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/**
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 * @date    2021-05-16
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 * Copyright (C) 2013-2021 Jos de Jong <wjosdejong@gmail.com>
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 * https://www.apache.org/licenses/LICENSE-2.0
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 * the License.
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r.value=this(r.value,t.value),r.fixPrefix=!1,r}})})),Kr=Qe("cbrt",["config","typed","isNegative","unaryMinus","matrix","Complex","BigNumber","Fraction"],(function(e){var t=e.config,r=e.typed,n=e.isNegative,i=e.unaryMinus,a=e.matrix,o=e.Complex,f=e.BigNumber,l=e.Fraction;return r("cbrt",{number:Tr,Complex:p,"Complex, boolean":p,BigNumber:function(e){return e.cbrt()},Unit:function(e){if(e.value&&u(e.value)){var t=e.clone();return t.value=1,(t=t.pow(1/3)).value=p(e.value),t}var r,a=n(e.value);a&&(e.value=i(e.value)),r=s(e.value)?new f(1).div(3):c(e.value)?new l(1,3):1/3;var o=e.pow(r);return a&&(o.value=i(o.value)),o},"Array | Matrix":function(e){return $t(e,this,!0)}});function p(e,r){var n=e.arg()/3,i=e.abs(),s=new o(Tr(i),0).mul(new o(0,n).exp());if(r){var u=[s,new o(Tr(i),0).mul(new o(0,n+2*Math.PI/3).exp()),new o(Tr(i),0).mul(new o(0,n-2*Math.PI/3).exp())];return"Array"===t.matrix?u:a(u)}return s}})),en=r(13),tn=r.n(en),rn=Qe("algorithm11",["typed","equalScalar"],(function(e){var t=e.typed,r=e.equalScalar;return function(e,n,i,a){var o=e._values,s=e._index,u=e._ptr,c=e._size,f=e._datatype;if(!o)throw new Error("Cannot perform operation on Pattern Sparse Matrix and Scalar value");var l,p=c[0],m=c[1],h=r,d=0,y=i;"string"==typeof f&&(l=f,h=t.find(r,[l,l]),d=t.convert(0,l),n=t.convert(n,l),y=t.find(i,[l,l]));for(var g=[],v=[],x=[],b=0;b<m;b++){x[b]=v.length;for(var w=u[b],N=u[b+1],M=w;M<N;M++){var E=s[M],S=a?y(n,o[M]):y(o[M],n);h(S,d)||(v.push(E),g.push(S))}}return x[m]=v.length,e.createSparseMatrix({values:g,index:v,ptr:x,size:[p,m],datatype:l})}})),nn=Qe("algorithm14",["typed"],(function(e){var t=e.typed;return function(e,r,n,i){var a,o=e._data,s=e._size,u=e._datatype,c=n;"string"==typeof u&&(a=u,r=t.convert(r,a),c=t.find(n,[a,a]));var f=s.length>0?function e(t,r,n,i,a,o,s){var u=[];if(r===n.length-1)for(var c=0;c<i;c++)u[c]=s?t(o,a[c]):t(a[c],o);else for(var f=0;f<i;f++)u[f]=e(t,r+1,n,n[r+1],a[f],o,s);return u}(c,0,s,s[0],o,r,i):[];return e.createDenseMatrix({data:f,size:$e(s),datatype:a})}})),an=Qe("ceil",["typed","config","round","matrix","equalScalar"],(function(e){var t=e.typed,r=e.config,n=e.round,i=e.matrix,a=e.equalScalar,o=rn({typed:t,equalScalar:a}),s=nn({typed:t});return t("ceil",{number:function(e){return ue(e,n(e),r.epsilon)?n(e):zr(e)},"number, number":function(e,t){if(ue(e,n(e,t),r.epsilon))return n(e,t);var i="".concat(e,"e").split("e"),a=tn()(i,2),o=a[0],s=a[1],u=Math.ceil(Number("".concat(o,"e").concat(Number(s)+t))),c="".concat(u,"e").split("e"),f=tn()(c,2);return o=f[0],s=f[1],Number("".concat(o,"e").concat(Number(s)-t))},Complex:function(e){return e.ceil()},"Complex, number":function(e,t){return e.ceil(t)},BigNumber:function(e){return or(e,n(e),r.epsilon)?n(e):e.ceil()},"BigNumber, BigNumber":function(e,t){return or(e,n(e,t),r.epsilon)?n(e,t):e.toDecimalPlaces(t.toNumber(),At.a.ROUND_CEIL)},Fraction:function(e){return e.ceil()},"Fraction, number":function(e,t){return e.ceil(t)},"Array | 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t=Math.exp(e.re);return new r(t*Math.cos(e.im)-1,t*Math.sin(e.im))},BigNumber:function(e){return e.exp().minus(1)},"Array | Matrix":function(e){return $t(e,this)}})})),cn=Qe("fix",["typed","Complex","matrix","ceil","floor"],(function(e){var t=e.typed,r=e.Complex,n=e.matrix,i=e.ceil,a=e.floor,o=nn({typed:t});return t("fix",{number:function(e){return e>0?a(e):i(e)},"number, number | BigNumber":function(e,t){return e>0?a(e,t):i(e,t)},Complex:function(e){return new r(e.re>0?Math.floor(e.re):Math.ceil(e.re),e.im>0?Math.floor(e.im):Math.ceil(e.im))},"Complex, number | BigNumber":function(e,t){return new r(e.re>0?a(e.re,t):i(e.re,t),e.im>0?a(e.im,t):i(e.im,t))},BigNumber:function(e){return e.isNegative()?i(e):a(e)},"BigNumber, number | BigNumber":function(e,t){return e.isNegative()?i(e,t):a(e,t)},Fraction:function(e){return e.s<0?e.ceil():e.floor()},"Fraction, number | BigNumber":function(e,t){return e.s<0?e.ceil(t):e.floor(t)},"Array | Matrix":function(e){return $t(e,this,!0)},"Array | Matrix, number | BigNumber":function(e,t){var r=this;return $t(e,(function(e){return r(e,t)}),!0)},"number | Complex | BigNumber, Array":function(e,t){return o(n(t),e,this,!0).valueOf()}})})),fn=Qe("floor",["typed","config","round","matrix","equalScalar"],(function(e){var t=e.typed,r=e.config,n=e.round,i=e.matrix,a=e.equalScalar,o=rn({typed:t,equalScalar:a}),s=nn({typed:t});return t("floor",{number:function(e){return ue(e,n(e),r.epsilon)?n(e):Math.floor(e)},"number, number":function(e,t){if(ue(e,n(e,t),r.epsilon))return n(e,t);var i="".concat(e,"e").split("e"),a=tn()(i,2),o=a[0],s=a[1],u=Math.floor(Number("".concat(o,"e").concat(Number(s)+t))),c="".concat(u,"e").split("e"),f=tn()(c,2);return o=f[0],s=f[1],Number("".concat(o,"e").concat(Number(s)-t))},Complex:function(e){return e.floor()},"Complex, number":function(e,t){return e.floor(t)},BigNumber:function(e){return or(e,n(e),r.epsilon)?n(e):e.floor()},"BigNumber, BigNumber":function(e,t){return or(e,n(e,t),r.epsilon)?n(e,t):e.toDecimalPlaces(t.toNumber(),At.a.ROUND_FLOOR)},Fraction:function(e){return e.floor()},"Fraction, number":function(e,t){return e.floor(t)},"Array | Matrix":function(e){return $t(e,this,!0)},"Array | Matrix, number":function(e,t){var r=this;return $t(e,(function(e){return r(e,t)}),!0)},"SparseMatrix, number | BigNumber":function(e,t){return o(e,t,this,!1)},"DenseMatrix, number | BigNumber":function(e,t){return s(e,t,this,!1)},"number | Complex | BigNumber, Array":function(e,t){return s(i(t),e,this,!0).valueOf()}})})),ln=Qe("algorithm01",["typed"],(function(e){var t=e.typed;return function(e,r,n,i){var a=e._data,o=e._size,s=e._datatype,u=r._values,c=r._index,f=r._ptr,l=r._size,p=r._datatype;if(o.length!==l.length)throw new Me(o.length,l.length);if(o[0]!==l[0]||o[1]!==l[1])throw new RangeError("Dimension mismatch. Matrix A ("+o+") must match Matrix B ("+l+")");if(!u)throw new Error("Cannot perform operation on Dense Matrix and Pattern Sparse Matrix");var m,h,d=o[0],y=o[1],g="string"==typeof s&&s===p?s:void 0,v=g?t.find(n,[g,g]):n,x=[];for(m=0;m<d;m++)x[m]=[];var b=[],w=[];for(h=0;h<y;h++){for(var N=h+1,M=f[h],E=f[h+1],S=M;S<E;S++)b[m=c[S]]=i?v(u[S],a[m][h]):v(a[m][h],u[S]),w[m]=N;for(m=0;m<d;m++)w[m]===N?x[m][h]=b[m]:x[m][h]=a[m][h]}return e.createDenseMatrix({data:x,size:[d,y],datatype:g})}})),pn=Qe("algorithm04",["typed","equalScalar"],(function(e){var t=e.typed,r=e.equalScalar;return function(e,n,i){var a=e._values,o=e._index,s=e._ptr,u=e._size,c=e._datatype,f=n._values,l=n._index,p=n._ptr,m=n._size,h=n._datatype;if(u.length!==m.length)throw new Me(u.length,m.length);if(u[0]!==m[0]||u[1]!==m[1])throw new RangeError("Dimension mismatch. Matrix A ("+u+") must match Matrix B ("+m+")");var d,y=u[0],g=u[1],v=r,x=0,b=i;"string"==typeof c&&c===h&&(d=c,v=t.find(r,[d,d]),x=t.convert(0,d),b=t.find(i,[d,d]));var w,N,M,E,S,A=a&&f?[]:void 0,O=[],_=[],C=a&&f?[]:void 0,T=a&&f?[]:void 0,z=[],q=[];for(N=0;N<g;N++){_[N]=O.length;var k=N+1;for(E=s[N],S=s[N+1],M=E;M<S;M++)w=o[M],O.push(w),z[w]=k,C&&(C[w]=a[M]);for(E=p[N],S=p[N+1],M=E;M<S;M++)if(z[w=l[M]]===k){if(C){var I=b(C[w],f[M]);v(I,x)?z[w]=null:C[w]=I}}else O.push(w),q[w]=k,T&&(T[w]=f[M]);if(C&&T)for(M=_[N];M<O.length;)z[w=O[M]]===k?(A[M]=C[w],M++):q[w]===k?(A[M]=T[w],M++):O.splice(M,1)}return _[g]=O.length,e.createSparseMatrix({values:A,index:O,ptr:_,size:[y,g],datatype:d})}})),mn=Qe("algorithm10",["typed","DenseMatrix"],(function(e){var t=e.typed,r=e.DenseMatrix;return function(e,n,i,a){var o=e._values,s=e._index,u=e._ptr,c=e._size,f=e._datatype;if(!o)throw new Error("Cannot perform operation on Pattern Sparse Matrix and Scalar value");var l,p=c[0],m=c[1],h=i;"string"==typeof f&&(l=f,n=t.convert(n,l),h=t.find(i,[l,l]));for(var d=[],y=[],g=[],v=0;v<m;v++){for(var x=v+1,b=u[v],w=u[v+1],N=b;N<w;N++){var M=s[N];y[M]=o[N],g[M]=x}for(var E=0;E<p;E++)0===v&&(d[E]=[]),g[E]===x?d[E][v]=a?h(n,y[E]):h(y[E],n):d[E][v]=n}return new r({data:d,size:[p,m],datatype:l})}})),hn=Qe("algorithm13",["typed"],(function(e){var t=e.typed;return function(e,r,n){var i,a=e._data,o=e._size,s=e._datatype,u=r._data,c=r._size,f=r._datatype,l=[];if(o.length!==c.length)throw new Me(o.length,c.length);for(var p=0;p<o.length;p++){if(o[p]!==c[p])throw new RangeError("Dimension mismatch. Matrix A ("+o+") must match Matrix B ("+c+")");l[p]=o[p]}var m=n;"string"==typeof s&&s===f&&(i=s,m=t.find(n,[i,i]));var h=l.length>0?function e(t,r,n,i,a,o){var s=[];if(r===n.length-1)for(var u=0;u<i;u++)s[u]=t(a[u],o[u]);else for(var c=0;c<i;c++)s[c]=e(t,r+1,n,n[r+1],a[c],o[c]);return s}(m,0,l,l[0],a,u):[];return e.createDenseMatrix({data:h,size:l,datatype:i})}})),dn=Qe("gcd",["typed","matrix","equalScalar","BigNumber","DenseMatrix"],(function(e){var t=e.typed,r=e.matrix,n=e.equalScalar,i=e.BigNumber,a=e.DenseMatrix,o=ln({typed:t}),s=pn({typed:t,equalScalar:n}),u=mn({typed:t,DenseMatrix:a}),c=hn({typed:t}),f=nn({typed:t});return t("gcd",{"number, number":Br,"BigNumber, BigNumber":function(e,t){if(!e.isInt()||!t.isInt())throw new Error("Parameters in function gcd must be integer numbers");var r=new i(0);for(;!t.isZero();){var n=e.mod(t);e=t,t=n}return e.lt(r)?e.neg():e},"Fraction, Fraction":function(e,t){return e.gcd(t)},"SparseMatrix, SparseMatrix":function(e,t){return s(e,t,this)},"SparseMatrix, DenseMatrix":function(e,t){return o(t,e,this,!0)},"DenseMatrix, SparseMatrix":function(e,t){return o(e,t,this,!1)},"DenseMatrix, DenseMatrix":function(e,t){return c(e,t,this)},"Array, Array":function(e,t){return this(r(e),r(t)).valueOf()},"Array, Matrix":function(e,t){return this(r(e),t)},"Matrix, Array":function(e,t){return this(e,r(t))},"SparseMatrix, number | BigNumber":function(e,t){return u(e,t,this,!1)},"DenseMatrix, number | BigNumber":function(e,t){return f(e,t,this,!1)},"number | BigNumber, SparseMatrix":function(e,t){return u(t,e,this,!0)},"number | BigNumber, DenseMatrix":function(e,t){return f(t,e,this,!0)},"Array, number | BigNumber":function(e,t){return f(r(e),t,this,!1).valueOf()},"number | BigNumber, Array":function(e,t){return f(r(t),e,this,!0).valueOf()},"Array | Matrix | number | BigNumber, Array | Matrix | number | BigNumber, ...Array | Matrix | number | BigNumber":function(e,t,r){for(var n=this(e,t),i=0;i<r.length;i++)n=this(n,r[i]);return n}})})),yn=Qe("algorithm02",["typed","equalScalar"],(function(e){var t=e.typed,r=e.equalScalar;return function(e,n,i,a){var o=e._data,s=e._size,u=e._datatype,c=n._values,f=n._index,l=n._ptr,p=n._size,m=n._datatype;if(s.length!==p.length)throw new Me(s.length,p.length);if(s[0]!==p[0]||s[1]!==p[1])throw new RangeError("Dimension mismatch. Matrix A ("+s+") must match Matrix B ("+p+")");if(!c)throw new Error("Cannot perform operation on Dense Matrix and Pattern Sparse Matrix");var h,d=s[0],y=s[1],g=r,v=0,x=i;"string"==typeof u&&u===m&&(h=u,g=t.find(r,[h,h]),v=t.convert(0,h),x=t.find(i,[h,h]));for(var b=[],w=[],N=[],M=0;M<y;M++){N[M]=w.length;for(var E=l[M],S=l[M+1],A=E;A<S;A++){var O=f[A],_=a?x(c[A],o[O][M]):x(o[O][M],c[A]);g(_,v)||(w.push(O),b.push(_))}}return N[y]=w.length,n.createSparseMatrix({values:b,index:w,ptr:N,size:[d,y],datatype:h})}})),gn=Qe("algorithm06",["typed","equalScalar"],(function(e){var t=e.typed,r=e.equalScalar;return function(e,n,i){var a=e._values,o=e._size,s=e._datatype,u=n._values,c=n._size,f=n._datatype;if(o.length!==c.length)throw new Me(o.length,c.length);if(o[0]!==c[0]||o[1]!==c[1])throw new RangeError("Dimension mismatch. Matrix A ("+o+") must match Matrix B ("+c+")");var l,p=o[0],m=o[1],h=r,d=0,y=i;"string"==typeof s&&s===f&&(l=s,h=t.find(r,[l,l]),d=t.convert(0,l),y=t.find(i,[l,l]));for(var g=a&&u?[]:void 0,v=[],x=[],b=g?[]:void 0,w=[],N=[],M=0;M<m;M++){x[M]=v.length;var E=M+1;if(Zt(e,M,w,b,N,E,v,y),Zt(n,M,w,b,N,E,v,y),b)for(var S=x[M];S<v.length;){var A=v[S];if(N[A]===E){var O=b[A];h(O,d)?v.splice(S,1):(g.push(O),S++)}else v.splice(S,1)}else for(var _=x[M];_<v.length;){N[v[_]]!==E?v.splice(_,1):_++}}return x[m]=v.length,e.createSparseMatrix({values:g,index:v,ptr:x,size:[p,m],datatype:l})}})),vn=Qe("lcm",["typed","matrix","equalScalar"],(function(e){var t=e.typed,r=e.matrix,n=e.equalScalar,i=yn({typed:t,equalScalar:n}),a=gn({typed:t,equalScalar:n}),o=rn({typed:t,equalScalar:n}),s=hn({typed:t}),u=nn({typed:t});return t("lcm",{"number, number":Dr,"BigNumber, BigNumber":function(e,t){if(!e.isInt()||!t.isInt())throw new Error("Parameters in function lcm must be integer numbers");if(e.isZero())return e;if(t.isZero())return t;var r=e.times(t);for(;!t.isZero();){var n=t;t=e.mod(n),e=n}return r.div(e).abs()},"Fraction, Fraction":function(e,t){return e.lcm(t)},"SparseMatrix, SparseMatrix":function(e,t){return a(e,t,this)},"SparseMatrix, DenseMatrix":function(e,t){return i(t,e,this,!0)},"DenseMatrix, SparseMatrix":function(e,t){return i(e,t,this,!1)},"DenseMatrix, DenseMatrix":function(e,t){return s(e,t,this)},"Array, Array":function(e,t){return this(r(e),r(t)).valueOf()},"Array, Matrix":function(e,t){return this(r(e),t)},"Matrix, Array":function(e,t){return this(e,r(t))},"SparseMatrix, number | BigNumber":function(e,t){return o(e,t,this,!1)},"DenseMatrix, number | BigNumber":function(e,t){return u(e,t,this,!1)},"number | BigNumber, SparseMatrix":function(e,t){return o(t,e,this,!0)},"number | BigNumber, DenseMatrix":function(e,t){return u(t,e,this,!0)},"Array, number | BigNumber":function(e,t){return u(r(e),t,this,!1).valueOf()},"number | BigNumber, Array":function(e,t){return u(r(t),e,this,!0).valueOf()},"Array | Matrix | number | BigNumber, Array | Matrix | number | BigNumber, ...Array | Matrix | number | BigNumber":function(e,t,r){for(var n=this(e,t),i=0;i<r.length;i++)n=this(n,r[i]);return n}})})),xn=Qe("log10",["typed","config","Complex"],(function(e){var t=e.typed,r=e.config,n=e.Complex;return t("log10",{number:function(e){return e>=0||r.predictable?Fr(e):new n(e,0).log().div(Math.LN10)},Complex:function(e){return new n(e).log().div(Math.LN10)},BigNumber:function(e){return!e.isNegative()||r.predictable?e.log():new n(e.toNumber(),0).log().div(Math.LN10)},"Array | Matrix":function(e){return $t(e,this)}})})),bn=Qe("log2",["typed","config","Complex"],(function(e){var t=e.typed,r=e.config,n=e.Complex;return t("log2",{number:function(e){return e>=0||r.predictable?jr(e):i(new n(e,0))},Complex:i,BigNumber:function(e){return!e.isNegative()||r.predictable?e.log(2):i(new n(e.toNumber(),0))},"Array | Matrix":function(e){return $t(e,this)}});function i(e){var t=Math.sqrt(e.re*e.re+e.im*e.im);return new n(Math.log2?Math.log2(t):Math.log(t)/Math.LN2,Math.atan2(e.im,e.re)/Math.LN2)}})),wn=Qe("algorithm03",["typed"],(function(e){var t=e.typed;return function(e,r,n,i){var a=e._data,o=e._size,s=e._datatype,u=r._values,c=r._index,f=r._ptr,l=r._size,p=r._datatype;if(o.length!==l.length)throw new Me(o.length,l.length);if(o[0]!==l[0]||o[1]!==l[1])throw new RangeError("Dimension mismatch. Matrix A ("+o+") must match Matrix B ("+l+")");if(!u)throw new Error("Cannot perform operation on Dense Matrix and Pattern Sparse Matrix");var m,h=o[0],d=o[1],y=0,g=n;"string"==typeof s&&s===p&&(m=s,y=t.convert(0,m),g=t.find(n,[m,m]));for(var v=[],x=0;x<h;x++)v[x]=[];for(var b=[],w=[],N=0;N<d;N++){for(var M=N+1,E=f[N],S=f[N+1],A=E;A<S;A++){var O=c[A];b[O]=i?g(u[A],a[O][N]):g(a[O][N],u[A]),w[O]=M}for(var _=0;_<h;_++)w[_]===M?v[_][N]=b[_]:v[_][N]=i?g(y,a[_][N]):g(a[_][N],y)}return e.createDenseMatrix({data:v,size:[h,d],datatype:m})}})),Nn=Qe("algorithm05",["typed","equalScalar"],(function(e){var t=e.typed,r=e.equalScalar;return function(e,n,i){var a=e._values,o=e._index,s=e._ptr,u=e._size,c=e._datatype,f=n._values,l=n._index,p=n._ptr,m=n._size,h=n._datatype;if(u.length!==m.length)throw new Me(u.length,m.length);if(u[0]!==m[0]||u[1]!==m[1])throw new RangeError("Dimension mismatch. Matrix A ("+u+") must match Matrix B ("+m+")");var d,y=u[0],g=u[1],v=r,x=0,b=i;"string"==typeof c&&c===h&&(d=c,v=t.find(r,[d,d]),x=t.convert(0,d),b=t.find(i,[d,d]));var w,N,M,E,S=a&&f?[]:void 0,A=[],O=[],_=S?[]:void 0,C=S?[]:void 0,T=[],z=[];for(N=0;N<g;N++){O[N]=A.length;var q=N+1;for(M=s[N],E=s[N+1];M<E;M++)w=o[M],A.push(w),T[w]=q,_&&(_[w]=a[M]);for(M=p[N],E=p[N+1];M<E;M++)T[w=l[M]]!==q&&A.push(w),z[w]=q,C&&(C[w]=f[M]);if(S)for(M=O[N];M<A.length;){var k=T[w=A[M]],I=z[w];if(k===q||I===q){var B=b(k===q?_[w]:x,I===q?C[w]:x);v(B,x)?A.splice(M,1):(S.push(B),M++)}}}return O[g]=A.length,e.createSparseMatrix({values:S,index:A,ptr:O,size:[y,g],datatype:d})}})),Mn=Qe("algorithm12",["typed","DenseMatrix"],(function(e){var t=e.typed,r=e.DenseMatrix;return function(e,n,i,a){var o=e._values,s=e._index,u=e._ptr,c=e._size,f=e._datatype;if(!o)throw new Error("Cannot perform operation on Pattern Sparse Matrix and Scalar value");var l,p=c[0],m=c[1],h=i;"string"==typeof f&&(l=f,n=t.convert(n,l),h=t.find(i,[l,l]));for(var d=[],y=[],g=[],v=0;v<m;v++){for(var x=v+1,b=u[v],w=u[v+1],N=b;N<w;N++){var M=s[N];y[M]=o[N],g[M]=x}for(var E=0;E<p;E++)0===v&&(d[E]=[]),g[E]===x?d[E][v]=a?h(n,y[E]):h(y[E],n):d[E][v]=a?h(n,0):h(0,n)}return new r({data:d,size:[p,m],datatype:l})}})),En=Qe("mod",["typed","matrix","equalScalar","DenseMatrix"],(function(e){var t=e.typed,r=e.matrix,n=e.equalScalar,i=e.DenseMatrix,a=yn({typed:t,equalScalar:n}),o=wn({typed:t}),s=Nn({typed:t,equalScalar:n}),u=rn({typed:t,equalScalar:n}),c=Mn({typed:t,DenseMatrix:i}),f=hn({typed:t}),l=nn({typed:t});return t("mod",{"number, number":Pr,"BigNumber, BigNumber":function(e,t){if(t.isNeg())throw new Error("Cannot calculate mod for a negative divisor");return t.isZero()?e:e.mod(t)},"Fraction, Fraction":function(e,t){if(t.compare(0)<0)throw new Error("Cannot calculate mod for a negative divisor");return e.compare(0)>=0?e.mod(t):e.mod(t).add(t).mod(t)},"SparseMatrix, SparseMatrix":function(e,t){return s(e,t,this,!1)},"SparseMatrix, DenseMatrix":function(e,t){return a(t,e,this,!0)},"DenseMatrix, SparseMatrix":function(e,t){return o(e,t,this,!1)},"DenseMatrix, DenseMatrix":function(e,t){return f(e,t,this)},"Array, Array":function(e,t){return this(r(e),r(t)).valueOf()},"Array, Matrix":function(e,t){return this(r(e),t)},"Matrix, Array":function(e,t){return this(e,r(t))},"SparseMatrix, any":function(e,t){return u(e,t,this,!1)},"DenseMatrix, any":function(e,t){return l(e,t,this,!1)},"any, SparseMatrix":function(e,t){return c(t,e,this,!0)},"any, DenseMatrix":function(e,t){return l(t,e,this,!0)},"Array, any":function(e,t){return l(r(e),t,this,!1).valueOf()},"any, Array":function(e,t){return l(r(t),e,this,!0).valueOf()}})})),Sn=Qe("multiplyScalar",["typed"],(function(e){return(0,e.typed)("multiplyScalar",{"number, number":Or,"Complex, Complex":function(e,t){return e.mul(t)},"BigNumber, BigNumber":function(e,t){return e.times(t)},"Fraction, Fraction":function(e,t){return e.mul(t)},"number | Fraction | BigNumber | Complex, Unit":function(e,t){var r=t.clone();return r.value=null===r.value?r._normalize(e):this(r.value,e),r},"Unit, number | Fraction | BigNumber | Complex":function(e,t){var r=e.clone();return r.value=null===r.value?r._normalize(t):this(r.value,t),r},"Unit, Unit":function(e,t){return e.multiply(t)}})})),An=Qe("multiply",["typed","matrix","addScalar","multiplyScalar","equalScalar","dot"],(function(e){var t=e.typed,r=e.matrix,n=e.addScalar,i=e.multiplyScalar,a=e.equalScalar,o=e.dot,s=rn({typed:t,equalScalar:a}),u=nn({typed:t});function c(e,t){switch(e.length){case 1:switch(t.length){case 1:if(e[0]!