Simple matrix library in C++
3
$begingroup$
Today I started learning C++ and at the end of the day have made a simple generic matrix class. I'm looking for feedback on techniques and features. It's still not complete, though. But everything works!
I put some functions outside the class and inside a namespace because I was trouble defining template member functions with partial specialization.
Matrix.hpp
#pragma once
#include <iostream>
template <typename T, int m, int n = m>
class mat {
template <typename, int, int>
friend class mat;
private:
T * data;
public:
mat(const std::initializer_list<T> & ini) {
std::copy(ini.begin(), ini.end(), data);
}
mat() : data(new T[m * n]) {
}
mat(T * values) : data(values) {
}
mat(const mat & mat2) : mat(){
for (int i = 0; i < m; ++i)
for (int j = 0; j < n; ++j)
data[i * n + j] = mat2(i, j);
}
~mat() {
delete data;
}
void fill(T val) {
for (int i = 0; i < m; ++i)
for (int j = 0; j < n; ++j)
data[i * n + j] = val;
}
void print() {
for (int i = 0; i < m; ++i) {
for (int j = 0; j < n; ++j)
std::cout << data[i * n + j] << " ";
std::cout << std::endl;
}
}
mat<T, m, 1> col(int j) const {
mat<T, m, 1> col;
for (int i = 0; i < m; ++i)
col.data[i] = data[i * n + j];
return col;
}
mat<T, 1, n> row(int i) const {
mat<T, 1, n> row;
std::copy_n(data + i * n, n, row.data);
return row;
}
T operator () (int row, int col) const {
return data[row * n + col];
}
T & operator () (int row, int col) {
return data[row * n + col];
}
mat<T, n, m> transpose() const {
mat<T, n, m> res;
for (int i = 0; i < m; ++i)
for (int j = 0; j < n; ++j)
res(j, i) = this->data[i * n + j];
return res;
}
template <int p>
mat<T, m, p> operator * (const mat<T, n, p> & other) const {
mat<T, m, p> res;
for (int i = 0; i < m; ++i)
for (int j = 0; j < p; ++j) {
T sum = 0;
for (int k = 0; k < n; ++k)
sum += this->data[i * n + k] * other.data[k * n + j];
res(i, j) = sum;
}
return res;
}
mat<T, m, n> & operator *= (T val) {
for (int i = 0; i < m; ++i)
for (int j = 0; j < n; ++j)
data[i * n + j] *= val;
return *this;
}
mat<T, m, n> & operator /= (T val) {
return this *= 1 / val;
}
mat<T, m, n> & operator += (const mat & other) {
for (int i = 0; i < m; ++i)
for (int j = 0; j < n; ++j)
data[i * n + j] += other(i, j);
return *this;
}
mat<T, m, n> & operator -= (const mat & other) {
for (int i = 0; i < m; ++i)
for (int j = 0; j < n; ++j)
data[i * n + j] -= other(i, j);
return *this;
}
mat<T, m, n> operator * (T val) const {
auto res(*this);
res *= val;
return res;
}
mat<T, m, n> operator / (T val) const {
return (*this) * (1 / val);
}
mat<T, m, n> operator + (const mat & other) const {
auto res(*this);
res += other;
return res;
}
mat<T, m, n> operator - (const mat & other) const {
auto res(*this);
res -= other;
return res;
}
mat<T, m - 1, n - 1> cut(int row, int col) const {
mat<T, m - 1, n - 1> res;
int index = 0;
for (int i = 0; i < m; ++i)
for (int j = 0; j < n; ++j) {
if (i == row || j == col)
continue;
res.data[index++] = data[i * n + j];
}
return res;
}
};
namespace matrix {
template <typename T>
T det(const mat<T, 1, 1> & arg) {
return arg(0, 0);
}
template <typename T>
T det(const mat<T, 2, 2> & arg) {
return arg(0, 0) * arg(1, 1) - arg(1, 0) * arg(0, 1);
}
template <typename T, int n>
T det(const mat<T, n, n> & arg) {
T res = 0, coef = 1;
for (int i = 0; i < n; ++i, coef *= -1) {
res += coef * arg(0, i) * matrix::det(arg.cut(0, i));
}
return res;
}
template <typename T>
mat<T, 2, 2> inv(const mat<T, 2, 2> & arg) {
mat<T, 2, 2> helper;
helper(1, 1) = arg(0, 0);
helper(0, 0) = arg(1, 1);
helper(0, 1) = -arg(0, 1);
helper(1, 0) = -arg(1, 0);
return helper / det(arg);
}
template <typename T, int m>
mat<T, m, m> id() {
mat<T, m, m> res;
for (int i = 0; i < m; ++i)
res(i, i) = 1;
return res;
}
};
Main.cpp
#include <iostream>
#include <exception>
#include "Matrix.hpp"
using namespace std;
int main() {
constexpr int size = 4;
long * data = new long[size * size]{ 0 };
for (int i = 0; i < size; ++i)
data[size * i + i] = 2;
mat<long, size> big(data);
cout << matrix::det(big) << endl;
return 0;
}
c++ beginner matrix
edited 17 mins ago
200_success
129k15153415
asked 2 hours ago
Afonso MatosAfonso Matos
36528
$endgroup$
add a comment |
3
$begingroup$
Today I started learning C++ and at the end of the day have made a simple generic matrix class. I'm looking for feedback on techniques and features. It's still not complete, though. But everything works!
