ml-matrix/matrix.umd.js

Matrix manipulation and computation library

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r=t.toString();if(r.length<=e)return r;let s=t.toFixed(e);if(s.length>e&&(s=t.toFixed(Math.max(0,e-(s.length-e)))),s.length<=e&&!s.startsWith("0.000")&&!s.startsWith("-0.000"))return s;let o=t.toExponential(e);return o.length>e&&(o=t.toExponential(Math.max(0,e-(o.length-e)))),o.slice(0)}function l(t,e,r){let s=r?t.rows:t.rows-1;if(e<0||e>s)throw new RangeError("Row index out of range")}function a(t,e,r){let s=r?t.columns:t.columns-1;if(e<0||e>s)throw new RangeError("Column index out of range")}function f(t,e){if(e.to1DArray&&(e=e.to1DArray()),e.length!==t.columns)throw new RangeError("vector size must be the same as the number of columns");return e}function c(t,e){if(e.to1DArray&&(e=e.to1DArray()),e.length!==t.rows)throw new RangeError("vector size must be the same as the number of rows");return e}function m(t,e){if(!r(e))throw new TypeError("row indices must be an array");for(let r=0;r<e.length;r++)if(e[r]<0||e[r]>=t.rows)throw new RangeError("row indices are out of range")}function g(t,e){if(!r(e))throw new TypeError("column indices must be an array");for(let r=0;r<e.length;r++)if(e[r]<0||e[r]>=t.columns)throw new RangeError("column indices are out of range")}function w(t,e,r,s,o){if(5!==arguments.length)throw new RangeError("expected 4 arguments");if(d("startRow",e),d("endRow",r),d("startColumn",s),d("endColumn",o),e>r||s>o||e<0||e>=t.rows||r<0||r>=t.rows||s<0||s>=t.columns||o<0||o>=t.columns)throw new RangeError("Submatrix indices are out of range")}function p(t,e=0){let r=[];for(let s=0;s<t;s++)r.push(e);return r}function d(t,e){if("number"!=typeof e)throw new TypeError(`${t} must be a number`)}function y(t){if(t.isEmpty())throw new Error("Empty matrix has no elements to index")}class M{static from1DArray(t,e,r){if(t*e!==r.length)throw new RangeError("data length does not match given dimensions");let s=new x(t,e);for(let o=0;o<t;o++)for(let t=0;t<e;t++)s.set(o,t,r[o*e+t]);return s}static rowVector(t){let e=new x(1,t.length);for(let r=0;r<t.length;r++)e.set(0,r,t[r]);return e}static columnVector(t){let e=new x(t.length,1);for(let r=0;r<t.length;r++)e.set(r,0,t[r]);return e}static zeros(t,e){return new x(t,e)}static ones(t,e){return new x(t,e).fill(1)}static rand(t,e,r={}){if("object"!=typeof r)throw new TypeError("options must be an object");const{random:s=Math.random}=r;let o=new x(t,e);for(let r=0;r<t;r++)for(let t=0;t<e;t++)o.set(r,t,s());return o}static randInt(t,e,r={}){if("object"!=typeof r)throw new TypeError("options must be an object");const{min:s=0,max:o=1e3,random:i=Math.random}=r;if(!Number.isInteger(s))throw new TypeError("min must be an integer");if(!Number.isInteger(o))throw new TypeError("max must be an integer");if(s>=o)throw new RangeError("min must be smaller than max");let n=o-s,h=new x(t,e);for(let r=0;r<t;r++)for(let t=0;t<e;t++){let e=s+Math.round(i()*n);h.set(r,t,e)}return h}static eye(t,e,r){void 0===e&&(e=t),void 0===r&&(r=1);let s=Math.min(t,e),o=this.zeros(t,e);for(let 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unimplemented")}repeat(t={}){if("object"!=typeof t)throw new TypeError("options must be an object");const{rows:e=1,columns:r=1}=t;if(!Number.isInteger(e)||e<=0)throw new TypeError("rows must be a positive integer");if(!Number.isInteger(r)||r<=0)throw new TypeError("columns must be a positive integer");let s=new x(this.rows*e,this.columns*r);for(let t=0;t<e;t++)for(let e=0;e<r;e++)s.setSubMatrix(this,this.rows*t,this.columns*e);return s}fill(t){for(let e=0;e<this.rows;e++)for(let r=0;r<this.columns;r++)this.set(e,r,t);return this}neg(){return this.mulS(-1)}getRow(t){l(this,t);let e=[];for(let r=0;r<this.columns;r++)e.push(this.get(t,r));return e}getRowVector(t){return x.rowVector(this.getRow(t))}setRow(t,e){l(this,t),e=f(this,e);for(let r=0;r<this.columns;r++)this.set(t,r,e[r]);return this}swapRows(t,e){l(this,t),l(this,e);for(let r=0;r<this.columns;r++){let s=this.get(t,r);this.set(t,r,this.get(e,r)),this.set(e,r,s)}return this}getColumn(t){a(this,t);let e=[];for(let 