希望创建一个名为Matrix的类作为基础 [英] wish to creat a class called Matrix as a base
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问题描述
#include<iostream.h>
#include<conio.h>
class Matrix
{
public: // constructors
Matrix()
{ //printf("Executing constructor Matrix() ...\n");
// create a Matrix object without content
p = NULL;
rows = 0;
cols = 0;
}
Matrix(const int row_count, const int column_count)
{ // create a Matrix object with given number of rows and columns
//printf("Executing constructor Matrix(const int column_count, const int row_count) ...\n");
p = NULL;
if (row_count > 0 && column_count > 0)
{
rows = row_count;
cols = column_count;
p = new double*[rows];
for (int r = 0; r < rows; r++)
{
p[r] = new double[rows];
// initially fill in zeros for all values in the matrix;
for (int c = 0; c < cols; c++)
{
p[r][c] = 0;
}
}
}
}
// assignment operator
Matrix(const Matrix& a)
{
//printf("Executing constructor Matrix(const Matrix& a) ...\n");
rows = a.rows;
cols = a.cols;
p = new double*[a.rows];
for (int r = 0; r < a.rows; r++)
{
p[r] = new double[a.cols];
// copy the values from the matrix a
for (int c = 0; c < a.cols; c++)
{
p[r][c] = a.p[r][c];
}
}
}
// index operator. You can use this class like myMatrix(col, row)
// the indexes are one-based, not zero based.
double& operator()(const int r, const int c)
{
//printf("Executing Matrix operator() ...\n");
if (p != NULL && r > 0 && r <= rows && c > 0 && c <= cols)
{
return p[r-1][c-1];
}
else
{
throw Exception("Subscript out of range");
}
}
// assignment operator
Matrix& operator= (const Matrix& a)
{
//printf("Executing Matrix operator= ...\n");
rows = a.rows;
cols = a.cols;
p = new double*[a.rows];
for (int r = 0; r < a.rows; r++)
{
p[r] = new double[a.cols];
// copy the values from the matrix a
for (int c = 0; c < a.cols; c++)
{
p[r][c] = a.p[r][c];
}
}
return *this;
}
// operator addition 1
friend Matrix operator+(const Matrix& a, const Matrix& B)
{
// check if the dimensions match
/* if (a.rows == b.rows && a.cols == b.cols)*/
{
Matrix res(a.rows, a.cols);
for (int r = 0; r < a.rows; r++)
{
for (int c = 0; c < a.cols; c++)
{
// res.p[r][c] = a.p[r][c] + b.p[r][c];
}
}
return res;
}
else
{
// give an error
throw Exception("Dimensions does not match");
}
// return an empty matrix (this never happens but just for safety)
return Matrix();
}
// add a double value (elements wise)
Matrix& add(double v)
{
for (int r = 0; r < rows; r++)
{
for (int c = 0; c < cols; c++)
{
p[r][c] += v;
}
}
return *this;
}
// subtract a double value (elements wise)
Matrix& subtract(double v)
{
return add(-v);
}
// multiply a double value (elements wise)
Matrix& multiply(double v)
{
for (int r = 0; r < rows; r++)
{
for (int c = 0; c < cols; c++)
{
p[r][c] *= v;
}
}
return *this;
}
// operator subtraction 2
friend Matrix operator- (const Matrix& a, const Matrix& b)
{
// check if the dimensions match
if (a.rows == b.rows && a.cols == b.cols)
{
Matrix res(a.rows, a.cols);
for (int r = 0; r < a.rows; r++)
{
for (int c = 0; c < a.cols; c++)
{
res.p[r][c] = a.p[r][c] - b.p[r][c];
}
}
return res;
}
else
{
// give an error
throw Exception("Dimensions does not match");
}
// return an empty matrix (this never happens but just for safety)
