**-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

**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

**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.

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

[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.

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*.)

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: 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

2.3 12.0 12. .81

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)"

- 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 < 0

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

**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.

* ( ) > & |

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

'result = volume * 2'

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

r3.mapcalc < file

r3.mapcalc <<EOF foo = 1 EOF

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

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.

*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"

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())"

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.

ave = (a + b)/2

ave = (5*a + 3*b)/8.0

mask = a != 0

mask = if(a)

result = if(a,b)

newmap = if(map < 5, null(), map)

newmap = graph(map, 1,10, 2,25, 3,50)

0, 10 1, 10 1.5, 17.5 2.9, 47.5 4, 50 100, 50

~~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.

**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)

tpaudits@mailbox.sk, hofierka@geomodel.sk

Glynn Clements

Available at: r3.mapcalc source code (history)

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