#include<iostream>
#include<vector>
#include<cmath>
#include<iomanip>
 
 
std::vector<std::vector<int>> mat_voigt_ind(const int N)
{
    /** this function will create pointer vector of matrix mat
     * in voigt notation
     */
 
    /** for every element A(i,j) of given
     * it will stores it index in the voigt vetor
     * given that matrix is square matrix of size N x N*/
    std::vector<std::vector<int>> mat = std::vector<std::vector<int>>(N, std::vector<int>(N, 0)) ;
 
 
    // starting and end index of the column to be filled
    std::size_t row_s = 0 ;
    std::size_t row_e = N - 1 ;
 
    std::size_t col_s = 0 ;
    std::size_t col_e = N - 1 ;
 
    /**we will fill diagonal first
     * then the last column
     * then first row
     * 
     * now next iteration
     */
 
    // starting index for matrix
    int i = row_s ;
    int j = col_s ;
 
    // k upto (N*N + N)/2 means we will run loop only for upper triangulat matrix
    for(std::size_t k = 0; k < (N*N + N)/2; k++)
    {
        mat[i][j] = k ;
 
        /** if non diagonal el, then add the el of lower triangle also */
        if(i != j)
            mat[j][i] = k + (N*N - N)/2 ;
 
        /** now update the index for matrix */
 
        // last column
        if(j == col_e and i > row_s)
            i-- ;
 
        // first row
        else if(i == row_s and j > col_s + 1)
            j-- ;
 
        // condition for next cycle
        else if(i == row_s and j == col_s + 1)
        {
            row_s += 1 ;
            row_e -= 2 ;
 
            col_s += 2 ;
            col_e -= 1 ;
 
            i = row_s ;
            j = col_s ;
        }
 
        // along the diagonal
        else
        {
            i++ ;
            j++ ;
        }
    }
 
    return mat ;
}
 
 
template <class T>
std::vector<std::vector<T>> dyadic(const std::vector<std::vector<T>>& A, const std::vector<std::vector<T>>& B)
{
    /** it will retun C as A dyadic B
     * given dimensions of A and B are equal
     */
 
    int N = A.size() ;
 
    std::vector<std::vector<T>> C(N*N, std::vector<float>(N*N,0)) ;  // N is the size of matrix A, i.e. which is calling the function
 
    /** if size of A and B are not equal */
    if(A.size() != B.size())
        return C ;
 
    /** generate a matrix of same size as A and B
     * which will store the index of voigt's matrix for that index of matrix
     */
    std::vector<std::vector<int>> voigt_mat = mat_voigt_ind(N) ;
 
    /** Cijkl = Aij * Bkl */
    for(int i= 0; i<N; i++)
        for(int j= 0; j<N; j++)
            for(int k= 0; k<N; k++)
                for(int l= 0; l<N; l++)
                    C[voigt_mat[i][j]][voigt_mat[k][l]] =  A[i][j] * B[k][l] ;
                    // C ij kl = A ij * B kl
 
    return C ;
}
 
template <class T>
std::vector<std::vector<T>> dyadic_up(const std::vector<std::vector<T>>& A, const std::vector<std::vector<T>>& B)
{
    /** it will retun C as A dyadic up B
     * given dimensions of A and B are equal
     */
 
    int N = A.size() ;
 
    std::vector<std::vector<T>> C(N*N, std::vector<float>(N*N,0)) ;  // N is the size of matrix A, i.e. which is calling the function
 
    /** if size of A and B are not equal */
    if(A.size() != B.size())
        return C ;
 
    /** generate a matrix of same size as A and B
     * which will store the index of voigt's matrix for that index of matrix
     */
    std::vector<std::vector<int>> voigt_mat = mat_voigt_ind(N) ;
 
    /** Cijkl = Aik * Bjl */
    for(int i= 0; i<N; i++)
        for(int j= 0; j<N; j++)
            for(int k= 0; k<N; k++)
                for(int l= 0; l<N; l++)
                    C[voigt_mat[i][j]][voigt_mat[k][l]] =  A[i][k] * B[j][l] ;
                    // C ij kl = A ik * B jl
 
    return C ;
}
 
template <class T>
std::vector<std::vector<T>> dyadic_down(const std::vector<std::vector<T>>& A, const std::vector<std::vector<T>>& B)
{
    /** it will retun C as A dyadic down B
     * given dimensions of A and B are equal
     */
 
    int N = A.size() ;
 
    std::vector<std::vector<T>> C(N*N, std::vector<float>(N*N,0)) ;  // N is the size of matrix A, i.e. which is calling the function
 
    /** if size of A and B are not equal */
    if(A.size() != B.size())
        return C ;
 
    /** generate a matrix of same size as A and B
     * which will store the index of voigt's matrix for that index of matrix
     */
    std::vector<std::vector<int>> voigt_mat = mat_voigt_ind(N) ;
 
