Trifon — Wed, 17 Mar 2004 23:32:23 GMT

Yes, Matrix ActiveX Component can do what you want. I have prepared some sample code for you, that demonstrates just this, how to perform a least squares fit of a 3rd order polynomial for a given set of a (x,y) pairs using Singular Value Decomposition.

This is some sample code in NET Basic:
[code]
Imports BluebitMatrix31

Module Module1
' The following code will demonstrate how to find
' the coeficients of a 3rd order polynomial
' in order to have a least squares fit solution
' for a set of (x, y) data pairs
'
' 3rd order polynomial
' a*1 + b*x + c*x^2 + d*x^3 = y
'
' Data set
' - x - - y -
' x0 = 2 y0 = 2
' x1 = 4 y1 = 3
' x2 = 5 y2 = 5
' x3 = 6 y3 = 7
' x4 = 8 y4 = 5
' x5 = 7 y5 = 6
'
' We need a least squares fit solution for the
' system of equations :
'
' X * C = Y
'
' Matrix X contains the powers of xn of the dataset
' x0^0, x0^1, x0^2, x0^3
' x1^0, x1^1, x1^2, x1^3
' x2^0, x2^1, x2^2, x2^3
' x3^0, x3^1, x3^2, x3^3
' x4^0, x4^1, x4^2, x4^3
' x5^0, x5^1, x5^2, x5^3
'
' Matrix Y contains the right hand tems y0 to yn
'
' Matrix C contains the coeficients
'
' Using Singular Value decomposition we calculate the
' pseudoinverse of X, Xinv and then C becomes:
'
' C = Xinv * Y

Sub Main()
Dim X As Matrix, Y As Matrix, C As Matrix

X = New MatrixClass
X.Size(6, 4)

'Entering data in the X matrix
X(0, 0) = 1 : X(0, 1) = 2 : X(0, 2) = 2 * 2 : X(0, 3) = 2 * 2 * 2
X(1, 0) = 1 : X(1, 1) = 4 : X(1, 2) = 4 * 4 : X(1, 3) = 4 * 4 * 4
X(2, 0) = 1 : X(2, 1) = 5 : X(2, 2) = 5 * 5 : X(2, 3) = 5 * 5 * 5
X(3, 0) = 1 : X(3, 1) = 6 : X(3, 2) = 6 * 6 : X(3, 3) = 6 * 6 * 6
X(4, 0) = 1 : X(4, 1) = 8 : X(4, 2) = 8 * 8 : X(4, 3) = 8 * 8 * 8
X(5, 0) = 1 : X(5, 1) = 7 : X(5, 2) = 7 * 7 : X(5, 3) = 7 * 7 * 7

Y = New MatrixClass
Y.Size(6, 1)

'Entering data for the Y matrix
Y(0, 0) = 2
Y(1, 0) = 3
Y(2, 0) = 5
Y(3, 0) = 7
Y(4, 0) = 5
Y(5, 0) = 6

'Calculating the pseudoinverse of X using SVD
Dim U As Matrix, S As Matrix, V As Matrix, Xinv As Matrix, i As Integer

U = New MatrixClass
S = New MatrixClass
V = New MatrixClass

X.SVD(U, S, V)

' Xinv = V * SInv * UInv

' Matrix S is a diagonal matrix. In order to find its
' inverse is faster to replace its diagonal elements by
' their reciprocals
For i = 0 To 3
S(i, i) = 1 / S(i, i)
Next

' Matrix U is an orthogonal matrix - its inverse equals
' its transpose

' Finally the X pseudoinverse becomes :
Xinv = V.Times(S).Times(U.Transpose)

' and the C matrix containg the coeficients :

C = Xinv.Times(Y)
'now C(0,0) contains a
' C(1,0) contains b
' C(2,0) contains c
' C(3,0) contains d

' In order to generate y based on C coeficients
' we just need to multiply matrix X by C
Dim nY As Matrix = X.Times(C)

' calculating DY = Y - nY
Dim dY As Matrix = Y.Minus(nY)

' calculating the sum of squares
Dim sumDY2 As Double = dY.ColsDotProduct(0, 0)

'Writing down the results:
Console.WriteLine("Dataset:")
Console.WriteLine("- x - - y -")
For i = 0 To 5
Console.WriteLine(String.Format(" x{0}={1} y{0}={2}", i, X(i, 1), Y(i, 0)))
Next

Console.WriteLine()
Console.WriteLine("3rd order polynomial coeficients.")
Console.WriteLine(String.Format("a= {0:+0.0000;-0.0000}", C(0, 0)))
Console.WriteLine(String.Format("a= {0:+0.0000;-0.0000}", C(1, 0)))
Console.WriteLine(String.Format("a= {0:+0.0000;-0.0000}", C(2, 0)))
Console.WriteLine(String.Format("a= {0:+0.0000;-0.0000}", C(3, 0)))

Console.WriteLine()
Console.WriteLine("3rd order polynomial.")
Console.WriteLine(String.Format("{0: + 0.0000}{1: + 0.0000; - 0.0000}*x{2: + 0.0000; - 0.0000}*x^2{3: + 0.0000; - 0.0000}*x^3", C(0, 0), C(1, 0), C(2, 0), C(3, 0)))

Console.WriteLine()
Console.WriteLine(" = Y values =")
Console.WriteLine("Observed Estimated Error")
For i = 0 To 5
Console.WriteLine(String.Format(" {0:+0.0000;-0.0000} {1:+0.0000;-0.0000} {2:+0.0000;-0.0000}", Y(i, 0), nY(i, 0), dY(i, 0)))
Next
Console.WriteLine()
Console.WriteLine(String.Format("Sum of error squares : {0:+0.0000;-0.0000}", sumDY2))

Console.Read()
End Sub

End Module
[/code]
Free Trial edition will let you to use up to 6x6 matrices, meaning that you can test up to 6 (x,y) pairs, but I think this is enough for evaluation.

You will need to buy Advanced or Advanced II edition of MaXC since SVD method is not supported in Standard edition.

There are not any limitations, you'll be able to calculate linear regressions for thousands lines of data and that will be done very fast.

Least Squares Fit of a 3rd order polynomial

anonymous — Wed, 17 Mar 2004 23:23:43 GMT

I am interested in using your matrix component in a project and would like to know if it will do what is needed.Project: Using linear regression, extract roots or coeficients from a set of ordered pairs (x,y). These coeficients will then be used in a 3rd order polynomial to generate y based on x. The platform is Visual Basic .NET.Questions:1. Will your software do this? 2. Do you have any example code or suggestions?3. What are the limitations.Thanks

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Least Squares Fit of a 3rd order polynomial