I put some functions outside the class and inside a namespace because I was trouble defining template member functions with partial specialization.
Matrix.hpp
#pragma once
#include <iostream>
template <typename T, int m, int n = m>
class mat {
template <typename, int, int>
friend class mat;
private:
T * data;
public:
mat(const std::initializer_list<T> & ini) {
std::copy(ini.begin(), ini.end(), data);
}
mat() : data(new T[m * n]) {
}
mat(T * values) : data(values) {
}
mat(const mat & mat2) : mat(){
for (int i = 0; i < m; ++i)
for (int j = 0; j < n; ++j)
data[i * n + j] = mat2(i, j);
}
~mat() {
delete data;
}
void fill(T val) {
for (int i = 0; i < m; ++i)
for (int j = 0; j < n; ++j)
data[i * n + j] = val;
}
void print() {
for (int i = 0; i < m; ++i) {
for (int j = 0; j < n; ++j)
std::cout << data[i * n + j] << " ";
std::cout << std::endl;
}
}
mat<T, m, 1> col(int j) const {
mat<T, m, 1> col;
for (int i = 0; i < m; ++i)
col.data[i] = data[i * n + j];
return col;
}
mat<T, 1, n> row(int i) const {
mat<T, 1, n> row;
std::copy_n(data + i * n, n, row.data);
return row;
}
T operator () (int row, int col) const {
return data[row * n + col];
}
T & operator () (int row, int col) {
return data[row * n + col];
}
mat<T, n, m> transpose() const {
mat<T, n, m> res;
for (int i = 0; i < m; ++i)
for (int j = 0; j < n; ++j)
res(j, i) = this->data[i * n + j];
return res;
}
template <int p>
mat<T, m, p> operator * (const mat<T, n, p> & other) const {
mat<T, m, p> res;
for (int i = 0; i < m; ++i)
for (int j = 0; j < p; ++j) {
T sum = 0;
for (int k = 0; k < n; ++k)
sum += this->data[i * n + k] * other.data[k * n + j];
res(i, j) = sum;
}
return res;
}
mat<T, m, n> & operator *= (T val) {
for (int i = 0; i < m; ++i)
for (int j = 0; j < n; ++j)
data[i * n + j] *= val;
return *this;
}
mat<T, m, n> & operator /= (T val) {
return this *= 1 / val;
}
mat<T, m, n> & operator += (const mat & other) {
for (int i = 0; i < m; ++i)
for (int j = 0; j < n; ++j)
data[i * n + j] += other(i, j);
return *this;
}
mat<T, m, n> & operator -= (const mat & other) {
for (int i = 0; i < m; ++i)
for (int j = 0; j < n; ++j)
data[i * n + j] -= other(i, j);
return *this;
}
mat<T, m, n> operator * (T val) const {
auto res(*this);
res *= val;
return res;
}
mat<T, m, n> operator / (T val) const {
return (*this) * (1 / val);
}
mat<T, m, n> operator + (const mat & other) const {
auto res(*this);
res += other;
return res;
}
mat<T, m, n> operator - (const mat & other) const {
auto res(*this);
res -= other;
return res;
}
mat<T, m - 1, n - 1> cut(int row, int col) const {
mat<T, m - 1, n - 1> res;
int index = 0;
for (int i = 0; i < m; ++i)
for (int j = 0; j < n; ++j) {
if (i == row || j == col)
continue;
res.data[index++] = data[i * n + j];
}
return res;
}
};
namespace matrix {
template <typename T>
T det(const mat<T, 1, 1> & arg) {
return arg(0, 0);
}
template <typename T>
T det(const mat<T, 2, 2> & arg) {
return arg(0, 0) * arg(1, 1) - arg(1, 0) * arg(0, 1);
}
template <typename T, int n>
T det(const mat<T, n, n> & arg) {
T res = 0, coef = 1;
for (int i = 0; i < n; ++i, coef *= -1) {
res += coef * arg(0, i) * matrix::det(arg.cut(0, i));
}
return res;
}
template <typename T>
mat<T, 2, 2> inv(const mat<T, 2, 2> & arg) {
mat<T, 2, 2> helper;
helper(1, 1) = arg(0, 0);
helper(0, 0) = arg(1, 1);
helper(0, 1) = -arg(0, 1);
helper(1, 0) = -arg(1, 0);
return helper / det(arg);
}
template <typename T, int m>
mat<T, m, m> id() {
mat<T, m, m> res;
for (int i = 0; i < m; ++i)
