/// Partially updated Matrix Class. /// Original Code : https://code.sololearn.com/cq24J951TxgI/?ref=app #ifndef KV_MATRIX_H_INCLUDED #define KV_MATRIX_H_INCLUDED #include #include #include #include #include #include #include #include #include #include #include #include ///#include "kv_complex.h" /// Refers to the code : Complex Numbers in C++. #define elif(x) else if(x) #define for_range(x) for(int i=0;i::infinity(); const ld NINF = -(numeric_limits::infinity()); /// |____________UTILITY_FUNCTIONS____________| /// ------------------------------------------- template void ColCopy(vector> mat,vector>& cmat) { size_t r = mat.size(), c = mat.begin()->size(); vector tmp; cmat.clear(); cmat.resize(c); for(int i=0;i size_t len(M type) { stringstream ss; ss< void CoFactors(T **A, T** temp, int r, int c, int n) { int i = 0, j = 0; for (int row = 0; row < n; row++) { for (int col = 0; col < n; col++) { if (row != r && col != c) { temp[i][j++] = A[row][col]; if (j == n - 1) { j = 0; i++; } } } } } template T Determinant(T **A, int n) { T D = 0; if (n == 1) return A[0][0]; T ** temp; temp = new T*[n]; for(int i=0;i T** Adjoint(T** A,int n) { T** adj; adj=new T*[n]; for(int i=0;i T** Inverse(T** A, int n) { T det = Determinant(A, n); if (det == 0) { return A; } T**adj,**inv; adj=new T*[n]; for(int i=0;i class Matrix; template ostream& operator<<(ostream& os, Matrix matrix); ostream& operator<<(ostream& os, Matrix mc); template fstream& operator<<(fstream& obj, Matrix matrix); /// Original Definition of the Class Matrix template class Matrix { private: size_t r,c; vector> mat,cmat; public: /// Matrix Constructor - Initializes Matrix and Sets Elements to 0 Matrix(unsigned short row=1,unsigned short col=1):r(row),c(col) { if((row<=0||col<=0)) throw length_error("MATRIX_ERROR : Rows / Columns must be greater than 0!"); vector temp; temp.assign(c,0); for (int i = 0; i < r; ++i) { mat.push_back(temp); } temp.assign(r,0); for (int i = 0; i < c; ++i) { cmat.push_back(temp); } } /// Matrix Constructor - Initializes Matrix using Initializer Lists Matrix(initializer_list> lst) { r = lst.size()?lst.size():1; c = lst.begin()->size()?lst.begin()->size():1; if((lst.size()<=0||lst.begin()->size()<=0)) throw length_error("MATRIX_ERROR : Rows / Columns must be greater than 0!"); mat.assign(lst.begin(),lst.end()); ColCopy(mat,cmat); } /// Matrix Copy Constructor - Deep Copies the Matrix Matrix(const Matrix& M2) : r(M2.r), c(M2.c) { mat.assign(M2.mat.begin(),M2.mat.end()); ColCopy(mat,cmat); } void Random(int,int); //void Conjugate(); //void Part(string); //Matrix CTranspose(); /// Returns const_iterator to First Row of Matrix typename vector>::const_iterator row_begin() { return mat.begin(); } /// Returns const_iterator to next element after Last Row of Matrix typename vector>::const_iterator row_end() { return mat.end(); } /// Returns const_iterator to First Column of Matrix typename vector>::const_iterator col_begin() { return cmat.begin(); } /// Returns const_iterator to next element after Last Column of Matrix typename vector>::const_iterator col_end() { return cmat.end(); } /// Returns const_iterator to First Row of Matrix typename vector>::const_iterator begin() { return mat.begin(); } /// Returns const_iterator to next element after Last Row of Matrix typename vector>::const_iterator end() { return mat.end(); } /// Returns const_iterator to Last Row of Matrix typename