I am trying to analyse some data using a C# app and need to calculate trend lines. I am aware that there are multiple types of trend line but for now I am trying to calculate exponential growth; I am going to be using it to predict future values. The equation I have been working off is
x(t) = x(0) * ((1+r)^t)
And this is the code that I have written to try and replicate the graph:
public void ExponentialBestFit(List<DateTime> xvalues, List<double> yvalues)
{
//Find the first value of y (The start value) and the first value of x (The start date)
xzero = Convert.ToDouble(xvalues[0].ToOADate());
yzero = yvalues[0];
if (yzero == 0)
yzero += 0.1;
//For every value of x (exluding the 1st value) find the r value
//
// | y | Where t = the time sinse the start time (time period)
//Equation for r = t root|-------| - 1 Where y = the current y value
// | y[0] | Where y[0] = the first y value #IMPROVMENT - Average 1st y value in range
//
double r = 0;
//c is a count of how many r values are added; it is not equal to the count of all the values
int c = 0;
for (int i = 1; i < xvalues.Count; i++)
{
r += Math.Pow(yvalues[i]/yzero, 1/(Convert.ToDouble(xvalues[i].ToOADate()) - xzero)) - 1;
c++;
}
r = r / c;
}
The data I am passing in is over a period of time however the increments in which the time increases are not the same. When I created a chart in excel they use a different formula
x(t) = x(0)*(e^kt)
I think however I have no idea where the k value is being generated from. The two lists that I am passing in are Date and Value and each row in each list corresponds to the same row in the other list. The question is - Is there a better way of creating the equation and variables and are the variables I am getting the most accurate it can be for my data?
This is the c# version of the javascript provided.
// Calculate Exponential Trendline / Growth
IEnumerable<double> Growth(IList<double> knownY, IList<double> knownX, IList<double> newX, bool useConst)
{
// Credits: Ilmari Karonen
// Default values for optional parameters:
if (knownY == null) return null;
if (knownX == null)
{
knownX = new List<double>();
for (var i = 0; i<=knownY.Count; i++)
knownX.Add(i);
}
if (newX == null)
{
newX = new List<double>();
for (var i = 0; i <= knownY.Count; i++)
newX.Add(i);
}
int n = knownY.Count;
double avg_x = 0.0;
double avg_y = 0.0;
double avg_xy = 0.0;
double avg_xx = 0.0;
double beta = 0.0;
double alpha = 0.0;
for (var i = 0; i < n; i++)
{
var x = knownX[i];
var y = Math.Log(knownY[i]);
avg_x += x;
avg_y += y;
avg_xy += x * y;
avg_xx += x * x;
}
avg_x /= n;
avg_y /= n;
avg_xy /= n;
avg_xx /= n;
// Compute linear regression coefficients:
if (useConst)
{
beta = (avg_xy - avg_x * avg_y) / (avg_xx - avg_x * avg_x);
alpha = avg_y - beta * avg_x;
}
else
{
beta = avg_xy / avg_xx;
alpha = 0.0;
}
// Compute and return result array:
return newX.Select(t => Math.Exp(alpha + beta*t)).ToList();
}
The following JavaScript code should help. I used it to implement Excel's GROWTH function. It's written in JavaScript, but porting it to C# should be very easy. Please note that most of it was written by someone else (credits in the code).
function GROWTH(known_y, known_x, new_x, use_const) {
// Credits: Ilmari Karonen
// Default values for optional parameters:
if (typeof(known_x) == 'undefined') {
known_x = [];
for (var i = 1; i <= known_y.length; i++) known_x.push(i);
}
if (typeof(new_x) == 'undefined') {
new_x = [];
for (var i = 1; i <= known_y.length; i++) new_x.push(i);
}
if (typeof(use_const) == 'undefined') use_const = true;
// Calculate sums over the data:
var n = known_y.length;
var avg_x = 0;
var avg_y = 0;
var avg_xy = 0;
var avg_xx = 0;
for (var i = 0; i < n; i++) {
var x = known_x[i];
var y = Math.log(known_y[i]);
avg_x += x;
avg_y += y;
avg_xy += x*y;
avg_xx += x*x;
}
avg_x /= n;
avg_y /= n;
avg_xy /= n;
avg_xx /= n;
// Compute linear regression coefficients:
if (use_const) {
var beta = (avg_xy - avg_x*avg_y) / (avg_xx - avg_x*avg_x);
var alpha = avg_y - beta*avg_x;
} else {
var beta = avg_xy / avg_xx;
var alpha = 0;
}
// Compute and return result array:
var new_y = [];
for (var i = 0; i < new_x.length; i++) {
new_y.push(Math.exp(alpha + beta * new_x[i]));
}
return new_y;
}
Since x(t)=x(0)*e^{kt}, we can take logarithms to get ln x(t)=ln x(0) + kt. This means that to find ln x(0) and k, you can find the least squares fit for the data {(t,ln x(t))}. This will tell you that ln x(t) = b + at, so that k=a and x(0)=e^b.