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r=0;r<this.columns;r++)this.set(e,r,this.get(e,r)+t[e]);return this}subColumnVector(t){t=c(this,t);for(let e=0;e<this.rows;e++)for(let r=0;r<this.columns;r++)this.set(e,r,this.get(e,r)-t[e]);return this}mulColumnVector(t){t=c(this,t);for(let e=0;e<this.rows;e++)for(let r=0;r<this.columns;r++)this.set(e,r,this.get(e,r)*t[e]);return this}divColumnVector(t){t=c(this,t);for(let e=0;e<this.rows;e++)for(let r=0;r<this.columns;r++)this.set(e,r,this.get(e,r)/t[e]);return this}mulRow(t,e){l(this,t);for(let r=0;r<this.columns;r++)this.set(t,r,this.get(t,r)*e);return this}mulColumn(t,e){a(this,t);for(let r=0;r<this.rows;r++)this.set(r,t,this.get(r,t)*e);return this}max(t){if(this.isEmpty())return NaN;switch(t){case"row":{const t=new Array(this.rows).fill(Number.NEGATIVE_INFINITY);for(let e=0;e<this.rows;e++)for(let r=0;r<this.columns;r++)this.get(e,r)>t[e]&&(t[e]=this.get(e,r));return t}case"column":{const t=new Array(this.columns).fill(Number.NEGATIVE_INFINITY);for(let e=0;e<this.rows;e++)for(let r=0;r<this.columns;r++)this.get(e,r)>t[r]&&(t[r]=this.get(e,r));return t}case void 0:{let t=this.get(0,0);for(let e=0;e<this.rows;e++)for(let r=0;r<this.columns;r++)this.get(e,r)>t&&(t=this.get(e,r));return t}default:throw new Error(`invalid option: ${t}`)}}maxIndex(){y(this);let t=this.get(0,0),e=[0,0];for(let r=0;r<this.rows;r++)for(let s=0;s<this.columns;s++)this.get(r,s)>t&&(t=this.get(r,s),e[0]=r,e[1]=s);return e}min(t){if(this.isEmpty())return NaN;switch(t){case"row":{const t=new Array(this.rows).fill(Number.POSITIVE_INFINITY);for(let e=0;e<this.rows;e++)for(let r=0;r<this.columns;r++)this.get(e,r)<t[e]&&(t[e]=this.get(e,r));return t}case"column":{const t=new Array(this.columns).fill(Number.POSITIVE_INFINITY);for(let e=0;e<this.rows;e++)for(let r=0;r<this.columns;r++)this.get(e,r)<t[r]&&(t[r]=this.get(e,r));return t}case void 0:{let t=this.get(0,0);for(let e=0;e<this.rows;e++)for(let r=0;r<this.columns;r++)this.get(e,r)<t&&(t=this.get(e,r));return t}default:throw new Error(`invalid option: ${t}`)}}minIndex(){y(this);let t=this.get(0,0),e=[0,0];for(let r=0;r<this.rows;r++)for(let s=0;s<this.columns;s++)this.get(r,s)<t&&(t=this.get(r,s),e[0]=r,e[1]=s);return e}maxRow(t){if(l(this,t),this.isEmpty())return NaN;let e=this.get(t,0);for(let r=1;r<this.columns;r++)this.get(t,r)>e&&(e=this.get(t,r));return e}maxRowIndex(t){l(this,t),y(this);let e=this.get(t,0),r=[t,0];for(let s=1;s<this.columns;s++)this.get(t,s)>e&&(e=this.get(t,s),r[1]=s);return r}minRow(t){if(l(this,t),this.isEmpty())return NaN;let e=this.get(t,0);for(let r=1;r<this.columns;r++)this.get(t,r)<e&&(e=this.get(t,r));return e}minRowIndex(t){l(this,t),y(this);let e=this.get(t,0),r=[t,0];for(let s=1;s<this.columns;s++)this.get(t,s)<e&&(e=this.get(t,s),r[1]=s);return r}maxColumn(t){if(a(this,t),this.isEmpty())return NaN;let e=this.get(0,t);for(let r=1;r<this.rows;r++)this.get(r,t)>e&&(e=this.get(r,t));return e}maxColumnIndex(t){a(this,t),y(this);let e=this.get(0,t),r=[0,t];for(let s=1;s<this.rows;s++)this.get(s,t)>e&&(e=this.get(s,t),r[0]=s);return r}minColumn(t){if(a(this,t),this.isEmpty())return NaN;let e=this.get(0,t);for(let r=1;r<this.rows;r++)this.get(r,t)<e&&(e=this.get(r,t));return e}minColumnIndex(t){a(this,t),y(this);let e=this.get(0,t),r=[0,t];for(let s=1;s<this.rows;s++)this.get(s,t)<e&&(e=this.get(s,t),r[0]=s);return r}diag(){let t=Math.min(this.rows,this.columns),e=[];for(let r=0;r<t;r++)e.push(this.get(r,r));return e}norm(t="frobenius"){switch(t){case"max":return this.max();case"frobenius":return Math.sqrt(this.dot(this));default:throw new RangeError(`unknown norm type: ${t}`)}}cumulativeSum(){let t=0;for(let e=0;e<this.rows;e++)for(let r=0;r<this.columns;r++)t+=this.get(e,r),this.set(e,r,t);return this}dot(t){M.isMatrix(t)&&(t=t.to1DArray());let e=this.to1DArray();if(e.length!