mirror of
https://github.com/CoolProp/CoolProp.git
synced 2026-01-22 12:28:04 -05:00
440 lines
14 KiB
C++
440 lines
14 KiB
C++
#ifndef MATRIXMATH_H
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#define MATRIXMATH_H
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#include "CoolPropTools.h"
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#include "Exceptions.h"
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#include <vector>
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#include <string>
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#include <numeric> // inner_product
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#include <sstream>
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#include "float.h"
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namespace CoolProp{
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///// Publish the linear algebra solver
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//template<class T> std::vector<T> linsolve(std::vector<std::vector<T> > const& A, std::vector<T> const& b);
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//template<class T> std::vector<std::vector<T> > linsolve(std::vector<std::vector<T> > const& A, std::vector<std::vector<T> > const& B);
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//
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///// Some shortcuts and regularly needed operations
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//template<class T> std::size_t num_rows (std::vector<std::vector<T> > const& in);
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//template<class T> std::size_t num_cols (std::vector<std::vector<T> > const& in);
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//template<class T> std::size_t max_cols (std::vector<std::vector<T> > const& in);
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//template<class T> std::vector<T> get_row (std::vector<std::vector<T> > const& in, size_t row);
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//template<class T> std::vector<T> get_col (std::vector<std::vector<T> > const& in, size_t col);
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//template<class T> bool is_squared(std::vector<std::vector<T> > const& in);
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//template<class T> std::vector<std::vector<T> > make_squared(std::vector<std::vector<T> > const& in);
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//
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///// Define some basic math operations for vectors
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//template<class T> T multiply( std::vector<T> const& A, std::vector<T> const& B);
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//template<class T> std::vector<T> multiply(std::vector<std::vector<T> > const& A, std::vector<T> const& B);
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//template<class T> std::vector<std::vector<T> > multiply(std::vector<std::vector<T> > const& A, std::vector<std::vector<T> > const& B);
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//
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//template<class T> T dot_product(std::vector<T> const& a, std::vector<T> const& b);
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//template<class T> std::vector<T> cross_product(std::vector<T> const& a, std::vector<T> const& b);
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//
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//template<class T> std::vector<std::vector<T> > transpose(std::vector<std::vector<T> > const& in);
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//template<class T> std::vector<std::vector<T> > invert(std::vector<std::vector<T> > const& in);
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//
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//template<class T> std::string vec_to_string( T const& a);
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//template<class T> std::string vec_to_string( std::vector<T> const& a);
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//template<class T> std::string vec_to_string(std::vector<std::vector<T> > const& A);
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//
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//template<class T> std::string vec_to_string( std::vector<T> const& a, const char *fmt);
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//template<class T> std::string vec_to_string(std::vector<std::vector<T> > const& A, const char *fmt);
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// Forward definitions
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template<class T> std::size_t num_rows (std::vector<std::vector<T> > const& in);
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template<class T> std::size_t max_cols (std::vector<std::vector<T> > const& in);
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template<class T> bool is_squared(std::vector<std::vector<T> > const& in){
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std::size_t cols = max_cols(in);
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if (cols!=num_rows(in)) { return false;}
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else {
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for (std::size_t i = 0; i < in.size(); i++) {
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if (cols!=in[i].size()) {return false; }
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}
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}
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return true;
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};
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template<class T> std::size_t max_cols (std::vector<std::vector<T> > const& in){
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std::size_t cols = 0;
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std::size_t col = 0;
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for (std::size_t i = 0; i < in.size(); i++) {
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col = in[i].size();
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if (cols<col) {cols = col;}
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}
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return cols;
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};
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/// Some shortcuts and regularly needed operations
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template<class T> std::size_t num_rows (std::vector<std::vector<T> > const& in){ return in.size(); }
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template<class T> std::size_t num_cols (std::vector<std::vector<T> > const& in){
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if (num_rows(in)>0) {
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if (is_squared(in)) {
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return in[0].size();
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} else {
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return max_cols(in);
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}
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} else {
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return 0;
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}
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};
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/*
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Owe a debt of gratitude to http://sole.ooz.ie/en - very clear treatment of GJ
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*/
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template<typename T> void swap_rows(std::vector<std::vector<T> > *A, size_t row1, size_t row2)
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{
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for (size_t col = 0; col < (*A)[0].size(); col++){
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std::swap((*A)[row1][col],(*A)[row2][col]);
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}
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};
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template<typename T> void subtract_row_multiple(std::vector<std::vector<T> > *A, size_t row, T multiple, size_t pivot_row)
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{
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for (size_t col = 0; col < (*A)[0].size(); col++){
