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CoolProp/include/MatrixMath.h
Ian Bell e119cbca29 Fix remove row and column functions
2015-11-14 21:46:45 -07:00

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#ifndef MATRIXMATH_H
#define MATRIXMATH_H
#include "CoolPropTools.h"
#include "Exceptions.h"
#include <vector>
#include <string>
#include <numeric> // inner_product
#include <sstream>
#include "float.h"
#include "Eigen/Core"
/// A wrapper around std::vector
/** This wrapper makes the standard vector multi-dimensional.
* A useful thing even though we might not need it that
* much. However, it makes the code look better and the
* polynomial class really is a mess...
* Source: http://stackoverflow.com/questions/13105514/n-dimensional-vector
*/
template<size_t dimcount, typename T> struct VectorNd {
typedef std::vector< typename VectorNd<dimcount-1, T>::type > type;
};
template<typename T> struct VectorNd<0,T> {
typedef T type;
};
namespace CoolProp{
/// Some shortcuts and regularly needed operations
template<class T> std::size_t num_rows ( std::vector<T> const& in){ return in.size(); }
template<class T> std::size_t num_rows (std::vector<std::vector<T> > const& in){ return in.size(); }
template<class T> std::size_t max_cols (std::vector<std::vector<T> > const& in){
std::size_t cols = 0;
std::size_t col = 0;
for (std::size_t i = 0; i < in.size(); i++) {
col = in[i].size();
if (cols<col) {cols = col;}
}
return cols;
};
template<class T> bool is_squared(std::vector<std::vector<T> > const& in){
std::size_t cols = max_cols(in);
if (cols!=num_rows(in)) { return false;}
else {
for (std::size_t i = 0; i < in.size(); i++) {
if (cols!=in[i].size()) {return false; }
}
}
return true;
};
template<class T> std::size_t num_cols ( std::vector<T> const& in){ return 1; }
template<class T> std::size_t num_cols (std::vector<std::vector<T> > const& in){
if (num_rows(in)>0) {
if (is_squared(in)) {
return in[0].size();
} else {
return max_cols(in);
}
} else {
return 0;
}
};
/// Convert vectors and matrices
/** Conversion functions for the different kinds of object-like
* parameters. This might be obsolete at a later stage, but now
* it is still needed.
* @param coefficients matrix containing the ordered coefficients
* @param axis axis along which to extract
*/
template <typename T> std::vector<T> eigen_to_vec1D(const Eigen::Matrix<T,Eigen::Dynamic,Eigen::Dynamic> &coefficients, int axis = 0){
std::vector<T> result;
size_t r = coefficients.rows(), c = coefficients.cols();
if (axis==0) {
if (c!=1) throw ValueError(format("Your matrix has the wrong dimensions: %d,%d",r,c));
result.resize(r);
for (size_t i = 0; i < r; ++i) {
result[i] = coefficients(i,0);
}
} else if (axis==1) {
if (r!=1) throw ValueError(format("Your matrix has the wrong dimensions: %d,%d",r,c));
result.resize(c);
for (size_t i = 0; i < c; ++i) {
result[i] = coefficients(0,i);
}
} else {
throw ValueError(format("You have to provide axis information: %d is not valid. ",axis));
}
return result;
}
/// @param coefficients matrix containing the ordered coefficients
template <class T> std::vector<std::vector<T> > eigen_to_vec(const Eigen::Matrix<T,Eigen::Dynamic,Eigen::Dynamic> &coefficients){
// Eigen uses columns as major axis, this might be faster than the row iteration.
// However, the 2D vector stores things differently, no idea what is faster...
