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А в чем конкретно сложности? Не знаете, как перемножать матрицы? Не можете организовать класс, понять, какие данные нужно хранить? Не знаете синтаксис перегрузки? У меня есть класс матриц, но он реализован через вектора. Если такое подойдет, то вот. Иначе просто смотрим, разбираемся, задаем вопросы, делаем то, что требуется. | Код |
#include "stdafx.h"
#include <iostream>
#include <stdio.h>
using namespace std;
class Vector {
private:
int s;
double* c;
public:
Vector();
Vector(int _s);
Vector(int _s, double cs);
Vector(const Vector& v);
~Vector();
void print() const;
Vector& operator = (const Vector& v);
Vector& operator = (double cs);
Vector& operator += (const Vector& q);
Vector& operator += (double cs);
Vector& operator *= (double cs);
Vector& operator -= (const Vector& p);
Vector& operator -= (double cs);
Vector& operator /= (double cs);
Vector& operator <<= (int n);
Vector& operator >>= (int n);
double& operator [] (int n) const;
friend Vector operator + (const Vector& p, const Vector& q);
friend Vector operator + (const Vector& p, double cs);
friend Vector operator + (double cs, const Vector& p);
friend Vector operator * (const Vector& p, double cs);
friend Vector operator * (double cs, const Vector& p);
friend double operator * (const Vector& p, const Vector& q);
friend Vector operator - (const Vector& p);
friend Vector operator - (const Vector& p, const Vector& q);
friend Vector operator - (const Vector& p, double cs);
friend Vector operator - (double cs, const Vector& p);
friend Vector operator / (const Vector& p, double cs);
friend Vector operator << (const Vector& p, int n);
friend Vector operator >> (const Vector& p, int n);
friend bool operator == (const Vector& p, const Vector& q);
friend bool operator != (const Vector& p, const Vector& q);
friend bool operator <= (const Vector& p, const Vector& q);
friend bool operator < (const Vector& p, const Vector& q);
friend bool operator >= (const Vector& p, const Vector& q);
friend bool operator > (const Vector& p, const Vector& q);
};
class Matrix {
private:
int m, n;
Vector* a;
Matrix Opposite() const;
public:
Matrix();
Matrix(int _m, int _n);
Matrix(int _m, int _n, double e);
Matrix(const Matrix& A);
~Matrix();
Vector GetRow(int i) const;
void SetRow(int i, Vector r);
Vector GetColumn(int j) const;
void SetColumn(int j, Vector c);
void print() const;
Matrix Minor(int il, int jl, int ir, int jr) const;
Matrix LeftOpposite() const;
Matrix RightOpposite() const;
double Det() const;
Matrix Transp() const;
Matrix& operator = (const Matrix& A);
Matrix& operator = (double e);
Matrix& operator += (const Matrix& A);
Matrix& operator += (double e);
Matrix& operator *= (const Matrix& A);
Matrix& operator *= (double e);
Matrix& operator /= (double e);
Matrix& operator /= (const Matrix& A);
Vector& operator [] (int i) const;
friend Matrix operator + (const Matrix& A, const Matrix& B);
friend Matrix operator + (const Matrix& A, double e);
friend Matrix operator + (double e, const Matrix& A);
friend Matrix operator - (const Matrix& A, const Matrix& B);
friend Matrix operator - (const Matrix& A, double e);
friend Matrix operator - (double e, const Matrix& A);
friend Matrix operator - (const Matrix& A);
friend Matrix operator * (const Matrix& A, const Matrix& B);
friend Matrix operator * (const Matrix& A, double e);
friend Matrix operator * (double e, const Matrix& A);
friend Matrix operator / (const Matrix& A, const Matrix& B);
friend Matrix operator / (const Matrix& A, double e);
friend Matrix operator / (double e, const Matrix& A);
friend bool operator == (const Matrix& A, const Matrix& B);
friend bool operator == (const Matrix& A, double e);
