ml-matrix - npm Package Compare versions

Comparing version 6.5.2 to 6.5.3

matrix.d.ts

@@ -0,0 +0,0 @@ type MaybeMatrix = AbstractMatrix | number[][];

matrix.umd.js

@@ -1,1 +0,1 @@
-!function(t,e){"object"==typeof exports&&"undefined"!=typeof module?e(exports):"function"==typeof define&&define.amd?define(["exports"],e):e((t="undefined"!=typeof globalThis?globalThis:t||self).mlMatrix={})}(this,(function(t){"use strict";const e=Object.prototype.toString;function r(t){return e.call(t).endsWith("Array]")}function s(t){var e=arguments.length>1&&void 0!==arguments[1]?arguments[1]:{};if(!r(t))throw new TypeError("input must be an array");if(0===t.length)throw new TypeError("input must not be empty");var s=e.fromIndex,o=void 0===s?0:s,n=e.toIndex,i=void 0===n?t.length:n;if(o<0||o>=t.length||!Number.isInteger(o))throw new Error("fromIndex must be a positive integer smaller than length");if(i<=o||i>t.length||!Number.isInteger(i))throw new Error("toIndex must be an integer greater than fromIndex and at most equal to length");for(var h=t[o],u=o+1;u<i;u++)t[u]>h&&(h=t[u]);return h}function o(t){var e=arguments.length>1&&void 0!==arguments[1]?arguments[1]:{};if(!r(t))throw new TypeError("input must be an array");if(0===t.length)throw new TypeError("input must not be empty");var s=e.fromIndex,o=void 0===s?0:s,n=e.toIndex,i=void 0===n?t.length:n;if(o<0||o>=t.length||!Number.isInteger(o))throw new Error("fromIndex must be a positive integer smaller than length");if(i<=o||i>t.length||!Number.isInteger(i))throw new Error("toIndex must be an integer greater than fromIndex and at most equal to length");for(var h=t[o],u=o+1;u<i;u++)t[u]<h&&(h=t[u]);return h}function n(t){var e,n=arguments.length>1&&void 0!==arguments[1]?arguments[1]:{};if(!r(t))throw new TypeError("input must be an array");if(0===t.length)throw new TypeError("input must not be empty");if(void 0!==n.output){if(!r(n.output))throw new TypeError("output option must be an array if specified");e=n.output}else e=new Array(t.length);var i=o(t),h=s(t);if(i===h)throw new RangeError("minimum and maximum input values are equal. Cannot rescale a constant array");var u=n.min,l=void 0===u?n.autoMinMax?i:0:u,a=n.max,f=void 0===a?n.autoMinMax?h:1:a;if(l>=f)throw new RangeError("min option must be smaller than max option");for(var c=(f-l)/(h-i),g=0;g<t.length;g++)e[g]=(t[g]-i)*c+l;return e}const i=" ".repeat(2),h=" ".repeat(4);function u(t,e={}){const{maxRows:r=15,maxColumns:s=10,maxNumSize:o=8}=e;return`${t.constructor.name} {\n${i}[\n${h}${function(t,e,r,s){const{rows:o,columns:n}=t,i=Math.min(o,e),u=Math.min(n,r),a=[];for(let e=0;e<i;e++){let r=[];for(let o=0;o<u;o++)r.push(l(t.get(e,o),s));a.push(""+r.join(" "))}u!==n&&(a[a.length-1]+=` ... ${n-r} more columns`);i!==o&&a.push(`... ${o-e} more rows`);return a.join("\n"+h)}(t,r,s,o)}\n${i}]\n${i}rows: ${t.rows}\n${i}columns: ${t.columns}\n}`}function l(t,e){const r=String(t);if(r.length<=e)return r.padEnd(e," ");const s=t.toPrecision(e-2);if(s.length<=e)return s;const o=t.toExponential(e-2),n=o.indexOf("e"),i=o.slice(n);return o.slice(0,e-i.length)+i}function a(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 f(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 c(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 g(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,r){return{row:w(t,e),column:p(t,r)}}function w(t,e){if("object"!=typeof e)throw new TypeError("unexpected type for row indices");if(e.some(e=>e<0||e>=t.rows))throw new RangeError("row indices are out of range");return Array.isArray(e)||(e=Array.from(e)),e}function p(t,e){if("object"!=typeof e)throw new TypeError("unexpected type for column indices");if(e.some(e=>e<0||e>=t.columns))throw new RangeError("column indices are out of range");return Array.isArray(e)||(e=Array.from(e)),e}function d(t,e,r,s,o){if(5!==arguments.length)throw new RangeError("expected 4 arguments");if(b("startRow",e),b("endRow",r),b("startColumn",s),b("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 M(t,e=0){let r=[];for(let s=0;s<t;s++)r.push(e);return r}function b(t,e){if("number"!=typeof e)throw new TypeError(t+" must be a number")}class y{static from1DArray(t,e,r){if(t*e!==r.length)throw new RangeError("data length does not match given dimensions");let s=new v(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 v(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 v(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 v(t,e)}static ones(t,e){return new v(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 v(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:n=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 i=o-s,h=new v(t,e);for(let r=0;r<t;r++)for(let t=0;t<e;t++){let e=s+Math.round(n()*i);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 t=0;t<s;t++)o.set(t,t,r);return o}static diag(t,e,r){let s=t.length;void 0===e&&(e=s),void 0===r&&(r=e);let o=Math.min(s,e,r),n=this.zeros(e,r);for(let e=0;e<o;e++)n.set(e,e,t[e]);return n}static min(t,e){t=this.checkMatrix(t),e=this.checkMatrix(e);let r=t.rows,s=t.columns,o=new v(r,s);for(let n=0;n<r;n++)for(let r=0;r<s;r++)o.set(n,r,Math.min(t.get(n,r),e.get(n,r)));return o}static max(t,e){t=this.checkMatrix(t),e=this.checkMatrix(e);let r=t.rows,s=t.columns,o=new this(r,s);for(let n=0;n<r;n++)for(let r=0;r<s;r++)o.set(n,r,Math.max(t.get(n,r),e.get(n,r)));return o}static checkMatrix(t){return y.isMatrix(t)?t:new v(t)}static isMatrix(t){return null!=t&&"Matrix"===t.klass}get size(){return this.rows*this.columns}apply(t){if("function"!=typeof t)throw new TypeError("callback must be a function");for(let e=0;e<this.rows;e++)for(let r=0;r<this.columns;r++)t.call(this,e,r);return this}to1DArray(){let t=[];for(let e=0;e<this.rows;e++)for(let r=0;r<this.columns;r++)t.push(this.get(e,r));return t}to2DArray(){let t=[];for(let e=0;e<this.rows;e++){t.push([]);for(let r=0;r<this.columns;r++)t[e].push(this.get(e,r))}return t}toJSON(){return this.to2DArray()}isRowVector(){return 1===this.rows}isColumnVector(){return 1===this.columns}isVector(){return 1===this.rows||1===this.columns}isSquare(){return this.rows===this.columns}isSymmetric(){if(this.isSquare()){for(let t=0;t<this.rows;t++)for(let e=0;e<=t;e++)if(this.get(t,e)!==this.get(e,t))return!1;return!0}return!1}isEchelonForm(){let t=0,e=0,r=-1,s=!0,o=!1;for(;t<this.rows&&s;){for(e=0,o=!1;e<this.columns&&!1===o;)0===this.get(t,e)?e++:1===this.get(t,e)&&e>r?(o=!0,r=e):(s=!1,o=!0);t++}return s}isReducedEchelonForm(){let t=0,e=0,r=-1,s=!0,o=!1;for(;t<this.rows&&s;){for(e=0,o=!1;e<this.columns&&!1===o;)0===this.get(t,e)?e++:1===this.get(t,e)&&e>r?(o=!0,r=e):(s=!1,o=!0);for(let r=e+1;r<this.rows;r++)0!==this.get(t,r)&&(s=!1);t++}return s}echelonForm(){let t=this.clone(),e=0,r=0;for(;e<t.rows&&r<t.columns;){let s=e;for(let o=e;o<t.rows;o++)t.get(o,r)>t.get(s,r)&&(s=o);if(0===t.get(s,r))r++;else{t.swapRows(e,s);let o=t.get(e,r);for(let s=r;s<t.columns;s++)t.set(e,s,t.get(e,s)/o);for(let s=e+1;s<t.rows;s++){let o=t.get(s,r)/t.get(e,r);t.set(s,r,0);for(let n=r+1;n<t.columns;n++)t.set(s,n,t.get(s,n)-t.get(e,n)*o)}e++,r++}}return t}reducedEchelonForm(){let t=this.echelonForm(),e=t.columns,r=t.rows,s=r-1;for(;s>=0;)if(0===t.maxRow(s))s--;else{let o=0,n=!1;for(;o<r&&!1===n;)1===t.get(s,o)?n=!0:o++;for(let r=0;r<s;r++){let n=t.get(r,o);for(let i=o;i<e;i++){let e=t.get(r,i)-n*t.get(s,i);t.set(r,i,e)}}s--}return t}set(){throw new Error("set method is unimplemented")}get(){throw new Error("get method is 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 v(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){a(this,t);let e=[];for(let r=0;r<this.columns;r++)e.push(this.get(t,r));return e}getRowVector(t){return v.rowVector(this.getRow(t))}setRow(t,e){a(this,t),e=c(this,e);for(let r=0;r<this.columns;r++)this.set(t,r,e[r]);return this}swapRows(t,e){a(this,t),a(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){f(this,t);let e=[];for(let r=0;r<this.rows;r++)e.push(this.get(r,t));return e}getColumnVector(t){return v.columnVector(this.getColumn(t))}setColumn(t,e){f(this,t),e=g(this,e);for(let r=0;r<this.rows;r++)this.set(r,t,e[r]);return this}swapColumns(t,e){f(this,t),f(this,e);for(let r=0;r<this.rows;r++){let s=this.get(r,t);this.set(r,t,this.get(r,e)),this.set(r,e,s)}return this}addRowVector(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[r]);return this}subRowVector(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[r]);return this}mulRowVector(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[r]);return this}divRowVector(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[r]);return this}addColumnVector(t){t=g(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}subColumnVector(t){t=g(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=g(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=g(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){a(this,t);for(let r=0;r<this.columns;r++)this.set(t,r,this.get(t,r)*e);return this}mulColumn(t,e){f(this,t);for(let r=0;r<this.rows;r++)this.set(r,t,this.get(r,t)*e);return this}max(){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}maxIndex(){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(){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}minIndex(){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){a(this,t);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){a(this,t);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){a(this,t);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){a(this,t);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){f(this,t);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){f(this,t);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){f(this,t);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){f(this,t);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"){let e=0;if("max"===t)return this.max();if("frobenius"===t){for(let t=0;t<this.rows;t++)for(let r=0;r<this.columns;r++)e+=this.get(t,r)*this.get(t,r);return Math.sqrt(e)}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){y.