/** Special Thanks to Jay - For Providing the Awesome Split Function... */ /// I recommend to use this in a PC for Best Results... /// *** Last Updated - 18th May 2016 *** /// =========================================================================================================== /// The Matrix Class /// ==========================================================================================================+ /// /// Made By - Kinshuk Vasisht /// Version - 3.0.5 - (v1.0.0 Created 25th April, 2017) /// Status - 0xFFFFFF (Complete) - CF (BETA) /// Features - Matrix Operations, Coordinate Marking, Decimal Rounding /// Overloads - Generic Templates and Multiple Declarations... /// Functions - Matrix Class Methods, Coords Class Methods and decimal()... /// Main Data Type - Long Double ( as Alias - ld , Real ) /// Templates - typenames & classes. /// Macros - elif() - for else if(), for_range() /// Classes - Matrix ( Operators and Functions ), Coords ( Operators and Functions ) /// Complex ( Operators and Functions ) /// -> Features - Initializes Matrix using Rows and Columns or Initializer Lists, /// Reads and Prints a Matrix (Any Stream), Sets the Rows and Columns, /// Returns Number of Rows or Columns, Assigns a value to an element, /// Returns an element of a Matrix located at rc and cc, /// Returns Upper or Lower Triangle of a Square Matrix, /// Checks If the Matrix is a Triangle Matrix, Prints the Triangle, /// Searches for an Element and Returns its Coordinates, /// Clears the Matrix to Zero, Sorts a Row/Column of a Matrix, /// Finds the Greatest & Smallest Element from the Matrix, /// Returns Coordinates of the Greatest & the Smallest Element, /// Checks if a Matrix has elements in a set Range, /// Finds the Range of the elements of the Matrix, /// Returns a SubMatrix from a Matrix, /// Checks if Row rn or Column cn is Zero, /// Checks if the Diagonal is Zero, Checks if any element is Infinity, /// Flips a Matrix along X or Y Axis, /// Extracts the Row, Column, or Diagonal from a Matrix, /// Extracts Non Zero Elements in a Vector, /// Fills the Row, Column or Diagonal with an arr, /// Extracts elements that Satisfy a Condition into a Vector, /// Replaces Matched elements with a New Value, Swaps two Rows / Columns, /// Generates a Symmetric and a Skew-Symmetric Matrix from Matrix A, /// Shifts a Row/Column to a New Position in a Matrix, /// Performs Elementary Transformations (Gauss-Jordan Method) on Matrix, /// Returns the Matrix as a Clockwise Spiral, /// Multiplies a Row or Column by a constant, /// Resizes the Matrix,Restoring Old Values or Deleting Them, /// Returns the Sum of All Elements of the Matrix, /// Fills a Value in the Entire Matrix, /// Fills V2 in the Diagonal and V1 in the rest of the Matrix, /// Converts the Matrix to I ( Identity Matrix ), /// Transforms values using a Relation, /// Fills values using a Relation, /// Returns the Position when Compared to a Sorted Matrix, /// Returns the Matrix as a 1D Array, /// Sorts the Matrix in Ascending/Descending Order /// Returns A^-1 of Matrix A, Returns Adjoint of M1, /// Returns a Cofactor Matrix of Matrix a, Returns Determinant of M1, /// Returns Scalar Product of M1 with a Constant, /// Joins Two Matrices into a Single Matrix /// Breaks/Slices a Matrix (2D) into a Matrix of Matrices (4D). /// Saves Absolute Value Matrix of a Matrix A in A. /// -> Spl. Features - Randomly fills Integer Matrix According to a Range, /// Converts Complex Matrix to Polar Form, /// Converts Complex Matrix to Conjugate Matrix, /// Returns Real or Imaginary Part Matrix, /// Converts Complex Matrix to Identity Matrix, /// Returns Conjugate Transpose Matrix of a Complex Matrix. /// -> Operators - +, -, *, /, +=, -=, /=, *=, ^, |, =, ==, !