Flags:¶

-s

Generate random seed (result is non-deterministic)

-l

List input and output maps

--overwrite

Allow output files to overwrite existing files

--help

Print usage summary

--verbose

Verbose module output

--quiet

Quiet module output

--ui

Force launching GUI dialog

Parameters:¶

expression=string

Expression to evaluate

region=string

The computational region that should be used.
- current uses the current region of the mapset.
- intersect computes the intersection region between
all input maps and uses the smallest resolution
- union computes the union extent of all map regions
and uses the smallest resolution
Options: current, intersect, union
Default: current

file=name

File containing expression(s) to evaluate

seed=integer

Seed for rand() function

Program use¶

r3.mapcalc expression have the form:

result = expression

where result is the name of a raster map layer to contain the result of the calculation and expression is any legal arithmetic expression involving existing raster map layers (except result itself), integer or floating point constants, and functions known to the calculator. Parentheses are allowed in the expression and may be nested to any depth. result will be created in the user’s current mapset.

As expression= is the first option, it is the default. This means that passing an expression on the command line is possible as long as the expression is quoted and a space is included before the first = sign. Example (’foo’ is the resulting map):

r3.mapcalc "foo = 1"

r3.mapcalc ’foo = 1’

r3.mapcalc ’foo=1’
Sorry, <foo> is not a valid parameter

r3.mapcalc < file

r3.mapcalc <<EOF
foo = 1
EOF

r3.mapcalc file=file

r3.mapcalc file=- <<EOF
foo = 1
EOF

The formula entered to r3.mapcalc by the user is recorded both in the result map title (which appears in the category file for result) and in the history file for result.

Some characters have special meaning to the command shell. If the user is entering input to r3.mapcalc on the command line, expressions should be enclosed within single quotes. See NOTES, below.

Operators and order of precedence¶

The following operators are supported:

     Operator   Meaning                    Type        Precedence


     --------------------------------------------------------------


     -          negation                   Arithmetic  12


     ~          one’s complement           Bitwise     12


     !          not                        Logical     12


     ^          exponentiation             Arithmetic  11


     %          modulus                    Arithmetic  10


     /          division                   Arithmetic  10


     *          multiplication             Arithmetic  10


     +          addition                   Arithmetic   9


     -          subtraction                Arithmetic   9


     <<         left shift                 Bitwise      8


     >>         right shift                Bitwise      8


     >>>        right shift (unsigned)     Bitwise      8


     >          greater than               Logical      7


     >=         greater than or equal      Logical      7


     <          less than                  Logical      7


     <=         less than or equal         Logical      7


     ==         equal                      Logical      6


     !=         not equal                  Logical      6


     &          bitwise and                Bitwise      5


     |          bitwise or                 Bitwise      4


     &&         logical and                Logical      3


     &&&        logical and[1]             Logical      3


     ||         logical or                 Logical      2


     |||        logical or[1]              Logical      2


     ?:         conditional                Logical      1

(modulus is the remainder upon division)

[1] The &&& and ||| operators handle null values differently to other operators. See the section entitled NULL support below for more details.

The operators are applied from left to right, with those of higher precedence applied before those with lower precedence. Division by 0 and modulus by 0 are acceptable and give a NULL result. The logical operators give a 1 result if the comparison is true, 0 otherwise.

3D Grid names¶

Anything in the expression which is not a number, operator, or function name is taken to be a 3D grid name. Examples:

volume
x3
3d.his

Most GRASS raster map layers and 3D grids meet this naming convention. However, if a 3D grid has a name which conflicts with the above rule, it should be quoted. For example, the expression

x = a-b

would be interpreted as: x equals a minus b, whereas

x = "a-b"

would be interpreted as: x equals the 3D grid named a-b

Also

x = 3107

would create x filled with the number 3107, while

x = "3107"

would copy the 3D grid 3107 to the 3D grid x.

Quotes are not required unless the 3D grid names look like numbers or contain operators, OR unless the program is run non-interactively. Examples given here assume the program is run interactively. See NOTES, below.

r3.mapcalc will look for the 3D grids according to the user’s current mapset search path. It is possible to override the search path and specify the mapset from which to select the 3D grid. This is done by specifying the 3D grid name in the form:

name@mapset

For example, the following is a legal expression:

result = x@PERMANENT / y@SOILS

The mapset specified does not have to be in the mapset search path. (This method of overriding the mapset search path is common to all GRASS commands, not just r3.mapcalc.)

