
Comments and Discussions



Hi Paul,
Wiki has an example you can use:
http://en.wikipedia.org/wiki/QR_decomposition
I used the following:
A =
0 1.0000
0.6931 1.0000
1.3863 1.0000
2.0794 1.0000
2.7726 1.0000
3.4657 1.0000
Correct answer from MATLAB:
>> [Q,R] = qr(A)
Q =
0 0.7237 0.3248 0.3381 0.3513 0.3646
0.1348 0.5264 0.1776 0.1156 0.4088 0.7020
0.2697 0.3290 0.8999 0.0761 0.0520 0.0280
0.4045 0.1316 0.1163 0.8451 0.1936 0.2322
0.5394 0.0658 0.1325 0.2338 0.6649 0.4365
0.6742 0.2632 0.1487 0.3127 0.4767 0.3593
R =
5.1405 2.0226
0 1.3817
0 0
0 0
0 0
0 0
DotNetMatrix doesn't work correctly because it only gives the first two columns of Q.
I did this to use the DotNetMatrix:
// Create a jagged "array" based on A suitable for Method 1
// Create a b vector for use in the QR decomposition of A
double[][] array = new double[A.GetLength(0)  1][];
double[][] bMeth1 = new double[A.GetLength(0)  1][];
(assign array & bMeth1)
// Create a GeneralMatrix AMeth1
GeneralMatrix AMeth1 = new GeneralMatrix(array);
//// Perform the QR decomposition
QRDecomposition QRofA = new QRDecomposition(AMeth1);
GeneralMatrix QRsoln = QRofA.Solve(new GeneralMatrix(bMeth1));
GeneralMatrix QMeth1 = QRofA.Q;
GeneralMatrix RMeth1 = QRofA.R;
Best regards,
Ralf





Thanks for the information. I used these to test the classes for the next update. BTW, you have posted to a wrong thread. Also, this is the easy way to do the QRD class Program { static void Main(string[] args) { double[] values = { 0, 0.6931, 1.3863, 2.0794, 2.7726, 3.4657, 1.0000, 1.0000, 1.0000, 1.0000, 1.0000, 1.0000 }; GeneralMatrix matrix = new GeneralMatrix(values, 6); Print("The Matrix A", matrix); QRDecomposition qr = matrix.QRD(); Print("The Matrix Q", qr.Q); Print("The Matrix R", qr.R); } static void Print(string caption, GeneralMatrix matrix) { Console.WriteLine(caption); int m = matrix.RowDimension; int n = matrix.ColumnDimension; for (int i = 0; i < m; i++) { for (int j = 0; j < n; j++) { double dE = matrix.GetElement(i, j); if (dE >= 0) { Console.Write(" {0:f4} ", dE); } else { Console.Write("{0:f4} ", dE); } } Console.WriteLine(); } Console.WriteLine(); } } Best regards, Paul. Jesus Christ is LOVE! Please tell somebody.





Oops, sorry Paul about posting in the wrong place; I was in a bit of a hurry this morning. Anyway, you got the information. Glad to see that you are generously providing this.
Sincerely,
Ralf





Please try "QR(A,0)" in matlab and see the results.
Best regards,
Paul.
Jesus Christ is LOVE! Please tell somebody.





Here you go, Paul:
QR(A,0)
ans =
5.1405 2.0226
0.1348 1.3817
0.2697 0.0936
0.4045 0.1138
0.5394 0.3193
0.6742 0.5257
Best,
Ralf





I hope you see this is the result the DotNetMatrix gives, it is the "economic size" results as documented by the DotNetMatrix.
You will really not need the full size matrix Q that the Matlab gives in qr(A),
but I will see how to add that support too in the next update, if really required.
Best regards,
Paul.
Jesus Christ is LOVE! Please tell somebody.





Hi Paul,
The alglib.net code worked well enough for me, and so that is what I wound up using. I was not able to use the DotNetMatrix "economic size" results code because I was duplicating another algorithm that uses the full Q and R (whether that's really necessary, I'm not in a position to dig into right now). I certainly do not want to create more work for you. Unless others are asking for the full Q, I would not bother. I would not add this feature in lieu of say, providing some more fully documented examples of the code that is already in there.
I know I was not entirely sure how to properly use the code and what it could do when it came down to the details. I seems to me that any improvements in the documentation for the existing features (e.g., more examples) would be high yield.
Best wishes,
Ralf





Hi. In the CholeskyDecomposition constructor, a flag isspd is set. I have an example where this flag turned out to give me the wrong value.
When looking in the code, I can see a line like this:
isspd = isspd & (A[k][j] == A[j][k]);
since we are dealing with double's, this is a very dangerous way of checking for equality. Dangerous enough, at least, to make the code not work for my example.
I always recommend to use something like this:
isspd = isspd & CloseEnoughToEqual(A[k][j], A[j][k]);
where
CloseEnoughToEqual(a,b)
{
return Math.Abs(ab) < SOMESMALLTHRESHOULD
}
SOMESMALLTHRESHOULD could then be 0.0000001 or less depending on precision. In my case, the values were 0.38490014055502542 versus 0.38490014055503252 making the code believe those two values weren't suppose to be the same
Beside this, I have found the library very useful, and well working.
Claws





You are right, when dealing with double, precision and its effect on robustness is a great factor.
In any case, this library needs a lot of updates and I hope to do that soon.
With love,
Paul.
Jesus Christ is LOVE! Please tell somebody.