==t[0])throw new RangeError("Dimension mismatch in multiplication. Vectors must have the same length");break;case 2:if(e[0]!==t[0])throw new RangeError("Dimension mismatch in multiplication. Vector length ("+e[0]+") must match Matrix rows ("+t[0]+")");break;default:throw new Error("Can only multiply a 1 or 2 dimensional matrix (Matrix B has "+t.length+" dimensions)")}break;case 2:switch(t.length){case 1:if(e[1]!==t[0])throw new RangeError("Dimension mismatch in multiplication. Matrix columns ("+e[1]+") must match Vector length ("+t[0]+")");break;case 2:if(e[1]!==t[0])throw new RangeError("Dimension mismatch in multiplication. Matrix A columns ("+e[1]+") must match Matrix B rows ("+t[0]+")");break;default:throw new Error("Can only multiply a 1 or 2 dimensional matrix (Matrix B has "+t.length+" dimensions)")}break;default:throw new Error("Can only multiply a 1 or 2 dimensional matrix (Matrix A has "+e.length+" dimensions)")}}function f(e,r){if("dense"!==r.storage())throw new Error("Support for SparseMatrix not implemented");return function(e,r){var a,o=e._data,s=e._size,u=e._datatype,c=r._data,f=r._size,l=r._datatype,p=s[0],m=f[1],h=n,d=i;u&&l&&u===l&&"string"==typeof u&&(a=u,h=t.find(n,[a,a]),d=t.find(i,[a,a]));for(var y=[],g=0;g<m;g++){for(var v=d(o[0],c[0][g]),x=1;x<p;x++)v=h(v,d(o[x],c[x][g]));y[g]=v}return e.createDenseMatrix({data:y,size:[m],datatype:a})}(e,r)}var l=t("_multiplyMatrixVector",{"DenseMatrix, any":function(e,r){var a,o=e._data,s=e._size,u=e._datatype,c=r._data,f=r._datatype,l=s[0],p=s[1],m=n,h=i;u&&f&&u===f&&"string"==typeof u&&(a=u,m=t.find(n,[a,a]),h=t.find(i,[a,a]));for(var d=[],y=0;y<l;y++){for(var g=o[y],v=h(g[0],c[0]),x=1;x<p;x++)v=m(v,h(g[x],c[x]));d[y]=v}return e.createDenseMatrix({data:d,size:[l],datatype:a})},"SparseMatrix, any":function(e,r){var o=e._values,s=e._index,u=e._ptr,c=e._datatype;if(!o)throw new Error("Cannot multiply Pattern only Matrix times Dense Matrix");var f,l=r._data,p=r._datatype,m=e._size[0],h=r._size[0],d=[],y=[],g=[],v=n,x=i,b=a,w=0;c&&p&&c===p&&"string"==typeof c&&(f=c,v=t.find(n,[f,f]),x=t.find(i,[f,f]),b=t.find(a,[f,f]),w=t.convert(0,f));var N=[],M=[];g[0]=0;for(var E=0;E<h;E++){var S=l[E];if(!b(S,w))for(var A=u[E],O=u[E+1],_=A;_<O;_++){var C=s[_];M[C]?N[C]=v(N[C],x(S,o[_])):(M[C]=!0,y.push(C),N[C]=x(S,o[_]))}}for(var T=y.length,z=0;z<T;z++){var q=y[z];d[z]=N[q]}return g[1]=y.length,e.createSparseMatrix({values:d,index:y,ptr:g,size:[m,1],datatype:f})}}),p=t("_multiplyMatrixMatrix",{"DenseMatrix, DenseMatrix":function(e,r){var a,o=e._data,s=e._size,u=e._datatype,c=r._data,f=r._size,l=r._datatype,p=s[0],m=s[1],h=f[1],d=n,y=i;u&&l&&u===l&&"string"==typeof u&&(a=u,d=t.find(n,[a,a]),y=t.find(i,[a,a]));for(var g=[],v=0;v<p;v++){var x=o[v];g[v]=[];for(var b=0;b<h;b++){for(var w=y(x[0],c[0][b]),N=1;N<m;N++)w=d(w,y(x[N],c[N][b]));g[v][b]=w}}return e.createDenseMatrix({data:g,size:[p,h],datatype:a})},"DenseMatrix, SparseMatrix":function(e,r){var o=e._data,s=e._size,u=e._datatype,c=r._values,f=r._index,l=r._ptr,p=r._size,m=r._datatype;if(!c)throw new Error("Cannot multiply Dense Matrix times Pattern only Matrix");var h,d=s[0],y=p[1],g=n,v=i,x=a,b=0;u&&m&&u===m&&"string"==typeof u&&(h=u,g=t.find(n,[h,h]),v=t.find(i,[h,h]),x=t.find(a,[h,h]),b=t.convert(0,h));for(var w=[],N=[],M=[],E=r.createSparseMatrix({values:w,index:N,ptr:M,size:[d,y],datatype:h}),S=0;S<y;S++){M[S]=N.length;var A=l[S],O=l[S+1];if(O>A)for(var _=0,C=0;C<d;C++){for(var T=C+1,z=void 0,q=A;q<O;q++){var k=f[q];_!==T?(z=v(o[C][k],c[q]),_=T):z=g(z,v(o[C][k],c[q]))}_!==T||x(z,b)||(N.push(C),w.push(z))}}return M[y]=N.length,E},"SparseMatrix, DenseMatrix":function(e,r){var o=e._values,s=e._index,u=e._ptr,c=e._datatype;if(!o)throw new Error("Cannot multiply Pattern only Matrix times Dense Matrix");var f,l=r._data,p=r._datatype,m=e._size[0],h=r._size[0],d=r._size[1],y=n,g=i,v=a,x=0;c&&p&&c===p&&"string"==typeof c&&(f=c,y=t.find(n,[f,f]),g=t.find(i,[f,f]),v=t.find(a,[f,f]),x=t.convert(0,f));for(var b=[],w=[],N=[],M=e.createSparseMatrix({values:b,index:w,ptr:N,size:[m,d],datatype:f}),E=[],S=[],A=0;A<d;A++){N[A]=w.length;for(var O=A+1,_=0;_<h;_++){var C=l[_][A];if(!v(C,x))for(var T=u[_],z=u[_+1],q=T;q<z;q++){var k=s[q];S[k]!==O?(S[k]=O,w.push(k),E[k]=g(C,o[q])):E[k]=y(E[k],g(C,o[q]))}}for(var I=N[A],B=w.length,D=I;D<B;D++){var R=w[D];b[D]=E[R]}}return N[d]=w.length,M},"SparseMatrix, SparseMatrix":function(e,r){var a,o=e._values,s=e._index,u=e._ptr,c=e._datatype,f=r._values,l=r._index,p=r._ptr,m=r._datatype,h=e._size[0],d=r._size[1],y=o&&f,g=n,v=i;c&&m&&c===m&&"string"==typeof c&&(a=c,g=t.find(n,[a,a]),v=t.find(i,[a,a]));for(var x,b,w,N,M,E,S,A,O=y?[]:void 0,_=[],C=[],T=e.createSparseMatrix({values:O,index:_,ptr:C,size:[h,d],datatype:a}),z=y?[]:void 0,q=[],k=0;k<d;k++){C[k]=_.length;var I=k+1;for(M=p[k],E=p[k+1],N=M;N<E;N++)if(A=l[N],y)for(b=u[A],w=u[A+1],x=b;x<w;x++)S=s[x],q[S]!==I?(q[S]=I,_.push(S),z[S]=v(f[N],o[x])):z[S]=g(z[S],v(f[N],o[x]));else for(b=u[A],w=u[A+1],x=b;x<w;x++)S=s[x],q[S]!==I&&(q[S]=I,_.push(S));if(y)for(var B=C[k],D=_.length,R=B;R<D;R++){var F=_[R];O[R]=z[F]}}return C[d]=_.length,T}});return t("multiply",Ve({"Array, Array":function(e,t){c(Se(e),Se(t));var n=this(r(e),r(t));return m(n)?n.valueOf():n},"Matrix, Matrix":function(e,t){var r=e.size(),n=t.size();return c(r,n),1===r.length?1===n.length?function(e,t,r){if(0===r)throw new Error("Cannot multiply two empty vectors");return o(e,t)}(e,t,r[0]):f(e,t):1===n.length?l(e,t):p(e,t)},"Matrix, Array":function(e,t){return this(e,r(t))},"Array, Matrix":function(e,t){return this(r(e,t.storage()),t)},"SparseMatrix, any":function(e,t){return s(e,t,i,!1)},"DenseMatrix, any":function(e,t){return u(e,t,i,!1)},"any, SparseMatrix":function(e,t){return s(t,e,i,!0)},"any, DenseMatrix":function(e,t){return u(t,e,i,!0)},"Array, any":function(e,t){return u(r(e),t,i,!1).valueOf()},"any, Array":function(e,t){return u(r(t),e,i,!0).valueOf()},"any, any":i,"any, any, ...any":function(e,t,r){for(var n=this(e,t),i=0;i<r.length;i++)n=this(n,r[i]);return n}},i.signatures))})),On=Qe("nthRoot",["typed","matrix","equalScalar","BigNumber"],(function(e){var t=e.typed,r=e.matrix,n=e.equalScalar,i=e.BigNumber,a=ln({typed:t}),o=yn({typed:t,equalScalar:n}),s=gn({typed:t,equalScalar:n}),u=rn({typed:t,equalScalar:n}),c=hn({typed:t}),f=nn({typed:t}),l="Complex number not supported in function nthRoot. Use nthRoots instead.";return t("nthRoot",{number:function(e){return Ur(e,2)},"number, number":Ur,BigNumber:function(e){return p(e,new i(2))},Complex:function(e){throw new Error(l)},"Complex, number":function(e,t){throw new Error(l)},"BigNumber, BigNumber":p,"Array | Matrix":function(e){return this(e,2)},"SparseMatrix, SparseMatrix":function(e,t){if(1===t.density())return s(e,t,this);throw new Error("Root must be non-zero")},"SparseMatrix, DenseMatrix":function(e,t){return o(t,e,this,!0)},"DenseMatrix, SparseMatrix":function(e,t){if(1===t.density())return a(e,t,this,!1);throw new Error("Root must be non-zero")},"DenseMatrix, DenseMatrix":function(e,t){return c(e,t,this)},"Array, Array":function(e,t){return this(r(e),r(t)).valueOf()},"Array, Matrix":function(e,t){return this(r(e),t)},"Matrix, Array":function(e,t){return this(e,r(t))},"SparseMatrix, number | BigNumber":function(e,t){return u(e,t,this,!1)},"DenseMatrix, number | BigNumber":function(e,t){return f(e,t,this,!1)},"number | BigNumber, SparseMatrix":function(e,t){if(1===t.density())return u(t,e,this,!0);throw new Error("Root must be non-zero")},"number | BigNumber, DenseMatrix":function(e,t){return f(t,e,this,!0)},"Array, number | BigNumber":function(e,t){return this(r(e),t).valueOf()},"number | BigNumber, Array":function(e,t){return this(e,r(t)).valueOf()}});function p(e,t){var r=i.precision,n=i.clone({precision:r+2}),a=new i(0),o=new n(1),s=t.isNegative();if(s&&(t=t.neg()),t.isZero())throw new Error("Root must be non-zero");if(e.isNegative()&&!t.abs().mod(2).equals(1))throw new Error("Root must be odd when a is negative.");if(e.isZero())return s?new n(1/0):0;if(!e.isFinite())return s?a:e;var u=e.abs().pow(o.div(t));return u=e.isNeg()?u.neg():u,new i((s?o.div(u):u).toPrecision(r))}})),_n=Qe("sign",["typed","BigNumber","Fraction","complex"],(function(e){var t=e.typed,r=e.BigNumber,n=e.complex,i=e.Fraction;return t("sign",{number:Lr,Complex:function(e){return 0===e.im?n(Lr(e.re)):e.sign()},BigNumber:function(e){return new r(e.cmp(0))},Fraction:function(e){return new i(e.s,1)},"Array | Matrix":function(e){return $t(e,this,!0)},Unit:function(e){return this(e.value)}})})),Cn=Qe("sqrt",["config","typed","Complex"],(function(e){var t=e.config,r=e.typed,n=e.Complex;return r("sqrt",{number:i,Complex:function(e){return e.sqrt()},BigNumber:function(e){return!e.isNegative()||t.predictable?e.sqrt():i(e.toNumber())},"Array | Matrix":function(e){return $t(e,this,!0)},Unit:function(e){return e.pow(.5)}});function i(e){return isNaN(e)?NaN:e>=0||t.predictable?Math.sqrt(e):new n(e,0).sqrt()}})),Tn=Qe("square",["typed"],(function(e){return(0,e.typed)("square",{number:Hr,Complex:function(e){return e.mul(e)},BigNumber:function(e){return e.times(e)},Fraction:function(e){return e.mul(e)},"Array | Matrix":function(e){return $t(e,this,!0)},Unit:function(e){return e.pow(2)}})})),zn=Qe("subtract",["typed","matrix","equalScalar","addScalar","unaryMinus","DenseMatrix"],(function(e){var t=e.typed,r=e.matrix,n=e.equalScalar,i=e.addScalar,a=e.unaryMinus,o=e.DenseMatrix,s=ln({typed:t}),u=wn({typed:t}),c=Nn({typed:t,equalScalar:n}),f=mn({typed:t,DenseMatrix:o}),l=hn({typed:t}),p=nn({typed:t});return t("subtract",{"number, number":function(e,t){return e-t},"Complex, Complex":function(e,t){return e.sub(t)},"BigNumber, BigNumber":function(e,t){return e.minus(t)},"Fraction, Fraction":function(e,t){return e.sub(t)},"Unit, Unit":function(e,t){if(null===e.value)throw new Error("Parameter x contains a unit with undefined value");if(null===t.value)throw new Error("Parameter y contains a unit with undefined value");if(!e.equalBase(t))throw new Error("Units do not match");var r=e.clone();return r.value=this(r.value,t.value),r.fixPrefix=!1,r},"SparseMatrix, SparseMatrix":function(e,t){return qn(e,t),c(e,t,this)},"SparseMatrix, DenseMatrix":function(e,t){return qn(e,t),u(t,e,this,!0)},"DenseMatrix, SparseMatrix":function(e,t){return qn(e,t),s(e,t,this,!1)},"DenseMatrix, DenseMatrix":function(e,t){return qn(e,t),l(e,t,this)},"Array, Array":function(e,t){return this(r(e),r(t)).valueOf()},"Array, Matrix":function(e,t){return this(r(e),t)},"Matrix, Array":function(e,t){return this(e,r(t))},"SparseMatrix, any":function(e,t){return f(e,a(t),i)},"DenseMatrix, any":function(e,t){return p(e,t,this)},"any, SparseMatrix":function(e,t){return f(t,e,this,!0)},"any, DenseMatrix":function(e,t){return p(t,e,this,!0)},"Array, any":function(e,t){return p(r(e),t,this,!1).valueOf()},"any, Array":function(e,t){return p(r(t),e,this,!0).valueOf()}})}));function qn(e,t){var r=e.size(),n=t.size();if(r.length!==n.length)throw new Me(r.length,n.length)}var kn=Qe("xgcd",["typed","config","matrix","BigNumber"],(function(e){var t=e.typed,r=e.config,n=e.matrix,i=e.BigNumber;return t("xgcd",{"number, number":function(e,t){var i=$r(e,t);return"Array"===r.matrix?i:n(i)},"BigNumber, BigNumber":function(e,t){var a,o,s,u,c=new i(0),f=new i(1),l=c,p=f,m=f,h=c;if(!e.isInt()||!t.isInt())throw new Error("Parameters in function xgcd must be integer numbers");for(;!t.isZero();)o=e.div(t).floor(),s=e.mod(t),a=l,l=p.minus(o.times(l)),p=a,a=m,m=h.minus(o.times(m)),h=a,e=t,t=s;u=e.lt(c)?[e.neg(),p.neg(),h.neg()]:[e,e.isZero()?0:p,h];return"Array"===r.matrix?u:n(u)}})})),In=Qe("algorithm09",["typed","equalScalar"],(function(e){var t=e.typed,r=e.equalScalar;return function(e,n,i){var a=e._values,o=e._index,s=e._ptr,u=e._size,c=e._datatype,f=n._values,l=n._index,p=n._ptr,m=n._size,h=n._datatype;if(u.length!==m.length)throw new Me(u.length,m.length);if(u[0]!==m[0]||u[1]!==m[1])throw new RangeError("Dimension mismatch. Matrix A ("+u+") must match Matrix B ("+m+")");var d,y=u[0],g=u[1],v=r,x=0,b=i;"string"==typeof c&&c===h&&(d=c,v=t.find(r,[d,d]),x=t.convert(0,d),b=t.find(i,[d,d]));var w,N,M,E,S,A=a&&f?[]:void 0,O=[],_=[],C=A?[]:void 0,T=[];for(N=0;N<g;N++){_[N]=O.length;var z=N+1;if(C)for(E=p[N],S=p[N+1],M=E;M<S;M++)T[w=l[M]]=z,C[w]=f[M];for(E=s[N],S=s[N+1],M=E;M<S;M++)if(w=o[M],C){var q=T[w]===z?C[w]:x,k=b(a[M],q);v(k,x)||(O.push(w),A.push(k))}else O.push(w)}return _[g]=O.length,e.createSparseMatrix({values:A,index:O,ptr:_,size:[y,g],datatype:d})}})),Bn=Qe("dotMultiply",["typed","matrix","equalScalar","multiplyScalar"],(function(e){var t=e.typed,r=e.matrix,n=e.equalScalar,i=e.multiplyScalar,a=yn({typed:t,equalScalar:n}),o=In({typed:t,equalScalar:n}),s=rn({typed:t,equalScalar:n}),u=hn({typed:t}),c=nn({typed:t});return t("dotMultiply",{"any, any":i,"SparseMatrix, SparseMatrix":function(e,t){return o(e,t,i,!1)},"SparseMatrix, DenseMatrix":function(e,t){return a(t,e,i,!0)},"DenseMatrix, SparseMatrix":function(e,t){return a(e,t,i,!1)},"DenseMatrix, DenseMatrix":function(e,t){return u(e,t,i)},"Array, Array":function(e,t){return this(r(e),r(t)).valueOf()},"Array, Matrix":function(e,t){return this(r(e),t)},"Matrix, Array":function(e,t){return this(e,r(t))},"SparseMatrix, any":function(e,t){return s(e,t,i,!1)},"DenseMatrix, any":function(e,t){return c(e,t,i,!1)},"any, SparseMatrix":function(e,t){return s(t,e,i,!0)},"any, DenseMatrix":function(e,t){return c(t,e,i,!0)},"Array, any":function(e,t){return c(r(e),t,i,!1).valueOf()},"any, Array":function(e,t){return c(r(t),e,i,!0).valueOf()}})}));function Dn(e,t){if(e.isFinite()&&!e.isInteger()||t.isFinite()&&!t.isInteger())throw new Error("Integers expected in function bitAnd");var r=e.constructor;if(e.isNaN()||t.isNaN())return new r(NaN);if(e.isZero()||t.eq(-1)||e.eq(t))return e;if(t.isZero()||e.eq(-1))return t;if(!e.isFinite()||!t.isFinite()){if(!e.isFinite()&&!t.isFinite())return e.isNegative()===t.isNegative()?e:new r(0);if(!e.isFinite())return t.isNegative()?e:e.isNegative()?new r(0):t;if(!t.isFinite())return e.isNegative()?t:t.isNegative()?new r(0):e}return jn(e,t,(function(e,t){return e&t}))}function Rn(e){if(e.isFinite()&&!e.isInteger())throw new Error("Integer expected in function bitNot");var t=e.constructor,r=t.precision;t.config({precision:1e9});var n=e.plus(new t(1));return n.s=-n.s||null,t.config({precision:r}),n}function Fn(e,t){if(e.isFinite()&&!e.isInteger()||t.isFinite()&&!t.isInteger())throw new Error("Integers expected in function bitOr");var r=e.constructor;if(e.isNaN()||t.isNaN())return new r(NaN);var n=new r(-1);return e.isZero()||t.eq(n)||e.eq(t)?t:t.isZero()||e.eq(n)?e:e.isFinite()&&t.isFinite()?jn(e,t,(function(e,t){return e|t})):!e.isFinite()&&!e.isNegative()&&t.isNegative()||e.isNegative()&&!t.isNegative()&&!t.isFinite()?n:e.isNegative()&&t.isNegative()?e.isFinite()?e:t:e.isFinite()?t:e}function jn(e,t,r){var n,i,a,o,s,u=e.constructor,c=+(e.s<0),f=+(t.s<0);if(c){n=Pn(Rn(e));for(var l=0;l<n.length;++l)n[l]^=1}else n=Pn(e);if(f){i=Pn(Rn(t));for(var p=0;p<i.length;++p)i[p]^=1}else i=Pn(t);n.length<=i.length?(a=n,o=i,s=c):(a=i,o=n,s=f);var m=a.length,h=o.length,d=1^r(c,f),y=new u(1^d),g=new u(1),v=new u(2),x=u.precision;for(u.config({precision:1e9});m>0;)r(a[--m],o[--h])===d&&(y=y.plus(g)),g=g.times(v);for(;h>0;)r(s,o[--h])===d&&(y=y.plus(g)),g=g.times(v);return u.config({precision:x}),0===d&&(y.s=-y.s),y}function Pn(e){for(var t=e.d,r=t[0]+"",n=1;n<t.length;++n){for(var i=t[n]+"",a=7-i.length;a--;)i="0"+i;r+=i}for(var o=r.length;"0"===r.charAt(o);)o--;var s=e.e,u=r.slice(0,o+1||1),c=u.length;if(s>0)if(++s>c)for(s-=c;s--;)u+="0";else s<c&&(u=u.slice(0,s)+"."+u.slice(s));for(var f=[0],l=0;l<u.length;){for(var p=f.length;p--;)f[p]*=10;f[0]+=parseInt(u.charAt(l++));for(var m=0;m<f.length;++m)f[m]>1&&(null!==f[m+1]&&void 0!==f[m+1]||(f[m+1]=0),f[m+1]+=f[m]>>1,f[m]&=1)}return f.reverse()}function Un(e,t){if(e.isFinite()&&!e.isInteger()||t.isFinite()&&!t.isInteger())throw new Error("Integers expected in function bitXor");var r=e.constructor;if(e.isNaN()||t.isNaN())return new r(NaN);if(e.isZero())return t;if(t.isZero())return e;if(e.eq(t))return new r(0);var n=new r(-1);return e.eq(n)?Rn(t):t.eq(n)?Rn(e):e.isFinite()&&t.isFinite()?jn(e,t,(function(e,t){return e^t})):e.isFinite()||t.isFinite()?new r(e.isNegative()===t.isNegative()?1/0:-1/0):n}function Ln(e,t){if(e.isFinite()&&!e.isInteger()||t.isFinite()&&!t.isInteger())throw new Error("Integers expected in function leftShift");var r=e.constructor;return e.isNaN()||t.isNaN()||t.isNegative()&&!t.isZero()?new r(NaN):e.isZero()||t.isZero()?e:e.isFinite()||t.isFinite()?t.lt(55)?e.times(Math.pow(2,t.toNumber())+""):e.times(new r(2).pow(t)):new r(NaN)}function Hn(e,t){if(e.isFinite()&&!e.isInteger()||t.isFinite()&&!t.isInteger())throw new Error("Integers expected in function rightArithShift");var r=e.constructor;return e.isNaN()||t.isNaN()||t.isNegative()&&!t.isZero()?new r(NaN):e.isZero()||t.isZero()?e:t.isFinite()?t.lt(55)?e.div(Math.pow(2,t.toNumber())+"").floor():e.div(new r(2).pow(t)).floor():e.isNegative()?new r(-1):e.isFinite()?new r(0):new r(NaN)}var $n="number, number";function Gn(e,t){if(!Z(e)||!Z(t))throw new Error("Integers expected in function bitAnd");return e&t}function Vn(e){if(!Z(e))throw new Error("Integer expected in function bitNot");return~e}function Zn(e,t){if(!Z(e)||!Z(t))throw new Error("Integers expected in function bitOr");return e|t}function Wn(e,t){if(!Z(e)||!Z(t))throw new Error("Integers expected in function bitXor");return e^t}function Jn(e,t){if(!Z(e)||!Z(t))throw new Error("Integers expected in function leftShift");return e<<t}function Yn(e,t){if(!Z(e)||!Z(t))throw new Error("Integers expected in function rightArithShift");return e>>t}function Xn(e,t){if(!Z(e)||!Z(t))throw new Error("Integers expected in function rightLogShift");return e>>>t}Gn.signature=$n,Vn.signature="number",Zn.signature=$n,Wn.signature=$n,Jn.signature=$n,Yn.signature=$n,Xn.signature=$n;var Qn=Qe("bitAnd",["typed","matrix","equalScalar"],(function(e){var t=e.typed,r=e.matrix,n=e.equalScalar,i=yn({typed:t,equalScalar:n}),a=gn({typed:t,equalScalar:n}),o=rn({typed:t,equalScalar:n}),s=hn({typed:t}),u=nn({typed:t});return t("bitAnd",{"number, number":Gn,"BigNumber, BigNumber":Dn,"SparseMatrix, SparseMatrix":function(e,t){return a(e,t,this,!1)},"SparseMatrix, DenseMatrix":function(e,t){return i(t,e,this,!0)},"DenseMatrix, SparseMatrix":function(e,t){return i(e,t,this,!1)},"DenseMatrix, DenseMatrix":function(e,t){return s(e,t,this)},"Array, Array":function(e,t){return this(r(e),r(t)).valueOf()},"Array, Matrix":function(e,t){return this(r(e),t)},"Matrix, Array":function(e,t){return this(e,r(t))},"SparseMatrix, any":function(e,t){return o(e,t,this,!1)},"DenseMatrix, any":function(e,t){return u(e,t,this,!1)},"any, SparseMatrix":function(e,t){return o(t,e,this,!0)},"any, DenseMatrix":function(e,t){return u(t,e,this,!0)},"Array, any":function(e,t){return u(r(e),t,this,!1).valueOf()},"any, Array":function(e,t){return u(r(t),e,this,!0).valueOf()}})})),Kn=Qe("bitNot",["typed"],(function(e){return(0,e.typed)("bitNot",{number:Vn,BigNumber:Rn,"Array | Matrix":function(e){return $t(e,this)}})})),ei=Qe("bitOr",["typed","matrix","equalScalar","DenseMatrix"],(function(e){var t=e.typed,r=e.matrix,n=e.equalScalar,i=e.DenseMatrix,a=ln({typed:t}),o=pn({typed:t,equalScalar:n}),s=mn({typed:t,DenseMatrix:i}),u=hn({typed:t}),c=nn({typed:t});return t("bitOr",{"number, number":Zn,"BigNumber, BigNumber":Fn,"SparseMatrix, SparseMatrix":function(e,t){return o(e,t,this)},"SparseMatrix, DenseMatrix":function(e,t){return a(t,e,this,!0)},"DenseMatrix, SparseMatrix":function(e,t){return a(e,t,this,!1)},"DenseMatrix, DenseMatrix":function(e,t){return u(e,t,this)},"Array, Array":function(e,t){return this(r(e),r(t)).valueOf()},"Array, Matrix":function(e,t){return this(r(e),t)},"Matrix, Array":function(e,t){return this(e,r(t))},"SparseMatrix, any":function(e,t){return s(e,t,this,!1)},"DenseMatrix, any":function(e,t){return c(e,t,this,!1)},"any, SparseMatrix":function(e,t){return s(t,e,this,!0)},"any, DenseMatrix":function(e,t){return c(t,e,this,!0)},"Array, any":function(e,t){return c(r(e),t,this,!1).valueOf()},"any, Array":function(e,t){return c(r(t),e,this,!0).valueOf()}})})),ti=Qe("algorithm07",["typed","DenseMatrix"],(function(e){var t=e.typed,r=e.DenseMatrix;return function(e,i,a){var o=e._size,s=e._datatype,u=i._size,c=i._datatype;if(o.length!