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Posted
12 Jan 2004

Comments and Discussions


Kuryn wrote: You should never make a class virtual.
Hmmm, I do not know about this new rule in town. However, you have the source codes, so please do whatever you like with it  it is a public domain license.
Best regards,
Paul.
Jesus Christ is LOVE! Please tell somebody.





Well you should make a class virtual when needed. But not a mathematical class, because nothing changes different. Like in a Vector, a dotProduct is a dotProduct.





Thanks for this library, it is very useful!
I have a question: I arrive at some point with a Matrix that is singular, and I want to perform an Inverse on it.
GeneralMatrix matrixInvertQ = matrixMultiplyN.Inverse();
...
public virtual Matrix Inverse()
{
return Solve(Identity(m, m));
}
The Inverse method calls Solve, which instantiates a LUDecomposition object and calls its Solve method. There it tests for singularity, and I get the "Matrix is singular" exception.
I have very limited knowledge in mathematics, so bear with me. At the point where the matrix is considered singular, shouldn't a pseudoinverse by performed?
In the comments for the Inverse method, it says "inverse(A) if A is square, pseudoinverse otherwise".
Is there a part missing from implementation?
Thanks!





Hello,
Singularity and pseudoinverse are different.
To understand the pseudoinverse, see the following
1. In PlanetMath[^]
2. Example[^]
Best regards,
Paul.
Jesus Christ is LOVE! Please tell somebody.





Hi:
There is a bug in the svd decomposition, inherited from Jama. The problem is with the V matrix, when n>m. The correction is:
<code>
if (wantv)
{
for (int k = n  1; k >= 0; k)
{
if ((k < nrt) & (e[k] != 0.0))
{
//for (int j = k + 1; j < nu; j++) error
for (int j = k + 1; j < n; j++) //correction
{
double t = 0;
</code>
The bug is reported here:
http://cio.nist.gov/esd/emaildir/lists/jama/msg00430.html





Thank you, I will take a look.
Best regards,
Paul.
Jesus Christ is LOVE! Please tell somebody.





Thank you!
I'm no math guy but I have a question upon another thing (may be a "bug"?):
The SVD is A[mxn] = U[mxm]*S[mxn]*V[nxn]^T  so U should be a square matrix. But it is defined here as:
<br />
m = Arg.RowDimension;<br />
n = Arg.ColumnDimension;<br />
int nu = System.Math.Min(m, n);<br />
U = new double[m][];<br />
for (int i = 0; i < m; i++)<br />
{<br />
U[i] = new double[<big>nu</big>];<br />
}<br />
Shouldn't it be like this:
m = Arg.RowDimension;<br />
n = Arg.ColumnDimension;<br />
int nu = System.Math.Min(m, n);<br />
s = new double[System.Math.Min(m + 1, n)];<br />
U = new double[m][];<br />
for (int i = 0; i < m; i++)<br />
{<br />
U[i] = new double[<big>m</big>];<br />
}<br />





Hello everybody,
I am new using matrix in C# and I would like to thank and congratulate to the author of General Matrix. This is a very usefull and easy class to work with it.
Currently I am working with the SVD descomposition to obtain the PseudoInverse... But it doesn't work. The code blocks during the SVD calculation. Does anybody have the same problem?
Thanks in advance





Hi there,
I encountered two problems when solving underdetermined equation systems:
The first problem is an ArrayIndexOutOfBoundsException when trying to get the SMatrix. I think the problem is the wrong size of S, because of A[mxn] = U[mxm]*S[mxn]*V[nxn]' the dimensions should be mbyn but in the code they are nbyn:
/// <summary>Return the diagonal matrix of singular values</summary><br />
/// <returns> S<br />
/// </returns><br />
virtual public GeneralMatrix S<br />
{<br />
get<br />
{<br />
GeneralMatrix X = new GeneralMatrix(n, n); // this should be (m, n)<br />
double[][] S = X.Array;<br />
for (int i = 0; i < n; i++) // this loop should go till m not n<br />
{<br />
for (int j = 0; j < n; j++)<br />
{<br />
S[i][j] = 0.0;<br />
}<br />
S[i][i] = this.s[i];<br />
}<br />
return X;<br />
}<br />
}
Then there is a problem with the dimension of the singular values vector in the constructor of SingularValueDecomposition:
s = new double[System.Math.Min(m + 1, n)];<br />
For example, my equation system has six equations and eight variables, so m=6 and n=8. Then s will be the size of seven and there will be a singular value that doesn't really exists.
In addition to this, I get different results when using the svdfunction of Matlab. The singular values and the Umatrix are exactly the same, but in the Vmatrix the last nm coloumns have different values, the others have the same like in Matlab. But I didn't find a suitable place in the code for that problem.
Please correct me, if I understood something mathematically wrong.
modified on Friday, August 29, 2008 10:16 AM