=, &, %, (), <<, >>. /// Constants - Eu(Euler's Number), Pi, PINF (Positive Infinity) , NINF (Negative Infinity) /// No. of Lines - 1947 (No Extras, Excluding Comments and Docstrings) /// Sub-Headers - , , , , , , /// /// Contributions - Special Thanks to Jay for his Wonderful Contribution - The Split Function... /// /// =========================================================================================================== /* Hello This is a Beta Version of the Matrix Class I have been Making for the past few days. It is a Beta Version and so, all functions which have bugs or which are not working for general cases are not here... I will update this code as soon as I finish with the debugging and Improvements... Till then, feel free to use the available functions and Please leave your doubts or suggestions to help me improve it to a better state... (Thus, I uploaded the Beta version)... There are 3 Classes in Total here - Matrix, Complex(from my earlier work), & Coords, along with necessary includes and utility functions to make the tasks as easy as possible... NOTE - I have left some example programs to get familiar on how to use this class to get the desired results... There are 8 Sample Programs Here, ready to be copied in main and use. And in their Comments I have specified the type of matrix the person will be able to use... But of Course, you may Change the Data Type to a New One, But that will require changing other details as well... NOTE - I also recommend using this Program in Code::Blocks, as Code Playground Takes a 'lot' of time... Plus, the Inputs are not so good here, and some Complex Numbers are being wrongly Printed here... Thank You for Viewing my Code! - Please reward my hardwork with your suggestions! If you have ANY Doubts, Please don't hesistate to ask! Kinshuk Vasisht -Created 25th April 2017 */ #include #include #include #include #include #include #include #include #define elif(x) else if(x) #define for_range(x) for(int i=0;i::infinity(); const ld NINF = -(numeric_limits::infinity()); const ld Pi = 3.141592653589793; const ld Eu = 2.7182818284590452354; template void Swap(sort& a, sort& b) { sort temp; temp=a; a=b; b=temp; } template void SwapArr(sort* a,sort* b,int n) { sort* temp; temp=new sort[n]; for(int i=0;i void QuickSortA(sort arr[],int begin, int end) { int i = begin, j = end; sort tmp; sort pivot = arr[(begin + end) / 2]; while (i <= j) { while (arr[i] < pivot) i++; while (arr[j] > pivot) j--; if (i <= j) { tmp = arr[i]; arr[i] = arr[j]; arr[j] = tmp; i++; j--;}}; if (begin < j) QuickSortA(arr,begin,j); if (i < end) QuickSortA(arr,i,end); } template void QuickSortD(sort arr[],int begin, int end) { int i = begin, j = end; sort tmp; sort pivot = arr[(begin + end) / 2]; while (i <= j) { while (arr[i] > pivot) i++; while (arr[j] < pivot) j--; if (i <= j) { tmp = arr[i]; arr[i] = arr[j]; arr[j] = tmp; i++; j--;}}; if (begin < j) QuickSortD(arr,begin,j); if (i < end) QuickSortD(arr,i,end); } bool decimal(double no) { no=floor(no*100000000)/100000000.0; if(no!