res(i, i) = 1;
return res;
}
};
Main.cpp
#include <iostream>
#include <exception>
#include "Matrix.hpp"
using namespace std;
int main() {
constexpr int size = 4;
long * data = new long[size * size]{ 0 };
for (int i = 0; i < size; ++i)
data[size * i + i] = 2;
mat<long, size> big(data);
cout << matrix::det(big) << endl;
return 0;
}
c++ beginner matrix
edited 17 mins ago
200_success
129k15153415
asked 2 hours ago
Afonso MatosAfonso Matos
36528
$endgroup$
add a comment |
3
3
3
$begingroup$
Today I started learning C++ and at the end of the day have made a simple generic matrix class. I'm looking for feedback on techniques and features. It's still not complete, though. But everything works!
I put some functions outside the class and inside a namespace because I was trouble defining template member functions with partial specialization.
Matrix.hpp
#pragma once
#include <iostream>
template <typename T, int m, int n = m>
class mat {
template <typename, int, int>
friend class mat;
private:
T * data;
public:
mat(const std::initializer_list<T> & ini) {
std::copy(ini.begin(), ini.end(), data);
}
mat() : data(new T[m * n]) {
}
mat(T * values) : data(values) {
}
mat(const mat & mat2) : mat(){
for (int i = 0; i < m; ++i)
for (int j = 0; j < n; ++j)
data[i * n + j] = mat2(i, j);
}
~mat() {
delete data;
}
void fill(T val) {
for (int i = 0; i < m; ++i)
for (int j = 0; j < n; ++j)
data[i * n + j] = val;
}
void print() {
for (int i = 0; i < m; ++i) {
for (int j = 0; j < n; ++j)
std::cout << data[i * n + j] << " ";
std::cout << std::endl;
}
}
mat<T, m, 1> col(int j) const {
mat<T, m, 1> col;
for (int i = 0; i < m; ++i)
col.data[i] = data[i * n + j];
return col;
}
mat<T, 1, n> row(int i) const {
mat<T, 1, n> row;
std::copy_n(data + i * n, n, row.data);
return row;
}
T operator () (int row, int col) const {
return data[row * n + col];
}
T & operator () (int row, int col) {
return data[row * n + col];
}
mat<T, n, m> transpose() const {
mat<T, n, m> res;
for (int i = 0; i < m; ++i)
for (int j = 0; j < n; ++j)
res(j, i) = this->data[i * n + j];
return res;
}
template <int p>
mat<T, m, p> operator * (const mat<T, n, p> & other) const {
mat<T, m, p> res;
for (int i = 0; i < m; ++i)
for (int j = 0; j < p; ++j) {
T sum = 0;
for (int k = 0; k < n; ++k)
sum += this->data[i * n + k] * other.data[k * n + j];
res(i, j) = sum;
}
return res;
}
mat<T, m, n> & operator *= (T val) {
for (int i = 0; i < m; ++i)
for (int j = 0; j < n; ++j)
data[i * n + j] *= val;
return *this;
}
mat<T, m, n> & operator /= (T val) {
return this *= 1 / val;
}
mat<T, m, n> & operator += (const mat & other) {
for (int i = 0; i < m; ++i)
for (int j = 0; j < n; ++j)
data[i * n + j] += other(i, j);
return *this;
}
mat<T, m, n> & operator -= (const mat & other) {
for (int i = 0; i < m; ++i)
for (int j = 0; j < n; ++j)
data[i * n + j] -= other(i, j);
return *this;
}
mat<T, m, n> operator * (T val) const {
auto res(*this);
res *= val;
return res;
}
mat<T, m, n> operator / (T val) const {
return (*this) * (1 / val);
}
mat<T, m, n> operator + (const mat & other) const {
auto res(*this);
res += other;
return res;
}
mat<T, m, n> operator - (const mat & other) const {
auto res(*this);
res -= other;
return res;
}
mat<T, m - 1, n - 1> cut(int row, int col) const {
mat<T, m - 1, n - 1> res;
int index = 0;
for (int i = 0; i < m; ++i)
for (int j = 0; j < n; ++j) {
if (i == row || j == col)
continue;
res.data[index++] = data[i * n + j];
}
return res;
}
};
namespace matrix {