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=v.checkMatrix(t);let e=this.rows,r=this.columns,s=t.columns,o=new v(e,s),n=new Float64Array(r);for(let i=0;i<s;i++){for(let e=0;e<r;e++)n[e]=t.get(e,i);for(let t=0;t<e;t++){let e=0;for(let s=0;s<r;s++)e+=this.get(t,s)*n[s];o.set(t,i,e)}}return o}strassen2x2(t){t=v.checkMatrix(t);let e=new v(2,2);const r=this.get(0,0),s=t.get(0,0),o=this.get(0,1),n=t.get(0,1),i=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=(i+u)*s,c=r*(n-l),g=u*(h-s),m=(r+o)*l,w=a+g-m+(o-u)*(h+l),p=c+m,d=f+g,M=a-f+c+(i-r)*(s+n);return e.set(0,0,w),e.set(0,1,p),e.set(1,0,d),e.set(1,1,M),e}strassen3x3(t){t=v.checkMatrix(t);let e=new v(3,3);const r=this.get(0,0),s=this.get(0,1),o=this.get(0,2),n=this.get(1,0),i=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),g=t.get(0,2),m=t.get(1,0),w=t.get(1,1),p=t.get(1,2),d=t.get(2,0),M=t.get(2,1),b=t.get(2,2),y=(r-n)*(-c+w),x=(-r+n+i)*(f-c+w),E=(n+i)*(-f+c),S=r*f,R=(-r+u+l)*(f-g+p),A=(-r+u)*(g-p),I=(u+l)*(-f+g),k=(-o+l+a)*(w+d-M),V=(o-a)*(w-M),T=o*d,q=(l+a)*(-d+M),C=(-o+i+h)*(p+d-b),N=(o-h)*(p-b),F=(i+h)*(-d+b),D=S+T+s*m,j=(r+s+o-n-i-l-a)*w+x+E+S+k+T+q,L=S+R+I+(r+s+o-i-h-u-l)*p+T+C+F,z=y+i*(-f+c+m-w-p-d+b)+x+S+T+C+N,P=y+x+E+S+h*M,U=T+C+N+F+n*g,$=S+R+A+l*(-f+g+m-w-p-d+M)+k+V+T,O=k+V+T+q+u*c,_=S+R+A+I+a*b;return e.set(0,0,D),e.set(0,1,j),e.set(0,2,L),e.set(1,0,z),e.set(1,1,P),e.set(1,2,U),e.set(2,0,$),e.set(2,1,O),e.set(2,2,_),e}mmulStrassen(t){t=v.checkMatrix(t);let e=this.clone(),r=e.rows,s=e.columns,o=t.rows,n=t.columns;function i(t,e,r){let s=t.rows,o=t.columns;if(s===e&&o===r)return t;{let s=y.zeros(e,r);return s=s.setSubMatrix(t,0,0),s}}s!==o&&console.warn(`Multiplying ${r} x ${s} and ${o} x ${n} matrix: dimensions do not match.`);let h=Math.max(r,o),u=Math.max(s,n);return e=i(e,h,u),function t(e,r,s,o){if(s<=512||o<=512)return e.mmul(r);s%2==1&&o%2==1?(e=i(e,s+1,o+1),r=i(r,s+1,o+1)):s%2==1?(e=i(e,s+1,o),r=i(r,s+1,o)):o%2==1&&(e=i(e,s,o+1),r=i(r,s,o+1));let n=parseInt(e.rows/2,10),h=parseInt(e.columns/2,10),u=e.subMatrix(0,n-1,0,h-1),l=r.subMatrix(0,n-1,0,h-1),a=e.subMatrix(0,n-1,h,e.columns-1),f=r.subMatrix(0,n-1,h,r.columns-1),c=e.subMatrix(n,e.rows-1,0,h-1),g=r.subMatrix(n,r.rows-1,0,h-1),m=e.subMatrix(n,e.rows-1,h,e.columns-1),w=r.subMatrix(n,r.rows-1,h,r.columns-1),p=t(y.add(u,m),y.add(l,w),n,h),d=t(y.add(c,m),l,n,h),M=t(u,y.sub(f,w),n,h),b=t(m,y.sub(g,l),n,h),x=t(y.add(u,a),w,n,h),v=t(y.sub(c,u),y.add(l,f),n,h),E=t(y.sub(a,m),y.add(g,w),n,h),S=y.add(p,b);S.sub(x),S.add(E);let R=y.add(M,x),A=y.add(d,b),I=y.sub(p,d);I.add(M),I.add(v);let k=y.zeros(2*S.rows,2*S.columns);return k=k.setSubMatrix(S,0,0),k=k.setSubMatrix(R,S.rows,0),k=k.setSubMatrix(A,0,S.columns),k=k.setSubMatrix(I,S.rows,S.columns),k.subMatrix(0,s-1,0,o-1)}(e,t=i(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 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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 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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,Math.pow(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,Math.pow(this.get(e,r),t.get(e,r)));return this}}(y,v);class E extends y{constructor(t,e,r){super(),this.matrix=t,this.rows=e,this.columns=r}}class S extends E{constructor(t,e,r){let s=m(t,e,r);super(t,s.row.length,s.column.length),this.rowIndices=s.row,this.columnIndices=s.column}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 R extends y{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 A extends y{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 I{constructor(t){let e,r,s,o,n,i,h,u,l,a=(t=A.checkMatrix(t)).clone(),f=a.rows,c=a.columns,g=new Float64Array(f),m=1;for(e=0;e<f;e++)g[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),n=0,s=0;s<l;s++)n+=a.get(e,s)*u[s];u[e]-=n,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++)i=a.get(o,s),a.set(o,s,a.get(r,s)),a.set(r,s,i);h=g[o],g[o]=g[r],g[r]=h,m=-m}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=g,this.pivotSign=m}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=v.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,n=t.columns,i=t.subMatrixRow(this.pivotVector,0,n-1),h=e.columns;for(o=0;o<h;o++)for(r=o+1;r<h;r++)for(s=0;s<n;s++)i.set(r,s,i.get(r,s)-i.get(o,s)*e.get(r,o));for(o=h-1;o>=0;o--){for(s=0;s<n;s++)i.set(o,s,i.get(o,s)/e.get(o,o));for(r=0;r<o;r++)for(s=0;s<n;s++)i.set(r,s,i.get(r,s)-i.get(o,s)*e.get(r,o))}return i}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 v(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 v(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 k(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,n=(t=A.checkMatrix(t)).clone(),i=t.rows,h=t.columns,u=new Float64Array(h);for(s=0;s<h;s++){let t=0;for(e=s;e<i;e++)t=k(t,n.get(e,s));if(0!==t){for(n.get(s,s)<0&&(t=-t),e=s;e<i;e++)n.set(e,s,n.get(e,s)/t);for(n.set(s,s,n.get(s,s)+1),r=s+1;r<h;r++){for(o=0,e=s;e<i;e++)o+=n.get(e,s)*n.get(e,r);for(o=-o/n.get(s,s),e=s;e<i;e++)n.set(e,r,n.get(e,r)+o*n.get(e,s))}}u[s]=-t}this.QR=n,this.Rdiag=u}solve(t){t=v.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,n,i,h=t.columns,u=t.clone(),l=e.columns;for(n=0;n<l;n++)for(o=0;o<h;o++){for(i=0,s=n;s<r;s++)i+=e.get(s,n)*u.get(s,o);for(i=-i/e.get(n,n),s=n;s<r;s++)u.set(s,o,u.get(s,o)+i*e.get(s,n))}for(n=l-1;n>=0;n--){for(o=0;o<h;o++)u.set(n,o,u.get(n,o)/this.Rdiag[n]);for(s=0;s<n;s++)for(o=0;o<h;o++)u.set(s,o,u.get(s,o)-u.get(n,o)*e.get(s,n))}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 v(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,n=o.rows,i=o.columns,h=new v(n,i);for(r=i-1;r>=0;r--){for(t=0;t<n;t++)h.set(t,r,0);for(h.set(r,r,1),e=r;e<i;e++)if(0!==o.get(r,r)){for(s=0,t=r;t<n;t++)s+=o.get(t,r)*h.get(t,e);for(s=-s/o.get(r,r),t=r;t<n;t++)h.set(t,e,h.get(t,e)+s*o.get(t,r))}}return h}}class T{constructor(t,e={}){let r=(t=A.checkMatrix(t)).rows,s=t.columns;const{computeLeftSingularVectors:o=!0,computeRightSingularVectors:n=!0,autoTranspose:i=!1}=e;let h,u=Boolean(o),l=Boolean(n),a=!1;if(r<s)if(i){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),g=new Float64Array(c),m=new v(r,f),w=new v(s,s),p=new Float64Array(s),d=new Float64Array(r),M=new Float64Array(c);for(let t=0;t<c;t++)M[t]=t;let b=Math.min(r-1,s),y=Math.max(0,Math.min(s-2,r)),x=Math.max(b,y);for(let t=0;t<x;t++){if(t<b){g[t]=0;for(let e=t;e<r;e++)g[t]=k(g[t],h.get(e,t));if(0!==g[t]){h.get(t,t)<0&&(g[t]=-g[t]);for(let e=t;e<r;e++)h.set(e,t,h.get(e,t)/g[t]);h.set(t,t,h.get(t,t)+1)}g[t]=-g[t]}for(let e=t+1;e<s;e++){if(t<b&&0!==g[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<b)for(let e=t;e<r;e++)m.set(e,t,h.get(e,t));if(t<y){p[t]=0;for(let e=t+1;e<s;e++)p[t]=k(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 E=Math.min(s,r+1);if(b<s&&(g[b]=h.get(b,b)),r<E&&(g[E-1]=0),y+1<E&&(p[y]=h.get(y,E-1)),p[E-1]=0,u){for(let t=b;t<f;t++){for(let e=0;e<r;e++)m.set(e,t,0);m.set(t,t,1)}for(let t=b-1;t>=0;t--)if(0!==g[t]){for(let e=t+1;e<f;e++){let s=0;for(let o=t;o<r;o++)s+=m.get(o,t)*m.get(o,e);s=-s/m.get(t,t);for(let o=t;o<r;o++)m.set(o,e,m.get(o,e)+s*m.get(o,t))}for(let e=t;e<r;e++)m.set(e,t,-m.get(e,t));m.set(t,t,1+m.get(t,t));for(let e=0;e<t-1;e++)m.set(e,t,0)}else{for(let e=0;e<r;e++)m.set(e,t,0);m.set(t,t,1)}}if(l)for(let t=s-1;t>=0;t--){if(t<y&&0!==p[t])for(let e=t+1;e<s;e++){let r=0;for(let o=t+1;o<s;o++)r+=w.get(o,t)*w.get(o,e);r=-r/w.get(t+1,t);for(let o=t+1;o<s;o++)w.set(o,e,w.get(o,e)+r*w.get(o,t))}for(let e=0;e<s;e++)w.set(e,t,0);w.set(t,t,1)}let S=E-1,R=Number.EPSILON;for(;E>0;){let t,e;for(t=E-2;t>=-1&&-1!==t;t--){const e=Number.MIN_VALUE+R*Math.abs(g[t]+Math.abs(g[t+1]));if(Math.abs(p[t])<=e||Number.isNaN(p[t])){p[t]=0;break}}if(t===E-2)e=4;else{let r;for(r=E-1;r>=t&&r!==t;r--){let e=(r!==E?Math.abs(p[r]):0)+(r!==t+1?Math.abs(p[r-1]):0);if(Math.abs(g[r])<=R*e){g[r]=0;break}}r===t?e=3:r===E-1?e=1:(e=2,t=r)}switch(t++,e){case 1:{let e=p[E-2];p[E-2]=0;for(let r=E-2;r>=t;r--){let o=k(g[r],e),n=g[r]/o,i=e/o;if(g[r]=o,r!==t&&(e=-i*p[r-1],p[r-1]=n*p[r-1]),l)for(let t=0;t<s;t++)o=n*w.get(t,r)+i*w.get(t,E-1),w.set(t,E-1,-i*w.get(t,r)+n*w.get(t,E-1)),w.set(t,r,o)}break}case 2:{let e=p[t-1];p[t-1]=0;for(let s=t;s<E;s++){let o=k(g[s],e),n=g[s]/o,i=e/o;if(g[s]=o,e=-i*p[s],p[s]=n*p[s],u)for(let e=0;e<r;e++)o=n*m.get(e,s)+i*m.get(e,t-1),m.set(e,t-1,-i*m.get(e,s)+n*m.get(e,t-1)),m.set(e,s,o)}break}case 3:{const e=Math.max(Math.abs(g[E-1]),Math.abs(g[E-2]),Math.abs(p[E-2]),Math.abs(g[t]),Math.abs(p[t])),o=g[E-1]/e,n=g[E-2]/e,i=p[E-2]/e,h=g[t]/e,a=p[t]/e,f=((n+o)*(n-o)+i*i)/2,c=o*i*(o*i);let d=0;0===f&&0===c||(d=f<0?0-Math.sqrt(f*f+c):Math.sqrt(f*f+c),d=c/(f+d));let M=(h+o)*(h-o)+d,b=h*a;for(let e=t;e<E-1;e++){let o=k(M,b);0===o&&(o=Number.MIN_VALUE);let n=M/o,i=b/o;if(e!