==t.length)throw new RangeError("vectors do not have the same size");let r=0;for(let s=0;s<e.length;s++)r+=e[s]*t[s];return r}mmul(t){t=x.checkMatrix(t);let e=this.rows,r=this.columns,s=t.columns,o=new x(e,s),i=new Float64Array(r);for(let n=0;n<s;n++){for(let e=0;e<r;e++)i[e]=t.get(e,n);for(let t=0;t<e;t++){let e=0;for(let s=0;s<r;s++)e+=this.get(t,s)*i[s];o.set(t,n,e)}}return o}mpow(t){if(!this.isSquare())throw new RangeError("Matrix must be square");if(!Number.isInteger(t)||t<0)throw new RangeError("Exponent must be a non-negative integer");let e=x.eye(this.rows),r=this;for(let s=t;s>1;s/=2)1&s&&(e=e.mmul(r)),r=r.mmul(r);return e}strassen2x2(t){t=x.checkMatrix(t);let e=new x(2,2);const r=this.get(0,0),s=t.get(0,0),o=this.get(0,1),i=t.get(0,1),n=this.get(1,0),h=t.get(1,0),u=this.get(1,1),l=t.get(1,1),a=(r+u)*(s+l),f=(n+u)*s,c=r*(i-l),m=u*(h-s),g=(r+o)*l,w=a+m-g+(o-u)*(h+l),p=c+g,d=f+m,y=a-f+c+(n-r)*(s+i);return e.set(0,0,w),e.set(0,1,p),e.set(1,0,d),e.set(1,1,y),e}strassen3x3(t){t=x.checkMatrix(t);let e=new x(3,3);const r=this.get(0,0),s=this.get(0,1),o=this.get(0,2),i=this.get(1,0),n=this.get(1,1),h=this.get(1,2),u=this.get(2,0),l=this.get(2,1),a=this.get(2,2),f=t.get(0,0),c=t.get(0,1),m=t.get(0,2),g=t.get(1,0),w=t.get(1,1),p=t.get(1,2),d=t.get(2,0),y=t.get(2,1),M=t.get(2,2),b=(r-i)*(-c+w),E=(-r+i+n)*(f-c+w),S=(i+n)*(-f+c),v=r*f,R=(-r+u+l)*(f-m+p),I=(-r+u)*(m-p),k=(u+l)*(-f+m),T=(-o+l+a)*(w+d-y),N=(o-a)*(w-y),V=o*d,C=(l+a)*(-d+y),q=(-o+n+h)*(p+d-M),A=(o-h)*(p-M),D=(n+h)*(-d+M),F=v+V+s*g,z=(r+s+o-i-n-l-a)*w+E+S+v+T+V+C,$=v+R+k+(r+s+o-n-h-u-l)*p+V+q+D,j=b+n*(-f+c+g-w-p-d+M)+E+v+V+q+A,P=b+E+S+v+h*y,L=V+q+A+D+i*m,U=v+R+I+l*(-f+m+g-w-p-d+y)+T+N+V,O=T+N+V+C+u*c,_=v+R+I+k+a*M;return e.set(0,0,F),e.set(0,1,z),e.set(0,2,$),e.set(1,0,j),e.set(1,1,P),e.set(1,2,L),e.set(2,0,U),e.set(2,1,O),e.set(2,2,_),e}mmulStrassen(t){t=x.checkMatrix(t);let e=this.clone(),r=e.rows,s=e.columns,o=t.rows,i=t.columns;function n(t,e,r){let s=t.rows,o=t.columns;if(s===e&&o===r)return t;{let s=M.zeros(e,r);return 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T=T.setSubMatrix(v,0,0),T=T.setSubMatrix(R,v.rows,0),T=T.setSubMatrix(I,0,v.columns),T=T.setSubMatrix(k,v.rows,v.columns),T.subMatrix(0,s-1,0,o-1)}(e,t=n(t,h,u),h,u)}scaleRows(t={}){if("object"!=typeof t)throw new TypeError("options must be an object");const{min:e=0,max:r=1}=t;if(!Number.isFinite(e))throw new TypeError("min must be a number");if(!Number.isFinite(r))throw new TypeError("max must be a number");if(e>=r)throw new RangeError("min must be smaller than max");let o=new x(this.rows,this.columns);for(let t=0;t<this.rows;t++){const i=this.getRow(t);i.length>0&&s(i,{min:e,max:r,output:i}),o.setRow(t,i)}return o}scaleColumns(t={}){if("object"!=typeof t)throw new TypeError("options must be an object");const{min:e=0,max:r=1}=t;if(!Number.isFinite(e))throw new TypeError("min must be a number");if(!Number.isFinite(r))throw new TypeError("max must be a number");if(e>=r)throw new RangeError("min must be smaller than max");let o=new x(this.rows,this.columns);for(let 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${t}`)}}variance(t,e={}){if("object"==typeof t&&(e=t,t=void 0),"object"!=typeof e)throw new TypeError("options must be an object");const{unbiased:s=!0,mean:o=this.mean(t)}=e;if("boolean"!=typeof s)throw new TypeError("unbiased must be a boolean");switch(t){case"row":if(!r(o))throw new TypeError("mean must be an array");return function(t,e,r){const s=t.rows,o=t.columns,i=[];for(let n=0;n<s;n++){let s=0,h=0,u=0;for(let e=0;e<o;e++)u=t.get(n,e)-r[n],s+=u,h+=u*u;e?i.push((h-s*s/o)/(o-1)):i.push((h-s*s/o)/o)}return i}(this,s,o);case"column":if(!r(o))throw new TypeError("mean must be an array");return function(t,e,r){const s=t.rows,o=t.columns,i=[];for(let n=0;n<o;n++){let o=0,h=0,u=0;for(let e=0;e<s;e++)u=t.get(e,n)-r[n],o+=u,h+=u*u;e?i.push((h-o*o/s)/(s-1)):i.push((h-o*o/s)/s)}return i}(this,s,o);case void 0:if("number"!=typeof o)throw new TypeError("mean must be a number");return function(t,e,r){const s=t.rows,o=t.columns,i=s*o;let n=0,h=0,u=0;for(let e=0;e<s;e++)for(let 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e(t).sub(r)},t.prototype.subtract=t.prototype.sub,t.prototype.subtractS=t.prototype.subS,t.prototype.subtractM=t.prototype.subM,t.subtract=t.sub,t.prototype.mul=function(t){return"number"==typeof t?this.mulS(t):this.mulM(t)},t.prototype.mulS=function(t){for(let e=0;e<this.rows;e++)for(let r=0;r<this.columns;r++)this.set(e,r,this.get(e,r)*t);return this},t.prototype.mulM=function(t){if(t=e.checkMatrix(t),this.rows!