friend bool operator == (double e, const Matrix& A);
friend bool operator != (const Matrix& A, const Matrix& B);
friend bool operator != (const Matrix& A, double e);
friend bool operator != (double e, const Matrix& A);
};
Vector::Vector() {
s = 1;
c = new double[1];
c[0] = 0;
}
Vector::Vector(int _s) {
s = _s;
c = new double[s];
for (int i = 0; i < s; i++) c[i] = 0;
}
Vector::Vector(int _s, double cs) {
s = _s;
c = new double[s];
for (int i = 0; i < s; i++) c[i] = cs;
}
Vector::Vector(const Vector& v) { *this = v; }
Vector::~Vector() { delete [] c; }
void Vector::print() const {
cout<<"("<<c[0];
for (int i = 1; i < s; i++) cout<<", "<<c[i];
cout<<")";
}
Vector& Vector::operator = (const Vector& v) {
s = v.s;
c = new double[s];
for (int i = 0; i < s; i++) c[i] = v.c[i];
return *this;
}
Vector& Vector::operator = (double cs) {
for (int i = 0; i < s; i++) c[i] = cs;
return *this;
}
Vector& Vector::operator += (const Vector& q) { return *this = *this + q; }
Vector& Vector::operator += (double cs) { return *this = *this + cs; }
Vector& Vector::operator *= (double cs) { return *this = *this * cs; }
Vector& Vector::operator -= (const Vector& p) { return *this = *this - p; }
Vector& Vector::operator -= (double cs) { return *this = *this - cs; }
Vector& Vector::operator /= (double cs) { return *this = *this / cs; }
double& Vector::operator [] (int n) const {
while (n < 0) n += s;
n %= s;
return c[n];
}
Vector operator + (const Vector& p, const Vector& q) {
Vector t;
if (p.s >= q.s) {
t = p;
for (int i = 0; i < q.s; i++) t.c[i] += q.c[i];
} else {
t = q;
for (int i = 0; i < p.s; i++) t.c[i] = p.c[i] + t.c[i];
}
return t;
}
Vector operator + (const Vector& p, double cs) {
Vector t(p.s, cs);
return p + t;
}
Vector operator + (double cs, const Vector& p) {
Vector t(p.s, cs);
return t + p;
}
Vector operator - (const Vector& p) {
Vector t = p;
for (int i = 0; i < t.s; i++) t.c[i] = -t.c[i];
return t;
}
Vector operator - (const Vector& p, const Vector& q) {
Vector t;
if (p.s >= q.s) {
t = p;
for (int i = 0; i < q.s; i++) t.c[i] -= q.c[i];
} else {
t = q;
for (int i = 0; i < p.s; i++) t.c[i] = p.c[i] - t.c[i];
}
return t;
}
Vector operator - (const Vector& p, double cs) {
Vector t(p.s, cs);
return p - t;
}
Vector operator - (double cs, const Vector& p) {
Vector t(p.s, cs);
return t - p;
}
Vector operator * (const Vector& p, double cs) {
Vector t = p;
for (int i = 0; i < t.s; i++) t.c[i] *= cs;
return t;
}
Vector operator * (double cs, const Vector& p) {
Vector t = p;
for (int i = 0; i < t.s; i++) t.c[i] = cs * t.c[i];
return t;
}
double operator * (const Vector& p, const Vector& q) {
int s = p.s; if (p.s > q.s) s = q.s;
double sc = 0;
for (int i = 0; i < s; i++) sc += p.c[i] * q.c[i];
return sc;
}
Vector operator / (const Vector& p, double cs) { return p * (1 / cs); }
Vector operator << (const Vector& p, int n) {
if (n < 0) return p >> (-n);
Vector t(p.s);
for (int i = 0; i < p.s; i++) t.c[i] = p.c[(i + n) % p.s];
return t;
}
Vector operator >> (const Vector& p, int n) {
if (n < 0) return p << (-n);
Vector t(p.s);
for (int i = 0; i < p.s; i++) t.c[(i + n) % p.s] = p.c[i];
return t;
}
Vector& Vector::operator <<= (int n) {
Vector t = *this;
return *this = t << n;
}
Vector& Vector::operator >>= (int n) {
Vector t = *this;
return *this = t >> n;
}
bool operator == (const Vector& p, const Vector& q) {
if (p.s != q.s) return false;
for (int i = 0; i < p.s; i++) if (p.c[i] != q.c[i]) return false;
return true;
}
bool operator != (const Vector& p, const Vector& q) { return ! (p == q); }
bool operator <= (const Vector& p, const Vector& q) {
if (p == q) return true;
int s = p.s; if (s > q.s) s = q.s;
for (int i = 0; i < s; i++) {
if (p.c[i] < q.c[i]) return true;
if (p.c[i] > q.c[i]) return false;
