mathjslab/lib/mathjslab.web.umd2022.js

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

/*! For license information please see mathjslab.web.umd2022.js.LICENSE.txt */
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h.FunctionHandle}})},115(e,t,r){"use strict";t.BLAS=t.cT=void 0;const n=r(845),i=r(679);t.cT=["blockThreshold","blockSize"];const s={blockThreshold:1e5,blockSize:64};class a{static defaultSettings=Object.assign({},s);static settings=a.defaultSettings;static set=e=>{Object.entries(e).forEach(e=>{if(!t.cT.includes(e[0]))throw new Error(`BLAS.set: invalid configuration parameter: ${e[0]}`);a.settings[e[0]]=e[1]})};static axpy=(e,t,r)=>{const i=t.length,s=t[0].length;for(let a=0;a<i;a++){const i=t[a],o=r[a];for(let t=0;t<s;t++)o[t]=n.Complex.add(o[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 s=r;s<i;s++)t[s]=n.Complex.mul(e,t[s])};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 s=0;s<r;s++)n.Complex.mulAndSumTo(i,e[s],t[s]);return i};static dot=a.dotu;static dotc=(e,t)=>{const r=e.length;let i=n.Complex.zero();for(let s=0;s<r;s++)n.Complex.mulAndSumTo(i,n.Complex.conj(e[s]),t[s]);return i};static nrm2sq=(e,t,r,i)=>{let s=n.Complex.zero();for(let a=r;a<i;a++)n.Complex.mulAndSumTo(s,e.array[a][t],n.Complex.conj(e.array[a][t]));return n.Complex.create(s.re)};static nrm2=e=>{let t=n.Complex.zero(),r=n.Complex.one();for(let i=0;i<e.length;i++){const s=e[i],a=n.Complex.abs(n.Complex.real(s)),o=n.Complex.abs(n.Complex.imag(s));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))}if(n.Complex.toBoolean(n.Complex.ne(o,n.Complex.zero())))if(n.Complex.lt(t,o)){const e=n.Complex.rdiv(t,o);r=n.Complex.add(n.Complex.one(),n.Complex.mul(r,n.Complex.mul(e,e))),t=o}else{const e=n.Complex.rdiv(o,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,s,a,o,l,c,u,m,h="N")=>{const p="N"===h?t:r,d="N"===h?r:t;for(let e=0;e<p;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<p;t++){let r=n.Complex.zero();for(let l=0;l<d;l++){const c="N"===h?e[i+t][s+l]:"T"===h?e[i+l][s+t]:n.Complex.conj(e[i+l][s+t]);n.Complex.mulAndSumTo(r,c,a[o+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 a.trsm(e,i,{side:"left",uplo:r.uplo,transA:r.transA,unitDiagonal:r.unitDiagonal}).map(e=>e[0])};static ger=(e,t,r,i,s,a,o,l,c,u,m,h)=>{if(!n.Complex.realIsZero(n.Complex.abs(a)))for(let p=0;p<i;p++){const i=o[l+p][c],d=n.Complex.mul(a,i),x=e[t+p];for(let e=0;e<s;e++)n.Complex.mulAndSumTo(x[r+e],d,n.Complex.conj(u[m+e][h]))}};static geru=(e,t,r,i,s,a)=>{if(!n.Complex.realIsZero(n.Complex.abs(r)))for(let o=0;o<e.length;o++){const l=e[o],c=i[s+o];for(let e=0;e<t.length;e++)n.Complex.mulAndSumTo(c[a+e],r,n.Complex.mul(l,t[e]))}};static gerc=(e,t,r,i,s=0,a=0)=>{for(let o=0;o<e.length;o++){const l=e[o],c=i[s+o];for(let e=0;e<t.length;e++)c[a+e]=n.Complex.add(c[a+e],n.Complex.mul(r,n.Complex.mul(l,n.Complex.conj(t[e]))))}};static gerc_nd=(e,t,r)=>{const s=[];for(let t=0;t<i.MultiArray.linearLength(e);t++){const[r,n]=i.MultiArray.linearIndexToMultiArrayRowColumn(e.dimension[0],e.dimension[1],t);s.push(e.array[r][n])}const a=[];for(let e=0;e<i.MultiArray.linearLength(t);e++){const[r,n]=i.MultiArray.linearIndexToMultiArrayRowColumn(t.dimension[0],t.dimension[1],e);a.push(t.array[r][n])}const o=s.length,l=a.length;if(r.dimension[0]!==o||r.dimension[1]!==l)throw new Error(`BLAS.gerc_nd: dimension mismatch (C is ${r.dimension[0]}x${r.dimension[1]}, x is ${o}, y is ${l})`);for(let e=0;e<o;e++){const t=n.Complex.conj(s[e]);for(let i=0;i<l;i++){const s=n.Complex.mul(t,a[i]);r.array[e][i]?r.array[e][i]=n.Complex.add(r.array[e][i],s):r.array[e][i]=n.Complex.copy(s)}}i.MultiArray.setType(r)};static gerc_nd_direct=(e,t,r)=>{const s=i.MultiArray.linearLength(e),a=i.MultiArray.linearLength(t);if(r.dimension[0]!==s||r.dimension[1]!