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(*A)[row][col] -= multiple*(*A)[pivot_row][col];
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}
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};
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template<typename T> void divide_row_by(std::vector<std::vector<T> > *A, size_t row, T value)
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{
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for (size_t col = 0; col < (*A)[0].size(); col++){
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(*A)[row][col] /= value;
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}
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};
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template<typename T> size_t get_pivot_row(std::vector<std::vector<T> > *A, size_t col)
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{
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int index = col;
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T max = 0, val;
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for (size_t row = col; row < (*A).size(); row++)
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{
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val = (*A)[row][col];
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if (fabs(val) > max)
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{
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max = fabs(val);
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index = row;
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}
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}
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return index;
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};
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template<typename T> std::vector<std::vector<T> > linsolve_Gauss_Jordan(std::vector<std::vector<T> > const& A, std::vector<std::vector<T> > const& B) {
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std::vector<std::vector<T> > AB;
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std::vector<std::vector<T> > X;
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size_t pivot_row;
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T pivot_element;
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size_t NrowA = num_rows(A);
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size_t NrowB = num_rows(B);
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size_t NcolA = num_cols(A);
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size_t NcolB = num_cols(B);
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if (NrowA!=NrowB) throw ValueError(format("You have to provide matrices with the same number of rows: %d is not %d. ",NrowA,NrowB));
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AB.resize(NrowA, std::vector<T>(NcolA+NcolB, 0));
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X.resize(NrowA, std::vector<T>(NcolB, 0));
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// Build the augmented matrix
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for (size_t row = 0; row < NrowA; row++){
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for (size_t col = 0; col < NcolA; col++){
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AB[row][col] = A[row][col];
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}
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for (size_t col = NcolA; col < NcolA+NcolB; col++){
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AB[row][col] = B[row][col-NcolA];
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}
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}
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for (size_t col = 0; col < NcolA; col++){
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// Find the pivot value
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pivot_row = get_pivot_row(&AB, col);
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if (fabs(AB[pivot_row][col]) < 10*DBL_EPSILON){ throw ValueError(format("Zero occurred in row %d, the matrix is singular. ",pivot_row));}
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if (pivot_row>=col){
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// Swap pivot row and current row
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swap_rows(&AB, col, pivot_row);
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}
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// Get the pivot element
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pivot_element = AB[col][col];
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// Divide the pivot row by the pivot element
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divide_row_by(&AB,col,pivot_element);
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if (col < NrowA-1)
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{
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// All the rest of the rows, subtract the value of the [r][c] combination
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for (size_t row = col + 1; row < NrowA; row++)
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{
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subtract_row_multiple(&AB,row,AB[row][col],col);
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}
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}
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}
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for (int col = NcolA - 1; col > 0; col--)
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{
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for (int row = col - 1; row >=0; row--)
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{
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subtract_row_multiple(&AB,row,AB[row][col],col);
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}
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}
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// Set the output value
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for (size_t row = 0; row < NrowA; row++){
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for (size_t col = 0; col < NcolB; col++){
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X[row][col] = AB[row][NcolA+col];
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}
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}
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return X;
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};
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//std::vector<std::vector<double> > linsolve_Gauss_Jordan_reimpl(std::vector<std::vector<double> > const& A, std::vector<std::vector<double> > const& B) {
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// std::vector<std::vector<double> > AB;
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// std::vector<std::vector<double> > X;
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// size_t pivot_row;
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// double pivot_element;
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// double tmp_element;
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//
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// size_t NrowA = num_rows(A);
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// size_t NrowB = num_rows(B);
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// size_t NcolA = num_cols(A);
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// size_t NcolB = num_cols(B);
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//
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// if (NrowA!=NrowB) throw ValueError(format("You have to provide matrices with the same number of rows: %d is not %d. ",NrowA,NrowB));
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//
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// AB.resize(NrowA, std::vector<double>(NcolA+NcolB, 0));
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// X.resize(NrowA, std::vector<double>(NcolB, 0));
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//
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// // Build the augmented matrix
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// for (size_t row = 0; row < NrowA; row++){
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// for (size_t col = 0; col < NcolA; col++){
