C++实现R语言向量化运算（向量类：c 矩阵类：matrix）2015.9.11

类源代码：

#includeusing std::cout;using std::endl;using std::cin;using std::istream;using std::ios_base;#includeusing std::vector;#includeusing std::initializer_list;#includeusing std::for_each;using std::sort;using std::copy;using std::find;#includeusing std::runtime_error;#includeusing std::srand;using std::rand;using std::system;#includeusing std::time;#includeusing std::sqrt;#includeusing std::pair;using std::make_pair;#includeusing std::setw;#includeusing std::multiset;using std::set;#includeusing std::unordered_map;using std::unordered_multimap;#includeusing std::multimap;using std::map; class matrix;class c{private:    vector c_val;    size_t dim;public:    c():c_val(vector()),dim(0){}    c(initializer_listlst);    c(const vector&c_v):c_val(c_v),dim(c_v.size()){}    c(const matrix&m);    void out(size_t n=1)const{cout<<"The vector is:\n";for(size_t i=0;i<<setw(n)<<c_val[i]<<" ";cout<<endl<<endl;}    double operator[](size_t i)const{return c_val[i];}    double& operator[](size_t i){return c_val[i];}    size_t re_dim()const{return dim;}    friend c operator+(const c&a,const c&b);    friend c operator-(const c&a);    friend c operator-(const c&a,const c&b);    friend c rep(const double&d,size_t n);    friend c operator+(const c&a,const double&d);    friend c operator-(const c&a,const double&d);    friend c operator+(const double&d,const c&a);    friend c operator-(const double&d,const c&a);    friend c operator*(const double&d,const c&a);    friend c operator*(const c&a,const double&d);    friend c operator/(const double&d,const c&a);    friend c operator/(const c&a,const double&d);    friend c operator*(const c&a,const c&b);    friend bool operator==(const c&a,const c&b){return a.c_val==b.c_val;}    friend bool operator!=(const c&a,const c&b){return a.c_val!=b.c_val;}    vector const_re_c_val()const{return c_val;}};class matrix{private:    vector m_val;    size_t rdim;    size_t cdim;public:    matrix():m_val(vector()),rdim(0),cdim(0){}    matrix(const vector&m):m_val(m),rdim(m_val.size()),cdim(m_val[0].re_dim()){}    matrix(size_t m,size_t n,const double&d):m_val(vector(m,vector(n,d))),rdim(m),cdim(n){}    matrix(const c&v,size_t r,size_t c);    matrix(const c&v);    c operator[](size_t i)const{return m_val[i];}    c& operator[](size_t i){return m_val[i];}    void out(size_t n=3)const;    c col(size_t i)const;    void col_change(size_t i,const c&a);    friend matrix operator+(const matrix&a,const matrix&b);    friend matrix operator-(const matrix&a);    friend matrix operator-(const matrix&a,const matrix&b);    friend matrix operator+(const matrix&a,const double&d);    friend matrix operator+(const double&d,const matrix&a);    friend matrix operator-(const matrix&a,const double&d);    friend matrix operator-(const double&b,const matrix&a);    friend matrix operator*(const matrix&a,const double&d);    friend matrix operator*(const double&d,const matrix&a);    friend matrix operator/(const matrix&a,const double&d);    friend matrix operator/(const double&d,const matrix&a);    void Swap(size_t i,size_t j)    {c temp=this->operator[](i);this->operator[](i)=this->operator[](j);this->operator[](j)=temp;}    void col_Swap(size_t i,size_t j)    {        auto temp=this->col(i);        this->col_change(i,this->col(j));        this->col_change(j,temp);    }    friend bool operator==(const matrix&a,const matrix&b){return a.m_val==b.m_val;}    friend bool operator!