矩陣、分數、點、線類

Matrix,Fraction,Point,Line

//計算幾何偏差修正Math.EPS=0.00000001;//判斷x的符號Math.cmp=function(x) {    if(Math.abs(x)<Math.EPS)return 0;    if(x>0){        return 1;    }else{        return -1;    }}//矩陣類class Matrix {    //將一個數組構建成一個矩陣，行Row、列Column    constructor(data,Row,Column){        this.data=data||[];        this.Row=Row;//行        this.Column=Column;//豎    }    //根據行、列返回矩陣元素    getItem(r,c){        return this.data[r*this.Column+c]||0;    }    //根據行、列設置矩陣元素    setItem(r,c,item){        this.data[r*this.Column+c]=item;    }    //換行    swapRow(r1,r2){        for(let c=0;c<this.Column;c++){            const cache=this.getItem(r1,c)            this.setItem(r1,c,this.getItem(r2,c))            this.setItem(r2,c,cache);        }    }    oneRowEach(r,callback){        for(let c=0;c<this.Column;c++){            callback(this.getItem(r,c),r,c)        }    }    //按行遍歷矩陣元素,返回元素item，行r，列c    rowEach(callback){        for(let r=0;r<this.Row;r++){            for(let c=0;c<this.Column;c++){                callback(this.getItem(r,c),r,c)            }        }    }    //按豎遍歷矩陣元素,返回元素item，行r，列c    columnEach(callback){        for(let c=0;c<this.Column;c++){            for(let r=0;r<this.Row;r++){                callback(this.getItem(r,c),r,c)            }        }    }    //行循環    oneRowMap(r,callback){        this.oneRowEach(r,(item,r,c)=> {            this.setItem(r,c,callback(item,r,c));        })    }    //按行map矩陣元素    rowMap(callback){        this.rowEach((item,r,c)=> {            this.setItem(r,c,callback(item,r,c));        })    }    //相加    add(matrix){        if(matrix instanceof Matrix&& this.Row === matrix.Row && this.Column === matrix.Column){            const nMatrix=new Matrix([],this.Row,this.Column)            this.rowEach(function (item,r,c) {                nMatrix.setItem(r,c,item+matrix.getItem(r,c))            })            return nMatrix;        }else{            throw '方法plus 參數錯誤';        }    }    //相減    sub(matrix){        if(matrix instanceof Matrix&& this.Row === matrix.Row && this.Column === matrix.Column){            const nMatrix=new Matrix([],this.Row,this.Column)            this.rowEach(function (item,r,c) {                nMatrix.setItem(r,c,item-matrix.getItem(r,c))            })            return nMatrix;        }else{            throw '方法minus 參數錯誤';        }    }    //相乘    multiply(obj){        if(obj instanceof Matrix){            return this.multiplyMatrix(obj)        }else if(typeof obj=='number'){            return this.multiplyNumber(obj)        }else{            throw 'multiply 輸入的參數類型錯誤';        }    }    //矩陣與數相乘,返回一個新的矩陣    multiplyNumber(number){        const nMatrix=new Matrix([],this.Row,this.Column)        this.rowEach((item,r,c)=> {            nMatrix.setItem(r,c,item*number)        })        return nMatrix;    }    //矩陣與矩陣相乘 矩陣A的行必須與矩陣B的列數相等    multiplyMatrix(matrix){        if(this.Row!==matrix.Column){            throw '矩陣A的行必須與矩陣B的列數相等';        }        const nMatrix=new Matrix([],this.Row,matrix.Column)        for(let r=0;r<this.Row;r++){            for(let mc=0;mc<matrix.Column;mc++){                let num=0;                for(let c=0;c<this.Column;c++){                    num=num+this.getItem(r,c)*matrix.getItem(c,mc)                }                nMatrix.setItem(r,mc,num)            }        }        return nMatrix;    }    //切割    cut({r,c,w,h}){        const mt=this;        const nMt=new Matrix([],h,w);        nMt.rowMap(function (item,r1,c1) {            return mt.getItem(r+r1,c+c1)        })        return nMt;    }    //複製生成一個新的矩陣    clone(){        return new Matrix([].concat(this.data),this.Row,this.Column)    }    //轉換成字符圖形    toString(){        let str='[';        for(let