Comments for YALL1: Your ALgorithms for L1 http://yall1.blogs.rice.edu Sun, 30 May 2010 04:34:41 +0000 hourly 1 http://wordpress.org/?v=3.3.1 Comment on RandCirc Discussions by wy1 http://yall1.blogs.rice.edu/?p=51#comment-4 wy1 Sun, 30 May 2010 04:34:41 +0000 http://yall1.blogs.rice.edu/?p=51#comment-4 If the circulant matrix is generated of Type 2 above and all the entries of diag(D) have amplitude 1, then the circulant ensember A = P*C satisfies A*A' = I. So, the rows of A are orthogonal each other, and one should set opts.nonorth = 0 to take the full advantage of YALL1. If the circulant matrix is generated of Type 2 above and all the entries of diag(D) have amplitude 1, then the circulant ensember A = P*C satisfies A*A’ = I. So, the rows of A are orthogonal each other, and one should set

opts.nonorth = 0

to take the full advantage of YALL1.

]]> Comment on YALL1 discussions by wy1 http://yall1.blogs.rice.edu/?p=49#comment-3 wy1 Fri, 28 May 2010 02:38:17 +0000 http://yall1.blogs.rice.edu/?p=49#comment-3 This area is designated to discussions on the YALL1 solver. We will regularly visit this place and join the discussions. This area is designated to discussions on the YALL1 solver. We will regularly visit this place and join the discussions.

]]> Comment on RandCirc Discussions by wy1 http://yall1.blogs.rice.edu/?p=51#comment-2 wy1 Thu, 27 May 2010 23:30:31 +0000 http://yall1.blogs.rice.edu/?p=51#comment-2 A partial random circulant matrix can be formed as [Downsample]*[Circulant Matrix], where in code both the downsample and circulant matrices are formed implicitly. Below are some types of circulant matrices and downsampling schemes. [Circulant Matrix] Types: 1. Random 1st row: Gaussian, Bernoulli, ... 2. F*DF where F is a Fourier matrix and D is a diagonal matrix. 2A: diag(D) is random 2B: diag(D) has a uniform amplitude and random phases diag(D) can be conjugate symmetric (yielding real F*DF) or not (yielding complex F*DF). [Downsample] Types: 1. First m rows 2. Equally-spaced m rows 3. Randomly picked m rows They can give different performances. See Rice CAAM TR10-01 for a comparison. A partial random circulant matrix can be formed as [Downsample]*[Circulant Matrix], where in code both the downsample and circulant matrices are formed implicitly. Below are some types of circulant matrices and downsampling schemes.

[Circulant Matrix] Types:

1. Random 1st row: Gaussian, Bernoulli, …

2. F*DF where F is a Fourier matrix and D is a diagonal matrix.
2A: diag(D) is random
2B: diag(D) has a uniform amplitude and random phases

diag(D) can be conjugate symmetric (yielding real F*DF) or not (yielding complex F*DF).

[Downsample] Types:

1. First m rows
2. Equally-spaced m rows
3. Randomly picked m rows

They can give different performances. See Rice CAAM TR10-01 for a comparison.

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