==u.length)throw new Me(o.length,u.length);if(o[0]!==u[0]||o[1]!==u[1])throw new RangeError("Dimension mismatch. Matrix A ("+o+") must match Matrix B ("+u+")");var f,l,p,m=o[0],h=o[1],d=0,y=a;"string"==typeof s&&s===c&&(f=s,d=t.convert(0,f),y=t.find(a,[f,f]));var g=[];for(l=0;l<m;l++)g[l]=[];var v=[],x=[],b=[],w=[];for(p=0;p<h;p++){var N=p+1;for(n(e,p,b,v,N),n(i,p,w,x,N),l=0;l<m;l++){var M=b[l]===N?v[l]:d,E=w[l]===N?x[l]:d;g[l][p]=y(M,E)}}return new r({data:g,size:[m,h],datatype:f})};function n(e,t,r,n,i){for(var a=e._values,o=e._index,s=e._ptr,u=s[t],c=s[t+1];u<c;u++){var f=o[u];r[f]=i,n[f]=a[u]}}})),ri=Qe("bitXor",["typed","matrix","DenseMatrix"],(function(e){var t=e.typed,r=e.matrix,n=e.DenseMatrix,i=wn({typed:t}),a=ti({typed:t,DenseMatrix:n}),o=Mn({typed:t,DenseMatrix:n}),s=hn({typed:t}),u=nn({typed:t});return t("bitXor",{"number, number":Wn,"BigNumber, BigNumber":Un,"SparseMatrix, SparseMatrix":function(e,t){return a(e,t,this)},"SparseMatrix, DenseMatrix":function(e,t){return i(t,e,this,!0)},"DenseMatrix, SparseMatrix":function(e,t){return i(e,t,this,!1)},"DenseMatrix, 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r=null!=arguments[t]?arguments[t]:{};t%2?Ma(Object(r),!0).forEach((function(t){Na()(e,t,r[t])})):Object.getOwnPropertyDescriptors?Object.defineProperties(e,Object.getOwnPropertyDescriptors(r)):Ma(Object(r)).forEach((function(t){Object.defineProperty(e,t,Object.getOwnPropertyDescriptor(r,t))}))}return e}var Sa="Number of decimals in function round must be an integer",Aa=Qe("round",["typed","matrix","equalScalar","zeros","BigNumber","DenseMatrix"],(function(e){var t=e.typed,r=e.matrix,n=e.equalScalar,i=e.zeros,a=e.BigNumber,o=e.DenseMatrix,s=rn({typed:t,equalScalar:n}),u=Mn({typed:t,DenseMatrix:o}),c=nn({typed:t});return t("round",Ea(Ea({},Oa),{},{Complex:function(e){return e.round()},"Complex, number":function(e,t){if(t%1)throw new TypeError(Sa);return e.round(t)},"Complex, BigNumber":function(e,t){if(!t.isInteger())throw new TypeError(Sa);var r=t.toNumber();return e.round(r)},"number, BigNumber":function(e,t){if(!t.isInteger())throw new TypeError(Sa);return new 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TypeError(Sa);if(t<0||t>15)throw new Error("Number of decimals in function round must be in the range of 0-15");return Vr(e,t)}},_a=Qe("log",["config","typed","divideScalar","Complex"],(function(e){var t=e.typed,r=e.config,n=e.divideScalar,i=e.Complex;return t("log",{number:function(e){return e>=0||r.predictable?Rr(e):new i(e,0).log()},Complex:function(e){return e.log()},BigNumber:function(e){return!e.isNegative()||r.predictable?e.ln():new i(e.toNumber(),0).log()},"Array | Matrix":function(e){return $t(e,this)},"any, any":function(e,t){return n(this(e),this(t))}})})),Ca=Qe("log1p",["typed","config","divideScalar","log","Complex"],(function(e){var t=e.typed,r=e.config,n=e.divideScalar,i=e.log,a=e.Complex;return t("log1p",{number:function(e){return e>=-1||r.predictable?X(e):o(new a(e,0))},Complex:o,BigNumber:function(e){var t=e.plus(1);return!t.isNegative()||r.predictable?t.ln():o(new a(e.toNumber(),0))},"Array | Matrix":function(e){return $t(e,this)},"any, any":function(e,t){return n(this(e),i(t))}});function o(e){var t=e.re+1;return new a(Math.log(Math.sqrt(t*t+e.im*e.im)),Math.atan2(e.im,t))}})),Ta=Qe("nthRoots",["config","typed","divideScalar","Complex"],(function(e){var t=e.typed,r=(e.config,e.divideScalar,e.Complex),n=[function(e){return new r(e,0)},function(e){return new r(0,e)},function(e){return new r(-e,0)},function(e){return new r(0,-e)}];function i(e,t){if(t<0)throw new Error("Root must be greater than zero");if(0===t)throw new Error("Root must be non-zero");if(t%1!=0)throw new Error("Root must be an integer");if(0===e||0===e.abs())return[new r(0,0)];var i,a="number"==typeof e;(a||0===e.re||0===e.im)&&(i=a?2*+(e<0):0===e.im?2*+(e.re<0):2*+(e.im<0)+1);for(var o=e.arg(),s=e.abs(),u=[],c=Math.pow(s,1/t),f=0;f<t;f++){var l=(i+4*f)/t;l!==Math.round(l)?u.push(new r({r:c,phi:(o+2*Math.PI*f)/t})):u.push(n[l%4](c))}return u}return t("nthRoots",{Complex:function(e){return i(e,2)},"Complex, number":i})})),za=Qe("dotPow",["typed","equalScalar","matrix","pow","DenseMatrix"],(function(e){var t=e.typed,r=e.equalScalar,n=e.matrix,i=e.pow,a=e.DenseMatrix,o=wn({typed:t}),s=ti({typed:t,DenseMatrix:a}),u=rn({typed:t,equalScalar:r}),c=Mn({typed:t,DenseMatrix:a}),f=hn({typed:t}),l=nn({typed:t});return t("dotPow",{"any, any":i,"SparseMatrix, SparseMatrix":function(e,t){return s(e,t,i,!1)},"SparseMatrix, DenseMatrix":function(e,t){return o(t,e,i,!0)},"DenseMatrix, SparseMatrix":function(e,t){return o(e,t,i,!1)},"DenseMatrix, DenseMatrix":function(e,t){return f(e,t,i)},"Array, Array":function(e,t){return this(n(e),n(t)).valueOf()},"Array, Matrix":function(e,t){return this(n(e),t)},"Matrix, Array":function(e,t){return this(e,n(t))},"SparseMatrix, any":function(e,t){return u(e,t,this,!1)},"DenseMatrix, any":function(e,t){return l(e,t,this,!1)},"any, SparseMatrix":function(e,t){return c(t,e,this,!0)},"any, DenseMatrix":function(e,t){return l(t,e,this,!0)},"Array, any":function(e,t){return l(n(e),t,this,!1).valueOf()},"any, Array":function(e,t){return l(n(t),e,this,!0).valueOf()}})})),qa=Qe("dotDivide",["typed","matrix","equalScalar","divideScalar","DenseMatrix"],(function(e){var t=e.typed,r=e.matrix,n=e.equalScalar,i=e.divideScalar,a=e.DenseMatrix,o=yn({typed:t,equalScalar:n}),s=wn({typed:t}),u=ti({typed:t,DenseMatrix:a}),c=rn({typed:t,equalScalar:n}),f=Mn({typed:t,DenseMatrix:a}),l=hn({typed:t}),p=nn({typed:t});return t("dotDivide",{"any, any":i,"SparseMatrix, SparseMatrix":function(e,t){return u(e,t,i,!1)},"SparseMatrix, DenseMatrix":function(e,t){return o(t,e,i,!0)},"DenseMatrix, SparseMatrix":function(e,t){return s(e,t,i,!1)},"DenseMatrix, DenseMatrix":function(e,t){return l(e,t,i)},"Array, Array":function(e,t){return this(r(e),r(t)).valueOf()},"Array, Matrix":function(e,t){return this(r(e),t)},"Matrix, Array":function(e,t){return this(e,r(t))},"SparseMatrix, any":function(e,t){return c(e,t,i,!1)},"DenseMatrix, any":function(e,t){return p(e,t,i,!1)},"any, 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Matrix columns must match vector length.");for(var c=0;c<a;c++)o[c]=[u[c]];return new t({data:o,size:[a,1],datatype:r._datatype})}if(2===s.length){if(s[0]!==a||1!==s[1])throw new RangeError("Dimension mismatch. Matrix columns must match vector length.");if(d(r)){if(n){o=[];for(var f=0;f<a;f++)o[f]=[u[f][0]];return new t({data:o,size:[a,1],datatype:r._datatype})}return r}if(y(r)){for(var l=0;l<a;l++)o[l]=[0];for(var h=r._values,g=r._index,v=r._ptr,x=v[1],b=v[0];b<x;b++){o[g[b]][0]=h[b]}return new t({data:o,size:[a,1],datatype:r._datatype})}}throw new RangeError("Dimension mismatch. The right side has to be either 1- or 2-dimensional vector.")}if(p(r)){var w=Se(r);if(1===w.length){if(w[0]!==a)throw new RangeError("Dimension mismatch. Matrix columns must match vector length.");for(var N=0;N<a;N++)o[N]=[r[N]];return new t({data:o,size:[a,1]})}if(2===w.length){if(w[0]!==a||1!==w[1])throw new RangeError("Dimension mismatch. Matrix columns must match vector length.");for(var M=0;M<a;M++)o[M]=[r[M][0]];return new t({data:o,size:[a,1]})}throw new RangeError("Dimension mismatch. The right side has to be either 1- or 2-dimensional vector.")}}}var Ia=Qe("lsolve",["typed","matrix","divideScalar","multiplyScalar","subtract","equalScalar","DenseMatrix"],(function(e){var t=e.typed,r=e.matrix,n=e.divideScalar,i=e.multiplyScalar,a=e.subtract,o=e.equalScalar,s=e.DenseMatrix,u=ka({DenseMatrix:s});return t("lsolve",{"SparseMatrix, Array | Matrix":function(e,t){return function(e,t){for(var r=(t=u(e,t,!0))._data,c=e._size[0],f=e._size[1],l=e._values,p=e._index,m=e._ptr,h=[],d=0;d<f;d++){var y=r[d][0]||0;if(o(y,0))h[d]=[0];else{for(var g=0,v=[],x=[],b=m[d],w=m[d+1],N=b;N<w;N++){var M=p[N];M===d?g=l[N]:M>d&&(v.push(l[N]),x.push(M))}if(o(g,0))throw new Error("Linear system cannot be solved since matrix is singular");for(var E=n(y,g),S=0,A=x.length;S<A;S++){var O=x[S];r[O]=[a(r[O][0]||0,i(E,v[S]))]}h[d]=[E]}}return new s({data:h,size:[c,1]})}(e,t)},"DenseMatrix, Array | Matrix":function(e,t){return c(e,t)},"Array, Array | Matrix":function(e,t){return c(r(e),t).valueOf()}});function c(e,t){for(var r=(t=u(e,t,!0))._data,c=e._size[0],f=e._size[1],l=[],p=e._data,m=0;m<f;m++){var h=r[m][0]||0,d=void 0;if(o(h,0))d=0;else{var y=p[m][m];if(o(y,0))throw new Error("Linear system cannot be solved since matrix is singular");d=n(h,y);for(var g=m+1;g<c;g++)r[g]=[a(r[g][0]||0,i(d,p[g][m]))]}l[m]=[d]}return new s({data:l,size:[c,1]})}})),Ba=Qe("usolve",["typed","matrix","divideScalar","multiplyScalar","subtract","equalScalar","DenseMatrix"],(function(e){var t=e.typed,r=e.matrix,n=e.divideScalar,i=e.multiplyScalar,a=e.subtract,o=e.equalScalar,s=e.DenseMatrix,u=ka({DenseMatrix:s});return t("usolve",{"SparseMatrix, Array | Matrix":function(e,t){return function(e,t){for(var r=(t=u(e,t,!0))._data,c=e._size[0],f=e._size[1],l=e._values,p=e._index,m=e._ptr,h=[],d=f-1;d>=0;d--){var y=r[d][0]||0;if(o(y,0))h[d]=[0];else{for(var g=0,v=[],x=[],b=m[d],w=m[d+1]-1;w>=b;w--){var N=p[w];N===d?g=l[w]:N<d&&(v.push(l[w]),x.push(N))}if(o(g,0))throw new Error("Linear system cannot be solved since matrix is singular");for(var M=n(y,g),E=0,S=x.length;E<S;E++){var A=x[E];r[A]=[a(r[A][0],i(M,v[E]))]}h[d]=[M]}}return new s({data:h,size:[c,1]})}(e,t)},"DenseMatrix, Array | Matrix":function(e,t){return c(e,t)},"Array, Array | Matrix":function(e,t){return c(r(e),t).valueOf()}});function c(e,t){for(var r=(t=u(e,t,!0))._data,c=e._size[0],f=e._size[1],l=[],p=e._data,m=f-1;m>=0;m--){var h=r[m][0]||0,d=void 0;if(o(h,0))d=0;else{var y=p[m][m];if(o(y,0))throw new Error("Linear system cannot be solved since matrix is singular");d=n(h,y);for(var g=m-1;g>=0;g--)r[g]=[a(r[g][0]||0,i(d,p[g][m]))]}l[m]=[d]}return new s({data:l,size:[c,1]})}})),Da=r(2),Ra=r.n(Da),Fa=Qe("lsolveAll",["typed","matrix","divideScalar","multiplyScalar","subtract","equalScalar","DenseMatrix"],(function(e){var t=e.typed,r=e.matrix,n=e.divideScalar,i=e.multiplyScalar,a=e.subtract,o=e.equalScalar,s=e.DenseMatrix,u=ka({DenseMatrix:s});return t("lsolveAll",{"SparseMatrix, Array | Matrix":function(e,t){return function(e,t){for(var r=[u(e,t,!0)._data.map((function(e){return e[0]}))],c=e._size[0],f=e._size[1],l=e._values,p=e._index,m=e._ptr,h=0;h<f;h++)for(var d=r.length,y=0;y<d;y++){for(var g=r[y],v=[],x=[],b=m[h],w=m[h+1],N=0,M=b;M<w;M++){var E=p[M];E===h?N=l[M]:E>h&&(v.push(l[M]),x.push(E))}if(o(N,0))if(o(g[h],0)){if(0===y){var S=Ra()(g);S[h]=1;for(var A=0,O=x.length;A<O;A++){var _=x[A];S[_]=a(S[_],v[A])}r.push(S)}}else{if(0===y)return[];r.splice(y,1),y-=1,d-=1}else{g[h]=n(g[h],N);for(var C=0,T=x.length;C<T;C++){var z=x[C];g[z]=a(g[z],i(g[h],v[C]))}}}return r.map((function(e){return new s({data:e.map((function(e){return[e]})),size:[c,1]})}))}(e,t)},"DenseMatrix, Array | Matrix":function(e,t){return c(e,t)},"Array, Array | Matrix":function(e,t){return c(r(e),t).map((function(e){return e.valueOf()}))}});function c(e,t){for(var r=[u(e,t,!0)._data.map((function(e){return e[0]}))],c=e._data,f=e._size[0],l=e._size[1],p=0;p<l;p++)for(var m=r.length,h=0;h<m;h++){var d=r[h];if(o(c[p][p],0))if(o(d[p],0)){if(0===h){var y=Ra()(d);y[p]=1;for(var g=p+1;g<l;g++)y[g]=a(y[g],c[g][p]);r.push(y)}}else{if(0===h)return[];r.splice(h,1),h-=1,m-=1}else{d[p]=n(d[p],c[p][p]);for(var v=p+1;v<l;v++)d[v]=a(d[v],i(d[p],c[v][p]))}}return r.map((function(e){return new s({data:e.map((function(e){return[e]})),size:[f,1]})}))}})),ja=Qe("usolveAll",["typed","matrix","divideScalar","multiplyScalar","subtract","equalScalar","DenseMatrix"],(function(e){var t=e.typed,r=e.matrix,n=e.divideScalar,i=e.multiplyScalar,a=e.subtract,o=e.equalScalar,s=e.DenseMatrix,u=ka({DenseMatrix:s});return t("usolveAll",{"SparseMatrix, Array | Matrix":function(e,t){return function(e,t){for(var r=[u(e,t,!0)._data.map((function(e){return e[0]}))],c=e._size[0],f=e._size[1],l=e._values,p=e._index,m=e._ptr,h=f-1;h>=0;h--)for(var d=r.length,y=0;y<d;y++){for(var g=r[y],v=[],x=[],b=m[h],w=m[h+1],N=0,M=w-1;M>=b;M--){var E=p[M];E===h?N=l[M]:E<h&&(v.push(l[M]),x.push(E))}if(o(N,0))if(o(g[h],0)){if(0===y){var S=Ra()(g);S[h]=1;for(var A=0,O=x.length;A<O;A++){var _=x[A];S[_]=a(S[_],v[A])}r.push(S)}}else{if(0===y)return[];r.splice(y,1),y-=1,d-=1}else{g[h]=n(g[h],N);for(var C=0,T=x.length;C<T;C++){var z=x[C];g[z]=a(g[z],i(g[h],v[C]))}}}return r.map((function(e){return new s({data:e.map((function(e){return[e]})),size:[c,1]})}))}(e,t)},"DenseMatrix, Array | Matrix":function(e,t){return c(e,t)},"Array, Array | Matrix":function(e,t){return c(r(e),t).map((function(e){return e.valueOf()}))}});function c(e,t){for(var r=[u(e,t,!0)._data.map((function(e){return e[0]}))],c=e._data,f=e._size[0],l=e._size[1]-1;l>=0;l--)for(var p=r.length,m=0;m<p;m++){var h=r[m];if(o(c[l][l],0))if(o(h[l],0)){if(0===m){var d=Ra()(h);d[l]=1;for(var y=l-1;y>=0;y--)d[y]=a(d[y],c[y][l]);r.push(d)}}else{if(0===m)return[];r.splice(m,1),m-=1,p-=1}else{h[l]=n(h[l],c[l][l]);for(var g=l-1;g>=0;g--)h[g]=a(h[g],i(h[l],c[g][l]))}}return r.map((function(e){return new s({data:e.map((function(e){return[e]})),size:[f,1]})}))}})),Pa=Qe("algorithm08",["typed","equalScalar"],(function(e){var t=e.typed,r=e.equalScalar;return function(e,n,i){var a=e._values,o=e._index,s=e._ptr,u=e._size,c=e._datatype,f=n._values,l=n._index,p=n._ptr,m=n._size,h=n._datatype;if(u.length!==m.length)throw new Me(u.length,m.length);if(u[0]!==m[0]||u[1]!==m[1])throw new RangeError("Dimension mismatch. 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t=e.typed,r=e.isNumeric,n=e.isNaN,i=e.compare,a=i,o=function(e,t){return-i(e,t)};return t("partitionSelect",{"Array | Matrix, number":function(e,t){return s(e,t,a)},"Array | Matrix, number, string":function(e,t,r){if("asc"===r)return s(e,t,a);if("desc"===r)return s(e,t,o);throw new Error('Compare string must be "asc" or "desc"')},"Array | Matrix, number, function":s});function s(e,t,r){if(!Z(t)||t<0)throw new Error("k must be a non-negative integer");if(m(e)){if(e.size().length>1)throw new Error("Only one dimensional matrices supported");return u(e.valueOf(),t,r)}if(Array.isArray(e))return u(e,t,r)}function u(e,t,i){if(t>=e.length)throw new Error("k out of bounds");for(var a=0;a<e.length;a++)if(r(e[a])&&n(e[a]))return e[a];for(var o=0,s=e.length-1;o<s;){for(var u=o,c=s,f=e[Math.floor(Math.random()*(s-o+1))+o];u<c;)if(i(e[u],f)>=0){var l=e[c];e[c]=e[u],e[u]=l,--c}else++u;i(e[u],f)>0&&--u,t<=u?s=u:o=u+1}return 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t=e.typed,r=e.config,n=e.numeric,i=e.larger;return t("max",{"Array | Matrix":o,"Array | Matrix, number | BigNumber":function(e,t){return Gt(e,t.valueOf(),a)},"...":function(e){if(Lt(e))throw new TypeError("Scalar values expected in function max");return o(e)}});function a(e,t){try{return i(e,t)?e:t}catch(e){throw ua(e,"max",t)}}function o(e){var t;if(Ht(e,(function(e){try{isNaN(e)&&"number"==typeof e?t=NaN:(void 0===t||i(e,t))&&(t=e)}catch(t){throw ua(t,"max",e)}})),void 0===t)throw new Error("Cannot calculate max of an empty array");return"string"==typeof t&&(t=n(t,r.number)),t}})),so=Qe("min",["typed","config","numeric","smaller"],(function(e){var t=e.typed,r=e.config,n=e.numeric,i=e.smaller;return t("min",{"Array | Matrix":o,"Array | Matrix, number | BigNumber":function(e,t){return Gt(e,t.valueOf(),a)},"...":function(e){if(Lt(e))throw new TypeError("Scalar values expected in function min");return o(e)}});function a(e,t){try{return i(e,t)?e:t}catch(e){throw ua(e,"min",t)}}function 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0===this._size},i.prototype.extractMinimum=function(){var e=this._minimum;if(null===e)return e;for(var i=this._minimum,a=e.degree,s=e.child;a>0;){var u=s.right;s.left.right=s.right,s.right.left=s.left,s.left=i,s.right=i.right,i.right=s,s.right.left=s,s.parent=null,s=u,a--}return e.left.right=e.right,e.right.left=e.left,i=e===e.right?null:function(e,i){var a,s=Math.floor(Math.log(i)*n)+1,u=new Array(s),c=0,f=e;if(f)for(c++,f=f.right;f!==e;)c++,f=f.right;for(;c>0;){for(var l=f.degree,p=f.right;a=u[l];){if(r(f.key,a.key)){var m=a;a=f,f=m}o(a,f),u[l]=null,l++}u[l]=f,f=p,c--}e=null;for(var h=0;h<s;h++)(a=u[h])&&(e?(a.left.right=a.right,a.right.left=a.left,a.left=e,a.right=e.right,e.right=a,a.right.left=a,t(a.key,e.key)&&(e=a)):e=a);return e}(i=e.right,this._size),this._size--,this._minimum=i,e},i.prototype.remove=function(e){this._minimum=function(e,r,n){r.key=n;var i=r.parent;i&&t(r.key,i.key)&&(a(e,r,i),function e(t,r){var 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n=this._values[e];n?n.value=t(n.value,r):(n=this._heap.insert(e,r),this._values[e]=n)},i.prototype.forEach=function(e,t,n){var i=this._heap,a=this._values,o=[],s=i.extractMinimum();for(s&&o.push(s);s&&s.key<=t;)s.key>=e&&(r(s.value,0)||n(s.key,s.value,this)),(s=i.extractMinimum())&&o.push(s);for(var u=0;u<o.length;u++){var c=o[u];a[(s=i.insert(c.key,c.value)).key]=s}},i.prototype.swap=function(e,t){var r=this._values[e],n=this._values[t];if(!r&&n)r=this._heap.insert(e,n.value),this._heap.remove(n),this._values[e]=r,this._values[t]=void 0;else if(r&&!n)n=this._heap.insert(t,r.value),this._heap.remove(r),this._values[t]=n,this._values[e]=void 0;else if(r&&n){var i=r.value;r.value=n.value,n.value=i}},i}),{isClass:!0}),po=r(3),mo=r.n(po),ho=wi((function(e){return new e(1).exp()}),{hasher:xo}),yo=wi((function(e){return new e(1).plus(new e(5).sqrt()).div(2)}),{hasher:xo}),go=wi((function(e){return e.acos(-1)}),{hasher:xo}),vo=wi((function(e){return go(e).times(2)}),{hasher:xo});function 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t,r,n,i=e.on,o=e.config,s=e.addScalar,c=e.subtract,l=e.multiplyScalar,p=e.divideScalar,m=e.pow,h=e.abs,d=e.fix,y=e.round,g=e.equal,v=e.isNumeric,x=e.format,b=e.number,w=e.Complex,N=e.BigNumber,M=e.Fraction,E=b;function S(e,t){if(!(this instanceof S))throw new Error("Constructor must be called with the new operator");if(null!=e&&!v(e)&&!u(e))throw new TypeError("First parameter in Unit constructor must be number, BigNumber, Fraction, Complex, or undefined");if(void 0!==t&&("string"!=typeof t||""===t))throw new TypeError("Second parameter in Unit constructor must be a string");if(void 0!==t){var r=S.parse(t);this.units=r.units,this.dimensions=r.dimensions}else{this.units=[{unit:j,prefix:B.NONE,power:0}],this.dimensions=[];for(var n=0;n<D.length;n++)this.dimensions[n]=0}this.value=null!