mathjslab/lib/mathjslab.node.cjs2022.js

MathJSLab - An interpreter with language syntax like MATLAB®/Octave, ISBN 978-65-00-82338-7.

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l.CharString}});var c=r(845);Object.defineProperty(t,"Complex",{enumerable:!0,get:function(){return c.Complex}});var u=r(679);Object.defineProperty(t,"MultiArray",{enumerable:!0,get:function(){return u.MultiArray}});var m=r(212);Object.defineProperty(t,"Structure",{enumerable:!0,get:function(){return m.Structure}});var p=r(271);Object.defineProperty(t,"FunctionHandle",{enumerable:!0,get:function(){return p.FunctionHandle}})},115(e,t,r){"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.BLAS=t.BLASConfigKeyTable=void 0;const n=r(845),i=r(679);t.BLASConfigKeyTable=["blockThreshold","blockSize"];const o={blockThreshold:1e5,blockSize:64};class s{static defaultSettings=Object.assign({},o);static settings=s.defaultSettings;static set=e=>{Object.entries(e).forEach(e=>{if(!t.BLASConfigKeyTable.includes(e[0]))throw new Error(`BLAS.set: invalid configuration parameter: ${e[0]}`);s.settings[e[0]]=e[1]})};static axpy=(e,t,r)=>{const i=t.length,o=t[0].length;for(let s=0;s<i;s++){const i=t[s],a=r[s];for(let t=0;t<o;t++)a[t]=n.Complex.add(a[t],n.Complex.mul(e,i[t]))}return r};static scal=(e,t,r,i)=>{if(n.Complex.realToNumber(n.Complex.eq(e,n.Complex.zero())))for(let e=r;e<i;e++)t[e]=n.Complex.zero();else if(!n.Complex.realToNumber(n.Complex.eq(e,n.Complex.one())))for(let o=r;o<i;o++)t[o]=n.Complex.mul(e,t[o])};static copy=e=>{if(Array.isArray(e))return Array.isArray(e[0])?Array.from({length:e.length},(t,r)=>Array.from({length:e[0].length},(t,i)=>n.Complex.copy(e[r][i]))):Array.from({length:e.length},(t,r)=>n.Complex.copy(e[r]));throw new Error("BLAS.copy: invalid argument")};static dotu=(e,t)=>{const r=e.length;let i=n.Complex.zero();for(let o=0;o<r;o++)n.Complex.mulAndSumTo(i,e[o],t[o]);return i};static dot=s.dotu;static dotc=(e,t)=>{const r=e.length;let i=n.Complex.zero();for(let o=0;o<r;o++)n.Complex.mulAndSumTo(i,n.Complex.conj(e[o]),t[o]);return i};static nrm2sq=(e,t,r,i)=>{let o=n.Complex.zero();for(let s=r;s<i;s++)n.Complex.mulAndSumTo(o,e.array[s][t],n.Complex.conj(e.array[s][t]));return n.Complex.create(o.re)};static nrm2=e=>{let t=n.Complex.zero(),r=n.Complex.one();for(let i=0;i<e.length;i++){const o=e[i],s=n.Complex.abs(n.Complex.real(o)),a=n.Complex.abs(n.Complex.imag(o));if(n.Complex.toBoolean(n.Complex.ne(s,n.Complex.zero())))if(n.Complex.lt(t,s)){const e=n.Complex.rdiv(t,s);r=n.Complex.add(n.Complex.one(),n.Complex.mul(r,n.Complex.mul(e,e))),t=s}else{const e=n.Complex.rdiv(s,t);r=n.Complex.add(r,n.Complex.mul(e,e))}if(n.Complex.toBoolean(n.Complex.ne(a,n.Complex.zero())))if(n.Complex.lt(t,a)){const e=n.Complex.rdiv(t,a);r=n.Complex.add(n.Complex.one(),n.Complex.mul(r,n.Complex.mul(e,e))),t=a}else{const e=n.Complex.rdiv(a,t);r=n.Complex.add(r,n.Complex.mul(e,e))}}return n.Complex.toBoolean(n.Complex.eq(t,n.Complex.zero()))?n.Complex.zero():n.Complex.mul(t,n.Complex.sqrt(r))};static gemv=(e,t,r,i,o,s,a,l,c,u,m,p="N")=>{const h="N"===p?t:r,d="N"===p?r:t;for(let e=0;e<h;e++)l[c+e]=n.Complex.eq(m,n.Complex.zero())?n.Complex.zero():n.Complex.eq(m,n.Complex.one())?l[c+e]:n.Complex.mul(m,l[c+e]);for(let t=0;t<h;t++){let r=n.Complex.zero();for(let l=0;l<d;l++){const c="N"===p?e[i+t][o+l]:"T"===p?e[i+l][o+t]:n.Complex.conj(e[i+l][o+t]);n.Complex.mulAndSumTo(r,c,s[a+l])}n.Complex.mulAndSumTo(l[c+t],u,r)}};static trsv=(e,t,r)=>{const n=e.length;if(e.some(e=>e.length!