}
return p.s < q.s;
}
bool operator < (const Vector& p, const Vector& q) { return p <= q && p != q; }
bool operator >= (const Vector& p, const Vector& q) { return ! (p < q); }
bool operator > (const Vector& p, const Vector& q) { return ! (p <= q); }
Matrix::Matrix() {
m = 1; n = 1;
a = new Vector[1];
}
Matrix::Matrix(int _m, int _n) {
m = _m; n = _n;
a = new Vector[m];
for (int i = 0; i < m; i++) {
a[i] = Vector(n);
if (i < n) a[i][i] = 1;
}
}
Matrix::Matrix(int _m, int _n, double e) {
m = _m; n = _n;
a = new Vector[m];
for (int i = 0; i < m; i++) {
a[i] = Vector(n);
if (i < n) a[i][i] = e;
}
}
Matrix::Matrix(const Matrix& A) { *this = A; }
Matrix::~Matrix() { delete [] a; }
void Matrix::print() const {
for (int i = 0; i < m; i++) {
for (int j = 0; j < n; j++) printf("%8.3f", a[i][j]);
cout<<"\n";
}
}
Vector Matrix::GetRow(int i) const { return operator [] (i); }
void Matrix::SetRow(int i, Vector r) { operator [] (i) = r; }
Vector Matrix::GetColumn(int j) const {
while (j < 0) j += n; j %= n;
Vector t(m);
for (int i = 0; i < m; i++) t[i] = a[i][j];
return t;
}
void Matrix::SetColumn(int j, Vector c) {
while (j < 0) j += n; j %= n;
for (int i = 0; i < m; i++) a[i][j] = c[i];
}
Matrix Matrix::Minor(int il, int jl, int ir, int jr) const {
if (--il < 0) il = 0; if (il > m - 1) il = m - 1;
if (--jl < 0) jl = 0; if (jl > n - 1) jl = n - 1;
if (--ir > m - 1) ir = m - 1; if (ir < 0) ir = 0;
if (--jr > n - 1) jr = n - 1; if (jr < 0) jr = 0;
if (il > ir) { int t = ir; ir = il; il = t; }
if (jl > jr) { int t = jl; jl = jr; jr = t; }
Matrix C(ir - il + 1, jr - jl + 1);
for (int i = 0; i <= ir - il; i++) for (int j = 0; j <= jr - jl; j++) C.a[i][j] = a[i + il][j + jl];
return C;
}
Matrix Matrix::Transp() const {
Matrix T(n, m);
for (int i = 0; i < m; i++) T.SetColumn(i, a[i]);
return T;
}
Matrix Matrix::Opposite() const {
if (m != n) { cout<<"Wrong implementation\n"; exit(0); }
Matrix C(m, 2 * n, 1);
for (int j = 0; j < n; j++) C.SetColumn(j + n, GetColumn(j));
for (int i = 0; i < m; i++) {
int j = i;
while (j < m && C[j][i + n] == 0) j++;
if (j == m) { cout<<"No opposite matrix\n"; return Matrix(1, 1, 0); }
if (i != j) { Vector t = C[i]; C[i] = C[j]; C[j] = t; }
C[i] /= C[i][i + n];
for (int j = i + 1; j < m; j++) C[j] -= C[j][i + n] * C[i];
}
for (int i = m - 1; i >= 0; i--) for (int j = i - 1; j >= 0; j--) C[j] -= C[j][i + n] * C[i];
return C.Minor(1, 1, m, n);
}
Matrix Matrix::LeftOpposite() const {
if (m == n) return Opposite();
if (m < n) { cout<<"No opposite matrix\n"; return Matrix(1, 1, 0); }
Matrix C(m, m + n);
for (int i = 0; i < m; i++) for (int j = 0; j < n; j++) C[i][j + m] = a[i][j];
for (int i = 0; i < n; i++) {
int j = i;
while (j < m && C.a[j][i + m] == 0) j++;
if (j == m) { cout<<"Failed\n"; return Matrix(1, 1, 0); }
if (i != j) { Vector t = C[i]; C[i] = C[j]; C[j] = t; }
C[i] /= C[i][i + m];
for (int j = i + 1; j < m; j++) C[j] -= C[j][i + m] * C[i];
}
for (int i = n - 1; i >= 0; i--) for (int j = i - 1; j >= 0; j--) C[j] -= C[j][i + m] * C[i];
return C.Minor(1, 1, n, m);
}
Matrix Matrix::RightOpposite() const {
if (m == n) return Opposite();
if (m > n) { cout<<"No opposite matrix\n"; return Matrix(1, 1, 0); }
Matrix C(m + n, n);
for (int i = 0; i < m; i++) for (int j = 0; j < n; j++) C[i + n][j] = a[i][j];
for (int i = 0; i < m; i++) {
int j = i;
while (j < n && C[i + n][j] == 0) j++;
if (j == n) { cout<<"Failed\n"; return Matrix(1, 1, 0); }
if (i != j) {
Vector t = C.GetColumn(i);
C.SetColumn(i, C.GetColumn(j));
C.SetColumn(j, t);
}
C.SetColumn(i, C.GetColumn(i) / C[i + n][i]);
for (int j = i + 1; j < n; j++)
C.SetColumn(j, C.GetColumn(j) - C[i + n][j] * C.GetColumn(i));
}
for (int i = m - 1; i >= 0; i--) for (int j = i - 1; j >= 0; j--)
