(t,r){return u.data[r-1]-u.data[t-1]}),E=it.zeros(e,1),M=it.zeros(e,e);for(P=1;P<=e;++P){var z=A[P-1];E.data[P-1]=u.data[z-1];for(R=1;R<=e;++R)M.data[(R-1)*M.nbColumns+(P-1)]=s.data[(R-1)*s.nbColumns+(z-1)]}}return[M,E]},it.nullSpace=function(t,r){void 0===r&&(r={});var n=r.eps||void 0;if(!(t instanceof it))throw new Error("first input must be a matrix");var o=t.nbRows,i=t.nbColumns,e=null;if(i<=o){var a=(h=it.svdDecomposition(t,{maxIter:-1}))[0],s=h[1],u=h[2];for(void 0===n&&(n=o*(p(s.data[0])-s.data[0])),m=i;1<=m&&!(s.data[(m-1)*s.nbColumns+(m-1)]>n);--m);if((c=m)==i)e=it.zeros(i,1);else{e=new it.zeros(i,i-c);for(var l=c+1;l<=i;++l)for(var f=1;f<=i;++f)e.data[(f-1)*e.nbColumns+(l-(c+1)+1-1)]=u.data[(f-1)*u.nbColumns+(l-1)]}}else{var h,m,c;a=(h=it.svdDecomposition(t.transpose(),{maxIter:-1,svdForm:"full"}))[0],s=h[1],u=h[2];for(void 0===n&&(n=i*(p(s.data[0])-s.data[0])),m=o;1<=m&&!(s.data[(m-1)*s.nbColumns+(m-1)]>n);--m);if((c=m)==o)e=it.zeros(i,1);else{var d=new it.zeros(i,c);for(l=1;l<=c;++l)for(f=1;f<=i;++f)d.data[(f-1)*d.nbColumns+(l-1)]=a.data[(f-1)*a.nbColumns+(l-1)];var w=it.qrDecomposition(d)[0];for(e=new it.zeros(i,i-c),l=c+1;l<=i;++l)for(f=1;f<=i;++f)e.data[(f-1)*e.nbColumns+(l-(c+1)+1-1)]=w.data[(f-1)*w.nbColumns+(l-1)]}}return e},it.linsolveBackSubstitution=function(t,r){if(!(t instanceof it))throw new Error("first input must be a matrix");if(!(r instanceof it))throw new Error("second input must be a matrix");if(!t.isSquare())throw new Error("matrix is not square: ("+t.nbRows+","+t.nbColumns+")");if(t.nbRows!==r.nbRows)throw new Error("matrix and second member sizes do not match: ("+t.nbRows+","+t.nbColumns+") - ("+r.nbRows+","+r.nbColumns+")");if(1!==r.nbColumns)throw new Error("b is not a vector: ("+r.nbRows+","+r.nbColumns+")");for(var n=t.nbColumns,o=new it(r),i=n;1<=i;--i){var e=t.data[(i-1)*t.nbColumns+(i-1)];if(0==e)throw new Error("input matrix is not invertible: zero diagonal coefficient at index "+i);for(var a=i+1;a<=n;++a)o.data[i-1]-=t.data[(i-1)*t.nbColumns+(a-1)]*o.data[a-1];o.data[i-1]/=e}return o},it.linsolveForwardSubstitution=function(t,r){if(!(t instanceof it))throw new Error("first input must be a matrix");if(!(r instanceof it))throw new Error("second input must be a matrix");if(!t.isSquare())throw new Error("matrix is not square: ("+t.nbRows+","+t.nbColumns+")");if(t.nbRows!==r.nbRows)throw new Error("matrix and second member sizes do not match: ("+t.nbRows+","+t.nbColumns+") - ("+r.nbRows+","+r.nbColumns+")");if(1!==r.nbColumns)throw new Error("b is not a vector: ("+r.nbRows+","+r.nbColumns+")");for(var n=t.nbColumns,o=new it(r),i=1;i<=n;++i){var e=t.data[(i-1)*t.nbColumns+(i-1)];if(0==e)throw new Error("input matrix is not invertible: zero diagonal coefficient at index "+i);for(var a=1;a<=i-1;++a)o.data[i-1]-=t.data[(i-1)*t.nbColumns+(a-1)]*o.data[a-1];o.data[i-1]/=e}return o},it.randomOrthogonal=function(t){var r=it.normrnd(t,t),n=it.qrDecomposition(r),o=n[0],i=n[1],e=it.fill(1,t,function(t,r){return 0<=i.data[(r-1)*i.nbColumns+(r-1)]?1:-1});return it.elementwiseProduct(o,e)},it.randomCorrelation=function(t,n){if(void 0===n&&(n={}),void 0===n.eps&&(n.eps=1e-14),void 0===n.epsLambda&&(n.epsLambda=1e-8),void 0===n.lambda){n.lambda=new K(t).sample();for(var r=0;r<t;++r)n.lambda[r]*=t}if(n.lambda.length!=t)throw new Error("number of input eigenvalues not equal to "+t+", but to "+n.lambda.length);var o=0;for(r=0;r<t;++r)o+=n.lambda[r];if(Math.abs(o-t)>n.epsLambda)throw new Error("input eigenvalues not summing to "+t);for(var i=n.eps,e=it.fill(1,t,function(t,r){return n.lambda[r-1]}),a=it.randomOrthogonal(t),s=it.axty(1,it.elementwiseProduct(a,e),a),u=1;u<t;++u){for(var l=!0,f=1;f<=t;++f){var h=s.data[(f-1)*s.nbColumns+(f-1)];if(Math.abs(h-1)>i){l=!1;break}1!=h&&(s.data[(f-1)*s.nbColumns+(f-1)]=1)}if(l)break;r=-1;var m=-1;for(f=1;f<=t;++f)s.data[(f-1)*s.nbColumns+(f-1)]<1&&-1===r&&(r=f),1<s.data[(f-1)*s.nbColumns+(f-1)]&&(m=f);if(m<r){m=r=-1;for(f=1;f<=t;++f)1<s.data[(f-1)*s.nbColumns+(f-1)]&&-1===r&&(r=f),s.data[(f-1)*s.nbColumns+(f-1)]<1&&(m=f)}var c=s.data[(r-1)*s.nbColumns+(r-1)],d=s.data[(r-1)*s.nbColumns+(m-1)],w=s.data[(m-1)*s.nbColumns+(m-1)],p=(d+Math.sqrt(d*d-(c-1)*(w-1)))/(w-1),v=1/Math.sqrt(1+p*p),b=v*p;for(f=1;f<=t;++f){var y=s.data[(r-1)*s.nbColumns+(f-1)],g=s.data[(m-1)*s.nbColumns+(f-1)];s.data[(r-1)*s.nbColumns+(f-1)]=v*y-b*g,s.data[(m-1)*s.nbColumns+(f-1)]=b*y+v*g}for(f=1;f<=t;++f){y=s.data[(f-1)*s.nbColumns+(r-1)],g=s.data[(f-1)*s.nbColumns+(m-1)];s.data[(f-1)*s.nbColumns+(r-1)]=v*y-b*g,s.data[(f-1)*s.nbColumns+(m-1)]=b*y+v*g}s.data[(r-1)*s.nbColumns+(r-1)]=1}for(f=1;f<=t;++f)s.data[(f-1)*s.nbColumns+(f-1)]=1;for(r=1;r<=t;++r)for(m=r+1;m<=t;++m){d=s.data[(r-1)*s.nbColumns+(m-1)];var x=s.data[(m-1)*s.nbColumns+(r-1)],C=Math.min(1,Math.max(-1,(d+x)/2));s.data[(r-1)*s.nbColumns+(m-1)]=C,s.data[(m-1)*s.nbColumns+(r-1)]=C}return s},it.linsolveExtendedKaczmarz=function(t,r,n){void 0===n&&(n={});var o=n.eps||1e-12,i=n.maxIter||1e5,e=!1;if(void 0!==n.randomized&&(e=n.randomized),!(t instanceof it))throw new Error("first input must be a matrix");if(!(r instanceof it))throw new Error("second input must be a matrix");if(t.nbRows!==r.nbRows)throw new Error("matrix and second member sizes do not match: 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d=y.equalRiskContributionWeights(m,{eps:r.eps,maxCycles:-1,outputPortfolioVolatility:!0,constraints:{minWeights:u,maxWeights:l}}),w=d[0],p=d[1],v=p*p/h;v<o&&(o=v,i=f,e=w)}catch(t){if("infeasible problem detected: the restricted simplex is empty"!==t.message&&"internal error: maximum number of iterations reached when searching for a bracketing interval, the problem might be infeasible"!