==t&&(p[e-1]=o),M=n*g[e]+i*p[e],p[e]=n*p[e]-i*g[e],b=i*g[e+1],g[e+1]=n*g[e+1],l)for(let t=0;t<s;t++)o=n*w.get(t,e)+i*w.get(t,e+1),w.set(t,e+1,-i*w.get(t,e)+n*w.get(t,e+1)),w.set(t,e,o);if(o=k(M,b),0===o&&(o=Number.MIN_VALUE),n=M/o,i=b/o,g[e]=o,M=n*p[e]+i*g[e+1],g[e+1]=-i*p[e]+n*g[e+1],b=i*p[e+1],p[e+1]=n*p[e+1],u&&e<r-1)for(let t=0;t<r;t++)o=n*m.get(t,e)+i*m.get(t,e+1),m.set(t,e+1,-i*m.get(t,e)+n*m.get(t,e+1)),m.set(t,e,o)}p[E-2]=M;break}case 4:if(g[t]<=0&&(g[t]=g[t]<0?-g[t]:0,l))for(let e=0;e<=S;e++)w.set(e,t,-w.get(e,t));for(;t<S&&!(g[t]>=g[t+1]);){let e=g[t];if(g[t]=g[t+1],g[t+1]=e,l&&t<s-1)for(let r=0;r<s;r++)e=w.get(r,t+1),w.set(r,t+1,w.get(r,t)),w.set(r,t,e);if(u&&t<r-1)for(let s=0;s<r;s++)e=m.get(s,t+1),m.set(s,t+1,m.get(s,t)),m.set(s,t,e);t++}E--}}if(a){let t=w;w=m,m=t}this.m=r,this.n=s,this.s=g,this.U=m,this.V=w}solve(t){let e=t,r=this.threshold,s=this.s.length,o=v.zeros(s,s);for(let t=0;t<s;t++)Math.abs(this.s[t])<=r?o.set(t,t,0):o.set(t,t,1/this.s[t]);let n=this.U,i=this.rightSingularVectors,h=i.mmul(o),u=i.rows,l=n.rows,a=v.zeros(u,l);for(let t=0;t<u;t++)for(let e=0;e<l;e++){let r=0;for(let o=0;o<s;o++)r+=h.get(t,o)*n.get(e,o);a.set(t,e,r)}return a.mmul(e)}solveForDiagonal(t){return this.solve(v.diag(t))}inverse(){let t=this.V,e=this.threshold,r=t.rows,s=t.columns,o=new v(r,this.s.length);for(let n=0;n<r;n++)for(let r=0;r<s;r++)Math.abs(this.s[r])>e&&o.set(n,r,t.get(n,r)/this.s[r]);let n=this.U,i=n.rows,h=n.columns,u=new v(r,i);for(let t=0;t<r;t++)for(let e=0;e<i;e++){let r=0;for(let s=0;s<h;s++)r+=o.get(t,s)*n.get(e,s);u.set(t,e,r)}return u}get condition(){return this.s[0]/this.s[Math.min(this.m,this.n)-1]}get norm2(){return this.s[0]}get rank(){let t=Math.max(this.m,this.n)*this.s[0]*Number.EPSILON,e=0,r=this.s;for(let s=0,o=r.length;s<o;s++)r[s]>t&&e++;return e}get diagonal(){return Array.from(this.s)}get threshold(){return Number.EPSILON/2*Math.max(this.m,this.n)*this.s[0]}get leftSingularVectors(){return this.U}get rightSingularVectors(){return this.V}get diagonalMatrix(){return v.diag(this.s)}}function q(t,e,r=!1){return t=A.checkMatrix(t),e=A.checkMatrix(e),r?new T(t).solve(e):t.isSquare()?new I(t).solve(e):new V(t).solve(e)}function C(t,e){let r=[];for(let s=0;s<t;s++)s!==e&&r.push(s);return r}function N(t,e,r,s=1e-9,o=1e-9){if(t>o)return new Array(e.rows+1).fill(0);{let t=e.addRow(r,[0]);for(let e=0;e<t.rows;e++)Math.abs(t.get(e,0))<s&&t.set(e,0,0);return t.to1DArray()}}class F{constructor(t,e={}){const{assumeSymmetric:r=!1}=e;if(!(t=A.checkMatrix(t)).isSquare())throw new Error("Matrix is not a square matrix");let s,o,n=t.columns,i=new v(n,n),h=new Float64Array(n),u=new Float64Array(n),l=t,a=!1;if(a=!!r||t.isSymmetric(),a){for(s=0;s<n;s++)for(o=0;o<n;o++)i.set(s,o,l.get(s,o));!function(t,e,r,s){let o,n,i,h,u,l,a,f;for(u=0;u<t;u++)r[u]=s.get(t-1,u);for(h=t-1;h>0;h--){for(f=0,i=0,l=0;l<h;l++)f+=Math.abs(r[l]);if(0===f)for(e[h]=r[h-1],u=0;u<h;u++)r[u]=s.get(h-1,u),s.set(h,u,0),s.set(u,h,0);else{for(l=0;l<h;l++)r[l]/=f,i+=r[l]*r[l];for(o=r[h-1],n=Math.sqrt(i),o>0&&(n=-n),e[h]=f*n,i-=o*n,r[h-1]=o-n,u=0;u<h;u++)e[u]=0;for(u=0;u<h;u++){for(o=r[u],s.set(u,h,o),n=e[u]+s.get(u,u)*o,l=u+1;l<=h-1;l++)n+=s.get(l,u)*r[l],e[l]+=s.get(l,u)*o;e[u]=n}for(o=0,u=0;u<h;u++)e[u]/=i,o+=e[u]*r[u];for(a=o/(i+i),u=0;u<h;u++)e[u]-=a*r[u];for(u=0;u<h;u++){for(o=r[u],n=e[u],l=u;l<=h-1;l++)s.set(l,u,s.get(l,u)-(o*e[l]+n*r[l]));r[u]=s.get(h-1,u),s.set(h,u,0)}}r[h]=i}for(h=0;h<t-1;h++){if(s.set(t-1,h,s.get(h,h)),s.set(h,h,1),i=r[h+1],0!==i){for(l=0;l<=h;l++)r[l]=s.get(l,h+1)/i;for(u=0;u<=h;u++){for(n=0,l=0;l<=h;l++)n+=s.get(l,h+1)*s.get(l,u);for(l=0;l<=h;l++)s.set(l,u,s.get(l,u)-n*r[l])}}for(l=0;l<=h;l++)s.set(l,h+1,0)}for(u=0;u<t;u++)r[u]=s.get(t-1,u),s.set(t-1,u,0);s.set(t-1,t-1,1),e[0]=0}(n,u,h,i),function(t,e,r,s){let o,n,i,h,u,l,a,f,c,g,m,w,p,d,M,b;for(i=1;i<t;i++)e[i-1]=e[i];e[t-1]=0;let y=0,x=0,v=Number.EPSILON;for(l=0;l<t;l++){for(x=Math.max(x,Math.abs(r[l])+Math.abs(e[l])),a=l;a<t&&!(Math.abs(e[a])<=v*x);)a++;if(a>l)do{for(o=r[l],f=(r[l+1]-o)/(2*e[l]),c=k(f,1),f<0&&(c=-c),r[l]=e[l]/(f+c),r[l+1]=e[l]*(f+c),g=r[l+1],n=o-r[l],i=l+2;i<t;i++)r[i]-=n;for(y+=n,f=r[a],m=1,w=m,p=m,d=e[l+1],M=0,b=0,i=a-1;i>=l;i--)for(p=w,w=m,b=M,o=m*e[i],n=m*f,c=k(f,e[i]),e[i+1]=M*c,M=e[i]/c,m=f/c,f=m*r[i]-M*o,r[i+1]=n+M*(m*o+M*r[i]),u=0;u<t;u++)n=s.get(u,i+1),s.set(u,i+1,M*s.get(u,i)+m*n),s.set(u,i,m*s.get(u,i)-M*n);f=-M*b*p*d*e[l]/g,e[l]=M*f,r[l]=m*f}while(Math.abs(e[l])>v*x);r[l]=r[l]+y,e[l]=0}for(i=0;i<t-1;i++){for(u=i,f=r[i],h=i+1;h<t;h++)r[h]<f&&(u=h,f=r[h]);if(u!==i)for(r[u]=r[i],r[i]=f,h=0;h<t;h++)f=s.get(h,i),s.set(h,i,s.get(h,u)),s.set(h,u,f)}}(n,u,h,i)}else{let t=new v(n,n),e=new Float64Array(n);for(o=0;o<n;o++)for(s=0;s<n;s++)t.set(s,o,l.get(s,o));!function(t,e,r,s){let o,n,i,h,u,l,a,f=t-1;for(l=1;l<=f-1;l++){for(a=0,h=l;h<=f;h++)a+=Math.abs(e.get(h,l-1));if(0!==a){for(i=0,h=f;h>=l;h--)r[h]=e.get(h,l-1)/a,i+=r[h]*r[h];for(n=Math.sqrt(i),r[l]>0&&(n=-n),i-=r[l]*n,r[l]=r[l]-n,u=l;u<t;u++){for(o=0,h=f;h>=l;h--)o+=r[h]*e.get(h,u);for(o/=i,h=l;h<=f;h++)e.set(h,u,e.get(h,u)-o*r[h])}for(h=0;h<=f;h++){for(o=0,u=f;u>=l;u--)o+=r[u]*e.get(h,u);for(o/=i,u=l;u<=f;u++)e.set(h,u,e.get(h,u)-o*r[u])}r[l]=a*r[l],e.set(l,l-1,a*n)}}for(h=0;h<t;h++)for(u=0;u<t;u++)s.set(h,u,h===u?1:0);for(l=f-1;l>=1;l--)if(0!==e.get(l,l-1)){for(h=l+1;h<=f;h++)r[h]=e.get(h,l-1);for(u=l;u<=f;u++){for(n=0,h=l;h<=f;h++)n+=r[h]*s.get(h,u);for(n=n/r[l]/e.get(l,l-1),h=l;h<=f;h++)s.set(h,u,s.get(h,u)+n*r[h])}}}(n,t,e,i),function(t,e,r,s,o){let n,i,h,u,l,a,f,c,g,m,w,p,d,M,b,y=t-1,x=t-1,v=Number.EPSILON,E=0,S=0,R=0,A=0,I=0,k=0,V=0,T=0;for(n=0;n<t;n++)for((n<0||n>x)&&(r[n]=o.get(n,n),e[n]=0),i=Math.max(n-1,0);i<t;i++)S+=Math.abs(o.get(n,i));for(;y>=0;){for(u=y;u>0&&(k=Math.abs(o.get(u-1,u-1))+Math.abs(o.get(u,u)),0===k&&(k=S),!(Math.abs(o.get(u,u-1))<v*k));)u--;if(u===y)o.set(y,y,o.get(y,y)+E),r[y]=o.get(y,y),e[y]=0,y--,T=0;else if(u===y-1){if(f=o.get(y,y-1)*o.get(y-1,y),R=(o.get(y-1,y-1)-o.get(y,y))/2,A=R*R+f,V=Math.sqrt(Math.abs(A)),o.set(y,y,o.get(y,y)+E),o.set(y-1,y-1,o.get(y-1,y-1)+E),c=o.get(y,y),A>=0){for(V=R>=0?R+V:R-V,r[y-1]=c+V,r[y]=r[y-1],0!==V&&(r[y]=c-f/V),e[y-1]=0,e[y]=0,c=o.get(y,y-1),k=Math.abs(c)+Math.abs(V),R=c/k,A=V/k,I=Math.sqrt(R*R+A*A),R/=I,A/=I,i=y-1;i<t;i++)V=o.get(y-1,i),o.set(y-1,i,A*V+R*o.get(y,i)),o.set(y,i,A*o.get(y,i)-R*V);for(n=0;n<=y;n++)V=o.get(n,y-1),o.set(n,y-1,A*V+R*o.get(n,y)),o.set(n,y,A*o.get(n,y)-R*V);for(n=0;n<=x;n++)V=s.get(n,y-1),s.set(n,y-1,A*V+R*s.get(n,y)),s.set(n,y,A*s.get(n,y)-R*V)}else r[y-1]=c+R,r[y]=c+R,e[y-1]=V,e[y]=-V;y-=2,T=0}else{if(c=o.get(y,y),g=0,f=0,u<y&&(g=o.get(y-1,y-1),f=o.get(y,y-1)*o.get(y-1,y)),10===T){for(E+=c,n=0;n<=y;n++)o.set(n,n,o.get(n,n)-c);k=Math.abs(o.get(y,y-1))+Math.abs(o.get(y-1,y-2)),c=g=.75*k,f=-.4375*k*k}if(30===T&&(k=(g-c)/2,k=k*k+f,k>0)){for(k=Math.sqrt(k),g<c&&(k=-k),k=c-f/((g-c)/2+k),n=0;n<=y;n++)o.set(n,n,o.get(n,n)-k);E+=k,c=g=f=.964}for(T+=1,l=y-2;l>=u&&(V=o.get(l,l),I=c-V,k=g-V,R=(I*k-f)/o.get(l+1,l)+o.get(l,l+1),A=o.get(l+1,l+1)-V-I-k,I=o.get(l+2,l+1),k=Math.abs(R)+Math.abs(A)+Math.abs(I),R/=k,A/=k,I/=k,l!==u)&&!(Math.abs(o.get(l,l-1))*(Math.abs(A)+Math.abs(I))<v*(Math.abs(R)*(Math.abs(o.get(l-1,l-1))+Math.abs(V)+Math.abs(o.get(l+1,l+1)))));)l--;for(n=l+2;n<=y;n++)o.set(n,n-2,0),n>l+2&&o.set(n,n-3,0);for(h=l;h<=y-1&&(M=h!==y-1,h!==l&&(R=o.get(h,h-1),A=o.get(h+1,h-1),I=M?o.get(h+2,h-1):0,c=Math.abs(R)+Math.abs(A)+Math.abs(I),0!==c&&(R/=c,A/=c,I/=c)),0!==c);h++)if(k=Math.sqrt(R*R+A*A+I*I),R<0&&(k=-k),0!==k){for(h!==l?o.set(h,h-1,-k*c):u!==l&&o.set(h,h-1,-o.get(h,h-1)),R+=k,c=R/k,g=A/k,V=I/k,A/=R,I/=R,i=h;i<t;i++)R=o.get(h,i)+A*o.get(h+1,i),M&&(R+=I*o.get(h+2,i),o.set(h+2,i,o.get(h+2,i)-R*V)),o.set(h,i,o.get(h,i)-R*c),o.set(h+1,i,o.get(h+1,i)-R*g);for(n=0;n<=Math.min(y,h+3);n++)R=c*o.get(n,h)+g*o.get(n,h+1),M&&(R+=V*o.get(n,h+2),o.set(n,h+2,o.get(n,h+2)-R*I)),o.set(n,h,o.get(n,h)-R),o.set(n,h+1,o.get(n,h+1)-R*A);for(n=0;n<=x;n++)R=c*s.get(n,h)+g*s.get(n,h+1),M&&(R+=V*s.get(n,h+2),s.set(n,h+2,s.get(n,h+2)-R*I)),s.set(n,h,s.get(n,h)-R),s.set(n,h+1,s.get(n,h+1)-R*A)}}}if(0===S)return;for(y=t-1;y>=0;y--)if(R=r[y],A=e[y],0===A)for(u=y,o.set(y,y,1),n=y-1;n>=0;n--){for(f=o.get(n,n)-R,I=0,i=u;i<=y;i++)I+=o.get(n,i)*o.get(i,y);if(e[n]<0)V=f,k=I;else if(u=n,0===e[n]?o.set(n,y,0!==f?-I/f:-I/(v*S)):(c=o.get(n,n+1),g=o.get(n+1,n),A=(r[n]-R)*(r[n]-R)+e[n]*e[n],a=(c*k-V*I)/A,o.set(n,y,a),o.set(n+1,y,Math.abs(c)>Math.abs(V)?(-I-f*a)/c:(-k-g*a)/V)),a=Math.abs(o.get(n,y)),v*a*a>1)for(i=n;i<=y;i++)o.set(i,y,o.get(i,y)/a)}else if(A<0)for(u=y-1,Math.abs(o.get(y,y-1))>Math.abs(o.get(y-1,y))?(o.set(y-1,y-1,A/o.get(y,y-1)),o.set(y-1,y,-(o.get(y,y)-R)/o.get(y,y-1))):(b=D(0,-o.get(y-1,y),o.get(y-1,y-1)-R,A),o.set(y-1,y-1,b[0]),o.set(y-1,y,b[1])),o.set(y,y-1,0),o.set(y,y,1),n=y-2;n>=0;n--){for(m=0,w=0,i=u;i<=y;i++)m+=o.get(n,i)*o.get(i,y-1),w+=o.get(n,i)*o.get(i,y);if(f=o.get(n,n)-R,e[n]<0)V=f,I=m,k=w;else if(u=n,0===e[n]?(b=D(-m,-w,f,A),o.set(n,y-1,b[0]),o.set(n,y,b[1])):(c=o.get(n,n+1),g=o.get(n+1,n),p=(r[n]-R)*(r[n]-R)+e[n]*e[n]-A*A,d=2*(r[n]-R)*A,0===p&&0===d&&(p=v*S*(Math.abs(f)+Math.abs(A)+Math.abs(c)+Math.abs(g)+Math.abs(V))),b=D(c*I-V*m+A*w,c*k-V*w-A*m,p,d),o.set(n,y-1,b[0]),o.set(n,y,b[1]),Math.abs(c)>Math.abs(V)+Math.abs(A)?