==t.rows||this.columns!==t.columns)throw new RangeError("Matrices dimensions must be equal");for(let e=0;e<this.rows;e++)for(let r=0;r<this.columns;r++)this.set(e,r,this.get(e,r)*t.get(e,r));return this},t.mul=function(t,r){return new e(t).mul(r)},t.prototype.multiply=t.prototype.mul,t.prototype.multiplyS=t.prototype.mulS,t.prototype.multiplyM=t.prototype.mulM,t.multiply=t.mul,t.prototype.div=function(t){return"number"==typeof t?this.divS(t):this.divM(t)},t.prototype.divS=function(t){for(let e=0;e<this.rows;e++)for(let r=0;r<this.columns;r++)this.set(e,r,this.get(e,r)/t);return this},t.prototype.divM=function(t){if(t=e.checkMatrix(t),this.rows!==t.rows||this.columns!==t.columns)throw new RangeError("Matrices dimensions must be equal");for(let e=0;e<this.rows;e++)for(let r=0;r<this.columns;r++)this.set(e,r,this.get(e,r)/t.get(e,r));return this},t.div=function(t,r){return new e(t).div(r)},t.prototype.divide=t.prototype.div,t.prototype.divideS=t.prototype.divS,t.prototype.divideM=t.prototype.divM,t.divide=t.div,t.prototype.mod=function(t){return"number"==typeof t?this.modS(t):this.modM(t)},t.prototype.modS=function(t){for(let e=0;e<this.rows;e++)for(let r=0;r<this.columns;r++)this.set(e,r,this.get(e,r)%t);return this},t.prototype.modM=function(t){if(t=e.checkMatrix(t),this.rows!==t.rows||this.columns!==t.columns)throw new RangeError("Matrices dimensions must be equal");for(let e=0;e<this.rows;e++)for(let r=0;r<this.columns;r++)this.set(e,r,this.get(e,r)%t.get(e,r));return this},t.mod=function(t,r){return new e(t).mod(r)},t.prototype.modulus=t.prototype.mod,t.prototype.modulusS=t.prototype.modS,t.prototype.modulusM=t.prototype.modM,t.modulus=t.mod,t.prototype.and=function(t){return"number"==typeof t?this.andS(t):this.andM(t)},t.prototype.andS=function(t){for(let e=0;e<this.rows;e++)for(let r=0;r<this.columns;r++)this.set(e,r,this.get(e,r)&t);return this},t.prototype.andM=function(t){if(t=e.checkMatrix(t),this.rows!==t.rows||this.columns!==t.columns)throw new RangeError("Matrices dimensions must be equal");for(let e=0;e<this.rows;e++)for(let r=0;r<this.columns;r++)this.set(e,r,this.get(e,r)&t.get(e,r));return this},t.and=function(t,r){return new e(t).and(r)},t.prototype.or=function(t){return"number"==typeof t?this.orS(t):this.orM(t)},t.prototype.orS=function(t){for(let e=0;e<this.rows;e++)for(let r=0;r<this.columns;r++)this.set(e,r,this.get(e,r)|t);return this},t.prototype.orM=function(t){if(t=e.checkMatrix(t),this.rows!==t.rows||this.columns!==t.columns)throw new RangeError("Matrices dimensions must be equal");for(let e=0;e<this.rows;e++)for(let r=0;r<this.columns;r++)this.set(e,r,this.get(e,r)|t.get(e,r));return this},t.or=function(t,r){return new e(t).or(r)},t.prototype.xor=function(t){return"number"==typeof t?this.xorS(t):this.xorM(t)},t.prototype.xorS=function(t){for(let e=0;e<this.rows;e++)for(let r=0;r<this.columns;r++)this.set(e,r,this.get(e,r)^t);return this},t.prototype.xorM=function(t){if(t=e.checkMatrix(t),this.rows!==t.rows||this.columns!==t.columns)throw new RangeError("Matrices dimensions must be equal");for(let e=0;e<this.rows;e++)for(let r=0;r<this.columns;r++)this.set(e,r,this.get(e,r)^t.get(e,r));return this},t.xor=function(t,r){return new e(t).xor(r)},t.prototype.leftShift=function(t){return"number"==typeof t?this.leftShiftS(t):this.leftShiftM(t)},t.prototype.leftShiftS=function(t){for(let e=0;e<this.rows;e++)for(let r=0;r<this.columns;r++)this.set(e,r,this.get(e,r)<<t);return this},t.prototype.leftShiftM=function(t){if(t=e.checkMatrix(t),this.rows!==t.rows||this.columns!==t.columns)throw new RangeError("Matrices dimensions must be equal");for(let e=0;e<this.rows;e++)for(let r=0;r<this.columns;r++)this.set(e,r,this.get(e,r)<<t.get(e,r));return this},t.leftShift=function(t,r){return new e(t).leftShift(r)},t.prototype.signPropagatingRightShift=function(t){return"number"==typeof t?this.signPropagatingRightShiftS(t):this.signPropagatingRightShiftM(t)},t.prototype.signPropagatingRightShiftS=function(t){for(let e=0;e<this.rows;e++)for(let r=0;r<this.columns;r++)this.set(e,r,this.get(e,r)>>t);return this},t.prototype.signPropagatingRightShiftM=function(t){if(t=e.checkMatrix(t),this.rows!