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

 

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• 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 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

-- 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