C# Math Library
Updated: April 14th, 2015 (06:11 AM) Views / Replies: 16,388 / 15
Created: March 18th, 2010 (09:30 AM) by MXASJ Attachments: 1

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January 9th, 2012, 07:22 AM
#11 (permalink )
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Here's the ALGLIB file. It's a NinjaTrader "Indicator", but it's just the entire ALGLIB 3.4 C# math library merged into a single file, put into a namespace called "ALGLIB". It's callable from strategies also.
I don't have time right now to give much of an example, but below are some static examples of matrix operations (least-squares fit, matrix multiplication, inverse, pseudoinverse, left divide & right divide, an OLS routine originally from MATLAB, and some helper routines). This (static) approach is easy to use (no instantiation required); it's fine for indicators but it falls down if you use it in a strategy which you run through the optimizer. That's because "new" is computationally expensive in C#, if you do "new" repeatedly it hits your performance and fills up all your memory. The alternative is to instantiate classes which allocate storage once and then re-use it, which helps a lot but it's more complicated and you still can eventually hit a wall for other reasons.
The code below is a bunch of copy & pastes; I think everything needed to compile it is here, but I haven't tested to be sure.
To use it:
Code
using ALGLIB;
public static void lsfitlinear(double[] y, double[,] x, out double[] beta)
{
int nobs = y.Length;
if (nobs != x.GetLength(0))
throw new ArgumentException("ols: y and x must have same length");
int nvar = x.GetLength(1);
int info;
alglib.lsfitreport rep;
alglib.lsfitlinear(y, x, nobs, nvar, out info, out beta, out rep);
}
public static double[,] mtimes(double[,] a, double[,] b, bool transposeA, bool transposeB)
{
int ra = a.GetLength(transposeA ? 1 : 0);
int ca = a.GetLength(transposeA ? 0 : 1);
int cb = b.GetLength(transposeB ? 0 : 1);
if (ca != b.GetLength(transposeB ? 1 : 0))
throw new ArgumentException("mtimes: columns(matrix a) must equal rows(matrix b)");
double [,] output = new double[ra,cb];
alglib.ablas.rmatrixgemm(ra,cb,ca,1,a,0,0,transposeA ? 1 : 0,b,0,0,transposeB ? 1 : 0,0,ref output,0,0);
return output;
}
public static double[,] inverse(double[,] a)
{
if (a.GetLength(0) != a.GetLength(1))
throw new ArgumentException("inverse: matrix must be square");
double[,] output = copy(a);
alglib.matinv.matinvreport rep = new alglib.matinv.matinvreport();
int info = new int();
alglib.matinv.rmatrixinverse(ref output,output.GetLength(0),ref info,rep);
return output;
}
public static double[,] copy(double[,] a)
{ // create a copy of a matrix
int r = a.GetLength(0);
int c = a.GetLength(1);
double[,] output = new double[r,c];
for (int i=0; i < r; i++)
{
for (int j=0; j < c; j++)
{
output[i,j] = a[i,j];
}
}
return output;
}
public static double[,] pseudoinverse(double[,] a)
{
int r = a.GetLength(0);
int c = a.GetLength(1);
int minrc = Math.Min(r,c);
double[] w = new double[minrc];
double[,] winv = new double[minrc,minrc];
double[,] u = new double[r,minrc];
double[,] vt = new double[minrc,c];
double[,] temp = new double[c,minrc];
double[,] output = new double[c,r];
alglib.svd.rmatrixsvd(a,r,c,1,1,2,ref w,ref u, ref vt);
// generate inverse winv of matrix W from the vector w from SVD
// to do this we transpose the matrix, and take the inverse of each vector element
// see: http://en.wikipedia.org/wiki/Singular_value_decomposition
// http://www.alglib.net/matrixops/general/svd.php
for (int i = 0; i < minrc; i++)
{
for (int j = 0; j < minrc; j++)
{
winv[i,j] = ((i == j) && (w[i] > alglib.math.machineepsilon)) ? 1.0/w[i] : 0.0; // inverse of w
}
}
alglib.ablas.rmatrixgemm(c,minrc,minrc,1,vt,0,0,1,winv,0,0,0,0,ref temp,0,0);
alglib.ablas.rmatrixgemm(c,r,minrc,1,temp,0,0,0,u,0,0,1,0,ref output,0,0);
return output;
}
public static double[,] mldivide(double[,] a, double[,] b)
