我需要编写一个从逗号分隔值文件中读入矩阵的程序，然后使用高斯消元法计算反转并将此反转写入新文件。
阅读它很好，就像把它写回来一样。我想我理解高斯消除是如何工作的，并且能够通过使用数组来实现这一点。
#include <iostream>
#include <fstream>
#include <iomanip>
#include <vector>
#include <string>
using namespace std;
// main program starts here
int main() {
// create a vector of a vector to store original matrix
// and matrices after each calculation
vector<vector<double>> data;
int n_com = 0;
// try to read input file
ifstream readFile("test_data.txt");
if (readFile.is_open()){
while (!readFile.eof()){
int i;
// declare temporary line vector and line string
vector<double> vline;
string aLine;
// assign line of file to line string
getline(readFile, aLine);
// count number of commas in line string
n_com = count(aLine.begin(), aLine.end(), ',');
// define integer for start of each element
int start = 0;
// loop over all but final element
for (i=0; i < n_com; i++) {
// declare and find position of next comma
int comma_pos;
comma_pos = aLine.find(',', start);
// declare string for element and assign substring to it
string elems;
elems = aLine.substr(start, comma_pos - start);
// convert string to double
double elemd = atof(elems.c_str());
// push back double to temporary vector
vline.push_back(elemd);
// redefine start for next iteration
start = comma_pos + 1;
}
// assign final element to string
string final_elems = aLine.substr(start, aLine.length() - start);
// convert final element to double and push back to vector
double final_elemd = atof(final_elems.c_str());
vline.push_back(final_elemd);
// push back line vector to data vector
data.push_back(vline);
}
}
else {
// print error if unable to open file
printf("Error unable to open input file!\n");
// exit program
exit(1);
}
// close input file
readFile.close();
所以这就是我在原始矩阵中读到的内容。
这是我用于数组
的高斯消除的代码// calculate width and length of original data (no. of rows and columns)
int length = data.size();
int width = n_com + 1;
// create new file to write to
ofstream writeFile ("tranpose.txt");
// check outfile is open
if (writeFile.is_open()){
// declare indices
// width (columns)
int i;
// length (rows)0
int j;
// k
int k;
// declare a float?
float data[10][10] = {0},d;
// identity matrix
for (i=1; i <= length; i++){
for (j=1; j <= 2 * length; j++){
if (j == (i + length)){
data[i][j] = 1;
}
}
}
// partial pivoting
for (i=length; i > 1; i--){
if (data[i-1][1] < data[i][1]){
for(j=1;j <= length * 2; j++){
d = data[i][j];
data[i][j] = data[i-1][j];
data[i-1][j] = d;
}
}
}
cout<<"Augmented Matrix: "<<endl;
for (i=1; i <= length; i++){
for (j=1;j <= length * 2; j++){
cout<<data[i][j]<<" ";
}
cout<<endl;
}
// reducing to diagonal matrix
for (i=1; i <= length; i++){
for (j=1; j <= length * 2; j++){
if (j != i){
d = data[j][i] / data [i][i];
for (k=1; k<= length * 2; k++){
data[j][k] = data[j][k] - (data[i][k] * d);
}
}
}
}
// reducing to unit matrix
for (i=1; i <= length; i++){
d = data[i][i];
for (j=1; j <= length * 2; j++){
data[i][j] = data[i][j] / d;
}
}
// print inverse matrix in console
cout<<"Inverse Matrix "<<endl;
for (i=1; i <= length; i++){
for (j = length + 1; j <= length * 2; j++){
cout<<data[i][j]<<" ";
}
cout<<endl;
}
// loop over all rows
for (i=1; i <= length; i++){
// loop over all columns
for (j = length + 1; j <= length * 2; j++){
// print data in transposed positions excluding last value
// i.e. [j][i] instead of [i][j]
writeFile << setw(4) << fixed << setprecision(2) << data[i][j] << ",";
}
// print onto new line
int i = length - 1;
writeFile << setw(4) << fixed << setprecision(2) << data[i][j] << "\n";
}
// close written file
writeFile.close();
如何编写它以便它将使用我的矢量或矩阵文件中存储的数据而不是正常的数字数组？
答案 0 :(得分：0)
我对整个事情进行了改进，因为你的算法对我不合适。
using Matrix = std::vector<std::vector<double>>;
Matrix inverse(Matrix mat)
{
// Use Gaussian elimination
// Using two matrixs instead of one agumented
// to improve peformance
auto height = mat.size();
auto width = mat[0].size();
// Create an identity matrix
Matrix result(height, Matrix::value_type(width));
for (auto i = 0;i < width;++i) {
result[i][i] = 1;
}
cout << "Augmented Matrix: " << endl;
printTwo(mat, result);
// reduce to Echelon form
for (auto j = 0;j < width;++j) {
// partial pivoting
auto maxRow = j;
for (auto i = j;i < height;++i) {
maxRow = mat[i][j]>mat[maxRow][j] ? i : maxRow;
}
mat[j].swap(mat[maxRow]);
result[j].swap(result[maxRow]);
cout << "pivotted Matrix: " << endl;
printTwo(mat, result);
// Reduce row by row
auto pivot = mat[j][j];
auto& row1L = mat[j];
auto& row1R = result[j];
for (auto i = j + 1;i < height;++i) {
auto& row2L = mat[i];
auto& row2R = result[i];
auto temp = row2L[j];
for (auto k = 0;k < width;++k) {
row2L[k] -= temp / pivot*row1L[k];
row2R[k] -= temp / pivot*row1R[k];
}
}
// Make diaganal elements to 1
for (auto k = 0;k < width;++k) {
row1L[k] /= pivot;
row1R[k] /= pivot;
}
cout << "reduced Matrix: " << endl;
printTwo(mat, result);
}
//back subsitution
for (auto j = width - 1;;--j) {
auto& row1L = mat[j];
auto& row1R = result[j];
for (auto i = 0;i < j;++i) {
auto& row2L = mat[i];
auto& row2R = result[i];
auto temp = row2L[j];
for (auto k = 0;k < width;++k) {
row2L[k] -= temp*row1L[k];
row2R[k] -= temp*row1R[k];
}
}
cout << "subsituted Matrix: " << endl;
printTwo(mat, result);
if (j == 0) break;
}
return result;
}
以下是代码中使用的帮助程序：
void printTwo(const Matrix& lhs, const Matrix& rhs)
{
for (auto i = 0;i < lhs.size();++i) {
for (auto elm : lhs[i]) {
cout << setw(4) << elm << ' ';
}
for (auto elm : rhs[i]) {
cout << setw(4) << elm << ' ';
}
cout << endl;
}
}