## table of contents

r3.mapcalc(1grass) | GRASS GIS User's Manual | r3.mapcalc(1grass) |

# NAME¶

**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:¶

## 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 parameterIf no options are given, it manufactures "file=-" (which reads from stdin), so you can continue to use e.g.:

r3.mapcalc < fileor:

r3.mapcalc <<EOF foo = 1 EOFBut unless you need compatibility with previous versions, use file= explicitly, e.g.:

r3.mapcalc file=fileor:

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 * 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:Note, that the row(), col() and depth() indexing starts with 1.

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¶

- Division by zero should result in NULL.
- Modulus by zero should result in NULL.
- NULL-values 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

- NULL-values 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 non-zero; 0 otherwise if(x,a,b) NULL if x is NULL; a if x is non-zero; 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.
- Non-NULL, 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 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 < 0More 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 NULLeval() 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 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=1However, 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* 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"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 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.

# 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 x-y 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 2-D graph and then linearly interpolated. The graph()
function provides the opportunity to accomplish this. An x-axis 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,
row-by-row (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 1591-092X) (PDF)

# AUTHORS¶

Tomas Paudits & Jaro Hofierka, funded by GeoModel s.r.o.,
Slovakia

tpaudits@mailbox.sk, hofierka@geomodel.sk

Glynn Clements

# SOURCE CODE¶

Available at: r3.mapcalc source code (history)

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© 2003-2020 GRASS Development Team, GRASS GIS 7.8.5 Reference Manual

GRASS 7.8.5 |