==t.message)throw t}s=a.next()}if(o==1/0)throw new Error("no feasible portfolio generated");var b=it.zeros(n,1);for(c=0;c<i.length;++c)b.setValueAt(i[c],1,e[c]);return b.toArray()},y.equalRiskContributionWeights=function(t,r){var n=(t=new it(t)).nbRows,o=it.fill(n,1,function(t,r){return 1/n});return y.riskBudgetingWeights(t,o,r)},y.equalWeights=function(n,t){return it.fill(n,1,function(t,r){return 1/n}).toArray()},y.globalMinimumVarianceWeights=function(t,r){void 0===r&&(r={}),void 0===r.constraints&&(r.constraints={}),void 0===r.optimizationMethodParams&&(r.optimizationMethodParams={});var n,o=(t=new 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e,a=o.epsVolatility;if(void 0===a&&(a=1e-4),"automatic"==i)e=new J(t,r,o);else if("critical-line"==i)e=new Z(t,r,o);else{if("gsmo"!=i)throw new Error("internal error: unsupported optimisation method");e=new et(t,r,o)}return e.restrict("minVolatility",a),e.restrict("minReturn",n),e.computeMaximumSharpeRatioEfficientPortfolio(n)[0].toArray()},((Z.prototype=Object.create(e.prototype)).constructor=Z).prototype.getHighestRiskTolerancePortfolio=function(t){return this.cornerPortfolios[0][0]},Z.prototype.getHighestRiskTolerance=function(t){return this.cornerPortfolios[0][1]},Z.prototype.getLowestRiskTolerancePortfolio=function(t){return this.cornerPortfolios[this.cornerPortfolios.length-1][0]},Z.prototype.getLowestRiskTolerance=function(t){return this.cornerPortfolios[this.cornerPortfolios.length-1][1]},Z.prototype.computeEfficientPortfolio=function(t,r){if(null==t)throw new Error("missing constraint type");var n,e=this;if("return"==t)n=function(t){return e.computePortfolioReturn(t[0])};else if("volatility"==t)n=function(t){return e.computePortfolioVolatility(t[0])};else{if("riskTolerance"!=t)throw new Error("unknown constraint type");n=function(t){return t[1]}}if(null==r)throw new Error("missing constraint value");var o=function(t,r,n,o){var i=n.length-1,e=0,a=(n[i][0],n[e][0],t(n[i])),s=t(n[e]);if(s+o<r||r<a-o)return[];{if(Math.abs(r-a)<=o)return[i];if(Math.abs(r-s)<=o)return[e]}for(;i-e!=1;){var u=Math.floor((i+e)/2),l=t(n[u]);if(r<l)e=u;else{if(!(l<r))return[u];i=u}}return[i,e]}(n,r,this.cornerPortfolios,this.epsEfficientPortfolioComputation);if(0==o.length)return[];if(1==o.length){var i=o[0];return[this.cornerPortfolios[i][0],this.cornerPortfolios[i][1]]}i=o[0];var a,s=this.cornerPortfolios[i][0],u=n(this.cornerPortfolios[i]),l=o[1],f=this.cornerPortfolios[l][0],h=n(this.cornerPortfolios[l]);if("return"===t)a=(h-r)/(h-u);else if("volatility"===t){var m=it.vectorDotProduct(it.xy(this.sigma,s),f),c=u*u+h*h-2*m,d=h*h-r*r,w=-2*(h*h-m)/2,p=0<=w?1:-1,v=w*w-c*d;if(v<0)throw new Error("internal error; the covariance matrix might not be semi-definite positive");var b=-(w+p*Math.sqrt(v)),y=b/c,g=d/b;if(0<y&&y<1)a=y;else{if(!(0<g&&g<1))throw new Error("internal error: the covariance matrix might not be semi-definite positive");a=g}}else{if("riskTolerance"!==t)throw new Error("internal error: unknown constraint type");a=(h-r)/(h-u)}e=this;return[it.fill(s.nbRows,1,function(t,r){var n=a*s.getValue(t,1)+(1-a)*f.getValue(t,1),o=e.lowerBounds.data[t-1],i=e.upperBounds.data[t-1];return Math.max(Math.min(n,i),o)}),a*this.cornerPortfolios[i][1]+(1-a)*this.cornerPortfolios[l][1]]},Z.prototype.getCornerPortfolios=function(){for(var t=new Array(this.cornerPortfolios.length),r=0;r<t.length;++r)t[r]=new it(this.cornerPortfolios[r][0]);return t},Z.prototype.restrict=function(t,r){if(null==t)throw new Error("missing constraint type");if(null==r)throw new Error("missing constraint value");if("minReturn"==t){if(this.getLowestReturn()<r){if(this.getHighestReturn()<r)throw new Error("impossible to restrict the efficient frontier: the minimum return constraint is not feasible");if(0==(a=this.computeEfficientPortfolio("return",r+.5*this.epsEfficientPortfolioComputation)).length)throw new Error("internal error: no efficient portfolio with a return greater than "+r);var n=a[0],o=a[1],e=new Array;for(i=0;i<this.cornerPortfolios.length-1&&this.cornerPortfolios[i][1]>o;++i)e.push(this.cornerPortfolios[i]);e.push([n,o]),this.cornerPortfolios=e}}else{if("minVolatility"!=t)throw new Error("unknown constraint type");if(this.getLowestVolatility()<r){var a;if(this.getHighestVolatility()<r)throw new Error("impossible to restrict the efficient frontier: the minimum volatility constraint is not feasible");if(0==(a=this.computeEfficientPortfolio("volatility",r+.5*this.epsEfficientPortfolioComputation)).length)throw new Error("internal error: no efficient portfolio with a volatility greater than "+r+": the covariance matrix might not be semi-definite positive");n=a[0],o=a[1],e=new Array;for(i=0;i<this.cornerPortfolios.length-1&&this.cornerPortfolios[i][1]>o;++i)e.push(this.cornerPortfolios[i]);e.push([n,o]),this.cornerPortfolios=e}}},Z.prototype.computeMaximumSharpeRatioEfficientPortfolio=function(t){var r=function(t){var r=this.cornerPortfolios.length-1,n=0;if(r==n)return r;for(;r-n!=1;){var o=Math.floor((r+n)/2),i=this.cornerPortfolios[o][0],e=this.computePortfolioSharpeRatio(i,t),a=o+1,s=this.cornerPortfolios[a][0],u=this.computePortfolioSharpeRatio(s,t);if(u<e)r=o;else{if(!