std::vector<std::vector<T> > result;
size_t r = coefficients.rows(), c = coefficients.cols();
result.resize(r, std::vector<T>(c, 0)); // extends vector if necessary
for (size_t i = 0; i < r; ++i) {
result[i].resize(c, 0);
for (size_t j = 0; j < c; ++j) {
result[i][j] = coefficients(i,j);
}
}
return result;
}
/// @param coefficients matrix containing the ordered coefficients
template <class T> Eigen::Matrix<T,Eigen::Dynamic,Eigen::Dynamic> vec_to_eigen(const std::vector<std::vector<T> > &coefficients){
size_t nRows = num_rows(coefficients), nCols = num_cols(coefficients);
Eigen::Matrix<T,Eigen::Dynamic,Eigen::Dynamic> result(nRows,nCols);
for (size_t i = 0; i < nCols; ++i) {
for (size_t j = 0; j < nRows; ++j) {
result(j,i) = coefficients[j][i];
}
}
return result;
}
/**
* @param coefficients matrix containing the ordered coefficients
* @param axis axis along which to extract data
*/
template <class T> Eigen::Matrix<T,Eigen::Dynamic,Eigen::Dynamic> vec_to_eigen(const std::vector<T> &coefficients, int axis = 0){
size_t nRows = num_rows(coefficients);
Eigen::Matrix<T,Eigen::Dynamic,Eigen::Dynamic> result;
if (axis==0) result.resize(nRows,1);
else if (axis==1) result.resize(1,nRows);
else throw ValueError(format("You have to provide axis information: %d is not valid. ",axis));
for (size_t i = 0; i < nRows; ++i) {
if (axis==0) result(i,0) = coefficients[i];
if (axis==1) result(0,i) = coefficients[i];
}
return result;
}
/// @param coefficient
template <class T> Eigen::Matrix<T,Eigen::Dynamic,Eigen::Dynamic> vec_to_eigen(const T &coefficient){
Eigen::Matrix<T,Eigen::Dynamic,Eigen::Dynamic> result = Eigen::Matrix<T,Eigen::Dynamic,Eigen::Dynamic>(1,1);
result(0,0) = coefficient;
return result;
}
/// Convert 1D matrix to vector
/** Returns either a row- or a column-based
* vector. By default, Eigen prefers column
* major ordering, just like Fortran.
*/
template< class T> Eigen::Matrix<T,Eigen::Dynamic,1> makeColVector(const Eigen::Matrix<T,Eigen::Dynamic,Eigen::Dynamic> &matrix){
std::size_t r = matrix.rows();
std::size_t c = matrix.cols();
Eigen::Matrix<T,Eigen::Dynamic,1> vector;
if (r==1&&c>=1) { // Check passed, matrix can be transformed
vector = matrix.transpose().block(0,0,c,r);
} else if ( r>=1&&c==1) { // Check passed, matrix can be transformed
vector = matrix.block(0,0,r,c);
} else { // Check failed, throw error
throw ValueError(format("Your matrix (%d,%d) cannot be converted into a vector (x,1).",r,c));
}
return vector;
}
template< class T> Eigen::Matrix<T,Eigen::Dynamic,1> makeVector(const Eigen::Matrix<T,Eigen::Dynamic,Eigen::Dynamic> &matrix) {
return makeColVector(matrix);
}
template< class T> Eigen::Matrix<T,1,Eigen::Dynamic> makeRowVector(const Eigen::Matrix<T,Eigen::Dynamic,Eigen::Dynamic> &matrix){
std::size_t r = matrix.rows();
std::size_t c = matrix.cols();
Eigen::Matrix<T,1,Eigen::Dynamic> vector;
if (r==1&&c>=1) { // Check passed, matrix can be transformed
vector = matrix.block(0,0,r,c);
} else if ( r>=1&&c==1) { // Check passed, matrix can be transformed
vector = matrix.transpose().block(0,0,c,r);
} else { // Check failed, throw error
throw ValueError(format("Your matrix (%d,%d) cannot be converted into a vector (1,x).",r,c));
}
return vector;
}
/// Remove rows and columns from matrices
/** A set of convenience functions inspired by http://stackoverflow.com/questions/13290395/how-to-remove-a-certain-row-or-column-while-using-eigen-library-c
* but altered to respect templates.