{ // matrix left divide: inv(a)*b
int r = a.GetLength(0);
if (r != b.GetLength(0))
throw new ArgumentException ("mldivide: both matrices must have the same number of rows");
int ca = a.GetLength(1);
int cb = b.GetLength(1);
double[,] output = new double[ca,cb];
alglib.ablas.rmatrixgemm(ca,cb,r,1,pseudoinverse(a),0,0,0,b,0,0,0,0,ref output,0,0);
return output;
}
public static double[,] mrdivide(double[,] b, double[,] a)
{ // matrix right divide: b*inv(a)
int c = a.GetLength(1);
if (c != b.GetLength(1))
throw new ArgumentException ("mrdivide: both matrices must have the same number of columns");
int ra = a.GetLength(0);
int rb = b.GetLength(0);
double[,] output = new double[rb,ra];
alglib.ablas.rmatrixgemm(rb,ra,c,1,b,0,0,0,pseudoinverse(a),0,0,0,0,ref output,0,0);
return output;
}
public static void ols(double[] y, double[,] x, out double[] beta, out double[] yhat, out double[] residuals, out double sige, out double rsqr, out double rbar /*, out double[] tstats, out double[] bstd, out double dw*/)
{
// function results=ols(y,x)
// % PURPOSE: least-squares regression
// %---------------------------------------------------
// % USAGE: results = ols(y,x)
// % where: y = dependent variable vector (nobs x 1)
// % x = independent variables matrix (nobs x nvar)
// %---------------------------------------------------
// % RETURNS: a structure
// % results.meth = 'ols'
// % results.beta = bhat (nvar x 1)
// % results.tstat = t-stats (nvar x 1)
// % results.bstd = std deviations for bhat (nvar x 1)
// % results.yhat = yhat (nobs x 1)
// % results.resid = residuals (nobs x 1)
// % results.sige = e'*e/(n-k) scalar
// % results.rsqr = rsquared scalar
// % results.rbar = rbar-squared scalar
// % results.dw = Durbin-Watson Statistic
// % results.nobs = nobs
// % results.nvar = nvars
// % results.y = y data vector (nobs x 1)
// % results.bint = (nvar x2 ) vector with 95% confidence intervals on beta
// %---------------------------------------------------
int nobs = y.Length;
if (nobs != x.GetLength(0))
throw new ArgumentException("ols: y and x must have same length");
int nvar = x.GetLength(1);
int info;
yhat = new double[nobs];
alglib.lsfitreport rep;
alglib.lsfitlinear(y,x,nobs,nvar,out info, out beta, out rep); // least squares fit
alglib.ablas.rmatrixmv(x.GetLength(0),x.GetLength(1),x,0,0,0,beta,0,ref yhat,0); // calculate yhat (predicted values of Y)
residuals = minus(y,yhat);
double sigu = mtimes(residuals,residuals);
sige = sigu/System.Convert.ToDouble(nobs-nvar);
double[] ym = minus(y,mean(y));
double rsqr1 = sigu;
double rsqr2 = mtimes(ym,ym);
rsqr = 1.0 - rsqr1/rsqr2; // r-squared
rsqr1 = rsqr1/System.Convert.ToDouble(nobs-nvar);
rsqr2 = rsqr2/System.Convert.ToDouble(nobs-1);
rbar = rsqr2 == 0 ? rsqr : 1.0 - rsqr1/rsqr2;
// bstd, dw, tstat, bint not implemented
}
public static double mtimes(double[] x, double[] y)
{ // multiply 2 vectors (matrix multiply on 1-row and 1-col matrices)
int lx = x.Length;
if (lx != y.Length)
throw new ArgumentException("mtimes - input vectors must have the same length");
double output = 0;
for (int i = 0; i < lx; i++)
output += x[i] * y[i];
return output;
}
public static double mean(double[] x)
{ // mean of a vector
int len = x.Length;
double output = 0;
for (int i = 0; i < len; i++)
output += x[i];
return output / len;
}
public static double[] minus(double[] x, double[] y)
{ // subtract 2 vectors (element by element)
int len = x.Length;
if (len != y.Length)
{
if (y.Length == 1)
return minus(x,y[0]);
else
throw new ArgumentException("minus - input vectors must have the same length");
}
double[] output = new double[len];
for (int i = 0; i < len; i++)
{
output[i] = x[i] - y[i];
}
return output;
}
public static double[] minus(double[] x, double y)
{ // subtract a scalar from a vector
int len = x.Length;
double[] output = new double[len];
for (int i = 0; i < len; i++)
{
output[i] = x[i] - y;
}
return output;
}