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// AB[row][col] = A[row][col];
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// }
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// for (size_t col = NcolA; col < NcolA+NcolB; col++){
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// AB[row][col] = B[row][col-NcolA];
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// }
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// }
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//
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// for (size_t col = 0; col < NcolA; col++){
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// // Find the pivot row
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// pivot_row = 0;
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// pivot_element = 0.0;
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// for (size_t row = col; row < NrowA; row++){
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// tmp_element = fabs(AB[row][col]);
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// if (tmp_element>pivot_element) {
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// pivot_element = tmp_element;
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// pivot_row = row;
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// }
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// }
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// // Check for errors
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// if (AB[pivot_row][col]<1./_HUGE) throw ValueError(format("Zero occurred in row %d, the matrix is singular. ",pivot_row));
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// // Swap the rows
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// if (pivot_row>col) {
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// for (size_t colInt = 0; colInt < NcolA; colInt++){
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// std::swap(AB[pivot_row][colInt],AB[pivot_row][colInt]);
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// }
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// }
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// // Process the entries below current element
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// for (size_t row = col; row < NrowA; row++){
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// // Entries to the right of current element (until end of A)
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// for (size_t colInt = col+1; colInt < NcolA; colInt++){
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// // All entries in augmented matrix
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// for (size_t colFull = col; colFull < NcolA+NcolB; colFull++){
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// AB[colInt][colFull] -= AB[col][colFull] * AB[colInt][col] / AB[col][col];
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// }
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// AB[colInt][col] = 0.0;
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// }
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// }
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// }
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// return AB;
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//}
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template<class T> std::vector<std::vector<T> > linsolve(std::vector<std::vector<T> > const& A, std::vector<std::vector<T> > const& B){
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return linsolve_Gauss_Jordan(A, B);
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};
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template<class T> std::vector<T> linsolve(std::vector<std::vector<T> > const& A, std::vector<T> const& b){
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std::vector<std::vector<T> > B;
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for (size_t i = 0; i < b.size(); i++){
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B.push_back(std::vector<T>(1,b[i]));
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}
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B = linsolve(A, B);
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B[0].resize(B.size(),0.0);
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for (size_t i = 1; i < B.size(); i++){
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B[0][i] = B[i][0];
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}
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return B[0];
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};
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template<class T> std::vector<T> get_row(std::vector< std::vector<T> > const& in, size_t row) { return in[row]; };
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template<class T> std::vector<T> get_col(std::vector< std::vector<T> > const& in, size_t col) {
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std::size_t sizeX = in.size();
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if (sizeX<1) throw ValueError(format("You have to provide values, a vector length of %d is not valid. ",sizeX));
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size_t sizeY = in[0].size();
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if (sizeY<1) throw ValueError(format("You have to provide values, a vector length of %d is not valid. ",sizeY));
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std::vector<T> out;
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for (std::size_t i = 0; i < sizeX; i++) {
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sizeY = in[i].size();
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if (sizeY-1<col) throw ValueError(format("Your matrix does not have enough entries in row %d, last index %d is less than %d. ",i,sizeY-1,col));
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out.push_back(in[i][col]);
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}
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return out;
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};
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template<class T> std::vector<std::vector<T> > make_squared(std::vector<std::vector<T> > const& in){
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std::size_t cols = max_cols(in);
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std::size_t rows = num_rows(in);
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std::size_t maxVal = 0;
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std::vector<std::vector<T> > out;
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std::vector<T> tmp;
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if (cols>rows) {maxVal = cols; }
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else {maxVal = rows; }
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out.clear();
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for (std::size_t i = 0; i < in.size(); i++) {
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tmp.clear();
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for (std::size_t j = 0; j < in[i].size(); j++) {
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tmp.push_back(in[i][j]);
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}
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while (maxVal>tmp.size()) {
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tmp.push_back(0.0);
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}
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out.push_back(tmp);
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}
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// Check rows
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tmp.clear();
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tmp.resize(maxVal,0.0);
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while (maxVal>out.size()) {
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out.push_back(tmp);
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}
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return out;
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};
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template<class T> T multiply( std::vector<T> const& a, std::vector<T> const& b){
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return dot_product(a,b);
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};