(e<u)){r=a,n=o;break}n=o}}return r}.call(this,t),n=this.cornerPortfolios[r][0],o=[[n,this.computePortfolioSharpeRatio(n,t),this.cornerPortfolios[r][1]]];r<=this.cornerPortfolios.length-2&&o.push(e.call(this,t,r+1,r)),1<=r&&o.push(e.call(this,t,r,r-1));var i=W(o,function(t,r){return t[1]-r[1]})[0];return[i[0],i[2]];function e(t,r,n){var o=this.cornerPortfolios,i=o[r][0],e=o[n][0],a=this.computePortfolioSharpeRatio(i,t),s=this.computePortfolioReturn(i),u=this.computePortfolioVolatility(i),l=u*u,f=this.computePortfolioSharpeRatio(e,t),h=this.computePortfolioReturn(e),m=this.computePortfolioVolatility(e),c=m*m,d=s-h,w=h-t,p=d*d,v=2*d*w,b=w*w,y=it.vectorDotProduct(it.xy(this.sigma,i),e),g=l+c-2*y,x=-2*(c-y),C=p*x-v*g,R=v*c-b*x,E=2*(p*c-b*g)/2,M=0<=E?1:-1,A=E*E-C*R;if(Math.abs(A)<=1e-16&&(A=0),A<0)throw new Error("internal error, the covariance matrix might not be semi-definite positive");var P=-(E+M*Math.sqrt(A)),z=P/C,k=R/P,_=[[i,a,o[r][1]],[e,f,o[n][1]]];if(0<z&&z<1){var I=it.fill(i.nbRows,1,function(t,r){return z*i.getValue(t,1)+(1-z)*e.getValue(t,1)}),V=this.computePortfolioSharpeRatio(I,t),F=z*o[r][1]+(1-z)*o[n][1];_.push([I,V,F])}if(0<k&&k<1){var O=it.fill(i.nbRows,1,function(t,r){return k*i.getValue(t,1)+(1-k)*e.getValue(t,1)}),T=this.computePortfolioSharpeRatio(O,t),S=k*o[r][1]+(1-k)*o[n][1];_.push([O,T,S])}return W(_,function(t,r){return t[1]-r[1]})[0]}},((et.prototype=Object.create(e.prototype)).constructor=et).prototype.getHighestRiskTolerancePortfolio=function(t){return this.highestRiskTolerancePortfolio},et.prototype.getHighestRiskTolerance=function(t){return this.highestRiskTolerance},et.prototype.getLowestRiskTolerancePortfolio=function(t){return this.lowestRiskTolerancePortfolio},et.prototype.getLowestRiskTolerance=function(t){return this.lowestRiskTolerance},et.prototype.computeEfficientPortfolio=function(t,i){if(null==t)throw new Error("internal error: missing constraint type");var e,a,s=this;if("return"==t)e=function(t){return s.computePortfolioReturn(t)},a=function(t){return t.ret};else if("volatility"==t)e=function(t){return s.computePortfolioVolatility(t)},a=function(t){return t.volatility};else if("riskTolerance"!=t)throw new Error("internal error: unknown constraint type");if(null==i)throw new Error("internal error: missing constraint value");var u,r,n=this.nbAssets,l=this.mu,o=this.sigma,f=this.lowerBounds,h=this.upperBounds,m=this.epsEfficientPortfolioComputation,c=o,d=it.ones(n,1),w=f,p=h;if("return"===t||"volatility"===t){var v=this.getLowestRiskTolerancePortfolio(),b=e(v),y=this.getHighestRiskTolerancePortfolio(),g=e(y);if(g+m<i||i<b-m)return[];if(Math.abs(i-b)<=m)u=v,r=this.getLowestRiskTolerance();else if(Math.abs(i-g)<=m)u=y,r=this.getHighestRiskTolerance();else{var x=it.fill(n,1,function(t,r){return 1/n}),C=U(it.ones(n,1),x,d,1,w,p);u=C[0];s=this;r=L(function(t){var r=s.cachedEfficientPortfolios.get(t);if(r)return u=r.weights,a(r)-i;var n=it.ax(-t,l),o=T(c,n,d,1,w,p,{x0:u,antiCycling:s.antiCyclingGsmo,eps:s.epsGsmo,maxIter:s.maxIterationsGsmo});return u=o[0],s.cachedEfficientPortfolios.set(t,{weights:u,ret:s.computePortfolioReturn(u),volatility:s.computePortfolioVolatility(u)}),e(u)-i},this.getLowestRiskTolerance(),this.getHighestRiskTolerance())}}else{if("riskTolerance"!==t)throw new Error("internal error: unknown constraint type");var R=i,E=it.ax(-R,l),M=T(c,E,d,1,w,p,{antiCycling:this.antiCyclingGsmo,eps:this.epsGsmo,maxIter:this.maxIterationsGsmo});u=M[0],r=R}return[u,r]},et.prototype.restrict=function(t,r){if(null==t)throw new Error("missing constraint type");if(null==r)throw new Error("missing constraint value");if("minReturn"==t){if(this.getLowestReturn()<r){if(this.getHighestReturn()<r)throw new Error("impossible to restrict the efficient frontier: the minimum return constraint is not feasible");if(0==(i=this.computeEfficientPortfolio("return",r+.5*this.epsEfficientPortfolioComputation)).length)throw new Error("internal error: no efficient portfolio with a return greater than "+r);var n=i[0],o=i[1];this.lowestRiskTolerancePortfolio=n,this.lowestRiskTolerance=o,this.lowestRiskTolerance>=this.highestRiskTolerance&&(this.highestRiskTolerancePortfolio=n,this.highestRiskTolerance=o)}}else{if("minVolatility"!=t)throw new Error("unknown constraint type");if(this.getLowestVolatility()<r){var i;if(this.getHighestVolatility()<r)throw new Error("impossible to restrict the efficient frontier: the minimum volatility constraint is not feasible");if(0==(i=this.computeEfficientPortfolio("volatility",r+.5*this.epsEfficientPortfolioComputation)).length)throw new Error("internal error: no efficient portfolio with a volatility greater than "+r+": the covariance matrix might not be semi-definite positive");n=i[0],o=i[1];this.lowestRiskTolerancePortfolio=n,this.lowestRiskTolerance=o,this.lowestRiskTolerance>=this.highestRiskTolerance&&(this.highestRiskTolerancePortfolio=n,this.highestRiskTolerance=o)}}},et.prototype.computeMaximumSharpeRatioEfficientPortfolio=function(o){var i,t=this.nbAssets,e=this.mu,r=this.sigma,n=this.lowerBounds,a=this.upperBounds,s=(this.epsEfficientPortfolioComputation,r),u=it.ones(t,1),l=n,f=a,h=this,m=function(t,r,n,o){void 0===o&&(o={});var i=o.maxIter;void 0===i&&(i=-1);var e=o.eps;void 0===e&&(e=1e-6);var a=(Math.sqrt(5)-1)/2,s=r,u=n,l=u-a*(u-s),f=s+a*(u-s),h=t(r),m=t(n),c=t(l),d=t(f);if(n<r)throw new Error("bracketing interval lower bound "+r+" greater than bracketing interval upper bound "+n);for(var w=0;;){if(-1!==i&&i<w)throw new Error("maximum number of iterations reached: "+i);if(++w,c<=d?(u=f,f=l,d=c,c=t(l=u-a*(u-s))):d<c&&(s=l,l=f,c=d,d=t(f=s+a*(u-s))),Math.abs(u-s)<=e)return c<d?h<c?[r,h]:[l,c]:m<d?[n,m]:[f,d]}}(function(t){var r=it.ax(-t,e),n=T(s,r,u,1,l,f,{antiCycling:h.antiCyclingGsmo,eps:h.epsGsmo,maxIter:h.maxIterationsGsmo});return i=n[0],-h.computePortfolioSharpeRatio(i,o)},this.getLowestRiskTolerance(),this.getHighestRiskTolerance());return[i,m[0]]},((J.prototype=Object.create(e.prototype)).constructor=J).prototype.getHighestRiskTolerancePortfolio=function(t){return this.efficientFrontier.getHighestRiskTolerancePortfolio(t)},J.prototype.getHighestRiskTolerance=function(t){return this.efficientFrontier.getHighestRiskTolerance()},J.prototype.getLowestRiskTolerancePortfolio=function(t){return this.efficientFrontier.getLowestRiskTolerancePortfolio(t)},J.prototype.getLowestRiskTolerance=function(t){return this.efficientFrontier.getLowestRiskTolerance()},J.prototype.computeEfficientPortfolio=function(t,r){return