==n))throw new Error("BLAS.trsv: A must be square.");if(t.length!==n)throw new Error("BLAS.trsv: x has incompatible dimension.");const i=Array.from({length:n},(e,r)=>[t[r]]);return s.trsm(e,i,{side:"left",uplo:r.uplo,transA:r.transA,unitDiagonal:r.unitDiagonal}).map(e=>e[0])};static ger=(e,t,r,i,o,s,a,l,c,u,m,p)=>{if(!n.Complex.realIsZero(n.Complex.abs(s)))for(let h=0;h<i;h++){const i=a[l+h][c],d=n.Complex.mul(s,i),x=e[t+h];for(let e=0;e<o;e++)n.Complex.mulAndSumTo(x[r+e],d,n.Complex.conj(u[m+e][p]))}};static geru=(e,t,r,i,o,s)=>{if(!n.Complex.realIsZero(n.Complex.abs(r)))for(let a=0;a<e.length;a++){const l=e[a],c=i[o+a];for(let e=0;e<t.length;e++)n.Complex.mulAndSumTo(c[s+e],r,n.Complex.mul(l,t[e]))}};static gerc=(e,t,r,i,o=0,s=0)=>{for(let a=0;a<e.length;a++){const l=e[a],c=i[o+a];for(let e=0;e<t.length;e++)c[s+e]=n.Complex.add(c[s+e],n.Complex.mul(r,n.Complex.mul(l,n.Complex.conj(t[e]))))}};static gerc_nd=(e,t,r)=>{const o=[];for(let t=0;t<i.MultiArray.linearLength(e);t++){const[r,n]=i.MultiArray.linearIndexToMultiArrayRowColumn(e.dimension[0],e.dimension[1],t);o.push(e.array[r][n])}const s=[];for(let e=0;e<i.MultiArray.linearLength(t);e++){const[r,n]=i.MultiArray.linearIndexToMultiArrayRowColumn(t.dimension[0],t.dimension[1],e);s.push(t.array[r][n])}const a=o.length,l=s.length;if(r.dimension[0]!==a||r.dimension[1]!==l)throw new Error(`BLAS.gerc_nd: dimension mismatch (C is ${r.dimension[0]}x${r.dimension[1]}, x is ${a}, y is ${l})`);for(let e=0;e<a;e++){const t=n.Complex.conj(o[e]);for(let i=0;i<l;i++){const o=n.Complex.mul(t,s[i]);r.array[e][i]?r.array[e][i]=n.Complex.add(r.array[e][i],o):r.array[e][i]=n.Complex.copy(o)}}i.MultiArray.setType(r)};static gerc_nd_direct=(e,t,r)=>{const o=i.MultiArray.linearLength(e),s=i.MultiArray.linearLength(t);if(r.dimension[0]!==o||r.dimension[1]!==s)throw new Error(`BLAS.gerc_nd_direct: dimension mismatch (C is ${r.dimension[0]}x${r.dimension[1]}, x is ${o}, y is ${s})`);e.dimension[0],e.dimension[1],t.dimension[0],t.dimension[1],r.dimension[0],r.dimension[1];for(let a=0;a<o;a++){const[l,c]=i.MultiArray.linearIndexToMultiArrayRowColumn(e.dimension[0],e.dimension[1]||1,a),u=n.Complex.conj(e.array[l][c]);for(let e=0;e<s;e++){const[s,l]=i.MultiArray.linearIndexToMultiArrayRowColumn(t.dimension[0],t.dimension[1]||1,e),c=t.array[s][l],[m,p]=i.MultiArray.linearIndexToMultiArrayRowColumn(r.dimension[0],r.dimension[1],a+e*o);r.array[m][p]?r.array[m][p]=n.Complex.add(r.array[m][p],n.Complex.mul(u,c)):r.array[m][p]=n.Complex.mul(u,c)}}i.MultiArray.setType(r)};static gemm_kernel=(e,t,r,i,o,s,a,l,c)=>{for(let u=i;u<o;u++){const i=e[u],o=r[u];for(let e=s;e<a;e++){let r=o[e]??n.Complex.zero();for(let o=l;o<c;o++)n.Complex.mulAndSumTo(r,i[o],t[o][e]);o[e]=r}}};static gemm=(e,t,r,i,o,a,l,c,u)=>{if(n.Complex.realIsZero(n.Complex.abs(e)))for(let e=0;e<r;e++){const