Develop Reference

How to use the Nelder Meade Simplex algorithm in mathdotnet for function maximization

In my C# program I have a dataset where each data point consists of:
a stimulus intensity (intensity) as x-coordinate
the percentage of correct response (percentageCorrect) to stimulus as y-coordinate
When the intensity is low percentageCorrect is low. When the intensity is high the percentageCorrect is high. The function graph is an S-shaped curve as the percentageCorrect reaches an asymptote at low and high ends.
I am trying to find the threshold intensity where percentageCorrect is half way between the asymtotes at either end (center of the S-shaped curve)
I understand this to be a function maximization problem that can be solved by the Nelder Meade Simplex algorithm.
I am trying to solve my problem using the Nelder Meade Simplex algorithm in mathdotnet and its IObjectiveFunction parameter.
However, I am having trouble understanding the API of the NedlerMeadeSimplex class FindMinimum method and the IObjectiveFunction EvaluateAt method.
I am new to numerical analysis that is pre-requisite for this question.
Specific questions are:
For the NedlerMeadeSimplex class FindMinimum method what are the initialGuess and initialPertubation parameters?
For the IObjectiveFunction EvaluateAt method, what is the point parameter? I vaguely understand that the point parameter is a datum in the dataset being minimized
How can I map my data set to this API and solve my problem?
Thanks for any guidance on this.

The initial guess is a guess at the model parameters.
I've always used the forms that don't require an entry of the initialPertubation parameter, so I can't help you there.
The objective function is what your are trying to minimize. For example, for a least squares fit, it would calculate the sum of squared areas at the point given in the argument. Something like this:
private double SumSqError(Vector<double> v)
{
double err = 0;
for (int i = 0; i < 100; i++)
{
double y_val = v[0] + v[1] * Math.Exp(v[2] * x[i]);
err += Math.Pow(y_val - y[i], 2);
}
return err;
}
You don't have to supply the point. The algorithm does that over and over while searching for the minimum. Note that the subroutine as access to the vector x.
Here is the code for a test program fitting a function to random data:
private void btnMinFit_Click(object sender, EventArgs e)
{
Random RanGen = new Random();
x = new double[100];
y = new double[100];
// fit exponential expression with three parameters
double a = 5.0;
double b = 0.5;
double c = 0.05;
// create data set
for (int i = 0; i < 100; i++) x[i] = 10 + Convert.ToDouble(i) * 90.0 / 99.0; // values span 10 to 100
for (int i = 0; i < 100; i++)
{
double y_val = a + b * Math.Exp(c * x[i]);
y[i] = y_val + 0.1 * RanGen.NextDouble() * y_val; // add error term scaled to y-value
}
// var fphv = new Func<double, double, double, double>((x, A, B) => A * x + B * x + A * B * x * x); extraneous test
var f1 = new Func<Vector<double>, double>(x => LogEval(x));
var obj = ObjectiveFunction.Value(f1);
var solver = new NelderMeadSimplex(1e-5, maximumIterations: 10000);
var initialGuess = new DenseVector(new[] { 3.0, 6.0, 0.6 });
var result = solver.FindMinimum(obj, initialGuess);
Console.WriteLine(result.MinimizingPoint.ToString());
}