this.efficientFrontier.computeEfficientPortfolio(t,r)},J.prototype.getCornerPortfolios=function(){if("critical-line"==this.efficientFrontierOptimizationMethod)return this.efficientFrontier.getCornerPortfolios();throw new Error("internal error: unsupported method")},J.prototype.restrict=function(t,r){return this.efficientFrontier.restrict(t,r)},J.prototype.computeMaximumSharpeRatioEfficientPortfolio=function(t){return this.efficientFrontier.computeMaximumSharpeRatioEfficientPortfolio(t)},e.prototype.getHighestReturnPortfolio=function(t){return this.getHighestRiskTolerancePortfolio()},e.prototype.getHighestReturn=function(t){return this.computePortfolioReturn(this.getHighestReturnPortfolio())},e.prototype.getLowestReturnPortfolio=function(t){return this.getLowestRiskTolerancePortfolio()},e.prototype.getLowestReturn=function(t){return this.computePortfolioReturn(this.getLowestReturnPortfolio())},e.prototype.getHighestVolatilityPortfolio=function(t){return this.getHighestRiskTolerancePortfolio()},e.prototype.getHighestVolatility=function(t){return this.computePortfolioVolatility(this.getHighestVolatilityPortfolio())},e.prototype.getLowestVolatilityPortfolio=function(t){return this.getLowestRiskTolerancePortfolio()},e.prototype.getLowestVolatility=function(t){return this.computePortfolioVolatility(this.getLowestVolatilityPortfolio())},e.prototype.getHighestRiskTolerancePortfolio=function(t){throw new Error("internal error: function is not implemented")},e.prototype.getHighestRiskTolerance=function(t){throw new Error("internal error: function is not implemented")},e.prototype.getLowestRiskTolerancePortfolio=function(t){throw new Error("internal error: unction is not implemented")},e.prototype.getLowestRiskTolerance=function(t){throw new Error("internal error: function is not implemented")},e.prototype.computePortfolioReturn=function(t){return it.vectorDotProduct(this.mu,t)},e.prototype.computePortfolioVolatility=function(t){var r=it.vectorDotProduct(it.xy(this.sigma,t),t);if(Math.abs(r)<=this.epsPortfolioVolatility)r=0;else if(r<0&&r<-this.epsPortfolioVolatility)throw new Error("internal error: negative volatility, covariance matrix might not be semi-definite positive");return Math.sqrt(r)},e.prototype.computePortfolioSharpeRatio=function(t,r){if(null==r||null==r)throw new Error("internal error: missing risk free rate");var n=this.computePortfolioReturn(t)-r,o=Math.max(this.epsPortfolioVolatility,this.computePortfolioVolatility(t));if(0==o)throw new Error("internal error: null volatility when computing the Sharpe ratio");return n/o},e.prototype.computeEfficientPortfolio=function(t,r){throw new Error("internal error: function is not implemented")},e.prototype.restrict=function(t,r){throw new Error("internal error: function is not implemented")},e.prototype.computeMaximumSharpeRatioEfficientPortfolio=function(t){throw new Error("internal error: function is not implemented")},y.meanVarianceOptimizationWeights=function(t,r,n){void 0===n&&(n={constraints:{}}),void 0===n.constraints&&(n.constraints={}),void 0===n.optimizationMethodParams&&(n.optimizationMethodParams={});var o=n.optimizationMethod;if(void 0===o&&(o="automatic"),"critical-line"!=o&&"gsmo"!=o&&"automatic"!=o)throw new Error("unsupported optimisation method");var i,e,a=n.constraints.return,s=n.constraints.volatility,u=n.constraints.maxVolatility,l=n.constraints.riskTolerance;if(void 0===a&&void 0===s&&void 0===u&&null==l)throw new Error("missing return, volatility or risk tolerance constraints");if(void 0!==a&&void 0!==s||void 0!==a&&void 0!==u)throw new Error("simultaneous return and volatility constraints");if(void 0!==l&&(void 0!==a||void 0!==u||void 0!==s))throw new Error("simultaneous risk tolerance and return or volatility constraints");if("automatic"==o)i=new J(t,r,n);else if("critical-line"==o)i=new Z(t,r,n);else{if("gsmo"!=o)throw new Error("internal error: unsupported optimisation method");i=new et(t,r,n)}if(void 0!==a){if(0==(p=i.computeEfficientPortfolio("return",a)).length)throw new Error("no matching efficient portfolio with a return equal to "+a);e=p[0]}else if(void 0!==s){if(0==(p=i.computeEfficientPortfolio("volatility",s)).length)throw new Error("no matching efficient portfolio with a volatility equal to "+s);e=p[0]}else if(void 0!==l){var f=i.getHighestRiskTolerancePortfolio(),h=i.getHighestRiskTolerance(),m=i.getLowestRiskTolerancePortfolio(),c=i.getLowestRiskTolerance();if(h-(d=i.epsEfficientPortfolioComputation)<l)e=f;else if(l<c+d)e=m;else{if(0==(p=i.computeEfficientPortfolio("riskTolerance",l)).length)throw new Error("internal error: no matching efficient portfolio with a risk tolerance equal to "+l);e=p[0]}}else if(void 0!==u){var d,w=i.getHighestVolatilityPortfolio();if(i.getHighestVolatility()-(d=i.epsEfficientPortfolioComputation)<u)e=w;else{var p;if(0==(p=i.computeEfficientPortfolio("volatility",u)).length)throw new Error("no matching efficient portfolio with a volatility lower than or equal to "+u);e=p[0]}}return e.toArray()},y.meanVarianceEfficientFrontierNearestWeights=function(t,r,n,o){void 0===o&&(o={constraints:{}}),void 0===o.constraints&&(o.constraints={}),void 0===o.optimizationMethodParams&&(o.optimizationMethodParams={});var i=o.optimizationMethod;if(void 0===i&&(i="automatic"),"critical-line"!=i&&"gsmo"!=i&&"automatic"!=i)throw new Error("unsupported optimisation method");var e,a;t=new it(t);if("automatic"==i)e=new J(r,n,o);else if("critical-line"==i)e=new Z(r,n,o);else{if("gsmo"!=i)throw new Error("internal error: unsupported optimisation method");e=new et(r,n,o)}if("critical-line"==i||"critical-line"==e.efficientFrontierOptimizationMethod)a=e.getCornerPortfolios();else{if("gsmo"!=i&&"gsmo"!