t=c[e];for(let e=0;e<a;e++)t[e]=n.Complex.mul(l,t[e])}else{if(!n.Complex.eq(l,n.Complex.one()))for(let e=0;e<r;e++){const t=c[e];for(let e=0;e<a;e++)t[e]=n.Complex.mul(l,t[e])}if(r*i*a>s.settings.blockThreshold)for(let e=0;e<r;e+=u??s.settings.blockSize){const n=Math.min(e+(u??s.settings.blockSize),r);for(let r=0;r<i;r+=u??s.settings.blockSize){const l=Math.min(r+(u??s.settings.blockSize),i);for(let i=0;i<a;i+=u??s.settings.blockSize){const m=Math.min(i+(u??s.settings.blockSize),a);s.gemm_kernel(t,o,c,e,n,i,m,r,l)}}}else for(let s=0;s<r;s++){const r=t[s],l=c[s];for(let t=0;t<a;t++){let s=n.Complex.zero();for(let e=0;e<i;e++)n.Complex.mulAndSumTo(s,r[e],o[e][t]);l[t]=n.Complex.add(l[t],n.Complex.mul(e,s))}}}};static gemm_block=(e,t,r,i,o,a)=>{const l=e.length,c=e[0]?.length??0,u=t.length,m=t[0]?.length??0;if(c!==u)throw new Error("BLAS.gemm_block: inner dimensions mismatch A.cols != B.rows");if(r.length!==l||r[0]?.length!==m)throw new Error("BLAS.gemm_block: output dimension mismatch with C");if(n.Complex.realIsZero(n.Complex.abs(i))){if(n.Complex.realIsZero(n.Complex.abs(o)))for(let e=0;e<l;e++)for(let t=0;t<m;t++)r[e][t]=n.Complex.zero();else if(n.Complex.toBoolean(n.Complex.ne(o,n.Complex.one())))for(let e=0;e<l;e++)for(let t=0;t<m;t++)r[e][t]=n.Complex.mul(o,r[e][t]);return}const p=Math.max(1,Math.floor(a??s.settings.blockSize));for(let s=0;s<l;s+=p){const a=Math.min(s+p,l);for(let l=0;l<m;l+=p){const u=Math.min(l+p,m);for(let e=s;e<a;e++)for(let t=l;t<u;t++)n.Complex.realIsZero(n.Complex.abs(o))?r[e][t]=n.Complex.zero():n.Complex.toBoolean(n.Complex.ne(o,n.Complex.one()))&&(r[e][t]=n.Complex.mul(o,r[e][t]));for(let o=0;o<c;o+=p){const m=Math.min(o+p,c);for(let c=s;c<a;c++){const s=e[c],a=r[c];for(let e=o;e<m;e++){const r=s[e];if(!n.Complex.realIsZero(n.Complex.abs(r)))for(let o=l;o<u;o++){const s=n.Complex.mul(r,t[e][o]),l=n.Complex.mul(i,s);a[o]=n.Complex.add(a[o],l)}}}}}}};static trsm=(e,t,r)=>{const i=r?.side??"left",o=r?.uplo??"upper",s=r?.transA??"N",a=r?.unitDiagonal??!1,l=t.length,c=t[0]?.length??0;if(e.length!==e[0]?.length)throw new Error("BLAS.trsm: A must be square.");if("left"===i&&e.length!==l||"right"===i&&e.length!==c)throw new Error("BLAS.trsm: nonconformant dimensions.");const u=t.map(e=>e.map(e=>e)),m=(t,r)=>"N"===s?e[t][r]:"T"===s?e[r][t]:n.Complex.conj(e[r][t]);if("left"===i)if("upper"===o&&"N"===s||"lower"===o&&"N"!==s)for(let e=0;e<c;e++)for(let t=l-1;t>=0;t--){let r=u[t][e];for(let i=t+1;i<l;i++)r=n.Complex.sub(r,n.Complex.mul(m(t,i),u[i][e]));a||(r=n.Complex.rdiv(r,m(t,t))),u[t][e]=r}else for(let e=0;e<c;e++)for(let t=0;t<l;t++){let r=u[t][e];for(let i=0;i<t;i++)r=n.Complex.sub(r,n.Complex.mul(m(t,i),u[i][e]));a||(r=n.Complex.rdiv(r,m(t,t))),u[t][e]=r}else if("upper"===o&&"N"===s||"lower"===o&&"N"!