C++_Eigen函数库用法笔记——The Array class and Coefficient-wise operations

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
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()

the .abs() method takes the absolute value of each coefficient

the .sqrt() computes the square root of the coefficients

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

Converting between array and matrix expressions

Mixing matrices and arrays in an expression is forbidden

Matrix expressions have an .array() method that 'converts' them into array expressions

Array expressions have 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

-- 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

-- Combination 2: --

41 58

117 170