=e?this._normalize(e):null,this.fixPrefix=!1,this.skipAutomaticSimplification=!0}function A(){for(;" "===n||"\t"===n;)_()}function O(e){return e>="0"&&e<="9"}function _(){r++,n=t.charAt(r)}function 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Array.isArray(e)?Ie(e).length:Ie(e.toArray()).length;for(var n=Ie(Array.isArray(e)?e:e.toArray()).sort(r),i=1,a=1;a<n.length;a++)0!==r(n[a],n[a-1])&&i++;return i}})})),ws=Qe("setSymDifference",["typed","size","concat","subset","setDifference","Index"],(function(e){var t=e.typed,r=e.size,n=e.concat,i=e.subset,a=e.setDifference,o=e.Index;return t("setSymDifference",{"Array | Matrix, Array | Matrix":function(e,t){if(0===i(r(e),new o(0)))return Ie(t);if(0===i(r(t),new o(0)))return Ie(e);var s=Ie(e),u=Ie(t);return n(a(s,u),a(u,s))}})})),Ns=Qe("setUnion",["typed","size","concat","subset","setIntersect","setSymDifference","Index"],(function(e){var t=e.typed,r=e.size,n=e.concat,i=e.subset,a=e.setIntersect,o=e.setSymDifference,s=e.Index;return t("setUnion",{"Array | Matrix, Array | Matrix":function(e,t){if(0===i(r(e),new s(0)))return Ie(t);if(0===i(r(t),new s(0)))return Ie(e);var u=Ie(e),c=Ie(t);return n(o(u,c),a(u,c))}})})),Ms=Qe("add",["typed","matrix","addScalar","equalScalar","DenseMatrix","SparseMatrix"],(function(e){var t=e.typed,r=e.matrix,n=e.addScalar,i=e.equalScalar,a=e.DenseMatrix,o=(e.SparseMatrix,ln({typed:t})),s=pn({typed:t,equalScalar:i}),u=mn({typed:t,DenseMatrix:a}),c=hn({typed:t}),f=nn({typed:t});return t("add",Ve({"DenseMatrix, DenseMatrix":function(e,t){return c(e,t,n)},"DenseMatrix, SparseMatrix":function(e,t){return o(e,t,n,!1)},"SparseMatrix, DenseMatrix":function(e,t){return o(t,e,n,!0)},"SparseMatrix, SparseMatrix":function(e,t){return s(e,t,n)},"Array, Array":function(e,t){return this(r(e),r(t)).valueOf()},"Array, Matrix":function(e,t){return this(r(e),t)},"Matrix, Array":function(e,t){return this(e,r(t))},"DenseMatrix, any":function(e,t){return f(e,t,n,!1)},"SparseMatrix, any":function(e,t){return u(e,t,n,!1)},"any, DenseMatrix":function(e,t){return f(t,e,n,!0)},"any, SparseMatrix":function(e,t){return u(t,e,n,!0)},"Array, any":function(e,t){return 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n(e.value)},n.createProxy=function(e,t){if("string"==typeof e)u=e,"function"==typeof(c=t)&&(n.prototype[u]=a(c));else{var r=function(t){Ye(e,t)&&void 0===o[t]&&i(t,(function(){return e[t]}))};for(var s in e)r(s)}var u,c};var o={expression:!0,docs:!0,type:!0,classes:!0,json:!0,error:!0,isChain:!0};return n.createProxy(r),t&&t("import",(function(e,t,r){r||i(e,t)})),n}),{isClass:!0}),Iu={name:"pi",category:"Constants",syntax:["pi"],description:"The number pi is a mathematical constant that is the ratio of a circle's circumference to its diameter, and is approximately equal to 3.14159",examples:["pi","sin(pi/2)"],seealso:["tau"]},Bu={name:"e",category:"Constants",syntax:["e"],description:"Euler's number, the base of the natural logarithm. Approximately equal to 2.71828",examples:["e","e ^ 2","exp(2)","log(e)"],seealso:["exp"]},Du={bignumber:{name:"bignumber",category:"Construction",syntax:["bignumber(x)"],description:"Create a big number from a number or string.",examples:["0.1 + 0.2","bignumber(0.1) + bignumber(0.2)",'bignumber("7.2")','bignumber("7.2e500")',"bignumber([0.1, 0.2, 0.3])"],seealso:["boolean","complex","fraction","index","matrix","string","unit"]},boolean:{name:"boolean",category:"Construction",syntax:["x","boolean(x)"],description:"Convert a string or number into a boolean.",examples:["boolean(0)","boolean(1)","boolean(3)",'boolean("true")','boolean("false")',"boolean([1, 0, 1, 1])"],seealso:["bignumber","complex","index","matrix","number","string","unit"]},complex:{name:"complex",category:"Construction",syntax:["complex()","complex(re, im)","complex(string)"],description:"Create a complex number.",examples:["complex()","complex(2, 3)",'complex("7 - 2i")'],seealso:["bignumber","boolean","index","matrix","number","string","unit"]},createUnit:{name:"createUnit",category:"Construction",syntax:["createUnit(definitions)","createUnit(name, definition)"],description:"Create a user-defined unit and register it with the Unit type.",examples:['createUnit("foo")','createUnit("knot", {definition: "0.514444444 m/s", aliases: ["knots", "kt", "kts"]})','createUnit("mph", "1 mile/hour")'],seealso:["unit","splitUnit"]},fraction:{name:"fraction",category:"Construction",syntax:["fraction(num)","fraction(num,den)"],description:"Create a fraction from a number or from a numerator and denominator.",examples:["fraction(0.125)","fraction(1, 3) + fraction(2, 5)"],seealso:["bignumber","boolean","complex","index","matrix","string","unit"]},index:{name:"index",category:"Construction",syntax:["[start]","[start:end]","[start:step:end]","[start1, start 2, ...]","[start1:end1, start2:end2, ...]","[start1:step1:end1, start2:step2:end2, ...]"],description:"Create an index to get or replace a subset of a matrix",examples:["[]","[1, 2, 3]","A = [1, 2, 3; 4, 5, 6]","A[1, :]","A[1, 2] = 50","A[0:2, 0:2] = ones(2, 2)"],seealso:["bignumber","boolean","complex","matrix,","number","range","string","unit"]},matrix:{name:"matrix",category:"Construction",syntax:["[]","[a1, b1, ...; a2, b2, ...]","matrix()",'matrix("dense")',"matrix([...])"],description:"Create a matrix.",examples:["[]","[1, 2, 3]","[1, 2, 3; 4, 5, 6]","matrix()","matrix([3, 4])",'matrix([3, 4; 5, 6], "sparse")','matrix([3, 4; 5, 6], "sparse", "number")'],seealso:["bignumber","boolean","complex","index","number","string","unit","sparse"]},number:{name:"number",category:"Construction",syntax:["x","number(x)","number(unit, valuelessUnit)"],description:"Create a number or convert a string or boolean into a number.",examples:["2","2e3","4.05","number(2)",'number("7.2")',"number(true)","number([true, false, true, true])",'number(unit("52cm"), "m")'],seealso:["bignumber","boolean","complex","fraction","index","matrix","string","unit"]},sparse:{name:"sparse",category:"Construction",syntax:["sparse()","sparse([a1, b1, ...; a1, b2, ...])",'sparse([a1, b1, ...; a1, b2, ...], "number")'],description:"Create a sparse matrix.",examples:["sparse()","sparse([3, 4; 5, 6])",'sparse([3, 0; 5, 0], "number")'],seealso:["bignumber","boolean","complex","index","number","string","unit","matrix"]},splitUnit:{name:"splitUnit",category:"Construction",syntax:["splitUnit(unit: Unit, parts: Unit[])"],description:"Split a unit in an array of units whose sum is equal to the original unit.",examples:['splitUnit(1 m, ["feet", "inch"])'],seealso:["unit","createUnit"]},string:{name:"string",category:"Construction",syntax:['"text"',"string(x)"],description:"Create a string or convert a value to a string",examples:['"Hello World!"',"string(4.2)","string(3 + 2i)"],seealso:["bignumber","boolean","complex","index","matrix","number","unit"]},unit:{name:"unit",category:"Construction",syntax:["value unit","unit(value, unit)","unit(string)"],description:"Create a unit.",examples:["5.5 mm","3 inch",'unit(7.1, "kilogram")','unit("23 deg")'],seealso:["bignumber","boolean","complex","index","matrix","number","string"]},e:Bu,E:Bu,false:{name:"false",category:"Constants",syntax:["false"],description:"Boolean value false",examples:["false"],seealso:["true"]},i:{name:"i",category:"Constants",syntax:["i"],description:"Imaginary unit, defined as i*i=-1. A complex number is described as a + b*i, where a is the real part, and b is the imaginary part.",examples:["i","i * i","sqrt(-1)"],seealso:[]},Infinity:{name:"Infinity",category:"Constants",syntax:["Infinity"],description:"Infinity, a number which is larger than the maximum number that can be handled by a floating point number.",examples:["Infinity","1 / 0"],seealso:[]},LN2:{name:"LN2",category:"Constants",syntax:["LN2"],description:"Returns the natural logarithm of 2, approximately equal to 0.693",examples:["LN2","log(2)"],seealso:[]},LN10:{name:"LN10",category:"Constants",syntax:["LN10"],description:"Returns the natural logarithm of 10, approximately equal to 2.302",examples:["LN10","log(10)"],seealso:[]},LOG2E:{name:"LOG2E",category:"Constants",syntax:["LOG2E"],description:"Returns the base-2 logarithm of E, approximately equal to 1.442",examples:["LOG2E","log(e, 2)"],seealso:[]},LOG10E:{name:"LOG10E",category:"Constants",syntax:["LOG10E"],description:"Returns the base-10 logarithm of E, approximately equal to 0.434",examples:["LOG10E","log(e, 10)"],seealso:[]},NaN:{name:"NaN",category:"Constants",syntax:["NaN"],description:"Not a number",examples:["NaN","0 / 0"],seealso:[]},null:{name:"null",category:"Constants",syntax:["null"],description:"Value null",examples:["null"],seealso:["true","false"]},pi:Iu,PI:Iu,phi:{name:"phi",category:"Constants",syntax:["phi"],description:"Phi is the golden ratio. Two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. Phi is defined as `(1 + sqrt(5)) / 2` and is approximately 1.618034...",examples:["phi"],seealso:[]},SQRT1_2:{name:"SQRT1_2",category:"Constants",syntax:["SQRT1_2"],description:"Returns the square root of 1/2, approximately equal to 0.707",examples:["SQRT1_2","sqrt(1/2)"],seealso:[]},SQRT2:{name:"SQRT2",category:"Constants",syntax:["SQRT2"],description:"Returns the square root of 2, approximately equal to 1.414",examples:["SQRT2","sqrt(2)"],seealso:[]},tau:{name:"tau",category:"Constants",syntax:["tau"],description:"Tau is the ratio constant of a circle's circumference to radius, equal to 2 * pi, approximately 6.2832.",examples:["tau","2 * pi"],seealso:["pi"]},true:{name:"true",category:"Constants",syntax:["true"],description:"Boolean value true",examples:["true"],seealso:["false"]},version:{name:"version",category:"Constants",syntax:["version"],description:"A string with the version number of math.js",examples:["version"],seealso:[]},speedOfLight:{description:"Speed of light in vacuum",examples:["speedOfLight"]},gravitationConstant:{description:"Newtonian constant of gravitation",examples:["gravitationConstant"]},planckConstant:{description:"Planck constant",examples:["planckConstant"]},reducedPlanckConstant:{description:"Reduced Planck constant",examples:["reducedPlanckConstant"]},magneticConstant:{description:"Magnetic constant (vacuum permeability)",examples:["magneticConstant"]},electricConstant:{description:"Electric constant (vacuum permeability)",examples:["electricConstant"]},vacuumImpedance:{description:"Characteristic impedance of vacuum",examples:["vacuumImpedance"]},coulomb:{description:"Coulomb's constant",examples:["coulomb"]},elementaryCharge:{description:"Elementary charge",examples:["elementaryCharge"]},bohrMagneton:{description:"Borh magneton",examples:["bohrMagneton"]},conductanceQuantum:{description:"Conductance quantum",examples:["conductanceQuantum"]},inverseConductanceQuantum:{description:"Inverse conductance quantum",examples:["inverseConductanceQuantum"]},magneticFluxQuantum:{description:"Magnetic flux quantum",examples:["magneticFluxQuantum"]},nuclearMagneton:{description:"Nuclear magneton",examples:["nuclearMagneton"]},klitzing:{description:"Von Klitzing constant",examples:["klitzing"]},bohrRadius:{description:"Borh radius",examples:["bohrRadius"]},classicalElectronRadius:{description:"Classical electron radius",examples:["classicalElectronRadius"]},electronMass:{description:"Electron mass",examples:["electronMass"]},fermiCoupling:{description:"Fermi coupling constant",examples:["fermiCoupling"]},fineStructure:{description:"Fine-structure constant",examples:["fineStructure"]},hartreeEnergy:{description:"Hartree energy",examples:["hartreeEnergy"]},protonMass:{description:"Proton mass",examples:["protonMass"]},deuteronMass:{description:"Deuteron Mass",examples:["deuteronMass"]},neutronMass:{description:"Neutron mass",examples:["neutronMass"]},quantumOfCirculation:{description:"Quantum of circulation",examples:["quantumOfCirculation"]},rydberg:{description:"Rydberg constant",examples:["rydberg"]},thomsonCrossSection:{description:"Thomson cross section",examples:["thomsonCrossSection"]},weakMixingAngle:{description:"Weak mixing angle",examples:["weakMixingAngle"]},efimovFactor:{description:"Efimov factor",examples:["efimovFactor"]},atomicMass:{description:"Atomic mass constant",examples:["atomicMass"]},avogadro:{description:"Avogadro's number",examples:["avogadro"]},boltzmann:{description:"Boltzmann constant",examples:["boltzmann"]},faraday:{description:"Faraday constant",examples:["faraday"]},firstRadiation:{description:"First radiation constant",examples:["firstRadiation"]},loschmidt:{description:"Loschmidt constant at T=273.15 K and p=101.325 kPa",examples:["loschmidt"]},gasConstant:{description:"Gas constant",examples:["gasConstant"]},molarPlanckConstant:{description:"Molar Planck constant",examples:["molarPlanckConstant"]},molarVolume:{description:"Molar volume of an ideal gas at T=273.15 K and p=101.325 kPa",examples:["molarVolume"]},sackurTetrode:{description:"Sackur-Tetrode constant at T=1 K and p=101.325 kPa",examples:["sackurTetrode"]},secondRadiation:{description:"Second radiation constant",examples:["secondRadiation"]},stefanBoltzmann:{description:"Stefan-Boltzmann constant",examples:["stefanBoltzmann"]},wienDisplacement:{description:"Wien displacement law constant",examples:["wienDisplacement"]},molarMass:{description:"Molar mass constant",examples:["molarMass"]},molarMassC12:{description:"Molar mass constant of carbon-12",examples:["molarMassC12"]},gravity:{description:"Standard acceleration of gravity (standard acceleration of free-fall on Earth)",examples:["gravity"]},planckLength:{description:"Planck length",examples:["planckLength"]},planckMass:{description:"Planck mass",examples:["planckMass"]},planckTime:{description:"Planck time",examples:["planckTime"]},planckCharge:{description:"Planck charge",examples:["planckCharge"]},planckTemperature:{description:"Planck temperature",examples:["planckTemperature"]},derivative:{name:"derivative",category:"Algebra",syntax:["derivative(expr, variable)","derivative(expr, variable, {simplify: boolean})"],description:"Takes the derivative of an expression expressed in parser Nodes. The derivative will be taken over the supplied variable in the second parameter. If there are multiple variables in the expression, it will return a partial derivative.",examples:['derivative("2x^3", "x")','derivative("2x^3", "x", {simplify: false})','derivative("2x^2 + 3x + 4", "x")','derivative("sin(2x)", "x")','f = parse("x^2 + x")','x = parse("x")',"df = derivative(f, x)","df.evaluate({x: 3})"],seealso:["simplify","parse","evaluate"]},lsolve:{name:"lsolve",category:"Algebra",syntax:["x=lsolve(L, b)"],description:"Finds one solution of the linear system L * x = b where L is an [n x n] lower triangular matrix and b is a [n] column vector.",examples:["a = [-2, 3; 2, 1]","b = [11, 9]","x = lsolve(a, b)"],seealso:["lsolveAll","lup","lusolve","usolve","matrix","sparse"]},lsolveAll:{name:"lsolveAll",category:"Algebra",syntax:["x=lsolveAll(L, b)"],description:"Finds all solutions of the linear system L * x = b where L is an [n x n] lower triangular matrix and b is a [n] column vector.",examples:["a = [-2, 3; 2, 1]","b = [11, 9]","x = lsolve(a, b)"],seealso:["lsolve","lup","lusolve","usolve","matrix","sparse"]},lup:{name:"lup",category:"Algebra",syntax:["lup(m)"],description:"Calculate the Matrix LU decomposition with partial pivoting. Matrix A is decomposed in three matrices (L, U, P) where P * A = L * U",examples:["lup([[2, 1], [1, 4]])","lup(matrix([[2, 1], [1, 4]]))","lup(sparse([[2, 1], [1, 4]]))"],seealso:["lusolve","lsolve","usolve","matrix","sparse","slu","qr"]},lusolve:{name:"lusolve",category:"Algebra",syntax:["x=lusolve(A, b)","x=lusolve(lu, b)"],description:"Solves the linear system A * x = b where A is an [n x n] matrix and b is a [n] column vector.",examples:["a = [-2, 3; 2, 1]","b = [11, 9]","x = lusolve(a, b)"],seealso:["lup","slu","lsolve","usolve","matrix","sparse"]},simplify:{name:"simplify",category:"Algebra",syntax:["simplify(expr)","simplify(expr, rules)"],description:"Simplify an expression tree.",examples:['simplify("3 + 2 / 4")','simplify("2x + x")','f = parse("x * (x + 2 + x)")',"simplified = simplify(f)","simplified.evaluate({x: 2})"],seealso:["derivative","parse","evaluate"]},rationalize:{name:"rationalize",category:"Algebra",syntax:["rationalize(expr)","rationalize(expr, scope)","rationalize(expr, scope, detailed)"],description:"Transform a rationalizable expression in a rational fraction. If rational fraction is one variable polynomial then converts the numerator and denominator in canonical form, with decreasing exponents, returning the coefficients of numerator.",examples:['rationalize("2x/y - y/(x+1)")','rationalize("2x/y - y/(x+1)", true)'],seealso:["simplify"]},slu:{name:"slu",category:"Algebra",syntax:["slu(A, order, threshold)"],description:"Calculate the Matrix LU decomposition with full pivoting. Matrix A is decomposed in two matrices (L, U) and two permutation vectors (pinv, q) where P * A * Q = L * U",examples:["slu(sparse([4.5, 0, 3.2, 0; 3.1, 2.9, 0, 0.9; 0, 1.7, 3, 0; 3.5, 0.4, 0, 1]), 1, 0.001)"],seealso:["lusolve","lsolve","usolve","matrix","sparse","lup","qr"]},usolve:{name:"usolve",category:"Algebra",syntax:["x=usolve(U, b)"],description:"Finds one solution of the linear system U * x = b where U is an [n x n] upper triangular matrix and b is a [n] column vector.",examples:["x=usolve(sparse([1, 1, 1, 1; 0, 1, 1, 1; 0, 0, 1, 1; 0, 0, 0, 1]), [1; 2; 3; 4])"],seealso:["usolveAll","lup","lusolve","lsolve","matrix","sparse"]},usolveAll:{name:"usolveAll",category:"Algebra",syntax:["x=usolve(U, b)"],description:"Finds all solutions of the linear system U * x = b where U is an [n x n] upper triangular matrix and b is a [n] column vector.",examples:["x=usolve(sparse([1, 1, 1, 1; 0, 1, 1, 1; 0, 0, 1, 1; 0, 0, 0, 1]), [1; 2; 3; 4])"],seealso:["usolve","lup","lusolve","lsolve","matrix","sparse"]},qr:{name:"qr",category:"Algebra",syntax:["qr(A)"],description:"Calculates the Matrix QR decomposition. Matrix `A` is decomposed in two matrices (`Q`, `R`) where `Q` is an orthogonal matrix and `R` is an upper triangular matrix.",examples:["qr([[1, -1,  4], [1,  4, -2], [1,  4,  2], [1,  -1, 0]])"],seealso:["lup","slu","matrix"]},abs:{name:"abs",category:"Arithmetic",syntax:["abs(x)"],description:"Compute the absolute value.",examples:["abs(3.5)","abs(-4.2)"],seealso:["sign"]},add:{name:"add",category:"Operators",syntax:["x + y","add(x, y)"],description:"Add two values.",examples:["a = 2.1 + 3.6","a - 3.6","3 + 2i","3 cm + 2 inch",'"2.3" + "4"'],seealso:["subtract"]},cbrt:{name:"cbrt",category:"Arithmetic",syntax:["cbrt(x)","cbrt(x, allRoots)"],description:"Compute the cubic root value. If x = y * y * y, then y is the cubic root of x. When `x` is a number or complex number, an optional second argument `allRoots` can be provided to return all three cubic roots. If not provided, the principal root is returned",examples:["cbrt(64)","cube(4)","cbrt(-8)","cbrt(2 + 3i)","cbrt(8i)","cbrt(8i, true)","cbrt(27 m^3)"],seealso:["square","sqrt","cube","multiply"]},ceil:{name:"ceil",category:"Arithmetic",syntax:["ceil(x)"],description:"Round a value towards plus infinity. If x is complex, both real and imaginary part are rounded towards plus infinity.",examples:["ceil(3.2)","ceil(3.8)","ceil(-4.2)"],seealso:["floor","fix","round"]},cube:{name:"cube",category:"Arithmetic",syntax:["cube(x)"],description:"Compute the cube of a value. The cube of x is x * x * x.",examples:["cube(2)","2^3","2 * 2 * 2"],seealso:["multiply","square","pow"]},divide:{name:"divide",category:"Operators",syntax:["x / y","divide(x, y)"],description:"Divide two values.",examples:["a = 2 / 3","a * 3","4.5 / 2","3 + 4 / 2","(3 + 4) / 2","18 km / 4.5"],seealso:["multiply"]},dotDivide:{name:"dotDivide",category:"Operators",syntax:["x ./ y","dotDivide(x, y)"],description:"Divide two values element wise.",examples:["a = [1, 2, 3; 4, 5, 6]","b = [2, 1, 1; 3, 2, 5]","a ./ b"],seealso:["multiply","dotMultiply","divide"]},dotMultiply:{name:"dotMultiply",category:"Operators",syntax:["x .