How to correctly calculate Fisher Transform indicator

I'm writing a small technical analysis library that consists of items that are not availabile in TA-lib. I've started with an example I found on cTrader and matched it against the code found in the TradingView version.
Here's the Pine Script code from TradingView:
len = input(9, minval=1, title="Length")
high_ = highest(hl2, len)
low_ = lowest(hl2, len)
round_(val) => val > .99 ? .999 : val < -.99 ? -.999 : val
value = 0.0
value := round_(.66 * ((hl2 - low_) / max(high_ - low_, .001) - .5) + .67 * nz(value[1]))
fish1 = 0.0
fish1 := .5 * log((1 + value) / max(1 - value, .001)) + .5 * nz(fish1[1])
fish2 = fish1[1]
Here's my attempt to implement the indicator:
public class FisherTransform : IndicatorBase
{
public int Length = 9;
public decimal[] Fish { get; set; }
public decimal[] Trigger { get; set; }
decimal _maxHigh;
decimal _minLow;
private decimal _value1;
private decimal _lastValue1;
public FisherTransform(IEnumerable<Candle> candles, int length)
: base(candles)
{
Length = length;
RequiredCount = Length;
_lastValue1 = 1;
}
protected override void Initialize()
{
Fish = new decimal[Series.Length];
Trigger = new decimal[Series.Length];
}
public override void Compute(int startIndex = 0, int? endIndex = null)
{
if (endIndex == null)
endIndex = Series.Length;
for (int index = 0; index < endIndex; index++)
{
if (index == 1)
{
Fish[index - 1] = 1;
}
_minLow = Series.Average.Lowest(Length, index);
_maxHigh = Series.Average.Highest(Length, index);
_value1 = Maths.Normalize(0.66m * ((Maths.Divide(Series.Average[index] - _minLow, Math.Max(_maxHigh - _minLow, 0.001m)) - 0.5m) + 0.67m * _lastValue1));
_lastValue1 = _value1;
Fish[index] = 0.5m * Maths.Log(Maths.Divide(1 + _value1, Math.Max(1 - _value1, .001m))) + 0.5m * Fish[index - 1];
Trigger[index] = Fish[index - 1];
}
}
}
IndicatorBase class and CandleSeries class
Math Helpers
The problem
The output values appear to be within the expected range however my Fisher Transform cross-overs do not match up with what I am seeing on TradingView's version of the indicator.
Question
How do I properly implement the Fisher Transform indicator in C#? I'd like this to match TradingView's Fisher Transform output.
What I Know
I've check my data against other indicators that I have personally written and indicators from TA-Lib and those indicators pass my unit tests. I've also checked my data against the TradingView data candle by candle and found that my data matches as expected. So I don't suspect my data is the issue.
Specifics
CSV Data - NFLX 5 min agg
Pictured below is the above-shown Fisher Transform code applied to a TradingView chart. My goal is to match this output as close as possible.
Fisher Cyan
Trigger Magenta
Expected Outputs:
Crossover completed at 15:30 ET
Approx Fisher Value is 2.86
Approx Trigger Value is 1.79
Crossover completed at 10:45 ET
Approx Fisher Value is -3.67
Approx Trigger Value is -3.10
My Actual Outputs:
Crossover completed at 15:30 ET
My Fisher Value is 1.64
My Trigger Value is 1.99
Crossover completed at 10:45 ET
My Fisher Value is -1.63
My Trigger Value is -2.00
Bounty
To make your life easier I'm including a small console application
complete with passing and failing unit tests. All unit tests are
conducted against the same data set. The passing unit tests are from a
tested working Simple Moving Average indicator. The failing unit
tests are against the Fisher Transform indicator in question.
Project Files (updated 5/14)
Help get my FisherTransform tests to pass and I'll award the bounty.
Just comment if you need any additional resources or information.
Alternative Answers that I'll consider
Submit your own working FisherTransform in C#
Explain why my FisherTransform is actually working as expected

The code has two errors.
1) wrong extra brackets. The correct line is:
_value1 = Maths.Normalize(0.66m * (Maths.Divide(Series.Average[index] - _minLow, Math.Max(_maxHigh - _minLow, 0.001m)) - 0.5m) + 0.67m * _lastValue1);
2) Min and max functions must be:
public static decimal Highest(this decimal[] series, int length, int index)
{
var maxVal = series[index]; // <----- HERE WAS AN ERROR!
var lookback = Math.Max(index - length, 0);
for (int i = index; i-- > lookback;)
maxVal = Math.Max(series[i], maxVal);
return maxVal;
}
public static decimal Lowest(this decimal[] series, int length, int index)
{
var minVal = series[index]; // <----- HERE WAS AN ERROR!
var lookback = Math.Max(index - length, 0);
for (int i = index; i-- > lookback;)
{
//if (series[i] != 0) // <----- HERE WAS AN ERROR!
minVal = Math.Min(series[i], minVal);
}
return minVal;
}
3) confusing test params. Please recheck your unittest values. AFTER THE UPDATE TESTS STILL NOT FIXED. For an example, the first FisherTransforms_ValuesAreReasonablyClose_First() has mixed values
var fish = result.Fish.Last(); //is equal to -3.1113144510775780365063063706
var trig = result.Trigger.Last(); //is equal to -3.6057793808025449204415435710
// TradingView Values for NFLX 5m chart at 10:45 ET
var fisherValue = -3.67m;
var triggerValue = -3.10m;