Related
This question already has answers here:
How to generate random 5 digit number depend on user summary
(2 answers)
Closed 4 years ago.
i have some problem like this.
user(A) enter 500000 to my application and then i want to generate 50 random 5 digit number and when summary 50 random number need to equal 500000, How to do like i tried already but it's not working this is my code
int balane = 500000;
int nums = 50;
int max = balane / nums;
Random rand = new Random();
int newNum = 0;
int[] ar = new int[nums];
for (int i = 0; i < nums - 1; i++)
{
newNum = rand.Next(max);
ar[i] = newNum;
balane -= newNum;
max = balane / (nums - i - 1);
ar[nums - 1] = balane;
}
int check = 0;
foreach (int x in ar)
{
check += x;
}
the result that i tell you not working because in my array list i have value more than 5 digit but the result equal 500000.
How to solve this issue ? Thank you very much.
This works for me
public static void test(int balance = 500000, int nums = 50, int max_digits = 5)
{
int rest = balance;
var max_value = (int)Math.Pow(10, max_digits) - 1;
var rand = new Random();
int[] ar = new int[nums];
for (int i = 0; i < nums - 1; i++)
{
var max = rest / (nums - i);
if (max > max_value) max = max_value;
var newNum = rand.Next(max);
ar[i] = newNum;
rest -= newNum;
}
while (rest > max_value)
{
var all_values_are_max = true;
for (int i = 0; i < nums - 1; i++)
{
if (ar[i] < max_value)
{
var d = (int)((max_value - ar[i]) / 10.0); // 10% increase
ar[i] += d;
rest -= d;
all_values_are_max = false;
}
}
if (all_values_are_max)
throw new Exception("This is not possible at all!");
}
while (rest < 0)
{
for (int i = 0; i < nums - 1; i++)
{
if (ar[i] > 0)
{
var d = (int)(ar[i] / 20.0); // %5 decrease
ar[i] -= d;
rest += d;
}
}
}
ar[nums - 1] = rest;
int check_sum = 0;
foreach (int x in ar)
{
check_sum += x;
if (x > max_value || x < 0)
MessageBox.Show("wrong value");
}
if (check_sum != balance)
MessageBox.Show("Error: sum is " + check_sum);
MessageBox.Show("ok");
}
For example, test(500000,50) works fine all times, but test(500000, 5) throw an exception, because is not possible
Perhaps try this:
var rnd = new Random();
var numbers = Enumerable.Range(0, 50).Select(x => rnd.Next(500_000)).OrderBy(x => x).ToArray();
numbers = numbers.Skip(1).Zip(numbers, (x1, x0) => x1 - x0).ToArray();
numbers = numbers.Append(500_000 - numbers.Sum()).ToArray();
Console.WriteLine(numbers.Count());
Console.WriteLine(numbers.Sum());
This outputs:
50
500000
This works by generating 50 random numbers between 0 and 499,999 inclusively. It then sorts them ascendingly and then gets the difference between each successive pair. This by definition produces a set of 49 values that almost adds up to 500,000. It's then just a matter of adding the one missing number by doing 500_000 - numbers.Sum().
I am calculating values by using weights and bias from MATLAB trained ANN. trying to code a sigmoid simulation equation, but for some reason C# calculations vary too much than that of MATLAB. i.e. error is too high. I tried to check each step of the equation and found out the specific part that is creating the problem (Emphasized part), but I don't know how to solve this issue, if someone could help, would be a huge favour.