=static_cast(no)) return false; return true; } int signum(ld x) { return (x>0)-(0>x); } ld degtorad(ld deg) { cout.setf(ios::fixed); cout.precision(8); ld cnst=Pi/180.0; return deg*cnst; } ld radtodeg(ld rad) { cout.setf(ios::fixed); cout.precision(8); ld cnst=180.0/Pi; return rad*cnst; } struct Coords { ld x,y; Coords(ld xx=0,ld yy=0):x(xx),y(yy){} ~Coords(){} friend ostream& operator<<(ostream& os,const Coords& co) { os<<"R - "<0) { cout<>arg; cout<<"Enter the Modulus - ";cin>>mod; cout<0) z[k]=Complex(rn*cos(narg+k*npi),rn*sin(narg+k*npi)); else z[k]=Complex(rn*cos(narg+(-k)*npi),rn*sin(narg+(-k)*npi)); } return z; } void Rotate(ld angle) ///Rotates the Complex Number by 'angle' Degrees { ld a=Modulus(),b=Argument(); b+=angle; ld bx=degtorad(b); real=a*cos(bx); imag=a*sin(bx); } void RaiseToComplex(ld a,Complex& z) ///Returns a raised to Complex z { cout.precision(8); cout.setf(ios::fixed); ld t1,t2,t3; t1=pow(a,z.real); t2=cos(z.imag*log(a)); t3=sin(z.imag*log(a)); real=t1*t2; imag=t1*t3; } Complex Cos() ///Returns Cosine of Complex z { Complex res,t1(0,1),t2(0,-1),t3,t4,t5,t6,t7; t3.real=(real*t1.real)-(imag*t1.imag); t3.imag=(real*t1.imag)+(imag*t1.real); t4.real=(real*t2.real)-(imag*t2.imag); t4.imag=(real*t2.imag)+(imag*t2.real); t5.RaiseToComplex(2.718281828459045,t3); t6.RaiseToComplex(2.718281828459045,t4); t7=t5+t6; res.real=t7.real/2; res.imag=t7.imag/2; return res; } Complex Cosh() ///Returns Hyperbolic Cosine of Complex z { Complex res,t1(real,imag),t2(-real,-imag),t3,t4,t5; t3.RaiseToComplex(2.718281828459045,t1); t4.RaiseToComplex(2.718281828459045,t2); t5=t4+t3; res.real=t5.real/2; res.imag=t5.imag/2; return res; } Complex Sin() ///Returns Sine of Complex z { Complex res,t(0,1),t1(0,1),t2(0,-1),t3,t4,t5,t6,t7,t8; t3.real=(real*t1.real)-(imag*t1.imag); t3.imag=(real*t1.imag)+(imag*t1.real); t4.real=(real*t2.real)-(imag*t2.imag); t4.imag=(real*t2.imag)+(imag*t2.real); t5.RaiseToComplex(2.718281828459045,t3); t6.RaiseToComplex(2.718281828459045,t4); t7=t6-t5; t8=t7*t; res.real=t8.real/2; res.imag=t8.imag/2; return res; } Complex Sinh() ///Returns Hyperbolic Sine of Complex z { Complex res,t1(real,imag),t2(-real,-imag),t3,t4,t5; t3.RaiseToComplex(2.718281828459045,t1); t4.RaiseToComplex(2.718281828459045,t2); t5=t3-t4; res.real=t5.real/2; res.imag=t5.imag/2; return res; } Complex Tan() ///Returns Tangent of Complex z { Complex res,t1,t2; t1=Sin(); t2=Cos(); res=t1/t2; return res; } Complex Tanh() ///Returns Hyperbolic Tangent of Complex z { Complex res,t1,t2; t1=Sinh(); t2=Cosh(); res=t1/t2; return res; } Complex Exp() ///Returns Eu raised to the Complex Number { Complex res; res.RaiseToComplex(Eu,*this); return res; } Complex Log(ld base) ///Returns Log of the Complex No. to the base { Complex res; res.real=log(Modulus())/((log(base))); res.imag=degtorad(Argument())/((log(base))); return res; } bool operator==(const Complex& rhs) ///Checks if the Complex Numbers are Equal { return(real==rhs.real&&imag==rhs.imag); } bool operator!=(const Complex& rhs) ///Checks if the Complex Numbers are Unequal { return(real!=rhs.real&&imag!=rhs.imag); } bool operator>(const Complex& rhs) ///Checks if Complex Number is Greater or not { return((real>rhs.real)||(imag>rhs.imag)); } bool operator<(const Complex& rhs) ///Checks if Complex Number is Greater or not { return((real>(istream& is,Complex& c) { is>>c.real>>c.imag; return is; } friend Complex abs(Complex c) { return Complex(abs(c.real),abs(c.imag)); } friend void Write(const Complex& c,fstream& fs) { fs.setf(ios::fixed); fs< 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 T** Kronecker_Product(T** A,T** B,int r1,int r2,int c1,int c2) { T** KP; KP=new T*[r1*r2]; 