(o.set(n+1,y-1,(-m-f*o.get(n,y-1)+A*o.get(n,y))/c),o.set(n+1,y,(-w-f*o.get(n,y)-A*o.get(n,y-1))/c)):(b=D(-I-g*o.get(n,y-1),-k-g*o.get(n,y),V,A),o.set(n+1,y-1,b[0]),o.set(n+1,y,b[1]))),a=Math.max(Math.abs(o.get(n,y-1)),Math.abs(o.get(n,y))),v*a*a>1)for(i=n;i<=y;i++)o.set(i,y-1,o.get(i,y-1)/a),o.set(i,y,o.get(i,y)/a)}for(n=0;n<t;n++)if(n<0||n>x)for(i=n;i<t;i++)s.set(n,i,o.get(n,i));for(i=t-1;i>=0;i--)for(n=0;n<=x;n++){for(V=0,h=0;h<=Math.min(i,x);h++)V+=s.get(n,h)*o.get(h,i);s.set(n,i,V)}}(n,u,h,i,t)}this.n=n,this.e=u,this.d=h,this.V=i}get realEigenvalues(){return Array.from(this.d)}get imaginaryEigenvalues(){return Array.from(this.e)}get eigenvectorMatrix(){return this.V}get diagonalMatrix(){let t,e,r=this.n,s=this.e,o=this.d,n=new v(r,r);for(t=0;t<r;t++){for(e=0;e<r;e++)n.set(t,e,0);n.set(t,t,o[t]),s[t]>0?n.set(t,t+1,s[t]):s[t]<0&&n.set(t,t-1,s[t])}return n}}function D(t,e,r,s){let o,n;return Math.abs(r)>Math.abs(s)?(o=s/r,n=r+o*s,[(t+o*e)/n,(e-o*t)/n]):(o=r/s,n=s+o*r,[(o*t+e)/n,(o*e-t)/n])}class j{constructor(t){if(!(t=A.checkMatrix(t)).isSymmetric())throw new Error("Matrix is not symmetric");let e,r,s,o=t,n=o.rows,i=new v(n,n),h=!0;for(r=0;r<n;r++){let t=0;for(s=0;s<r;s++){let n=0;for(e=0;e<s;e++)n+=i.get(s,e)*i.get(r,e);n=(o.get(r,s)-n)/i.get(s,s),i.set(r,s,n),t+=n*n}for(t=o.get(r,r)-t,h&=t>0,i.set(r,r,Math.sqrt(Math.max(t,0))),s=r+1;s<n;s++)i.set(r,s,0)}this.L=i,this.positiveDefinite=Boolean(h)}isPositiveDefinite(){return this.positiveDefinite}solve(t){t=A.checkMatrix(t);let e=this.L,r=e.rows;if(t.rows!==r)throw new Error("Matrix dimensions do not match");if(!1===this.isPositiveDefinite())throw new Error("Matrix is not positive definite");let s,o,n,i=t.columns,h=t.clone();for(n=0;n<r;n++)for(o=0;o<i;o++){for(s=0;s<n;s++)h.set(n,o,h.get(n,o)-h.get(s,o)*e.get(n,s));h.set(n,o,h.get(n,o)/e.get(n,n))}for(n=r-1;n>=0;n--)for(o=0;o<i;o++){for(s=n+1;s<r;s++)h.set(n,o,h.get(n,o)-h.get(s,o)*e.get(s,n));h.set(n,o,h.get(n,o)/e.get(n,n))}return h}get lowerTriangularMatrix(){return this.L}}class L{constructor(t,e={}){t=A.checkMatrix(t);let{Y:r}=e;const{scaleScores:s=!1,maxIterations:o=1e3,terminationCriteria:n=1e-10}=e;let i;if(r){if(r=Array.isArray(r)&&"number"==typeof r[0]?v.columnVector(r):A.checkMatrix(r),!r.isColumnVector()||r.rows!==t.rows)throw new Error("Y must be a column vector of length X.rows");i=r}else i=t.getColumnVector(0);let h,u,l,a,f=1;for(let e=0;e<o&&f>n;e++)l=t.transpose().mmul(i).div(i.transpose().mmul(i).get(0,0)),l=l.div(l.norm()),h=t.mmul(l).div(l.transpose().mmul(l).get(0,0)),e>0&&(f=h.clone().sub(a).pow(2).sum()),a=h.clone(),r?(u=r.transpose().mmul(h).div(h.transpose().mmul(h).get(0,0)),u=u.div(u.norm()),i=r.mmul(u).div(u.transpose().mmul(u).get(0,0))):i=h;if(r){let e=t.transpose().mmul(h).div(h.transpose().mmul(h).get(0,0));e=e.div(e.norm());let s=t.clone().sub(h.clone().mmul(e.transpose())),o=i.transpose().mmul(h).div(h.transpose().mmul(h).get(0,0)),n=r.clone().sub(h.clone().mulS(o.get(0,0)).mmul(u.transpose()));this.t=h,this.p=e.transpose(),this.w=l.transpose(),this.q=u,this.u=i,this.s=h.transpose().mmul(h),this.xResidual=s,this.yResidual=n,this.betas=o}else this.w=l.transpose(),this.s=h.transpose().mmul(h).sqrt(),this.t=s?h.clone().div(this.s.get(0,0)):h,this.xResidual=t.sub(h.mmul(l.transpose()))}}t.AbstractMatrix=y,t.CHO=j,t.CholeskyDecomposition=j,t.EVD=F,t.EigenvalueDecomposition=F,t.LU=I,t.LuDecomposition=I,t.Matrix=v,t.MatrixColumnSelectionView=class extends E{constructor(t,e){e=p(t,e),super(t,t.rows,e.length),this.columnIndices=e}set(t,e,r){return this.matrix.set(t,this.columnIndices[e],r),this}get(t,e){return this.matrix.get(t,this.columnIndices[e])}},t.MatrixColumnView=class extends E{constructor(t,e){f(t,e),super(t,t.rows,1),this.column=e}set(t,e,r){return this.matrix.set(t,this.column,r),this}get(t){return this.matrix.get(t,this.column)}},t.MatrixFlipColumnView=class extends E{constructor(t){super(t,t.rows,t.columns)}set(t,e,r){return this.matrix.set(t,this.columns-e-1,r),this}get(t,e){return this.matrix.get(t,this.columns-e-1)}},t.MatrixFlipRowView=class extends E{constructor(t){super(t,t.rows,t.columns)}set(t,e,r){return this.matrix.set(this.rows-t-1,e,r),this}get(t,e){return this.matrix.get(this.rows-t-1,e)}},t.MatrixRowSelectionView=class extends E{constructor(t,e){super(t,(e=w(t,e)).length,t.columns),this.rowIndices=e}set(t,e,r){return this.matrix.set(this.rowIndices[t],e,r),this}get(t,e){return this.matrix.get(this.rowIndices[t],e)}},t.MatrixRowView=class extends E{constructor(t,e){a(t,e),super(t,1,t.columns),this.row=e}set(t,e,r){return this.matrix.set(this.row,e,r),this}get(t,e){return this.matrix.get(this.row,e)}},t.MatrixSelectionView=S,t.MatrixSubView=class extends E{constructor(t,e,r,s,o){d(t,e,r,s,o),super(t,r-e+1,o-s+1),this.startRow=e,this.startColumn=s}set(t,e,r){return this.matrix.set(this.startRow+t,this.startColumn+e,r),this}get(t,e){return this.matrix.get(this.startRow+t,this.startColumn+e)}},t.MatrixTransposeView=class extends E{constructor(t){super(t,t.columns,t.rows)}set(t,e,r){return this.matrix.set(e,t,r),this}get(t,e){return this.matrix.get(e,t)}},t.NIPALS=L,t.Nipals=L,t.QR=V,t.QrDecomposition=V,t.SVD=T,t.SingularValueDecomposition=T,t.WrapperMatrix1D=R,t.WrapperMatrix2D=A,t.correlation=function(t,e=t,r={}){t=new v(t);let s=!1;if("object"!=typeof e||v.isMatrix(e)||Array.isArray(e)?e=new v(e):(r=e,e=t,s=!0),t.rows!==e.rows)throw new TypeError("Both matrices must have the same number of rows");const{center:o=!0,scale:n=!0}=r;o&&(t.center("column"),s||e.center("column")),n&&(t.scale("column"),s||e.scale("column"));const i=t.standardDeviation("column",{unbiased:!0}),h=s?i:e.standardDeviation("column",{unbiased:!0}),u=t.transpose().mmul(e);for(let e=0;e<u.rows;e++)for(let r=0;r<u.columns;r++)u.set(e,r,u.get(e,r)*(1/(i[e]*h[r]))*(1/(t.rows-1)));return u},t.covariance=function(t,e=t,r={}){t=new v(t);let s=!1;if("object"!=typeof e||v.isMatrix(e)||Array.isArray(e)?e=new v(e):(r=e,e=t,s=!0),t.rows!==e.rows)throw new TypeError("Both matrices must have the same number of rows");const{center:o=!0}=r;o&&(t=t.center("column"),s||(e=e.center("column")));const n=t.transpose().mmul(e);for(let e=0;e<n.rows;e++)for(let r=0;r<n.columns;r++)n.set(e,r,n.get(e,r)*(1/(t.rows-1)));return n},t.default=v,t.determinant=function t(e){if((e=v.checkMatrix(e)).isSquare()){let r,s,o,n;if(2===e.columns)return r=e.get(0,0),s=e.get(0,1),o=e.get(1,0),n=e.get(1,1),r*n-s*o;if(3===e.columns){let n,i,h;return n=new S(e,[1,2],[1,2]),i=new S(e,[1,2],[0,2]),h=new S(e,[1,2],[0,1]),r=e.get(0,0),s=e.get(0,1),o=e.get(0,2),r*t(n)-s*t(i)+o*t(h)}return new I(e).determinant}throw Error("determinant can only be calculated for a square matrix")},t.inverse=function(t,e=!1){return t=A.checkMatrix(t),e?new T(t).inverse():q(t,v.eye(t.rows))},t.linearDependencies=function(t,e={}){const{thresholdValue:r=1e-9,thresholdError:s=1e-9}=e;let o=(t=v.checkMatrix(t)).rows,n=new v(o,o);for(let e=0;e<o;e++){let i=v.columnVector(t.getRow(e)),h=t.subMatrixRow(C(o,e)).transpose(),u=new T(h).solve(i),l=v.sub(i,h.mmul(u)).abs().max();n.setRow(e,N(l,u,e,r,s))}return n},t.pseudoInverse=function(t,e=Number.EPSILON){t=v.checkMatrix(t);let r=new T(t,{autoTranspose:!0}),s=r.leftSingularVectors,o=r.rightSingularVectors,n=r.diagonal;for(let t=0;t<n.length;t++)Math.abs(n[t])>e?n[t]=1/n[t]:n[t]=0;return o.mmul(v.diag(n).mmul(s.transpose()))},t.solve=q,t.wrap=function(t,e){if(Array.isArray(t))return t[0]&&Array.isArray(t[0])?new A(t):new R(t,e);throw new Error("the argument is not an array")},Object.defineProperty(t,"__esModule",{value:!0})}));
+!function(t,e){"object"==typeof exports&&"undefined"!=typeof module?e(exports):"function"==typeof define&&define.amd?define(["exports"],e):e((t="undefined"!=typeof globalThis?globalThis:t||self).mlMatrix={})}(this,(function(t){"use strict";const e=Object.prototype.toString;function r(t){return e.call(t).endsWith("Array]")}function s(t){var e=arguments.length>1&&void 0!==arguments[1]?arguments[1]:{};if(!r(t))throw new TypeError("input must be an array");if(0===t.length)throw new TypeError("input must not be empty");var s=e.fromIndex,o=void 0===s?0:s,n=e.toIndex,i=void 0===n?t.length:n;if(o<0||o>=t.length||!Number.isInteger(o))throw new Error("fromIndex must be a positive integer smaller than length");if(i<=o||i>t.length||!Number.isInteger(i))throw new Error("toIndex must be an integer greater than fromIndex and at most equal to length");for(var h=t[o],u=o+1;u<i;u++)t[u]>h&&(h=t[u]);return h}function o(t){var e=arguments.length>1&&void 0!==arguments[1]?arguments[1]:{};if(!r(t))throw new TypeError("input must be an array");if(0===t.length)throw new TypeError("input must not be empty");var s=e.fromIndex,o=void 0===s?0:s,n=e.toIndex,i=void 0===n?t.length:n;if(o<0||o>=t.length||!Number.isInteger(o))throw new Error("fromIndex must be a positive integer smaller than length");if(i<=o||i>t.length||!Number.isInteger(i))throw new Error("toIndex must be an integer greater than fromIndex and at most equal to length");for(var h=t[o],u=o+1;u<i;u++)t[u]<h&&(h=t[u]);return h}function n(t){var e,n=arguments.length>1&&void 0!==arguments[1]?arguments[1]:{};if(!r(t))throw new TypeError("input must be an array");if(0===t.length)throw new TypeError("input must not be empty");if(void 0!==n.output){if(!r(n.output))throw new TypeError("output option must be an array if specified");e=n.output}else e=new Array(t.length);var i=o(t),h=s(t);if(i===h)throw new RangeError("minimum and maximum input values are equal. 