template <typename T>
T det(const mat<T, 1, 1> & arg) {
return arg(0, 0);
}
template <typename T>
T det(const mat<T, 2, 2> & arg) {
return arg(0, 0) * arg(1, 1) - arg(1, 0) * arg(0, 1);
}
template <typename T, int n>
T det(const mat<T, n, n> & arg) {
T res = 0, coef = 1;
for (int i = 0; i < n; ++i, coef *= -1) {
res += coef * arg(0, i) * matrix::det(arg.cut(0, i));
}
return res;
}
template <typename T>
mat<T, 2, 2> inv(const mat<T, 2, 2> & arg) {
mat<T, 2, 2> helper;
helper(1, 1) = arg(0, 0);
helper(0, 0) = arg(1, 1);
helper(0, 1) = -arg(0, 1);
helper(1, 0) = -arg(1, 0);
return helper / det(arg);
}
template <typename T, int m>
mat<T, m, m> id() {
mat<T, m, m> res;
for (int i = 0; i < m; ++i)
res(i, i) = 1;
return res;
}
};
Main.cpp
#include <iostream>
#include <exception>
#include "Matrix.hpp"
using namespace std;
int main() {
constexpr int size = 4;
long * data = new long[size * size]{ 0 };
for (int i = 0; i < size; ++i)
data[size * i + i] = 2;
mat<long, size> big(data);
cout << matrix::det(big) << endl;
return 0;
}
c++ beginner matrix
edited 17 mins ago
200_success
129k15153415
asked 2 hours ago
Afonso MatosAfonso Matos
36528
$endgroup$
Today I started learning C++ and at the end of the day have made a simple generic matrix class. I'm looking for feedback on techniques and features. It's still not complete, though. But everything works!
I put some functions outside the class and inside a namespace because I was trouble defining template member functions with partial specialization.
Matrix.hpp
#pragma once
#include <iostream>
template <typename T, int m, int n = m>
class mat {
template <typename, int, int>
friend class mat;
private:
T * data;
public:
mat(const std::initializer_list<T> & ini) {
std::copy(ini.begin(), ini.end(), data);
}
mat() : data(new T[m * n]) {
}
mat(T * values) : data(values) {
}
mat(const mat & mat2) : mat(){
for (int i = 0; i < m; ++i)
for (int j = 0; j < n; ++j)
data[i * n + j] = mat2(i, j);
}
~mat() {
delete data;
}
void fill(T val) {
for (int i = 0; i < m; ++i)
for (int j = 0; j < n; ++j)
data[i * n + j] = val;
}
void print() {
for (int i = 0; i < m; ++i) {
for (int j = 0; j < n; ++j)
std::cout << data[i * n + j] << " ";
std::cout << std::endl;
}
}
mat<T, m, 1> col(int j) const {
mat<T, m, 1> col;
for (int i = 0; i < m; ++i)
col.data[i] = data[i * n + j];
return col;
}
mat<T, 1, n> row(int i) const {
mat<T, 1, n> row;
std::copy_n(data + i * n, n, row.data);
return row;
}
T operator () (int row, int col) const {
return data[row * n + col];
}
T & operator () (int row, int col) {
return data[row * n + col];
}
mat<T, n, m> transpose() const {
mat<T, n, m> res;
for (int i = 0; i < m; ++i)
for (int j = 0; j < n; ++j)
res(j, i) = this->data[i * n + j];
return res;
}
template <int p>
mat<T, m, p> operator * (const mat<T, n, p> & other) const {
mat<T, m, p> res;
for (int i = 0; i < m; ++i)
for (int j = 0; j < p; ++j) {
T sum = 0;
for (int k = 0; k < n; ++k)
sum += this->data[i * n + k] * other.data[k * n + j];
res(i, j) = sum;
}
return res;
}
mat<T, m, n> & operator *= (T val) {
for (int i = 0; i < m; ++i)
for (int j = 0; j < n; ++j)
data[i * n + j] *= val;
return *this;
}
mat<T, m, n> & operator /= (T val) {
return this *= 1 / val;
}
mat<T, m, n> & operator += (const mat & other) {
for (int i = 0; i < m; ++i)
for (int j = 0; j < n; ++j)
data[i * n + j] += other(i, j);
return *this;
}
mat<T, m, n> & operator -= (const mat & other) {
for (int i = 0; i < m; ++i)
for (int j = 0; j < n; ++j)