=(const matrix&a,const matrix&b){return a.m_val!=b.m_val;}    pair re_dim()const{return make_pair(rdim,cdim);}    friend c operator%(const matrix&m,const c&v);    friend matrix operator%(const matrix&a,const matrix&b);    friend matrix operator%(const c&v,const matrix&m);}; //类c的有关定义c::c(initializer_listlst){    vectorout;    for_each(lst.begin(),lst.end(),[&](const double&d){out.push_back(d);});    c_val=out;    dim=out.size();}c operator+(const c&a,const c&b){    size_t MAX=b.re_dim();    if(a.re_dim()>b.re_dim())        MAX=a.re_dim();    vectortemp0(MAX,0);    vectortemp1(MAX,0);    vectortemp2(MAX,0);    copy(a.c_val.begin(),a.c_val.end(),temp0.begin());    copy(b.c_val.begin(),b.c_val.end(),temp1.begin());    for(size_t i=0;i        temp2[i]=temp0[i]+temp1[i];    return c(temp2);}c operator-(const c&a){    c out(a);    for(size_t i=0;i        out[i]=-out[i];    return out;}c operator-(const c&a,const c&b){    return (a+(-b));}c rep(const double&d,size_t n){    return c(vector(n,d));}c operator+(const c&a,const double&d){    return a+rep(d,a.re_dim());}c operator-(const c&a,const double&d){    return (a+(-d));}c operator+(const double&d,const c&a){    return a+d;}c operator-(const double&d,const c&a){    return (-a)+d;}c operator*(const double&d,const c&a){    c out(a);    for(size_t i=0;i        out[i]*=d;    return out;}c operator*(const c&a,const double&d){    return d*a;}c operator/(const double&d,const c&a){    c out(a);    for(size_t i=0;i        out[i]=d/a[i];    return out;}c operator/(const c&a,const double&d){    c out(a);    for(size_t i=0;i        out[i]=a[i]/d;    return out;}c::c(const matrix&m){    vectortemp;        for(size_t j=0;j                for(size_t i=0;i        temp.push_back(m[i][j]);    c_val=temp;    dim=temp.size();}c operator*(const c&a,const c&b){    if(a.re_dim()!=b.re_dim())        throw runtime_error("dim error!\n");    c out(a);    for(size_t i=0;i        out[i]*=b[i];    return out;} //类matrix的有关定义void matrix::out(size_t n)const{    cout<<"The matrix is:\n";    for(size_t i=0;i    {        for(size_t j=0;j            cout<<setw(n)<<(*this)[i][j]<<" ";        cout<<endl;    }    cout<<endl;}c matrix::col(size_t i)const{    c out(rep(0,rdim));    for(size_t j=0;j        out[j]=(*this)[j][i];    return out;}void matrix::col_change(size_t i,const c&a){    for(size_t j=0;j        (*this)[j][i]=a[j];}matrix::matrix(const c&v,size_t r,size_t c):rdim(r),cdim(c){    matrix out(r,c,0);    for(size_t i=0;i        out[i%r][i/r]=v[i];    (this->m_val)=out.m_val;}matrix::matrix(const c&v):rdim(v.re_dim()),cdim(1){    matrix out(v.re_dim(),1,0);    for(size_t i=0;i        out[i][0]=v[i];    this->m_val=out.m_val;}matrix operator+(const matrix&a,const matrix&b){    size_t r_MAX=a.rdim,c_MAX=a.cdim;    if(a.rdim        r_MAX=b.rdim;    if(a.cdim        c_MAX=b.cdim;    matrix tempa(r_MAX,c_MAX,0);    for(size_t i=0;i        for(size_t j=0;j        tempa[i][j]=a[i][j];    matrix tempb(r_MAX,c_MAX,0);    for(size_t i=0;i        for(size_t j=0;j        tempb[i][j]=b[i][j];    matrix tempout(r_MAX,c_MAX,0);    for(size_t i=0;i        for(size_t j=0;j        tempout[i][j]=tempa[i][j]+tempb[i][j];    return tempout;}matrix operator-(const matrix&a){    matrix out(a);    for(size_t i=0;i        for(size_t j=0;j        out[i][j]=-out[i][j];    return out;}matrix operator-(const