The neighborhood modifier¶

3D grids are data base files stored in voxel format, i.e., three-dimensional matrices of float/double values. In r3.mapcalc, 3D grids may be followed by a neighborhood modifier that specifies a relative offset from the current cell being evaluated. The format is map[r,c,d], where r is the row offset, c is the column offset and d is the depth offset. For example, map[1,2,3] refers to the cell one row below, two columns to the right and 3 levels below of the current cell, map[-3,-2,-1] refers to the cell three rows above, two columns to the left and one level below of the current cell, and map[0,1,0] refers to the cell one column to the right of the current cell. This syntax permits the development of neighborhood-type filters within a single 3D grid or across multiple 3D grids.

Functions¶

The functions currently supported are listed in the table below. The type of the result is indicated in the last column. F means that the functions always results in a floating point value, I means that the function gives an integer result, and * indicates that the result is float if any of the arguments to the function are floating point values and integer if all arguments are integer.

function                description                                     type
---------------------------------------------------------------------------
abs(x)                  return absolute value of x                      *
acos(x)                 inverse cosine of x (result is in degrees)      F
asin(x)                 inverse sine of x (result is in degrees)        F
atan(x)                 inverse tangent of x (result is in degrees)     F
atan(x,y)               inverse tangent of y/x (result is in degrees)   F
ceil(x)                 the smallest integral value not less than x     *
cos(x)                  cosine of x (x is in degrees)                   F
double(x)               convert x to double-precision floating point    F
eval([x,y,...,]z)       evaluate values of listed expr, pass results to z
exp(x)                  exponential function of x                       F
exp(x,y)                x to the power y                                F
float(x)                convert x to single-precision floating point    F
floor(x)                the largest integral value not greater than x   *
graph(x,x1,y1[x2,y2..]) convert the x to a y based on points in a graph F
graph2(x,x1[,x2,..],y1[,y2..])


                        alternative form of graph()                     F
if                      decision options:                               *
if(x)                   1 if x not zero, 0 otherwise
if(x,a)                 a if x not zero, 0 otherwise
if(x,a,b)               a if x not zero, b otherwise
if(x,a,b,c)             a if x > 0, b if x is zero, c if x < 0
int(x)                  convert x to integer [ truncates ]              I
isnull(x)               check if x = NULL
log(x)                  natural log of x                                F
log(x,b)                log of x base b                                 F
max(x,y[,z...])         largest value of those listed                   *
median(x,y[,z...])      median value of those listed                    *
min(x,y[,z...])         smallest value of those listed                  *
mod(x,y)                return the modulus (the remainder) of x/y       *
mode(x,y[,z...])        mode value of those listed                      *
nmax(x,y[,z...])        largest value of those listed, excluding NULLs  *
nmedian(x,y[,z...])     median value of those listed, excluding NULLs   *
nmin(x,y[,z...])        smallest value of those listed, excluding NULLs *
nmode(x,y[,z...])       mode value of those listed, excluding NULLs     *
not(x)                  1 if x is zero, 0 otherwise
pow(x,y)                x to the power y                                *
rand(a,b)               random value x : a <= x < b                     *
round(x)                round x to nearest integer                      I
round(x,y)              round x to nearest multiple of y
round(x,y,z)            round x to nearest y*i+z for some integer i
sin(x)                  sine of x (x is in degrees)                     F
sqrt(x)                 square root of x                                F
tan(x)                  tangent of x (x is in degrees)                  F
xor(x,y)                exclusive-or (XOR) of x and y                   I

Internal variables:


 row()                  current row of moving window                    I


 col()                  current col of moving window                    I


 depth()                return current depth                            I


 nrows()                number of rows in computation region            I


 ncols()                number of columns in computation region         I


 ndepths()              number of depth levels in computation region    I


 x()                    current x-coordinate of moving window           F


 y()                    current y-coordinate of moving window           F


 z()                    return current z value                          F


 ewres()                current east-west resolution                    F


 nsres()                current north-south resolution                  F


 tbres()                current top-bottom resolution                   F


 area()                 area of current cell in square meters           F


 null()                 NULL value

Floating point values in the expression¶

Floating point numbers are allowed in the expression. A floating point number is a number which contains a decimal point:

    2.3   12.0   12.   .81

Floating point values in the expression are handled in a special way. With arithmetic and logical operators, if either operand is float, the other is converted to float and the result of the operation is float. This means, in particular that division of integers results in a (truncated) integer, while division of floats results in an accurate floating point value. With functions of type * (see table above), the result is float if any argument is float, integer otherwise.

Note: If you calculate with integer numbers, the resulting map will be integer. If you want to get a float result, add the decimal point to integer number(s).

If you want floating point division, at least one of the arguments has to be a floating point value. Multiplying one of them by 1.0 will produce a floating-point result, as will using float():

      r3.mapcalc "ratio = float(soil.4 - soil.3) / soil.3)"

NULL support¶

NULL support: Please note that any math performed with NULL cells always results in a NULL value for these cells. If you want to replace a NULL cell on-the-fly, use the isnull() test function in a if-statement.

