NAME

KEYWORDS

SYNOPSIS

DESCRIPTION

Program use

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

     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.

3D Grid names

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

Functions

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

    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)"

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 < 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.

NOTES

Usage from command line

* ( ) > & |

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

'result = volume * 2'

Multiple computations

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

Backwards compatibility

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

Interactive input in command line

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"

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.

EXAMPLES

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

KNOWN ISSUES

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.

REFERENCES

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)

SEE ALSO

AUTHORS

Glynn Clements

SOURCE CODE

Available at: r3.mapcalc source code (history)

Latest change: Sunday Feb 12 15:51:56 2023 in commit: 7d6ff54e985c1579e11b74c230cb8fa68a9aa928

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© 2003-2023 GRASS Development Team, GRASS GIS 8.3.dev Reference Manual