==t.rows||this.columns!==t.columns)throw new RangeError("Matrices dimensions must be equal");for(let e=0;e<this.rows;e++)for(let r=0;r<this.columns;r++)this.set(e,r,this.get(e,r)>>t.get(e,r));return this},t.signPropagatingRightShift=function(t,r){return new e(t).signPropagatingRightShift(r)},t.prototype.rightShift=function(t){return"number"==typeof t?this.rightShiftS(t):this.rightShiftM(t)},t.prototype.rightShiftS=function(t){for(let e=0;e<this.rows;e++)for(let r=0;r<this.columns;r++)this.set(e,r,this.get(e,r)>>>t);return this},t.prototype.rightShiftM=function(t){if(t=e.checkMatrix(t),this.rows!==t.rows||this.columns!==t.columns)throw new RangeError("Matrices dimensions must be equal");for(let e=0;e<this.rows;e++)for(let r=0;r<this.columns;r++)this.set(e,r,this.get(e,r)>>>t.get(e,r));return this},t.rightShift=function(t,r){return new e(t).rightShift(r)},t.prototype.zeroFillRightShift=t.prototype.rightShift,t.prototype.zeroFillRightShiftS=t.prototype.rightShiftS,t.prototype.zeroFillRightShiftM=t.prototype.rightShiftM,t.zeroFillRightShift=t.rightShift,t.prototype.not=function(){for(let t=0;t<this.rows;t++)for(let e=0;e<this.columns;e++)this.set(t,e,~this.get(t,e));return this},t.not=function(t){return new e(t).not()},t.prototype.abs=function(){for(let t=0;t<this.rows;t++)for(let e=0;e<this.columns;e++)this.set(t,e,Math.abs(this.get(t,e)));return this},t.abs=function(t){return new e(t).abs()},t.prototype.acos=function(){for(let t=0;t<this.rows;t++)for(let e=0;e<this.columns;e++)this.set(t,e,Math.acos(this.get(t,e)));return this},t.acos=function(t){return new e(t).acos()},t.prototype.acosh=function(){for(let t=0;t<this.rows;t++)for(let e=0;e<this.columns;e++)this.set(t,e,Math.acosh(this.get(t,e)));return this},t.acosh=function(t){return new e(t).acosh()},t.prototype.asin=function(){for(let t=0;t<this.rows;t++)for(let e=0;e<this.columns;e++)this.set(t,e,Math.asin(this.get(t,e)));return this},t.asin=function(t){return new e(t).asin()},t.prototype.asinh=function(){for(let t=0;t<this.rows;t++)for(let e=0;e<this.columns;e++)this.set(t,e,Math.asinh(this.get(t,e)));return this},t.asinh=function(t){return new e(t).asinh()},t.prototype.atan=function(){for(let t=0;t<this.rows;t++)for(let e=0;e<this.columns;e++)this.set(t,e,Math.atan(this.get(t,e)));return this},t.atan=function(t){return new e(t).atan()},t.prototype.atanh=function(){for(let t=0;t<this.rows;t++)for(let e=0;e<this.columns;e++)this.set(t,e,Math.atanh(this.get(t,e)));return this},t.atanh=function(t){return new e(t).atanh()},t.prototype.cbrt=function(){for(let t=0;t<this.rows;t++)for(let e=0;e<this.columns;e++)this.set(t,e,Math.cbrt(this.get(t,e)));return this},t.cbrt=function(t){return new e(t).cbrt()},t.prototype.ceil=function(){for(let t=0;t<this.rows;t++)for(let e=0;e<this.columns;e++)this.set(t,e,Math.ceil(this.get(t,e)));return this},t.ceil=function(t){return new e(t).ceil()},t.prototype.clz32=function(){for(let t=0;t<this.rows;t++)for(let e=0;e<this.columns;e++)this.set(t,e,Math.clz32(this.get(t,e)));return this},t.clz32=function(t){return new e(t).clz32()},t.prototype.cos=function(){for(let t=0;t<this.rows;t++)for(let e=0;e<this.columns;e++)this.set(t,e,Math.cos(this.get(t,e)));return this},t.cos=function(t){return new e(t).cos()},t.prototype.cosh=function(){for(let t=0;t<this.rows;t++)for(let e=0;e<this.columns;e++)this.set(t,e,Math.cosh(this.get(t,e)));return this},t.cosh=function(t){return new e(t).cosh()},t.prototype.exp=function(){for(let t=0;t<this.rows;t++)for(let e=0;e<this.columns;e++)this.set(t,e,Math.exp(this.get(t,e)));return this},t.exp=function(t){return new e(t).exp()},t.prototype.expm1=function(){for(let t=0;t<this.rows;t++)for(let e=0;e<this.columns;e++)this.set(t,e,Math.expm1(this.get(t,e)));return this},t.expm1=function(t){return new e(t).expm1()},t.prototype.floor=function(){for(let t=0;t<this.rows;t++)for(let e=0;e<this.columns;e++)this.set(t,e,Math.floor(this.get(t,e)));return this},t.floor=function(t){return new