Convert seconds to hhh:mm:ss in a chart

I have a MsSql database which calculates the timespan between two dates in seconds. That works fine. I use this column afterwards in C# and write them in an array.
This array is the input for a chart later on.
So far this works well, but I cannot find a way to display the seconds in a format like hhh:mm:ss as the timespan can be greater than 24h.
I tried ChartArea.AxisY.LabelStyle.Format = "hhmmss"; but it does not work at all.
Does anybody has an idea how I could do that?
EDIT:
I add the data this way:
chart2.Series.Clear();
chart2.ChartAreas.Clear();
Series BoxPlotSeries = new Series();
ChartArea ChartArea2 = new ChartArea();
ChartArea ChartArea3 = new ChartArea();
chart2.ChartAreas.Add(ChartArea2);
chart2.ChartAreas.Add(ChartArea3);
ChartArea2.Name = "Data Chart Area";
ChartArea3.Name = "BoxPlotArea";
BoxPlotSeries.Name = "BoxPlotSeries";
BoxPlotSeries.ChartType = SeriesChartType.BoxPlot;
BoxPlotSeries.ChartArea = "BoxPlotArea";
chart2.Series.Add(BoxPlotSeries);
Series Input1 = new Series();
Input1.Name = "Input1";
Input1.ChartType = SeriesChartType.Point;
Input1.ChartArea = "Data Chart Area";
chart2.Series.Add(Input1);
chart2.Series["Input1"].Points.DataBindY(InputArray);
chart2.ChartAreas["BoxPlotArea"].AxisX.CustomLabels.Add(2, 0.0, "BoxPlot1");
chart2.Series["BoxPlotSeries"]["BoxPlotSeries"] = "Input1";
chart2.Series["BoxPlotSeries"]["BoxPlotShowMedian"] = "true";
chart2.Series["BoxPlotSeries"]["BoxPlotShowUnusualValues"] = "false";
chart2.Series["BoxPlotSeries"]["PointWidth"] = "0.5";
chart2.Series["BoxPlotSeries"].IsValueShownAsLabel = false;
ChartArea2.Visible = false;
ChartArea3.BackColor = Color.FromArgb(224,224,224);
//I tried to format it this way but it didn't work
//ChartArea3.AxisY.LabelStyle.Format = "{0:HHHmmss}";
chart2.ChartAreas["BoxPlotArea"].AxisX.LabelStyle.Angle = -90;
EDIT2:
And here's how I populate the input array
int[] InputArray = new int[1000000];
int c = 0;
con.Open();
dr = cmd.ExecuteReader();
if (dr.HasRows)
{
while (dr.Read())
{
int n;
if (int.TryParse(dr[0].ToString(),out n) == true)
{
InputArray[c] = Convert.ToInt32(dr[0].ToString());
c++;
}
}
}
if (c == 0) { c = 1; }
Array.Resize(ref InputArray, c - 1);
EDIT 3:
The Boxplot should look like this in the end:
In Excel the format to display hours greater than 24 is called "[h]:mm:ss;#"
EDIT4:
Thanks to #TAW I nearly managed to solve my problem. I made some adjustments to his solution and came up with this:
In the chart code block:
The Value "max" is set before.
ChartArea3.AxisY.MajorTickMark.Interval = addCustomLabels(ChartArea3, BoxPlotSeries, 60 * 60, max);
int addCustomLabels(ChartArea ca, Series series, int interval, int max)
{
int tickNo = 0;
ca.AxisY.CustomLabels.Clear();
if(max / interval > 10)
{
interval = (max / 10) - (max / 10) % (60*30);
tickNo = (max / 10) - (max / 10) % (60*30);
}
if (max / interval <= 2 )
{
interval = (max / 4) - (max / 4) % (60 * 15);
tickNo = (max / 4) - (max / 4) % (60 * 15);
}
for (int i = 0; i < max; i += interval)
{
CustomLabel cl = new CustomLabel();
cl.FromPosition = i - interval / 2;
cl.ToPosition = i + interval / 2;
cl.Text = hhh_mm_ss(i);
ca.AxisY.CustomLabels.Add(cl);
}
return tickNo;
}
My problem is now, that sometimes no axis lable (apart from 0:00) is shown even when the code runs through it without any problems.
Has anybody and idea what could be wrong?