* y","dotMultiply(x, y)"],description:"Multiply two values element wise.",examples:["a = [1, 2, 3; 4, 5, 6]","b = [2, 1, 1; 3, 2, 5]","a .* b"],seealso:["multiply","divide","dotDivide"]},dotPow:{name:"dotPow",category:"Operators",syntax:["x .^ y","dotPow(x, y)"],description:"Calculates the power of x to y element wise.",examples:["a = [1, 2, 3; 4, 5, 6]","a .^ 2"],seealso:["pow"]},exp:{name:"exp",category:"Arithmetic",syntax:["exp(x)"],description:"Calculate the exponent of a value.",examples:["exp(1.3)","e ^ 1.3","log(exp(1.3))","x = 2.4","(exp(i*x) == cos(x) + i*sin(x))   # Euler's formula"],seealso:["expm","expm1","pow","log"]},expm:{name:"expm",category:"Arithmetic",syntax:["exp(x)"],description:"Compute the matrix exponential, expm(A) = e^A. The matrix must be square. Not to be confused with exp(a), which performs element-wise exponentiation.",examples:["expm([[0,2],[0,0]])"],seealso:["exp"]},expm1:{name:"expm1",category:"Arithmetic",syntax:["expm1(x)"],description:"Calculate the value of subtracting 1 from the exponential value.",examples:["expm1(2)","pow(e, 2) - 1","log(expm1(2) + 1)"],seealso:["exp","pow","log"]},fix:{name:"fix",category:"Arithmetic",syntax:["fix(x)"],description:"Round a value towards zero. If x is complex, both real and imaginary part are rounded towards zero.",examples:["fix(3.2)","fix(3.8)","fix(-4.2)","fix(-4.8)"],seealso:["ceil","floor","round"]},floor:{name:"floor",category:"Arithmetic",syntax:["floor(x)"],description:"Round a value towards minus infinity.If x is complex, both real and imaginary part are rounded towards minus infinity.",examples:["floor(3.2)","floor(3.8)","floor(-4.2)"],seealso:["ceil","fix","round"]},gcd:{name:"gcd",category:"Arithmetic",syntax:["gcd(a, b)","gcd(a, b, c, ...)"],description:"Compute the greatest common divisor.",examples:["gcd(8, 12)","gcd(-4, 6)","gcd(25, 15, -10)"],seealso:["lcm","xgcd"]},hypot:{name:"hypot",category:"Arithmetic",syntax:["hypot(a, b, c, ...)","hypot([a, b, c, ...])"],description:"Calculate the hypotenusa of a list with values. ",examples:["hypot(3, 4)","sqrt(3^2 + 4^2)","hypot(-2)","hypot([3, 4, 5])"],seealso:["abs","norm"]},lcm:{name:"lcm",category:"Arithmetic",syntax:["lcm(x, y)"],description:"Compute the least common multiple.",examples:["lcm(4, 6)","lcm(6, 21)","lcm(6, 21, 5)"],seealso:["gcd"]},log:{name:"log",category:"Arithmetic",syntax:["log(x)","log(x, base)"],description:"Compute the logarithm of a value. If no base is provided, the natural logarithm of x is calculated. If base if provided, the logarithm is calculated for the specified base. log(x, base) is defined as log(x) / log(base).",examples:["log(3.5)","a = log(2.4)","exp(a)","10 ^ 4","log(10000, 10)","log(10000) / log(10)","b = log(1024, 2)","2 ^ b"],seealso:["exp","log1p","log2","log10"]},log2:{name:"log2",category:"Arithmetic",syntax:["log2(x)"],description:"Calculate the 2-base of a value. This is the same as calculating `log(x, 2)`.",examples:["log2(0.03125)","log2(16)","log2(16) / log2(2)","pow(2, 4)"],seealso:["exp","log1p","log","log10"]},log1p:{name:"log1p",category:"Arithmetic",syntax:["log1p(x)","log1p(x, base)"],description:"Calculate the logarithm of a `value+1`",examples:["log1p(2.5)","exp(log1p(1.4))","pow(10, 4)","log1p(9999, 10)","log1p(9999) / log(10)"],seealso:["exp","log","log2","log10"]},log10:{name:"log10",category:"Arithmetic",syntax:["log10(x)"],description:"Compute the 10-base logarithm of a value.",examples:["log10(0.00001)","log10(10000)","10 ^ 4","log(10000) / log(10)","log(10000, 10)"],seealso:["exp","log"]},mod:{name:"mod",category:"Operators",syntax:["x % y","x mod y","mod(x, y)"],description:"Calculates the modulus, the remainder of an integer division.",examples:["7 % 3","11 % 2","10 mod 4","isOdd(x) = x % 2","isOdd(2)","isOdd(3)"],seealso:["divide"]},multiply:{name:"multiply",category:"Operators",syntax:["x * y","multiply(x, y)"],description:"multiply two values.",examples:["a = 2.1 * 3.4","a / 3.4","2 * 3 + 4","2 * (3 + 4)","3 * 2.1 km"],seealso:["divide"]},norm:{name:"norm",category:"Arithmetic",syntax:["norm(x)","norm(x, p)"],description:"Calculate the norm of a number, vector or matrix.",examples:["abs(-3.5)","norm(-3.5)","norm(3 - 4i)","norm([1, 2, -3], Infinity)","norm([1, 2, -3], -Infinity)","norm([3, 4], 2)","norm([[1, 2], [3, 4]], 1)",'norm([[1, 2], [3, 4]], "inf")','norm([[1, 2], [3, 4]], "fro")']},nthRoot:{name:"nthRoot",category:"Arithmetic",syntax:["nthRoot(a)","nthRoot(a, root)"],description:'Calculate the nth root of a value. The principal nth root of a positive real number A, is the positive real solution of the equation "x^root = A".',examples:["4 ^ 3","nthRoot(64, 3)","nthRoot(9, 2)","sqrt(9)"],seealso:["nthRoots","pow","sqrt"]},nthRoots:{name:"nthRoots",category:"Arithmetic",syntax:["nthRoots(A)","nthRoots(A, root)"],description:'Calculate the nth roots of a value. An nth root of a positive real number A, is a positive real solution of the equation "x^root = A". This function returns an array of complex values.',examples:["nthRoots(1)","nthRoots(1, 3)"],seealso:["sqrt","pow","nthRoot"]},pow:{name:"pow",category:"Operators",syntax:["x ^ y","pow(x, y)"],description:"Calculates the power of x to y, x^y.",examples:["2^3","2*2*2","1 + e ^ (pi * i)"],seealso:["multiply","nthRoot","nthRoots","sqrt"]},round:{name:"round",category:"Arithmetic",syntax:["round(x)","round(x, n)"],description:"round a value towards the nearest integer.If x is complex, both real and imaginary part are rounded towards the nearest integer. When n is specified, the value is rounded to n decimals.",examples:["round(3.2)","round(3.8)","round(-4.2)","round(-4.8)","round(pi, 3)","round(123.45678, 2)"],seealso:["ceil","floor","fix"]},sign:{name:"sign",category:"Arithmetic",syntax:["sign(x)"],description:"Compute the sign of a value. The sign of a value x is 1 when x>1, -1 when x<0, and 0 when x=0.",examples:["sign(3.5)","sign(-4.2)","sign(0)"],seealso:["abs"]},sqrt:{name:"sqrt",category:"Arithmetic",syntax:["sqrt(x)"],description:"Compute the square root value. If x = y * y, then y is the square root of x.",examples:["sqrt(25)","5 * 5","sqrt(-1)"],seealso:["square","sqrtm","multiply","nthRoot","nthRoots","pow"]},sqrtm:{name:"sqrtm",category:"Arithmetic",syntax:["sqrtm(x)"],description:"Calculate the principal square root of a square matrix. The principal square root matrix `X` of another matrix `A` is such that `X * X = A`.",examples:["sqrtm([[1, 2], [3, 4]])"],seealso:["sqrt","abs","square","multiply"]},square:{name:"square",category:"Arithmetic",syntax:["square(x)"],description:"Compute the square of a value. The square of x is x * x.",examples:["square(3)","sqrt(9)","3^2","3 * 3"],seealso:["multiply","pow","sqrt","cube"]},subtract:{name:"subtract",category:"Operators",syntax:["x - y","subtract(x, y)"],description:"subtract two values.",examples:["a = 5.3 - 2","a + 2","2/3 - 1/6","2 * 3 - 3","2.1 km - 500m"],seealso:["add"]},unaryMinus:{name:"unaryMinus",category:"Operators",syntax:["-x","unaryMinus(x)"],description:"Inverse the sign of a value. Converts booleans and strings to numbers.",examples:["-4.5","-(-5.6)",'-"22"'],seealso:["add","subtract","unaryPlus"]},unaryPlus:{name:"unaryPlus",category:"Operators",syntax:["+x","unaryPlus(x)"],description:"Converts booleans and strings to numbers.",examples:["+true",'+"2"'],seealso:["add","subtract","unaryMinus"]},xgcd:{name:"xgcd",category:"Arithmetic",syntax:["xgcd(a, b)"],description:"Calculate the extended greatest common divisor for two values. The result is an array [d, x, y] with 3 entries, where d is the greatest common divisor, and d = x * a + y * b.",examples:["xgcd(8, 12)","gcd(8, 12)","xgcd(36163, 21199)"],seealso:["gcd","lcm"]},bitAnd:{name:"bitAnd",category:"Bitwise",syntax:["x & y","bitAnd(x, y)"],description:"Bitwise AND operation. Performs the logical AND operation on each pair of the corresponding bits of the two given values by multiplying them. If both bits in the compared position are 1, the bit in the resulting binary representation is 1, otherwise, the result is 0",examples:["5 & 3","bitAnd(53, 131)","[1, 12, 31] & 42"],seealso:["bitNot","bitOr","bitXor","leftShift","rightArithShift","rightLogShift"]},bitNot:{name:"bitNot",category:"Bitwise",syntax:["~x","bitNot(x)"],description:"Bitwise NOT operation. Performs a logical negation on each bit of the given value. Bits that are 0 become 1, and those that are 1 become 0.",examples:["~1","~2","bitNot([2, -3, 4])"],seealso:["bitAnd","bitOr","bitXor","leftShift","rightArithShift","rightLogShift"]},bitOr:{name:"bitOr",category:"Bitwise",syntax:["x | y","bitOr(x, y)"],description:"Bitwise OR operation. Performs the logical inclusive OR operation on each pair of corresponding bits of the two given values. The result in each position is 1 if the first bit is 1 or the second bit is 1 or both bits are 1, otherwise, the result is 0.",examples:["5 | 3","bitOr([1, 2, 3], 4)"],seealso:["bitAnd","bitNot","bitXor","leftShift","rightArithShift","rightLogShift"]},bitXor:{name:"bitXor",category:"Bitwise",syntax:["bitXor(x, y)"],description:"Bitwise XOR operation, exclusive OR. Performs the logical exclusive OR operation on each pair of corresponding bits of the two given values. The result in each position is 1 if only the first bit is 1 or only the second bit is 1, but will be 0 if both are 0 or both are 1.",examples:["bitOr(1, 2)","bitXor([2, 3, 4], 4)"],seealso:["bitAnd","bitNot","bitOr","leftShift","rightArithShift","rightLogShift"]},leftShift:{name:"leftShift",category:"Bitwise",syntax:["x << y","leftShift(x, y)"],description:"Bitwise left logical shift of a value x by y number of bits.",examples:["4 << 1","8 >> 1"],seealso:["bitAnd","bitNot","bitOr","bitXor","rightArithShift","rightLogShift"]},rightArithShift:{name:"rightArithShift",category:"Bitwise",syntax:["x >> y","rightArithShift(x, y)"],description:"Bitwise right arithmetic shift of a value x by y number of bits.",examples:["8 >> 1","4 << 1","-12 >> 2"],seealso:["bitAnd","bitNot","bitOr","bitXor","leftShift","rightLogShift"]},rightLogShift:{name:"rightLogShift",category:"Bitwise",syntax:["x >>> y","rightLogShift(x, y)"],description:"Bitwise right logical shift of a value x by y number of bits.",examples:["8 >>> 1","4 << 1","-12 >>> 2"],seealso:["bitAnd","bitNot","bitOr","bitXor","leftShift","rightArithShift"]},bellNumbers:{name:"bellNumbers",category:"Combinatorics",syntax:["bellNumbers(n)"],description:"The Bell Numbers count the number of partitions of a set. A partition is a pairwise disjoint subset of S whose union is S. `bellNumbers` only takes integer arguments. The following condition must be enforced: n >= 0.",examples:["bellNumbers(3)","bellNumbers(8)"],seealso:["stirlingS2"]},catalan:{name:"catalan",category:"Combinatorics",syntax:["catalan(n)"],description:"The Catalan Numbers enumerate combinatorial structures of many different types. catalan only takes integer arguments. The following condition must be enforced: n >= 0.",examples:["catalan(3)","catalan(8)"],seealso:["bellNumbers"]},composition:{name:"composition",category:"Combinatorics",syntax:["composition(n, k)"],description:"The composition counts of n into k parts. composition only takes integer arguments. The following condition must be enforced: k <= n.",examples:["composition(5, 3)"],seealso:["combinations"]},stirlingS2:{name:"stirlingS2",category:"Combinatorics",syntax:["stirlingS2(n, k)"],description:"he Stirling numbers of the second kind, counts the number of ways to partition a set of n labelled objects into k nonempty unlabelled subsets. `stirlingS2` only takes integer arguments. The following condition must be enforced: k <= n. If n = k or k = 1, then s(n,k) = 1.",examples:["stirlingS2(5, 3)"],seealso:["bellNumbers"]},config:{name:"config",category:"Core",syntax:["config()","config(options)"],description:"Get configuration or change configuration.",examples:["config()","1/3 + 1/4",'config({number: "Fraction"})',"1/3 + 1/4"],seealso:[]},import:{name:"import",category:"Core",syntax:["import(functions)","import(functions, options)"],description:"Import functions or constants from an object.",examples:["import({myFn: f(x)=x^2, myConstant: 32 })","myFn(2)","myConstant"],seealso:[]},typed:{name:"typed",category:"Core",syntax:["typed(signatures)","typed(name, signatures)"],description:"Create a typed function.",examples:['double = typed({ "number, number": f(x)=x+x })',"double(2)",'double("hello")'],seealso:[]},arg:{name:"arg",category:"Complex",syntax:["arg(x)"],description:"Compute the argument of a complex value. If x = a+bi, the argument is computed as atan2(b, a).",examples:["arg(2 + 2i)","atan2(3, 2)","arg(2 + 3i)"],seealso:["re","im","conj","abs"]},conj:{name:"conj",category:"Complex",syntax:["conj(x)"],description:"Compute the complex conjugate of a complex value. If x = a+bi, the complex conjugate is a-bi.",examples:["conj(2 + 3i)","conj(2 - 3i)","conj(-5.2i)"],seealso:["re","im","abs","arg"]},re:{name:"re",category:"Complex",syntax:["re(x)"],description:"Get the real part of a complex number.",examples:["re(2 + 3i)","im(2 + 3i)","re(-5.2i)","re(2.4)"],seealso:["im","conj","abs","arg"]},im:{name:"im",category:"Complex",syntax:["im(x)"],description:"Get the imaginary part of a complex number.",examples:["im(2 + 3i)","re(2 + 3i)","im(-5.2i)","im(2.4)"],seealso:["re","conj","abs","arg"]},evaluate:{name:"evaluate",category:"Expression",syntax:["evaluate(expression)","evaluate([expr1, expr2, expr3, ...])"],description:"Evaluate an expression or an array with expressions.",examples:['evaluate("2 + 3")','evaluate("sqrt(" + 4 + ")")'],seealso:[]},help:{name:"help",category:"Expression",syntax:["help(object)","help(string)"],description:"Display documentation on a function or data type.",examples:["help(sqrt)",'help("complex")'],seealso:[]},distance:{name:"distance",category:"Geometry",syntax:["distance([x1, y1], [x2, y2])","distance([[x1, y1], [x2, y2]])"],description:"Calculates the Euclidean distance between two points.",examples:["distance([0,0], [4,4])","distance([[0,0], [4,4]])"],seealso:[]},intersect:{name:"intersect",category:"Geometry",syntax:["intersect(expr1, expr2, expr3, expr4)","intersect(expr1, expr2, expr3)"],description:"Computes the intersection point of lines and/or planes.",examples:["intersect([0, 0], [10, 10], [10, 0], [0, 10])","intersect([1, 0, 1],  [4, -2, 2], [1, 1, 1, 6])"],seealso:[]},and:{name:"and",category:"Logical",syntax:["x and y","and(x, y)"],description:"Logical and. Test whether two values are both defined with a nonzero/nonempty value.",examples:["true and false","true and true","2 and 4"],seealso:["not","or","xor"]},not:{name:"not",category:"Logical",syntax:["not x","not(x)"],description:"Logical not. Flips the boolean value of given argument.",examples:["not true","not false","not 2","not 0"],seealso:["and","or","xor"]},or:{name:"or",category:"Logical",syntax:["x or y","or(x, y)"],description:"Logical or. Test if at least one value is defined with a nonzero/nonempty value.",examples:["true or false","false or false","0 or 4"],seealso:["not","and","xor"]},xor:{name:"xor",category:"Logical",syntax:["x xor y","xor(x, y)"],description:"Logical exclusive or, xor. Test whether one and only one value is defined with a nonzero/nonempty value.",examples:["true xor false","false xor false","true xor true","0 xor 4"],seealso:["not","and","or"]},concat:{name:"concat",category:"Matrix",syntax:["concat(A, B, C, ...)","concat(A, B, C, ..., dim)"],description:"Concatenate matrices. By default, the matrices are concatenated by the last dimension. The dimension on which to concatenate can be provided as last argument.",examples:["A = [1, 2; 5, 6]","B = [3, 4; 7, 8]","concat(A, B)","concat(A, B, 1)","concat(A, B, 2)"],seealso:["det","diag","identity","inv","ones","range","size","squeeze","subset","trace","transpose","zeros"]},count:{name:"count",category:"Matrix",syntax:["count(x)"],description:"Count the number of elements of a matrix, array or string.",examples:["a = [1, 2; 3, 4; 5, 6]","count(a)","size(a)",'count("hello world")'],seealso:["size"]},cross:{name:"cross",category:"Matrix",syntax:["cross(A, B)"],description:"Calculate the cross product for two vectors in three dimensional space.",examples:["cross([1, 1, 0],  [0, 1, 1])","cross([3, -3, 1], [4, 9, 2])","cross([2, 3, 4],  [5, 6, 7])"],seealso:["multiply","dot"]},column:{name:"column",category:"Matrix",syntax:["column(x, index)"],description:"Return a column from a matrix or array.",examples:["A = [[1, 2], [3, 4]]","column(A, 1)","column(A, 2)"],seealso:["row","matrixFromColumns"]},ctranspose:{name:"ctranspose",category:"Matrix",syntax:["x'","ctranspose(x)"],description:"Complex Conjugate and Transpose a matrix",examples:["a = [1, 2, 3; 4, 5, 6]","a'","ctranspose(a)"],seealso:["concat","det","diag","identity","inv","ones","range","size","squeeze","subset","trace","zeros"]},det:{name:"det",category:"Matrix",syntax:["det(x)"],description:"Calculate the determinant of a matrix",examples:["det([1, 2; 3, 4])","det([-2, 2, 3; -1, 1, 3; 2, 0, -1])"],seealso:["concat","diag","identity","inv","ones","range","size","squeeze","subset","trace","transpose","zeros"]},diag:{name:"diag",category:"Matrix",syntax:["diag(x)","diag(x, k)"],description:"Create a diagonal matrix or retrieve the diagonal of a matrix. When x is a vector, a matrix with the vector values on the diagonal will be returned. When x is a matrix, a vector with the diagonal values of the matrix is returned. When k is provided, the k-th diagonal will be filled in or retrieved, if k is positive, the values are placed on the super diagonal. When k is negative, the values are placed on the sub diagonal.",examples:["diag(1:3)","diag(1:3, 1)","a = [1, 2, 3; 4, 5, 6; 7, 8, 9]","diag(a)"],seealso:["concat","det","identity","inv","ones","range","size","squeeze","subset","trace","transpose","zeros"]},diff:{name:"diff",category:"Matrix",syntax:["diff(arr)","diff(arr, dim)"],description:["Create a new matrix or array with the difference of the passed matrix or array.","Dim parameter is optional and used to indicant the dimension of the array/matrix to apply the difference","If no dimension parameter is passed it is assumed as dimension 0","Dimension is zero-based in javascript and one-based in the parser","Arrays must be 'rectangular' meaning arrays like [1, 2]","If something is passed as a matrix it will be returned as a matrix but other than that all matrices are converted to arrays"],examples:["diff([1, 2, 4, 7, 0])","diff([1, 2, 4, 7, 0], 0)","diff(matrix([1, 2, 4, 7, 0]))","diff([[1, 2], [3, 4]])","diff([[1, 2], [3, 4]], 0)","diff([[1, 2], [3, 4]], 1)","diff([[1, 2], [3, 4]], bignumber(1))","diff(matrix([[1, 2], [3, 4]]), 1)","diff([[1, 2], matrix([3, 4])], 1)"],seealso:["subtract","partitionSelect"]},dot:{name:"dot",category:"Matrix",syntax:["dot(A, B)","A * B"],description:"Calculate the dot product of two vectors. The dot product of A = [a1, a2, a3, ..., an] and B = [b1, b2, b3, ..., bn] is defined as dot(A, B) = a1 * b1 + a2 * b2 + a3 * b3 + ... + an * bn",examples:["dot([2, 