*/
template< class T> void removeRow(Eigen::Matrix<T,Eigen::Dynamic,Eigen::Dynamic> &matrix, std::size_t rowToRemove){
//template<class T> void removeRow(Eigen::MatrixXd& matrix, std::size_t rowToRemove){
//void removeRow(Eigen::MatrixXd& matrix, unsigned int rowToRemove){
//template <typename Derived> void removeRow(Eigen::MatrixBase<Derived> &matrix, std::size_t rowToRemove){
std::size_t numRows = matrix.rows()-1;
std::size_t numCols = matrix.cols();
if( rowToRemove < numRows ){
matrix.block(rowToRemove,0,numRows-rowToRemove,numCols) = matrix.block(rowToRemove+1,0,numRows-rowToRemove,numCols);
} else {
if( rowToRemove > numRows ){
throw ValueError(format("Your matrix does not have enough rows, %d is not greater or equal to %d.",numRows,rowToRemove));
}
// Do nothing, resize removes the last row
}
matrix.conservativeResize(numRows,numCols);
}
template <class T> void removeColumn(Eigen::Matrix<T,Eigen::Dynamic,Eigen::Dynamic> &matrix, std::size_t colToRemove){
//template<class T> void removeColumn(Eigen::MatrixXd& matrix, std::size_t colToRemove){
//void removeColumn(Eigen::MatrixXd& matrix, unsigned int colToRemove){
//template <typename Derived> void removeColumn(Eigen::MatrixBase<Derived> &matrix, std::size_t colToRemove){
std::size_t numRows = matrix.rows();
std::size_t numCols = matrix.cols()-1;
if( colToRemove < numCols ) {
matrix.block(0,colToRemove,numRows,numCols-colToRemove) = matrix.block(0,colToRemove+1,numRows,numCols-colToRemove);
} else {
if( colToRemove > numCols ) {
throw ValueError(format("Your matrix does not have enough columns, %d is not greater or equal to %d.",numCols,colToRemove));
}
// Do nothing, resize removes the last column
}
matrix.conservativeResize(numRows,numCols);
}
///// @param coefficients matrix containing the ordered coefficients
//template <class T> Eigen::Matrix<T, Eigen::Dynamic,Eigen::Dynamic> convert(const std::vector<std::vector<T> > &coefficients){
// size_t nRows = num_rows(coefficients), nCols = num_cols(coefficients);
// Eigen::MatrixBase<T> result(nRows,nCols);
// for (size_t i = 0; i < nCols; ++i) {
// for (size_t j = 0; j < nRows; ++j) {
// result(j,i) = coefficients[j][i];
// }
// }
// return result;
//}
//
///// @param coefficients matrix containing the ordered coefficients
//template <class T, int R, int C> void convert(const std::vector<std::vector<T> > &coefficients, Eigen::Matrix<T,R,C> &result){
// size_t nRows = num_rows(coefficients), nCols = num_cols(coefficients);
// //Eigen::MatrixBase<T> result(nRows,nCols);
// for (size_t i = 0; i < nCols; ++i) {
// for (size_t j = 0; j < nRows; ++j) {
// result(j,i) = coefficients[j][i];
// }
// }
// //return result;
//}
//
//template <class T> void convert(const std::vector<std::vector<T> > &coefficients, Eigen::MatrixBase<T> &result){
// size_t nRows = num_rows(coefficients), nCols = num_cols(coefficients);
// //Eigen::MatrixBase<T> result;
// //if ((R!=nRows) || (C!=nCols))
// result.resize(nRows,nCols);
// for (size_t i = 0; i < nCols; ++i) {
// for (size_t j = 0; j < nRows; ++j) {
// result(j,i) = coefficients[j][i];
// }
// }
// //return result;
//}
//template <class Derived>
//inline void func1(MatrixBase<Derived> &out_mat ){
// // Do something then return a matrix
// out_mat = ...
//}
//template <class Derived>
//Eigen::Matrix<class Derived::Scalar, Derived::RowsAtCompileTime, Derived::ColsAtCompileTime>
//Multiply(const Eigen::MatrixBase<DerivedA>& p1,
// const Eigen::MatrixBase<DerivedB>& p2)
//{
// return (p1 * p2);
//}
//
//
//template <typename DerivedA, typename DerivedB>
//Eigen::Matrix<typename DerivedA::Scalar, DerivedA::RowsAtCompileTime, DerivedB::ColsAtCompileTime>
//Multiply(const Eigen::MatrixBase<DerivedA>& p1,
// const Eigen::MatrixBase<DerivedB>& p2)
//{
// return (p1 * p2);
//}
/// Templates for printing numbers, vectors and matrices
static const char* stdFmt = "%8.3f";
///Templates for turning vectors (1D-matrices) into strings
template<class T> std::string vec_to_string(const std::vector<T> &a, const char *fmt) {
if (a.size()<1) return std::string("");