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); fstream& operator<<(fstream& obj, Matrix& mc); /// Original Definition of the Class Matrix template class Matrix { private: int r,c; M **mat; public: Matrix(int row=1,int col=1):r(row),c(col) /// Matrix Constructor - Initializes Matrix and Sets Elements to 0 { mat = new M*[r]; for (int i = 0; i < r; ++i) { mat[i] = new M[c]; for (int j = 0; j < c; ++j) mat[i][j] = 0; } } Matrix(initializer_list> lst) : Matrix(lst.size(), lst.size() ? lst.begin()->size() : 0) /// Matrix Constructor - Initializes Matrix using Initializer Lists { int i = 0, j = 0; for (const auto& l : lst) { for (const auto& v : l) { mat[i][j]=v; ++j; } j = 0; ++i; } } ///Template Specializations void Random(int,int); void Polar(); void Conjugate(); void Part(string); Matrix CTranspose(); ///Member Functions void Read(fstream& obj) /// Reads a Matrix { obj>>r>>c; for(int i=0;i>mat[i][j]; } void Print(fstream& obj) /// Prints a Matrix { for(int i=0;i=i;j--) res.mat[i][j]=mat[i][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; } } void PrintTriangle(char dir) /// Prints the Triangle of a Matrix as a Triangle { if(r==c) { Matrix res(r,c); if(dir=='U') { res=this->Triangle('U'); for(int i=0;iTriangle('L'); for(int i=0;imax) max=mat[i][j]; return max; } M Min() /// Finds the Smallest Element from the Matrix { M min=mat[0][0]; for(int i=0;i=min))&&(!(mat[i][j]<=max))) return false; return true; } Coords Range() /// Finds the Range of the elements of the Matrix { return Coords(Min(),Max()); } void RowSort(int r_no) /// Sorts a Particular Row of a Matrix { M* arr; arr=new M[c]; for(int i=0;i Non_Zero() /// Extracts Non Zero Elements in a Vector { vectorres; for(int i=0;i vector Specials(Fn f) /// Extracts elements that Satisfy a Condition into a Vector { vectorres; for(int i=0;i 2R1 /// 2) 1 2 -1 is the same as - R1 -> R1 + 2R2 - R3 Matrix temp(r,c); for(int i=0;i=cc;--i) ar[a++]=mat[m-1][i]; m--; } if (cc=cr;--i) ar[a++]=mat[i][cc]; cc++; } } return ar; } void Resize(int rr,int cc) /// Resizes the Matrix, Restoring Old Values... { M** Buffer; int a=r,b=c; Buffer=new M*[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); return res2; } else { Matrix res(r,c),res2(r,c); res2=(res^0); for(int i=0;i friend void Alter(Matrix a,Func f) /// Transforms values using a Relation { for(int i=0;i friend void Fill(Matrix a,Func f,int no) /// Fills values using a Relation { if(no==1) { for(int i=0;i>(istream& is, Matrix& matrix) /// Overload of >> Operator for cin { for(int i=0;i>matrix.mat[i][j]; } return is; } friend fstream& operator>>(fstream& ibf, Matrix& matrix) /// Overload of >> Operator for Files { int rr,cc; ibf>>rr>>cc; matrix.Reset(rr,cc); for(int i=0;i>matrix.mat[i][j]; } return ibf; } ///Non-Member Friend Overload Specializations friend ostream& operator<<<>(ostream& os,Matrix&matrix ); /// Overload of << Operator for cout friend ostream& operator<<(ostream& os,Matrix& mc); /// Overload of << Operator for cout - Complex Numbers friend fstream& operator<<<>(fstream& obj, Matrix& matrix );/// Overload of << Operator for Files friend fstream& operator<<(fstream& obj, Matrix& mc );/// Overload of << Operator for Files - Complex Numbers }; ///Specialized Template friend Functions for Particular Data Types template ostream& operator<<(ostream& os, Matrix& matrix) { for (int i = 0; i < matrix.r; ++i) { ///cout.width(3); - @OnlyIfYouNeedAlignment for (int j = 0; j < matrix.c; ++j) os << right << matrix.mat[i][j]<<" "; os << endl; } return