I ( [BAJ] ) use a lot of numerical methods in my work and use the Apache Commons Math library (written in Java) in my code.  This term I'm teaching a course in Computer Applications in Chemistry at http://www.umbc.edu and we're using MATLAB for part of it.  That inspired me to think about adding a scriptable interface in the [JTcl Interpreter] to the Apache Commons Math Library.
I whipped up a quick prototype to see if it's feasible.  As the following demo shows it's actually reasonably useful already.  The prototype requires, at least at present, changes in a few core Jacl Java classes.

See http://amath4jtcl.kenai.com/gettingstarted.html for info on getting started with the library.  You can either just use the library (as jar file) or use the a version that embeds JTcl and Commons Math.


Load the utility procs and java code
======
source resource:/tcl/pkg/jtcllib/library/amath/amath.tcl

======




****Vectors and matrices can be created either from Tcl lists:****




======

    #A 2 row by 3 column matrix:

         set m {{1 2 3} {4 5 6}} 

   #A 3 element vector

        set v {1 2 3}
======


****or by using the matrix command.****


======

    # matrix create -rows numberOfRows -col numberOfCols ?-var varName? ?-identity? ?-randn sdevValue? ?-complex?

       set m [matrix create -rows 5 -cols 4 -randn 0.3]
    # or
       matrix create -rows 5 -cols 4 -randn 0.3 -var m

======

using the 2nd form ensures that, in interactive use, the contents of the matrix will
not be converted to a string and displayed in the console, a bad situation for a really 
large matrix.



***The = command***


This command works much like Tcl's built-in expression command (and is in fact derived from it). The "expr" and "=" commands essentially provide a domain-specific language inside of Tcl for performing math.  Some aspects of "=" were inspired by the http://elf.org/etc/tcl-expr-patch.htmll%|%Tcl Expr Patch%|%

There are four main differences that the "=" command has compared to "expr".


   1. There is no need to use braces around the arguments.
   2.  Variables do not need to be prefixed with a "$".
   3. Variables can be math or vector objects
   4. There are additional functions available.

As an example, the equation of a line would be expressed using the "expr" command as:

======
     set y [expr {$a*$x + $b}]
======

whereas with the "=" command it would be:

======
     set y [= a*x + b]
======

Since the arguments to the "=" command can be vectors or matrices one can often eliminate one or more levels of loops in calculations. So using the above equations to calculate the y coordinates for a series of x coordinates in Tcl would be something like:

======
   set xValues {1 2 3 4 5 6}
   set yValues [list]
   foreach x $xValues {
        set y [expr {$a*$x+$b}]
        lappend yValues $y
   }
======
with the "=" command it can be expressed as:
======
   set x {1 2 3 4 5 6}
   set y [= a*x+b]
======


****More examples****


======

source resource:/tcl/pkg/jtcllib/library/amath/amath.tcl
 
 # create vector from Tcl list
 set a {1 2 3}
 
 # Do math on vector (gets converted internally to an Apache Commons RealVector]
 set b [= a*4]
 set c [= a+b]

 # Create matrix with ::amath::matrix command
 
 set myMat [matrix create -rows 3 -cols 3]

 # Create a matrix and do some linear algebra (singular value decomposition)
 set m {{1 2} {3 4}}
 set m [= tr(m)]
 lassign [svd $m] u s v
 set vt [= tr(v)]
 set usvt [= u*s*vt]
 set diffM [= m-usvt]
 set diffNorm [norm $diffM]
 puts $diffNorm

 # Use math function on matrix
 set mlog [= log(m)]
 
 # Element-wise multiplication ( .* operator)
 
 set mElemSq [= m.*m]
 puts $mElemSq

 # use mset command and colon notation to set all elements of the first column to 5
 mset m(:,0) 5

# create a complex value and do some math

set xc {3+4i}

set yc [= 4*xc]
puts $yc

======


<<categories>> Category Java | Category Mathematics