Last edited by kevind; January 9th, 2012 at 10:27 PM .

The following 6 users say Thank You to kevind for this post:

April 10th, 2015, 08:22 AM
#12 (permalink )
Elite Member

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1
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kevind
Here's the ALGLIB file. It's a

NinjaTrader "Indicator", but it's just the entire ALGLIB 3.4 C# math library merged into a single file, put into a namespace called "ALGLIB". It's callable from strategies also.

I don't have time right now to give much of an example, but below are some static examples of matrix operations (least-squares fit, matrix multiplication, inverse, pseudoinverse, left divide & right divide, an OLS routine originally from MATLAB, and some helper routines). This (static) approach is easy to use (no instantiation required); it's fine for indicators but it falls down if you use it in a strategy which you run through the optimizer. That's because "new" is computationally expensive in C#, if you do "new" repeatedly it hits your performance and fills up all your memory. The alternative is to instantiate classes which allocate storage once and then re-use it, which helps a lot but it's more complicated and you still can eventually hit a wall for other reasons.

The code below is a bunch of copy & pastes; I think everything needed to compile it is here, but I haven't tested to be sure.

To use it:

Code
using ALGLIB;
public static void lsfitlinear(double[] y, double[,] x, out double[] beta)
{
int nobs = y.Length;
if (nobs != x.GetLength(0))
throw new ArgumentException("ols: y and x must have same length");
int nvar = x.GetLength(1);
int info;
alglib.lsfitreport rep;
alglib.lsfitlinear(y, x, nobs, nvar, out info, out beta, out rep);
}
public static double[,] mtimes(double[,] a, double[,] b, bool transposeA, bool transposeB)
{
int ra = a.GetLength(transposeA ? 1 : 0);
int ca = a.GetLength(transposeA ? 0 : 1);
int cb = b.GetLength(transposeB ? 0 : 1);
if (ca != b.GetLength(transposeB ? 1 : 0))
throw new ArgumentException("mtimes: columns(matrix a) must equal rows(matrix b)");
double [,] output = new double[ra,cb];
alglib.ablas.rmatrixgemm(ra,cb,ca,1,a,0,0,transposeA ? 1 : 0,b,0,0,transposeB ? 1 : 0,0,ref output,0,0);
return output;
}
public static double[,] inverse(double[,] a)
{
if (a.GetLength(0) != a.GetLength(1))
throw new ArgumentException("inverse: matrix must be square");
double[,] output = copy(a);
alglib.matinv.matinvreport rep = new alglib.matinv.matinvreport();
int info = new int();
alglib.matinv.rmatrixinverse(ref output,output.GetLength(0),ref info,rep);
return output;
}
public static double[,] copy(double[,] a)
{ // create a copy of a matrix
int r = a.GetLength(0);
int c = a.GetLength(1);
double[,] output = new double[r,c];
for (int i=0; i < r; i++)
{
for (int j=0; j < c; j++)
{
output[i,j] = a[i,j];
}
}
return output;
}
public static double[,] pseudoinverse(double[,] a)
{
int r = a.GetLength(0);
int c = a.GetLength(1);
int minrc = Math.Min(r,c);
double[] w = new double[minrc];
double[,] winv = new double[minrc,minrc];
double[,] u = new double[r,minrc];
double[,] vt = new double[minrc,c];
double[,] temp = new double[c,minrc];
double[,] output = new double[c,r];
alglib.svd.rmatrixsvd(a,r,c,1,1,2,ref w,ref u, ref vt);
// generate inverse winv of matrix W from the vector w from SVD
// to do this we transpose the matrix, and take the inverse of each vector element
// see: http://en.wikipedia.org/wiki/Singular_value_decomposition
// http://www.alglib.net/matrixops/general/svd.php
for (int i = 0; i < minrc; i++)
{
for (int j = 0; j < minrc; j++)
{
winv[i,j] = ((i == j) && (w[i] > alglib.math.machineepsilon)) ? 1.0/w[i] : 0.0; // inverse of w
}
}
alglib.ablas.rmatrixgemm(c,minrc,minrc,1,vt,0,0,1,winv,0,0,0,0,ref temp,0,0);
alglib.ablas.rmatrixgemm(c,r,minrc,1,temp,0,0,0,u,0,0,1,0,ref output,0,0);
return output;
}
public static double[,] mldivide(double[,] a, double[,] b)
