Comments and Ratings

Thank you very much for this nice function which works perfectly

Thanks. Very useful!

Could anybody tell me how to evaluate the time required by the SVD. Please kindly note the svd.m called directly by the workspace is a built-in function, which is much faster than the svd.m available on the Matlab website. So which one is more suitable to evaluate the required time?

Actually, I am trying to compare a new algorithm with the SVD in computational cost or time. I suppose the built-in SVD function might be faster than the source-code SVD function. Could anybody help me? Thanks a lot for your kindly helps in advance! My email address is huanglei8rsp@yahoo.com.cn.

I need a function that can makes symbolic fourier transform

Mr. Godfrey I thank you. There are a few bullies running around on the Matlab exchange randomly attacking authors. Most authors just ignore them, but I fear some may be turned away from the site because of them. So thank you for sticking up for yourself and demonstrating how shrill, petty, and useless their comments usually are. These people seem to want published, polished, ready-for-sale code. The truth is matlab isn't for hardcore programmers. It is for people who want a TOOL to solve a particular PROBLEM THEY need solved, not a product development suite. So most programs found on the file exchange will be imperfect and have a very limited scope.

I'm amazed by the sense of entitlement these commenters display. Contributors have, out of the goodness of their hearts, given free code to the world. It is FREE. If they don't like it, they need not use it.

Thanks again Mr. Godfrey.
I will give Mr. D'Errico credit for engaging you in the discussion, regardless of the tone. I am also very impressed that he changed is rating after some discussion.
Jos x@y.z however seems to have a habit of being the first and least knowledgable commenter on many programs. He also rarely returns to apologize or retract his statements when he is shown to be very wrong. His rediculous snap judgments are exactly the type of thing my whole comment is about.

This program satisfy
A * Inv(A) = I
with Inv(A) = Adj(A)/det(A)
When I tried contrary Inv(A)*A ~= I, the result isn't I anymore.
I think this situation should satisfy both condition.

My sincere thanks to the author. Very useful method. I compared the result with matlab inbuilt function on SVD, both match well. I had done in my application QR decomposition, I thought of reusing it for SVD computation, this helped me a lot. Good work.

Regarding the comments of John D'Errico:
"So why should anyone bother to use your code, when they can copy a better version out of this review?"
Because it's publicly available as a submitted .m file.
Why don't you go ahead and submit your own version?
Won't that make it easy for all Matlab users to find and use?

"Can you show ANY reason why the svd version is clearly the best answer as you claim?"
I never claimed that the SVD algorithm was the best one to use for computing DETT.
I claimed that the SVD algorithm is the best one to use when "solving" a singular set of equations.
It is common knowledge that the SVD gives you the Least squares solution for over determined systems, the exact answer for full rank systems, and the minimum norm answer for under determined systems.

Why did you take a discussion about solutions of linear systems and twist it into a claim about the best algorithm to use?

IMHO, you appear to want to try and win some kind of argument or contest of some sort.
Your postings have been in a rather belligerent and "in your face" style.
I prefer a more thought based rational discussion instead.

"dett, based on the svd is slower than it needs to be"
Ok, good for you.

"nicely on sparse matrices. Can that be said for dett?"
Well, I never claimed that it was designed for sparse matrices.

"Error in ==> dett at 20"
So, go ahead and submit it.

"So, no, I don't consider a poor implementation of any tool to be worth an excellent rating"
Ok, but I never asked you to rate it.
Why do you think that I care?

"Not when a superior one is so trivial to write."
Sigh.
You really want to win something here don't you?
I can't help but ask:
Before you saw this submission, how did you calculate the Determinant and Adjoint of non-square matrices?

Regarding the comments of John D'Errico:
"...WHEN A is nonsingular. Obviously this fails for singular arguments."
And that "failure" is the correct answer for a singular matrix.
For any matrix,(square or non-square), with one or more singular values equal to 0, no inverse (left, unique, or right) is going to exist.
In that case we resort to the SVD to provide the "best" answer under those circumstances.

"Were there other uses proposed for this extension of dett, I might up my rating further..."
Well, some of us consider a consistant extended definition of Det() to be "use" enough... ;)

Regarding the comments of John D'Errico:
A right or left pseudo-inverse MAY exist. But this "determinant" seems to tell you nothing that rank or cond will not say better.
<I agree. But the purpose of my Adj() and Dett() programs is to provide meaningful values for non-square matrices.>

If your goal is merely to compute a pseudo-inverse, then use pinv - a far faster solution than one based on the adjoint.
<No, my goal is to extend the definition in a meaningfull manner>

Looking more closely at the author's claim, I'll note that adj fails when applied to non-square matrices. I just download the latest version of adj.
<Sigh, you don't have the latest version.
Is your version dated April 1998 or October 2006?>