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a(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 f(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 c(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 g(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,r){return{row:w(t,e),column:p(t,r)}}function w(t,e){if("object"!=typeof e)throw new TypeError("unexpected type for row indices");if(e.some((e=>e<0||e>=t.rows)))throw new RangeError("row indices are out of range");return Array.isArray(e)||(e=Array.from(e)),e}function p(t,e){if("object"!=typeof e)throw new TypeError("unexpected type for column indices");if(e.some((e=>e<0||e>=t.columns)))throw new RangeError("column indices are out of range");return 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be an array");return function(t,e,r){const s=t.rows,o=t.columns,n=[];for(let i=0;i<o;i++){let o=0,h=0,u=0;for(let e=0;e<s;e++)u=t.get(e,i)-r[i],o+=u,h+=u*u;e?n.push((h-o*o/s)/(s-1)):n.push((h-o*o/s)/s)}return n}(this,r,s);case void 0:if("number"!=typeof s)throw new TypeError("mean must be a number");return function(t,e,r){const s=t.rows,o=t.columns,n=s*o;let i=0,h=0,u=0;for(let e=0;e<s;e++)for(let s=0;s<o;s++)u=t.get(e,s)-r,i+=u,h+=u*u;return e?(h-i*i/n)/(n-1):(h-i*i/n)/n}(this,r,s);default:throw new Error("invalid option: "+t)}}standardDeviation(t,e){"object"==typeof t&&(e=t,t=void 0);const r=this.variance(t,e);if(void 0===t)return Math.sqrt(r);for(let t=0;t<r.length;t++)r[t]=Math.sqrt(r[t]);return r}center(t,e={}){if("object"==typeof t&&(e=t,t=void 0),"object"!=typeof e)throw new TypeError("options must be an object");const{center:r=this.mean(t)}=e;switch(t){case"row":if(!Array.isArray(r))throw new TypeError("center must be an array");return function(t,e){for(let r=0;r<t.rows;r++)for(let s=0;s<t.columns;s++)t.set(r,s,t.get(r,s)-e[r])}(this,r),this;case"column":if(!Array.isArray(r))throw new TypeError("center must be an array");return function(t,e){for(let r=0;r<t.rows;r++)for(let s=0;s<t.columns;s++)t.set(r,s,t.get(r,s)-e[s])}(this,r),this;case void 0:if("number"!=typeof r)throw new TypeError("center must be a number");return function(t,e){for(let r=0;r<t.rows;r++)for(let s=0;s<t.columns;s++)t.set(r,s,t.get(r,s)-e)}(this,r),this;default:throw new Error("invalid option: "+t)}}scale(t,e={}){if("object"==typeof t&&(e=t,t=void 0),"object"!=typeof e)throw new TypeError("options must be an object");let r=e.scale;switch(t){case"row":if(void 0===r)r=function(t){const e=[];for(let r=0;r<t.rows;r++){let s=0;for(let e=0;e<t.columns;e++)s+=Math.pow(t.get(r,e),2)/(t.columns-1);e.push(Math.sqrt(s))}return e}(this);else if(!Array.isArray(r))throw new TypeError("scale must be an array");return function(t,e){for(let r=0;r<t.rows;r++)for(let s=0;s<t.columns;s++)t.set(r,s,t.get(r,s)/e[r])}(this,r),this;case"column":if(void 0===r)r=function(t){const e=[];for(let r=0;r<t.columns;r++){let s=0;for(let e=0;e<t.rows;e++)s+=Math.pow(t.get(e,r),2)/(t.rows-1);e.push(Math.sqrt(s))}return e}(this);else if(!Array.isArray(r))throw new TypeError("scale must be an array");return function(t,e){for(let r=0;r<t.rows;r++)for(let s=0;s<t.columns;s++)t.set(r,s,t.get(r,s)/e[s])}(this,r),this;case void 0:if(void 0===r)r=function(t){const e=t.size-1;let r=0;for(let s=0;s<t.columns;s++)for(let o=0;o<t.rows;o++)r+=Math.pow(t.get(o,s),2)/e;return Math.sqrt(r)}(this);else if("number"!=typeof r)throw new TypeError("scale must be a number");return function(t,e){for(let r=0;r<t.rows;r++)for(let s=0;s<t.columns;s++)t.set(r,s,t.get(r,s)/e)}(this,r),this;default:throw new Error("invalid option: "+t)}}toString(t){return u(this,t)}}function x(t,e){return t-e}y.prototype.klass="Matrix","undefined"!=typeof Symbol&&(y.prototype[Symbol.for("nodejs.util.inspect.custom")]=function(){return u(this)}),y.random=y.rand,y.randomInt=y.randInt,y.diagonal=y.diag,y.prototype.diagonal=y.prototype.diag,y.identity=y.eye,y.prototype.negate=y.prototype.neg,y.prototype.tensorProduct=y.prototype.kroneckerProduct;class v extends y{constructor(t,e){if(super(),v.isMatrix(t))return t.clone();if(Number.isInteger(t)&&t>0){if(this.data=[],!(Number.isInteger(e)&&e>0))throw new TypeError("nColumns must be a positive integer");for(let r=0;r<t;r++)this.data.push(new Float64Array(e))}else{if(!Array.isArray(t))throw new TypeError("First argument must be a positive number or an array");{const r=t;if(t=r.length,"number"!=typeof(e=r[0].length)||0===e)throw new TypeError("Data must be a 2D array with at least one element");this.data=[];for(let s=0;s<t;s++){if(r[s].length!==e)throw new RangeError("Inconsistent array dimensions");this.data.push(Float64Array.from(r[s]))}}}this.rows=t,this.columns=e}set(t,e,r){return 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this.columns+=1,this}}!function(t,e){t.prototype.add=function(t){return"number"==typeof t?this.addS(t):this.addM(t)},t.prototype.addS=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.addM=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.add=function(t,r){return new e(t).add(r)},t.prototype.sub=function(t){return"number"==typeof t?this.subS(t):this.subM(t)},t.prototype.subS=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.subM=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 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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 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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,Math.pow(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,Math.pow(this.get(e,r),t.get(e,r)));return this}}(y,v);class E extends y{constructor(t,e,r){super(),this.matrix=t,this.rows=e,this.columns=r}}class S extends E{constructor(t,e,r){let s=m(t,e,r);super(t,s.row.length,s.column.length),this.rowIndices=s.row,this.columnIndices=s.column}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 R extends y{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 A extends y{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 I{constructor(t){let e,r,s,o,n,i,h,u,l,a=(t=A.checkMatrix(t)).clone(),f=a.rows,c=a.columns,g=new Float64Array(f),m=1;for(e=0;e<f;e++)g[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),n=0,s=0;s<l;s++)n+=a.get(e,s)*u[s];u[e]-=n,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++)i=a.get(o,s),a.set(o,s,a.get(r,s)),a.set(r,s,i);h=g[o],g[o]=g[r],g[r]=h,m=-m}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=g,this.pivotSign=m}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=v.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,n=t.columns,i=t.subMatrixRow(this.pivotVector,0,n-1),h=e.columns;for(o=0;o<h;o++)for(r=o+1;r<h;r++)for(s=0;s<n;s++)i.set(r,s,i.get(r,s)-i.get(o,s)*e.get(r,o));for(o=h-1;o>=0;o--){for(s=0;s<n;s++)i.set(o,s,i.get(o,s)/e.get(o,o));for(r=0;r<o;r++)for(s=0;s<n;s++)i.set(r,s,i.get(r,s)-i.get(o,s)*e.get(r,o))}return i}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 v(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 v(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 k(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,n=(t=A.checkMatrix(t)).clone(),i=t.rows,h=t.columns,u=new Float64Array(h);for(s=0;s<h;s++){let t=0;for(e=s;e<i;e++)t=k(t,n.get(e,s));if(0!==t){for(n.get(s,s)<0&&(t=-t),e=s;e<i;e++)n.set(e,s,n.get(e,s)/t);for(n.set(s,s,n.get(s,s)+1),r=s+1;r<h;r++){for(o=0,e=s;e<i;e++)o+=n.get(e,s)*n.get(e,r);for(o=-o/n.get(s,s),e=s;e<i;e++)n.set(e,r,n.get(e,r)+o*n.get(e,s))}}u[s]=-t}this.QR=n,this.Rdiag=u}solve(t){t=v.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,n,i,h=t.columns,u=t.clone(),l=e.columns;for(n=0;n<l;n++)for(o=0;o<h;o++){for(i=0,s=n;s<r;s++)i+=e.get(s,n)*u.get(s,o);for(i=-i/e.get(n,n),s=n;s<r;s++)u.set(s,o,u.get(s,o)+i*e.get(s,n))}for(n=l-1;n>=0;n--){for(o=0;o<h;o++)u.set(n,o,u.get(n,o)/this.Rdiag[n]);for(s=0;s<n;s++)for(o=0;o<h;o++)u.set(s,o,u.get(s,o)-u.get(n,o)*e.get(s,n))}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 v(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,n=o.rows,i=o.columns,h=new v(n,i);for(r=i-1;r>=0;r--){for(t=0;t<n;t++)h.set(t,r,0);for(h.set(r,r,1),e=r;e<i;e++)if(0!==o.get(r,r)){for(s=0,t=r;t<n;t++)s+=o.get(t,r)*h.get(t,e);for(s=-s/o.get(r,r),t=r;t<n;t++)h.set(t,e,h.get(t,e)+s*o.get(t,r))}}return h}}class T{constructor(t,e={}){let r=(t=A.checkMatrix(t)).rows,s=t.columns;const{computeLeftSingularVectors:o=!0,computeRightSingularVectors:n=!0,autoTranspose:i=!1}=e;let h,u=Boolean(o),l=Boolean(n),a=!1;if(r<s)if(i){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),g=new Float64Array(c),m=new v(r,f),w=new v(s,s),p=new Float64Array(s),d=new Float64Array(r),M=new Float64Array(c);for(let t=0;t<c;t++)M[t]=t;let b=Math.min(r-1,s),y=Math.max(0,Math.min(s-2,r)),x=Math.max(b,y);for(let t=0;t<x;t++){if(t<b){g[t]=0;for(let e=t;e<r;e++)g[t]=k(g[t],h.get(e,t));if(0!==g[t]){h.get(t,t)<0&&(g[t]=-g[t]);for(let e=t;e<r;e++)h.set(e,t,h.get(e,t)/g[t]);h.set(t,t,h.get(t,t)+1)}g[t]=-g[t]}for(let e=t+1;e<s;e++){if(t<b&&0!==g[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<b)for(let e=t;e<r;e++)m.set(e,t,h.get(e,t));if(t<y){p[t]=0;for(let e=t+1;e<s;e++)p[t]=k(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 E=Math.min(s,r+1);if(b<s&&(g[b]=h.get(b,b)),r<E&&(g[E-1]=0),y+1<E&&(p[y]=h.get(y,E-1)),p[E-1]=0,u){for(let t=b;t<f;t++){for(let e=0;e<r;e++)m.set(e,t,0);m.set(t,t,1)}for(let t=b-1;t>=0;t--)if(0!