    /** Cijkl = Aik * Bjl */
    for(int i= 0; i<N; i++)
        for(int j= 0; j<N; j++)
            for(int k= 0; k<N; k++)
                for(int l= 0; l<N; l++)
                    C[voigt_mat[i][j]][voigt_mat[k][l]] =  A[i][l] * B[j][k] ;
                    // C ij kl = A il * B jk
 
    return C ;
}
 
template <class T>
void printMatrix(const std::vector<std::vector<T>>& C, int N = 3)
{
    for(int i=0; i<C.size(); i++)
    {
        for(int j= 0; j<C[i].size(); j++)
        {
            std::cout<<std::setw(10) << std::fixed << std::setprecision(4)<<C[i][j] ;
 
            if((j+1)%N == 0)
                std::cout<<"\t" ;
        }
 
 
        if((i+1)%N == 0)
            std::cout<<std::endl ; 
 
        std::cout<<std::endl ; 
    }
}
 
 
int main()
{
    constexpr int N = 3 ;
 
    std::vector<std::vector<float>> A(N, std::vector<float>(N,0)) ;
    std::vector<std::vector<float>> B(N, std::vector<float>(N,0)) ;
 
 
    /** Problem no 5.3
     * considering alpha as 0
    */
    float alp = M_PI/2 ;
 
    // Rotation Matrix about V1
    A = { {1 , 0 , 0}, {0 , cos(alp), sin(alp)}, {0, -sin(alp), cos(alp)}} ;
 
    std::cout<<"\nTransformation Matrix for second order tensor for rotation about e1:"<<std::endl ;
    printMatrix(dyadic_up(A, A)) ;
 
    // Rotation Matrix about V2
    B = { {cos(alp), 0, -sin(alp)}, {0 , 1, 0}, {sin(alp), 0, cos(alp)}} ;
 
    std::cout<<"\nTransformation Matrix for second order tensor for rotation about e2:"<<std::endl ;
    printMatrix(dyadic_up(B, B)) ;
 
 
    /** for problem 5.4 */
    A = { {5, 3, 0}, {2, 4, 6}, {0, 6, 2}} ;
    B = { {4, 5, 2}, {0, 3, 4}, {0, 2, 5}} ;
 
    std::cout<<"\nA dyadic B:"<<std::endl ;
    printMatrix(dyadic(A, B)) ;
 
    std::cout<<"\nA dyadic up B:"<<std::endl ;
    printMatrix(dyadic_up(A, B)) ;
 
    return 0 ;
}
 
 

#include<iostream>
#include<vector>
#include<cmath>
#include<iomanip>


std::vector<std::vector<int>> mat_voigt_ind(const int N)
{
    /** this function will create pointer vector of matrix mat
     * in voigt notation
     */

    /** for every element A(i,j) of given
     * it will stores it index in the voigt vetor
     * given that matrix is square matrix of size N x N*/
    std::vector<std::vector<int>> mat = std::vector<std::vector<int>>(N, std::vector<int>(N, 0)) ;


    // starting and end index of the column to be filled
    std::size_t row_s = 0 ;
    std::size_t row_e = N - 1 ;

    std::size_t col_s = 0 ;
    std::size_t col_e = N - 1 ;

    /**we will fill diagonal first
     * then the last column
     * then first row
     * 
     * now next iteration
     */

    // starting index for matrix
    int i = row_s ;
    int j = col_s ;

    // k upto (N*N + N)/2 means we will run loop only for upper triangulat matrix
    for(std::size_t k = 0; k < (N*N + N)/2; k++)
    {
        mat[i][j] = k ;

        /** if non diagonal el, then add the el of lower triangle also */
        if(i != j)
            mat[j][i] = k + (N*N - N)/2 ;

        /** now update the index for matrix */

        // last column
        if(j == col_e and i > row_s)
            i-- ;
        
        // first row
        else if(i == row_s and j > col_s + 1)
            j-- ;

        // condition for next cycle
        else if(i == row_s and j == col_s + 1)
        {
            row_s += 1 ;
            row_e -= 2 ;

            col_s += 2 ;
            col_e -= 1 ;

            i = row_s ;
            j = col_s ;
        }

        // along the diagonal
        else
        {
            i++ ;
            j++ ;
        }
    }

    return mat ;
}


template <class T>
std::vector<std::vector<T>> dyadic(const std::vector<std::vector<T>>& A, const std::vector<std::vector<T>>& B)
{
    /** it will retun C as A dyadic B
     * given dimensions of A and B are equal
     */

    int N = A.size() ;

    std::vector<std::vector<T>> C(N*N, std::vector<float>(N*N,0)) ;  // N is the size of matrix A, i.e. which is calling the function

    /** if size of A and B are not equal */
    if(A.size() != B.size())
        return C ;