std::stringstream out;
out << "[ " << format(fmt,a[0]);
for (size_t j = 1; j < a.size(); j++) {
out << ", " << format(fmt, a[j]);
}
out << " ]";
return out.str();
};
template<class T> std::string vec_to_string(const std::vector<T> &a) {
return vec_to_string(std::vector<double>(a.begin(), a.end()), stdFmt);
};
///Templates for turning vectors (1D-matrices) into strings
inline std::string stringvec_to_string(const std::vector<std::string> &a) {
if (a.size()<1) return std::string("");
std::stringstream out;
out << "[ " << format("%s", a[0].c_str());
for (size_t j = 1; j < a.size(); j++) {
out << ", " << format("%s", a[j].c_str());
}
out << " ]";
return out.str();
};
/// Templates for turning numbers (0D-matrices) into strings
template<class T> std::string vec_to_string(const T &a, const char *fmt) {
std::vector<T> vec;
vec.push_back(a);
return vec_to_string(vec, fmt);
};
template<class T> std::string vec_to_string(const T &a) {
return vec_to_string((double) a, stdFmt);
};
///Templates for turning 2D-matrices into strings
template<class T> std::string vec_to_string(const std::vector<std::vector<T> > &A, const char *fmt) {
if (A.size()<1) return std::string("");
std::stringstream out;
out << "[ " << vec_to_string(A[0], fmt);
for (size_t j = 1; j < A.size(); j++) {
out << ", " << std::endl << " " << vec_to_string(A[j], fmt);
}
out << " ]";
return out.str();
};
template<class T> std::string vec_to_string(const std::vector<std::vector<T> > &A) {
return vec_to_string(A, stdFmt);
};
///Templates for turning Eigen matrices into strings
template <class T> std::string mat_to_string(const Eigen::Matrix<T,Eigen::Dynamic,Eigen::Dynamic> &A, const char *fmt) {
//std::string mat_to_string(const Eigen::MatrixXd &A, const char *fmt) {
std::size_t r = A.rows();
std::size_t c = A.cols();
if ((r<1)||(c<1)) return std::string("");
std::stringstream out;
out << "[ ";
if (r==1) {
out << format(fmt, A(0,0));
for (size_t j = 1; j < c; j++) {
out << ", " << format(fmt, A(0,j));
}
} else {
out << mat_to_string(Eigen::Matrix<T,Eigen::Dynamic,Eigen::Dynamic>(A.row(0)), fmt);
for (size_t i = 1; i < r; i++) {
out << ", " << std::endl << " " << mat_to_string(Eigen::Matrix<T,Eigen::Dynamic,Eigen::Dynamic>(A.row(i)), fmt);
}
}
out << " ]";
return out.str();
};
template <class T> std::string mat_to_string(const Eigen::Matrix<T,Eigen::Dynamic,Eigen::Dynamic> &A) {
//std::string vec_to_string(const Eigen::MatrixXd &A) {
return mat_to_string(A, stdFmt);
};
///// Templates for printing numbers, vectors and matrices
//static const char* stdFmt = "%8.3f";
//
/////Templates for turning vectors (1D-matrices) into strings
//template<class T> std::string vec_to_string(const std::vector<T> &a, const char *fmt) {
// if (a.size()<1) return std::string("");
// std::stringstream out;
// out << "[ " << format(fmt,a[0]);
// for (size_t j = 1; j < a.size(); j++) {
// out << ", " << format(fmt, a[j]);
// }
// out << " ]";
// return out.str();
//};
//template<class T> std::string vec_to_string(const std::vector<T> &a) {
// return vec_to_string(a, stdFmt);
//};
//
///// Templates for turning numbers (0D-matrices) into strings
//template<class T> std::string vec_to_string(const T &a, const char *fmt) {
// std::vector<T> vec;
// vec.push_back(a);
// return vec_to_string(vec, fmt);
//};
//template<class T> std::string vec_to_string(const T &a) {
// return vec_to_string(a, stdFmt);
//};
//
/////Templates for turning 2D-matrices into strings
//template<class T> std::string vec_to_string(const std::vector<std::vector<T> > &A, const char *fmt) {
// if (A.size()<1) return std::string("");
// std::stringstream out;
// out << "[ " << vec_to_string(A[0], fmt);
// for (size_t j = 1; j < A.size(); j++) {
// out << ", " << std::endl << " " << vec_to_string(A[j], fmt);
// }
// out << " ]";
// return out.str();
//};
//template<class T> std::string vec_to_string(const std::vector<std::vector<T> > &A) {
// return vec_to_string(A, stdFmt);
//};
//
/////Templates for turning Eigen matrices into strings
//template <class T> std::string mat_to_string(const Eigen::Matrix<T,Eigen::Dynamic,Eigen::Dynamic> &A, const char *fmt) {