4, 1], [2, 2, 3])","[2, 4, 1] * [2, 2, 3]"],seealso:["multiply","cross"]},getMatrixDataType:{name:"getMatrixDataType",category:"Matrix",syntax:["getMatrixDataType(x)"],description:'Find the data type of all elements in a matrix or array, for example "number" if all items are a number and "Complex" if all values are complex numbers. If a matrix contains more than one data type, it will return "mixed".',examples:["getMatrixDataType([1, 2, 3])","getMatrixDataType([[5 cm], [2 inch]])",'getMatrixDataType([1, "text"])',"getMatrixDataType([1, bignumber(4)])"],seealso:["matrix","sparse","typeOf"]},identity:{name:"identity",category:"Matrix",syntax:["identity(n)","identity(m, n)","identity([m, n])"],description:"Returns the identity matrix with size m-by-n. The matrix has ones on the diagonal and zeros elsewhere.",examples:["identity(3)","identity(3, 5)","a = [1, 2, 3; 4, 5, 6]","identity(size(a))"],seealso:["concat","det","diag","inv","ones","range","size","squeeze","subset","trace","transpose","zeros"]},filter:{name:"filter",category:"Matrix",syntax:["filter(x, test)"],description:"Filter items in a matrix.",examples:["isPositive(x) = x > 0","filter([6, -2, -1, 4, 3], isPositive)","filter([6, -2, 0, 1, 0], x != 0)"],seealso:["sort","map","forEach"]},flatten:{name:"flatten",category:"Matrix",syntax:["flatten(x)"],description:"Flatten a multi dimensional matrix into a single dimensional matrix.",examples:["a = [1, 2, 3; 4, 5, 6]","size(a)","b = flatten(a)","size(b)"],seealso:["concat","resize","size","squeeze"]},forEach:{name:"forEach",category:"Matrix",syntax:["forEach(x, callback)"],description:"Iterates over all elements of a matrix/array, and executes the given callback function.",examples:["forEach([1, 2, 3], function(val) { console.log(val) })"],seealso:["map","sort","filter"]},inv:{name:"inv",category:"Matrix",syntax:["inv(x)"],description:"Calculate the inverse of a matrix",examples:["inv([1, 2; 3, 4])","inv(4)","1 / 4"],seealso:["concat","det","diag","identity","ones","range","size","squeeze","subset","trace","transpose","zeros"]},eigs:{name:"eigs",category:"Matrix",syntax:["eigs(x)"],description:"Calculate the eigenvalues and eigenvectors of a real symmetric matrix",examples:["eigs([[5, 2.3], [2.3, 1]])"],seealso:["inv"]},kron:{name:"kron",category:"Matrix",syntax:["kron(x, y)"],description:"Calculates the kronecker product of 2 matrices or vectors.",examples:["kron([[1, 0], [0, 1]], [[1, 2], [3, 4]])","kron([1,1], [2,3,4])"],seealso:["multiply","dot","cross"]},matrixFromFunction:{name:"matrixFromFunction",category:"Matrix",syntax:["math.matrixFromFunction(size, fn)","math.matrixFromFunction(size, fn, format)","math.matrixFromFunction(size, fn, format, datatype)","math.matrixFromFunction(size, format, fn)","math.matrixFromFunction(size, format, datatype, fn)"],description:"Create a matrix by evaluating a generating function at each index.",examples:["f(I) = I[1] - I[2]","matrixFromFunction([3,3], f)","g(I) = I[1] - I[2] == 1 ? 4 : 0",'matrixFromFunction([100, 100], "sparse", g)',"matrixFromFunction([5], random)"],seealso:["matrix","matrixFromRows","matrixFromColumns","zeros"]},matrixFromRows:{name:"matrixFromRows",category:"Matrix",syntax:["math.matrixFromRows(...arr)","math.matrixFromRows(row1, row2)","math.matrixFromRows(row1, row2, row3)"],description:"Create a dense matrix from vectors as individual rows.",examples:["matrixFromRows([1, 2, 3], [[4],[5],[6]])"],seealso:["matrix","matrixFromColumns","matrixFromFunction","zeros"]},matrixFromColumns:{name:"matrixFromColumns",category:"Matrix",syntax:["math.matrixFromColumns(...arr)","math.matrixFromColumns(row1, row2)","math.matrixFromColumns(row1, row2, row3)"],description:"Create a dense matrix from vectors as individual columns.",examples:["matrixFromColumns([1, 2, 3], [[4],[5],[6]])"],seealso:["matrix","matrixFromRows","matrixFromFunction","zeros"]},map:{name:"map",category:"Matrix",syntax:["map(x, callback)"],description:"Create a new matrix or array with the results of the callback function executed on each entry of the matrix/array.",examples:["map([1, 2, 3], square)"],seealso:["filter","forEach"]},ones:{name:"ones",category:"Matrix",syntax:["ones(m)","ones(m, n)","ones(m, n, p, ...)","ones([m])","ones([m, n])","ones([m, n, p, ...])"],description:"Create a matrix containing ones.",examples:["ones(3)","ones(3, 5)","ones([2,3]) * 4.5","a = [1, 2, 3; 4, 5, 6]","ones(size(a))"],seealso:["concat","det","diag","identity","inv","range","size","squeeze","subset","trace","transpose","zeros"]},partitionSelect:{name:"partitionSelect",category:"Matrix",syntax:["partitionSelect(x, k)","partitionSelect(x, k, compare)"],description:"Partition-based selection of an array or 1D matrix. Will find the kth smallest value, and mutates the input array. Uses Quickselect.",examples:["partitionSelect([5, 10, 1], 2)",'partitionSelect(["C", "B", "A", "D"], 1)'],seealso:["sort"]},range:{name:"range",category:"Type",syntax:["start:end","start:step:end","range(start, end)","range(start, end, step)","range(string)"],description:"Create a range. Lower bound of the range is included, upper bound is excluded.",examples:["1:5","3:-1:-3","range(3, 7)","range(0, 12, 2)",'range("4:10")',"a = [1, 2, 3, 4; 5, 6, 7, 8]","a[1:2, 1:2]"],seealso:["concat","det","diag","identity","inv","ones","size","squeeze","subset","trace","transpose","zeros"]},resize:{name:"resize",category:"Matrix",syntax:["resize(x, size)","resize(x, size, defaultValue)"],description:"Resize a matrix.",examples:["resize([1,2,3,4,5], [3])","resize([1,2,3], [5])","resize([1,2,3], [5], -1)","resize(2, [2, 3])",'resize("hello", [8], "!")'],seealso:["size","subset","squeeze","reshape"]},reshape:{name:"reshape",category:"Matrix",syntax:["reshape(x, sizes)"],description:"Reshape a multi dimensional array to fit the specified dimensions.",examples:["reshape([1, 2, 3, 4, 5, 6], [2, 3])","reshape([[1, 2], [3, 4]], [1, 4])","reshape([[1, 2], [3, 4]], [4])"],seealso:["size","squeeze","resize"]},rotate:{name:"rotate",category:"Matrix",syntax:["rotate(w, theta)","rotate(w, theta, v)"],description:"Returns a 2-D rotation matrix (2x2) for a given angle (in radians). Returns a 2-D rotation matrix (3x3) of a given angle (in radians) around given axis.",examples:["rotate([1, 0], math.pi / 2)",'rotate(matrix([1, 0]), unit("35deg"))','rotate([1, 0, 0], unit("90deg"), [0, 0, 1])','rotate(matrix([1, 0, 0]), unit("90deg"), matrix([0, 0, 1]))'],seealso:["matrix","rotationMatrix"]},rotationMatrix:{name:"rotationMatrix",category:"Matrix",syntax:["rotationMatrix(theta)","rotationMatrix(theta, v)","rotationMatrix(theta, v, format)"],description:"Returns a 2-D rotation matrix (2x2) for a given angle (in radians). Returns a 2-D rotation matrix (3x3) of a given angle (in radians) around given axis.",examples:["rotationMatrix(pi / 2)",'rotationMatrix(unit("45deg"), [0, 0, 1])','rotationMatrix(1, matrix([0, 0, 1]), "sparse")'],seealso:["cos","sin"]},row:{name:"row",category:"Matrix",syntax:["row(x, index)"],description:"Return a row from a matrix or array.",examples:["A = [[1, 2], [3, 4]]","row(A, 1)","row(A, 2)"],seealso:["column","matrixFromRows"]},size:{name:"size",category:"Matrix",syntax:["size(x)"],description:"Calculate the size of a matrix.",examples:["size(2.3)",'size("hello world")',"a = [1, 2; 3, 4; 5, 6]","size(a)","size(1:6)"],seealso:["concat","count","det","diag","identity","inv","ones","range","squeeze","subset","trace","transpose","zeros"]},sort:{name:"sort",category:"Matrix",syntax:["sort(x)","sort(x, compare)"],description:'Sort the items in a matrix. Compare can be a string "asc", "desc", "natural", or a custom sort function.',examples:["sort([5, 10, 1])",'sort(["C", "B", "A", "D"])',"sortByLength(a, b) = size(a)[1] - size(b)[1]",'sort(["Langdon", "Tom", "Sara"], sortByLength)','sort(["10", "1", "2"], "natural")'],seealso:["map","filter","forEach"]},squeeze:{name:"squeeze",category:"Matrix",syntax:["squeeze(x)"],description:"Remove inner and outer singleton dimensions from a matrix.",examples:["a = zeros(3,2,1)","size(squeeze(a))","b = zeros(1,1,3)","size(squeeze(b))"],seealso:["concat","det","diag","identity","inv","ones","range","size","subset","trace","transpose","zeros"]},subset:{name:"subset",category:"Matrix",syntax:["value(index)","value(index) = replacement","subset(value, [index])","subset(value, [index], replacement)"],description:"Get or set a subset of a matrix or string. Indexes are one-based. Both the ranges lower-bound and upper-bound are included.",examples:["d = [1, 2; 3, 4]","e = []","e[1, 1:2] = [5, 6]","e[2, :] = [7, 8]","f = d * e","f[2, 1]","f[:, 1]"],seealso:["concat","det","diag","identity","inv","ones","range","size","squeeze","trace","transpose","zeros"]},trace:{name:"trace",category:"Matrix",syntax:["trace(A)"],description:"Calculate the trace of a matrix: the sum of the elements on the main diagonal of a square matrix.",examples:["A = [1, 2, 3; -1, 2, 3; 2, 0, 3]","trace(A)"],seealso:["concat","det","diag","identity","inv","ones","range","size","squeeze","subset","transpose","zeros"]},transpose:{name:"transpose",category:"Matrix",syntax:["x'","transpose(x)"],description:"Transpose a matrix",examples:["a = [1, 2, 3; 4, 5, 6]","a'","transpose(a)"],seealso:["concat","det","diag","identity","inv","ones","range","size","squeeze","subset","trace","zeros"]},zeros:{name:"zeros",category:"Matrix",syntax:["zeros(m)","zeros(m, n)","zeros(m, n, p, ...)","zeros([m])","zeros([m, n])","zeros([m, n, p, ...])"],description:"Create a matrix containing zeros.",examples:["zeros(3)","zeros(3, 5)","a = [1, 2, 3; 4, 5, 6]","zeros(size(a))"],seealso:["concat","det","diag","identity","inv","ones","range","size","squeeze","subset","trace","transpose"]},combinations:{name:"combinations",category:"Probability",syntax:["combinations(n, k)"],description:"Compute the number of combinations of n items taken k at a time",examples:["combinations(7, 5)"],seealso:["combinationsWithRep","permutations","factorial"]},combinationsWithRep:{name:"combinationsWithRep",category:"Probability",syntax:["combinationsWithRep(n, k)"],description:"Compute the number of combinations of n items taken k at a time with replacements.",examples:["combinationsWithRep(7, 5)"],seealso:["combinations","permutations","factorial"]},factorial:{name:"factorial",category:"Probability",syntax:["n!","factorial(n)"],description:"Compute the factorial of a value",examples:["5!","5 * 4 * 3 * 2 * 1","3!"],seealso:["combinations","combinationsWithRep","permutations","gamma"]},gamma:{name:"gamma",category:"Probability",syntax:["gamma(n)"],description:"Compute the gamma function. For small values, the Lanczos approximation is used, and for large values the extended Stirling approximation.",examples:["gamma(4)","3!","gamma(1/2)","sqrt(pi)"],seealso:["factorial"]},kldivergence:{name:"kldivergence",category:"Probability",syntax:["kldivergence(x, y)"],description:"Calculate the Kullback-Leibler (KL) divergence  between two distributions.",examples:["kldivergence([0.7,0.5,0.4], [0.2,0.9,0.5])"],seealso:[]},multinomial:{name:"multinomial",category:"Probability",syntax:["multinomial(A)"],description:"Multinomial Coefficients compute the number of ways of picking a1, a2, ..., ai unordered outcomes from `n` possibilities. multinomial takes one array of integers as an argument. The following condition must be enforced: every ai > 0.",examples:["multinomial([1, 2, 1])"],seealso:["combinations","factorial"]},permutations:{name:"permutations",category:"Probability",syntax:["permutations(n)","permutations(n, k)"],description:"Compute the number of permutations of n items taken k at a time",examples:["permutations(5)","permutations(5, 3)"],seealso:["combinations","combinationsWithRep","factorial"]},pickRandom:{name:"pickRandom",category:"Probability",syntax:["pickRandom(array)","pickRandom(array, number)","pickRandom(array, weights)","pickRandom(array, number, weights)","pickRandom(array, weights, number)"],description:"Pick a random entry from a given array.",examples:["pickRandom(0:10)","pickRandom([1, 3, 1, 6])","pickRandom([1, 3, 1, 6], 2)","pickRandom([1, 3, 1, 6], [2, 3, 2, 1])","pickRandom([1, 3, 1, 6], 2, [2, 3, 2, 1])","pickRandom([1, 3, 1, 6], [2, 3, 2, 1], 2)"],seealso:["random","randomInt"]},random:{name:"random",category:"Probability",syntax:["random()","random(max)","random(min, max)","random(size)","random(size, max)","random(size, min, max)"],description:"Return a random number.",examples:["random()","random(10, 20)","random([2, 3])"],seealso:["pickRandom","randomInt"]},randomInt:{name:"randomInt",category:"Probability",syntax:["randomInt(max)","randomInt(min, max)","randomInt(size)","randomInt(size, max)","randomInt(size, min, max)"],description:"Return a random integer number",examples:["randomInt(10, 20)","randomInt([2, 3], 10)"],seealso:["pickRandom","random"]},compare:{name:"compare",category:"Relational",syntax:["compare(x, y)"],description:"Compare two values. Returns 1 when x > y, -1 when x < y, and 0 when x == y.",examples:["compare(2, 3)","compare(3, 2)","compare(2, 2)","compare(5cm, 40mm)","compare(2, [1, 2, 3])"],seealso:["equal","unequal","smaller","smallerEq","largerEq","compareNatural","compareText"]},compareNatural:{name:"compareNatural",category:"Relational",syntax:["compareNatural(x, y)"],description:"Compare two values of any type in a deterministic, natural way. Returns 1 when x > y, -1 when x < y, and 0 when x == y.",examples:["compareNatural(2, 3)","compareNatural(3, 2)","compareNatural(2, 2)","compareNatural(5cm, 40mm)",'compareNatural("2", "10")',"compareNatural(2 + 3i, 2 + 4i)","compareNatural([1, 2, 4], [1, 2, 3])","compareNatural([1, 5], [1, 2, 3])","compareNatural([1, 2], [1, 2])","compareNatural({a: 2}, {a: 4})"],seealso:["equal","unequal","smaller","smallerEq","largerEq","compare","compareText"]},compareText:{name:"compareText",category:"Relational",syntax:["compareText(x, y)"],description:"Compare two strings lexically. Comparison is case sensitive. Returns 1 when x > y, -1 when x < y, and 0 when x == y.",examples:['compareText("B", "A")','compareText("A", "B")','compareText("A", "A")','compareText("2", "10")','compare("2", "10")',"compare(2, 10)",'compareNatural("2", "10")','compareText("B", ["A", "B", "C"])'],seealso:["compare","compareNatural"]},deepEqual:{name:"deepEqual",category:"Relational",syntax:["deepEqual(x, y)"],description:"Check equality of two matrices element wise. Returns true if the size of both matrices is equal and when and each of the elements are equal.",examples:["deepEqual([1,3,4], [1,3,4])","deepEqual([1,3,4], [1,3])"],seealso:["equal","unequal","smaller","larger","smallerEq","largerEq","compare"]},equal:{name:"equal",category:"Relational",syntax:["x == y","equal(x, y)"],description:"Check equality of two values. Returns true if the values are equal, and false if not.",examples:["2+2 == 3","2+2 == 4","a = 3.2","b = 6-2.8","a == b","50cm == 0.5m"],seealso:["unequal","smaller","larger","smallerEq","largerEq","compare","deepEqual","equalText"]},equalText:{name:"equalText",category:"Relational",syntax:["equalText(x, y)"],description:"Check equality of two strings. Comparison is case sensitive. Returns true if the values are equal, and false if not.",examples:['equalText("Hello", "Hello")','equalText("a", "A")','equal("2e3", "2000")','equalText("2e3", "2000")','equalText("B", ["A", "B", "C"])'],seealso:["compare","compareNatural","compareText","equal"]},larger:{name:"larger",category:"Relational",syntax:["x > y","larger(x, y)"],description:"Check if value x is larger than y. Returns true if x is larger than y, and false if not.",examples:["2 > 3","5 > 2*2","a = 3.3","b = 6-2.8","(a > b)","(b < a)","5 cm > 2 inch"],seealso:["equal","unequal","smaller","smallerEq","largerEq","compare"]},largerEq:{name:"largerEq",category:"Relational",syntax:["x >= y","largerEq(x, y)"],description:"Check if value x is larger or equal to y. Returns true if x is larger or equal to y, and false if not.",examples:["2 >= 1+1","2 > 1+1","a = 3.2","b = 6-2.8","(a >= b)"],seealso:["equal","unequal","smallerEq","smaller","compare"]},smaller:{name:"smaller",category:"Relational",syntax:["x < y","smaller(x, y)"],description:"Check if value x is smaller than value y. Returns true if x is smaller than y, and false if not.",examples:["2 < 3","5 < 2*2","a = 3.3","b = 6-2.8","(a < b)","5 cm < 2 inch"],seealso:["equal","unequal","larger","smallerEq","largerEq","compare"]},smallerEq:{name:"smallerEq",category:"Relational",syntax:["x <= y","smallerEq(x, y)"],description:"Check if value x is smaller or equal to value y. Returns true if x is smaller than y, and false if not.",examples:["2 <= 1+1","2 < 1+1","a = 3.2","b = 6-2.8","(a <= b)"],seealso:["equal","unequal","larger","smaller","largerEq","compare"]},unequal:{name:"unequal",category:"Relational",syntax:["x != y","unequal(x, y)"],description:"Check unequality of two values. Returns true if the values are unequal, and false if they are equal.",examples:["2+2 != 3","2+2 != 4","a = 3.2","b = 6-2.8","a != b","50cm != 0.5m","5 cm != 2 inch"],seealso:["equal","smaller","larger","smallerEq","largerEq","compare","deepEqual"]},setCartesian:{name:"setCartesian",category:"Set",syntax:["setCartesian(set1, set2)"],description:"Create the cartesian product of two (multi)sets. Multi-dimension arrays will be converted to single-dimension arrays before the operation.",examples:["setCartesian([1, 2], [3, 4])"],seealso:["setUnion","setIntersect","setDifference","setPowerset"]},setDifference:{name:"setDifference",category:"Set",syntax:["setDifference(set1, set2)"],description:"Create the difference of two (multi)sets: every element of set1, that is not the element of set2. Multi-dimension arrays will be converted to single-dimension arrays before the operation.",examples:["setDifference([1, 2, 3, 4], [3, 4, 5, 6])","setDifference([[1, 2], [3, 4]], [[3, 4], [5, 6]])"],seealso:["setUnion","setIntersect","setSymDifference"]},setDistinct:{name:"setDistinct",category:"Set",syntax:["setDistinct(set)"],description:"Collect the distinct elements of a multiset. A multi-dimension array will be converted to a single-dimension array before the operation.",examples:["setDistinct([1, 1, 1, 2, 2, 3])"],seealso:["setMultiplicity"]},setIntersect:{name:"setIntersect",category:"Set",syntax:["setIntersect(set1, set2)"],description:"Create the intersection of two (multi)sets. Multi-dimension arrays will be converted to single-dimension arrays before the operation.",examples:["setIntersect([1, 2, 3, 4], [3, 4, 5, 6])","setIntersect([[1, 2], [3, 4]], [[3, 4], [5, 6]])"],seealso:["setUnion","setDifference"]},setIsSubset:{name:"setIsSubset",category:"Set",syntax:["setIsSubset(set1, set2)"],description:"Check whether a (multi)set is a subset of another (multi)set: every element of set1 is the element of set2. Multi-dimension arrays will be converted to single-dimension arrays before the operation.",examples:["setIsSubset([1, 2], [3, 4, 5, 6])","setIsSubset([3, 4], [3, 4, 5, 6])"],seealso:["setUnion","setIntersect","setDifference"]},setMultiplicity:{name:"setMultiplicity",category:"Set",syntax:["setMultiplicity(element, set)"],description:"Count the multiplicity of an element in a multiset. A multi-dimension array will be converted to a single-dimension array before the operation.",examples:["setMultiplicity(1, [1, 2, 2, 4])","setMultiplicity(2, [1, 2, 2, 4])"],seealso:["setDistinct","setSize"]},setPowerset:{name:"setPowerset",category:"Set",syntax:["setPowerset(set)"],description:"Create the powerset