=e.efficientFrontierOptimizationMethod)throw new Error("internal error: unsupported optimisation method");var s=o.optimizationMethodParams.nbPortfoliosGsmo;null==s&&(s=100),a=new Array(s);for(var u=e.getLowestReturn(),l=(e.getHighestReturn()-u)/(s-1),f=0;f<s;++f){var h,m=u+f*l;if(0==(h=e.computeEfficientPortfolio("return",m)).length)throw new Error("internal error: no matching efficient portfolio with a return of "+m);a[f]=h[0]}}var c=Number.POSITIVE_INFINITY;for(f=0;f<a.length-1;++f){var d=a[f],w=v(t,a[f+1],d),p=it.xmy(t,new it(w)).vectorNorm("two");p<=c&&(h=w,c=p)}return h},y.meanVarianceEfficientFrontierPortfolios=function(t,r,n){void 0===n&&(n={constraints:{}}),void 0===n.constraints&&(n.constraints={}),void 0===n.optimizationMethodParams&&(n.optimizationMethodParams={});var o=n.optimizationMethod;if(void 0===o&&(o="automatic"),"critical-line"!=o&&"gsmo"!=o&&"automatic"!=o)throw new Error("unsupported optimisation method");var i,e=n.nbPortfolios||100,a=n.discretizationType;if(null==a&&(a="return"),"return"!=a&&"volatility"!=a&&"riskTolerance"!=a)throw new Error("unsupported discretization type");if("automatic"==o)i=new J(t,r,n);else if("critical-line"==o)i=new Z(t,r,n);else{if("gsmo"!=o)throw new Error("internal error: unsupported optimisation method");i=new et(t,r,n)}var s,u,l=new Array(e);if("return"==a)s=i.getLowestReturn(),u=i.getHighestReturn();else if("volatility"==a)s=i.getLowestVolatility(),u=i.getHighestVolatility();else{if("riskTolerance"!=a)throw new Error("internal error: unsupported discretization type");s=i.getLowestRiskTolerance(),u=i.getHighestRiskTolerance()}for(var f=1==e?-1:(u-s)/(e-1),h=1==e?(s+u)/2:s,m=0;m<e;++m){var c=h+m*f,d=i.computeEfficientPortfolio(a,c);if(0==d.length)throw new Error("internal error: no matching efficient portfolio with a constraint value "+a+" equal to "+c);d=d[0];var w=i.computePortfolioReturn(d),p=i.computePortfolioVolatility(d);l[m]=[d.toArray(),w,p]}return l},y.minimaxWeights=function(n,t){void 0===t&&(t={constraints:{}}),void 0===t.constraints&&(t.constraints={});var r=!0;void 0!==t.constraints.fullInvestment&&(r=t.constraints.fullInvestment);var o=t.outputMinimumPortfolioReturn,i=n.length,e=n[0].length,a=it.fill(i+1,1,function(t,r){return t<=i?0:-1}),s=null,u=null;r&&(s=it.fill(1,i+1,function(t,r){return r<=i?1:0}),u=it.ones(1,1));var l=function(o,t,i,r,n,e,a,s){void 0===s&&(s={});var u=s.eps||1e-8,l=s.maxIter||1e5,f=!1,h=!1,m=!1;if(null!==o&&null!==t)f=!0;else{if(null!==o&&null===t)throw new Error("equality constraints vector is missing");if(null===o&&null!==t)throw new Error("equality constraints matrix is missing")}if(null!==i&&null!==r)h=!0;else{if(null!==i&&null===r)throw new Error("inequality constraints vector is missing");if(null===i&&null!==r)throw new Error("inequality constraints matrix is missing")}if(null!==e&&null!==a)m=!0;else{if(null!==e&&null===a)throw new Error("upper bounds constraints vector is missing");if(null===e&&null!==a)throw new Error("lower bounds constraints vector is missing")}if(!(n instanceof it))throw new Error("fifth input must be a matrix");if(1!==n.nbColumns)throw new Error("fifth input is not a vector: "+n.nbColumns+"-"+n.nbRows);if(f){if(!(o instanceof it))throw new Error("first input must be a matrix");if(!(t instanceof it))throw new Error("second input must be a matrix");if(o.nbRows!==t.nbRows)throw new Error("first and second inputs number of rows do not match: "+o.nbRows+"-"+t.nbRows);if(o.nbColumns!==n.nbRows)throw new Error("first input number of columns and fifth input number of rows do not match: "+o.nbColumns+"-"+n.nbRows);if(1!==t.nbColumns)throw new Error("second input is not a vector: "+t.nbColumns+"-"+t.nbRows)}if(h){if(!(i instanceof it))throw new Error("third input must be a matrix");if(!(r instanceof it))throw new Error("third input must be a matrix");if(i.nbRows!==r.nbRows)throw new Error("third and fourth inputs number of rows do not match: "+i.nbRows+"-"+r.nbRows);if(i.nbColumns!==n.nbRows)throw new Error("third input number of columns and fifth input number of rows do not match: "+i.nbColumns+"-"+n.nbRows);if(1!==r.nbColumns)throw new Error("fourth input is not a vector: "+r.nbColumns+"-"+r.nbRows)}if(m){if(null!==e.nbRows){if(!(e instanceof it))throw new Error("sixth input must be a matrix");if(e.nbRows!==n.nbRows)throw new Error("sixth input number of rows and fifth input number of rows do not match: "+e.nbRows+"-"+n.nbRows)}if(null!==a.nbRows){if(!(a instanceof it))throw new Error("seventh input must be a matrix");if(a.nbRows!==n.nbRows)throw new Error("seventh input number of rows and fifth input number of rows do not match: "+a.nbRows+"-"+n.nbRows)}}var c=0,d=null,w=null,p=null;f&&(c=o.nbRows,d=it.zeros(c,1),w=it.zeros(c,1),p=it.zeros(c,1));var v=0,b=null,y=null,g=null;h&&(v=i.nbRows,b=it.zeros(v,1),y=it.zeros(v,1),g=it.zeros(v,1));var x=n.nbRows,C=it.ones(x,1),R=it.ones(x,1),E=it.ones(x,1),M=it.zeros(x,1),A=it.zeros(x,1),P=it.zeros(x,1),z=null;f&&(z=it.zeros(c,1));var k=null;h&&(k=it.zeros(v,1));var _=it.fill(x,1,function(t,r){var n=0;f&&(n+=o.vectorNorm("one","column",t));h&&(n+=i.vectorNorm("one","column",t));return 0==n&&(n=1),.9995/n}),I=null;f&&(I=it.fill(c,1,function(t,r){var n=o.vectorNorm("one","row",t);return 0==n&&(n=1),.9995/n}));var V=null;h&&(V=it.fill(v,1,function(t,r){var n=i.vectorNorm("one","row",t);return 0==n&&(n=1),.9995/n}));for(var F=0;;){if(-1!