==g[t]){for(let e=t+1;e<f;e++){let s=0;for(let o=t;o<r;o++)s+=m.get(o,t)*m.get(o,e);s=-s/m.get(t,t);for(let o=t;o<r;o++)m.set(o,e,m.get(o,e)+s*m.get(o,t))}for(let e=t;e<r;e++)m.set(e,t,-m.get(e,t));m.set(t,t,1+m.get(t,t));for(let e=0;e<t-1;e++)m.set(e,t,0)}else{for(let e=0;e<r;e++)m.set(e,t,0);m.set(t,t,1)}}if(l)for(let t=s-1;t>=0;t--){if(t<y&&0!==p[t])for(let e=t+1;e<s;e++){let r=0;for(let o=t+1;o<s;o++)r+=w.get(o,t)*w.get(o,e);r=-r/w.get(t+1,t);for(let o=t+1;o<s;o++)w.set(o,e,w.get(o,e)+r*w.get(o,t))}for(let e=0;e<s;e++)w.set(e,t,0);w.set(t,t,1)}let S=E-1,R=Number.EPSILON;for(;E>0;){let t,e;for(t=E-2;t>=-1&&-1!==t;t--){const e=Number.MIN_VALUE+R*Math.abs(g[t]+Math.abs(g[t+1]));if(Math.abs(p[t])<=e||Number.isNaN(p[t])){p[t]=0;break}}if(t===E-2)e=4;else{let r;for(r=E-1;r>=t&&r!==t;r--){let e=(r!==E?Math.abs(p[r]):0)+(r!==t+1?Math.abs(p[r-1]):0);if(Math.abs(g[r])<=R*e){g[r]=0;break}}r===t?e=3:r===E-1?e=1:(e=2,t=r)}switch(t++,e){case 1:{let e=p[E-2];p[E-2]=0;for(let r=E-2;r>=t;r--){let o=k(g[r],e),n=g[r]/o,i=e/o;if(g[r]=o,r!==t&&(e=-i*p[r-1],p[r-1]=n*p[r-1]),l)for(let t=0;t<s;t++)o=n*w.get(t,r)+i*w.get(t,E-1),w.set(t,E-1,-i*w.get(t,r)+n*w.get(t,E-1)),w.set(t,r,o)}break}case 2:{let e=p[t-1];p[t-1]=0;for(let s=t;s<E;s++){let o=k(g[s],e),n=g[s]/o,i=e/o;if(g[s]=o,e=-i*p[s],p[s]=n*p[s],u)for(let e=0;e<r;e++)o=n*m.get(e,s)+i*m.get(e,t-1),m.set(e,t-1,-i*m.get(e,s)+n*m.get(e,t-1)),m.set(e,s,o)}break}case 3:{const e=Math.max(Math.abs(g[E-1]),Math.abs(g[E-2]),Math.abs(p[E-2]),Math.abs(g[t]),Math.abs(p[t])),o=g[E-1]/e,n=g[E-2]/e,i=p[E-2]/e,h=g[t]/e,a=p[t]/e,f=((n+o)*(n-o)+i*i)/2,c=o*i*(o*i);let d=0;0===f&&0===c||(d=f<0?0-Math.sqrt(f*f+c):Math.sqrt(f*f+c),d=c/(f+d));let M=(h+o)*(h-o)+d,b=h*a;for(let e=t;e<E-1;e++){let o=k(M,b);0===o&&(o=Number.MIN_VALUE);let n=M/o,i=b/o;if(e!==t&&(p[e-1]=o),M=n*g[e]+i*p[e],p[e]=n*p[e]-i*g[e],b=i*g[e+1],g[e+1]=n*g[e+1],l)for(let t=0;t<s;t++)o=n*w.get(t,e)+i*w.get(t,e+1),w.set(t,e+1,-i*w.get(t,e)+n*w.get(t,e+1)),w.set(t,e,o);if(o=k(M,b),0===o&&(o=Number.MIN_VALUE),n=M/o,i=b/o,g[e]=o,M=n*p[e]+i*g[e+1],g[e+1]=-i*p[e]+n*g[e+1],b=i*p[e+1],p[e+1]=n*p[e+1],u&&e<r-1)for(let t=0;t<r;t++)o=n*m.get(t,e)+i*m.get(t,e+1),m.set(t,e+1,-i*m.get(t,e)+n*m.get(t,e+1)),m.set(t,e,o)}p[E-2]=M;break}case 4:if(g[t]<=0&&(g[t]=g[t]<0?-g[t]:0,l))for(let e=0;e<=S;e++)w.set(e,t,-w.get(e,t));for(;t<S&&!(g[t]>=g[t+1]);){let e=g[t];if(g[t]=g[t+1],g[t+1]=e,l&&t<s-1)for(let r=0;r<s;r++)e=w.get(r,t+1),w.set(r,t+1,w.get(r,t)),w.set(r,t,e);if(u&&t<r-1)for(let s=0;s<r;s++)e=m.get(s,t+1),m.set(s,t+1,m.get(s,t)),m.set(s,t,e);t++}E--}}if(a){let t=w;w=m,m=t}this.m=r,this.n=s,this.s=g,this.U=m,this.V=w}solve(t){let e=t,r=this.threshold,s=this.s.length,o=v.zeros(s,s);for(let t=0;t<s;t++)Math.abs(this.s[t])<=r?o.set(t,t,0):o.set(t,t,1/this.s[t]);let n=this.U,i=this.rightSingularVectors,h=i.mmul(o),u=i.rows,l=n.rows,a=v.zeros(u,l);for(let t=0;t<u;t++)for(let e=0;e<l;e++){let r=0;for(let o=0;o<s;o++)r+=h.get(t,o)*n.get(e,o);a.set(t,e,r)}return a.mmul(e)}solveForDiagonal(t){return this.solve(v.diag(t))}inverse(){let t=this.V,e=this.threshold,r=t.rows,s=t.columns,o=new v(r,this.s.length);for(let n=0;n<r;n++)for(let r=0;r<s;r++)Math.abs(this.s[r])>e&&o.set(n,r,t.get(n,r)/this.s[r]);let n=this.U,i=n.rows,h=n.columns,u=new v(r,i);for(let t=0;t<r;t++)for(let e=0;e<i;e++){let r=0;for(let s=0;s<h;s++)r+=o.get(t,s)*n.get(e,s);u.set(t,e,r)}return u}get condition(){return this.s[0]/this.s[Math.min(this.m,this.n)-1]}get norm2(){return this.s[0]}get rank(){let t=Math.max(this.m,this.n)*this.s[0]*Number.EPSILON,e=0,r=this.s;for(let s=0,o=r.length;s<o;s++)r[s]>t&&e++;return e}get diagonal(){return Array.from(this.s)}get threshold(){return Number.EPSILON/2*Math.max(this.m,this.n)*this.s[0]}get leftSingularVectors(){return this.U}get rightSingularVectors(){return this.V}get diagonalMatrix(){return v.diag(this.s)}}function q(t,e,r=!1){return t=A.checkMatrix(t),e=A.checkMatrix(e),r?new T(t).solve(e):t.isSquare()?new I(t).solve(e):new V(t).solve(e)}function C(t,e){let r=[];for(let s=0;s<t;s++)s!==e&&r.push(s);return r}function N(t,e,r,s=1e-9,o=1e-9){if(t>o)return new Array(e.rows+1).fill(0);{let t=e.addRow(r,[0]);for(let e=0;e<t.rows;e++)Math.abs(t.get(e,0))<s&&t.set(e,0,0);return t.to1DArray()}}class F{constructor(t,e={}){const{assumeSymmetric:r=!1}=e;if(!(t=A.checkMatrix(t)).isSquare())throw new Error("Matrix is not a square matrix");let s,o,n=t.columns,i=new v(n,n),h=new Float64Array(n),u=new Float64Array(n),l=t,a=!1;if(a=!!r||t.isSymmetric(),a){for(s=0;s<n;s++)for(o=0;o<n;o++)i.set(s,o,l.get(s,o));!function(t,e,r,s){let o,n,i,h,u,l,a,f;for(u=0;u<t;u++)r[u]=s.get(t-1,u);for(h=t-1;h>0;h--){for(f=0,i=0,l=0;l<h;l++)f+=Math.abs(r[l]);if(0===f)for(e[h]=r[h-1],u=0;u<h;u++)r[u]=s.get(h-1,u),s.set(h,u,0),s.set(u,h,0);else{for(l=0;l<h;l++)r[l]/=f,i+=r[l]*r[l];for(o=r[h-1],n=Math.sqrt(i),o>0&&(n=-n),e[h]=f*n,i-=o*n,r[h-1]=o-n,u=0;u<h;u++)e[u]=0;for(u=0;u<h;u++){for(o=r[u],s.set(u,h,o),n=e[u]+s.get(u,u)*o,l=u+1;l<=h-1;l++)n+=s.get(l,u)*r[l],e[l]+=s.get(l,u)*o;e[u]=n}for(o=0,u=0;u<h;u++)e[u]/=i,o+=e[u]*r[u];for(a=o/(i+i),u=0;u<h;u++)e[u]-=a*r[u];for(u=0;u<h;u++){for(o=r[u],n=e[u],l=u;l<=h-1;l++)s.set(l,u,s.get(l,u)-(o*e[l]+n*r[l]));r[u]=s.get(h-1,u),s.set(h,u,0)}}r[h]=i}for(h=0;h<t-1;h++){if(s.set(t-1,h,s.get(h,h)),s.set(h,h,1),i=r[h+1],0!==i){for(l=0;l<=h;l++)r[l]=s.get(l,h+1)/i;for(u=0;u<=h;u++){for(n=0,l=0;l<=h;l++)n+=s.get(l,h+1)*s.get(l,u);for(l=0;l<=h;l++)s.set(l,u,s.get(l,u)-n*r[l])}}for(l=0;l<=h;l++)s.set(l,h+1,0)}for(u=0;u<t;u++)r[u]=s.get(t-1,u),s.set(t-1,u,0);s.set(t-1,t-1,1),e[0]=0}(n,u,h,i),function(t,e,r,s){let o,n,i,h,u,l,a,f,c,g,m,w,p,d,M,b;for(i=1;i<t;i++)e[i-1]=e[i];e[t-1]=0;let y=0,x=0,v=Number.EPSILON;for(l=0;l<t;l++){for(x=Math.max(x,Math.abs(r[l])+Math.abs(e[l])),a=l;a<t&&!(Math.abs(e[a])<=v*x);)a++;if(a>l)do{for(o=r[l],f=(r[l+1]-o)/(2*e[l]),c=k(f,1),f<0&&(c=-c),r[l]=e[l]/(f+c),r[l+1]=e[l]*(f+c),g=r[l+1],n=o-r[l],i=l+2;i<t;i++)r[i]-=n;for(y+=n,f=r[a],m=1,w=m,p=m,d=e[l+1],M=0,b=0,i=a-1;i>=l;i--)for(p=w,w=m,b=M,o=m*e[i],n=m*f,c=k(f,e[i]),e[i+1]=M*c,M=e[i]/c,m=f/c,f=m*r[i]-M*o,r[i+1]=n+M*(m*o+M*r[i]),u=0;u<t;u++)n=s.get(u,i+1),s.set(u,i+1,M*s.get(u,i)+m*n),s.set(u,i,m*s.get(u,i)-M*n);f=-M*b*p*d*e[l]/g,e[l]=M*f,r[l]=m*f}while(Math.abs(e[l])>v*x);r[l]=r[l]+y,e[l]=0}for(i=0;i<t-1;i++){for(u=i,f=r[i],h=i+1;h<t;h++)r[h]<f&&(u=h,f=r[h]);if(u!==i)for(r[u]=r[i],r[i]=f,h=0;h<t;h++)f=s.get(h,i),s.set(h,i,s.get(h,u)),s.set(h,u,f)}}(n,u,h,i)}else{let t=new v(n,n),e=new Float64Array(n);for(o=0;o<n;o++)for(s=0;s<n;s++)t.set(s,o,l.get(s,o));!function(t,e,r,s){let o,n,i,h,u,l,a,f=0,c=t-1;for(l=f+1;l<=c-1;l++){for(a=0,h=l;h<=c;h++)a+=Math.abs(e.get(h,l-1));if(0!==a){for(i=0,h=c;h>=l;h--)r[h]=e.get(h,l-1)/a,i+=r[h]*r[h];for(n=Math.sqrt(i),r[l]>0&&(n=-n),i-=r[l]*n,r[l]=r[l]-n,u=l;u<t;u++){for(o=0,h=c;h>=l;h--)o+=r[h]*e.get(h,u);for(o/=i,h=l;h<=c;h++)e.set(h,u,e.get(h,u)-o*r[h])}for(h=0;h<=c;h++){for(o=0,u=c;u>=l;u--)o+=r[u]*e.get(h,u);for(o/=i,u=l;u<=c;u++)e.set(h,u,e.get(h,u)-o*r[u])}r[l]=a*r[l],e.set(l,l-1,a*n)}}for(h=0;h<t;h++)for(u=0;u<t;u++)s.set(h,u,h===u?1:0);for(l=c-1;l>=f+1;l--)if(0!==e.get(l,l-1)){for(h=l+1;h<=c;h++)r[h]=e.get(h,l-1);for(u=l;u<=c;u++){for(n=0,h=l;h<=c;h++)n+=r[h]*s.get(h,u);for(n=n/r[l]/e.get(l,l-1),h=l;h<=c;h++)s.set(h,u,s.get(h,u)+n*r[h])}}}(n,t,e,i),function(t,e,r,s,o){let n,i,h,u,l,a,f,c,g,m,w,p,d,M,b,y=t-1,x=0,v=t-1,E=Number.EPSILON,S=0,R=0,A=0,I=0,k=0,V=0,T=0,q=0;for(n=0;n<t;n++)for((n<x||n>v)&&(r[n]=o.get(n,n),e[n]=0),i=Math.max(n-1,0);i<t;i++)R+=Math.abs(o.get(n,i));for(;y>=x;){for(u=y;u>x&&(V=Math.abs(o.get(u-1,u-1))+Math.abs(o.get(u,u)),0===V&&(V=R),!(Math.abs(o.get(u,u-1))<E*V));)u--;if(u===y)o.set(y,y,o.get(y,y)+S),r[y]=o.get(y,y),e[y]=0,y--,q=0;else if(u===y-1){if(f=o.get(y,y-1)*o.get(y-1,y),A=(o.get(y-1,y-1)-o.get(y,y))/2,I=A*A+f,T=Math.sqrt(Math.abs(I)),o.set(y,y,o.get(y,y)+S),o.set(y-1,y-1,o.get(y-1,y-1)+S),c=o.get(y,y),I>=0){for(T=A>=0?A+T:A-T,r[y-1]=c+T,r[y]=r[y-1],0!==T&&(r[y]=c-f/T),e[y-1]=0,e[y]=0,c=o.get(y,y-1),V=Math.abs(c)+Math.abs(T),A=c/V,I=T/V,k=Math.sqrt(A*A+I*I),A/=k,I/=k,i=y-1;i<t;i++)T=o.get(y-1,i),o.set(y-1,i,I*T+A*o.get(y,i)),o.set(y,i,I*o.get(y,i)-A*T);for(n=0;n<=y;n++)T=o.get(n,y-1),o.set(n,y-1,I*T+A*o.get(n,y)),o.set(n,y,I*o.get(n,y)-A*T);for(n=x;n<=v;n++)T=s.get(n,y-1),s.set(n,y-1,I*T+A*s.get(n,y)),s.set(n,y,I*s.get(n,y)-A*T)}else r[y-1]=c+A,r[y]=c+A,e[y-1]=T,e[y]=-T;y-=2,q=0}else{if(c=o.get(y,y),g=0,f=0,u<y&&(g=o.get(y-1,y-1),f=o.get(y,y-1)*o.get(y-1,y)),10===q){for(S+=c,n=x;n<=y;n++)o.set(n,n,o.get(n,n)-c);V=Math.abs(o.get(y,y-1))+Math.abs(o.get(y-1,y-2)),c=g=.75*V,f=-.4375*V*V}if(30===q&&(V=(g-c)/2,V=V*V+f,V>0)){for(V=Math.sqrt(V),g<c&&(V=-V),V=c-f/((g-c)/2+V),n=x;n<=y;n++)o.set(n,n,o.get(n,n)-V);S+=V,c=g=f=.964}for(q+=1,l=y-2;l>=u&&(T=o.get(l,l),k=c-T,V=g-T,A=(k*V-f)/o.get(l+1,l)+o.get(l,l+1),I=o.get(l+1,l+1)-T-k-V,k=o.get(l+2,l+1),V=Math.abs(A)+Math.abs(I)+Math.abs(k),A/=V,I/=V,k/=V,l!==u)&&!(Math.abs(o.get(l,l-1))*(Math.abs(I)+Math.abs(k))<E*(Math.abs(A)*(Math.abs(o.get(l-1,l-1))+Math.abs(T)+Math.abs(o.get(l+1,l+1)))));)l--;for(n=l+2;n<=y;n++)o.set(n,n-2,0),n>l+2&&o.set(n,n-3,0);for(h=l;h<=y-1&&(M=h!==y-1,h!==l&&(A=o.get(h,h-1),I=o.get(h+1,h-1),k=M?o.get(h+2,h-1):0,c=Math.abs(A)+Math.abs(I)+Math.abs(k),0!==c&&(A/=c,I/=c,k/=c)),0!