C.SetColumn(j, C.GetColumn(j) - C[i + n][j] * C.GetColumn(i));
return C.Minor(1, 1, n, m);
}
double Matrix::Det() const {
if (m != n) { cout<<"Non-square matrix\n"; return 0; }
Matrix t = *this;
for (int i = 0; i < m; i++) {
int j = i;
while (j < m && t[j][i] == 0) j++;
if (j == m) return 0;
if (i != j) { Vector r = t[i]; t[i] = t[j]; t[j] = r; }
for (int j = i + 1; j < m; j++) t[j] -= t[j][i] / t[i][i] * t[i];
}
double d = 1;
for (int i = 0; i < m; i++) d *= t[i][i];
return d;
}
Matrix& Matrix::operator = (const Matrix& A) {
m = A.m; n = A.n;
a = new Vector[m];
for (int i = 0; i < m; i++) {
a[i] = Vector(n);
for (int j = 0; j < n; j++) a[i][j] = A.a[i][j];
}
return *this;
}
Matrix& Matrix::operator = (double e) {
for (int i = 0; i < m; i++) for (int j = 0; j < n; j++) a[i][j] = i == j ? e : 0;
return *this;
}
Matrix& Matrix::operator += (const Matrix& A) { return *this = *this + A; }
Matrix& Matrix::operator += (double e) { return *this = *this + e; }
Matrix& Matrix::operator *= (const Matrix& A) { return *this = *this * A; }
Matrix& Matrix::operator *= (double e) { return *this = *this * e; }
Matrix& Matrix::operator /= (double e) { return *this = *this / e; }
Matrix& Matrix::operator /= (const Matrix& A) { return *this = *this / A; }
Vector& Matrix::operator [] (int i) const {
while (i < 0) i += m;
i %= m;
return a[i];
}
Matrix operator + (const Matrix& A, const Matrix& B) {
int a = A.m; if (a > B.m) a = B.m;
int b = A.n; if (b > B.n) b = B.n;
Matrix C(a, b);
for (int i = 0; i < a; i++) C[i] = A[i] + B[i];
return C;
}
Matrix operator + (const Matrix& A, double e) {
Matrix B(A.m, A.n, e);
return A + B;
}
Matrix operator + (double e, const Matrix& A) {
Matrix B(A.m, A.n, e);
return B + A;
}
Matrix operator - (const Matrix& A, const Matrix& B) {
int a = A.m; if (a > B.m) a = B.m;
int b = A.n; if (b > B.n) b = B.n;
Matrix C(a, b);
for (int i = 0; i < a; i++) C[i] = A[i] - B[i];
return C;
}
Matrix operator - (const Matrix& A, double e) {
Matrix B(A.m, A.n, e);
return A - B;
}
Matrix operator - (double e, const Matrix& A) {
Matrix B(A.m, A.n, e);
return B - A;
}
Matrix operator - (const Matrix& A) {
Matrix C(A.m, A.n);
for (int i = 0; i < C.m; i++) C[i] = -A[i];
return C;
}
Matrix operator * (const Matrix& A, const Matrix& B) {
Matrix C(A.m, B.n, 0);
int s = A.n; if (s > B.m) s = B.m;
for (int i = 0; i < C.m; i++) for (int j = 0; j < s; j++) C[i] += A[i][j] * B[j];
return C;
}
Matrix operator * (const Matrix& A, double e) {
Matrix C(A.m, A.n);
for (int i = 0; i < C.m; i++) C[i] = A[i] * e;
return C;
}
Matrix operator * (double e, const Matrix& A) {
Matrix C(A.m, A.n);
for (int i = 0; i < C.m; i++) C[i] = e * A[i];
return C;
}
Matrix operator / (const Matrix& A, double e) { return A * (1 / e); }
Matrix operator / (const Matrix& A, const Matrix& B) { return A * B.RightOpposite(); }
Matrix operator / (double e, const Matrix& A) { return e * A.RightOpposite(); }
bool operator == (const Matrix& A, const Matrix& B) {
if (A.m != B.m || A.n != B.n) return false;
for (int i = 0; i < A.m; i++) if (A[i] != B[i]) return false;
return true;
}
bool operator == (const Matrix& A, double e) {
Matrix C(A.m, A.n, e);
return A == C;
}
bool operator == (double e, const Matrix& A) {
Matrix C(A.m, A.n, e);
return C == A;
}
bool operator != (const Matrix& A, const Matrix& B) { return ! (A == B); }
bool operator != (const Matrix& A, double e) { return ! (A == e); }
bool operator != (double e, const Matrix& A) { return ! (e == A); }
void main() {
Matrix A(4, 4, 2); Matrix B(4, 4);
B[0][-1] = 1;
cout<<B.Det();
}
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Что непонятно - спрашиваем  |
[C] Перегрузка операций 
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