==a)throw new Error(`BLAS.gerc_nd_direct: dimension mismatch (C is ${r.dimension[0]}x${r.dimension[1]}, x is ${s}, y is ${a})`);e.dimension[0],e.dimension[1],t.dimension[0],t.dimension[1],r.dimension[0],r.dimension[1];for(let o=0;o<s;o++){const[l,c]=i.MultiArray.linearIndexToMultiArrayRowColumn(e.dimension[0],e.dimension[1]||1,o),u=n.Complex.conj(e.array[l][c]);for(let e=0;e<a;e++){const[a,l]=i.MultiArray.linearIndexToMultiArrayRowColumn(t.dimension[0],t.dimension[1]||1,e),c=t.array[a][l],[m,h]=i.MultiArray.linearIndexToMultiArrayRowColumn(r.dimension[0],r.dimension[1],o+e*s);r.array[m][h]?r.array[m][h]=n.Complex.add(r.array[m][h],n.Complex.mul(u,c)):r.array[m][h]=n.Complex.mul(u,c)}}i.MultiArray.setType(r)};static gemm_kernel=(e,t,r,i,s,a,o,l,c)=>{for(let u=i;u<s;u++){const i=e[u],s=r[u];for(let e=a;e<o;e++){let r=s[e]??n.Complex.zero();for(let s=l;s<c;s++)n.Complex.mulAndSumTo(r,i[s],t[s][e]);s[e]=r}}};static gemm=(e,t,r,i,s,o,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<o;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<o;e++)t[e]=n.Complex.mul(l,t[e])}if(r*i*o>a.settings.blockThreshold)for(let e=0;e<r;e+=u??a.settings.blockSize){const n=Math.min(e+(u??a.settings.blockSize),r);for(let r=0;r<i;r+=u??a.settings.blockSize){const l=Math.min(r+(u??a.settings.blockSize),i);for(let i=0;i<o;i+=u??a.settings.blockSize){const m=Math.min(i+(u??a.settings.blockSize),o);a.gemm_kernel(t,s,c,e,n,i,m,r,l)}}}else for(let a=0;a<r;a++){const r=t[a],l=c[a];for(let t=0;t<o;t++){let a=n.Complex.zero();for(let e=0;e<i;e++)n.Complex.mulAndSumTo(a,r[e],s[e][t]);l[t]=n.Complex.add(l[t],n.Complex.mul(e,a))}}}};static gemm_block=(e,t,r,i,s,o)=>{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(s)))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(s,n.Complex.one())))for(let e=0;e<l;e++)for(let t=0;t<m;t++)r[e][t]=n.Complex.mul(s,r[e][t]);return}const h=Math.max(1,Math.floor(o??a.settings.blockSize));for(let a=0;a<l;a+=h){const o=Math.min(a+h,l);for(let l=0;l<m;l+=h){const u=Math.min(l+h,m);for(let e=a;e<o;e++)for(let t=l;t<u;t++)n.Complex.realIsZero(n.Complex.abs(s))?r[e][t]=n.Complex.zero():n.Complex.toBoolean(n.Complex.ne(s,n.Complex.one()))&&(r[e][t]=n.Complex.mul(s,r[e][t]));for(let s=0;s<c;s+=h){const m=Math.min(s+h,c);for(let c=a;c<o;c++){const a=e[c],o=r[c];for(let e=s;e<m;e++){const r=a[e];if(!n.Complex.realIsZero(n.Complex.abs(r)))for(let s=l;s<u;s++){const a=n.Complex.mul(r,t[e][s]),l=n.Complex.mul(i,a);o[s]=n.Complex.add(o[s],l)}}}}}}};static trsm=(e,t,r)=>{const i=r?.side??"left",s=r?.uplo??"upper",a=r?.transA??"N",o=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"===a?e[t][r]:"T"===a?e[r][t]:n.Complex.conj(e[r][t]);if("left"===i)if("upper"===s&&"N"===a||"lower"===s&&"N"!==a)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]));o||(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]));o||(r=n.Complex.rdiv(r,m(t,t))),u[t][e]=r}else if("upper"===s&&"N"===a||"lower"===s&&"N"!==a)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)));o||(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)));o||(r=n.Complex.rdiv(r,m(t,t))),u[e][t]=r}return u};static functions={axpy:a.axpy,scal:a.scal,copy:a.copy,dotu:a.dotu,dotc:a.dotc,nrm2sq:a.nrm2sq,nrm2:a.nrm2,gemv:a.gemv,trsv:a.trsv,ger:a.ger,geru:a.geru,gerc:a.gerc,gerc_nd:a.gerc_nd,gerc_nd_direct:a.gerc_nd_direct,gemm_kernel:a.gemm_kernel,gemm:a.gemm,gemm_block:a.gemm_block,trsm:a.trsm}}t.BLAS=a},812(e,t){"use strict";t.CallFrame=void 0;t.CallFrame=class{scope;func;callSite;name;nargin;nargout;inputArgs;parentFrame;constructor(e,t,r,n,i=0,s=0,a=[],o){this.scope=e,this.func=t,this.callSite=r,this.name=n,this.nargin=i,this.nargout=s,this.inputArgs=a,this.parentFrame=o}}},225(e,t){"use strict";t.Callables=void 0;const r={builtin:e=>({type:"BUILTIN",node:e}),lambda:e=>({type:"LAMBDA",node:e}),functionDefinition:e=>({type:"FCNDEF",node:e}),fromFunctionNode(e){return"BUILTIN"===e.type?this.builtin(e):this.functionDefinition(e)},isBuiltin:e=>"BUILTIN"===e.type,isLambda:e=>"LAMBDA"===e.type,isFunctionDefinition:e=>"FCNDEF"===e.type};t.Callables=r},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-1).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-1).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]}),s=this&&this.__setModuleDefault||(Object.create?function(e,t){Object.definePropert