matrix&a,const matrix&b){    return ((-b)+a);}matrix operator+(const matrix&a,const double&d){    return a+matrix(a.rdim,a.cdim,d);}matrix operator+(const double&d,const matrix&a){    return a+d;}matrix operator-(const matrix&a,const double&d){    return a+(-d);}matrix operator-(const double&b,const matrix&a){    return (-a)+b;}matrix operator*(const matrix&a,const double&d){    matrix out(a);    for(size_t i=0;i        for(size_t j=0;j        out[i][j]*=d;    return out;}matrix operator*(const double&d,const matrix&a){    return a*d;}matrix operator/(const matrix&a,const double&d){    return a*(1/d);}matrix operator/(const double&d,const matrix&a){    matrix out(a.rdim,a.cdim,0);    for(size_t i=0;i        for(size_t j=0;j        out[i][j]=d/a[i][j];    return out;} //基本运算函数matrix diag(const c&v){    matrix out(v.re_dim(),v.re_dim(),0);    for(size_t i=0;i        out[i][i]=v[i];    return out;}matrix diag(const matrix&m){    if(m.re_dim().first!=m.re_dim().second)        throw runtime_error("dim error!\n");    matrix out(m.re_dim().first,m.re_dim().second,0);    for(size_t i=0;i        out[i][i]=m[i][i];    return out;}double inter_product(const c&a,const c&b){    if(a.re_dim()!=b.re_dim())        throw runtime_error("dim error!\n");    double out=0;    for(size_t i=0;i    out+=(a[i]*b[i]);    return out;}c operator%(const matrix&m,const c&v){    if(m.re_dim().second!=v.re_dim())        throw runtime_error("dim error!\n");    c out(rep(0,m.re_dim().first));    for(size_t i=0;i        out[i]=inter_product(m[i],v);    return out;}//同下double prod(const c&v){    double out=1;    for(size_t i=0;i        out*=v[i];    return out;}//对于matrix的求和由c复制构造函数的重载函数定义：c(const matrix&m)double sum(const c&v){    double out=v[0];    for(size_t i=1;i        out+=v[i];    return out;}matrix operator%(const c&v,const matrix&m){    if(v.re_dim()!=m.re_dim().first)        throw runtime_error("dim error!\n");    matrix out(1,m.re_dim().second,0);    for(size_t i=0;i        out[0][i]=inter_product(v,m.col(i));    return out;}matrix outer_product(const c&a,const c&b){    matrix out(a.re_dim(),b.re_dim(),0);    for(size_t i=0;i        for(size_t j=0;j        out[i][j]=a[i]*b[j];    return out;}size_t length(const c&v){    return v.re_dim();}c sort(const c&v){    vectorout;    for(size_t i=0;i        out.push_back(v[i]);    sort(out.begin(),out.end());    return c(out);}double mean(const c&v){    return sum(v)/length(v);}//其转换版本返回矩阵转为向量的方差double var(const c&v){    return mean((v-mean(v))*(v-mean(v)));}c connect(initializer_list lst){    vectortemp;    for_each(lst.begin(),lst.end(),[&](const c&v){for(auto a:v.const_re_c_val())temp.push_back(a);});    return c(temp);}//标准差templatedouble STD(const any&a){    return sqrt(var(a)*(length(a))/(length(a)-1));}matrix rbind(initializer_listlst){    size_t r=0;    auto a=lst.begin();    while(a!=lst.end())    {        a++;        r++;    }    size_t co=0;    for_each(lst.begin(),lst.end(),[&](const c&v){if(v.re_dim()>co)co=v.re_dim();});    matrix out(r,co,0);    size_t i=0;    a=lst.begin();    while(a!