    /** generate a matrix of same size as A and B
     * which will store the index of voigt's matrix for that index of matrix
     */
    std::vector<std::vector<int>> voigt_mat = mat_voigt_ind(N) ;

    /** Cijkl = Aij * Bkl */
    for(int i= 0; i<N; i++)
        for(int j= 0; j<N; j++)
            for(int k= 0; k<N; k++)
                for(int l= 0; l<N; l++)
                    C[voigt_mat[i][j]][voigt_mat[k][l]] =  A[i][j] * B[k][l] ;
                    // C ij kl = A ij * B kl

    return C ;
}

template <class T>
std::vector<std::vector<T>> dyadic_up(const std::vector<std::vector<T>>& A, const std::vector<std::vector<T>>& B)
{
    /** it will retun C as A dyadic up B
     * given dimensions of A and B are equal
     */

    int N = A.size() ;

    std::vector<std::vector<T>> C(N*N, std::vector<float>(N*N,0)) ;  // N is the size of matrix A, i.e. which is calling the function

    /** if size of A and B are not equal */
    if(A.size() != B.size())
        return C ;

    /** generate a matrix of same size as A and B
     * which will store the index of voigt's matrix for that index of matrix
     */
    std::vector<std::vector<int>> voigt_mat = mat_voigt_ind(N) ;

    /** Cijkl = Aik * Bjl */
    for(int i= 0; i<N; i++)
        for(int j= 0; j<N; j++)
            for(int k= 0; k<N; k++)
                for(int l= 0; l<N; l++)
                    C[voigt_mat[i][j]][voigt_mat[k][l]] =  A[i][k] * B[j][l] ;
                    // C ij kl = A ik * B jl

    return C ;
}

template <class T>
std::vector<std::vector<T>> dyadic_down(const std::vector<std::vector<T>>& A, const std::vector<std::vector<T>>& B)
{
    /** it will retun C as A dyadic down B
     * given dimensions of A and B are equal
     */

    int N = A.size() ;

    std::vector<std::vector<T>> C(N*N, std::vector<float>(N*N,0)) ;  // N is the size of matrix A, i.e. which is calling the function

    /** if size of A and B are not equal */
    if(A.size() != B.size())
        return C ;

    /** generate a matrix of same size as A and B
     * which will store the index of voigt's matrix for that index of matrix
     */
    std::vector<std::vector<int>> voigt_mat = mat_voigt_ind(N) ;

    /** Cijkl = Aik * Bjl */
    for(int i= 0; i<N; i++)
        for(int j= 0; j<N; j++)
            for(int k= 0; k<N; k++)
                for(int l= 0; l<N; l++)
                    C[voigt_mat[i][j]][voigt_mat[k][l]] =  A[i][l] * B[j][k] ;
                    // C ij kl = A il * B jk

    return C ;
}

template <class T>
void printMatrix(const std::vector<std::vector<T>>& C, int N = 3)
{
    for(int i=0; i<C.size(); i++)
    {
        for(int j= 0; j<C[i].size(); j++)
        {
            std::cout<<std::setw(10) << std::fixed << std::setprecision(4)<<C[i][j] ;

            if((j+1)%N == 0)
                std::cout<<"\t" ;
        }

        
        if((i+1)%N == 0)
            std::cout<<std::endl ; 

        std::cout<<std::endl ; 
    }
}


int main()
{
    constexpr int N = 3 ;

    std::vector<std::vector<float>> A(N, std::vector<float>(N,0)) ;
    std::vector<std::vector<float>> B(N, std::vector<float>(N,0)) ;


    /** Problem no 5.3
     * considering alpha as 0
    */
    float alp = M_PI/2 ;

    // Rotation Matrix about V1
    A = { {1 , 0 , 0}, {0 , cos(alp), sin(alp)}, {0, -sin(alp), cos(alp)}} ;

    std::cout<<"\nTransformation Matrix for second order tensor for rotation about e1:"<<std::endl ;
    printMatrix(dyadic_up(A, A)) ;

    // Rotation Matrix about V2
    B = { {cos(alp), 0, -sin(alp)}, {0 , 1, 0}, {sin(alp), 0, cos(alp)}} ;

    std::cout<<"\nTransformation Matrix for second order tensor for rotation about e2:"<<std::endl ;
    printMatrix(dyadic_up(B, B)) ;


    /** for problem 5.4 */
    A = { {5, 3, 0}, {2, 4, 6}, {0, 6, 2}} ;
    B = { {4, 5, 2}, {0, 3, 4}, {0, 2, 5}} ;

    std::cout<<"\nA dyadic B:"<<std::endl ;
    printMatrix(dyadic(A, B)) ;

    std::cout<<"\nA dyadic up B:"<<std::endl ;
    printMatrix(dyadic_up(A, B)) ;
    
    return 0 ;
}