==l&&l<=F)throw new Error("maximum number of iterations reached: "+l);if(++F,f&&h?R=it.xpy(it.xpy(it.txy(o,d,A),it.txy(i,b,P),A),n,R):f?R=it.xpy(it.txy(o,d,A),n,R):h&&(R=it.xpy(it.txy(i,b,A),n,R)),R=it.xmy(C,it.elementwiseProduct(R,_,A),R),m)for(var 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a=t.optimizationMethodParams.nDeltas;void 0===a&&(a=e);var s=t.optimizationMethodParams.maxIterationsInitPoint;void 0===s&&(s=1e4);for(var V=f.length,u=f[0].length,l=(h=new it(h),f=it.fill(u,V,function(t,r){return f[r-1][t-1]}),"function"==typeof Float64Array?new Float64Array(V):new Array(V)),m="function"==typeof Float64Array?new Float64Array(V):new Array(V),c=0;c<V;++c)l[c]=t.constraints.minWeights?t.constraints.minWeights[c]:0,m[c]=t.constraints.maxWeights?t.constraints.maxWeights[c]:1;if(o){function d(t,r){var n;t=new it(t);if(r){var o=r.x_c,i=r.x_c_updatedIndexes;r.f_x_c;n=new it(r.f_x_c_context.assetsReturnsTx_m_b);for(var e=0;e<i.length;++e)for(var a=i[e],s=t.data[a]-o[a],u=0;u<f.nbRows;++u)n.data[u]+=f.data[u*f.nbColumns+a]*s}else n=it.xmy(it.xy(f,t),h);var l=n.vectorNorm("two");return{f_x:.5*l*l,f_x_context:{assetsReturnsTx_m_b:n}}}try{var w=1;k||(w=Math.random()),v=y.randomWeights(V,{maxIter:s,constraints:{minExposure:w,maxExposure:1,minNbAssets:_,maxNbAssets:I,minWeights:l,maxWeights:m}})}catch(t){throw"maximum number of iterations reached"===t.message?new Error("infeasible problem detected"):t}var F=new q(V,void 0,!0),p=new it(z(d,v,{nSteps:e,nRounds:i,nDeltas:a,neighbourGenerator:function(t,r){for(var n=r.lowerBounds,o=r.upperBounds,i=t,e=0,a=1,s=0;s<V;++s)if(0<i[s]&&0==n[s]||i[s]>=n[s]&&0<n[s]){if(++e,a-=i[s],i[s]<n[s])throw new Error("internal error: asset present in the portfolio, but strictly below its lower bound");if(i[s]>o[s])throw new Error("internal error: asset present in the portfolio, but strictly above its upper bound")}if(a=Math.max(0,a),I<e)throw new Error("internal error: number of assets strictly greater than the allowed maximum number of assets");if(e<_)throw new Error("internal error: number of assets strictly lower than the allowed minimum number of assets");for(var u=[],l=F.next(),f=0;f<V;++f){if(0<i[s=l[f]-1]&&0==n[s]||i[s]>=n[s]&&0<n[s]){var h=i[s]-n[s],m=Math.min(0,h),c=i[s];k||(u.push([s,-1,m,h]),_<e&&u.push([s,-1,c]));for(var d=0;d<V;++d){if((i[d]<n[d]||0==i[d])&&i[d]<o[d]){var w=n[d],p=Math.max(w,o[d]-i[d]);if(e<I&&m<=w&&w<=h){var v=w,b=Math.min(p,h);u.push([s,d,v,b])}w<=c&&c<=p&&u.push([s,d,c])}if((0<i[d]&&0==n[d]||i[d]>=n[d]&&0<n[d])&&i[d]<o[d]){p=o[d]-i[d],w=Math.min(0,p);if(_<e&&w<=c&&c<=p&&u.push([s,d,c]),m<=w&&w<=h){v=w,b=Math.min(p,h);u.push([s,d,v,b])}}}}var y=!1;if(0!=u.length&&(y=!0),!k){if((0<i[s]&&0==n[s]||i[s]>=n[s]&&0<n[s])&&i[s]<o[s]){p=o[s]-i[s];if((w=Math.min(0,p))<=a){v=w,b=Math.min(p,a);u.push([-1,s,v,b])}}if((i[s]<n[s]||0==i[s])&&i[s]<o[s]&&e<I){w=n[s],p=Math.max(w,o[s]-i[s]);if(w<=a){v=w,b=Math.min(p,a);u.push([-1,s,v,b])}}}if(y)break}if(0==u.length)throw new Error("internal error: no feasible switch");var g,x,C,R,E,M=u[(g=0,x=u.length,Math.floor(Math.random()*(x-g))+g)],A=[],P=M[0],z=M[1];if(3==M.length)C=M[2],-1!=P&&(i[P]=0,A.push(P)),-1!=z&&(i[z]+=C,A.push(z));else{if(4!=M.length)throw new Error("internal error: unexpected lenght of the switches structure");R=M[2],E=M[3],C=Math.random()*(E-R)+R,-1!=P&&(i[P]-=C,A.push(P)),-1!=z&&(i[z]+=C,A.push(z))}return{xx:i,x_updated_indexes:A.filter(function(t,r,n){return n.indexOf(t)==r})}},neighbourGeneratorParameters:{assetsRandomIterator:F,lowerBounds:l,upperBounds:m}})[0])}else{function d(t){var r=it.xmy(it.xy(f,t),h).vectorNorm("two");return.5*r*r}var v;p=O(d,function(t){return it.txy(f,it.xmy(it.xy(f,t),h))},function(t){return S(t.data,l,m)},function(t){return new it(H(t.data,l,m))},v=new it(H(it.ones(f.nbColumns,1).data,l,m)),{eps:r,maxIter:n,maxLine:n})[0]}return p.toArray()},y.mostDiversifiedWeights=function(t,r){void 0===r&&(r={}),void 0===r.constraints&&(r.constraints={}),void 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h="function"==typeof UInt32Array?new UInt32Array(l):new Array(l),p=(f=0,0);f<d;++f)1e-12<c.data[f]&&(h[p]=f,++p);h[l-1]=d;var v=it.zeros(d+1,1).data;v[d]=m;for(p=0;p<l-1;++p){v[f=h[p]]=Math.floor(c.data[f]*m/w.data[f]),v[d]-=v[f]*w.data[f]}if(v[d]<0)throw new Error("internal error: negative cash during intitial feasible point generation");for(;;){var b=-1,y=u(v).f_x;for(p=0;p<l-1;++p){f=h[p];if(w.data[f]<=v[d]){v[f]+=1,v[d]-=w.data[f];var g=u(v).f_x;g<y&&(b=f,y=g),v[f]-=1,v[d]+=w.data[f]}}if(-1==b)break;v[b]+=1,v[d]-=w.data[b]}if(v[d]<0)throw new Error("internal error: negative cash during intitial feasible point generation");var x=z(u,v,{nSteps:e,nRounds:i,nDeltas:a,neighbourGenerator:function(t,r){function n(t,r){return Math.floor(Math.random()*(r-t))+t}for(var o,i=r.workingAssetsRandomIterator.next(),e=0;e<i.length&&(0==t[o=i[e]]&&o!=d);++e);var a=[];if(o!=d){var s=n(1,t[o]+1);t[o]-=s;var u=w.data[o]*s;t[d]+=u,a.push(o),a.push(d)}var l,f,h=r.workingAssetsRandomIterator.next();for(e=0;e<h.length&&(l=h[e])!=d&&0==(f=Math.floor(t[d]/w.data[l]));++e);if(l!=d){var m=n(1,f+1);t[l]+=m;var c=w.data[l]*m;t[d]-=c,a.push(l),a.push(d)}return{xx:t,x_updated_indexes:a.filter(function(t,r,n){return n.indexOf(t)==r})}},neighbourGeneratorParameters:{workingAssetsRandomIterator:new q(null,h.slice(),!0)}})[0],C=new it.fill(d,1,function(t,r){return x[t-1]*w.data[t-1]/m}).toArray();return[new it.fill(d,1,function(t,r){return x[t-1]}).toArray(),C,x[d]]},y.proportionalMinimumVarianceWeights=function(t,r){for(var n=(t=new it(t)).nbRows,o=t.toRowArray(),i=new Array(n),e=0;e<n;++e)i[e]=I(o[e]);var a=I(i),s=d(i),u=new it(i,1).elemMap(function(t,r,n){return 1-w((n-a)/s)});u=u.normalize(u);var l=t.diagonal().elemMap(function(t,r,n){return 1/n}).normalize();return(u=it.vectorHadamardProduct(u,l).normalize()).toArray()},y.randomSubspaceOptimizationWeights=function(t,r,n){void 0===n&&(n={}),void 0===n.constraints&&(n.constraints={}),void 0===n.subsetOptimizationFctOpt&&(n.subsetOptimizationFctOpt={}),void 0===n.subsetOptimizationFctOpt.constraints&&(n.subsetOptimizationFctOpt.constraints={});var o=n.constraints.minWeights;null==o&&(o=it.zeros(t,1).data);var i=n.constraints.maxWeights;if(null==i&&(i=it.ones(t,1).data),t<=1)return[1];var e=n.sizeSubsets;if(void 0===e&&(e=Math.max(2,Math.floor(Math.sqrt(t)))),e<=1||t+1<=e)throw new Error("the size of the subsets of assets must be between 2 and "+t.toString());var a=n.subsetsGenerationMethod;void 0===a&&(a="random");var s,u=n.nbRandomSubsets;if(void 0===u&&(u=128),e===t&&(u=1),"random"===a)s=u;else{if("deterministic"!