=lst.end())    {        vectortemp(co,0);        for(size_t i=0;iconst_re_c_val().size();i++)            temp[i]=a->operator[](i);        out[i]=c(temp);        i++;        a++;    }    return out;}size_t dim(const c&v){    return v.re_dim();}pair dim(const matrix&m){    return m.re_dim();}double min(const c&v){    double temp=v[0];    for(size_t i=1;i        if(v[i]        temp=v[i];    return temp;}double max(const c&v){    double temp=v[0];    for(size_t i=1;i        if(v[i]>temp)        temp=v[i];    return temp;}c pmin(initializer_listlst){    c temp=rep(0,lst.size());    auto a=lst.begin();    for(size_t i=0;i    {        temp[i]=min(*a);        a++;    }    return temp;}c pmax(initializer_listlst){    c temp=rep(0,lst.size());    auto a=lst.begin();    for(size_t i=0;i    {        temp[i]=max(*a);        a++;    }    return temp;}templatepair range(const any&v){    cout<<"MIN: "<<min(v)<<" MAX: "<<max(v)<<endl;    return make_pair(min(v),max(v));}double median(const c&v){    return sort(v)[length(v)/2];}double var(const c&a,const c&b){    if(length(a)!=length(b))        throw runtime_error("dim error!\n");    c t1(a-mean(a)),t2(b-mean(b));    return inter_product(t1,t2)/(length(a)-1);}double cov(const c&a,const c&b){    return var(a,b);}double cor(const c&a,const c&b){    return var(a,b)/STD(a)/STD(b);}matrix var(const matrix&a,const matrix&b){    if(a.re_dim().first!=b.re_dim().first)        throw runtime_error("dim error!\n");    matrix temp(a.re_dim().second,b.re_dim().second,0);    for(size_t i=0;i        for(size_t j=0;j        temp[i][j]=var(a.col(i),b.col(j));    return temp;}matrix cov(const matrix&a,const matrix&b){    return var(a,b);}matrix cor(const matrix&a,const matrix&b){    matrix temp=var(a,b);    for(size_t i=0;i        for(size_t j=0;j        temp[i][j]/=((STD(a.col(i))*STD(b.col(j))));    return temp;}matrix cov(const matrix&a){    return var(a,a);}matrix cor(const matrix&a){    return cor(a,a);}//由于关联容器的删除方法利用误差排序的方法//利用顺序容器迭代器的删除方法有困难c rank(const c&v){    vectortemp00(v.const_re_c_val());    for(size_t i=0;i        temp00[i]+=(0.00000001*i);    vectortemp0(temp00);    multisettemp2(temp0.begin(),temp0.end());    vectortemp1(v.re_dim());    size_t i=0,j=0;    double pre_val=min(c(vector(temp2.begin(),temp2.end())));    vector::iterator s0;    while(i    {    double val=min(c(vector(temp2.begin(),temp2.end())));    s0=find(temp0.begin(),temp0.end(),val);    if(sqrt((pre_val-val)*(pre_val-val))>0.000001)        j++;    temp1[s0-temp0.begin()]=j;    temp2.erase(val);    i++;    pre_val=val;    }    return  c(temp1);}c rev(const c&v){    vector temp;    auto a=v.const_re_c_val().rbegin();    while(a!=v.const_re_c_val().rend())    {        temp.push_back(*a);        a++;    }    return c(temp);}//向量先排序再输出排序前的下标值c order(const c&v){    unordered_multimapm0;    for(size_t i=0;i        m0.insert(make_pair(v[i],i));    multimapm1(m0.begin(),m0.end());    c temp(rep(0,length(v)));    auto a=m1.begin();    size_t i=0;    while(a!=m1.end())    {        temp[i]=a->second;        i++;        a++;    }    return temp;}c cumsum(const c&v){    c temp(v);    for(size_t i=1;i        temp[i]+=temp[i-1];    return temp;}c cumprod(const c&v){    c temp(v);    for(size_t i=1;i        temp[i]*=temp[i-1];    return temp;}matrix cumsum(const matrix&m){    c temp(m);    for(size_t i=1;i        temp[i]+=temp[i-1];    return matrix(temp,m.re_dim().first,m.re_dim().second);}matrix cumprod(const matrix&m){    c temp(m);    for(size_t i=1;i        temp[i]*=temp[i-1];    return matrix(temp,m.re_dim().first,m.re_dim().second);} //矩阵运算函数//初等行变换化上三角求解行列式double det(const matrix&m){auto f=[](const matrix&mm)->pair{    if(mm.re_dim().first!=mm.re_dim().second)       throw runtime_error("dim error!