README.md

H_Space

A mathematical API for tensors till rank 2 (Matrix) which takes user input for typenames and number of dimesions.

How it works

1. Include the necessary header file.

   #include "Matrix.h"

SCALER (RANK 0 TENSOR)

2. Create a scaler by creating an object of class scaler as given below.

   Scaler<double> x(5.2), y(1.9), z(2.1);   

3. Some Scaler functions.

   x.Data();             // This will give you the data inside the scaler object, in this case "5.2" .
   x1.addition(x2);      // addition of two scalers.
   x1.subtract(x2);      // subtraction of two scalers.
   x1.multiply(x2);      // multiplication of two scalers.
   x1.divide(x2);        // division of two scalers.

4. Some Scaler operations.

   x1 + x2;             // same as addition.
   x1 - x2;             // same as subtraction
   x1 * x2;             // same as multiply
   x1 / x2;             // same as division
   
   x1 += x2;            // x1 = x1 + x2
   x1 -= x2;            // x1 = x1 - x2
   x1 *= x2;            // x1 = x1 * x2
   x1 /= x2;            // x1 = x1 / x2
   x1 == x2;            // binary comparison

VECTOR (RANK 1 TENSOR)

5. After that, you can create a vector by 2 methods which are given as

a). Method 1 (by using scalers)

   Vector<double, 3> v({x, y, z});

b). Method 2 (by directly putting values in it)

   Vector<double, 3> v({3.1, 6.7, 5.2});

6. Vector functions.

   v.size();              // returns the size if the vector.
   v.Data();              // return a pointer to the first element of the vector array.
   
   v1.add(v2);            // returns a vector which is a sum of v1 and v2.
   v.addScaler(x);        // returns a vector which adds a scaler x into v. 
   
   v1.subtract(v2);       // returns a vector which is the difference of v1 and v2.
   v.subtractScaler(x);   // returns a vector which subtracts scaler x from v.
   
   v1.dotProduct(v2);     // returns a scaler which is the result of the dot product of v1 and v2.
   v1.crossProduct(v2);   // returns a vector which is the cross product of v1 and v2.
   v.prodScaler(x);       // returns a vector which multiplies a scaler x into v.

7. Vector operations.

   v[index];              // returns an element or a scaler at given index
   v_add = v1 + v2;       // same as Add
   v_sub = v1 - v2;       // same as Subtract
   v_dot = v1 * v2;       // same as DotProduct

MATRIX (RANK 2 TENSOR)

8. Create a Matrix by creating an object using two methods.

a). Method 1 (by a linear array of scalers with n_Rows x m_Columns length)

   Matrix<int, 3, 3> matrix({ 1, 2, 3, 4, 5, 6, 7, 8, 9 });

b). Method 2 (by an array of either row vectors of column vectors)

   Matrix<double, 3, 3> matrixR({ v1, v2, v3 },  'R') //  For Row Vectors
   Matrix<double, 3, 3> matrixC({ v1, v2, v3 },  'C') //  For Column Vectors

9. Basic functions.

   matrix.GetRows();     // returns the number of rows
   matrix.GetColumns();  // returns the number of columns
   matrix.GetLimit();    // returns the number of elements or scalers you can add in this matrix (n_Rows x m_Columns)
   
   matrix.GetLinearIndex(5));   // returns the index of the element 5 in the linear  matrixarray
   matrix.Data();               // returns a pointer to the first element of the linear matrix array.
   
   matrix.GetRowVector(1);     // returns a row vector of the matrix of index 1.
   matrix.GetColumnVector(2);  // returns a column vector of the matrix of index 2.
   
   matrix.GetScaler(0,1);      // returns the element or scaler of row index 0 and column index 1.

10. Mathematical functions.

   matrix.Transpose();            // This will transpose the matrix. (NOTE: This will change the matrix into its transpose)
   
   matrix1.add_Matrix(matrix2);    // returns a matrix which is a sum of matrix 1 and matrix 2.
   matrix.add_Scaler(scaler);      // returns a matrix which is a sum of a matrix and a scaler.
   
   matrix1.sub_Matrix(matrix2);    // returns a matrix which is a difference of matrix 1 and matrix 2.
   matrix.sub_Scaler(scaler);      // returns a matrix which is a difference of a matrix and a scaler.
   
   matrix1.prod_Matrix(matrix2);   // returns a matrix which is a product of matrix 1 and matrix 2.
   matrix.prod_Scaler(scaler);     // returns a matrix which is a product of matrix and a scaler.

11. Matrix operations.

   matrix[1];     // returns a row vector of index 1 by default.
   matrix[1][1];   // returns an element of index (1,1). 
   
   matrix_add_matrix = matrix1 + matrix2;   // same as add_Matrix.
   matrix_add_scaler = matrix + scaler;     // same as add_Scaler.
   
   matrix_sub_matrix = matrix1 - matrix2;   // same as sub_Matrix.
   matrix_sub_scaler = matrix - scaler;     // same as sub_Scaler.
   
   matrix_prod_matrix = matrix1 * matrix2;  // same as prod_Matrix.
   matrix_prod_scaler = matrix * scaler;    // same as prod_Scaler.

NOTE: The library is still in development stage and new functions will be added to make it more useful for complex mathematical problems.