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 [JTcl] 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
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source resource:/tcl/pkg/jtcllib/library/amath/amath.tcl
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****Vectors and matrices can be created either from Tcl lists:****
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#A 2 row by 3 column matrix:
set m {{1 2 3} {4 5 6}}
#A 3 element vector
set v {1 2 3}
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****or by using the matrix command.****
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# 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
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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 "$".
3. Variables can be math or vector objects
4. There are additional functions available.
As an example, the equation of a line would be expressed using the "expr" command as:
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set y [expr {$a*$x + $b}]
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whereas with the "=" command it would be:
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set y [= a*x + b]
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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:
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set xValues {1 2 3 4 5 6}
set yValues [list]
foreach x $xValues {
set y [expr {$a*$x+$b}]
lappend yValues $y
}
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with the "=" command it can be expressed as:
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set x {1 2 3 4 5 6}
set y [= a*x+b]
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****More examples****
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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
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<> Category Java | Category Mathematics