\n");    size_t MIN=mm.re_dim().first;    double mult=1;    size_t col=0;    size_t bar=0;    size_t b_c=0;    matrix t(mm);    while(b_c    {    for(size_t i=bar+1;i    {        if(t[i][col]==0)            i++;        else        {           t.Swap(i,bar);           mult*=(-1);           break;        }    }    if(bar!=MIN+1)    {    if(t[bar][col]!=0)    {       for(size_t i=bar+1;i     {        t[bar][i]=t[bar][i]/t[bar][col];        if(i==bar+1)        mult*=t[bar][col];     }        if(col!=MIN-1)        t[bar][col]=1;    }     for(size_t i=bar+1;i     {         t[i]=t[i]-t[i][col]*t[bar];     }    }      col++;      bar++;      b_c=bar;      if(col>bar);      b_c=col;    }return make_pair(t,mult);};    pair tt=f(m);    return tt.second*prod(diag(tt.first)%rep(1,m.re_dim().first));}//Cramer法则解线性方程组：要求自变量矩阵为方阵且相应行列式不为0c solve(const matrix&m,const c&v){    c temp(rep(0,v.re_dim()));    double low=det(m);    if(m.re_dim().first!=m.re_dim().second)      throw runtime_error("dim error!\n");    if(low==0)      throw runtime_error("singular!\n");    for(size_t i=0;i    {        matrix temp0(m);        temp0.col_change(i,v);        temp[i]=det(temp0)/low;    }    return temp;}double tr(const matrix&m){    if(m.re_dim().first!=m.re_dim().second)        throw runtime_error("dim error!\n");    return inter_product(diag(m)%rep(1,m.re_dim().first),rep(1,m.re_dim().first));}matrix T(const matrix&m){    matrix out(m.re_dim().second,m.re_dim().first,0);    for(size_t i=0;i        for(size_t j=0;j        out[i][j]=m[j][i];    return out;}matrix cbind(initializer_listlst){    return T(rbind(lst));}matrix operator%(const matrix&a,const matrix&b){    matrix out(a.re_dim().first,a.re_dim().second,0);    for(size_t i=0;i        for(size_t j=0;j        out[i][j]=inter_product(a[i],b.col(j));    return out;}double F_norm(const matrix&m){    return sqrt(tr(T(m)%m));} //a,b为区间 d为步长 e为精度 默认为求整数精度：以1为精度特征值 如所求特征值太少可通过减少d改善//只能求实值//可以用F_norm作为a、b的界（-F_norm(m),F_norm(m)）可确保值在范围中//可用于求解但效率低c eigen(const matrix&m,const double&a,const double& b,const double &d=0.0001,const double &e=1){    if(m.re_dim().first!=m.re_dim().second)        throw runtime_error("dim error!\n");    vectortemp;    double pre_beg=100000000;    for(double beg=a;beg    {        matrix mm0(diag(rep(beg,m.re_dim().first))-m);        double s0=det(mm0);        if(sqrt(s0*s0)        {            if(sqrt((pre_beg-beg)*(pre_beg-beg))>1)            {             temp.push_back(beg);             pre_beg=beg;             cout<<"Done!\n";             cout<<beg<<endl;//eigenvalue            }        }    }    return c(temp);}//重载求eign的函数 d:步长 可保证绝对求出所有特征值（利用循环增大精度）c eigen(const matrix&m,const double&d=0.1){    double dd=d;    double ra=F_norm(m);    double trr=tr(m);    c temp;    double r=0;    do    {        dd*=0.1;        temp=eigen(m,-ra,ra,dd);        if(temp.re_dim()==m.re_dim().first)            break;        r=sum(temp)-trr;    }    while(sqrt((r*r)>1));        //与迹的差距（精度）设定为1 绝对值小于此值的特征值被忽略        //此种方法的一个缺陷为异号特征值的抵消 对于同号特征值有把握        //只适用于所有特征值为实值的情况        //如有复特征值，只输出实数的并循环不能结束    return temp;}matrix M(const matrix&m,size_t k,size_t l){    matrix temp(m);    set s1;    for(size_t i=0;i        s1.insert(i);    set s2;    for(size_t i=0;i        s2.insert(i);    s1.erase(k);    s2.erase(l);    vectortemp00;    for(auto j:s2)        for(auto i:s1)        temp00.push_back(temp[i][j]);    return matrix (c(temp00),m.re_dim().first-1,m.re_dim().second-1);}matrix A_accompany(const matrix&m){    matrix out(m.re_dim().first,m.re_dim().second,0);    for(size_t i=0;i        for(size_t j=0;j        out[i][j]=det(M(m,i,j))*(((i+j)%2)?