**VecTcl ** is a package for efficiently doing numerical processing in Tcl using a natural syntax close to that of NumPy and Matlab.

It was presented at EuroTcl in 2014: PDF of presentation slides here

The internal representation of values is syntactically compatible with lists (and nested lists, and …) but is optimised internally for the case where all elements are of the same, numeric type.

In VecTcl, there is no distinction between a Tcl list and a vector or matrix. They are created by setting a variable with a list of doubles:

# create a vector set x { 1 2 3 } # create a matrix set A {{1.0 2.0 3.0} {4.0 5.0 6.0} {7.0 8.0 9.0}}

Of course, list commands such as list, lappend, linsert, lrepeat etc. can also be used. To evaluate an expression involving vector operations, pass the expression to vexpr:

vexpr { A*x } ;# compute the matrix-vector product # 14.0 32.0 50.0

In order for this to work, you must first load the package and import the commands:

package require vectcl namespace import vectcl::*

Vectors can contain integers, floating-point values or complex numbers:

set x {1 2 3} ;# an integer vector set y {2.0 3.0 5.0} ;# a floating-point vector set z {0+1i 2+3.5i 3.0+0i} ;# a complex vector

VecTcl includes support for linear equation solving

vexpr { x = A\y ;# solve A x = y for x # in the least squares sense if m>n }

array slicing, shaping and reductions

# define a vector with 3 elements set x {1 2 3} # ...and a 3x2 matrix set A {{2.0 3.0} {5.0 6.0} {7.0 8.0}} # replace column 1 in A with {9 10 11} # indices start from 0 vexpr { A[:,1] = {9 10 11} } # { {2.0 9.0} {5.0 10.0} {7.0 11.0} } # create a matrix with columns x and x.^2 vexpr { A=hstack(x, x.^2) } # {1.0 1.0} {2.0 4.0} {3.0 9.0} vexpr { sum(x.^2)} # 14.0

and elementary transcendental functions

vexpr { sinh(2+3i) } ;# complex hyperbolic sine # -3.5905645899857794+0.5309210862485197i

Any Tcl command can be called as a function

set x {1 2 3} vexpr { n=llength(x); puts(n) } # writes 3 to stdout # Caveat: llength(x) is inefficient, it # involves a conversion to a list. Use rows(x) instead.

Not only short expressions are supported. Looping and branching make it possible to write larger math functions in a single expression

vexpr { for i=1:5 { if i!=2 { puts(i) } } }

A second command, vproc defines a procedure fully in terms of a VecTcl expression

vproc rms {x} { # compute the root mean square xm=mean(x) sqrt(mean((x-xm).^2)) }

Vector expressions are compiled into Tcl procedures; the curious can peek into the compiler output

vectcl::compile { x, y = list(y, x) ;# swap x and y A= -3*x } # this outputs: upvar 1 y y upvar 1 x x upvar 1 A A set __temp1 [list [set y] [set x]] lassign $__temp1 x y set A [numarray::neg [numarray::* 3 [set x]]]

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