# The Yorick Programming Language

Yorick has a compact and sophisticated mechanism for describing array indexing and operations, which are used to precisely specify the desired operation to the interpreter. Applying an operation to an array causes the operation to be applied to each element of the array. For example:

> a = [1,2,3,4,5] > sqrt(a) [1,1.41421,1.73205,2,2.23607]

What about multiplying two vectors? The default is to perform an element by element multiplication.

> b = [2,4,6,8,10] > a*b [2,8,18,32,50]Those of you who remember physics or linear algebra will recall inner and outer products. The inner product is defined as the sum of the pairwise products:

> a(+)*b(+) 110The outer product creates a matrix out of each possible multiplication:

> a(-,)*b(,-) [[2,4,6,8,10], [4,8,12,16,20], [6,12,18,24,30], [8,16,24,32,40], [10,20,30,40,50]]The

**+**and

**-**symbols, used where an index would be placed, are called special subscripts and provide precise control over how array operations are executed. The

**+**is the matrix multiplication pseudo-index, which indicates to Yorick along which dimension the addition part of a matrix multiply should be performed. The

**-**is a pseudo-index, creating an index where one did not exist before.

The rank-reducing operators **sum**,
**min**, **max** and
**avg** can be used in place of indices.

> a(max) 5 > b(avg) 6

One might wonder why this is necessary, when the equivalent
function operators (i.e., **min()** or
**avg()**) exist? The reason is that
for matrices of rank 2 or greater, the rank-reducing index
operators allow you to specify exactly how to perform the
operation. For example, given a 3x3 array, do you want to average
across rows, columns or the entire array?

> c = [[1,2,3],[4,5,6],[7,8,9]] > dimsof(c) [2,3,3] > avg(c) 5 > c(avg,avg) 5 > c(avg,) [2,5,8] > c(,avg) [4,5,6]Here we have also introduced the

**dimsof()**function operator, which reports the dimensions of the argument. In this case, the result tells us that

**c**is an array of rank 2 with three elements in each direction.

Under Linux, Yorick is linked with the GIST graphics
subsystem, allowing immediate display of plots and diagrams. Plots
are interactive, allowing the user to zoom in and out, stretch
axes, and crop the displays using the mouse. Yorick is capable of
displaying sequences of plots over time as in a movie, and because
of this, the command to prepare for a new image is
**fma** or frame advance.

To plot the value of a function at evenly spaced points, we
must first create the **x** values:

> x = span(0,10,256) > dimsof(x) [1,256]

**x** is now a 256-element array with values
that range from 0 to 10.

The **plg** function, given
vectors for the **x** and **y**
values, plots x-y graphs.

plg, sin(x^2), x

The results of this command are shown in Figure 1. Note that
the arguments are supplied **y,x** (not
**x,y**). This allows Yorick to supply a default
**x** vector (ranging from **1** to
the number of **y** points), if desired.

Parametric plots are also supported. Consider the following commands which produced the spiral in Figure 2:

> window, style="vgbox.gs" > a = span(0,20,256) > x = a * sin(a) > y = a * cos(a) > plg, y, x

Surface plots are also available, either as a wire frame as in Figure 3:

> #include "plwf.i" > orient3 > x = span(-pi,pi,32)(,-:1:32) > y = transpose(x) > fma > plwf, sin(x)*cos(y)

Or a shaded surface rendition as in Figure 4:

> fma > plwf, sin(x)*cos(y), shade=1, edges=0

A host of advanced graphics options are used in the demonstration programs distributed with Yorick, and the latest copy of the documentation has an extensive description of graphics options. In addition, libraries to read, write, and display PNM-format images are provided.