r=0;r<this.Row;r++){            str=str+'\n'            for(let c=0;c<this.Column;c++){                if(r==this.Row-1&&c==this.Column-1){                    str=str+this.getItem(r,c);                }else{                    str=str+this.getItem(r,c)+',';                }            }        }        str=str+'\n]'        return str;    }}/*Gauss 消元傳入一個矩陣，傳出結果*/function Gauss(matrix){    let l=[];//是否爲自由元    let ans=[];//存儲解    const n=matrix.Column-1;//解的個數    let res=0,r=0;    for(let i=0;i<matrix.Column;i++){        for(let j=r;j<matrix.Row;j++){            if(Math.abs(matrix.getItem(j,i))>Math.EPS){                if(j!==r){                    //行交換位置                    for(let k=i;k<=n;k++){                        const temp1=matrix.getItem(j,k)                        const temp2=matrix.getItem(r,k)                        matrix.setItem(j,k,temp2)                        matrix.setItem(r,k,temp1)                    }                }                break;            }        }        // console.log(matrix.toString(),r,i)        if(Math.abs(matrix.getItem(r,i)<Math.EPS)){            ++res;            console.log('continue')            continue;        }        //方程相減，消除元        for(let j=0;j<matrix.Row;j++){            if(j!==r&&Math.abs(matrix.getItem(j,i))>Math.EPS){                let tmp=matrix.getItem(j,i)/matrix.getItem(r,i);                for(let k=i;k<=n;k++){                    const item=matrix.getItem(j,k)-tmp*matrix.getItem(r,k)                    matrix.setItem(j,k,item)                }            }        }        l[i]=true;        r++;    }    //輸出答案    for(let i=0;i<n;i++){        if(l[i]){            for(let j=0;j<n;j++){                if(Math.abs(matrix.getItem(j,i))>0){                    ans[i]=matrix.getItem(j,n)/a.getItem(j,i)                }            }        }    }    return ans;}//將一個矩陣轉換成上三角矩陣function upperMatrix(oriMatrix) {    const matrix=oriMatrix.clone();    let r=0;    //生成上三角矩陣    for(let i=0;i<matrix.Row;i++){        //循環行        for(let j=r;j<matrix.Row;j++){            if(Math.abs(matrix.getItem(j,i))>Math.EPS){                if(j!==r){                    //行交換位置                    matrix.swapRow(j,r)                }                break;            }        }        if(Math.abs(matrix.getItem(r,i)<Math.EPS)){            continue;        }        //方程相減，消除元        for(let j=0;j<matrix.Row;j++){            if(j!==r&&Math.abs(matrix.getItem(j,i))>Math.EPS){                let tmp=matrix.getItem(j,i)/matrix.getItem(r,i);                for(let k=i;k<matrix.Column;k++){                    const item=matrix.getItem(j,k)-tmp*matrix.getItem(r,k)                    matrix.setItem(j,k,item)                }            }        }        r++;    }    return matrix}//求矩陣的逆function Inverse(matrix){    if(matrix.Row!==matrix.Column){        throw '矩陣的行與列須要相等';    }    const N=matrix.Row;    //方程矩陣A    const A = new Matrix([],N,2*N);    for(let r=0;r<N;r++){        for(let c=0;c<N;c++){            A.setItem(r,c,matrix.getItem(r,c))        }    }    for(let r=0;r<N;r++){        for(let c=N;c<N*2;c++){            if(r===c-N){                A.setItem(r,c,1)            }else{                A.setItem(r,c,0)            }        }    }    //換成上三角矩陣    const B=upperMatrix(A)    //左邊轉成單位矩陣    for(let i=0;i<N;i++){        if(Math.abs(B.getItem(i,i))!