return Matrix();
}
// operator unary minus
friend Matrix operator- (const Matrix& a)
{
Matrix res(a.rows, a.cols);
for (int r = 0; r < a.rows; r++)
{
for (int c = 0; c < a.cols; c++)
{
res.p[r][c] = -a.p[r][c];
}
}
return res;
}
// operator multiplication 3
friend Matrix operator* (const Matrix& a, const Matrix& B)
{
// check if the dimensions match
if (a.cols == b.rows)
{
Matrix res(a.rows, b.cols);
for (int r = 0; r < a.rows; r++)
{
for (int c_res = 0; c_res < b.cols; c_res++)
{
for (int c = 0; c < a.cols; c++)
{
res.p[r][c_res] += a.p[r][c] * b.p[c][c_res];
}
}
}
return res;
}
else
{
// give an error
throw Exception("Dimensions does not match");
}
// return an empty matrix (this never happens but just for safety)
return Matrix();
}
/*
* returns the minor from the given matrix where
* the selected row and column are removed
*/
Matrix minor(const int row, const int col)
{
//printf("minor(row=%i, col=%i), rows=%i, cols=%i\n", row, col, rows, cols);
Matrix res;
if (row > 0 && row <= rows && col > 0 && col <= cols)
{
res = Matrix(rows - 1, cols - 1);
// copy the content of the matrix to the minor, except the selected
for (int r = 1; r <= (rows - (row >= rows)); r++)
{
for (int c = 1; c <= (cols - (col >= cols)); c++)
{
//printf("r=%i, c=%i, value=%f, rr=%i, cc=%i \n", r, c, p[r-1][c-1], r - (r > row), c - (c > col));
res(r - (r > row), c - (c > col)) = p[r-1][c-1];
}
}
}
else
{
throw Exception("Index for minor out of range");
}
return res;
}
/*
* returns the size of the i-th dimension of the matrix.
* i.e. for i=1 the function returns the number of rows,
* and for i=2 the function returns the number of columns
* else the function returns 0
*/
int size(const int i)
{
if (i == 1)
{
return rows;
}
else if (i == 2)
{
return cols;
}
return 0;
}
// returns the number of rows
int get_rows()
{
return rows;
}
// returns the number of columns
int get_cols()
{
return cols;
}
// print the contents of the matrix
void print()
{
if (p != NULL)
{
printf("[");
for (int r = 0; r < rows; r++)
{
if (r > 0)
{
printf(" ");
}
for (int c = 0; c < cols-1; c++)
{
printf("%.2f, ", p[r][c]);
}
if (r < rows-1)
{
printf("%.2f;\n", p[r][cols-1]);
}
else
{
printf("%.2f]\n", p[r][cols-1]);
}
}
}
else
{
// matrix is empty
printf("[ ]\n");
}
}
public:
// destructor
~Matrix()
{
// clean up allocated memory
for (int r = 0; r < rows; r++)
{
delete p[r];
}
delete p;
p = NULL;
}
private:
int rows;
int cols;
double** p; // pointer to a matrix with doubles
};
/*
* i.e. for i=1 the function returns the number of rows,
* and for i=2 the function returns the number of columns
* else the function returns 0
*/
int size(Matrix& a, const int i)
{
return a.size(i);
}
// addition of Matrix with double
Matrix operator+ (const Matrix& a, const double B)
{
Matrix res = a;
res.add(B);
return res;
}
// addition of double with Matrix
Matrix operator+ (const double b, const Matrix& a)
{
Matrix res = a;
res.add(b);
return res;
}
// subtraction of Matrix with double
Matrix operator- (const Matrix& a, const double B)
{
Matrix res = a;
res.subtract(B);
return res;
}
// subtraction of double with Matrix
Matrix operator- (const double b, const Matrix& a)
{
Matrix res = -a;
res.add(b);
return res;