e(t).floor()},t.prototype.fround=function(){for(let t=0;t<this.rows;t++)for(let e=0;e<this.columns;e++)this.set(t,e,Math.fround(this.get(t,e)));return this},t.fround=function(t){return new e(t).fround()},t.prototype.log=function(){for(let t=0;t<this.rows;t++)for(let e=0;e<this.columns;e++)this.set(t,e,Math.log(this.get(t,e)));return this},t.log=function(t){return new e(t).log()},t.prototype.log1p=function(){for(let t=0;t<this.rows;t++)for(let e=0;e<this.columns;e++)this.set(t,e,Math.log1p(this.get(t,e)));return this},t.log1p=function(t){return new e(t).log1p()},t.prototype.log10=function(){for(let t=0;t<this.rows;t++)for(let e=0;e<this.columns;e++)this.set(t,e,Math.log10(this.get(t,e)));return this},t.log10=function(t){return new e(t).log10()},t.prototype.log2=function(){for(let t=0;t<this.rows;t++)for(let e=0;e<this.columns;e++)this.set(t,e,Math.log2(this.get(t,e)));return this},t.log2=function(t){return new e(t).log2()},t.prototype.round=function(){for(let t=0;t<this.rows;t++)for(let e=0;e<this.columns;e++)this.set(t,e,Math.round(this.get(t,e)));return this},t.round=function(t){return new e(t).round()},t.prototype.sign=function(){for(let t=0;t<this.rows;t++)for(let e=0;e<this.columns;e++)this.set(t,e,Math.sign(this.get(t,e)));return this},t.sign=function(t){return new e(t).sign()},t.prototype.sin=function(){for(let t=0;t<this.rows;t++)for(let e=0;e<this.columns;e++)this.set(t,e,Math.sin(this.get(t,e)));return this},t.sin=function(t){return new e(t).sin()},t.prototype.sinh=function(){for(let t=0;t<this.rows;t++)for(let e=0;e<this.columns;e++)this.set(t,e,Math.sinh(this.get(t,e)));return this},t.sinh=function(t){return new e(t).sinh()},t.prototype.sqrt=function(){for(let t=0;t<this.rows;t++)for(let e=0;e<this.columns;e++)this.set(t,e,Math.sqrt(this.get(t,e)));return this},t.sqrt=function(t){return new e(t).sqrt()},t.prototype.tan=function(){for(let t=0;t<this.rows;t++)for(let e=0;e<this.columns;e++)this.set(t,e,Math.tan(this.get(t,e)));return this},t.tan=function(t){return new e(t).tan()},t.prototype.tanh=function(){for(let t=0;t<this.rows;t++)for(let e=0;e<this.columns;e++)this.set(t,e,Math.tanh(this.get(t,e)));return this},t.tanh=function(t){return new e(t).tanh()},t.prototype.trunc=function(){for(let t=0;t<this.rows;t++)for(let e=0;e<this.columns;e++)this.set(t,e,Math.trunc(this.get(t,e)));return this},t.trunc=function(t){return new e(t).trunc()},t.pow=function(t,r){return new e(t).pow(r)},t.prototype.pow=function(t){return"number"==typeof t?this.powS(t):this.powM(t)},t.prototype.powS=function(t){for(let e=0;e<this.rows;e++)for(let r=0;r<this.columns;r++)this.set(e,r,this.get(e,r)**t);return this},t.prototype.powM=function(t){if(t=e.checkMatrix(t),this.rows!==t.rows||this.columns!==t.columns)throw new RangeError("Matrices dimensions must be equal");for(let e=0;e<this.rows;e++)for(let r=0;r<this.columns;r++)this.set(e,r,this.get(e,r)**t.get(e,r));return this}}(M,x);class E extends M{#e;get size(){return this.#e.size}get rows(){return this.#e.rows}get columns(){return this.#e.columns}get diagonalSize(){return this.rows}static isSymmetricMatrix(t){return x.isMatrix(t)&&"SymmetricMatrix"===t.klassType}static zeros(t){return new this(t)}static ones(t){return new this(t).fill(1)}constructor(t){if(super(),x.isMatrix(t)){if(!t.isSymmetric())throw new TypeError("not symmetric data");this.#e=x.copy(t,new x(t.rows,t.rows))}else if(Number.isInteger(t)&&t>=0)this.#e=new x(t,t);else if(this.#e=new x(t),!this.isSymmetric())throw new TypeError("not symmetric data")}clone(){const t=new E(this.diagonalSize);for(const[e,r,s]of this.upperRightEntries())t.set(e,r,s);return t}toMatrix(){return new x(this)}get(t,e){return this.#e.get(t,e)}set(t,e,r){return this.#e.set(t,e,r),this.#e.set(e,t,r),this}removeCross(t){return this.#e.removeRow(t),this.#e.removeColumn(t),this}addCross(t,e){void 0===e&&(e=t,t=this.diagonalSize);const r=e.slice();return r.splice(t,1),this.#e.addRow(t,r),this.#e.addColumn(t,e),this}applyMask(t){if(t.length!