r3.mapcalc.1grass man page
r3.mapcalc — Raster map calculator.
Keywords
raster, algebra
Synopsis
r3.mapcalc
r3.mapcalc help
r3.mapcalc [sl] [expression=string] [region=string] [file=name] [seed=integer] [overwrite] [help] [verbose] [quiet] [ui]
Flags
 s
Generate random seed (result is nondeterministic)
 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
Description
r3.mapcalc performs arithmetic on raster map layers. New raster map layers can be created which are arithmetic expressions involving existing raster map layers, integer or floating point constants, and functions.
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"
or:
r3.mapcalc ’foo = 1’
An unquoted expression (i.e. split over multiple arguments) won’t work, nor will omitting the space before the = sign:
r3.mapcalc ’foo=1’
Sorry, <foo> is not a valid parameter
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 versions, use file= explicitly, e.g.:
r3.mapcalc file=file
or:
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 = ab
would be interpreted as: x equals a minus b, whereas
x = "ab"
would be interpreted as: x equals the 3D grid named ab
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 noninteractively. 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., threedimensional 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 neighborhoodtype 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
cos(x) cosine of x (x is in degrees) F
double(x) convert x to doubleprecision 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 singleprecision floating point F
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 *
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) exclusiveor (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 xcoordinate of moving window F
y() current ycoordinate of moving window F
z() return current z value F
ewres() current eastwest resolution F
nsres() current northsouth resolution F
tbres() current topbottom resolution F
area() area of current cell in square meters F
null() NULL value
Note, that the row(), col() and depth() indexing starts with 1.
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 floatingpoint result, as will using float():
r3.mapcalc "ratio = float(soil.4  soil.3) / soil.3)"
NULL support
 Division by zero should result in NULL.
 Modulus by zero should result in NULL.
 NULLvalues in any arithmetic or logical operation should result in NULL. (however, &&& and  are treated specially, as described below).

The &&& and  operators observe the following axioms even when x is NULL:
x &&& false == false false &&& x == false x  true == true true  x == true
 NULLvalues in function arguments should result in NULL (however, if(), eval() and isnull() are treated specially, as described below).
 The eval() function always returns its last argument

The situation for if() is:
if(x) NULL if x is NULL; 0 if x is zero; 1 otherwise if(x,a) NULL if x is NULL; a if x is nonzero; 0 otherwise if(x,a,b) NULL if x is NULL; a if x is nonzero; b otherwise if(x,n,z,p) NULL if x is NULL; n if x is negative; z if x is zero; p if x is positive
 The (new) function isnull(x) returns: 1 if x is NULL; 0 otherwise. The (new) function null() (which has no arguments) returns an integer NULL.

NonNULL, but invalid, arguments to functions should result in NULL.
Examples: log(2) sqrt(2) pow(a,b) where a is negative and b is not an integer
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 onthefly, use the isnull() test function in a ifstatement.
Example: The users wants the NULLvalued 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
More generally, all operators and most functions return NULL if *any* of their arguments are NULL.
The functions if(), isnull() and eval() are exceptions.
The function isnull() returns 1 if its argument is NULL and 0 otherwise. If the user wants the opposite, the ! operator, e.g. "!isnull(x)" must be used.
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
eval() always returns its last argument, so it only returns NULL if the last argument 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.
Notes
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 multiline 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
However, this syntax is not recommended as quotes as stated above more safe. Using quotes is both backwards compatible and valid in future.
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 noninteractively 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"
the created raster map is limited only by a computation region but it is not affected by an active MASK. This is expected because, as mentioned above, MASK is only applied when reading, not when writing a raster map.
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())"
When testing MASK related expressions keep in mind that when MASK is active you don’t see data in masked areas even if they are not NULL. See r.mask for details.
Random number generator initialization
The pseudorandom 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 pseudorandom 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.
Examples
To compute the average of two 3D grids a and b:
ave = (a + b)/2
To form a weighted average:
ave = (5*a + 3*b)/8.0
To produce a binary representation of 3D grid a so that category 0 remains 0 and all other categories become 1:
mask = a != 0
This could also be accomplished by:
mask = if(a)
To mask 3D grid b by 3D grid a:
result = if(a,b)
To change all values below 5 to NULL, keep otherwise:
newmap = if(map < 5, null(), map)
The graph() function allows users to specify a xy conversion using pairs of x,y coordinates. In some situations a transformation from one value to another is not easily established mathematically, but can be represented by a 2D graph and then linearly interpolated. The graph() function provides the opportunity to accomplish this. An xaxis value is provided to the graph function along with the associated graph represented by a series of x,y pairs. The x values must be monotonically increasing (each larger than or equal to the previous). The graph function linearly interpolates between pairs. Any x value lower the lowest x value (i.e. first) will have the associated y value returned. Any x value higher than the last will similarly have the associated y value returned. Consider the request:
newmap = graph(map, 1,10, 2,25, 3,50)
X (map) values supplied and y (newmap) values returned:
0, 10
1, 10
1.5, 17.5
2.9, 47.5
4, 50
100, 50
Known Issues
The result variable on the left hand side of the equation should not appear in the expression on the right hand side.
mymap = if( mymap > 0, mymap, 0)
Any maps generated by a r3.mapcalc command only exist after the entire command has completed. All maps are generated concurrently, rowbyrow (i.e. there is an implicit "for row in rows {...}" around the entire expression). Thus the #, @, and [ ] operators cannot be used on a map generated within same r3.mapcalc command run.
newmap = oldmap * 3.14
othermap = newmap[1, 0] / newmap[1, 0]
Continuation lines must end with a \ and have no trailing white space (blanks or tabs). If the user does leave white space at the end of continuation lines, the error messages produced by r3.mapcalc will be meaningless and the equation will not work as the user intended. This is particularly important for the eval() function.
Currently, there is no comment mechanism in r3.mapcalc. Perhaps adding a capability that would cause the entire line to be ignored when the user inserted a # at the start of a line as if it were not present, would do the trick.
The function should require the user to type "end" or "exit" instead of simply a blank line. This would make separation of multiple scripts separable by white space.
r3.mapcalc does not print a warning in case of operations on NULL cells. It is left to the user to utilize the isnull() function.
See Also
g.region, r3.colors, r.mapcalc
References
r.mapcalc: An Algebra for GIS and Image Processing, by Michael Shapiro and Jim Westervelt, U.S. Army Construction Engineering Research Laboratory (March/1991).
Performing Map Calculations on GRASS Data: r.mapcalc Program Tutorial, by Marji Larson, Michael Shapiro and Scott Tweddale, U.S. Army Construction Engineering Research Laboratory (December 1991)
Neteler, M. (2001): Volume modelling of soils using GRASS GIS 3D tools.  in: Brovelli, M. (ed.)(2001): The Geomatics Workbook N. 2. Politecnico di Milano, Italy (ISSN 1591092X) (PDF)
Authors
Tomas Paudits & Jaro Hofierka, funded by GeoModel s.r.o., Slovakia
tpaudits@mailbox.sk, hofierka@geomodel.sk
Glynn Clements
Last changed: $Date: 20161201 14:20:05 +0100 (Thu, 01 Dec 2016) $
Source Code
Available at: r3.mapcalc source code (history)
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