}
// multiplication of Matrix with double
Matrix operator* (const Matrix& a, const double B)
{
Matrix res = a;
res.multiply(B);
return res;
}
// multiplication of double with Matrix
Matrix operator* (const double b, const Matrix& a)
{
Matrix res = a;
res.multiply(b);
return res;
}
/**
* returns a matrix with size cols x rows with ones as values
*/
Matrix ones(const int rows, const int cols)
{
Matrix res = Matrix(rows, cols);
for (int r = 1; r < rows; r++)
{
for (int c = 1; c <= cols; c++)
{
res(r, c) = 1;
}
}
return res;
}
/**
* returns a matrix with size cols x rows with zeros as values
*/
Matrix zeros(const int rows, const int cols)
{
return Matrix(rows, cols);
}
/**
* returns a diagonal matrix with size n x n with ones at the diagonal
* @param v a vector
* @return a diagonal matrix with ones on the diagonal
*/
Matrix diag(const int n)
{
Matrix res = Matrix(n, n);
for (int i = 1; i <= n; i++)
{
res(i, i) = 1;
}
return res;
}
/**
* returns a diagonal matrix
* @param v a vector
* @return a diagonal matrix with the given vector v on the diagonal
*/
Matrix diag(Matrix& v)
{
Matrix res;
if (v.get_cols() == 1)
{
// the given matrix is a vector n x 1
int rows = v.get_rows();
res = Matrix(rows, rows);
// copy the values of the vector to the matrix
for (int r=1; r <= rows; r++)
{
res(r, r) = v(r, 1);
}
}
else if (v.get_rows() == 1)
{
// the given matrix is a vector 1 x n
int cols = v.get_cols();
res = Matrix(cols, cols);
// copy the values of the vector to the matrix
for (int c=1; c <= cols; c++)
{
res(c, c) = v(1, c);
}
}
else
{
throw Exception("Parameter for diag must be a vector");
}
return res;
}
/*
* returns the determinant of Matrix a
*/
double det(Matrix& a)
{
double d = 0; // value of the determinant
int rows = a.get_rows();
int cols = a.get_cols();
if (rows == cols)
{
// this is a square matrix
if (rows == 1)
{
// this is a 1 x 1 matrix
d = a(1, 1);
}
else if (rows == 2)
{
// this is a 2 x 2 matrix
// the determinant of [a11,a12;a21,a22] is det = a11*a22-a21*a12
d = a(1, 1) * a(2, 2) - a(2, 1) * a(1, 2);
}
else
{
// this is a matrix of 3 x 3 or larger
for (int c = 1; c <= cols; c++)
{
Matrix M = a.minor(1, c);
//d += pow(-1, 1+c) * a(1, c) * det(M);
d += (c%2 + c%2 - 1) * a(1, c) * det(M); // faster than with pow()
}
}
}
else
{
throw Exception("Matrix must be square");
}
return d;
}
// swap two values
void swap(double& a, double& b)
{
double temp = a;
a = b;
b = temp;
}
/*
* returns the inverse of Matrix a
*/
Matrix inv(Matrix& a)
{
Matrix res;
double d = 0; // value of the determinant
int rows = a.get_rows();
int cols = a.get_cols();
d = det(a);
if (rows == cols && d != 0)
{
// this is a square matrix
if (rows == 1)
{
// this is a 1 x 1 matrix
res = Matrix(rows, cols);
res(1, 1) = 1 / a(1, 1);
}
else if (rows == 2)
{
// this is a 2 x 2 matrix
res = Matrix(rows, cols);
res(1, 1) = a(2, 2);
res(1, 2) = -a(1, 2);
res(2, 1) = -a(2, 1);
res(2, 2) = a(1, 1);
res = (1/d) * res;
}
else
{
// this is a matrix of 3 x 3 or larger
// calculate inverse using gauss-jordan elimination
// [url="http://mathworld.wolfram.com/MatrixInverse.html"]http://mathworld.wolfram.com/MatrixInverse.html[/url]
// [url="http://math.uww.edu/~mcfarlat/inverse.htm"]http://math.uww.edu/~mcfarlat/inverse.htm[/url]