==this.diagonalSize)throw new RangeError("Mask size do not match with matrix size");const e=[];for(const[r,s]of t.entries())s||e.push(r);e.reverse();for(const t of e)this.removeCross(t);return this}toCompact(){const{diagonalSize:t}=this,e=new Array(t*(t+1)/2);for(let r=0,s=0,o=0;o<e.length;o++)e[o]=this.get(s,r),++r>=t&&(r=++s);return e}static fromCompact(t){const e=t.length,r=(Math.sqrt(8*e+1)-1)/2;if(!Number.isInteger(r))throw new TypeError(`This array is not a compact representation of a Symmetric Matrix, ${JSON.stringify(t)}`);const s=new E(r);for(let o=0,i=0,n=0;n<e;n++)s.set(o,i,t[n]),++o>=r&&(o=++i);return s}*upperRightEntries(){for(let t=0,e=0;t<this.diagonalSize;void 0){const r=this.get(t,e);yield[t,e,r],++e>=this.diagonalSize&&(e=++t)}}*upperRightValues(){for(let t=0,e=0;t<this.diagonalSize;void 0){const r=this.get(t,e);yield r,++e>=this.diagonalSize&&(e=++t)}}}E.prototype.klassType="SymmetricMatrix";class S extends E{static isDistanceMatrix(t){return E.isSymmetricMatrix(t)&&"DistanceMatrix"===t.klassSubType}constructor(t){if(super(t),!this.isDistance())throw new TypeError("Provided arguments do no produce a distance matrix")}set(t,e,r){return t===e&&(r=0),super.set(t,e,r)}addCross(t,e){return void 0===e&&(e=t,t=this.diagonalSize),(e=e.slice())[t]=0,super.addCross(t,e)}toSymmetricMatrix(){return new E(this)}clone(){const t=new S(this.diagonalSize);for(const[e,r,s]of this.upperRightEntries())e!==r&&t.set(e,r,s);return t}toCompact(){const{diagonalSize:t}=this,e=new Array((t-1)*t/2);for(let r=1,s=0,o=0;o<e.length;o++)e[o]=this.get(s,r),++r>=t&&(r=1+ ++s);return e}static fromCompact(t){const e=t.length;if(0===e)return new this(0);const r=(Math.sqrt(8*e+1)+1)/2;if(!Number.isInteger(r))throw new TypeError(`This array is not a compact representation of a DistanceMatrix, ${JSON.stringify(t)}`);const s=new this(r);for(let o=1,i=0,n=0;n<e;n++)s.set(o,i,t[n]),++o>=r&&(o=1+ ++i);return s}}S.prototype.klassSubType="DistanceMatrix";class v extends M{constructor(t,e,r){super(),this.matrix=t,this.rows=e,this.columns=r}}class R extends v{constructor(t,e,r){m(t,e),g(t,r),super(t,e.length,r.length),this.rowIndices=e,this.columnIndices=r}set(t,e,r){return this.matrix.set(this.rowIndices[t],this.columnIndices[e],r),this}get(t,e){return this.matrix.get(this.rowIndices[t],this.columnIndices[e])}}class I extends M{constructor(t,e={}){const{rows:r=1}=e;if(t.length%r!=0)throw new Error("the data length is not divisible by the number of rows");super(),this.rows=r,this.columns=t.length/r,this.data=t}set(t,e,r){let s=this._calculateIndex(t,e);return this.data[s]=r,this}get(t,e){let r=this._calculateIndex(t,e);return this.data[r]}_calculateIndex(t,e){return t*this.columns+e}}class k extends M{constructor(t){super(),this.data=t,this.rows=t.length,this.columns=t[0].length}set(t,e,r){return this.data[t][e]=r,this}get(t,e){return this.data[t][e]}}class T{constructor(t){let e,r,s,o,i,n,h,u,l,a=(t=k.checkMatrix(t)).clone(),f=a.rows,c=a.columns,m=new Float64Array(f),g=1;for(e=0;e<f;e++)m[e]=e;for(u=new Float64Array(f),r=0;r<c;r++){for(e=0;e<f;e++)u[e]=a.get(e,r);for(e=0;e<f;e++){for(l=Math.min(e,r),i=0,s=0;s<l;s++)i+=a.get(e,s)*u[s];u[e]-=i,a.set(e,r,u[e])}for(o=r,e=r+1;e<f;e++)Math.abs(u[e])>Math.abs(u[o])&&(o=e);if(o!==r){for(s=0;s<c;s++)n=a.get(o,s),a.set(o,s,a.get(r,s)),a.set(r,s,n);h=m[o],m[o]=m[r],m[r]=h,g=-g}if(r<f&&0!==a.get(r,r))for(e=r+1;e<f;e++)a.set(e,r,a.get(e,r)/a.get(r,r))}this.LU=a,this.pivotVector=m,this.pivotSign=g}isSingular(){let t=this.LU,e=t.columns;for(let r=0;r<e;r++)if(0===t.get(r,r))return!0;return!1}solve(t){t=x.checkMatrix(t);let e=this.LU;if(e.rows!==t.rows)throw new Error("Invalid matrix dimensions");if(this.isSingular())throw new Error("LU matrix is singular");let r,s,o,i=t.columns,n=t.subMatrixRow(this.pivotVector,0,i-1),h=e.columns;for(o=0;o<h;o++)for(r=o+1;r<h;r++)for(s=0;s<i;s++)n.set(r,s,n.get(r,s)-n.get(o,s)*e.get(r,o));for(o=h-1;o>=0;o--){for(s=0;s<i;s++)n.set(o,s,n.get(o,s)/e.get(o,o));for(r=0;r<o;r++)for(s=0;s<i;s++)n.set(r,s,n.get(r,s)-n.get(o,s)*e.get(r,o))}return n}get determinant(){let t=this.LU;if(!t.isSquare())throw new Error("Matrix must be square");let e=this.pivotSign,r=t.columns;for(let s=0;s<r;s++)e*=t.get(s,s);return e}get lowerTriangularMatrix(){let t=this.LU,e=t.rows,r=t.columns,s=new x(e,r);for(let o=0;o<e;o++)for(let e=0;e<r;e++)o>e?s.set(o,e,t.get(o,e)):o===e?s.set(o,e,1):s.set(o,e,0);return s}get upperTriangularMatrix(){let t=this.LU,e=t.rows,r=t.columns,s=new x(e,r);for(let o=0;o<e;o++)for(let e=0;e<r;e++)o<=e?s.set(o,e,t.get(o,e)):s.set(o,e,0);return s}get pivotPermutationVector(){return Array.from(this.pivotVector)}}function N(t,e){let r=0;return Math.abs(t)>Math.abs(e)?