1+(purelin(net.LW{2}×(tansig(net.IW{1}×(1-(abs(2×([inputs]-1)))))+net.b{1}))+net.b{2}))/2
//Normalization of Data
public double Normalization(double x, double xMAx, double xMin)
{
double xNorm = 0.0;
xNorm = (x - xMin) / (xMAx - xMin);
if (xNorm < 0)
xNorm = 0;
if (xNorm > 1)
xNorm = 1;
xNorm = Math.Round(xNorm, 4);
return xNorm;
}
// Equation to calculate ANN based Output Values
public double MetrixCalc(double[] Pn, double[,] W1, double[] W2, double[] b1, double b2, double maxValue, double minValue)
{
double FinalValue = 0;
double[] PnCalc1 = new double[Pn.Length];
double[] PnCalc2 = new double[W1.Length / Pn.Length];
for (int i = 0; i < Pn.Length; i++)
{
PnCalc1[i] = 1 - Math.Abs(2 * (Pn[i] - 1));
}
for (int i = 0; i < (W1.Length / Pn.Length); i++)
{
double PnCalc = 0.0;
for (int j = 0; j < Pn.Length; j++)
{
PnCalc = PnCalc + (W1[i, j] * PnCalc1[j]);
}
PnCalc2[i] = PnCalc;
}
for (int i = 0; i < PnCalc2.Length; i++)
{
//PnCalc2[i] = Math.Tanh(PnCalc2[i] + b1[i]);
PnCalc2[i] = PnCalc2[i] + b1[i];
PnCalc2[i] = 2.0 / (1 + Math.Exp(-2 * (PnCalc2[i]))) - 1;
PnCalc2[i] = Math.Round(PnCalc2[i], 4);
}
double FinalCalc = 0.0;
for (int i = 0; i < PnCalc2.Length; i++)
{
*FinalCalc = FinalCalc + (W2[i] * (PnCalc2[i]));*
//FinalValue = FinalCalc;
}
FinalValue = FinalCalc + b2;
FinalValue = 1 + FinalValue;
FinalValue = (1 + FinalValue) / 2.0;
FinalValue = (FinalValue * (maxValue - minValue)) + minValue;
FinalValue = Math.Round(FinalValue, 4);
FinalValue = Math.Abs(FinalValue);
return FinalValue;
}
Problem is solved.
Problem was with the weights matrix copied from MATLAB. debugging mode saved my life. :)
I got an array of data voltages and I want to get the RMS value from the FFT that has been applied before to that data. I've seen that RMS in time domain should be equal to RMS(fft) / sqrt(nFFT) from Parseval's Theorem, but gives me different results. I'm using these functions:
1)FFT
public static VectorDPoint FFT(double[] trama, double samplingFreq)
{
double fs = samplingFreq; // Sampling frequency
double t1 = 1 / fs; // Sample time
int l = trama.Length; // Length of signal
// Time vector
//Vector t = Normal(0, l, 1) * t1;
//// Values vector
//Vector y = new Vector(trama);
// We just use half of the data as the other half is simetric. The middle is found in NFFT/2 + 1
int nFFT = (int)Math.Pow(2, NextPow2(l));
if (nFFT > 655600)
{ }
// Create complex array for FFT transformation. Use 0s for imaginary part
Complex[] samples = new Complex[nFFT];
for (int i = 0; i < nFFT; i++)
{
if (i >= trama.Length)
{
samples[i] = new MathNet.Numerics.Complex(0, 0);
}
else
{
samples[i] = new MathNet.Numerics.Complex(trama[i], 0);
}
}
ComplexFourierTransformation fft = new ComplexFourierTransformation(TransformationConvention.Matlab);
fft.TransformForward(samples);
ComplexVector s = new ComplexVector(samples);
s = s / l;
Vector f = (fs / 2.0) * Linspace(0, 1, (nFFT / 2) + 1);
VectorDPoint result = new VectorDPoint();
for (int i = 0; i < (nFFT / 2) + 1; i++)
{
result.Add(new DPoint(f[i], 2 * s[i].Modulus));
}
s = null;
f = null;
samples = null;
return result;
2) RMS
public static double RMSCalculate(double[] channelValues, int samplesNumber, double sampleRate, DateTime currentDate)
{
double[] times = new double[channelValues.Length];
double sampleTime = 0.0;
double period = 0;
times[0] = currentDate.Second + currentDate.Millisecond / 1000.0;
sampleTime = 1 / sampleRate; //s
// Limited samples
for (int i = 1; i < channelValues.Length; i++)
{
times[i] = times[i - 1] + sampleTime;
}
DPoint RMSValues = new DPoint();
RMSValues.Y = 0;
if (channelValues.Length == 1)
{
double x = channelValues[0];
double y = channelValues[0];
RMSValues = new DPoint(x, Math.Abs(y));
}
else
{
for (int i = 0; i < times.Length - 1; i++)
{
period = 0;
if (i + 1 < times.Length)
{
RMSValues.Y += channelValues[i + 1] * channelValues[i + 1] * (times[i + 1] - times[i]);
}
}
period = times[times.Length - 1] - times[0];
RMSValues.Y = RMSValues.Y / period;
RMSValues.Y = Math.Sqrt(RMSValues.Y);
}
return RMSValues.Y;
}
I'm getting x,y,z values from gyro-sensor. Each variable is being sent 10 values per second. In 3 seconds I have;
x=[30values]
y=[30values]
z=[30values]
Some of the values are too different from the others cause of noise. With laplace transform I need to get the most frequent value from my array.