==1){            for(let k=N;k<2*N;k++){                B.setItem(i,k,B.getItem(i,k)/B.getItem(i,i))            }            B.setItem(i,i,1)        }    }    //輸出結果    const C = new Matrix([],N,N);    C.rowMap(function (item,r,c) {        return B.getItem(r,c+N);    })    return C;}//歐幾里得算法 求兩個數a、b的最大公約數function gcd(a,b){    return b===0?a:gcd(b,a%b)}//分數類 分子，分母class Fraction{    constructor(num=0,den=1){        if(den<0){            num=-num;            den=-den;        }        if(den===0){            throw '分母不能爲0'        }        let g=gcd(Math.abs(num),den)        this.num=num/g;        this.den=den/g;    }    //加    add(o){        return new Fraction(this.num*o.den+this.den*o.num,this.den*o.den)    }    //減    sub(o){        return new Fraction(this.num*o.den-this.den*o.num,this.den*o.den)    }    //乘    multiply(o){        return new Fraction(this.num*o.num,this.den*o.den);    }    //除    divide(o){        return new Fraction(this.num*o.den,this.den*o.num);    }    //小於    lessThan(o){        return this.num*o.den<this.den*o.num;    }    //等於    equal(o){        return this.num*o.den===this.den*o.num;    }}//點類function Point(x,y) {    if(this instanceof Point){        if(Math.cmp(x.toFixed(2)-x)==0){            x=Number(x.toFixed(2));        }        if(Math.cmp(y.toFixed(2)-y)==0){            y=Number(y.toFixed(2));        }        this.x=x;        this.y=y;    }else{        return new Point(x,y)    }}//向量的模長Point.prototype.norm=function(){    return Math.sqrt(this.x*this.x+this.y*this.y);}// 加Point.add=function(a,b){    return new Point(a.x+b.x,a.y+b.y)}// 減Point.sub=function(a,b){    return new Point(a.x-b.x,a.y-b.y);}// 等於Point.equals=function(a,b){    return Math.cmp(a.x-b.x)===0&&Math.cmp(a.y-b.y)===0;}//乘 向量與數字Point.multiply=function(a,b){    if(a instanceof Point&&typeof b=='number'){        return Point(a.x*b,a.y*b)    }    if(b instanceof Point&&typeof a=='number'){        return Point(a*b.x,a*b.y)    }}//除 向量與數字Point.divide=function(a,b){    return Point(a.x/b,a.y/b)}//向量的叉積Point.det=function (a,b) {    return a.x*b.y-a.y*b.x;}//向量的點積Point.dot=function (a,b) {    return a.x*b.x+a.y*b.y;}//兩個點的距離Point.dist=function (a,b) {    return Point.sub(a,b).norm()}//逆時針旋轉,a爲弧度Point.rotate=function (p,A) {    if(A===0){return p;}    const tx=p.x;    const ty=p.y;    return Point(tx*Math.cos(A)-ty*Math.sin(A),tx*Math.sin(A)+ty*Math.cos(A))}//計算幾何線段類function Line(a,b) {    if(this instanceof Line){        this.a=a;        this.b=b;    }else{        if(a instanceof Point&&b instanceof Point){            return new Line(a,b)        }else{            throw 'Line 參數錯誤'        }    }}//點p到線段s、t的距離Line.dis_point_segment=function(p,s,t){    if(Math.cmp(Point.dot(Point.sub(p,s),Point.sub(t,s)))<0){        return Point.sub(p,s).norm()    }    if(Math.cmp(Point.dot(Point.sub(p,t),Point.sub(s,t)))<0){        return Point.sub(p,t).norm()    }    return Math.abs(Point.det(Point.sub(s,p),Point.sub(t,p))/Point.dist(s,t))}//點到線段的垂足Line.pointProjLine=function(p,s,t){    const r=Point.dot(Point.sub(t,s),Point.sub(p,s))/Point.dot(Point.sub(t,s),Point.sub(t,s))    return Point.add(s,Point.multiply(r,Point.sub(t,s)))}//點是否在線段上Line.pointOnSegment=function(p,s,t){    return Math.cmp(Point.det(Point.sub(p,s),Point.sub(t,s)))===0&&Math.cmp(Point.det(Point.sub(p,s),Point.sub(p,t)))<=0}//判斷線段a、b是否平行,a、b 爲lineLine.parallel=function (a,b) {    return !Math.cmp(Point.det(Point.sub(a.a,a.b),Point.sub(b.a,b.b)))}//判斷線段a、b是否相交,返回交點Line.lineMakePoint=function (a,b) {    if(Line.parallel(a,b)){        return false;    }    const s1=Point.det(Point.sub(a.a,b.a),Point.sub(b.b,b.a));    const s2=Point.det(Point.sub(a.b,b.a),Point.sub(b.b,b.a));    return Point.divide(Point.sub(Point.multiply(s1,a.b),Point.multiply(s2,a.a)),s1-s2);}// 將直線a沿法向量方向平移距離len獲得的直線Line.moveD=function (a,len) {    let d=Point.sub(a.b,a.a)    d=Point.divide(d,d.norm());    d=Point.rotate(d,Math.PI/2);    return Line(Point.add(a.a,Point.multiply(d,len)),Point.add(a.b,Point.multiply(d,len)))}module.exports={    Matrix,    Fraction,    Point,    Line}