Hmm Does this Class handle or is able to handle the PenroseMoore Pseudo Inverse ?
I tried to modify it... however seems there are too many other functions that cannot handle the singular matrixs
also the SVD can it handle singular matrix ?





Hi, how could I calculate the matrix LEFT division
X = A\B
where A is af nonsquare matrix, with your library?
Thanks





In document, it said that GeneralMatrix.Inverse Method will "inverse(A) if A is square, pseudoinverse otherwise."
But I just got an error "Matrix is rank deficient"
The matrix data is
0 0 4 0 4
0 0 0 8 8
0 10 10 10 10
1 1 1 1 1
And if I try to SVD the matrix, the matrix has some problem.
The matrix from GetU() has ColumnDimension = 5, but the array A inside the atrix is 4 x 4.
Is this a bug?





as the author mentioned, the row_dimension must >= column_dimension
in the raw matrix.





public virtual GeneralMatrix Inverse()
{
if (this.m == this.n)
{
return Solve(Identity(m, m));
}
else if (this.m >= this.n)
{
SingularValueDecomposition SVD = this.SVD();
GeneralMatrix U = SVD.GetU();
GeneralMatrix S = SVD.S;
GeneralMatrix V = SVD.GetV();
GeneralMatrix TranS = S.Transpose();
return V*(TranS*S).Inverse()*TranS*U.Transpose();
}
else
{
SingularValueDecomposition SVD = this.Transpose().SVD();
GeneralMatrix U = SVD.GetU();
GeneralMatrix S = SVD.S;
GeneralMatrix V = SVD.GetV();
GeneralMatrix TranS = S.Transpose();
return (V*(TranS*S).Inverse()*TranS*U.Transpose()).Transpose();
}
}





Hi
I use your code and i have following problem.
VB.NET project and dll includes your classes with DotNetMatrix.
When I use GeneralMatrix objects in For ...Next there is OutOfMemory Exception in your source in differnt places at each time : more in constructors and sometimes in other methods. Stack memory and heap are not overflowed.
Exception was raised in line with "new double[][]" code
Can you help with solution problem? Maybe problem isn't in your sources...





Please post a simple code sample to examine.
Best regards,
Paul.
Jesus Christ is LOVE! Please tell somebody.





I am having the same problem but because I want to compute the SVD of a 500x65536 matrix, which is causing an Out of Memory Exception allocating the U matrix (65536x65536, double precision).
Do you have any smart implementation where the hard disk is used in place of the main memory to compute the SVD of really huge matrices?
Thanks,
Sebastian.





senrique wrote:
(65536x65536, double precision).
Wow! this is a simple library for very simple matrix operations.
senrique wrote:
Do you have any smart implementation where the hard disk is used in place of the main memory to compute the SVD of really huge matrices?
Currently no, in fact I never thought many would have interest in this matrix stuff. To handle huge matrix will involve defining complex data structures, we have to take on this when the generics support in .NET 2.0 is released.
Best regards,
Paul.
Jesus Christ is LOVE! Please tell somebody.





Great Matrix code. Very useful.
Just one thing: I can't seem to find out how to print the matrix's, even though its said "Methods for reading and printing matrices are also included." Maybe I'm being stupid or maybe these methods haven't been writen.
Anyway. I added my own, very simple ToString() method. I'll post it here as it might save someone a bit of time. Just paste it into the GeneralMatrix.cs file and compile.
///
/// Converts the array into a string.
/// "First row \n Second row \n Last row \n"
///
/// String of Array Elements
public override string ToString()
{
string elementsString = "";
for(int j=0; j < m; j++)
{
for(int i=0; i < n; i++)
elementsString += A[j][i].ToString() + " ";
elementsString += "\n";
}
return elementsString;
}
Mark Sugrue
Machine Vision Research Group
Royal Holloway, Uni of London
m.sugrue@rhul.ac.uk





seabhcan wrote:
t one thing:...
Just ignore it, it is a mistake in the documentations  sorry.
seabhcan wrote:
Anyway. I added my own, very simple ToString() method.
Use StringBuilder, it is more efficient for such work.
Best regards,
Paul.
Jesus Christ is LOVE! Please tell somebody.





thanks for your help, it is save me a lot of time...





Hi,
Is this library can resolve a least square non linear problem ??
Which algorithm is implemented for the least square (LevenbergMarquardt, Gauss, ...) ???
In advance, thanks.
See you,
Philippe





Sorry for the delay in responding.
The simple answer is no. This is a simple matrix library for simple matrix operations. Even though you can extend it for more complex algebra, it is not designed for such works.
Best regards,
Paul.
Jesus Christ is LOVE! Please tell somebody.





Sorry, I deleted your last mail you directly sent to me. But, I have read it and answer is:
If I have such library, I will not let you ask
Best regards,
Paul.
Jesus Christ is LOVE! Please tell somebody.





Great job! I just have a look at the code. I was wondering why the matrices are represented by a double[][] array instead of a double[ , ] array. Since, we will be dealing only with rectangular structures, I don't really see the advantage of using double[][]. Additionnaly, the use of double[][] implies one additionnal indirection to access to any element. That's not going to make a big change, but since the overall time of any operation on the matrix is going to be almost proportionnal to the element accessing time, it could still make a difference.
Also, there are details bothering me. Why implementing the IDisposable and destructor interfaces for GeneralMatrix ? As far, I have seen, it's not required. Remember that implementing IDisposable is really going to slow down the garbadge collection process (idem for destructor).
Idem for ISerializable, the attribute [Serializable] is itself sufficient. So why implementing the ISerializable interface ?







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First Posted  12 Jan 2004 
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