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 ====== <> Category Java | Category Mathematics