==c);h++)if(V=Math.sqrt(A*A+I*I+k*k),A<0&&(V=-V),0!==V){for(h!==l?o.set(h,h-1,-V*c):u!==l&&o.set(h,h-1,-o.get(h,h-1)),A+=V,c=A/V,g=I/V,T=k/V,I/=A,k/=A,i=h;i<t;i++)A=o.get(h,i)+I*o.get(h+1,i),M&&(A+=k*o.get(h+2,i),o.set(h+2,i,o.get(h+2,i)-A*T)),o.set(h,i,o.get(h,i)-A*c),o.set(h+1,i,o.get(h+1,i)-A*g);for(n=0;n<=Math.min(y,h+3);n++)A=c*o.get(n,h)+g*o.get(n,h+1),M&&(A+=T*o.get(n,h+2),o.set(n,h+2,o.get(n,h+2)-A*k)),o.set(n,h,o.get(n,h)-A),o.set(n,h+1,o.get(n,h+1)-A*I);for(n=x;n<=v;n++)A=c*s.get(n,h)+g*s.get(n,h+1),M&&(A+=T*s.get(n,h+2),s.set(n,h+2,s.get(n,h+2)-A*k)),s.set(n,h,s.get(n,h)-A),s.set(n,h+1,s.get(n,h+1)-A*I)}}}if(0===R)return;for(y=t-1;y>=0;y--)if(A=r[y],I=e[y],0===I)for(u=y,o.set(y,y,1),n=y-1;n>=0;n--){for(f=o.get(n,n)-A,k=0,i=u;i<=y;i++)k+=o.get(n,i)*o.get(i,y);if(e[n]<0)T=f,V=k;else if(u=n,0===e[n]?o.set(n,y,0!==f?-k/f:-k/(E*R)):(c=o.get(n,n+1),g=o.get(n+1,n),I=(r[n]-A)*(r[n]-A)+e[n]*e[n],a=(c*V-T*k)/I,o.set(n,y,a),o.set(n+1,y,Math.abs(c)>Math.abs(T)?(-k-f*a)/c:(-V-g*a)/T)),a=Math.abs(o.get(n,y)),E*a*a>1)for(i=n;i<=y;i++)o.set(i,y,o.get(i,y)/a)}else if(I<0)for(u=y-1,Math.abs(o.get(y,y-1))>Math.abs(o.get(y-1,y))?(o.set(y-1,y-1,I/o.get(y,y-1)),o.set(y-1,y,-(o.get(y,y)-A)/o.get(y,y-1))):(b=D(0,-o.get(y-1,y),o.get(y-1,y-1)-A,I),o.set(y-1,y-1,b[0]),o.set(y-1,y,b[1])),o.set(y,y-1,0),o.set(y,y,1),n=y-2;n>=0;n--){for(m=0,w=0,i=u;i<=y;i++)m+=o.get(n,i)*o.get(i,y-1),w+=o.get(n,i)*o.get(i,y);if(f=o.get(n,n)-A,e[n]<0)T=f,k=m,V=w;else if(u=n,0===e[n]?(b=D(-m,-w,f,I),o.set(n,y-1,b[0]),o.set(n,y,b[1])):(c=o.get(n,n+1),g=o.get(n+1,n),p=(r[n]-A)*(r[n]-A)+e[n]*e[n]-I*I,d=2*(r[n]-A)*I,0===p&&0===d&&(p=E*R*(Math.abs(f)+Math.abs(I)+Math.abs(c)+Math.abs(g)+Math.abs(T))),b=D(c*k-T*m+I*w,c*V-T*w-I*m,p,d),o.set(n,y-1,b[0]),o.set(n,y,b[1]),Math.abs(c)>Math.abs(T)+Math.abs(I)?(o.set(n+1,y-1,(-m-f*o.get(n,y-1)+I*o.get(n,y))/c),o.set(n+1,y,(-w-f*o.get(n,y)-I*o.get(n,y-1))/c)):(b=D(-k-g*o.get(n,y-1),-V-g*o.get(n,y),T,I),o.set(n+1,y-1,b[0]),o.set(n+1,y,b[1]))),a=Math.max(Math.abs(o.get(n,y-1)),Math.abs(o.get(n,y))),E*a*a>1)for(i=n;i<=y;i++)o.set(i,y-1,o.get(i,y-1)/a),o.set(i,y,o.get(i,y)/a)}for(n=0;n<t;n++)if(n<x||n>v)for(i=n;i<t;i++)s.set(n,i,o.get(n,i));for(i=t-1;i>=x;i--)for(n=x;n<=v;n++){for(T=0,h=x;h<=Math.min(i,v);h++)T+=s.get(n,h)*o.get(h,i);s.set(n,i,T)}}(n,u,h,i,t)}this.n=n,this.e=u,this.d=h,this.V=i}get realEigenvalues(){return Array.from(this.d)}get imaginaryEigenvalues(){return Array.from(this.e)}get eigenvectorMatrix(){return this.V}get diagonalMatrix(){let t,e,r=this.n,s=this.e,o=this.d,n=new v(r,r);for(t=0;t<r;t++){for(e=0;e<r;e++)n.set(t,e,0);n.set(t,t,o[t]),s[t]>0?n.set(t,t+1,s[t]):s[t]<0&&n.set(t,t-1,s[t])}return n}}function D(t,e,r,s){let o,n;return Math.abs(r)>Math.abs(s)?(o=s/r,n=r+o*s,[(t+o*e)/n,(e-o*t)/n]):(o=r/s,n=s+o*r,[(o*t+e)/n,(o*e-t)/n])}class j{constructor(t){if(!(t=A.checkMatrix(t)).isSymmetric())throw new Error("Matrix is not symmetric");let e,r,s,o=t,n=o.rows,i=new v(n,n),h=!0;for(r=0;r<n;r++){let t=0;for(s=0;s<r;s++){let n=0;for(e=0;e<s;e++)n+=i.get(s,e)*i.get(r,e);n=(o.get(r,s)-n)/i.get(s,s),i.set(r,s,n),t+=n*n}for(t=o.get(r,r)-t,h&=t>0,i.set(r,r,Math.sqrt(Math.max(t,0))),s=r+1;s<n;s++)i.set(r,s,0)}this.L=i,this.positiveDefinite=Boolean(h)}isPositiveDefinite(){return this.positiveDefinite}solve(t){t=A.checkMatrix(t);let e=this.L,r=e.rows;if(t.rows!==r)throw new Error("Matrix dimensions do not match");if(!1===this.isPositiveDefinite())throw new Error("Matrix is not positive definite");let s,o,n,i=t.columns,h=t.clone();for(n=0;n<r;n++)for(o=0;o<i;o++){for(s=0;s<n;s++)h.set(n,o,h.get(n,o)-h.get(s,o)*e.get(n,s));h.set(n,o,h.get(n,o)/e.get(n,n))}for(n=r-1;n>=0;n--)for(o=0;o<i;o++){for(s=n+1;s<r;s++)h.set(n,o,h.get(n,o)-h.get(s,o)*e.get(s,n));h.set(n,o,h.get(n,o)/e.get(n,n))}return h}get lowerTriangularMatrix(){return this.L}}class L{constructor(t,e={}){t=A.checkMatrix(t);let{Y:r}=e;const{scaleScores:s=!1,maxIterations:o=1e3,terminationCriteria:n=1e-10}=e;let i;if(r){if(r=Array.isArray(r)&&"number"==typeof r[0]?v.columnVector(r):A.checkMatrix(r),!r.isColumnVector()||r.rows!==t.rows)throw new Error("Y must be a column vector of length X.rows");i=r}else i=t.getColumnVector(0);let h,u,l,a,f=1;for(let e=0;e<o&&f>n;e++)l=t.transpose().mmul(i).div(i.transpose().mmul(i).get(0,0)),l=l.div(l.norm()),h=t.mmul(l).div(l.transpose().mmul(l).get(0,0)),e>0&&(f=h.clone().sub(a).pow(2).sum()),a=h.clone(),r?(u=r.transpose().mmul(h).div(h.transpose().mmul(h).get(0,0)),u=u.div(u.norm()),i=r.mmul(u).div(u.transpose().mmul(u).get(0,0))):i=h;if(r){let e=t.transpose().mmul(h).div(h.transpose().mmul(h).get(0,0));e=e.div(e.norm());let s=t.clone().sub(h.clone().mmul(e.transpose())),o=i.transpose().mmul(h).div(h.transpose().mmul(h).get(0,0)),n=r.clone().sub(h.clone().mulS(o.get(0,0)).mmul(u.transpose()));this.t=h,this.p=e.transpose(),this.w=l.transpose(),this.q=u,this.u=i,this.s=h.transpose().mmul(h),this.xResidual=s,this.yResidual=n,this.betas=o}else this.w=l.transpose(),this.s=h.transpose().mmul(h).sqrt(),this.t=s?h.clone().div(this.s.get(0,0)):h,this.xResidual=t.sub(h.mmul(l.transpose()))}}t.AbstractMatrix=y,t.CHO=j,t.CholeskyDecomposition=j,t.EVD=F,t.EigenvalueDecomposition=F,t.LU=I,t.LuDecomposition=I,t.Matrix=v,t.MatrixColumnSelectionView=class extends E{constructor(t,e){e=p(t,e),super(t,t.rows,e.length),this.columnIndices=e}set(t,e,r){return this.matrix.set(t,this.columnIndices[e],r),this}get(t,e){return this.matrix.get(t,this.columnIndices[e])}},t.MatrixColumnView=class extends E{constructor(t,e){f(t,e),super(t,t.rows,1),this.column=e}set(t,e,r){return this.matrix.set(t,this.column,r),this}get(t){return this.matrix.get(t,this.column)}},t.MatrixFlipColumnView=class extends E{constructor(t){super(t,t.rows,t.columns)}set(t,e,r){return this.matrix.set(t,this.columns-e-1,r),this}get(t,e){return this.matrix.get(t,this.columns-e-1)}},t.MatrixFlipRowView=class extends E{constructor(t){super(t,t.rows,t.columns)}set(t,e,r){return this.matrix.set(this.rows-t-1,e,r),this}get(t,e){return this.matrix.get(this.rows-t-1,e)}},t.MatrixRowSelectionView=class extends E{constructor(t,e){super(t,(e=w(t,e)).length,t.columns),this.rowIndices=e}set(t,e,r){return this.matrix.set(this.rowIndices[t],e,r),this}get(t,e){return this.matrix.get(this.rowIndices[t],e)}},t.MatrixRowView=class extends E{constructor(t,e){a(t,e),super(t,1,t.columns),this.row=e}set(t,e,r){return this.matrix.set(this.row,e,r),this}get(t,e){return this.matrix.get(this.row,e)}},t.MatrixSelectionView=S,t.MatrixSubView=class extends E{constructor(t,e,r,s,o){d(t,e,r,s,o),super(t,r-e+1,o-s+1),this.startRow=e,this.startColumn=s}set(t,e,r){return this.matrix.set(this.startRow+t,this.startColumn+e,r),this}get(t,e){return this.matrix.get(this.startRow+t,this.startColumn+e)}},t.MatrixTransposeView=class extends E{constructor(t){super(t,t.columns,t.rows)}set(t,e,r){return this.matrix.set(e,t,r),this}get(t,e){return this.matrix.get(e,t)}},t.NIPALS=L,t.Nipals=L,t.QR=V,t.QrDecomposition=V,t.SVD=T,t.SingularValueDecomposition=T,t.WrapperMatrix1D=R,t.WrapperMatrix2D=A,t.correlation=function(t,e=t,r={}){t=new v(t);let s=!1;if("object"!=typeof e||v.isMatrix(e)||Array.isArray(e)?e=new v(e):(r=e,e=t,s=!0),t.rows!==e.rows)throw new TypeError("Both matrices must have the same number of rows");const{center:o=!0,scale:n=!0}=r;o&&(t.center("column"),s||e.center("column")),n&&(t.scale("column"),s||e.scale("column"));const i=t.standardDeviation("column",{unbiased:!0}),h=s?i:e.standardDeviation("column",{unbiased:!0}),u=t.transpose().mmul(e);for(let e=0;e<u.rows;e++)for(let r=0;r<u.columns;r++)u.set(e,r,u.get(e,r)*(1/(i[e]*h[r]))*(1/(t.rows-1)));return u},t.covariance=function(t,e=t,r={}){t=new v(t);let s=!1;if("object"!=typeof e||v.isMatrix(e)||Array.isArray(e)?e=new v(e):(r=e,e=t,s=!0),t.rows!==e.rows)throw new TypeError("Both matrices must have the same number of rows");const{center:o=!0}=r;o&&(t=t.center("column"),s||(e=e.center("column")));const n=t.transpose().mmul(e);for(let e=0;e<n.rows;e++)for(let r=0;r<n.columns;r++)n.set(e,r,n.get(e,r)*(1/(t.rows-1)));return n},t.default=v,t.determinant=function t(e){if((e=v.checkMatrix(e)).isSquare()){let r,s,o,n;if(2===e.columns)return r=e.get(0,0),s=e.get(0,1),o=e.get(1,0),n=e.get(1,1),r*n-s*o;if(3===e.columns){let n,i,h;return n=new S(e,[1,2],[1,2]),i=new S(e,[1,2],[0,2]),h=new S(e,[1,2],[0,1]),r=e.get(0,0),s=e.get(0,1),o=e.get(0,2),r*t(n)-s*t(i)+o*t(h)}return new I(e).determinant}throw Error("determinant can only be calculated for a square matrix")},t.inverse=function(t,e=!1){return t=A.checkMatrix(t),e?new T(t).inverse():q(t,v.eye(t.rows))},t.linearDependencies=function(t,e={}){const{thresholdValue:r=1e-9,thresholdError:s=1e-9}=e;let o=(t=v.checkMatrix(t)).rows,n=new v(o,o);for(let e=0;e<o;e++){let i=v.columnVector(t.getRow(e)),h=t.subMatrixRow(C(o,e)).transpose(),u=new T(h).solve(i),l=v.sub(i,h.mmul(u)).abs().max();n.setRow(e,N(l,u,e,r,s))}return n},t.pseudoInverse=function(t,e=Number.EPSILON){t=v.checkMatrix(t);let r=new T(t,{autoTranspose:!0}),s=r.leftSingularVectors,o=r.rightSingularVectors,n=r.diagonal;for(let t=0;t<n.length;t++)Math.abs(n[t])>e?n[t]=1/n[t]:n[t]=0;return o.mmul(v.diag(n).mmul(s.transpose()))},t.solve=q,t.wrap=function(t,e){if(Array.isArray(t))return t[0]&&Array.isArray(t[0])?new A(t):new R(t,e);throw new Error("the argument is not an array")},Object.defineProperty(t,"__esModule",{value:!0})}));