Try this:
adj(rand(5,3))
<Works fine with the latest version.
Give the Mathworks people a day or to to make the latest version available.>

This does not even touch the question of complex (particularly self adjoint) matrices as brought up by a review of adj.
<It works fine for complex matrices as well.
There are multiple definitions of Adj().
My definition is based on Inv(A) = Adj(A)/Det(A)
as given on page 169 of "Applied Linear Algebra, 3rd edition" by B. Noble and J. Daniel

For square matrices, this code is also far slower than Matlab's existing det function anyway.
<True. And is also true the Matlab's own Det() function doesn't handle non-square matrices like mine does>

So at the very least users should be cautioned away from using this code on square systems.
<True>

Since apparently non-square systems are not handled as the author claims,
<Try again in a day or two.>

I see no use at all,
<Other than providing a meaningful extension of the definition of Adj() and Det()>

1) The adjugate is also only defined for square matrices.
2) orth(rand(3,2)) produces three rows that are NOT linearly independent, e.g., its rank is 2.

To Luis T. (ltirado@gmail.com):
Your professor is referring to one of the other definitions of "Adjoint"

This program was written to satisfy
A * Inv(A) = I
with Inv(A) = Adj(A)/det(A)
So, for your example, Adj(A) = [0 -j; j 0] ans det(A) = -1
We have A*Adj(A)/det(A) = [1 0; 0 1] = I, as required.

A few comments by the author...

To Scott Miller: Matlab's own SVD should always be, for many reasons, the program of first choice most SVD needs.
The purpose of this program was to demonstrate a very simple way to compute the SVD that was probably not well known.
To John D'Errico: Your first set of comments appear to be based on the assumption that this code is intended to compute with Matlab's own SVD code for all user applications. It is not.
Upon typing 'Help svdsim; the used clearly sees "A simple program that demonstrates..."
As such, I did not, originally, bother with a robust exit scheme since the program intent was algorithmic in nature and not efficiency oriented. However, I have updated the program to add a more sophiticated exit mechanism.
For your second comment and for the comments of Carlos López: The program could certainly be used to refine an existing SVD solution.
The required code would be trivial to add.
Also, QR decomposition routines (MGS) are easy to write by almost any programmer. However, an SVD routine is a more daunting task and is usually sent to a canned library routine.
This program provides an easy to implement algorithm that can be used whenever a more sophisticated math library is not available.

This is mathematical nonsense.
For non-square matrices, there are always rows/columns that are not indepenent of other rows/columns. So, by definition, the determinant of non-square matrices should be zero!
That is why textbooks always say that the determinant is only defined for square matrices.

While future higher precision computations might allow refinement using the scheme in this code, if higher precision is available in the future, then the svd code itself would far more efficiently call a higher precision version of svd at relatively little cost in time. An expensive refinement scheme would seem to be of little value.

This would appear to have NO advantages over svd. It will be immensely slower than svd. One exception - in theory, svdsim will work on sparse matrices. However, svdsim is so slow that even here you are far better off converting your matrix to a full one, then calling svd. For example:

>> X = sprand(50,50,.01);
>> tic,[u,s,v]= svdsim(X);toc
Elapsed time is 4.720246 seconds.
>> tic,[u,s,v]= svd(full(X));toc
Elapsed time is 0.002718 seconds.

Note, this gets far worse if X is less sparse.

>> X = sprand(50,50,.1);
>> tic,[u,s,v]= svdsim(X);toc
Elapsed time is 41.527362 seconds.
>> tic,[u,s,v]= svd(full(X));toc
Elapsed time is 0.012801 seconds.

Another problem with this code is the lack of a convergence tolerance. It merely loops an arbitrary number of times, then quits.

So don't use this code to compute the svd. Just use svd.

This leaves only one purpose - an expository one. It does that reasonably well, but even there the lack of any convergence criterion suggests a low rating. Good expository code might also suggest why there is no sort at the end on the singular values, and provide a reference for the student to read further on methods to compute the SVD.

I'll raise my rating with improvements in the exposition and code.

Does this take into account complex matrices?

In my graduate linear systems analysis course today, our professor today discussed that if a matrix is self-adjoint, then adj(T) = T.

For a real matrix, this means it must be symmetric, and for a complex matrix, it means that it must be hermitian.

For the hermitian and self-adjoint matrix:
T=[0,j;-j,0]

adj(T) should be equal to T

Using this program, it comes out to be conj(T). I believe that should not be the case, unless I'm totally mistaken.

some very nice coding here

Sure I should prefer a program which would suggest some optimal values of kn and kd. I hope to survive up to appearance of such a version in FEX, at least for kd=0.

Very nice. Thanks.

Very useful!

Implementation well done and I used to converto to another language.

This is exactly wat I needed, works perfect

Works very well