of a (multi)set: the powerset contains very possible subsets of a (multi)set. A multi-dimension array will be converted to a single-dimension array before the operation.",examples:["setPowerset([1, 2, 3])"],seealso:["setCartesian"]},setSize:{name:"setSize",category:"Set",syntax:["setSize(set)","setSize(set, unique)"],description:'Count the number of elements of a (multi)set. When the second parameter "unique" is true, count only the unique values. A multi-dimension array will be converted to a single-dimension array before the operation.',examples:["setSize([1, 2, 2, 4])","setSize([1, 2, 2, 4], true)"],seealso:["setUnion","setIntersect","setDifference"]},setSymDifference:{name:"setSymDifference",category:"Set",syntax:["setSymDifference(set1, set2)"],description:"Create the symmetric difference of two (multi)sets. Multi-dimension arrays will be converted to single-dimension arrays before the operation.",examples:["setSymDifference([1, 2, 3, 4], [3, 4, 5, 6])","setSymDifference([[1, 2], [3, 4]], [[3, 4], [5, 6]])"],seealso:["setUnion","setIntersect","setDifference"]},setUnion:{name:"setUnion",category:"Set",syntax:["setUnion(set1, set2)"],description:"Create the union of two (multi)sets. Multi-dimension arrays will be converted to single-dimension arrays before the operation.",examples:["setUnion([1, 2, 3, 4], [3, 4, 5, 6])","setUnion([[1, 2], [3, 4]], [[3, 4], [5, 6]])"],seealso:["setIntersect","setDifference"]},erf:{name:"erf",category:"Special",syntax:["erf(x)"],description:"Compute the erf function of a value using a rational Chebyshev approximations for different intervals of x",examples:["erf(0.2)","erf(-0.5)","erf(4)"],seealso:[]},mad:{name:"mad",category:"Statistics",syntax:["mad(a, b, c, ...)","mad(A)"],description:"Compute the median absolute deviation of a matrix or a list with values. The median absolute deviation is defined as the median of the absolute deviations from the median.",examples:["mad(10, 20, 30)","mad([1, 2, 3])"],seealso:["mean","median","std","abs"]},max:{name:"max",category:"Statistics",syntax:["max(a, b, c, ...)","max(A)","max(A, dim)"],description:"Compute the maximum value of a list of values.",examples:["max(2, 3, 4, 1)","max([2, 3, 4, 1])","max([2, 5; 4, 3])","max([2, 5; 4, 3], 1)","max([2, 5; 4, 3], 2)","max(2.7, 7.1, -4.5, 2.0, 4.1)","min(2.7, 7.1, -4.5, 2.0, 4.1)"],seealso:["mean","median","min","prod","std","sum","variance"]},mean:{name:"mean",category:"Statistics",syntax:["mean(a, b, c, ...)","mean(A)","mean(A, dim)"],description:"Compute the arithmetic mean of a list of values.",examples:["mean(2, 3, 4, 1)","mean([2, 3, 4, 1])","mean([2, 5; 4, 3])","mean([2, 5; 4, 3], 1)","mean([2, 5; 4, 3], 2)","mean([1.0, 2.7, 3.2, 4.0])"],seealso:["max","median","min","prod","std","sum","variance"]},median:{name:"median",category:"Statistics",syntax:["median(a, b, c, ...)","median(A)"],description:"Compute the median of all values. The values are sorted and the middle value is returned. In case of an even number of values, the average of the two middle values is returned.",examples:["median(5, 2, 7)","median([3, -1, 5, 7])"],seealso:["max","mean","min","prod","std","sum","variance","quantileSeq"]},min:{name:"min",category:"Statistics",syntax:["min(a, b, c, ...)","min(A)","min(A, dim)"],description:"Compute the minimum value of a list of values.",examples:["min(2, 3, 4, 1)","min([2, 3, 4, 1])","min([2, 5; 4, 3])","min([2, 5; 4, 3], 1)","min([2, 5; 4, 3], 2)","min(2.7, 7.1, -4.5, 2.0, 4.1)","max(2.7, 7.1, -4.5, 2.0, 4.1)"],seealso:["max","mean","median","prod","std","sum","variance"]},mode:{name:"mode",category:"Statistics",syntax:["mode(a, b, c, ...)","mode(A)","mode(A, a, b, B, c, ...)"],description:"Computes the mode of all values as an array. In case mode being more than one, multiple values are returned in an array.",examples:["mode(2, 1, 4, 3, 1)","mode([1, 2.7, 3.2, 4, 2.7])","mode(1, 4, 6, 1, 6)"],seealso:["max","mean","min","median","prod","std","sum","variance"]},prod:{name:"prod",category:"Statistics",syntax:["prod(a, b, c, ...)","prod(A)"],description:"Compute the product of all values.",examples:["prod(2, 3, 4)","prod([2, 3, 4])","prod([2, 5; 4, 3])"],seealso:["max","mean","min","median","min","std","sum","variance"]},quantileSeq:{name:"quantileSeq",category:"Statistics",syntax:["quantileSeq(A, prob[, sorted])","quantileSeq(A, [prob1, prob2, ...][, sorted])","quantileSeq(A, N[, sorted])"],description:"Compute the prob order quantile of a matrix or a list with values. The sequence is sorted and the middle value is returned. Supported types of sequence values are: Number, BigNumber, Unit Supported types of probablity are: Number, BigNumber. \n\nIn case of a (multi dimensional) array or matrix, the prob order quantile of all elements will be calculated.",examples:["quantileSeq([3, -1, 5, 7], 0.5)","quantileSeq([3, -1, 5, 7], [1/3, 2/3])","quantileSeq([3, -1, 5, 7], 2)","quantileSeq([-1, 3, 5, 7], 0.5, true)"],seealso:["mean","median","min","max","prod","std","sum","variance"]},std:{name:"std",category:"Statistics",syntax:["std(a, b, c, ...)","std(A)","std(A, normalization)"],description:'Compute the standard deviation of all values, defined as std(A) = sqrt(variance(A)). Optional parameter normalization can be "unbiased" (default), "uncorrected", or "biased".',examples:["std(2, 4, 6)","std([2, 4, 6, 8])",'std([2, 4, 6, 8], "uncorrected")','std([2, 4, 6, 8], "biased")',"std([1, 2, 3; 4, 5, 6])"],seealso:["max","mean","min","median","prod","sum","variance"]},sum:{name:"sum",category:"Statistics",syntax:["sum(a, b, c, ...)","sum(A)"],description:"Compute the sum of all values.",examples:["sum(2, 3, 4, 1)","sum([2, 3, 4, 1])","sum([2, 5; 4, 3])"],seealso:["max","mean","median","min","prod","std","sum","variance"]},variance:{name:"variance",category:"Statistics",syntax:["variance(a, b, c, ...)","variance(A)","variance(A, normalization)"],description:'Compute the variance of all values. Optional parameter normalization can be "unbiased" (default), "uncorrected", or "biased".',examples:["variance(2, 4, 6)","variance([2, 4, 6, 8])",'variance([2, 4, 6, 8], "uncorrected")','variance([2, 4, 6, 8], "biased")',"variance([1, 2, 3; 4, 5, 6])"],seealso:["max","mean","min","median","min","prod","std","sum"]},acos:{name:"acos",category:"Trigonometry",syntax:["acos(x)"],description:"Compute the inverse cosine of a value in radians.",examples:["acos(0.5)","acos(cos(2.3))"],seealso:["cos","atan","asin"]},acosh:{name:"acosh",category:"Trigonometry",syntax:["acosh(x)"],description:"Calculate the hyperbolic arccos of a value, defined as `acosh(x) = ln(sqrt(x^2 - 1) + x)`.",examples:["acosh(1.5)"],seealso:["cosh","asinh","atanh"]},acot:{name:"acot",category:"Trigonometry",syntax:["acot(x)"],description:"Calculate the inverse cotangent of a value.",examples:["acot(0.5)","acot(cot(0.5))","acot(2)"],seealso:["cot","atan"]},acoth:{name:"acoth",category:"Trigonometry",syntax:["acoth(x)"],description:"Calculate the hyperbolic arccotangent of a value, defined as `acoth(x) = (ln((x+1)/x) + ln(x/(x-1))) / 2`.",examples:["acoth(2)","acoth(0.5)"],seealso:["acsch","asech"]},acsc:{name:"acsc",category:"Trigonometry",syntax:["acsc(x)"],description:"Calculate the inverse cotangent of a value.",examples:["acsc(2)","acsc(csc(0.5))","acsc(0.5)"],seealso:["csc","asin","asec"]},acsch:{name:"acsch",category:"Trigonometry",syntax:["acsch(x)"],description:"Calculate the hyperbolic arccosecant of a value, defined as `acsch(x) = ln(1/x + sqrt(1/x^2 + 1))`.",examples:["acsch(0.5)"],seealso:["asech","acoth"]},asec:{name:"asec",category:"Trigonometry",syntax:["asec(x)"],description:"Calculate the inverse secant of a value.",examples:["asec(0.5)","asec(sec(0.5))","asec(2)"],seealso:["acos","acot","acsc"]},asech:{name:"asech",category:"Trigonometry",syntax:["asech(x)"],description:"Calculate the inverse secant of a value.",examples:["asech(0.5)"],seealso:["acsch","acoth"]},asin:{name:"asin",category:"Trigonometry",syntax:["asin(x)"],description:"Compute the inverse sine of a value in radians.",examples:["asin(0.5)","asin(sin(0.5))"],seealso:["sin","acos","atan"]},asinh:{name:"asinh",category:"Trigonometry",syntax:["asinh(x)"],description:"Calculate the hyperbolic arcsine of a value, defined as `asinh(x) = ln(x + sqrt(x^2 + 1))`.",examples:["asinh(0.5)"],seealso:["acosh","atanh"]},atan:{name:"atan",category:"Trigonometry",syntax:["atan(x)"],description:"Compute the inverse tangent of a value in radians.",examples:["atan(0.5)","atan(tan(0.5))"],seealso:["tan","acos","asin"]},atanh:{name:"atanh",category:"Trigonometry",syntax:["atanh(x)"],description:"Calculate the hyperbolic arctangent of a value, defined as `atanh(x) = ln((1 + x)/(1 - x)) / 2`.",examples:["atanh(0.5)"],seealso:["acosh","asinh"]},atan2:{name:"atan2",category:"Trigonometry",syntax:["atan2(y, x)"],description:"Computes the principal value of the arc tangent of y/x in radians.",examples:["atan2(2, 2) / pi","angle = 60 deg in rad","x = cos(angle)","y = sin(angle)","atan2(y, x)"],seealso:["sin","cos","tan"]},cos:{name:"cos",category:"Trigonometry",syntax:["cos(x)"],description:"Compute the cosine of x in radians.",examples:["cos(2)","cos(pi / 4) ^ 2","cos(180 deg)","cos(60 deg)","sin(0.2)^2 + cos(0.2)^2"],seealso:["acos","sin","tan"]},cosh:{name:"cosh",category:"Trigonometry",syntax:["cosh(x)"],description:"Compute the hyperbolic cosine of x in radians.",examples:["cosh(0.5)"],seealso:["sinh","tanh","coth"]},cot:{name:"cot",category:"Trigonometry",syntax:["cot(x)"],description:"Compute the cotangent of x in radians. Defined as 1/tan(x)",examples:["cot(2)","1 / tan(2)"],seealso:["sec","csc","tan"]},coth:{name:"coth",category:"Trigonometry",syntax:["coth(x)"],description:"Compute the hyperbolic cotangent of x in radians.",examples:["coth(2)","1 / tanh(2)"],seealso:["sech","csch","tanh"]},csc:{name:"csc",category:"Trigonometry",syntax:["csc(x)"],description:"Compute the cosecant of x in radians. Defined as 1/sin(x)",examples:["csc(2)","1 / sin(2)"],seealso:["sec","cot","sin"]},csch:{name:"csch",category:"Trigonometry",syntax:["csch(x)"],description:"Compute the hyperbolic cosecant of x in radians. Defined as 1/sinh(x)",examples:["csch(2)","1 / sinh(2)"],seealso:["sech","coth","sinh"]},sec:{name:"sec",category:"Trigonometry",syntax:["sec(x)"],description:"Compute the secant of x in radians. Defined as 1/cos(x)",examples:["sec(2)","1 / cos(2)"],seealso:["cot","csc","cos"]},sech:{name:"sech",category:"Trigonometry",syntax:["sech(x)"],description:"Compute the hyperbolic secant of x in radians. 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m=e,h=o,d=l(m,t),y=l(h,s),g=l(c(d[0],y[1]),c(y[0],d[1]));if(p(n(g),r.epsilon))return null;var v=c(y[0],m[1]),x=c(y[1],m[0]),b=c(y[0],h[1]),w=c(y[1],h[0]),N=f(a(l(l(v,x),b),w),g);return i(u(d,N),m)}(e,t,o,s)}if(3===e.length){if(!y(e))throw new TypeError("Array with 3 numbers or BigNumbers expected for first argument");if(!y(t))throw new TypeError("Array with 3 numbers or BigNumbers expected for second argument");if(!y(o))throw new TypeError("Array with 3 numbers or BigNumbers expected for third argument");if(!y(s))throw new TypeError("Array with 3 numbers or BigNumbers expected for fourth argument");return 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t=e.typed,r=e.matrix,n=e.divide,i=e.sum,a=e.multiply,o=e.dotDivide,s=e.log,u=e.isNumeric;return t("kldivergence",{"Array, Array":function(e,t){return c(r(e),r(t))},"Matrix, Array":function(e,t){return c(e,r(t))},"Array, Matrix":function(e,t){return c(r(e),t)},"Matrix, Matrix":function(e,t){return c(e,t)}});function c(e,t){var r=t.size().length,c=e.size().length;if(r>1)throw new Error("first object must be one dimensional");if(c>1)throw new Error("second object must be one dimensional");if(r!==c)throw new Error("Length of two vectors must be equal");if(0===i(e))throw new Error("Sum of elements in first object must be non zero");if(0===i(t))throw new Error("Sum of elements in second object must be non zero");var f=n(e,i(e)),l=n(t,i(t)),p=i(a(f,s(o(f,l))));return u(p)?p:Number.NaN}})),dc=Qe("multinomial",["typed","add","divide","multiply","factorial","isInteger","isPositive"],(function(e){var t=e.typed,r=e.add,n=e.divide,i=e.multiply,a=e.factorial,o=e.isInteger,s=e.isPositive;return t("multinomial",{"Array | Matrix":function(e){var t=0,u=1;return Ht(e,(function(e){if(!o(e)||!s(e))throw new TypeError("Positive integer value expected in function multinomial");t=r(t,e),u=i(u,a(e))})),n(a(t),u)}})})),yc=Qe("permutations",["typed","factorial"],(function(e){return(0,e.typed)("permutations",{"number | BigNumber":e.factorial,"number, number":function(e,t){if(!Z(e)||e<0)throw new TypeError("Positive integer value expected in function permutations");if(!Z(t)||t<0)throw new TypeError("Positive integer value expected in function permutations");if(t>e)throw new TypeError("second argument k must be less than or equal to first argument n");return nc(e-t+1,e)},"BigNumber, BigNumber":function(e,t){var r,n;if(!gc(e)||!gc(t))throw new TypeError("Positive integer value expected in function permutations");if(t.gt(e))throw new TypeError("second argument k must be less than or equal to first argument n");for(r=e.mul(0).add(1),n=e.minus(t).plus(1);n.lte(e);n=n.plus(1))r=r.times(n);return r}})}));function gc(e){return e.isInteger()&&e.gte(0)}var vc=r(15),xc=r.n(vc),bc=xc()(Date.now());function wc(e){var t,r;return t=null===(r=e)?bc:xc()(String(r)),function(){return t()}}var Nc=Qe("pickRandom",["typed","config","?on"],(function(e){var t=e.typed,r=e.config,n=e.on,i=wc(r.randomSeed);return n&&n("config",(function(e,t){e.randomSeed!==t.randomSeed&&(i=wc(e.randomSeed))})),t("pickRandom",{"Array | Matrix":function(e){return a(e,{})},"Array | Matrix, Object":function(e,t){return a(e,t)},"Array | Matrix, number":function(e,t){return a(e,{number:t})},"Array | Matrix, Array | Matrix":function(e,t){return a(e,{weights:t})},"Array | Matrix, Array | Matrix, number":function(e,t,r){return a(e,{number:r,weights:t})},"Array | Matrix, number, Array | Matrix":function(e,t,r){return a(e,{number:t,weights:r})}});function a(e,t){var r=t.number,n=t.weights,a=t.elementWise,s=void 0===a||a,u=void 0===r;u&&(r=1);var 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TypeError("Non-negative integer value expected in function bellNumbers");for(var t=0,o=0;o<=e;o++)t=r(t,a(e,o));return t}})})),_c=Qe("catalan",["typed","addScalar","divideScalar","multiplyScalar","combinations","isNegative","isInteger"],(function(e){var t=e.typed,r=e.addScalar,n=e.divideScalar,i=e.multiplyScalar,a=e.combinations,o=e.isNegative,s=e.isInteger;return t("catalan",{"number | BigNumber":function(e){if(!s(e)||o(e))throw new TypeError("Non-negative integer value expected in function catalan");return n(a(i(e,2),e),r(e,1))}})})),Cc=Qe("composition",["typed","addScalar","combinations","isNegative","isPositive","isInteger","larger"],(function(e){var t=e.typed,r=e.addScalar,n=e.combinations,i=e.isPositive,a=(e.isNegative,e.isInteger),o=e.larger;return t("composition",{"number | BigNumber, number | BigNumber":function(e,t){if(!(a(e)&&i(e)&&a(t)&&i(t)))throw new TypeError("Positive integer value expected in function composition");if(o(t,e))throw new TypeError("k must be less than or equal to n in function composition");return n(r(e,-1),r(t,-1))}})})),Tc=Qe("simplifyUtil",["FunctionNode","OperatorNode","SymbolNode"],(function(e){var t=e.FunctionNode,r=e.OperatorNode,n=e.SymbolNode,i={add:!0,multiply:!0},a={add:!0,multiply:!0};function o(e,t){if(!j(e))return!1;var r=e.fn.toString();return t&&Ye(t,r)&&Ye(t[r],"associative")?t[r].associative:a[r]||!1}function s(e){var t,r=[];return o(e)?(t=e.op,function e(n){for(var i=0;i<n.args.length;i++){var a=n.args[i];j(a)&&t===a.op?e(a):r.push(a)}}(e),r):e.args}function u(e){return j(e)?function(t){try{return new r(e.op,e.fn,t,e.implicit)}catch(e){return console.error(e),[]}}:function(r){return new t(new n(e.name),r)}}return{createMakeNodeFunction:u,isCommutative:function(e,t){if(!j(e))return!0;var r=e.fn.toString();return t&&Ye(t,r)&&Ye(t[r],"commutative")?t[r].commutative:i[r]||!1},isAssociative:o,flatten:function e(t){if(!t.args||0===t.args.length)return t;t.args=s(t);for(var 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t=e.typed,r=e.config,n=e.mathWithTransform,i=e.fraction,a=e.bignumber,o=e.ConstantNode,s=e.OperatorNode,u=e.FunctionNode,f=e.SymbolNode,l=Tc({FunctionNode:u,OperatorNode:s,SymbolNode:f}),p=l.isCommutative,m=l.isAssociative,h=l.allChildren,d=l.createMakeNodeFunction;function y(e,t,r){try{return x(n[e].apply(null,t),r)}catch(i){return t=t.map((function(e){return c(e)?e.valueOf():e})),x(n[e].apply(null,t),r)}}var g=t({Fraction:function(e){var t,r=e.s*e.n;t=r<0?new s("-","unaryMinus",[new o(-r)]):new o(r);if(1===e.d)return t;return new s("/","divide",[t,new o(e.d)])},number:function(e){return e<0?b(new o(-e)):new o(e)},BigNumber:function(e){return e<0?b(new o(-e)):new o(e)},Complex:function(e){throw new Error("Cannot convert Complex number to Node")}});function v(e,t){if(t&&!1!==t.exactFractions&&isFinite(e)&&i){var r=i(e),n=t&&"number"==typeof t.fractionsLimit?t.fractionsLimit:1/0;if(r.valueOf()===e&&r.n<n&&r.d<n)return r}return e}var x=t({"string, 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t=e.config,r=e.typed,n=e.parse,i=e.add,o=e.subtract,s=e.multiply,u=e.divide,c=e.pow,f=e.isZero,l=e.equal,p=e.fraction,m=e.bignumber,h=e.mathWithTransform,d=e.ConstantNode,y=e.FunctionNode,g=e.OperatorNode,v=e.ParenthesisNode,x=e.SymbolNode,b=qc({typed:r,config:t,mathWithTransform:h,fraction:p,bignumber:m,ConstantNode:d,OperatorNode:g,FunctionNode:y,SymbolNode:x}),w=zc({equal:l,isZero:f,add:i,subtract:o,multiply:s,divide:u,pow:c,ConstantNode:d,OperatorNode:g,FunctionNode:y,ParenthesisNode:v}),N=kc({parse:n,FunctionNode:y,OperatorNode:g,ParenthesisNode:v}),M=Tc({FunctionNode:y,OperatorNode:g,SymbolNode:x}),E=M.isCommutative,S=M.isAssociative,A=M.flatten,O=M.unflattenr,_=M.unflattenl,C=M.createMakeNodeFunction,T=r("simplify",{string:function(e){return this(n(e),this.rules,dt(),{})},"string, Map | Object":function(e,t){return this(n(e),this.rules,t,{})},"string, Map | Object, Object":function(e,t,r){return this(n(e),this.rules,t,r)},"string, Array":function(e,t){return this(n(e),t,dt(),{})},"string, Array, Map | Object":function(e,t,r){return this(n(e),t,r,{})},"string, Array, Map | Object, Object":function(e,t,r,i){return this(n(e),t,r,i)},"Node, Map | Object":function(e,t){return this(e,this.rules,t,{})},"Node, Map | Object, Object":function(e,t,r){return this(e,this.rules,t,r)},Node:function(e){return this(e,this.rules,dt(),{})},"Node, Array":function(e,t){return this(e,t,dt(),{})},"Node, Array, Map | Object":function(e,t,r){return this(e,t,r,{})},"Node, Array, Object, Object":function(e,t,r,n){return this(e,t,yt(r),n)},"Node, Array, Map, Object":function(e,t,r,i){t=function(e){for(var t=[],r=0;r<e.length;r++){var i=e[r],o=void 0,s=a()(i);switch(s){case"string":var u=i.split("->");if(2!==u.length)throw SyntaxError("Could not parse rule: "+i);i={l:u[0],r:u[1]};case"object":if(o={l:z(n(i.l)),r:z(n(i.r))},i.context&&(o.evaluate=i.context),i.evaluate&&(o.evaluate=n(i.evaluate)),S(o.l)){var c=C(o.l),f=new 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//# sourceMappingURL=math.js.map
]]>
  </script>
  <script
     id="options_continuous.js"
     type="text/javascript">
<![CDATA[
/*******************************************************************************
options_continuous.js
*******************************************************************************/