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template<class T> std::vector<T> multiply(std::vector<std::vector<T> > const& A, std::vector<T> const& b){
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std::vector<std::vector<T> > B;
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for (size_t i = 0; i < b.size(); i++){
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B.push_back(std::vector<T>(1,b[i]));
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}
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B = multiply(A, B);
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B[0].resize(B.size(),0.0);
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for (size_t i = 1; i < B.size(); i++){
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B[0][i] = B[i][0];
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}
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return B[0];
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}
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template<class T> std::vector<std::vector<T> > multiply(std::vector<std::vector<T> > const& A, std::vector<std::vector<T> > const& B){
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if (num_cols(A) != num_rows(B)){
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throw ValueError(format("You have to provide matrices with the same columns and rows: %d is not equal to %d. ",num_cols(A),num_rows(B)));
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}
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size_t rows = num_rows(A);
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size_t cols = num_cols(B);
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T tmp;
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std::vector<std::vector<T> > outVec;
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std::vector<T> tmpVec;
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outVec.clear();
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for (size_t i = 0; i < rows; i++){
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tmpVec.clear();
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for (size_t j = 0; j < cols; j++){
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tmp = 0.0;
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for (size_t k = 0; k < num_cols(A); k++){
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tmp += A[i][k] * B[k][j];
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}
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tmpVec.push_back(tmp);
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}
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outVec.push_back(tmpVec);
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}
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return outVec;
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};
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template<class T> T dot_product(std::vector<T> const& a, std::vector<T> const& b){
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if (a.size()==b.size()){
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return std::inner_product(a.begin(), a.end(), b.begin(), 0.0);
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}
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throw ValueError(format("You have to provide vectors with the same length: %d is not equal to %d. ",a.size(),b.size()));
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};
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template<class T> std::vector<T> cross_product(std::vector<T> const& a, std::vector<T> const& b){
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throw NotImplementedError("The cross product function has not been implemented, yet");
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};
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template<class T> std::vector< std::vector<T> > transpose(std::vector<std::vector<T> > const& in){
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size_t sizeX = in.size();
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if (sizeX<1) throw ValueError(format("You have to provide values, a vector length of %d is not a valid. ",sizeX));
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size_t sizeY = in[0].size();
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size_t sizeYOld = sizeY;
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if (sizeY<1) throw ValueError(format("You have to provide values, a vector length of %d is not a valid. ",sizeY));
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std::vector< std::vector<T> > out(sizeY,std::vector<T>(sizeX));
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for (size_t i = 0; i < sizeX; ++i){
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sizeY = in[i].size();
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if (sizeY!=sizeYOld) throw ValueError(format("You have to provide a rectangular matrix: %d is not equal to %d. ",sizeY,sizeYOld));
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for (size_t j = 0; j < sizeY; ++j){
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out[j][i] = in[i][j];
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}
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}
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return out;
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};
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template<class T> std::vector< std::vector<T> > invert(std::vector<std::vector<T> > const& in){
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if (!is_squared(in)) throw ValueError(format("Only square matrices can be inverted: %d is not equal to %d. ",num_rows(in),num_cols(in)));
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std::vector<std::vector<T> > identity;
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// Build the identity matrix
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size_t dim = num_rows(in);
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identity.resize(dim, std::vector<T>(dim, 0));
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for (size_t row = 0; row < dim; row++){
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identity[row][row] = 1.0;
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}
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return linsolve(in,identity);
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};
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template<class T> std::string vec_to_string( T const& a){
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std::stringstream out;
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out << format("[ %7.3f ]",a);
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return out.str();
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};
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template<class T> std::string vec_to_string( std::vector<T> const& a) {
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return vec_to_string(a,"%7.3g");
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};
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template<class T> std::string vec_to_string( std::vector<T> const& a, const char *fmt) {
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if (a.size()<1) {
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return std::string("");
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} else {
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std::stringstream out;
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out << format("[ ");
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out << format(fmt,a[0]);
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for (size_t j = 1; j < a.size(); j++) {
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|
out << ", ";
|
|
out << format(fmt,a[j]);
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|
}
|
|
out << " ]";
|
|
return out.str();
|
|
}
|
|
};
|
|
|
|
template<class T> std::string vec_to_string(std::vector<std::vector<T> > const& A) {
|
|
return vec_to_string(A, "%7.3g");
|
|
}
|
|
|
|
template<class T> std::string vec_to_string(std::vector<std::vector<T> > const& A, const char *fmt) {
|
|
std::stringstream out;
|
|
for (size_t j = 0; j < A.size(); j++) {
|
|
out << vec_to_string(A[j], fmt);
|
|
}
|
|
return out.str();
|
|
}
|
|
|
|
}; /* namespace CoolProp */
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#endif
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