- The advantages of Array
- Addition and subtraction
- Array multiplication
- abs() & sqrt()
- Converting between array and matrix expressions
- The advantage of Array
- provides an easy way to perform coefficient-wise operations, such as adding a constant to every coefficient in the array or multiplying two arrays coefficient-wise
- Addition and subtraction
int main()
{
ArrayXXf a(3,3);
a << 1,2,3,
4,5,6,
7,8,9;
cout << “a - 2 = “ <<endl << a - 2 << endl;
}
a - 2 =
-1 0 1
2 3 4
-1 0 1
2 3 4
5 6 7
- Array multiplication
- array multiply array, arrays interpret multiplication as coefficient-wise product.
- two arrays can be multiplied if and only if they have the same dimensions.
int main()
{
ArrayXXf a(2,2);
ArrayXXf b(2,2);
a << 1,2,
3,4;
b << 5,6,
7,8;
cout << "a * b = " << endl << a * b << endl;
｝
a * b =
5 12
21 32
- abs() & sqrt()
int main()
{
ArrayXf a = ArrayXf::Random(5);
a *= 2;
cout << "a =" << endl
<< a << endl;
cout << "a.abs() =" << endl
<< a.abs() << endl;
cout << "a.abs().sqrt() =" << endl
<< a.abs().sqrt() << endl;
cout << "a.min(a.abs().sqrt()) =" << endl
<< a.min(a.abs().sqrt()) << endl;
｝
a =
1.36
-0.422
1.13
1.19
1.65
a.abs() =
1.36
0.422
1.13
1.19
1.65
a.abs().sqrt() =
1.17
0.65
1.06
1.09
1.28
1.36
-0.422
1.13
1.19
1.65
a.abs() =
1.36
0.422
1.13
1.19
1.65
a.abs().sqrt() =
1.17
0.65
1.06
1.09
1.28
- Converting between array and matrix expressions
- Mixing matrices and arrays in an expression is forbidden
- Matrix expressionshave an .array()method that 'converts' them into array expressions
- Array expressionshave a .matrix()method
int main()
{
MatrixXf m(2,2);
MatrixXf n(2,2);
MatrixXf result(2,2);
m << 1,2,
3,4;
n << 5,6,
7,8;
result = m * n;
cout << "-- Matrix m*n: --" << endl << result << endl << endl;
result = m.array() * n.array();
cout << "-- Array m*n: --" << endl << result << endl << endl;
result = m.cwiseProduct(n);
｝
-- Matrix m*n: --
19 22
43 50
19 22
43 50
-- Array m*n: --
5 12
21 32
Here is a more advanced example
int main()
{
MatrixXf m(2,2);
MatrixXf n(2,2);
MatrixXf result(2,2);
m << 1,2,
3,4;
n << 5,6,
7,8;
result = (m.array() + 4).matrix() * m;
cout << "-- Combination 1: --" << endl << result << endl << endl;
result = (m.array() * n.array()).matrix() * m;
cout << "-- Combination 2: --" << endl << result << endl << endl;
-- Combination 1: --
23 34
31 46
23 34
31 46
-- Combination 2: --
41 58
117 170