-1:1);        //代数余子式    return T(out);}//求方阵的逆矩阵（利用伴随矩阵方法）matrix solve(const matrix&m){    double de=det(m);    if(sqrt(de*de)<0.000001)     throw runtime_error("singular!\n");    return A_accompany(m)/de;}//利用逆矩阵法求解方程组 要求自变量阵为方阵 且可逆c solve_eq(const matrix&m,const c&v){    c out;    double de=det(m);    if(sqrt(de*de)<0.000001)      throw runtime_error("singular!\n");    return solve(m)%v;}  测试程序：int main(){//测试程序：    c c0({35.1,12});    vectorv0;    for(size_t i=0;i<10;i++)        v0.push_back(i);    c c1(v0);    c0.out();    c1.out();    cout<<c0[1]<<endl;    c0[1]=10;    cout<<c0[1]<<endl;    (c0+c1).out();    (-c0).out();     (c0-c1).out();     rep(1,10).out();     (c0+rep(1,10)).out();    (c0-rep(1,10)).out();    (rep(1,10)+1).out();    (rep(1,10)-1).out();    (10/rep(1,10)).out();    (rep(1,10)/10).out();    cout<<((10/rep(1,10))==(rep(1,10)/10))<<endl;    matrix m0=matrix(3,4,10);    m0[1]=rep(4,4);    m0.out();    m0.col(2).out();    m0.col_change(0,c({1,2,3}));    m0.out();    matrix m1=(matrix(c({1,5,7,8,9,0,3,4,5}),3,3)+matrix(c({3,5,7,9}),2,2));    m1.out();    (-m1).out();    (m1-matrix(rep(1,10),5,2)).out();    (m1+1).out();    (m1*0.6).out();    (m1-1).out();    (1-m1).out();    (0.6*m1).out();    (1/m1).out();    (m1/10).out();    m1.out();    m1.Swap(1,2);    m1.out();    m1.col_Swap(1,2);    m1.out();    matrix    m2=m1;    m1.Swap(0,1);    cout<<(m1==m2)<<endl;    cout<<m1.re_dim().first<<" "<<m1.re_dim().second<<endl;    matrix A(c({1,2,1,4,7,1,5,2,1}),3,3);    cout<<det((A+diag(rep(10,A.re_dim().first))))<<endl;    solve(matrix(c({30,7.3,4.2,0,0,6,8,7,0}),3,3),c({11,12,13})).out();    m1.out();    cout<<F_norm(m1)<<endl;    eigen(matrix(c({50,1,1,9,7,1,4,1,13}),3,3)).out();    solve(matrix(c({50,1,1,9,7,1,4,1,13}),3,3),c({1,1,1})).out();    solve(matrix(c({50,1,1,9,7,1,4,1,13}),3,3)).out();    solve_eq(matrix(c({50,1,1,9,7,1,4,1,13}),3,3),c({1,1,1})).out();    m2.out();    M(m2,0,0).out();    cout<<sum(m2)<<endl;    cout<<prod(m2)<<endl;    (c({1,1})%matrix(c({5,6,7,8,9,10}),2,3)).out();    outer_product(c({1,1}),c({5,6,7})).out();    diag(m2).out();    diag(c(diag(m2))).out();    cout<<length(m2)<<endl;    cout<<length(m2[0])<<endl;    sort(c({3,2,1})).out();    cout<<mean(m2)<<endl;    cout<<mean(m2.col(0))<<endl;    cout<<var(matrix(c({1,2,3,4,5,6,7,8,9}),3,3))<<endl;    connect({c({1,1,1}),c({-1,1,-1})}).out();    cout<<STD(matrix(c({1,2,3,4,5,6,7,8,9}),3,3))<<endl;    matrix    m3=rbind({c({1,2}),c({3,4,5})});    cbind({c({1,2}),c({3,4,5})}).out();    cout<<dim(m3).first<<" "<<dim(m3).second<<endl;    m3.out();    cout<<dim(m3[0])<<endl;    cout<<min(m3)<<endl;    cout<<min(m3[0])<<endl;    cout<<max(m3)<<endl;    cout<<max(m3[0])<<endl;    c(m3).out();   pmin({m3[0],m3[1]}).out();   pmax({m3[0],m3[1]}).out();   range(m3);   cout<<median(m3)<<endl;   var(m3,m3).out();   cov(m3).out();   cor(m3).out();   rank(c({0,3,4,4,5,6,7,6,6,3})).out();   rev(c({1,5,7,6,9})).out();   order(c({0,3,4,4,5,6,7,6,3})).out();   m3.out();   cumsum(m3[0]).out();   cumsum(m3).out();   cumprod(m3[0]).out();   cumprod(m3).out();    cout<<det(matrix(c({50,7,8,9,10,4,3,2,9,4,8,7,1,1,1,10}),4,4))<<endl;    return 0;}