{ // matrix left divide: inv(a)*b
int r = a.GetLength(0);
if (r != b.GetLength(0))
throw new ArgumentException ("mldivide: both matrices must have the same number of rows");
int ca = a.GetLength(1);
int cb = b.GetLength(1);
double[,] output = new double[ca,cb];
alglib.ablas.rmatrixgemm(ca,cb,r,1,pseudoinverse(a),0,0,0,b,0,0,0,0,ref output,0,0);
return output;
}
public static double[,] mrdivide(double[,] b, double[,] a)
{ // matrix right divide: b*inv(a)
int c = a.GetLength(1);
if (c != b.GetLength(1))
throw new ArgumentException ("mrdivide: both matrices must have the same number of columns");
int ra = a.GetLength(0);
int rb = b.GetLength(0);
double[,] output = new double[rb,ra];
alglib.ablas.rmatrixgemm(rb,ra,c,1,b,0,0,0,pseudoinverse(a),0,0,0,0,ref output,0,0);
return output;
}
public static void ols(double[] y, double[,] x, out double[] beta, out double[] yhat, out double[] residuals, out double sige, out double rsqr, out double rbar /*, out double[] tstats, out double[] bstd, out double dw*/)
{
// function results=ols(y,x)
// % PURPOSE: least-squares regression
// %---------------------------------------------------
// % USAGE: results = ols(y,x)
// % where: y = dependent variable vector (nobs x 1)
// % x = independent variables matrix (nobs x nvar)
// %---------------------------------------------------
// % RETURNS: a structure
// % results.meth = 'ols'
// % results.beta = bhat (nvar x 1)
// % results.tstat = t-stats (nvar x 1)
// % results.bstd = std deviations for bhat (nvar x 1)
// % results.yhat = yhat (nobs x 1)
// % results.resid = residuals (nobs x 1)
// % results.sige = e'*e/(n-k) scalar
// % results.rsqr = rsquared scalar
// % results.rbar = rbar-squared scalar
// % results.dw = Durbin-Watson Statistic
// % results.nobs = nobs
// % results.nvar = nvars
// % results.y = y data vector (nobs x 1)
// % results.bint = (nvar x2 ) vector with 95% confidence intervals on beta
// %---------------------------------------------------
int nobs = y.Length;
if (nobs != x.GetLength(0))
throw new ArgumentException("ols: y and x must have same length");
int nvar = x.GetLength(1);
int info;
yhat = new double[nobs];
alglib.lsfitreport rep;
alglib.lsfitlinear(y,x,nobs,nvar,out info, out beta, out rep); // least squares fit
alglib.ablas.rmatrixmv(x.GetLength(0),x.GetLength(1),x,0,0,0,beta,0,ref yhat,0); // calculate yhat (predicted values of Y)
residuals = minus(y,yhat);
double sigu = mtimes(residuals,residuals);
sige = sigu/System.Convert.ToDouble(nobs-nvar);
double[] ym = minus(y,mean(y));
double rsqr1 = sigu;
double rsqr2 = mtimes(ym,ym);
rsqr = 1.0 - rsqr1/rsqr2; // r-squared
rsqr1 = rsqr1/System.Convert.ToDouble(nobs-nvar);
rsqr2 = rsqr2/System.Convert.ToDouble(nobs-1);
rbar = rsqr2 == 0 ? rsqr : 1.0 - rsqr1/rsqr2;
// bstd, dw, tstat, bint not implemented
}
public static double mtimes(double[] x, double[] y)
{ // multiply 2 vectors (matrix multiply on 1-row and 1-col matrices)
int lx = x.Length;
if (lx != y.Length)
throw new ArgumentException("mtimes - input vectors must have the same length");
double output = 0;
for (int i = 0; i < lx; i++)
output += x[i] * y[i];
return output;
}
public static double mean(double[] x)
{ // mean of a vector
int len = x.Length;
double output = 0;
for (int i = 0; i < len; i++)
output += x[i];
return output / len;
}
public static double[] minus(double[] x, double[] y)
{ // subtract 2 vectors (element by element)
int len = x.Length;
if (len != y.Length)
{
if (y.Length == 1)
return minus(x,y[0]);
else
throw new ArgumentException("minus - input vectors must have the same length");
}
double[] output = new double[len];
for (int i = 0; i < len; i++)
{
output[i] = x[i] - y[i];
}
return output;
}
public static double[] minus(double[] x, double y)
{ // subtract a scalar from a vector
int len = x.Length;
double[] output = new double[len];
for (int i = 0; i < len; i++)
{
output[i] = x[i] - y;
}
return output;
}

