The symbol diameter is computed as a function of the value z
to be plotted:
diameter = dmin + (dmax - dmin) * {(z - zmin)/(zmax - zmin)}^p
where dmin
and dmax
are defined as 0.1 and 1 units, so the symbol diameters range over an order of magnitude (and symbol areas over two); zmin
and zmax
are the observed range of the data, or the range over which the user wants the diameters to be computed; and p
is a power defined by the user. The value of (z - zmin)/(zmax - zmin)
is the value of z
normalized, 0 - 1, to the range over which the symbol diameters are to be computed. After being raised to the power p
, which will result in a number in the range 0 to 1, this value is multiplied by the permissable range of diameters and added to the minimum diameter. This results in a diameter between 0.1 and 1 units that is proportional to the value of z
.
A p
value of 1
results in a linear rate of change. Values of p
less than unity lead to a rapid intial rate of change with increasing value of z
which is often suitable for displaying positively skewed data sets, see the example below. In contrast, values of p
greater than unity result in an initial slow rate of change with increasing value of z
which is often suitable for displaying negatively skewed data sets. To obtain a logarithmic scaling set p = 0.3679
, i.e. 1/e
, and a value of p = 0.5
is equivalent to a square root transformation, the default, that is appropriate for a linear-area relationship. These values of p
are equivalent to plotting log(x)
or log10(x)
and sqrt(x)
, respectively. Experimentation is often necessary to obtain a satisfactory visual effect. See syms.pfunc
for a graphic demonstrating the effect of varying the p
parameter.
If zmin
or zmax
are defined this has the effect of setting a minimum or maximum value of z
, respectively, beyond which changes in the value of z
do not result in changes in symbol diameter. This can be useful in limiting the effect of one, or a few, extreme outlier(s) while still plotting them, they simply plot at the minimum or maximum symbol size and are not involved in the calculation of the range of z
over which the symbol diameters vary. Note: If the variable z
includes a transform, e.g., log10(z)
, the values of zmin
and/or zmax
must be in those transform units.
If zlab
and main
are undefined a default a map title is generated by appending the input variable name text string to "Proportional Symbol Map for "
. If no map title is required set zlab = ""
, and if some user defined map title is required it should be defined in main
, e.g. main = "Map Title Text"
.