////std::string mat_to_string(const Eigen::MatrixXd &A, const char *fmt) {
// std::size_t r = A.rows();
// std::size_t c = A.cols();
// if ((r<1)||(c<1)) return std::string("");
// std::stringstream out;
// out << "[ ";
// if (r==1) {
// out << format(fmt, A(0,0));
// for (size_t j = 1; j < c; j++) {
// out << ", " << format(fmt, A(0,j));
// }
// } else {
// out << mat_to_string(Eigen::Matrix<T,Eigen::Dynamic,Eigen::Dynamic>(A.row(0)), fmt);
// for (size_t i = 1; i < r; i++) {
// out << ", " << std::endl << " " << mat_to_string(Eigen::Matrix<T,Eigen::Dynamic,Eigen::Dynamic>(A.row(i)), fmt);
// }
// }
// out << " ]";
// return out.str();
//};
//template <class T> std::string mat_to_string(const Eigen::Matrix<T,Eigen::Dynamic,Eigen::Dynamic> &A) {
////std::string vec_to_string(const Eigen::MatrixXd &A) {
// return mat_to_string(A, stdFmt);
//};
/// Template class for turning numbers (0D-matrices) into strings
//template<class T> std::string vec_to_string(const T &a){
// return vec_to_string(a, stdFmt);
// std::stringstream out;
// out << format("[ %7.3f ]",a);
// return out.str();
//};
//template<class T> std::string vec_to_string(const VectorNd<0, T> &a){
// return vec_to_string(a, stdFmt);
//};
//template<class T> std::string vec_to_string(const VectorNd<0, T> &a, const char *fmt) {
// VectorNd<1, T> vec;
// vec.push_back(a);
// return vec_to_string(vec, fmt);
//};
//
/////Template classes for turning vectors (1D-matrices) into strings
//template<class T> std::string vec_to_string(const VectorNd<1, T> &a) {
// return vec_to_string(a, stdFmt);
//};
//template<class T> std::string vec_to_string(const VectorNd<1, T> &a, const char *fmt) {
// if (a.size()<1) {
// return std::string("");
// } else {
// std::stringstream out;
// out << "[ ";
// out << format(fmt,a[0]);
// for (size_t j = 1; j < a.size(); j++) {
// out << ", ";
// out << format(fmt,a[j]);
// }
// out << " ]";
// return out.str();
// }
//};
//
/////Template classes for turning 2D-matrices into strings
//template<class T> std::string vec_to_string(const VectorNd<2, T> &A) {
// return vec_to_string(A, stdFmt);
//}
//template<class T> std::string vec_to_string(const VectorNd<2, T> &A, const char *fmt) {
// if (A.size()<1) return std::string("");
// std::stringstream out;
// out << "[ " << format(fmt,A[0]);
// for (size_t j = 1; j < A.size(); j++) {
// out << ", " << std::endl << " " << vec_to_string(A[j], fmt);
// }
// out << " ]";
// return out.str();
//}
///// Publish the linear algebra solver
//template<class T> std::vector<T> linsolve(std::vector<std::vector<T> > const& A, std::vector<T> const& b);
//template<class T> std::vector<std::vector<T> > linsolve(std::vector<std::vector<T> > const& A, std::vector<std::vector<T> > const& B);
//
///// Some shortcuts and regularly needed operations
//template<class T> std::size_t num_rows (std::vector<std::vector<T> > const& in);
//template<class T> std::size_t num_cols (std::vector<std::vector<T> > const& in);
//template<class T> std::size_t max_cols (std::vector<std::vector<T> > const& in);
//template<class T> std::vector<T> get_row (std::vector<std::vector<T> > const& in, size_t row);
//template<class T> std::vector<T> get_col (std::vector<std::vector<T> > const& in, size_t col);
//template<class T> bool is_squared(std::vector<std::vector<T> > const& in);
//template<class T> std::vector<std::vector<T> > make_squared(std::vector<std::vector<T> > const& in);
//
///// Define some basic math operations for vectors
//template<class T> T multiply( std::vector<T> const& A, std::vector<T> const& B);
//template<class T> std::vector<T> multiply(std::vector<std::vector<T> > const& A, std::vector<T> const& B);
//template<class T> std::vector<std::vector<T> > multiply(std::vector<std::vector<T> > const& A, std::vector<std::vector<T> > const& B);
//
//template<class T> T dot_product(std::vector<T> const& a, std::vector<T> const& b);
//template<class T> std::vector<T> cross_product(std::vector<T> const& a, std::vector<T> const& b);
//