 

 

运行结果：

The vector is:
35.1 12

The vector is:
0 1 2 3 4 5 6 7 8 9

12
10
The vector is:
35.1 11 2 3 4 5 6 7 8 9

The vector is:
-35.1 -10

The vector is:
35.1 9 -2 -3 -4 -5 -6 -7 -8 -9

The vector is:
1 1 1 1 1 1 1 1 1 1

The vector is:
36.1 11 1 1 1 1 1 1 1 1

The vector is:
34.1 9 -1 -1 -1 -1 -1 -1 -1 -1

The vector is:
2 2 2 2 2 2 2 2 2 2

The vector is:
0 0 0 0 0 0 0 0 0 0

The vector is:
10 10 10 10 10 10 10 10 10 10

The vector is:
0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1

0
The matrix is:
 10  10  10  10
  4   4   4   4
 10  10  10  10

The vector is:
10 4 10

The matrix is:
  1  10  10  10
  2   4   4   4
  3  10  10  10

The matrix is:
  4  15   3
 10  18   4
  7   0   5

The matrix is:
 -4 -15  -3
-10 -18  -4
 -7  -0  -5

The matrix is:
  3  14   3
  9  17   4
  6  -1   5
 -1  -1   0
 -1  -1   0

The matrix is:
  5  16   4
 11  19   5
  8   1   6

The matrix is:
2.4   9 1.8
  6 10.8 2.4
4.2   0   3

The matrix is:
  3  14   2
  9  17   3
  6  -1   4

The matrix is:
 -3 -14  -2
 -9 -17  -3
 -6   1  -4

The matrix is:
2.4   9 1.8
  6 10.8 2.4
4.2   0   3

The matrix is:
0.25 0.0666667 0.333333
0.1 0.0555556 0.25
0.142857 inf 0.2

The matrix is:
0.4 1.5 0.3
  1 1.8 0.4
0.7   0 0.5

The matrix is:
  4  15   3
 10  18   4
  7   0   5

The matrix is:
  4  15   3
  7   0   5
 10  18   4

The matrix is:
  4   3  15
  7   5   0
 10   4  18

0
3 3
1880
The vector is:
-0.12533 2.2544 1.84499

The matrix is:
  7   5   0
  4   3  15
 10   4  18

27.6405
Done!
6.67574
Done!
6.67374
Done!
12.9967
Done!
50.3227
The vector is:
6.67374 12.9967 50.3227

The vector is:
-0.00961538 0.134615 0.0673077

The matrix is:
0.0206044 -0.02587 -0.00434982
-0.00274725 0.147894 -0.0105311
-0.00137363 -0.00938645 0.0780678

The vector is:
-0.00961538 0.134615 0.0673077

The matrix is:
  4   3  15
  7   5   0
 10   4  18

The matrix is:
  5   0
  4  18

66
0
The matrix is:
 11  15  19

The matrix is:
  5   6   7
  5   6   7

The matrix is:
  4   0   0
  0   5   0
  0   0  18

The matrix is:
  4   0   0   0   0   0   0   0   0
  0   0   0   0   0   0   0   0   0
  0   0   0   0   0   0   0   0   0
  0   0   0   0   0   0   0   0   0
  0   0   0   0   5   0   0   0   0
  0   0   0   0   0   0   0   0   0
  0   0   0   0   0   0   0   0   0
  0   0   0   0   0   0   0   0   0
  0   0   0   0   0   0   0   0  18

9
3
The vector is:
1 2 3

7.33333
7
6.66667
The vector is:
1 1 1 -1 1 -1

2.73861
The matrix is:
  1   3
  2   4
  0   5

2 3
The matrix is:
  1   2   0
  3   4   5

3
0
0
5
2
The vector is:
1 3 2 4 0 5

The vector is:
0 3

The vector is:
2 5

MIN: 0 MAX: 5
3
The matrix is:
  2   2   5
  2   2   5
  5   5 12.5

The matrix is:
  2   2   5
  2   2   5
  5   5 12.5

The matrix is:
  1   1   1
  1   1   1
  1   1   1

The vector is:
0 1 2 2 3 4 5 4 4 1

The vector is:
9 6 7 5 1

The vector is:
0 8 1 3 2 4 7 5 6

The matrix is:
  1   2   0
  3   4   5

The vector is:
1 3 3

The matrix is:
  1   6  10
  4  10  15

The vector is:
1 2 0

The matrix is:
  1   6   0
  3  24   0

6194

Process returned 0 (0x0)   execution time : 4.891 s
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