Not sure this discussion board is still active, but I recently discovered this library and found it extremely useful, so first of all thanks very much for making it available!
Unfortunately, I have also discovered problems with the SVD computation, and wrong dimensions of the resulting matrices.
If you do a test with the example provided on Wikipedia[^], this library produces wrong results as far as I can tell (FWIW, Matlab returns the same values given on Wikipedia).
After running the example (an SVD on a 4by5 matrix), the S matrix from the SVD object is a 5by5 matrix, whereas the correct result should be a 4by5 matrix. Also, the entries of the U and V matrix seem to be in the wrong order and/or have the wrong sign.
Also, the singular values vector returned by the SVD object has five elements in this example, but, according to Wikipedia
"An m × n matrix M has at least one and at most p = min(m,n) distinct singular values."
so there should be a maximum of four singular values, not five.
If anyone is still following this board, I'd very much like to hear whether anyone can confirm my findings and/or has a bug fix!
I'd really like to use this library for my work, but only if works with nonsquare matrices.
Thanks!
Martin





I do confirm you results my friend the sign of resulted U and V are messed up





I have problem with relation between eigenvalues and eigenvectors. My eigenvectors do not correspond with their eigenvalues. Instead they are mixed (for exaple eigenvalue a1 has vector v3, instead of v1). All eigenvalues i have are negative so can that be problem?
Thanks
Cukaric






sergiomad wrote: Is available a method for getting the KarhunenLoève vectors?
No, KarhunenLoève is not directly related to matrix.
sergiomad wrote: but I can't find methods like "times()"
This port uses the .NET naming, it should be "Multiply(...)"
Best regards,
Paul.
Jesus Christ is LOVE! Please tell somebody.





public GeneralMatrix(double[] vals, int m)<br />
{<br />
this.m = m;<br />
n = (m != 0?vals.Length / m:0);<br />
if (m * n != vals.Length)<br />
{<br />
throw new System.ArgumentException("Array length must be a multiple of m.");<br />
}<br />
A = new double[m][];<br />
for (int i = 0; i < m; i++)<br />
{<br />
A[i] = new double[n];<br />
}<br />
for (int i = 0; i < m; i++)<br />
{<br />
for (int j = 0; j < n; j++)<br />
{<br />
A[i][j] = vals[i + j * m];<br />
}<br />
}<br />
}
I think the statement
A[i][j] = vals[i + j * m];
should be revised as
A[i][j] = vals[j + i * m];





Sorry for the late response.
Well, not a bug. If you see the documentation of that constructor, vals is said to be packed by columns.
I think you needed the "packed by row" array filling, I kept the original implementations. I will update this library soon and give the user the options
to choose between the two with an extra parameter to avoid confusion.
Best regards,
Paul.
 modified at 11:32 Tuesday 17th July, 2007
Jesus Christ is LOVE! Please tell somebody.





Paul,
I am new to DotNet programming and I'm working on a project to determine whether a series of values over time are trending upward, down or steady. I'm working with performance data from the Windows OS.
I believe the simplest approach will be to run a least squares analysis on the data (40 points, each from a successive day). I would like to use your DotNetMatrix library but am a little out of my league. Do you have any script samples/instructions for implementing the library and especially for a least squares analyis.
Thanks for your help,
Tom
P.S. Love your message postscript, my brother.





Tom,
You have many options for least squares, although I'm unsure how to use this particular library for the job (it didn't do the QR decomposition as I expected ... I never got the expected Q matrix for some reason).
Anyway, here is a least squares solution using QR decomposition (sometimes called QR Factorization). Feel free to look up least squares on Wiki as well. Also, I give links to a much easier way of doing least squares at the end of this message.
http://www.alkires.com/teaching/ee103/Rec8_LLSAndQRFactorization.htm[^]
You can get QR decomposition and linear equation solvers which actually do work (they seem to be based on LAPACK) from here:
http://www.alglib.net/matrixops/general/qr.php routine, which seems to have come from LAPACK CGEQR
and
http://www.alglib.net/linequations/general/lu.php
Both of the links above have code samples and test code that seems to work.
**** However, you may want something much simpler, such as ... ****
http://www.codeguru.com/forum/showpost.php?p=1139483&postcount=2[^]
or
http://www.pdc.kth.se/training/Tutor/MPI/Pt2pt.Lab/leastsquares.c[^] (some adaptation required since this is C code, but it should be easy to adapt).
All the best,
Ralf





lukner wrote: (it didn't do the QR decomposition as I expected ... I never got the expected Q matrix for some reason).
I am currently trying to update this matrix, please can you give me some examples of the problems you have with the Qmatrix? (may be a matrix and expected Q).
Best regards,
Paul.
Jesus Christ is LOVE! Please tell somebody.





(reply is in the Dynamic size thread below by accident ...





This library is great! But it seems that it's lack the capability of handling dynamic size matrix. Sometime we won't know what the matrix size would be as it would grow/shrink with time, so it will be better if the library can support dynamic size.





Currently you can shink by using the GetMatrix method, which allows you to retrieve a submatrix.
I will add a general method, say Resize(int newRows, int newColumns), to support your request in the next version.
Best regards,
Paul.
Jesus Christ is LOVE! Please tell somebody.





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






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