//template<class T> std::vector<std::vector<T> > transpose(std::vector<std::vector<T> > const& in);
//template<class T> std::vector<std::vector<T> > invert(std::vector<std::vector<T> > const& in);
//
//template<class T> std::string vec_to_string( T const& a);
//template<class T> std::string vec_to_string( std::vector<T> const& a);
//template<class T> std::string vec_to_string(std::vector<std::vector<T> > const& A);
//
//template<class T> std::string vec_to_string( std::vector<T> const& a, const char *fmt);
//template<class T> std::string vec_to_string(std::vector<std::vector<T> > const& A, const char *fmt);
/*
Owe a debt of gratitude to http://sole.ooz.ie/en - very clear treatment of GJ
*/
template<typename T> void swap_rows(std::vector<std::vector<T> > *A, size_t row1, size_t row2)
{
for (size_t col = 0; col < (*A)[0].size(); col++){
std::swap((*A)[row1][col],(*A)[row2][col]);
}
};
template<typename T> void subtract_row_multiple(std::vector<std::vector<T> > *A, size_t row, T multiple, size_t pivot_row)
{
for (size_t col = 0; col < (*A)[0].size(); col++){
(*A)[row][col] -= multiple*(*A)[pivot_row][col];
}
};
template<typename T> void divide_row_by(std::vector<std::vector<T> > *A, size_t row, T value)
{
for (size_t col = 0; col < (*A)[0].size(); col++){
(*A)[row][col] /= value;
}
};
template<typename T> size_t get_pivot_row(std::vector<std::vector<T> > *A, size_t col)
{
std::size_t index = col;
T max = 0, val;
for (size_t row = col; row < (*A).size(); row++)
{
val = (*A)[row][col];
if (std::abs(val) > max)
{
max = std::abs(val);
index = row;
}
}
return index;
};
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) {
std::vector<std::vector<T> > AB;
std::vector<std::vector<T> > X;
size_t pivot_row;
T pivot_element;
size_t NrowA = num_rows(A);
size_t NrowB = num_rows(B);
size_t NcolA = num_cols(A);
size_t NcolB = num_cols(B);
if (NrowA!=NrowB) throw ValueError(format("You have to provide matrices with the same number of rows: %d is not %d. ",NrowA,NrowB));
AB.resize(NrowA, std::vector<T>(NcolA+NcolB, 0));
X.resize(NrowA, std::vector<T>(NcolB, 0));
// Build the augmented matrix
for (size_t row = 0; row < NrowA; row++){
for (size_t col = 0; col < NcolA; col++){
AB[row][col] = A[row][col];
}
for (size_t col = NcolA; col < NcolA+NcolB; col++){
AB[row][col] = B[row][col-NcolA];
}
}
for (size_t col = 0; col < NcolA; col++){
// Find the pivot value
pivot_row = get_pivot_row(&AB, col);
if (std::abs(AB[pivot_row][col]) < 10*DBL_EPSILON){ throw ValueError(format("Zero occurred in row %d, the matrix is singular. ",pivot_row));}
if (pivot_row>=col){
// Swap pivot row and current row
swap_rows(&AB, col, pivot_row);
}
// Get the pivot element
pivot_element = AB[col][col];
// Divide the pivot row by the pivot element
divide_row_by(&AB,col,pivot_element);
if (col < NrowA-1)
{
// All the rest of the rows, subtract the value of the [r][c] combination
for (size_t row = col + 1; row < NrowA; row++)
{
subtract_row_multiple(&AB,row,AB[row][col],col);
}
}
}
for (std::size_t col = NcolA - 1; col > 0; col--)
{
for (int row = static_cast<int>(col) - 1; row >=0; row--)
{
subtract_row_multiple(&AB,row,AB[row][col],col);
}
}
// Set the output value
for (size_t row = 0; row < NrowA; row++){
for (size_t col = 0; col < NcolB; col++){
X[row][col] = AB[row][NcolA+col];
}
}
return X;
};
//std::vector<std::vector<double> > linsolve_Gauss_Jordan_reimpl(std::vector<std::vector<double> > const& A, std::vector<std::vector<double> > const& B) {
// std::vector<std::vector<double> > AB;
// std::vector<std::vector<double> > X;
// size_t pivot_row;
// double pivot_element;
// double tmp_element;
//
// size_t NrowA = num_rows(A);
// size_t NrowB = num_rows(B);
// size_t NcolA = num_cols(A);
// size_t NcolB = num_cols(B);
//
// if (NrowA!=NrowB) throw ValueError(format("You have to provide matrices with the same number of rows: %d is not %d. ",NrowA,NrowB));
//
// AB.resize(NrowA, std::vector<double>(NcolA+NcolB, 0));
// X.resize(NrowA, std::vector<double>(NcolB, 0));
//
// // Build the augmented matrix
// for (size_t row = 0; row < NrowA; row++){