==a)throw new Error("unsupported subsets of assets generation method");s=function(t,r){if(t<0)throw new Error("n must be a positive integer");if(r<0)throw new Error("k must be a positive integer");if(t<r)throw new Error("k must be less than or equal to n");for(var n=1,o=1;o<=r;++o)n*=t+1-o,n/=o;return n}(t,e)}var l=n.subsetsAggregationMethod;if(void 0===l&&(l="average"),"average"!==l&&"median"!==l)throw new Error("unsupported aggregation method");var f,h=n.maxInfeasibleSubsetsRatio;if(void 0===h&&(h=0),"random"===a)f=new C(t,e,!1);else{if("deterministic"!==a)throw new Error("unsupported subsets generation method");f=new x(t,e,!1)}for(var m=n.subsetOptimizationFctOpt,c=0,d=new Array(s),w=0;w<s;++w){var p=f.next();m.constraints.minWeights="function"==typeof Float64Array?new Float64Array(e):new Array(e);for(var v=0;v<e;++v)m.constraints.minWeights[v]=o[p[v]-1];m.constraints.maxWeights="function"==typeof Float64Array?new Float64Array(e):new Array(e);for(v=0;v<e;++v)m.constraints.maxWeights[v]=i[p[v]-1];try{var b=r(p,m);if(b.length!=e)throw new Error("internal error: the portfolio optimization method did not return the expected number of weights")}catch(t){if("infeasible portfolio optimization problem"===t.message)continue;throw t}var y=it.zeros(t,1);for(v=0;v<e;++v)y.setValueAt(p[v],1,b[v]);d[c++]=y}if(0===(d.length=c))throw new 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u=t.constraints.minExposure;null==u&&(u=1);var l=t.constraints.maxExposure;null==l&&(l=1);a=new it(a);var r=(s=new it(s)).nbColumns;if(void 0===t.sizeSubsets){var n=-2*Math.sqrt(r*(r+3)/2),o=2.25-1*n,i=n/-(1.5+Math.sqrt(o));t.sizeSubsets=Math.max(2,Math.floor(i))}return t.subsetOptimizationFctOpt=t.subsetsOpt,y.randomSubspaceOptimizationWeights(r,function(t,n){var o=t.length,i=a.submatrix(t,[1]),e=s.submatrix(t,t);1!=u&&(i=it.fill(o+1,1,function(t,r){return t<=o?i.getValue(t,1):0}),e=it.fill(o+1,o+1,function(t,r){return t<=o&&r<=o?e.getValue(t,r):0}),n.constraints.minWeights=it.fill(o+1,1,function(t,r){return t<=o?n.constraints.minWeights[t-1]:1-l}).data,n.constraints.maxWeights=it.fill(o+1,1,function(t,r){return t<=o?n.constraints.maxWeights[t-1]:1-u}).data);try{var r=y.meanVarianceOptimizationWeights(i,e,n);return 1!=u&&(r=r.slice(0,o)),r}catch(t){throw t.message.includes("no matching efficient portfolio")||"infeasible problem detected: the restricted simplex is empty"===t.message?new Error("infeasible portfolio optimization problem"):t}},t)},y.randomSubspaceGlobalMinimumVarianceOptimizationWeights=function(a,t){void 0===t&&(t={}),void 0===t.constraints&&(t.constraints={}),void 0===t.subsetsOpt&&(t.subsetsOpt={}),void 0===t.subsetsOpt.optimizationMethodParams&&(t.subsetsOpt.optimizationMethodParams={}),void 0===t.subsetsOpt.constraints&&(t.subsetsOpt.constraints={});var s=t.constraints.minExposure;null==s&&(s=1);var u=t.constraints.maxExposure;null==u&&(u=1);var r=(a=new it(a)).nbColumns;if(void 0===t.sizeSubsets){var n=null==f?1:3,o=null==f?-2*Math.sqrt(r*(r+1)/2):-2*Math.sqrt(r*(r+3)/2),i=n/2,e=i*i-1*o,l=o/-(i+Math.sqrt(e));t.sizeSubsets=Math.max(2,Math.floor(l))}var f=t.mu;return f=null==f?it.zeros(r,1):new it(f),t.subsetOptimizationFctOpt=t.subsetsOpt,y.randomSubspaceOptimizationWeights(r,function(t,n){var o=t.length,i=a.submatrix(t,t),e=f.submatrix(t,[1]);n.mu=e,1!=s&&(e=it.fill(o+1,1,function(t,r){return t<=o?e.getValue(t,1):0}),n.mu=e,i=it.fill(o+1,o+1,function(t,r){return t<=o&&r<=o?i.getValue(t,r):0}),n.constraints.minWeights=it.fill(o+1,1,function(t,r){return t<=o?n.constraints.minWeights[t-1]:1-u}).data,n.constraints.maxWeights=it.fill(o+1,1,function(t,r){return t<=o?n.constraints.maxWeights[t-1]:1-s}).data);try{var r=y.globalMinimumVarianceWeights(i,n);return 1!=s&&(r=r.slice(0,o)),r}catch(t){throw"infeasible problem detected: the restricted simplex is empty"===t.message?new Error("infeasible portfolio optimization problem"):t}},t)},y.randomSubspaceMaximumSharpeRatioWeights=function(a,s,u,t){void 0===t&&(t={}),void 0===t.constraints&&(t.constraints={}),void 0===t.subsetsOpt&&(t.subsetsOpt={}),void 0===t.subsetsOpt.optimizationMethodParams&&(t.subsetsOpt.optimizationMethodParams={}),void 0===t.subsetsOpt.constraints&&(t.subsetsOpt.constraints={});var l=t.constraints.minExposure;null==l&&(l=1);var f=t.constraints.maxExposure;null==f&&(f=1);a=new it(a);var r=(s=new it(s)).nbColumns;if(void 0===t.sizeSubsets){var n=-2*Math.sqrt(r*(r+3)/2),o=2.25-1*n,i=n/-(1.5+Math.sqrt(o));t.sizeSubsets=Math.max(2,Math.floor(i))}return t.subsetOptimizationFctOpt=t.subsetsOpt,y.randomSubspaceOptimizationWeights(r,function(t,n){var o=t.length,i=a.submatrix(t,[1]),e=s.submatrix(t,t);1!=l&&(i=it.fill(o+1,1,function(t,r){return t<=o?i.getValue(t,1):0}),e=it.fill(o+1,o+1,function(t,r){return t<=o&&r<=o?e.getValue(t,r):0}),n.constraints.minWeights=it.fill(o+1,1,function(t,r){return t<=o?n.constraints.minWeights[t-1]:1-f}).data,n.constraints.maxWeights=it.fill(o+1,1,function(t,r){return t<=o?n.constraints.maxWeights[t-1]:1-l}).data);try{var r=y.maximumSharpeRatioWeights(i,e,u,n);return 1!=l&&(r=r.slice(0,o)),r}catch(t){throw"infeasible problem detected: the restricted simplex is empty"===t.message||"impossible to restrict the efficient frontier: the minimum return constraint is not feasible"===t.message||"impossible to restrict the efficient frontier: the minimum volatility constraint is not feasible"===t.message?new Error("infeasible portfolio optimization problem"):t}},t)},y.randomWeights=function(t,r){void 0===r&&(r={}),void 0===r.constraints&&(r.constraints={});var n=r.constraints.minNbAssets||r.constraints.maxNbAssets,o=r.constraints.minNbAssets;void 0===o&&(o=1);var i=r.constraints.maxNbAssets;void 0===i&&(i=t);var e=r.constraints.minExposure;void 0===e&&(e=1);var a=r.constraints.maxExposure;void 0===a&&(a=1);var s=r.maxIter;void 0===s&&(s=1e4);for(var u=-1;;){if(++u,-1!