I need to filter the array with Laplace Transform equation. I need to build the equation in C#. How can I implement the array with the equation?
Since this kind of filter (Laplace) is very specialized to certain area of Engineering and needs a person who has good understanding on both the programming language (in this case is C#) and the filter itself, I would recommend you to use such source, rather than code the filter by yourself.
Here is the snippet of the source code:
class Laplace
{
const int DefaultStehfest = 14;
public delegate double FunctionDelegate(double t);
static double[] V; // Stehfest coefficients
static double ln2; // log of 2
public static void InitStehfest(int N)
{
ln2 = Math.Log(2.0);
int N2 = N / 2;
int NV = 2 * N2;
V = new double[NV];
int sign = 1;
if ((N2 % 2) != 0)
sign = -1;
for (int i = 0; i < NV; i++)
{
int kmin = (i + 2) / 2;
int kmax = i + 1;
if (kmax > N2)
kmax = N2;
V[i] = 0;
sign = -sign;
for (int k = kmin; k <= kmax; k++)
{
V[i] = V[i] + (Math.Pow(k, N2) / Factorial(k)) * (Factorial(2 * k)
/ Factorial(2 * k - i - 1)) / Factorial(N2 - k)
/ Factorial(k - 1) / Factorial(i + 1 - k);
}
V[i] = sign * V[i];
}
}
public static double InverseTransform(FunctionDelegate f, double t)
{
double ln2t = ln2 / t;
double x = 0;
double y = 0;
for (int i = 0; i < V.Length; i++)
{
x += ln2t;
y += V[i] * f(x);
}
return ln2t * y;
}
public static double Factorial(int N)
{
double x = 1;
if (N > 1)
{
for (int i = 2; i <= N; i++)
x = i * x;
}
return x;
}
}
coded by Mr. Walt Fair Jr. in CodeProject.
I have got this method to get a polynomial with my desired degree:
public static double[] Polyfit(double[] x, double[] y, int degree)
{
// Vandermonde matrix
var v = new DenseMatrix(x.Length, degree + 1);
for (int i = 0; i < v.RowCount; i++)
for (int j = 0; j <= degree; j++) v[i, j] = Math.Pow(x[i], j);
var yv = new DenseVector(y).ToColumnMatrix();
QR qr = v.QR();
// Math.Net doesn't have an "economy" QR, so:
// cut R short to square upper triangle, then recompute Q
var r = qr.R.SubMatrix(0, degree + 1, 0, degree + 1);
var q = v.Multiply(r.Inverse());
var p = r.Inverse().Multiply(q.TransposeThisAndMultiply(yv));
Console.WriteLine(p.Column(0).ToString());
return p.Column(0).ToArray();
}
How can I feed the method above with values from my chart (x and y)?
chart.Series[0].Points.... ?
I think you need this:
chart1.Series[0].YValueMembers
chart1.Series[0].XValueMember
The Points property is a getter, so you cannot set a new instance of DataPointCollection to it. You should however be able to access methods on the current DataPointCollection.
You could try something along the lines of:
chart.Series[0].Points.AddXY(double, double)
You would then iterate the array(s) and set the points manually.
MSDN DataPointCollection for more information.
A working solution is:
////generate polynomial of degree 4 fiting to the points
double[] arrayX = new double[chart.Series[0].Points.Count()];
double[] arrayY = new double[chart.Series[0].Points.Count()];
double[] arrayResult = { };
for (int i = 0; i < chart.Series[0].Points.Count(); i++)
{
arrayX[i] = chart.Series[0].Points[i].XValue;
arrayY[i] = chart.Series[0].Points[i].YValues[0];
}
arrayResult = Polyfit(arrayX, arrayY, 4);
foreach (double element in arrayResult)
{
MessageBox.Show(element.ToString());
}
double functionVarE = arrayResult[0];
double functionVarD = arrayResult[1];
double functionVarC = arrayResult[2];
double functionVarB = arrayResult[3];
double functionVarA = arrayResult[4];
double equationVar = 0;
//prepare the function series in the graph
if (chart.Series.IndexOf("function") < 0)
chart.Series.Add("function");
chart.Series[2].Points.Clear();
chart.Series[2].ChartType = SeriesChartType.Line;
for (int x = -500; x < 1000; x++) //hardcoding
{
equationVar = functionVarA * (Math.Pow(x, 4)) + functionVarB * (Math.Pow(x, 3)) + functionVarC * (Math.Pow(x, 2)) + functionVarD * x + functionVarE;
chart.Series[2].Points.AddXY(Convert.ToDouble(x), equationVar);
}
This is a working solution I coded. If you see any improvement feel free to tell me!