Eigen实现matlab中的reshape

https://eigen.tuxfamily.org/dox-devel/group__TutorialReshape.html

注意，需要Eigen3.4版本

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Since the version 3.4, Eigen exposes convenient methods to reshape a matrix to another matrix of different sizes or vector. All cases are handled via the DenseBase::reshaped(NRowsType,NColsType) and DenseBase::reshaped() functions. Those functions do not perform in-place reshaping, but instead return a view on the input expression.

Reshaped 2D views 2维矩阵的重排

The more general reshaping transformation is handled via: reshaped(nrows,ncols). Here is an example reshaping a 4x4 matrix to a 2x8 one:

例子1

code:注意，默认是列优先，matlab的reshape是列优先

Matrix4i m = Matrix4i::Random();
cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here is m.reshaped(2, 8):" << endl << m.reshaped(2, 8) << endl;

output:

Here is the matrix m:
-10   1   4   7
 -8  -6   9 -10
  5 -10  -2  -9
 -1   4   0   1
Here is m.reshaped(2, 8):
-10   5   1 -10   4  -2   7  -9
 -8  -1  -6   4   9   0 -10   1

例子2

code:注意，默认是列优先，matlab的reshape是列优先

 Eigen::VectorXd M1(9);    // Column-major storage
 M1 << 1, 2, 3,  4,  5,  6, 7, 8, 9;
cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here is m.reshaped(3,3):" << endl << m.reshaped(3,3) << endl;

output:

Here is the matrix m:
1
2
3
4
5
6
7
8
9
Here is m.reshaped(2, 8):
1 4 7
2 5 8
3 6 9

By default, the input coefficients are always interpreted in column-major order regardless of the storage order of the input expression. For more control on ordering, compile-time sizes, and automatic size deduction, please see de documentation of DenseBase::reshaped(NRowsType,NColsType) that contains all the details with many examples.

1D linear views 1维矩阵的重排

A very common usage of reshaping is to create a 1D linear view over a given 2D matrix or expression. In this case, sizes can be deduced and thus omitted as in the following example:

例子3

Matrix4i m = Matrix4i::Random();
cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here is m.reshaped().transpose():" << endl << m.reshaped().transpose() << endl;
cout << "Here is m.reshaped().transpose():  " << endl << m.reshaped().transpose() << endl;

output:

Here is the matrix m:
-10   1   4   7
 -8  -6   9 -10
  5 -10  -2  -9
 -1   4   0   1
Here is m.reshaped().transpose():
-10  -8   5  -1   1  -6 -10   4   4   9  -2   0   7 -10  -9   1
Here is m.reshaped().transpose():  
-10   1   4   7  -8  -6   9 -10   5 -10  -2  -9  -1   4   0   1

This shortcut always returns a column vector and by default input coefficients are always interpreted in column-major order. Again, see the documentation of DenseBase::reshaped() for more control on the ordering.

TutorialReshapeInPlace 原地重排

The above examples create reshaped views, but what about reshaping inplace a given matrix? Of course this task in only conceivable for matrix and arrays having runtime dimensions. In many cases, this can be accomplished via PlainObjectBase::resize(Index,Index):

例子4

MatrixXi m = Matrix4i::Random();
cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here is m.reshaped(2, 8):" << endl << m.reshaped(2, 8) << endl;
m.resize(2,8);
cout << "Here is the matrix m after m.resize(2,8):" << endl << m << endl

output:

Here is the matrix m:
-10   1   4   7
 -8  -6   9 -10
  5 -10  -2  -9
 -1   4   0   1
Here is m.reshaped(2, 8):
-10   5   1 -10   4  -2   7  -9
 -8  -1  -6   4   9   0 -10   1
Here is the matrix m after m.resize(2,8):
-10   5   1 -10   4  -2   7  -9
 -8  -1  -6   4   9   0 -10   1

However beware that unlike reshaped, the result of resize depends on the input storage order. It thus behaves similarly to reshaped:

例子5

Matrix m = Matrix4i::Random();
cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here is m.reshaped(2, 8):" << endl << m.reshaped(2, 8) << endl;
cout << "Here is m.reshaped(2, 8):" << endl << m.reshaped(2, 8) << endl;
m.resize(2,8);
cout << "Here is the matrix m after m.resize(2,8):" << endl << m << endl;

output

Here is the matrix m:
-10  -8   5  -1
  1  -6 -10   4
  4   9  -2   0
  7 -10  -9   1
Here is m.reshaped(2, 8):
-10   4  -8   9   5  -2  -1   0
  1   7  -6 -10 -10  -9   4   1
Here is m.reshaped(2, 8):
-10  -8   5  -1   1  -6 -10   4
  4   9  -2   0   7 -10  -9   1
Here is the matrix m after m.resize(2,8):
-10  -8   5  -1   1  -6 -10   4
  4   9  -2   0   7 -10  -9   1

Finally, assigning a reshaped matrix to itself is currently not supported and will result to undefined-behavior because of aliasing . The following is forbidden:

A = A.reshaped(2,8); 

This is OK:

A = A.reshaped(2,8).eval();