Ito Calculus with Tensorial

Here is a short example on how to use the Tensorial package for Ito calculus (stochastic calculus)

ito.pdf

Numerical Linear Algebra and Quantum Control

Here is a poster about some of my recently published research

Poster pdf

MathLink example 4: Trace of a complex matrix

In this example, I introduce the ability to treat complex numbers.

-------------------------------------------------------
myTrace.c
-------------------------------------------------------

#include<stdio.h>
#include<string.h>

#include "mathlink.h"
extern void myTrace( void );

void myTrace( void )
{

 int i,j,n;
  
 double *matrix;

 int *dims;
 char **heads;
 int rank; 

 if( !MLGetReal64Array(stdlink,&matrix,&dims,&heads,&rank) ){ 
 // unable to read data

  printf(" MLGetReal64Array error reading data \n");
 };

 n = dims[0];

 double resum=0.;
 double imsum=0.;

 double sum[2];

 int outdims[1];

 char **outheads;
 int outrank = 1; 

 
 for(i=0;i<n;i++){

 resum = resum + matrix[2*i*n + 2*i];

 imsum = imsum + matrix[2*i*n + 2*i + 1];
 }

 
 MLReleaseReal64Array(stdlink,matrix,dims,heads,rank);
 
 MLPutFunction(stdlink,"Complex",2);

 MLPutFloat(stdlink,resum);
 MLPutFloat(stdlink,imsum);


}


#if WINDOWS_MATHLINK

#if __BORLANDC__
#pragma argsused
#endif

int PASCAL WinMain( HINSTANCE hinstCurrent, HINSTANCE hinstPrevious, LPSTR lpszCmdLine, int nCmdShow)
{

 char  buff[512];
 char FAR * buff_start = buff;

 char FAR * argv[32];
 char FAR * FAR * argv_end = argv + 32;

 hinstPrevious = hinstPrevious; /* suppress warning */

 if( !MLInitializeIcon( hinstCurrent, nCmdShow)) return 1;

 MLScanString( argv, &argv_end, &lpszCmdLine, &buff_start);
 return MLMain( (int)(argv_end - argv), argv);
}

#else

int main(int argc, char* argv[])
{

 return MLMain(argc, argv);
}

#endif

-----------------------------------------------------
myTrace.tm
-----------------------------------------------------

:Begin:
:Function:       myTrace

:Pattern:        myTrace[ L_List]
:Arguments:      { L  }
:ArgumentTypes:  { Manual  }
:ReturnType:     Manual

:End:

:Evaluate: myTrace::usage = "myTrace[M] gives the trace of complex matrix M"

------------------------------------------------------
Makefile
------------------------------------------------------

MPREP = /usr/bin/mprep
CXX = /usr/bin/c++

myTrace : myTracetm.c myTrace.c
 ${CXX} myTracetm.c myTrace.c -o myTrace -lML64i3 -lm -lpthread -lrt -lstdc++

myTracetm.c : myTrace.tm
 ${MPREP} myTrace.tm -o $@

---------------------------------------------------
myTrace.nb
---------------------------------------------------

link = Install["./myTrace"]

(m = {{1., 2., 1.}, {2., 2., 2.}, {3., 3., 3.}} + I) // MatrixForm

myTrace[m]

MathLink example 3: Trace of a real matrix

In this example we calculate the trace of a matrix of floating point numbers (double type in C)

---------------------------------------------------
myTrace.c
---------------------------------------------------

#include "mathlink.h"
extern double myTrace( void );

double myTrace( void )
{
 int i,j,n;
  
 double *matrix;
 int *dims;
 char **heads;

 int rank; 

 if( !MLGetReal64Array(stdlink,&matrix,&dims,&heads,&rank) ){ 
 // unable to read data

  return 0.;
 };

 n = dims[0];

 double sum=0;
 for(i=0;i<n;i++) sum = sum + matrix[i*n+i];
 
 MLReleaseReal64Array(stdlink,matrix,dims,heads,rank);

 return sum;
}

#if WINDOWS_MATHLINK

#if __BORLANDC__
#pragma argsused
#endif

int PASCAL WinMain( HINSTANCE hinstCurrent, HINSTANCE hinstPrevious, LPSTR lpszCmdLine, int nCmdShow)
{

 char  buff[512];
 char FAR * buff_start = buff;

 char FAR * argv[32];
 char FAR * FAR * argv_end = argv + 32;

 hinstPrevious = hinstPrevious; /* suppress warning */

 if( !MLInitializeIcon( hinstCurrent, nCmdShow)) return 1;

 MLScanString( argv, &argv_end, &lpszCmdLine, &buff_start);
 return MLMain( (int)(argv_end - argv), argv);
}

#else

int main(int argc, char* argv[])
{

 return MLMain(argc, argv);
}

#endif

----------------------------------------------
myTrace.tm
----------------------------------------------

:Begin:
:Function:       myTrace

:Pattern:        myTrace[ L_List]
:Arguments:      { L  }
:ArgumentTypes:  { Manual  }
:ReturnType:     Real

:End:

:Evaluate: myTrace::usage = "myTrace[M] gives the trace of matrix M"

---------------------------------------------
Makefile
---------------------------------------------

MPREP = /usr/bin/mprep
CXX = /usr/bin/c++

myTrace : myTracetm.c myTrace.c
 ${CXX} myTracetm.c myTrace.c -o myTrace -lML64i3 -lm -lpthread -lrt -lstdc++

myTracetm.c : myTrace.tm
 ${MPREP} myTrace.tm -o $@