vector>::const_reverse_iterator rbegin() { return mat.rbegin(); } /// Returns const_iterator to element before First Row of Matrix typename vector>::const_reverse_iterator rend() { return mat.rend(); } /// Refreshes the Matrix, removing any irregularities void Revise() { for(int i=0;i>r>>c; this->Reset(r,c); for(int i=0;i>mat.at(i).at(j); } } ColCopy(mat,cmat); } /// Prints a Matrix to a specified file stream void Print(fstream& obj) { obj<c)||(rc>r)||(cc<1)||(rc<1)) throw out_of_range("MATRIX_ERROR : Index Out of Bounds for Access!"); return (mat.at(rc-1).at(cc-1)); } /// Returns Upper or Lower Triangle of a Square Matrix Matrix Triangle(char dir) { if(r!=c) throw logic_error("MATRIX_ERROR : Matrix Must be Square!"); Matrix res(r,c); if(dir=='U') { for(int i=0;i=i;j--) res.mat.at(i).at(j)=mat.at(i).at(j); } else if(dir=='L') { for(int i=0;iTriangle('U'); if(b==(*this)) return true; else return false; } else { b=this->Triangle('L'); if(b==(*this)) return true; else return false; } } /// Prints the Triangle of a Matrix as a Triangle void PrintTriangle(char dir) { if(r!=c) throw logic_error("MATRIX_ERROR : Matrix Must be Square!"); Matrix res(r,c); if(dir=='U') { res=this->Triangle('U'); for(int i=0;iTriangle('L'); for(int i=0;i Coordinate Search(char Scope,int num,FX f,int st=1) { if(Scope=='G') /// The Entire Matrix. { for(int i=0;imax) max=mat.at(i).at(j); return max; } /// Finds the Smallest Element from the Matrix M Min() { M min=mat.at(0).at(0); for(int i=0;i=min))&&(!(mat.at(i).at(j)<=max))) return false; return true; } /// Finds the Range of the elements of the Matrix Coordinate Range() { return Coordinate(Min(),Max()); } /// Sorts a Particular Row of a Matrix void RowSort(int r_no) { sort(mat.at(r_no-1).begin(),mat.at(r_no-1).end()); ColCopy(mat,cmat); } /// Sorts a Particular Column of a Matrix void ColSort(int c_no) { vector arr; for(int i=0;i Has_Inf() { array ctr(0); for(int i=0;i Row(int r_no) { return mat.at(r_no-1); } /// Extracts the Column from a Matrix vector Column(int c_no) { vector arr; for(int i=0;i Diagonal(int d_no) { if(r!=c) throw logic_error("MATRIX_ERROR : Diagonal Must Exist!"); vector arr; if(d_no==1) { for(int i=0;i Non_Zero() { vector res; for(int i=0;i arr) { mat.at(rn-1).assign(arr.begin(),arr.end()); ColCopy(mat,cmat); } /// Fills the Column cn with arr void col_assign(int cn, vector arr) { for(int i=0;i arr) { if(r!=c) throw logic_error("MATRIX_ERROR : Diagonal Must Exist!"); for(int i=0;i vector Specials(Fn f) { vectorres; for(int i=0;i save1, save2; save1.resize(c); save2.resize(c); for(int i=0;i arr) { /// This overload of Transform helps the user perform /// Multiplication and Addition of Scalar Multiples of /// Rows and Columns of Matrices as used in the Gauss- /// Jordan Elementary Transformations for Matrices... /// /// The passed arr shall contain condition constants, /// for Multiplication and Addition of Scalar Multiples. /// If 0 is passed as a value, the row/column is not involved... /// /// Example - (Assuming rc = 1, thus R1 is to be modified) : /// 1) 2 0 0 is the same as - R1 -> 2R1 /// 2) 1 2 -1 is the same as - R1 -> R1 + 2R2 - R3 Matrix temp(r,c); for(int i=0;i save; if(ch=='R') { if(arr.size()!