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Vectors and Arithmetic

The basic unit of data in SM is the `vector', a named set of one or more numbers or strings. There is no limit to the number of vectors that may be defined. SM allows the user to read vectors from files or define them from the keyboard, to plot them and to perform arithmetic operations upon them. SM's string-valued vectors are less generally useful, but can be used for such purposes as labelling points on a graph.

To read a vector vec from a column of numbers in a file, where the filename has been specified using DATA and, possibly, the range of lines in the file to be used has been specified using the LINES command, use READ vec nn where nn is the column number, or READ { vec1 n1 vec2 n2 ... 2 to read many vectors. It is also possible to read a row, using READ ROW vec nn, where nn is the row number in the file. See READ for how to read a string-valued vector.

Instead of using simple column-orientated input it is possible to specify a format like those used by C's scanf functions (Fortran formats are not supported); if you provide your own format string you can only read numbers. For example, if your data file has lines like

	1:12:30  -45:30:11

A vector may also be defined as SET vec = x1,x2,dx to take on the values x1,x1+dx,...,x2, where dx defaults to 1 if omitted. If a scalar is encountered where a vector is expected, it is promoted to be a vector of the appropriate dimension; all other dimension mismatches are errors. Example:

SET value = 5
SET x = 0, 50, 2
SET y = x
SET y = x*0 + value
SET y[0] = 2*pi
SET y = value
SET x=0,1,.1 SET y=IMAGE(x,1.5)
SET s=str
SET s='str'
SET s[0]=1.23
SET x=1.23
SET s=x
SET s=STRING(x)

If you don't have many data points, rather than type them into a file, and use READ vec nn to define a vector, you can use the command@example SET vec = { list 2 For example@example SET r = 0,10 is equivalent to@example SET r = { 0 1 2 3 4 5 6 8 9 10 2 In fact, { list 2 is an expression, so SET vec = 2*{1 3 12 is also legal. If the first element of a list is a word, the vector is taken to be string-valued: SET s={ William William Henry Steven 2 defines a 4-element string vector, or you can use a string in quotes: SET s=<'1' 2 3 4> (if you used SET s={'1' 2 3 42 the first element would be '1' rather than 1). Once a vector is defined, you can write it to a file for later study using the PRINT command.

A scalar may be an integer, a floating point number, a scalar expression, DIMEN(vector), or WORD[expr]. The last two are the dimension of a vector, and an element of the vector with expr a scalar subscript. Note that subscripts start at 0 and that [ ] `not' () are used to subscript variables. The expression WORD[expr] is in fact allowed even if expr is not a scalar, in which case the result is a vector with the same dimension as expr, and with the values taken from WORD in the obvious way.

Once vectors are defined, they may be combined into expressions using the operators +, -, *, /, **, CONCAT and the functions COS(), SIN(), TAN(), ACOS(), ASIN(), ATAN(), ATAN2(), ABS(), DIMEN(), INT(), LG(), EXP(), LN(), SQRT(), STRING(), STRLEN(), and SUM(). The meaning of most of these is obvious, ATAN2 is like ATAN but takes two arguments, x and y and returns an angle in the proper sector. DIMEN returns the number of elements in a vector, SUM gives the sum of all the elements, CONCAT concatenates two vectors, INT gives the integral part of a vector, STRING converts a number to a string, and STRLEN gives the length of a string (in plotting units, not just the number of characters). STRING uses the same code as the axis-labelling routines, so FORMAT can be used to modify its behaviour; whether the x- or y-axis formats is used depends on whether the label is more nearly horizontal or vertical. An example would be

set x=3.08e16 define s (string(x)) relocate 0.5 0.5 putlabel 5 $s

y = 2 + sin(x)

You can also use WORD([ expr [ , ... ]]) as part of an expression, where WORD is a macro taking zero or more arguments. It is a bit dishonest to write the arguments as expr, as in fact they must be either the names of vectors or numbers. Suppose we define a macro pow with two arguments as@example SET $0 = $1**$2 then the command@example SET y = 10 + 2*pow(x,3) is equivalent to SET y = 10 + 2*x**3.

In addition to these arithmetic operations, there are also logical operators == (equals), != (not equals), >, >=, <, <=, && (logical and), and || (logical or). The meanings of the symbols are the same as in C, and as in C the value 0 is false while all other values are true.

String vectors may only be concatenated, added, or tested for (in)equality. Adding two string-valued vectors concatenates their elements, so

{ a b c 2 + { x y z 2

Testing equality for string vectors seems to cause some confusion. Consider

set str=<'a' b c d>
if('a' == 'str') {     # test if the strings `a' and `str' are equal
if('a' == str) {       # test if the string `a' equals the vector `str'
if(a == str) {         # test if the vector `a' equals the vector `str'

if('b' == str) {       # try to see if `b' is an element of str

if(sum('b' == str)) {  # is `b' an element of str?

There are also a number of less mathematical operations. If you have an IMAGE (@xref{IMAGE}) defined, you can extract a set of values using the expression IMAGE(expr,expr), where the two exprs give the coordinates where the values are desired. Note that this may be used as a way of reading large data files that are stored unformatted. The expression HISTOGRAM(expr : expr) can be used to convert a vector into a histogram. The second expression is taken to be the centres of the desired bins: bin boundaries are taken at the mean points (and points in the first expression lying on a boundary are taken to fall into the lower bin. Note the use of `:' not `,').

Vectors may be assigned to, using the syntax

SET vec = expr

If you want to define a vector to which you will subsequently assign values using SET vec[ expr ] = expr, you may use SET DIMEN(vec) = number which declares vec to be a vector of size number, and initialises it to zero. You can optionally supply a qualifier to the number, either a .f (the default), or a .s to specify that the vector is string valued.

If the IF clause is present, only those elements of expr1 for which the corresponding element of expr2 is true (non-zero) are copied into vec; in general vec will have a smaller dimension than expr1. The last SET statement (with ?:) again borrows from C. If expr1_i is true, then vec_i is set to expr2_i, otherwise it is set to expr3_i. In this form of conditional assignment, the dimension of vec is the same as that of the right hand side. It may look strange, but it can be just what you want.

Each vector also has a help field, which may be used to provide a string describing the vector. The field is set by

SET HELP vec str

HELP vec

PRINT [ file ] [format] { vec1, ..., vecn 2

DELETE vec

LIST SET

An IF clause has been added to the plotting commands, to allow only those elements of a vector which satisfy some condition to be plotted, for example

POINTS x y IF(z > 3*x)

SET log = z > 3*x SET x = x IF(log)  SET y = y IF(log) 
CONNECT x y

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