matlab constract an SRFT matrix S=D*F*E,where D is a diagonal projector onto s coordinates,E has independent Rademacher entries and F is a discrete cosine transform (DCT2)
时间: 2023-12-14 15:36:06 浏览: 33
Here is an example code in Matlab for constructing an SRFT matrix S:
```matlab
% Define the size of the matrix
n = 8;
% Construct the diagonal matrix D
s = randn(n, 1); % set the s coordinates randomly
D = spdiags(s, 0, n, n);
% Construct the matrix E with independent Rademacher entries
E = sign(randn(n));
% Construct the matrix F using DCT2
F = dct2(eye(n));
% Construct the SRFT matrix S
S = D * F * E;
```
In this code, we first define the size of the matrix `n`. Then we construct the diagonal matrix `D` using the `spdiags` function, where we set the `s` coordinates randomly. Next, we construct the matrix `E` using the `sign` function to generate independent Rademacher entries. Finally, we construct the matrix `F` using the `dct2` function to perform the discrete cosine transform on the identity matrix. Finally, we compute the SRFT matrix `S` as the product of `D`, `F`, and `E`.