Great stuff.
Do you have an example how I could create a forward moving OLS indicator, based on say 20 bars i.e calculates the coefficients on the last 20 bars, moves forward a bar and calculates for the next 20 and so on? I'll build on that. Thanks.

April 13th, 2015, 02:26 PM
#13 (permalink )
Elite Member

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Farmer George
Great stuff.
Do you have an example how I could create a forward moving OLS indicator, based on say 20 bars i.e calculates the coefficients on the last 20 bars, moves forward a bar and calculates for the next 20 and so on? I'll build on that. Thanks.

George, what platform / language are you using? Data-series are a native object to Ninjatrader .
If you are building your own app, the quickest way to go about this would be to include a time-series library in to your project.
If using C# or F#, check out Deedle
If using python, check out pandas
They both have examples of deriving rolling bar calculations.

April 13th, 2015, 02:54 PM
#14 (permalink )
Elite Member

Krakow Poland

Futures Experience: Intermediate

Platform: NinjaTrader

Favorite Futures: Stocks

Posts: 19 since Oct 2014

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1
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baywolf
George, what platform / language are you using? Data-series are a native object to

Ninjatrader .

If you are building your own app, the quickest way to go about this would be to include a time-series library in to your project.

If using C# or F#, check out

Deedle
If using python, check out

pandas
They both have examples of deriving rolling bar calculations.

Baywolf, many thanks for that, appreciated.
I'm on fast learning curve with C#. I will use NinjaScript to create an indicator with a rolling Beta , regressing a share's returns on the 'market' returns. Also, I'll estimate and look at the hedge ratio between pairs of stocks/segments. I still think that there may be opportunities in pairs trading .
George

April 13th, 2015, 10:56 PM
#15 (permalink )
Trading Apprentice

Toronto, Canada

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How about looking at the GNU/GSL library!!

April 14th, 2015, 06:11 AM
#16 (permalink )
Elite Member

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Platform: NinjaTrader

Favorite Futures: Stocks

Posts: 19 since Oct 2014

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received

markmycoin
How about looking at the GNU/GSL library!!

Ok, thanks. Had a quick look. Presumably one can get C# code?

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