All PAVE visualizations are generated using one or more formulas. A formula may be very simple. For example, the formula "O3a" refers to the variable "O3" in data set "a" - which is the first dataset that was loaded into PAVE. (Note that data sets are given sequential letters as they are loaded into PAVE, and are referred to by those letters in PAVE formulas.) An example of a formula to calculate the percent difference in O3 between datasets a and b is: "(O3a-O3b)*100/(O3b+0.001)".
Formulas must be in infix notation, and can contain the following operators, listed in their order of precedence:
Highest 1) abs, sqr, sqrt, exp, log, ln, sin, cos, tan,
Precedence sind, cosd, tand, minx, miny, minz, maxx, maxy, maxz,
mint, maxt, mean, sum, min, max,
2) **
3) /, *
4) +, -
5) <, <=, > >=
6) ==, !=
7) &&
Lowest 8) ||
Precedence
Explanations of these operations are given below. If you wish to
override the default operator precedence, or are uncertain as
to which operator will take precedence, you can feel free to use
parentheses in your formulas. This will force expressions within the
parentheses to be evaluated first.PAVE also has an occasionally used feature that allows you to specify a time step index after a variable name. For example, O3a:1 is the first hour of ozone. So, if you wanted to plot each cell averaged in time over the first six hours of your data, you could enter and plot the following formula:
(O3a:1+O3a:2+O3a:3+O3a:4+O3a:5+O3a:6)/6This is cumbersome and it also uses a lot of memory, but it may be useful for you.
There is another useful feature of the parser that not many people know about, that enables you to compute and visualize the the rate of change of a variable. For example, the formula d[O3a]/dt calculates the change in ozone concentration over time. A limitation of this feature is that the variable between the brackets must be an atomic variable, that is to say, it can not be a formula other than a basic variable from one of your datasets.
Formulas may also contain integer or floating point constants, or the following operands which are replaced by PAVE's formula parser to be the constant values noted:
E 2.7182818284590452354 PI 3.14159265358979323846 NROWS number of rows in the formula's currently selected domain NCOLS number of rows in the formula's currently selected domain NLEVELS number of levels in the formula's currently selected domainThe following operators are binary (they have an operand on both sides of the operator), and usually return an array of data by performing that operation on each cell of the operands' arrays. The only time these operators return a single number is when both operands (ops) are themselves a single number.
+ Returns the sum of the ops - Returns the difference of the ops * Returns the product of the ops / Returns ratio of the ops ** Returns the left op raised to the power of the right op, calculated using the C math library's pow() functionThe following operators are boolean binary operators. Boolean operators return either 0 or 1 for each cell of the resulting array of data, or in the case of two operands (ops) that are single numbers, just the single number 0 or 1. You may find these operators useful to "screen out" ranges of your data that are of particular interest. For example, if you are only concerned about the variable O3a when its value exceeds 0.080, you might look at the formula (O3a>0.080)*O3a. If O3a is less than or equal to 0.080, the result of the formula will be set to 0 in that cell. Otherwise, the value of O3a will be used in that cell.
< Returns 1 if the left op is less than the right op,
else 0
<= Returns 1 if the left op is less than or equal to
the right op, else 0
> Returns 1 if the left op is greater than the right
op, else 0
>= Returns 1 if the left op is greater than or equal
to the right op, else 0
!= Returns 1 if the left op is not equal to the
right op, else 0
== Returns 1 if the left op is equal to the right op, else 0
&& Returns 1 if both ops are non-zero, else 0
|| Returns 1 if either op is non-zero, else 0
The following operators are unary (they have a single operand on the
right side of the operator), and usually return a time-stepped matrix of
data by performing that operation on each cell of the operand's array.
The only time these operators return a single number is when the operand
is itself a single number. The C math library routines called are listed
with most of these operators. For further information on these routines,
please check your man pages.
abs fabs(op) sqrt sqrt(op) sqr Returns the square of the op log log10(op) exp exp(op) ln log(op) sin sin(op) cos cos(op) tan tan(op) sind sin(op*(PI/180.0)) cosd cos(op*(PI/180.0)) tand tan(op*(PI/180.0))The following unary operators return a single number in all cases. Their single operand must follow on the right hand side of the operator. The functionality is listed beside each operator name.
mean average cell value for all cells in currently selected domain sum sum of all cell values in currently selected domain mint time step index with minimum value in currently selected domain maxt time step index with maximum value in currently selected domain minx x index with minimum value in currently selected domain maxx x index with maximum value in currently selected domain miny y index with minimum value in currently selected domain maxy y index with maximum value in currently selected domain minz z index with minimum value in currently selected domain maxz z index with maximum value in currently selected domainwhere "currently selected domain" includes the currently selected rows, columns, layers, and time steps for the currently selected formula. Thus, the minimum and maximum values in the currently selected domain occur at the locations (minx,miny,minz,mint) and (maxx,maxy,maxz,maxt), respectively. An interesting use of the sum operator is to calculate the sum of the result of a boolean expression (e.g. sum(O3a>120)) to find the number of cell-hours that meet the boolean condition.
The unary min and max operators behave a little differently:
min For each cell (i,j,k) in the currently selected domain,
this calculates the minimum value for that cell
over the currently selected time steps. In other words,
the minimum value in cells (i,j,k,tmin..tmax).
max For each cell (i,j,k) in the currently selected domain,
this calculates the maximum value for that cell
over the currently selected time steps. In other words,
the maximum value in cells (i,j,k,tmin..tmax).
NOTE: currently the unary + and - operators [as in -1 or -(x+y)] are not supported, but hopefully these will be added later.