Vector-based pocket calculator for Tcl : a much faster alternative to long loops calling expr over vector data.
Compile using the Makefile provided (amending the Tcl lib path).
Run tests from the shell: tclsh test.tcl
Start Tcl interpreter: tclsh
Then load into Tcl interpreter: load vecexpr.so
Uses reverse Polish syntax (operands followed by operators). Uses a LIFO stack, plus an extra register (used via store and recall) Arguments: scalars, vectors (Tcl lists), matrices (flattened, row-major) and built-in operators.
Examples:
% set vec "1 2 3"
% vecexpr $vec "4 5 6" add >othervec
% puts $othervec
5.0 7.0 9.0
vecexpr "1.2 -2.3 3.2" floor >integers; puts $integers
(prints 1.0 -3.0 3.0)
pi (constant), height (current stack height, for debugging), <varName (push Tcl var - can be done with $varName as well), recall (after calling store)
abs cos sin tan exp floor log mean min max round sq sqrt sum >varName (pop into Tcl var), &varName (copy floor values to an int variable), store (recall is 0-ary) dup (duplicate in the stack), pop
add sub mult matmult (see below) dot div concat swap atan2
All binary functions except dot and matmult accept mixed scalar/vector operands.
Vector lengths must match, except for concat and swap.
Example usage of atan2, converting result to degrees (note order of operands: y, x):
% vecexpr 5 0 atan2 pi div 180 mult
90.0
vecexpr <data> <xmin> <dx> <nbins>
where xmin, dx and nbins are scalars. Will push on the stack a histogram of the data, with nbins bins of width dx starting at xmin.
The histogram can be saved as an integer-typed Tcl list using the '&' operator:
% vecexpr "1.1 2.1 2.2 3.5 4.1" 0. 1. 5 bin &histogram
1.1 2.1 2.2 3.5 4.1
% puts $histogram
0 1 2 1 1
Matrices are stored unrolled (in row-major order).
"Unary" matrix operations (min_ew, transp) are binary because they require the shape of the matrix, provided as the number of lines at the top of the stack.
Transposing a (2,3) matrix:
vecexpr "1 2 3 4 5 6" 2 transp -> 1.0 4.0 2.0 5.0 3.0 6.0
Transposing the (3,2) matrix with the same (flattened) elements:
vecexpr "1 2 3 4 5 6" 3 transp -> 1.0 3.0 5.0 2.0 4.0 6.0
For matrix multiplication, push both matrices on the stack, then the common dimension:
vecexpr "1 0 0 1" "1 2" 2 matmult -> "1.0 2.0"
vecexpr "1 0 0 1" "1 2" 1 matmult -> "1.0 2.0 0.0 0.0 0.0 0.0 1.0 2.0"
This table lists each operator, the number of operands it uses (top n vectors on the stack), and the change in stack height after execution, that is, how many items are added or removed.
| Operator | n. operands | Stack chg. | Action |
|---|---|---|---|
| <varName | 0 | +1 | push Tcl var. varName on the stack (in practice, $varName is faster) |
| >varName | 1 | -1 | pop into Tcl var. varName |
| &varName | 1 | 0 | copy integer-typed floor values to variable varName |
| abs | 1 | 0 | absolute value |
| add | 2 | -1 | add 2 same-length vectors, or vector and scalar (element-wise), or column-vector and matrix, or matrix and row-vector |
| atan2 | 2 | -1 | given vectors y and x, push element-wise arctangent of y / x (in radians) |
| bin | 4 | -3 | push on the stack a histogram of the data, with nbins bins of width dx starting at xmin |
| concat | 2 | -1 | concatenate two top vectors |
| cos | 1 | 0 | cosine (angles in radians) |
| div | 2 | -1 | division (same-length vectors or vector by scalar or scalar by vector) |
| dot | 2 | -1 | dot product |
| dup | 1 | +1 | push copy of top vector onto stack |
| exp | 1 | 0 | exponential |
| floor | 1 | 0 | floor (type: double) |
| height | 0 | 0 | push current stack height |
| log | 1 | 0 | natural log |
| matmult | 3 | 0 | multiply matrices, using 3 args: M1 M2 n, where n is the common dimension |
| max | 1 | +1 | push max element of top vector |
| mean | 1 | +1 | push mean of top vector |
| min | 1 | +1 | push min of top vector |
| min_ew | 2 | -1 | element-wise minimum between lines of the top matrix (M, n, where n is the number of lines) |
| mult | 2 | -1 | element-wise multiply vectors, or multiply vector and scalar |
| pi | 0 | +1 | push pi constant onto stack |
| pop | 1 | -1 | remove top vector from stack |
| recall | 0 | +1 | push stored data (register) |
| round | 1 | 0 | round all elements to nearest integer (keep double type) |
| sin | 1 | 0 | sine (angles in radians) |
| sq | 1 | 0 | square |
| sqrt | 1 | 0 | square root |
| store | 1 | 0 | copy top vector to register |
| sub | 2 | -1 | subtract (see add for details) |
| sum | 1 | +1 | push sum of values of top vector |
| swap | 2 | 0 | swap top two vectors of stack |
| tan | 1 | 0 | tangent (angles in radians) |
| transp | 2 | -1 | transpose top matrix (M, n, where n is the number of lines) |