res = diag(rows); // a diagonal matrix with ones at the diagonal
Matrix ai = a; // make a copy of Matrix a
for (int c = 1; c <= cols; c++)
{
// element (c, c) should be non zero. if not, swap content
// of lower rows
int r;
for (r = c; r <= rows && ai(r, c) == 0; r++)
{
}
if (r != c)
{
// swap rows
for (int s = 1; s <= cols; s++)
{
swap(ai(c, s), ai(r, s));
swap(res(c, s), res(r, s));
}
}
// eliminate non-zero values on the other rows at column c
for (int r = 1; r <= rows; r++)
{
if(r != c)
{
// eleminate value at column c and row r
if (ai(r, c) != 0)
{
double f = - ai(r, c) / ai(c, c);
// add (f * row c) to row r to eleminate the value
// at column c
for (int s = 1; s <= cols; s++)
{
ai(r, s) += f * ai(c, s);
res(r, s) += f * res(c, s);
}
}
}
else
{
// make value at (c, c) one,
// divide each value on row r with the value at ai(c,c)
double f = ai(c, c);
for (int s = 1; s <= cols; s++)
{
ai(r, s) /= f;
res(r, s) /= f;
}
}
}
}
}
}
else
{
if (rows == cols)
{
throw Exception("Matrix must be square");
}
else
{
throw Exception("Determinant of matrix is zero");
}
}
return res;
}
int main(int argc, char *argv[])
{
try
{
// create an empty matrix of 3x3 (will initially contain zeros)
int cols = 3;
int rows = 3;
Matrix A = Matrix(cols, rows);
// fill in some values in matrix a
int count = 0;
for (int r = 1; r <= rows; r++)
{
for (int c = 1; c <= cols; c++)
{
count ++;
A(r, c) = count;
}
}
// adjust a value in the matrix (indexes are one-based)
A(2,1) = 1.23;
// read a value from the matrix (indexes are one-based)
double centervalue = A(2,2);
printf("centervalue = %f \n", centervalue);
printf("\n");
// print the whole matrix
printf("A = \n");
A.print();
printf("\n");
Matrix B = ones(rows, cols) + diag(rows);
printf("B = \n");
B.print();
printf("\n");
Matrix B2 = Matrix(rows, 1); // a vector
count = 1;
for (int r = 1; r <= rows; r++)
{
count ++;
B2(r, 1) = count * 2;
}
printf("B2 = \n");
B2.print();
printf("\n");
Matrix C;
C = A + B;
printf("A + B = \n");
C.print();
printf("\n");
C = A - B;
printf("A - B = \n");
C.print();
printf("\n");
C = A * B2;
printf("A * B2 = \n");
C.print();
printf("\n");
// create a diagonal matrix
Matrix E = diag(B2);
printf("E = \n");
E.print();
printf("\n");
// calculate determinant
Matrix D = Matrix(2, 2);
D(1,1) = 2;
D(1,2) = 4;
D(2,1) = 1;
D(2,2) = -2;
printf("D = \n");
D.print();
printf("det(D) = %f\n\n", det(D));
printf("A = \n");
A.print();
printf("\n");
printf("det(A) = %f\n\n", det(A));
Matrix F;
F = 3 - A ;
printf("3 - A = \n");
F.print();
printf("\n");
// test inverse
Matrix G = Matrix(2, 2);
G(1, 1) = 1;
G(1, 2) = 2;
G(2, 1) = 3;
G(2, 2) = 4;
printf("G = \n");
G.print();
printf("\n");
Matrix G_inv = inv(G);
printf("inv(G) = \n");
G_inv.print();
printf("\n");
Matrix A_inv = inv(A);
printf("inv(A) = \n");
A_inv.print();
printf("\n");
}
catch (Exception err)
{
printf("Error: %s\n", "err.msg");
}
catch (...)
{
printf("An error occured...\n");
}
printf("\n");
system("PAUSE");
return EXIT_SUCCESS;
}
推荐答案
class COtherMatix : public Matrix
{
public:
virtual bool SomeFunction(void)
{
// Do derived class stuff....
}
};
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