I messed around with Geogebra yesterday for a couple hours and got close, but no cigar. My math professor hasn't figured it out either...
MATH NERDS! I need help with a pump formula!
- Thread starter aclockworkorange
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I messed around with Geogebra yesterday for a couple hours and got close, but no cigar. My math professor hasn't figured it out either...
if the graph was linear, it would be easy, using the equation of a line.
but its a curve.
as you know, derivatives take the slope of a point tangent to the curve, which is sort of what you are looking for.
I haven't taken first year calculus since 1997 so I won't be of much help LOL.
but its a curve.
as you know, derivatives take the slope of a point tangent to the curve, which is sort of what you are looking for.
I haven't taken first year calculus since 1997 so I won't be of much help LOL.
I forgot a lot of math from the 6 weeks between my summer and fall quarter this year, can't imagine you'd remember much from over a decade ago. 
Obviously you haven't made it to Stats, Physics or Higher level Math yet!
There are a variety of methods to compute a curve from a set of points. A basic algorithm is the "Gauss Newton" method. You plug in a series of points and it will give you a formula that approximates the curve. The more points the better the resulting formula.
Once you have generated a formula you can plug in your own values into the formula you generated and compute the resulting points.
http://en.wikipedia.org/wiki/Gauss%E2%80%93Newton_algorithm
The program that you want to use to do this for you is MatLab!!!!
Or, if you are adventurous here you go:
namespace NumericalMethods
{
public class GaussNewton
{
private Matrix _jacobian;
private Matrix _residuals;
private Matrix _regressionParameters0;
private Derivatives _derivatives;
private Parameter[] _regressionParameters;
private Parameter[] _observedParameters;
private Func<double> _regressionFunction;
private double[,] _data;
public GaussNewton(Func<double> regressionFunction, Parameter[] regressionParameters, Parameter[] observedParameters, double[,] data, int numberOfDerivativePoints)
{
Debug.Assert(data.GetLength(0) == observedParameters.Length + 1);
_data = data;
_observedParameters = observedParameters;
_regressionParameters = regressionParameters;
_regressionFunction = regressionFunction;
int numberOfParameters = _regressionParameters.Length;
int numberOfPoints = data.GetLength(1);
_derivatives = new Derivatives(numberOfDerivativePoints);
_jacobian = new Matrix(numberOfPoints, numberOfParameters);
_residuals = new Matrix(numberOfPoints, 1);
_regressionParameters0 = new Matrix(numberOfParameters, 1);
}
public GaussNewton(Func<double> function, Parameter[] regressionParameters, Parameter[] observedParameters, double[,] data) :
this(function, regressionParameters, observedParameters, data, 3)
{
}
public void Iterate()
{
int numberOfPoints = _data.GetLength(1);
int numberOfParameters = _regressionParameters.Length;
double currentResidual = 0.0;
for (int i = 0; i < numberOfPoints; i++)
{
for (int j = 0; j < _observedParameters.Length; j++)
{
_observedParameters[j].Value = _data[j, i];
}
double functionValue = _regressionFunction();
double residual = _data[_observedParameters.Length, i] - functionValue;
_residuals[i, 0] = residual;
currentResidual += residual * residual;
for (int j = 0; j < numberOfParameters; j++)
{
_jacobian[i, j] = _derivatives.ComputePartialDerivative(_regressionFunction, _regressionParameters[j], 1, functionValue);
}
}
for (int i = 0; i < numberOfParameters; i++)
{
_regressionParameters0[i, 0] = _regressionParameters;
}
Matrix matJacobianTrans = _jacobian.Transpose();
Matrix matJTranResid = matJacobianTrans * _residuals;
Matrix matJTranJ = matJacobianTrans * _jacobian;
Matrix matDelta = matJTranJ.SolveFor(matJTranResid); ;
Matrix matNewRegPars = _regressionParameters0 + matDelta;
for (int i = 0; i < numberOfParameters; i++)
{
_regressionParameters.Value = matNewRegPars[i, 0];
}
}
}
}
P.S. Calc 3 was in 1988 for me!
Nope, you're right, no statistics or calculus yet! My schedule is basically trig and statistics in the spring, calculus I this summer. Thanks, I'll forward that to my professor and sit down with him on Tuesday and have him explain it to me.
Nope, you're right, no statistics or calculus yet! My schedule is basically trig and statistics in the spring, calculus I this summer. Thanks, I'll forward that to my professor and sit down with him on Tuesday and have him explain it to me.
I don't think you can get a degree in CS without having implemented this algorithm along the way!!! Any CS prof should be able to write this code off the top of their head!
I don't think you can get a degree in CS without having implemented this algorithm along the way!!! Any CS prof should be able to write this code off the top of their head!
No comment.
just re-plot the graph in excel and try to have excel best fit it. There are other graphical analysis software that will fit curves too, you may have to fiddle and linearize the data first though.