=r) throw logic_error("MATRIX_ERROR : Invalid Row Manipulation!"); save.resize(c); for(int i=0;i Spiral() { vector ar; ar.resize(r*c); int i,cr=0,cc=0,a=0,m=r,n=c; while (cr=cc;--i) ar[a++]=mat.at(m-1)[i]; m--; } if (cc=cr;--i) ar[a++]=mat.at(i)[cc]; cc++; } } return ar; } /*/// Returns Matrix reduced to Echelon Form Matrix Echelon(char c) /// STILL NOT DONE { Matrix res(r,c); res = *this; Coordinate PV; auto zer = [](M v){return v!=M(0);}; if(c=='R') { int rowc=0,colc=0; while(rowc app; for(int i=0;iEchelon('R'); for(int i=1;i<=r;i++) if(! this->Row_Zero(i)) rnk++; return rnk; } *//// Resizes the Matrix, Restoring Old Values... void Resize(int rr,int cc) { if(rr<=0||cc<=0) throw length_error("MATRIX_ERROR : Invalid Matrix Dimensions!"); vector> temp(mat.begin(),mat.end()); mat.clear(); mat.resize(rr); for(int i=0;iReset(kk.c,kk.r); for (int i=0; i0) { Matrix res(r,c),res2(r,c); res2=(res^0); for(int i=1;i<=k;i++) res2*=(*this); ColCopy(res2.mat,res2.cmat); return res2; } else { Matrix res(r,c),res2(r,c); res2=(res^0); for(int i=0;ic)||(rr>r)||(cc<1)||(rr<1)) throw out_of_range("MATRIX_ERROR : Index Out of Bounds for Access!"); return mat.at(rr-1).at(cc-1); } /// Matrix Destructor ~Matrix(){} /// Joins Two Matrices into a Single Matrix friend Matrix Join(Matrix a,Matrix b,ltr ch) { if(ch=='R') { if(a.r!=b.r) throw logic_error("MATRIX_ERROR : Matrix has Unequal Rows!"); Matrix res(a.r,a.c+b.c); int k=1; vector ar; ar.resize(a.r); for(int i=0;i ar; ar.resize(a.c); for(int i=0;i friend void Transform(Matrix a,Func f) { for(int i=0;i friend void Fill(Matrix a,Func f,int no) { if(no==1) { for(int i=0;i Sort_Pos(Matrix a,char c) { Matrix m2(a); vector loc; if(c=='A') { Sort(m2,'A'); for(int i=0;i Convert_To_1D(const Matrix a) { vector arr; arr.resize(a.r*a.c); for(int i=0;i arr = Convert_To_1D(c); if(ch=='A') { sort(arr.begin(),arr.end()); for (int i=0;iV2;}); for (int i=0;i> Operator for cin friend istream& operator>>(istream& is, Matrix& matrix) { for(int i=0;i>matrix.mat.at(i).at(j); } } ColCopy(matrix.mat,matrix.cmat); return is; } /// Overload of >> Operator for Files friend fstream& operator>>(fstream& ibf, Matrix& matrix) { int rr,cc; ibf>>rr>>cc; matrix.Reset(rr,cc); for(int i=0;i>matrix.mat.at(i).at(j); } ColCopy(matrix.mat,matrix.cmat); return ibf; } /// Overload of << Operator for cout friend ostream& operator<<<>(ostream& os,Matrixmatrix ); /// Overload of << Operator for cout - Complex Numbers friend ostream& operator<<(ostream& os,Matrix mc); /// Overload of << Operator for Files friend fstream& operator<<<>(fstream& obj, Matrix matrix ); /// Overload of << Operator for Files - Complex Numbers friend fstream& operator<<(fstream& obj, Matrix mc ); }; ///Specialized Template friend Functions for Particular Data Types template ostream& operator<<(ostream& os, Matrix matrix) { uint d = len(matrix.Max()); for (int i = 0; i < matrix.r; ++i) { for (int j = 0; j < matrix.c; ++j) os< mc ) { uint d = len(mc.Max()); for (int i=0;i fstream& operator<<(fstream& obj, Matrix matrix ) { obj< void Matrix::Random(int range_start,int range_end) { for(int i=0;i void Matrix::Conjugate() { for(int i=0;i void Matrix::Part(string type) { if(type=="REAL"||type=="Real"||type=="real") { for(int i=0;i void Matrix::Identity() { Complex a,b(1,1); if(r==c) Fill(a,b); else Fill(a); ColCopy(mat,cmat); } /// Returns Conjugate Transpose Matrix of a Complex Matrix template<> Matrix Matrix::CTranspose() { Matrix res(c,r); res|(*this); res.Conjugate(); ColCopy(res.mat,res.cmat); return res; } */ #endif // KV_MATRIX_H_INCLUDED

The Matrix Class [Partially Updated/Header]