(r=e/t,Math.abs(t)*Math.sqrt(1+r*r)):0!==e?(r=t/e,Math.abs(e)*Math.sqrt(1+r*r)):0}class V{constructor(t){let e,r,s,o,i=(t=k.checkMatrix(t)).clone(),n=t.rows,h=t.columns,u=new Float64Array(h);for(s=0;s<h;s++){let t=0;for(e=s;e<n;e++)t=N(t,i.get(e,s));if(0!==t){for(i.get(s,s)<0&&(t=-t),e=s;e<n;e++)i.set(e,s,i.get(e,s)/t);for(i.set(s,s,i.get(s,s)+1),r=s+1;r<h;r++){for(o=0,e=s;e<n;e++)o+=i.get(e,s)*i.get(e,r);for(o=-o/i.get(s,s),e=s;e<n;e++)i.set(e,r,i.get(e,r)+o*i.get(e,s))}}u[s]=-t}this.QR=i,this.Rdiag=u}solve(t){t=x.checkMatrix(t);let e=this.QR,r=e.rows;if(t.rows!==r)throw new Error("Matrix row dimensions must agree");if(!this.isFullRank())throw new Error("Matrix is rank deficient");let s,o,i,n,h=t.columns,u=t.clone(),l=e.columns;for(i=0;i<l;i++)for(o=0;o<h;o++){for(n=0,s=i;s<r;s++)n+=e.get(s,i)*u.get(s,o);for(n=-n/e.get(i,i),s=i;s<r;s++)u.set(s,o,u.get(s,o)+n*e.get(s,i))}for(i=l-1;i>=0;i--){for(o=0;o<h;o++)u.set(i,o,u.get(i,o)/this.Rdiag[i]);for(s=0;s<i;s++)for(o=0;o<h;o++)u.set(s,o,u.get(s,o)-u.get(i,o)*e.get(s,i))}return u.subMatrix(0,l-1,0,h-1)}isFullRank(){let t=this.QR.columns;for(let e=0;e<t;e++)if(0===this.Rdiag[e])return!1;return!0}get upperTriangularMatrix(){let t,e,r=this.QR,s=r.columns,o=new x(s,s);for(t=0;t<s;t++)for(e=0;e<s;e++)t<e?o.set(t,e,r.get(t,e)):t===e?o.set(t,e,this.Rdiag[t]):o.set(t,e,0);return o}get orthogonalMatrix(){let t,e,r,s,o=this.QR,i=o.rows,n=o.columns,h=new x(i,n);for(r=n-1;r>=0;r--){for(t=0;t<i;t++)h.set(t,r,0);for(h.set(r,r,1),e=r;e<n;e++)if(0!==o.get(r,r)){for(s=0,t=r;t<i;t++)s+=o.get(t,r)*h.get(t,e);for(s=-s/o.get(r,r),t=r;t<i;t++)h.set(t,e,h.get(t,e)+s*o.get(t,r))}}return h}}class C{constructor(t,e={}){if((t=k.checkMatrix(t)).isEmpty())throw new Error("Matrix must be non-empty");let r=t.rows,s=t.columns;const{computeLeftSingularVectors:o=!0,computeRightSingularVectors:i=!0,autoTranspose:n=!1}=e;let h,u=Boolean(o),l=Boolean(i),a=!1;if(r<s)if(n){h=t.transpose(),r=h.rows,s=h.columns,a=!0;let e=u;u=l,l=e}else h=t.clone(),console.warn("Computing SVD on a matrix with more columns than rows. Consider enabling autoTranspose");else h=t.clone();let f=Math.min(r,s),c=Math.min(r+1,s),m=new Float64Array(c),g=new x(r,f),w=new x(s,s),p=new Float64Array(s),d=new Float64Array(r),y=new Float64Array(c);for(let t=0;t<c;t++)y[t]=t;let M=Math.min(r-1,s),b=Math.max(0,Math.min(s-2,r)),E=Math.max(M,b);for(let t=0;t<E;t++){if(t<M){m[t]=0;for(let e=t;e<r;e++)m[t]=N(m[t],h.get(e,t));if(0!==m[t]){h.get(t,t)<0&&(m[t]=-m[t]);for(let e=t;e<r;e++)h.set(e,t,h.get(e,t)/m[t]);h.set(t,t,h.get(t,t)+1)}m[t]=-m[t]}for(let e=t+1;e<s;e++){if(t<M&&0!==m[t]){let s=0;for(let o=t;o<r;o++)s+=h.get(o,t)*h.get(o,e);s=-s/h.get(t,t);for(let o=t;o<r;o++)h.set(o,e,h.get(o,e)+s*h.get(o,t))}p[e]=h.get(t,e)}if(u&&t<M)for(let e=t;e<r;e++)g.set(e,t,h.get(e,t));if(t<b){p[t]=0;for(let e=t+1;e<s;e++)p[t]=N(p[t],p[e]);if(0!==p[t]){p[t+1]<0&&(p[t]=0-p[t]);for(let e=t+1;e<s;e++)p[e]/=p[t];p[t+1]+=1}if(p[t]=-p[t],t+1<r&&0!==p[t]){for(let e=t+1;e<r;e++)d[e]=0;for(let e=t+1;e<r;e++)for(let r=t+1;r<s;r++)d[e]+=p[r]*h.get(e,r);for(let e=t+1;e<s;e++){let s=-p[e]/p[t+1];for(let o=t+1;o<r;o++)h.set(o,e,h.get(o,e)+s*d[o])}}if(l)for(let e=t+1;e<s;e++)w.set(e,t,p[e])}}let S=Math.min(s,r+1);if(M<s&&(m[M]=h.get(M,M)),r<S&&(m[S-1]=0),b+1<S&&(p[b]=h.get(b,S-1)),p[S-1]=0,u){for(let t=M;t<f;t++){for(let e=0;e<r;e++)g.set(e,t,0);g.set(t,t,1)}for(let t=M-1;t>=0;t--)if(0!==m[t]){for(let e=t+1;e<f;e++){let s=0;for(let o=t;o<r;o++)s+=g.get(o,t)*g.get(o,e);s=-s/g.get(t,t);for(let o=t;o<r;o++)g.set(o,e,g.get(o,e)+s*g.get(o,t))}for(let e=t;e<r;e++)g.set(e,t,-g.get(e,t));g.set(t,t,1+g.get(t,t));for(let e=0;e<t-1;e++)g.set(e,t,0)}else{for(let e=0;e<r;e++)g.set(e,t,0);g.set(t,t,1)}}if(l)for(let t=s-1;t>=0;t--){if(t<b&&