// Options for continuous motion of seconds or minutes (USER CHOICE)
var ContinuousSecondHand = true;
var ContinuousMinuteHand = false;
var EnableDynamicSimulation = true; // For a cool dynamic effect: true

// Dynamic of the second hand (physical parameters)
var M_sec = 0.1; // Mass [kg]
var c_sec = 0.3; // Viscous coefficient [N*s/m]
var k_sec = 8; // Stiffness [N/m]

// Dynamic of the minute hand (physical parameters)
var M_min = 0.2; // Mass [kg]
var c_min = 2; // Viscous coefficient [N*s/m]
var k_min = 50; // Stiffness [N/m]

// Dynamic of the hour hand (physical parameters)
var M_hour = 0.3; // Mass [kg]
var c_hour = 3; // Viscous coefficient [N*s/m]
var k_hour = 100; // Stiffness [N/m]

// Perturbation amplitude
var impulse_low = 12.5; // [kg*m/s] Small perturbation impulse (sampling time independent)
var impulse_high = 37.5; // [kg*m/s] Large perturbation impulse (sampling time independent)
]]>
  </script>
  <script
     id="engine_script.js"
     type="text/javascript">
<![CDATA[
/*******************************************************************************
engine_script.js
********************************************************************************

>>> Dynamical Simulation of the clock hands

Click on the hands to perturb them. Ctrl+click changes the direction of the
perturbation. Shift+click increases the perturbation impulse amplitude. Ctrl
and Shift can be combined.

********************************************************************************

This script uses Math.js (developed with version 6.2.3): <http://mathjs.org/>

All angles are assumed to be in degree. The physical units of the simulation
are linear units. Identify degrees with meters to retrieve consistency. That's
enough care for 'display-only' simulation purpose.

Use the share-object behavior of JavaScript to avoid using global variables.

********************************************************************************

Main data structure:

  > sim
  |---> display
  |---> options
  |---> time
  |---> dyna
      |---> sec
      |---> min
      |---> hour

********************************************************************************
V1.2 - 02.10.2019 - Fabien Fellay
********************************************************************************

This script is licensed under the GNU General Public License version 3.

<https://opensource.org/licenses/GPL-3.0>

Copyright (C) 2017-2019 by Fabien Fellay

This program is free software: you can redistribute it and/or modify it under
the terms of the GNU General Public License as published by the Free Software
Foundation, either version 3 of the License, or (at your option) any later
version.

This program is distributed in the hope that it will be useful, but WITHOUT ANY
WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A
PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with
this program. If not, see <http://www.gnu.org/licenses/>.

*******************************************************************************/

// This enables a stricter mode of parsing JavaScript (preventing accidental globals, for example)
'use strict';

// Message in log
console.log('This script uses math.js (version ' + math.version + '): <http://mathjs.org/>');
console.log('Click on the hands to perturb them.\n' +
    'Ctrl+click changes the direction of the perturbation.\n' +
    'Shift+click increases the perturbation impulse amplitude.\n' +
    'Ctrl and Shift can be combined.');

// On load automatic start of the animation
window.onload = Start;

// Main function called on SVG loading: launch the permanent animation..........
function Start(load_event) { // The load_event can be used in case of need

    // Simulation object (containing all data)
    var sim = {
        display:new Object(),
        options:new Object(),
        time:new Object(),
        dyna:new Object()
    };

    // Display: get the hands object from the svg (can be done only after load)
    sim.display.second_hand = document.getElementById('RotSecond');
    sim.display.minute_hand = document.getElementById('RotMinute');
    sim.display.hour_hand = document.getElementById('RotHour');

    // Display: get the hands shade object from the svg (can be done only after load)
    sim.display.second_hand_shade = document.getElementById('ShadeSecond');
    sim.display.minute_hand_shade = document.getElementById('ShadeMinute');
    sim.display.hour_hand_shade = document.getElementById('ShadeHour');

    // Display: make the clicks pass through the hands shade
    sim.display.second_hand_shade.setAttribute('pointer-events','none');
    sim.display.minute_hand_shade.setAttribute('pointer-events','none');
    sim.display.hour_hand_shade.setAttribute('pointer-events','none');

    // Options: for continuous motion of seconds or minutes
    sim.options.continuous_second_hand = ContinuousSecondHand;
    sim.options.continuous_minute_hand = ContinuousMinuteHand;
    sim.options.enable_dynamic_simulation = EnableDynamicSimulation;
    var np = 2.0; // [s] Duration of the pause of the second hand (if continuous), typical: 2 sec

    // Options: the overspeed ratio and pause of the second hand
    if (sim.options.continuous_second_hand !== true) np = 0.0;
    sim.options.overspeed_fraction = 60/(60-np); // Typical: 60/58 for 2 seconds pause

    // Time: variables for continuous time
    sim.time.sfrac = 0.0;
    sim.time.mfrac = 0.0;
    sim.time.hfrac = 1/60;
    sim.time.sec_hand_speed = 0.0;
    sim.time.min_hand_speed = 0.0;
    sim.time.hour_hand_speed = 0.0;

    // Time: hand speeds for initialization
    if (sim.options.continuous_second_hand === true){
        sim.time.sfrac = 1/1000;
        sim.time.sec_hand_speed = 6.0*sim.options.overspeed_fraction; // Normal speed: 360 deg per 60 sec -> 6 deg per sec
        if (sim.options.continuous_minute_hand === true){
            sim.time.min_hand_speed = 0.1; // Normal speed: 360 deg per 3600 sec -> 0.1 deg per sec
            sim.time.hour_hand_speed = 1/120; // Normal speed: 720 deg per 86400 sec -> 1/120 deg per sec
        }
    }
    if (sim.options.continuous_minute_hand === true) sim.time.mfrac = 1/60;

    // The sampling time in seconds (20ms or 50.0Hz), common to the computation and the display
    var T = 20e-3; // Sampling time [s] (try 25ms or 40.0Hz in case of poor performance)

    // State-space model generation (containing all the dynamic data)
    sim.dyna.sec = new SSM(M_sec,c_sec,k_sec,T,'second hand',sim.options);
    sim.dyna.min = new SSM(M_min,c_min,k_min,T,'minute hand',sim.options);
    sim.dyna.hour = new SSM(M_hour,c_hour,k_hour,T,'hour hand',sim.options);

    // Options: perturbations
    sim.options.pertubation_low = impulse_low/T; // [N] Small perturbation force value (during time T)
    sim.options.pertubation_high = impulse_high/T; // [N] Large perturbation force value (during time T)

    // Prepare the perturbation events
    sim.display.cover = document.getElementById('cover');
    sim.display.cover.setAttribute('pointer-events','none'); // The clicks will pass through the cover (important)
    sim.display.second_hand.onmousedown = function(click_event) {Perturbation(click_event,sim.dyna.sec,sim.options)};
    sim.display.minute_hand.onmousedown = function(click_event) {Perturbation(click_event,sim.dyna.min,sim.options)};
    sim.display.hour_hand.onmousedown = function(click_event) {Perturbation(click_event,sim.dyna.hour,sim.options)};

    // Initialization of the dynamic states
    InitializeAllDynamics(sim);

    // Repeat every fixed fraction of a second (no recursive function and call-stack overflow this way)
    var sim_timer = setInterval(SimStep,T*1e3,sim); // in ms (simulation timer)
}

// State-Space Model (SSM) Constructor..........................................
function SSM(M,c,k,T,name,Options) {

    // Input-Output-State
    this.ref_angle = 0; // Input
    this.ref_angle_p = 0; // Previous input
    this.pert_force = 0; // Perturbation input
    this.real_angle = 0; // Output

    this.X = math.zeros(2, 1); // Current state
    this.Z = math.zeros(2, 1); // Current warped state

    // Store the physical parameters
    this.M = M; // Mass [kg]
    this.c = c; // Viscous coefficient [N*s/m]
    this.k = k; // Stiffness [N/m]
    this.T = T; // Sampling time [s]
    this.name = name; // Name of the model

    // Classical dynamical variables
    var omega0_2 = k/M; // [1/s^2]
    var omega0 = Math.sqrt(omega0_2); // [1/s]

    this.lambda = c/(2*M); // [1/s]
    this.f = omega0/(2*math.PI); // [Hz] Free mode frequency without damping

    // Display basic information about dynamic
    if (Options.enable_dynamic_simulation == true) {
        var precision = 6;
        console.log('Eigen frequency of the ' + name + ': ' + math.format(this.f,precision) + ' [Hz]');
    }

    // Continuous state-space model
    this.A = math.matrix([[0,1],
        [-omega0_2,-2*this.lambda]]);
    this.B = math.matrix([[2*this.lambda,0],
        [omega0_2 - 4*math.pow(this.lambda,2),1/M]]);
    this.C = math.matrix([[1,0]]);
    this.D = math.matrix([[0,0]]);

    // Discrete state-space model by Tustin bilinear discretization
    var identity_matrix = math.identity(math.size(this.A));
    this.Trans_Mat = math.add(identity_matrix,math.multiply(this.A,-T/2));
    var Trans_Mat_Inv = math.inv(this.Trans_Mat);

    this.Ad = math.multiply(Trans_Mat_Inv,math.add(identity_matrix,math.multiply(this.A,T/2)));
    this.Bd = math.multiply(Trans_Mat_Inv,math.multiply(this.B,T) );
    this.Cd = math.multiply(this.C,Trans_Mat_Inv );
    this.Dd = math.add(math.multiply(this.Cd,math.multiply(this.B,T/2)),this.D);
    if (Options.enable_dynamic_simulation !== true) {
        // This will make output = input
        this.Cd = math.matrix([[0,0]]);
        this.Dd = math.matrix([[1,0]]);
    }

    // Input-state modulo correction
    this.Mod_Corr_Mat = math.matrix([[1],
        [-2*this.lambda]]); // Correction matrix
}

// To get the current time and thus the current hands reference angle...........
function GetTimeNAngle(sim) {

    // Get computer clock time
    var date = new Date();
    var ms = date.getMilliseconds();
    var s = date.getSeconds();
    var m = date.getMinutes();
    var h = date.getHours();

    // Process the time
    var scont = s + ms*sim.time.sfrac; // Seconds (continuous or discrete according to choice)
    var mcont = m + scont*sim.time.mfrac; // Minutes (continuous or discrete according to choice)
    var hcont = h + mcont*sim.time.hfrac; // Continuous hours (at min, sec or millisec increments based on previous choice)

    // Computation of the second reference angle (360 deg per 60 sec -> 6 deg per sec)
    sim.dyna.sec.ref_angle = Math.min(6.0*scont*sim.options.overspeed_fraction,360.0);

    // Computation of the minute reference angle (360 deg per 60 min -> 6 deg per min)
    sim.dyna.min.ref_angle = 6.0*mcont;

    // Computation of the hour reference angle (720 deg per 24 h -> 30 deg per h)
    sim.dyna.hour.ref_angle = 30.0*hcont;
}

// Initialization of one SSM model..............................................
function InitializeSSM(SSM,hand_speed) {

    // Initialize angle
    SSM.X.subset(math.index(0, 0),SSM.ref_angle);

    // This case is only relevant for the continuous second hand
    if ((SSM.name == 'second hand') && (SSM.ref_angle == 360.0)) {
        hand_speed = 0.0;
    }

    // Initialize angular velocity minus 2*lambda*angle (in motion case)
    SSM.X.subset(math.index(1, 0),hand_speed - 2*SSM.lambda*SSM.ref_angle);

    // Warped Z state initialization
    SSM.Z = math.add(math.multiply(SSM.Trans_Mat,SSM.X),
        math.multiply(math.multiply(SSM.B,-SSM.T/2),math.matrix([[SSM.ref_angle],[SSM.pert_force]])));

    // Previous input initialization
    SSM.ref_angle_p = SSM.ref_angle;
}

// Initialization of all models.................................................
function InitializeAllDynamics(sim) {

    // Get the reference angles
    GetTimeNAngle(sim); // Directly set in all SSM object

    // Initialize dynamics of second hand
    InitializeSSM(sim.dyna.sec,sim.time.sec_hand_speed);

    // Initialize dynamics of minute hand
    InitializeSSM(sim.dyna.min,sim.time.min_hand_speed);

    // Initialize dynamics of hour hand
    InitializeSSM(sim.dyna.hour,sim.time.hour_hand_speed);
}

// The step of one SSM model....................................................
function SSMStep(SSM) {

    // Deal with the reference angle modulo (not so trivial at first)
    var ref_angle_delta = SSM.ref_angle - SSM.ref_angle_p; // Difference of input

    if (math.abs(ref_angle_delta) > 180) {
        // Update state: jump to input, at 360 deg resolution
        SSM.Z = math.add(SSM.Z,math.multiply(SSM.Mod_Corr_Mat,
            math.round(ref_angle_delta/360)*360));
    }
    SSM.ref_angle_p = SSM.ref_angle; // Previous input update

    // Computation of the real angle (using state-space model)
    SSM.real_angle = math.subset(math.add(math.multiply(SSM.Cd,SSM.Z),
        math.multiply(SSM.Dd,math.matrix([[SSM.ref_angle],[SSM.pert_force]]))),
        math.index(0,0)); // Output (alternatively: use math.squeeze)
    SSM.Z = math.add(math.multiply(SSM.Ad,SSM.Z),
        math.multiply(SSM.Bd,math.matrix([[SSM.ref_angle],[SSM.pert_force]]))); // State update

    // Reset perturbation impulse
    SSM.pert_force = 0;
}

// The step of the animation....................................................
function SimStep(sim) {

    // Get the reference angles
    GetTimeNAngle(sim); // Directly set in all SSM object

    // Update of the second real angle and states
    SSMStep(sim.dyna.sec);

    // Update of the minute real angle and states
    SSMStep(sim.dyna.min);

    // Update of the hour real angle and states
    SSMStep(sim.dyna.hour);

    // Display of the second hand
    sim.display.second_hand.setAttribute('transform','rotate(' + sim.dyna.sec.real_angle.toString() + ')');
    sim.display.second_hand_shade.setAttribute('transform','rotate(' + sim.dyna.sec.real_angle.toString() + ')');

    // Display of the minute hand
    sim.display.minute_hand.setAttribute('transform','rotate(' + sim.dyna.min.real_angle.toString() + ')');
    sim.display.minute_hand_shade.setAttribute('transform','rotate(' + sim.dyna.min.real_angle.toString() + ')');

    // Display of the hour hand
    sim.display.hour_hand.setAttribute('transform','rotate(' + sim.dyna.hour.real_angle.toString() + ')');
    sim.display.hour_hand_shade.setAttribute('transform','rotate(' + sim.dyna.hour.real_angle.toString() + ')');
}

// The perturbation function....................................................
function Perturbation(click_event,SSM,Options) {

    var perturbation_value = Options.pertubation_low;
    if (click_event.shiftKey) {
        perturbation_value = Options.pertubation_high;
    }

    if ((click_event.ctrlKey) || (click_event.metaKey)) {
        SSM.pert_force -= perturbation_value;
    } else {
        SSM.pert_force += perturbation_value;
    }
}

// Debug function to output a value in the console..............................
function print(value) {
    // This function name overrides the regular print function, which opens the physical printer dialog.
    var precision = 14;
    console.log(math.format(value, precision));
}
]]>
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        <dc:title>Yet Another SVG+JavaScript Clock</dc:title>
        <dc:description>This interactive document is a SVG live clock inspired (though different) by the Swiss Railway (SBB CFF FFS) iconic station clock by Hans Hilfiker. See &lt;https://www.sbb.ch/&gt;.

The document also features vectorized portions of the free and open source font 'Fira Sans' (light weight used). See &lt;https://bboxtype.com/typefaces/FiraSans/&gt;.

The hand colors are chosen according the the RGB canonical color scheme. It is a mnemonic: Red for seconds, Green for minutes and Blue for hours.

V1.1 (06.10.2017): Design Update (the initial version was identical to the SBB CFF FFS clock, leading to potential copyright issues)
V1.2 (02.10.2019): Small Design Tweak (centering of the 'SWISS MADE' seal). Typos corrected in the engine script and adaptation to the latest math.js version

Created By Fabien Fellay, 2017-2019</dc:description>
        <dc:date>02.10.2019</dc:date>
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