// for (size_t col = 0; col < NcolA; col++){
// AB[row][col] = A[row][col];
// }
// for (size_t col = NcolA; col < NcolA+NcolB; col++){
// AB[row][col] = B[row][col-NcolA];
// }
// }
//
// for (size_t col = 0; col < NcolA; col++){
// // Find the pivot row
// pivot_row = 0;
// pivot_element = 0.0;
// for (size_t row = col; row < NrowA; row++){
// tmp_element = std::abs(AB[row][col]);
// if (tmp_element>pivot_element) {
// pivot_element = tmp_element;
// pivot_row = row;
// }
// }
// // Check for errors
// if (AB[pivot_row][col]<1./_HUGE) throw ValueError(format("Zero occurred in row %d, the matrix is singular. ",pivot_row));
// // Swap the rows
// if (pivot_row>col) {
// for (size_t colInt = 0; colInt < NcolA; colInt++){
// std::swap(AB[pivot_row][colInt],AB[pivot_row][colInt]);
// }
// }
// // Process the entries below current element
// for (size_t row = col; row < NrowA; row++){
// // Entries to the right of current element (until end of A)
// for (size_t colInt = col+1; colInt < NcolA; colInt++){
// // All entries in augmented matrix
// for (size_t colFull = col; colFull < NcolA+NcolB; colFull++){
// AB[colInt][colFull] -= AB[col][colFull] * AB[colInt][col] / AB[col][col];
// }
// AB[colInt][col] = 0.0;
// }
// }
// }
// return AB;
//}
template<class T> std::vector<std::vector<T> > linsolve(std::vector<std::vector<T> > const& A, std::vector<std::vector<T> > const& B){
return linsolve_Gauss_Jordan(A, B);
};
template<class T> std::vector<T> linsolve(std::vector<std::vector<T> > const& A, std::vector<T> const& b){
std::vector<std::vector<T> > B;
for (size_t i = 0; i < b.size(); i++){
B.push_back(std::vector<T>(1,b[i]));
}
B = linsolve(A, B);
B[0].resize(B.size(),0.0);
for (size_t i = 1; i < B.size(); i++){
B[0][i] = B[i][0];
}
return B[0];
};
template<class T> std::vector<T> get_row(std::vector< std::vector<T> > const& in, size_t row) { return in[row]; };
template<class T> std::vector<T> get_col(std::vector< std::vector<T> > const& in, size_t col) {
std::size_t sizeX = in.size();
if (sizeX<1) throw ValueError(format("You have to provide values, a vector length of %d is not valid. ",sizeX));
size_t sizeY = in[0].size();
if (sizeY<1) throw ValueError(format("You have to provide values, a vector length of %d is not valid. ",sizeY));
std::vector<T> out;
for (std::size_t i = 0; i < sizeX; i++) {
sizeY = in[i].size();
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));
out.push_back(in[i][col]);
}
return out;
};
template<class T> std::vector<std::vector<T> > make_squared(std::vector<std::vector<T> > const& in){
std::size_t cols = max_cols(in);
std::size_t rows = num_rows(in);
std::size_t maxVal = 0;
std::vector<std::vector<T> > out;
std::vector<T> tmp;
if (cols>rows) {maxVal = cols; }
else {maxVal = rows; }
out.clear();
for (std::size_t i = 0; i < in.size(); i++) {
tmp.clear();
for (std::size_t j = 0; j < in[i].size(); j++) {
tmp.push_back(in[i][j]);
}
while (maxVal>tmp.size()) {
tmp.push_back(0.0);
}
out.push_back(tmp);
}
// Check rows
tmp.clear();
tmp.resize(maxVal,0.0);
while (maxVal>out.size()) {
out.push_back(tmp);
}
return out;
};
template<class T> T multiply( std::vector<T> const& a, std::vector<T> const& b){
return dot_product(a,b);
};
template<class T> std::vector<T> multiply(std::vector<std::vector<T> > const& A, std::vector<T> const& b){
std::vector<std::vector<T> > B;
for (size_t i = 0; i < b.size(); i++){
B.push_back(std::vector<T>(1,b[i]));
}
B = multiply(A, B);
B[0].resize(B.size(),0.0);
for (size_t i = 1; i < B.size(); i++){
B[0][i] = B[i][0];
}
return B[0];
}
template<class T> std::vector<std::vector<T> > multiply(std::vector<std::vector<T> > const& A, std::vector<std::vector<T> > const& B){
if (num_cols(A) != num_rows(B)){
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)));
}
size_t rows = num_rows(A);
size_t cols = num_cols(B);
T tmp;
std::vector<std::vector<T> > outVec;
std::vector<T> tmpVec;
outVec.clear();
for (size_t i = 0; i < rows; i++){
tmpVec.clear();
for (size_t j = 0; j < cols; j++){
tmp = 0.0;
for (size_t k = 0; k < num_cols(A); k++){
tmp += A[i][k] * B[k][j];