Example: The users wants the NULL-valued cells to be treated like zeros. To add maps A and B (where B contains NULLs) to get a map C the user can use a construction like:

C = A + if(isnull(B),0,B)

NULL and conditions:

For the one argument form:

if(x) = NULL		if x is NULL
if(x) = 0		if x = 0
if(x) = 1		otherwise (i.e. x is neither NULL nor 0).

For the two argument form:

if(x,a) = NULL		if x is NULL
if(x,a) = 0		if x = 0
if(x,a) = a		otherwise (i.e. x is neither NULL nor 0).

For the three argument form:

if(x,a,b) = NULL	if x is NULL
if(x,a,b) = b		if x = 0
if(x,a,b) = a		otherwise (i.e. x is neither NULL nor 0).

For the four argument form:

if(x,a,b,c) = NULL	if x is NULL
if(x,a,b,c) = a		if x > 0
if(x,a,b,c) = b		if x = 0
if(x,a,b,c) = c		if x < 0

All forms of if() return NULL if the first argument is NULL. The 2, 3 and 4 argument forms of if() return NULL if the "selected" argument is NULL, e.g.:

if(0,a,b) = b	regardless of whether a is NULL
if(1,a,b) = a	regardless of whether b is NULL

Note: The user cannot test for NULL using the == operator, as that returns NULL if either or both arguments are NULL, i.e. if x and y are both NULL, then "x == y" and "x != y" are both NULL rather than 1 and 0 respectively.
The behaviour makes sense if the user considers NULL as representing an unknown quantity. E.g. if x and y are both unknown, then the values of "x == y" and "x != y" are also unknown; if they both have unknown values, the user doesn’t know whether or not they both have the same value.

Usage from command line¶

Extra care must be taken if the expression is given on the command line. Some characters have special meaning to the UNIX shell. These include, among others:

* ( ) > & |

It is advisable to put single quotes around the expression; e.g.:

’result = volume * 2’

Without the quotes, the *, which has special meaning to the UNIX shell, would be altered and r3.mapcalc would see something other than the *.

Multiple computations¶

In general, it’s preferable to do as much as possible in each r3.mapcalc command using multi-line input.

Backwards compatibility¶

For the backwards compatibility with GRASS 6, if no options are given, it manufactures file=- (which reads from stdin), so you can continue to use e.g.:

r3.mapcalc < file

or:

r3.mapcalc <<EOF
foo = 1
EOF

But unless you need compatibility with previous GRASS GIS versions, use file= explicitly, as stated above.

When the map name contains uppercase letter(s) or a dot which are not allowed to be in module option names, the r3.mapcalc command will be valid also without quotes:

r3.mapcalc volume_A=1
r3.mapcalc volume.1=1

Interactive input in command line¶

For formulas that the user enters from standard input (rather than from the command line), a line continuation feature now exists. If the user adds a backslash to the end of an input line, r3.mapcalc assumes that the formula being entered by the user continues on to the next input line. There is no limit to the possible number of input lines or to the length of a formula.

If the r3.mapcalc formula entered by the user is very long, the map title will contain only some of it, but most (if not all) of the formula will be placed into the history file for the result map.

When the user enters input to r3.mapcalc non-interactively on the command line, the program will not warn the user not to overwrite existing map layers. Users should therefore take care to assign program outputs raster map names that do not yet exist in their current mapsets.

3D GRID MASK handling¶

r3.mapcalc follows the common GRASS behavior of raster MASK handling, so the MASK is only applied when reading an existing GRASS raster map. This implies that, for example, the command:

r3.mapcalc "volume_amplified = volume * 3"

create a map respecting the masked pixels if MASK is active.

However, when creating a map which is not based on any map, e.g. a map from a constant:

r3.mapcalc "volume_const = 200.0"

If also in this case the MASK should be applied, an if() statement including the MASK should be used, e.g.:

r3.mapcalc "volume_const = if(MASK, 200.0, null())"

Random number generator initialization¶

The pseudo-random number generator used by the rand() function can be initialised to a specific value using the seed option. This can be used to replicate a previous calculation.

Alternatively, it can be initialised from the system time and the PID using the -r flag. This should result in a different seed being used each time.

In either case, the seed will be written to the map’s history, and can be seen using r.info.

If you want other people to be able to verify your results, it’s preferable to use the seed option to supply a seed which is either specified in the script or generated from a determenistic process such as a pseudo-random number generator given an explicit seed.

Note that the rand() function will generate a fatal error if neither the seed option nor the -s flag are given.