Your task involves two parts:
displaying seconds in the hhh:mm:ss format
putting them as labels on the y-axis
There is no suitable date-time formatting string for this in c#, so we can't make use of the built-in automatic labels and their formatting.
There also no way to use expressions that call a function on the automatic labels, unfortunately.
So we can't use those.
Instead we will have to add CustomLabels. This is not very hard but does take a few steps..
But let's start with a function that converts an int to the hhh:mm:ss string we want; this should do the job:
string hhh_mm_ss(int seconds)
{
int sec = seconds % 60;
int min = ((seconds - sec)/60) % 60;
int hhh = (seconds - sec - 60 * min) / 3600;
return hhh > 0 ? string.Format("{2}:{1:00}:{0:00}", sec, min, hhh)
: min + ":" + sec.ToString("00");
}
Maybe it can be optimized, but for our purpose it'll do.
Next we need to create the CustomLabels. They will replace the normal axis labels and we need to add them in a separate loop over the data after each binding.
One special thing about them is their positioning. Which is smack between two values we need to give them: the FromPosition and ToPosition, both in the unit of the axis-values.
Another difference to normal, automatic Labels is that it is up to us to create as many or few of them as we need..
This function tries to create a number that will go up to the maximum y-value and space the CustomLabels at a given interval:
void addCustomLabels(ChartArea ca, Series series, int interval)
{
// we get the maximum form the 1st y-value
int max = (int)series.Points.Select(x => x.YValues[0]).Max();
// we delete any CLs we have
ca.AxisY.CustomLabels.Clear();
// now we add new custom labels
for (int i = 0; i < max; i += interval)
{
CustomLabel cl = new CustomLabel();
cl.FromPosition = i - interval / 2;
cl.ToPosition = i + interval / 2;
cl.Text = hhh_mm_ss(i);
ca.AxisY.CustomLabels.Add(cl);
}
}
The first parameters to call this are obvious; the last one however is tricky:
You need to decide to interval you want your labels to have. It will depend on various details of your chart:
the range of values
the size of the chart area
the size of the font of the axis
I didn't set any special Font in the function; CustomLabels use the same Font as normal axis labels, i.e. AxisY.LabelStyle.Font.
For my screenshot I prepared the chart like this:
ca.AxisX.Minimum = 0;
ca.AxisY.MajorTickMark.Interval = 60 * 60; // one tick per hour
addCustomLabels(ca, s, 60 * 30); // one label every 30 minutes
I have also added DataPoint Labels for testing to show the values..:
series.Points[p].Label = hhh_mm_ss((int)y) + "\n" + y;
Here is the result:

UPDATE: This answer may be quite useful for other readers, but it pretty much misses the OP's issues. I'll leave it as it stands, but it will not help in creating specially formatted y-axis labels..
Most Chart problems stem from invalid or useless x-values. The following discussion tries to help avoiding or getting around them..
A number is a number and you can't simply display it as a DateTime, or for that matter a TimeSpan.
So you need to add the X-Values as either DateTime or as double that contain values that can be converted to DateTime. The fomer is what I prefer..
So instead of adding the seconds directly add them as offsets from a given DateTime:
Change something like this
series.Points.AddXY(sec, yValues);
To this:
var dt = new DateTime(0).AddSeconds(sec);
series.Points.AddXY(dt, yValues);
Now you can use the date and time formatting strings as needed..:
chartArea.AxisX.LabelStyle.Format = "{mm:ss}";
You could also add them as doubles that actually are calculated from DateTimes via the ToOADate:
series.Points.AddXY(dt.ToOADate(), yValues);
But now you will have to set the ChartValueType.DateTime and probably also AxisX.IntervalType and AxisX.Interval to make sure the chart gets the formatting right..:
s.XValueType = ChartValueType.DateTime;
ca.AxisX.Interval = 5;
ca.AxisX.IntervalType = DateTimeIntervalType.Seconds;
ca.AxisX.LabelStyle.Format = "{mm:ss}";
Pick values that suit your data!
Note that the problem with your original code is that the X-Values internally always are doubles, but the seconds are not integer values in them but fractional parts; so you need some kind of calculation. That's what ToOADate does. Here is a short test that shows what one second actually does amount to as a OADate double :
Best add the X-Values as DateTimes so all further processing can rely on the type..
Update I just saw that you have finally added the real code to your question and that is uses Points.DataBindY. This will not create meaningful X-Values, I'm afraid. Try to switch to Points.DataBindXY! Of course the X-Values you bind to also need to follow the rules I have explained above..!
You can do a loop over your array and convert the numbers like I shown above; here is a simple example:
int[] seconds = new int[5] { 1, 3, 88, 123, 3333 };
double[] oaSeconds = seconds.Select(x => new DateTime(0).AddSeconds(x).ToOADate())
.ToArray();

If you are trying to show more than 2 digits of hour I think this should work for you
//yourTimeSpan is the TimeSpan that you already have
var hoursDouble = Math.Floor(yourTimeSpan.TotalHours);
string hours;
string minutes;
string seconds;
//check hours
if(hoursDouble < 10)
{
hours = string.Format("0{0}", hoursDouble);
}
else
{
hours = hoursDouble.ToString();
}
//check minutes
if (yourTimeSpan.Minutes < 10)
{
minutes = string.Format("0{0}", yourTimeSpan.Minutes);
}
else
{
minutes = yourTimeSpan.Minutes.ToString();
}
//check seconds
if (yourTimeSpan.Seconds < 10)
{
seconds = string.Format("0{0}", yourTimeSpan.Seconds);
}
else
{
seconds = yourTimeSpan.Seconds.ToString();
}
string formattedSpan = String.Format("{0}:{1}:{2}", hours, minutes, seconds);
Update: I think this should solve the problem you were seeing with single digit numbers