}
tmpVec.push_back(tmp);
}
outVec.push_back(tmpVec);
}
return outVec;
};
template<class T> T dot_product(std::vector<T> const& a, std::vector<T> const& b){
if (a.size()==b.size()){
return std::inner_product(a.begin(), a.end(), b.begin(), 0.0);
}
throw ValueError(format("You have to provide vectors with the same length: %d is not equal to %d. ",a.size(),b.size()));
};
template<class T> std::vector<T> cross_product(std::vector<T> const& a, std::vector<T> const& b){
throw NotImplementedError("The cross product function has not been implemented, yet");
};
template<class T> std::vector< std::vector<T> > transpose(std::vector<std::vector<T> > const& in){
size_t sizeX = in.size();
if (sizeX<1) throw ValueError(format("You have to provide values, a vector length of %d is not a valid. ",sizeX));
size_t sizeY = in[0].size();
size_t sizeYOld = sizeY;
if (sizeY<1) throw ValueError(format("You have to provide values, a vector length of %d is not a valid. ",sizeY));
std::vector< std::vector<T> > out(sizeY,std::vector<T>(sizeX));
for (size_t i = 0; i < sizeX; ++i){
sizeY = in[i].size();
if (sizeY!=sizeYOld) throw ValueError(format("You have to provide a rectangular matrix: %d is not equal to %d. ",sizeY,sizeYOld));
for (size_t j = 0; j < sizeY; ++j){
out[j][i] = in[i][j];
}
}
return out;
};
template<class T> std::vector< std::vector<T> > invert(std::vector<std::vector<T> > const& in){
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)));
std::vector<std::vector<T> > identity;
// Build the identity matrix
size_t dim = num_rows(in);
identity.resize(dim, std::vector<T>(dim, 0));
for (size_t row = 0; row < dim; row++){
identity[row][row] = 1.0;
}
return linsolve(in,identity);
};
inline void removeRow(Eigen::MatrixXd& matrix, unsigned int rowToRemove)
{
unsigned int numRows = static_cast<unsigned int>(matrix.rows())- 1;
unsigned int numCols = static_cast<unsigned int>(matrix.cols());
if (rowToRemove <= numRows)
matrix.block(rowToRemove, 0, numRows-rowToRemove, numCols) = matrix.block(rowToRemove+1, 0, numRows-rowToRemove, numCols);
else{
throw ValueError(format("Trying to remove row index [%d] greater than max index [%d] ", rowToRemove, numRows));
}
matrix.conservativeResize(numRows, numCols);
};
inline void removeColumn(Eigen::MatrixXd& matrix, unsigned int colToRemove)
{
unsigned int numRows = static_cast<unsigned int>(matrix.rows());
unsigned int numCols = static_cast<unsigned int>(matrix.cols())-1;
if (colToRemove <= numCols)
matrix.block(0, colToRemove, numRows, numCols-colToRemove) = matrix.block(0, colToRemove+1, numRows, numCols-colToRemove);
else{
throw ValueError(format("Trying to remove column index [%d] greater than max index [%d] ", colToRemove, numCols));
}
matrix.conservativeResize(numRows, numCols);
};
template <typename Derived>
inline Eigen::MatrixXd minor_matrix(const Eigen::MatrixBase<Derived>& A, std::size_t i, std::size_t j)
{
Eigen::MatrixXd Am = A;
removeRow(Am, static_cast<unsigned int>(i));
removeColumn(Am, static_cast<unsigned int>(j));
return Am;
};
template <typename Derived>
static Eigen::MatrixXd adjugate(const Eigen::MatrixBase<Derived>& A)
{
std::size_t N = A.rows();
if (N==1){
Eigen::MatrixXd Aadj(1,1);
Aadj << 1;
return Aadj;
}
Eigen::MatrixXd Aadj(N, N);
for (std::size_t i = 0; i < N; ++i){
for (std::size_t j = 0; j < N; ++j){
int negative_1_to_the_i_plus_j = ((i+j)%2==0) ? 1 : -1;
Aadj(i, j) = negative_1_to_the_i_plus_j*minor_matrix(A, j, i).determinant();
}
}
return Aadj;
}
template <typename Derived>
static Eigen::MatrixXd adjugate_derivative(const Eigen::MatrixBase<Derived> &A, const Eigen::MatrixBase<Derived>& dAdt)
{
std::size_t N = A.rows();
Eigen::MatrixXd Aadj(N, N);
for (std::size_t i = 0; i < N; ++i){
for (std::size_t j = 0; j < N; ++j){
int negative_1_to_the_i_plus_j = ((i+j)%2==0) ? 1 : -1;
Eigen::MatrixXd mm = minor_matrix(A, j, i);
Aadj(i, j) = negative_1_to_the_i_plus_j*(adjugate(minor_matrix(A, j, i))*minor_matrix(dAdt,j,i)).trace();
}
}
return Aadj;
}
}; /* namespace CoolProp */
#endif
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