package.json

 {
   "name": "ml-matrix",
-  "version": "6.5.2",
+  "version": "6.5.3",
   "description": "Matrix manipulation and computation library",
@@ -18,3 +18,2 @@ "main": "matrix.js",
   "scripts": {
-    "build-docs": "typedoc --out docs --name \"ml-matrix\" --mode file --includeDeclarations --excludeExternals --hideGenerator --excludePrivate --moduleResolution node matrix.d.ts",
     "compile": "rollup -c",
@@ -60,23 +59,21 @@ "eslint": "eslint benchmark src testUtils.js",
     "@babel/plugin-transform-modules-commonjs": "^7.10.4",
-    "@rollup/plugin-commonjs": "^14.0.0",
-    "@rollup/plugin-node-resolve": "^8.4.0",
+    "@rollup/plugin-commonjs": "^15.1.0",
+    "@rollup/plugin-node-resolve": "^9.0.0",
     "benchmark": "^2.1.4",
-    "csv-parse": "^4.11.1",
-    "eslint": "^7.10.0",
+    "csv-parse": "^4.12.0",
+    "eslint": "^7.11.0",
     "eslint-config-cheminfo": "^5.2.2",
-    "jest": "^26.1.0",
+    "jest": "^26.5.2",
     "jest-matcher-deep-close-to": "^2.0.1",
-    "mathjs": "^7.1.0",
+    "mathjs": "^7.5.1",
     "ml-dataset-iris": "^1.1.1",
     "numeric": "^1.2.6",
-    "prettier": "^2.0.5",
+    "prettier": "^2.1.2",
     "pretty-hrtime": "^1.0.3",
-    "rollup": "^2.23.0",
-    "rollup-plugin-terser": "^6.1.0",
-    "typedoc": "^0.17.8",
-    "typescript": "^3.9.7"
+    "rollup": "^2.29.0",
+    "rollup-plugin-terser": "^7.0.2"
   },
   "dependencies": {
-    "ml-array-rescale": "^1.3.1"
+    "ml-array-rescale": "^1.3.2"
   }
 }

README.md

@@ -0,0 +0,0 @@ # ml-matrix

src/correlation.js

@@ -0,0 +0,0 @@ import Matrix from './matrix';

src/covariance.js

@@ -0,0 +0,0 @@ import Matrix from './matrix';

src/dc/cholesky.js

@@ -0,0 +0,0 @@ import Matrix from '../matrix';

src/dc/evd.js

@@ -0,0 +0,0 @@ import Matrix from '../matrix';

src/dc/lu.js

@@ -0,0 +0,0 @@ import Matrix from '../matrix';

src/dc/nipals.js

@@ -0,0 +0,0 @@ import Matrix from '../matrix';

src/dc/qr.js

@@ -0,0 +0,0 @@ import Matrix from '../matrix';

src/dc/svd.js

@@ -0,0 +0,0 @@ import Matrix from '../matrix';

src/dc/util.js

@@ -0,0 +0,0 @@ export function hypotenuse(a, b) {

src/decompositions.js

@@ -0,0 +0,0 @@ import LuDecomposition from './dc/lu';

src/determinant.js

@@ -0,0 +0,0 @@ import LuDecomposition from './dc/lu';

src/index.js

@@ -0,0 +0,0 @@ export { AbstractMatrix, default, default as Matrix } from './matrix';

src/inspect.js

@@ -0,0 +0,0 @@ const indent = ' '.repeat(2);

src/linearDependencies.js

@@ -0,0 +0,0 @@ import SingularValueDecomposition from './dc/svd';

src/mathOperations.js

@@ -0,0 +0,0 @@ export function installMathOperations(AbstractMatrix, Matrix) {

src/matrix.js

@@ -1430,2 +1430,3 @@ import rescale from 'ml-array-rescale';
     if (Matrix.isMatrix(nRows)) {
+      // eslint-disable-next-line no-constructor-return
       return nRows.clone();
@@ -1466,3 +1467,2 @@ } else if (Number.isInteger(nRows) && nRows > 0) {
     this.columns = nColumns;
-    return this;
   }
@@ -1469,0 +1469,0 @@

src/pseudoInverse.js

@@ -0,0 +0,0 @@ import SVD from './dc/svd';

src/stat.js

@@ -0,0 +0,0 @@ import { newArray } from './util';

src/util.js

@@ -0,0 +0,0 @@ /**

src/views/base.js

@@ -0,0 +0,0 @@ import { AbstractMatrix } from '../matrix';

src/views/column.js

@@ -0,0 +0,0 @@ import { checkColumnIndex } from '../util';

src/views/columnSelection.js

@@ -0,0 +0,0 @@ import { checkColumnIndices } from '../util';

src/views/flipColumn.js

@@ -0,0 +0,0 @@ import BaseView from './base';

src/views/flipRow.js

@@ -0,0 +0,0 @@ import BaseView from './base';

src/views/index.js

@@ -0,0 +0,0 @@ export { default as MatrixColumnView } from './column';

src/views/row.js

@@ -0,0 +0,0 @@ import { checkRowIndex } from '../util';

src/views/rowSelection.js

@@ -0,0 +0,0 @@ import { checkRowIndices } from '../util';

src/views/selection.js

@@ -0,0 +0,0 @@ import { checkIndices } from '../util';

src/views/sub.js

@@ -0,0 +0,0 @@ import { checkRange } from '../util';

src/views/transpose.js

@@ -0,0 +0,0 @@ import BaseView from './base';

src/wrap/wrap.js

@@ -0,0 +0,0 @@ import WrapperMatrix1D from './WrapperMatrix1D';

src/wrap/WrapperMatrix1D.js

@@ -0,0 +0,0 @@ import { AbstractMatrix } from '../matrix';

src/wrap/WrapperMatrix2D.js

@@ -0,0 +0,0 @@ import { AbstractMatrix } from '../matrix';

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decreased by-11.11%

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Dependency changes

• Updatedml-array-rescale@^1.3.2