==s&&s<u)throw new Error("maximum number of iterations reached");var l=Math.floor(Math.random()*(i-o+1))+o,f=new C(t,l,!1).next(),h=Math.random()*(a-e)+e,m=0;if(1!==h){m=1;for(var c="function"==typeof Float64Array?new Float64Array(l+m):new Array(l+m),d="function"==typeof Float64Array?new Float64Array(l+m):new Array(l+m),w=0;w<l;++w)c[w]=0,d[w]=1;var p=1-h;c[l]=p,d[l]=p}if(r.constraints.minWeights){if(1===h)c="function"==typeof Float64Array?new Float64Array(l):new 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V(S),f=0;-1==T||f!=T;){if(-1==T&&-1!=O&&O<=f)throw new Error("maximum number of cycles reached: "+O);var h;for(++f,l.generateCoordinates();;){var m=l.sampleCoordinate();if(-1==m)break;"acf"===_.coordinatesSampler&&(h=.5*a-s);var c=o.data[m-1],d=i.data[m-1],w=z.data[(m-1)*z.nbColumns+(m-1)],p=e.data[m-1]-o.data[m-1]*w,v=-t*k.data[m-1]*a,b=p/2,y=0<=b?1:-1,g=b*b-w*v;if(g<0)throw new Error("internal error: negative discriminant detected, the covariance matrix might not be semi-definite positive");var x,C=-(b+y*Math.sqrt(g)),R=C/w,E=v/C;if(0<R)x=R;else{if(!(0<E))throw new Error("internal error: no strictly positive root detected, the covariance matrix might not be semi-definite positive");x=E}r&&x<r[m-1]&&(x=r[m-1]),n&&x>n[m-1]&&(x=n[m-1]),o.data[m-1]=x,i.data[m-1]=Math.log(x),s-=d*k.data[m-1],s+=i.data[m-1]*k.data[m-1];for(var M=1;M<=S;++M)e.data[M-1]+=z.data[(M-1)*z.nbColumns+(m-1)]*x,e.data[M-1]-=z.data[(M-1)*z.nbColumns+(m-1)]*c;if(a=I(o,e),"acf"===_.coordinatesSampler){var A=h-(.5*a-s);1==f?l.updateAverageGain(A):l.updateSchedulingPreference(m,A)}}var P=.5*a-s;if(-1==T&&Math.abs(P-u)<=F)break;u=P}return o}void 0===_&&(_={}),void 0===_.constraints&&(_.constraints={}),void 0===_.eps&&(_.eps=1e-10),void 0===_.epsSdp&&(_.epsSdp=1e-12),void 0===_.maxCycles&&(_.maxCycles=1e4),void 0===_.nbCycles&&(_.nbCycles=-1),void 0===_.outputPortfolioVolatility&&(_.outputPortfolioVolatility=!1),void 0===_.coordinatesSampler&&(_.coordinatesSampler="cyclic");var V,F=_.eps,o=_.epsSdp,O=_.maxCycles,T=_.nbCycles,t=_.outputPortfolioVolatility;if("cyclic"===_.coordinatesSampler)V=function(t){this.n=t,this.k=t,this.sampleCoordinate=function(){return this.k==this.n?-1:++this.k},this.generateCoordinates=function(){this.k=0}};else if("shuffledCyclic"===_.coordinatesSampler)V=function(t){this.n=t,this.k=t,this.r="function"==typeof Uint32Array?new Uint32Array(t):new Array(t);for(var r=0;r<t;++r)this.r[r]=r+1;this.sampleCoordinate=function(){return this.k==this.n?-1:this.r[this.k++]},this.generateCoordinates=function(){this.r=new q(void 0,this.r,!0).next(),this.k=0}};else if("randomized"===_.coordinatesSampler)V=function(t){this.n=t,this.k=t;for(var r="function"==typeof Float64Array?new Float64Array(t):new Array(t),n=0;n<t;++n)r[n]=1/t;this.s=new N(r),this.sampleCoordinate=function(){return this.k==this.n?-1:(++this.k,this.s.sample()+1)},this.generateCoordinates=function(){this.k=0}};else{if("acf"!==_.coordinatesSampler)throw new Error("unsupported coordinates sampler");V=function(t){this.n=t,this.k=0,this.change_rate=.2,this.p_min=.05,this.p_max=20,this.idx_set_tmp="function"==typeof Uint32Array?new Uint32Array(2*t):new Array(2*t),this.idx_set=null,this.idx_set_len=0,this.pref="function"==typeof Float64Array?new Float64Array(t):new Array(t);for(var r=0;r<t;++r)this.pref[r]=1;for(this.prefsum=t,this.acc="function"==typeof Float64Array?new Float64Array(t):new Array(t),r=0;r<t;++r)this.acc[r]=.5;this.gain_learning_rate=1/t,this.average_gain=0,this.sampleCoordinate=function(){return this.k==this.idx_set_len?-1:this.idx_set[this.k++]},this.generateCoordinates=function(){this.k=0,this.idx_set_len=0;for(var t=this.n/this.prefsum,r=0;r<this.n;++r){for(var n=this.acc[r]+t*this.pref[r],o=Math.floor(n),i=0;i<o;++i)this.idx_set_tmp[this.idx_set_len]=r+1,this.idx_set_len++;this.acc[r]=n-o}this.idx_set=new q(void 0,this.idx_set_tmp.slice(0,this.idx_set_len),!0).next()},this.updateSchedulingPreference=function(t,r){var n=this.pref[t-1]*Math.exp(this.change_rate*(r/this.average_gain-1));n<this.p_min?n=this.p_min:n>this.p_max&&(n=this.p_max),this.prefsum=this.prefsum+n-this.pref[t-1],this.pref[t-1]=n,this.average_gain=(1-this.gain_learning_rate)*this.average_gain+this.gain_learning_rate*r},this.updateAverageGain=function(t){this.average_gain+=t/this.n}}}var S=(z=new it(z)).nbRows,n=(k=new it(k),null),i=null;if(_.constraints.minWeights&&(n=_.constraints.minWeights,!_.constraints.maxWeights)){i="function"==typeof Float64Array?new Float64Array(S):new Array(S);for(var e=0;e<i.length;++e)i[e]=1}if(_.constraints.maxWeights&&(i=_.constraints.maxWeights,!_.constraints.minWeights)){n="function"==typeof Float64Array?new Float64Array(S):new Array(S);for(e=0;e<n.length;++e)n[e]=0}var a,s=r(1);if(s=s.normalize(),n||i){G(S,n,i);for(var u=I(s,it.xy(z,s)),l=.5*u,f=r(l,n,i),h=0,m=54,c=!1;0<f.sum()-1;){if(m<++h)throw new Error("internal error: maximum number of iterations reached when searching for a bracketing interval, the problem might be infeasible");if(Math.abs(f.sum()-1)<=F){c=!0;break}f=r(l*=.5,n,i)}for(var d=2*u,w=r(d,n,i),p=(h=0,m=54,!1);w.sum()-1<0;){if(m<++h)throw new Error("internal error: maximum number of iterations reached when searching for a bracketing interval, the problem might be infeasible");if(Math.abs(w.sum()-1)<=F){p=!0;break}w=r(d*=2,n,i)}if(c)a=f;else if(p)a=w;else{a=r(L(function(t){return r(t,n,i).sum()-1},l,d),n,i)}}else a=s;return!0===t?[a.toArray(),I(a,it.xy(z,a))]:a.toArray()},y}(PortfolioAllocation||{}),"undefined"!=typeof module&&(module.exports=PortfolioAllocation);