==s)for(let e=0;e<l;e++)for(let t=0;t<c;t++){let r=u[e][t];for(let i=0;i<t;i++)r=n.Complex.sub(r,n.Complex.mul(u[e][i],m(i,t)));a||(r=n.Complex.rdiv(r,m(t,t))),u[e][t]=r}else for(let e=0;e<l;e++)for(let t=c-1;t>=0;t--){let r=u[e][t];for(let i=t+1;i<c;i++)r=n.Complex.sub(r,n.Complex.mul(u[e][i],m(i,t)));a||(r=n.Complex.rdiv(r,m(t,t))),u[e][t]=r}return u};static functions={axpy:s.axpy,scal:s.scal,copy:s.copy,dotu:s.dotu,dotc:s.dotc,nrm2sq:s.nrm2sq,nrm2:s.nrm2,gemv:s.gemv,trsv:s.trsv,ger:s.ger,geru:s.geru,gerc:s.gerc,gerc_nd:s.gerc_nd,gerc_nd_direct:s.gerc_nd_direct,gemm_kernel:s.gemm_kernel,gemm:s.gemm,gemm_block:s.gemm_block,trsm:s.trsm}}t.BLAS=s,t.default={BLAS:s}},956(e,t,r){"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.CharString=t.stringClass=t.doubleQuoteCharacter=t.singleQuoteCharacter=void 0;const n=r(845);t.singleQuoteCharacter="'",t.doubleQuoteCharacter='"',t.stringClass=3;class i{str;quote;static STRING=3;type=i.STRING;parent;constructor(e,t='"'){this.str=e,this.quote=t}static create=(e,t='"')=>new i(e,t);static isInstanceOf=e=>e instanceof i;static copy=e=>new i(e.str,e.quote);copy(){return new i(this.str,this.quote)}static parse=e=>new i(e);static unparse=(e,t=0)=>e.str;static toString=e=>e.str;toString(){return this.str}static unparseEscaped=e=>{let t=JSON.stringify(e.str);return t=t.substring(1,t.length-2).replace(/\\\\/,"\\").replace(/\\\"/,'""'),'"'+t+'"'};static unparseMathML=(e,t=0)=>"<mi><pre>"+e.str+"</pre></mi>";static unparseEscapedMathML=e=>{let t=JSON.stringify(e.str);return t=t.substring(1,t.length-2).replace(/\\\\/,"\\").replace(/\\\"/,'""'),'<mi><pre>"'+t+'"</pre></mi>'};static logical=e=>e.str?n.Complex.true():n.Complex.false();static toLogical=e=>i.logical(e);toLogical(){return i.logical(this)}}t.CharString=i,t.default={singleQuoteCharacter:"'",doubleQuoteCharacter:'"',stringClass:3,CharString:i}},845(e,t,r){"use strict";var n,i=this&&this.__createBinding||(Object.create?function(e,t,r,n){void 0===n&&(n=r);var i=Object.getOwnPropertyDescriptor(t,r);i&&!("get"in i?!t.__esModule:i.writable||i.configurable)||(i={enumerable:!0,get:function(){return t[r]}}),Object.defineProperty(e,n,i)}:function(e,t,r,n){void 0===n&&(n=r),e[n]=t[r]}),o=this&&this.__setModuleDefault||(Object.create?function(e,t){Object.defineProperty(e,"default",{enumerable:!0,value:t})}:function(e,t){e.default=t}),s=this&&this.__importStar||(n=function(e){return n=Object.getOwnPropertyNames||function(e){var t=[];for(var r in e)Object.prototype.hasOwnProperty.call(e,r)&&(t[t.length]=r);return t},n(e)},function(e){if(e&&e.__esModule)return e;var t={};if(null!=e)for(var r=n(e),s=0;s<r.length;s++)"default"!==r[s]&&i(t,e,r[s]);return o(t,e),t});Object.defineProperty(t,"__esModule",{value:!0}),t.toNumber=t.Complex=void 0;const a=s(r(142)),l=r(428),c=r(826);t.toNumber=e=>e instanceof c.Decimal?e.toNumber():Number(e);class u{static _engineBackend;static _engine;static get engineBackend(){return this._engineBackend}static get engine(){return this._engine}static set engine(e){switch(this._engine=e,e){case"number":this._engineBackend=l.ComplexNumber;break;case"decimal":this._engineBackend=c.ComplexDecimal;break;default:throw new Error(`invalid complex backend engine: '${e}'.`)}a.ComplexInterfaceStaticKeyTable.forEach(e=>{this[e]=this._engineBackend[e]}),this.set(this.defaultSettings)}static LOGICAL;static REAL;static COMPLEX;static defaultSettings;static settings;static isInstanceOf;static set;static setNumberType;static create;static realSet;static imagSet;static realApply;static imagApply;static from;static rea