os; } ostream& operator<<(ostream& os, Matrix& mc ) { for (int i = 0; i < mc.r; ++i) { ///cout.width(3); - @OnlyIfYouNeedAlignment for (int j = 0; j < mc.c; ++j) mc.mat[i][j].Print(os),os<<" "; os << endl; } return os; } template fstream& operator<<(fstream& obj, Matrix& matrix ) { obj<& mc ) { obj< void Matrix::Random(int range_start,int range_end) /// Randomly fills the Matrix According to a Range { for(int i=0;i void Matrix::Polar() /// Converts Complex Matrix to Polar Form { for(int i=0;i void Matrix::Conjugate() /// Converts Complex Matrix to Conjugate Matrix { for(int i=0;i void Matrix::Part(string type) /// Returns Real or Imaginary Part Matrix { if(type=="REAL"||type=="Real"||type=="real") { for(int i=0;i void Matrix::Identity() /// Converts Complex Matrix to Identity Matrix { Complex a,b(1,1); if(r==c) Fill(a,b); else Fill(a); } template<> Matrix Matrix::CTranspose() /// Returns Conjugate Transpose Matrix of a Complex Matrix { Matrix res(c,r); res|(*this); res.Conjugate(); return res; } /** // - Example Program 01 - To Perform Elementary Operations on a Matrix - Real Matrixa(1,1),b(1,1),c(1,1); char ch; int rr,cc,aa=0; ld* arr; cout<<"Enter the Rows - ";cin>>rr; cout<<"Enter the Columns - ";cin>>cc; a.Reset(rr,cc); b.Reset(rr,cc); c.Reset(rr,cc); b.Identity(); c.Identity(); cout<<"\nEnter a Matrix - "<>a;cout<>ch; for(int i=0;i<2*rr*cc;i++) { arr=new ld[rr]; for(int j=0;j>aa; cout<<"\nEnter the Condition Array - "; for(int k=0;k>arr[k]; cout<<"\nTransforming ..."; a.TransformC(ch,aa,arr); b.TransformC(ch,aa,arr); cout<<"\n\nPartial Result - \n\n"<a(2,2); cout<<"Enter a Matrix - "<>a; cout.flags(ios_base::fixed|ios_base::scientific); cout.precision(15); cout<vec; auto func=[&](ld val){if(decimal(log(val)))return true; return false;}; vec=a.Specials(func); vector::iterator it; it=vec.begin(); for(it;it a(2,2); cout<<"Enter a Matrix - "<>a;cout<a(1,1); cout<<"Enter a Choice - "<>ch; if(ch==1) { string nm; cout<<"\nEnter Name of the File - "; cin.ignore(); getline(cin,nm); nm+=".mrx"; fstream file; file.open(nm.c_str(),ios::in); if(bool(file)) { file>>a; file.close(); cout<<"\nYour Matrix - \n\n"<>rr>>cc; a.Reset(rr,cc); cout<<"\nEnter the Matrix - \n"<>a; fstream file; file.open(nm.c_str(),ios::out|ios::trunc); file<a(3,3); cout<<"Enter a Matrix - "<>a; cout<>r>>c; Matrixa(r,c); cout<<"\nEnter the Matrix - "<>a; vectornz=a.Non_Zero(); vector::iterator it=nz.begin(); cout<<"\nNon-Zero Elements - "; for(it;ita={{{1.23,1.23},{2.23,2.23},{3.23,3.23},{7.54,4.34}}, {{4.23,4.23},{5.23,5.23},{6.23,6.23},{7.54,4.34}}, {{7.23,7.23},{8.23,8.23},{9.23,9.23},{7.54,4.34}}}; cout<<"Your Initialized Matrix - \n\n"<a={{{1.23,1.23},{2.23,2.23},{3.23,3.23}}, {{4.23,4.23},{5.23,5.23},{6.23,6.23}}, {{7.23,7.23},{8.23,8.23},{-9.23,-9.23}}}; cout<<"Your Initialized Matrix - \n\n"<a(8,8),b(8,8),c(8,8); srand(time(nullptr)); a.Random(1,9); b=a.Triangle('U'); c=a.Triangle('L'); cout<<"The Matrix - \n\n"<>n; Matrix a(n,n),b(n,n),c(n,n),d(n,n); cout<<"\nEnter 4 "<>a; cout<>b; cout<>c; cout<>d; cout< a1(2*n,n),a2(2*n,n),af(2*n,2*n); a1=Join(a,c,'C'); a2=Join(b,d,'C'); af=Join(a1,a2,'R'); cout<<"The Final Matrix - \n\n"<**bf=new Matrix*[2]; for(int i=0;i<2;i++) bf[i]=new Matrix[2]; for(int i=0;i<2;i++) for(int j=0;j<2;j++) bf[i][j].Reset(n,n); bf=Split(af,n,n); for(int i=0;i<2;i++) for(int j=0;j<2;j++) cout<<"Matrix at - "<a(8,8),b(8,8),c(8,8); srand(time(nullptr)); a.Random(1,9); b=a.Triangle('U'); c=a.Triangle('L'); cout<<"The Matrix - \n\n"<

The Matrix Class - Beta