FFT Fundamental frequency calculation from LomontFFT

I am using the LomontFFT from http://www.lomont.org/Software/Misc/FFT/LomontFFT.html to get the fundamental frequency from sampled values of a signal. For testing if the fundamental frequency is correctly determined, I have used some samples from past (with known fundamental frequency).
Below is the code I have written to call the LomontFFT algo and determine the FFT:
private void buttonFFT_Click(object sender, EventArgs e)
{
//double fftavg = 0;
double fftmax = 0;
var fftData = new byte[512];
double[] fftValues = Enumerable.Repeat(0.0, 512).ToArray();
Array.Copy(sapmledDoubleValuesADC1, fftValues, sapmledDoubleValuesADC1.Length);
var fftMethod = new Lomont.LomontFFT();
fftMethod.RealFFT(fftValues, true);
for (int i = 0; i < 512; i += 2)
{
double fftmag = Math.Sqrt((fftValues[i] * fftValues[i]) + (fftValues[i + 1] * fftValues[i + 1]));
if (fftmag > fftmax)
fftmax = fftmag;
//fftavg += fftmag;
//fftData[i] = (byte)fftmag;
//fftData[i + 1] = fftData[i];
}
textBoxFundaFreq.Text = "Frey = " + fftmax.ToString();
for (int x = 1; x < 512; x++)
{
this.chart2.Series[0].Points.AddXY(x, fftValues[x]);
}
}
But the problem is the magnitude of the frequency is wrong. The FFT also doesn't match but that is possible as there are multiple solutions, but the frequency should be same. The algo is proven for many years so its definitely not wrong. Am I doing something wrong in calling code?
(I have only real values in sampled data)

Fundamental frequency extraction / pitch detection is not a simple algorithm. For most input signal (anything other than a single sine/cosine wave) the FFT will show several peaks and it is usually better to estimate the distance between this peaks.
Further you need to interpolate the FFT bins to get an acurate result for a single peak.
For most applications it is better to calculate the auto-correlation-function (ACF) anyway.

Creating a graph with relative distance (C#)

I have the following problem. I create a chart with migradoc in c#.
Suppose I have the following points for my xAxis:
20.4, 20.6, 30.6, 100.4, 200.3
The problem is that it sets every xpoint in the series on an equal distance in the chart.
While what I need is a graph who sets the xpoints on a relative distance. For example, the distance between points 20.6 and 30.6 needs to be way smaller than the distance between 30.6 and 100.4. (The points always differ, as do the number of points)
One way to make the distance good is to add extra points between the existing points. For example the first step is 0.2 extra, the second step is 10.0 extra. So I want to add for example 50 extra points between this step, so that the distance is relative the same.
This is the only thing I can come up with, can somebody give me some advice how to accomplish this? (Or another possible solution?)

This method worked out for me. I first made the distances relative:
Int64[] relAfstand = new Int64[afstand.Count()];
for(int i = 0; i < afstand.Count(); i++){
double tussenRel = Convert.ToDouble(afstand[i]);
double eindRel = Convert.ToDouble(afstand[afstand.Count()-1]);
double beginRel = Convert.ToDouble(afstand[0]);
double Rel = (((eindRel - beginRel) - (eindRel - tussenRel)) / (eindRel - beginRel));
relAfstand[i] = Convert.ToInt64((Rel)*100);
}
Then I converted the data to scale with relative with the same factor as the distances:
List<double> ConvertedData = new List<double>();
int c = 0;
int c2 = 1;
double steps = 0;
bool calcSteps = false;
bool calcDistance = false;
for (int i = 0; i < 100; i++) {
if (calcDistance == false) {
distance.Add(i);
}
if (relAfstand[c] == i) {
ConvertedData.Add(data[c]);
calcSteps = false;
c2 = 1;
c++;
}else {
if (calcSteps == false) {
steps = ((data[c] - data[c-1])/(relAfstand[c] - relAfstand[c-1]));
calcSteps = true;
}
ConvertedData.Add(data[c-1] + (steps * c2));
c2++;
}
}
calcDistance = true;
Probably not the best workaround, but it works. Since the percentages can come close together I scale both now with around 200-300 instead of 100.