data[i * n + j] -= other(i, j);
return *this;
}
mat<T, m, n> operator * (T val) const {
auto res(*this);
res *= val;
return res;
}
mat<T, m, n> operator / (T val) const {
return (*this) * (1 / val);
}
mat<T, m, n> operator + (const mat & other) const {
auto res(*this);
res += other;
return res;
}
mat<T, m, n> operator - (const mat & other) const {
auto res(*this);
res -= other;
return res;
}
mat<T, m - 1, n - 1> cut(int row, int col) const {
mat<T, m - 1, n - 1> res;
int index = 0;
for (int i = 0; i < m; ++i)
for (int j = 0; j < n; ++j) {
if (i == row || j == col)
continue;
res.data[index++] = data[i * n + j];
}
return res;
}
};
namespace matrix {
template <typename T>
T det(const mat<T, 1, 1> & arg) {
return arg(0, 0);
}
template <typename T>
T det(const mat<T, 2, 2> & arg) {
return arg(0, 0) * arg(1, 1) - arg(1, 0) * arg(0, 1);
}
template <typename T, int n>
T det(const mat<T, n, n> & arg) {
T res = 0, coef = 1;
for (int i = 0; i < n; ++i, coef *= -1) {
res += coef * arg(0, i) * matrix::det(arg.cut(0, i));
}
return res;
}
template <typename T>
mat<T, 2, 2> inv(const mat<T, 2, 2> & arg) {
mat<T, 2, 2> helper;
helper(1, 1) = arg(0, 0);
helper(0, 0) = arg(1, 1);
helper(0, 1) = -arg(0, 1);
helper(1, 0) = -arg(1, 0);
return helper / det(arg);
}
template <typename T, int m>
mat<T, m, m> id() {
mat<T, m, m> res;
for (int i = 0; i < m; ++i)
res(i, i) = 1;
return res;
}
};
Main.cpp
#include <iostream>
#include <exception>
#include "Matrix.hpp"
using namespace std;
int main() {
constexpr int size = 4;
long * data = new long[size * size]{ 0 };
for (int i = 0; i < size; ++i)
data[size * i + i] = 2;
mat<long, size> big(data);
cout << matrix::det(big) << endl;
return 0;
}
c++ beginner matrix
c++ beginner matrix
edited 17 mins ago
200_success
129k15153415
asked 2 hours ago
Afonso MatosAfonso Matos
36528
edited 17 mins ago
200_success
129k15153415
asked 2 hours ago
Afonso MatosAfonso Matos
36528
edited 17 mins ago
200_success
129k15153415
edited 17 mins ago
200_success
129k15153415
edited 17 mins ago
200_success
129k15153415
129k15153415
asked 2 hours ago
Afonso MatosAfonso Matos
36528
asked 2 hours ago
Afonso MatosAfonso Matos
36528
asked 2 hours ago
Afonso MatosAfonso Matos
36528
36528
add a comment |
add a comment |
0
active
oldest
votes
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["\$", "\$"]]);
});
});
}, "mathjax-editing");
StackExchange.ifUsing("editor", function () {
StackExchange.using("externalEditor", function () {
StackExchange.using("snippets", function () {
StackExchange.snippets.init();
});
});
}, "code-snippets");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "196"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: false,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: null,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
draft saved
draft discarded
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fcodereview.stackexchange.com%2fquestions%2f212178%2fsimple-matrix-library-in-c%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
0
active
oldest
votes
0
active
oldest
votes
active
oldest
votes
active
oldest
votes
draft saved
draft discarded
Thanks for contributing an answer to Code Review Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
draft saved
draft discarded
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fcodereview.stackexchange.com%2fquestions%2f212178%2fsimple-matrix-library-in-c%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
