Filtered_Boundary_Matrix.hpp

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#ifndef FBM_H
#define FBM_H
 
#include "../typedefs.hpp"
// #include "../PersistentLaplacians.hpp"
 
#include <vector>
#include <cassert>
#include <iostream>
 
namespace PersistentLaplacians{
template<typename FBMcoeff = int> 
class Filtered_Boundary_Matrix {
    /*********************************************************/
    /* Template: FBMcoeff: the type of entries in the matrix */
    /*********************************************************/
    private:
        /********************/
        /* Member variables */
        /********************/
        std::vector<filtration_type> domain_filtrations; 
        std::vector<filtration_type> range_filtrations; 
        Eigen::SparseMatrix<FBMcoeff, Eigen::ColMajor> matrix; 
        int num_rows; 
        int num_cols; 
 
    public:
        Filtered_Boundary_Matrix(Eigen::SparseMatrix<FBMcoeff, Eigen::ColMajor> _matrix,
            std::vector<filtration_type> _domain_filtrations,
            std::vector<filtration_type> _range_filtrations){
                matrix = _matrix;
                domain_filtrations = _domain_filtrations;
                range_filtrations = _range_filtrations;                                          
                num_rows = _range_filtrations.size();
                num_cols = _domain_filtrations.size();
        }
 
        /***********************/
        /* Getters and setters */
        /***********************/
 
        std::vector<filtration_type> get_domain_filtrations(){return domain_filtrations;}
        
        std::vector<filtration_type> get_range_filtrations(){return range_filtrations;}
 
        /*********************/
        /* useful operations */
        /*********************/
        
        Filtered_Boundary_Matrix transpose(){
             return Filtered_Boundary_Matrix(matrix.transpose(),range_filtrations,domain_filtrations);
        }
 
        int index_of_filtration(bool use_domain_filtrations, filtration_type a){
            int index = 0;
            int filtration_size;
            if (use_domain_filtrations){
                filtration_size = domain_filtrations.size();
                while (index < filtration_size && domain_filtrations[index] <= a){ 
                    index++; 
                }
            } else{ //range_filtrations
                filtration_size = range_filtrations.size();
                while (index < filtration_size && range_filtrations[index] <= a){ 
                    index++;
                }
            }
            return index-1;
        }
 
        // TODO: deprecated
        int get_low(SparseMatrix_PL &matrix, int col_index){
            //TODO: can probably get the low in constant time via https://eigen.tuxfamily.org/dox/classEigen_1_1DenseBase.html#ae71d079e16d91360d10066b316b48485
            int low_index = -1;
            matrix.makeCompressed();
            for(SparseMatrix_PL::InnerIterator it(matrix,col_index); it; ++it){
                assert(it.value() != 0);
                low_index = it.index();
            }
            return low_index;
        }
 
        void submatrix_at_filtration(filtration_type a, Eigen::SparseMatrix<FBMcoeff,Eigen::ColMajor> &M){
            int col_index = index_of_filtration(true,a);
            int row_index = index_of_filtration(false,a);
            M = matrix.block(0,0,row_index+1,col_index+1);
        }
 
        // TODO: deprecated
        std::tuple<SparseMatrix_PL,SparseMatrix_PL,std::vector<int>, int> reduce(int a_row_index,int b_row_index, int b_col_index){
            int lower_num_rows = b_row_index - a_row_index;
            // For explaining usage of .template see https://eigen.tuxfamily.org/dox-devel/TopicTemplateKeyword.html
            SparseMatrix_PL working_boundary = matrix.block(0,0,b_row_index+1,b_col_index+1).template cast<coefficient_type>();
 
            
            SparseMatrix_PL lower_working_boundary = working_boundary.block(a_row_index+1,0,lower_num_rows,b_col_index+1);
 
            
            SparseMatrix_PL augmented(b_col_index+1, b_col_index+1);
            augmented.setIdentity();
 
            //this is the big reduce loop
            //A column is reduced if it's low is unique among lows
            std::vector<int> lows(b_col_index+1);
            std::vector<int> zero_cols;
            if (lower_num_rows == 0){
                return std::make_tuple(working_boundary, augmented,zero_cols,a_row_index);
            } else {
                assert(lower_num_rows > 0);
            }
 
            lows[0] = 0;
            for (unsigned long int col_index = 0; col_index <= (unsigned long int) b_col_index; col_index++){
                
                bool unique_pivot = false;
                int current_low;
                while (!unique_pivot){
                    current_low = get_low(lower_working_boundary,col_index);
                    if (current_low == -1){//column is a zero-column
                        lows[col_index] = current_low;
                        zero_cols.push_back(col_index);
                        break;//while !unique_pivot
                    }       
 
                    unique_pivot = true;
                    coefficient_type pivot_val = lower_working_boundary.coeffRef(current_low,col_index);
                    
                    for(unsigned long int left_col_index = 0; left_col_index < col_index; left_col_index++){
                        if (lows[left_col_index] == current_low){
                            coefficient_type conflicting_pivot = lower_working_boundary.coeffRef(lows[left_col_index],left_col_index);
                            coefficient_type scale_factor = pivot_val/conflicting_pivot; 
                            // TODO: speed and single precision tradeoff?
 
                            // ************ TODO: DETERMINE PRUNE CUTOFF VALUE *************
                            augmented.col(col_index) = (augmented.col(col_index) - scale_factor * augmented.col(left_col_index)).pruned(PRUNE_CONSTANT);
                
                            lower_working_boundary.col(col_index) = (lower_working_boundary.col(col_index) - scale_factor * lower_working_boundary.col(left_col_index)).pruned(PRUNE_CONSTANT);
                            unique_pivot = false;
                            break;
                        } //end if lows[left_col_index] == current_low
                        
                    }//end for left_col_index
                }// end while !unique_pivot
                lows[col_index] = current_low;
            }//end for col_index
            return std::make_tuple(working_boundary, augmented,zero_cols,a_row_index); //TODO: replace 2nd with Y
 
        }
        
 
        /**********************************/
        /* Helpful input/output functions */
        /**********************************/
 
        void print_range_filtration(){
            std::cout << "\n[";
            for (unsigned long int i = 0; i < range_filtrations.size(); i++){
                std::cout << range_filtrations[i] << ",";
            }
            std::cout << "]\n";
        }
 
        void print_domain_filtration(){
            std::cout << "\n[";
            for (unsigned long int i = 0; i < domain_filtrations.size(); i++){
                std::cout << domain_filtrations[i] << ",";
            }
            std::cout << "]\n";
        }
        void print(){
            Eigen::IOFormat HeavyFmt(Eigen::FullPrecision, 0, ", ", ";\n", "[", "]", "[", "]");
            std::cout << Eigen::Matrix<FBMcoeff,Eigen::Dynamic, Eigen::Dynamic>(matrix).format(HeavyFmt) <<std::endl;
        }
};
}
#endif