**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, 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.

The formula entered to *r.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 *r.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.

elevation x3 3d.his

Most GRASS raster map layers meet this naming convention. However, if a raster map layer 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 raster map layer named *a-b*

Also

x = 3107

would create *x* filled with the number 3107, while

x = "3107"

would copy the raster map layer *3107* to the raster map layer *x*.

Quotes are not required unless the raster map layer 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.

*r.mapcalc* will look for the raster map layers 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 raster map layer.
This is done by specifying the raster map layer 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 *r.mapcalc*.)

For example, suppose that the raster map layer *soil.ph*
(representing soil pH values) has a category file with labels as follows:

cat label ------------------ 0 no data 1 1.4 2 2.4 3 3.5 4 5.8 5 7.2 6 8.8 7 9.4

Then the expression:

result = @soils.ph

would produce a result with category values 0, 1.4, 2.4, 3.5, 5.8, 7.2, 8.8 and 9.4.

Note that this operator may only be applied to raster map layers and produces a floating point value in the expression. Therefore, the category label must start with a valid number. If the category label is integer, it will be represented by a floating point number. I the category label does not start with a number or is missing, it will be represented by NULL (no data) in the resulting raster map.

The # operator can be used to either convert map category values to their grey scale equivalents or to extract the red, green, or blue components of a raster map layer into separate raster map layers.

result = #map

converts each category value in *map* to a value in the range 0-255 which
represents the grey scale level implied by the color for the category.
If the map has a grey scale color table, then the grey level is what
#map evaluates to. Otherwise, it is computed as:

0.10 * red + 0.81 * green + 0.01 * blue

Alternatively, you can use:

result = y#map

to use the NTSC weightings:

0.30 * red + 0.59 * green + 0.11 * blue

Or, you can use:

result = i#map

to use equal weightings:

0.33 * red + 0.33 * green + 0.33 * blue

The # operator has three other forms: r#map, g#map, b#map.
These extract the red, green, or blue components in the named raster map,
respectively. The GRASS shell script *r.blend* extracts each of these
components from two raster map layers, and combines them by a user-specified
percentage.
These forms allow color separates to be made. For example, to
extract the red component from *map*
and store it in the new 0-255 map layer *red*,
the user could type:

red = r#map

To assign this map grey colors type:

r.colors map=red color=rules black white

To assign this map red colors type:

r.colors map=red color=rules black red

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 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 graph(x,x1,y1[x2,y2..]) convert the x to a y based on points in a 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 * 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 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 col() current col of moving window x() current x-coordinate of moving window y() current y-coordinate of moving window ewres() current east-west resolution nsres() current north-south resolution 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():

r.mapcalc "ndvi=float(lsat.4 - lsat.3) / (lsat.4 + lsat.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 = 'elevation * 2'

In general, it's preferable to do as much as possible in each r.mapcalc command. E.g. rather than:

r.mapcalc "$GIS_OPT_OUTPUT.r = r#$GIS_OPT_FIRST * .$GIS_OPT_PERCENT + (1.0 - .$GIS_OPT_PERCENT) * r#$GIS_OPT_SECOND" r.mapcalc "$GIS_OPT_OUTPUT.g = g#$GIS_OPT_FIRST * .$GIS_OPT_PERCENT + (1.0 - .$GIS_OPT_PERCENT) * g#$GIS_OPT_SECOND" r.mapcalc "$GIS_OPT_OUTPUT.b = b#$GIS_OPT_FIRST * .$GIS_OPT_PERCENT + (1.0 - .$GIS_OPT_PERCENT) * b#$GIS_OPT_SECOND"

r.mapcalc <<EOF $GIS_OPT_OUTPUT.r = r#$GIS_OPT_FIRST * .$GIS_OPT_PERCENT + (1.0 - .$GIS_OPT_PERCENT) * r#$GIS_OPT_SECOND $GIS_OPT_OUTPUT.g = g#$GIS_OPT_FIRST * .$GIS_OPT_PERCENT + (1.0 - .$GIS_OPT_PERCENT) * g#$GIS_OPT_SECOND $GIS_OPT_OUTPUT.b = b#$GIS_OPT_FIRST * .$GIS_OPT_PERCENT + (1.0 - .$GIS_OPT_PERCENT) * b#$GIS_OPT_SECOND EOF

Quoting *result* is not allowed.
However, it is never necessary to quote *result* since
it is always taken to be a raster map layer name.

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, *r.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 *r.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 *r.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.

The environment variable GRASS_RND_SEED is read to initialise the random number generator.

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(), 5)

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

Error messages produced by *r.mapcalc* are almost useless.
In future, *r.mapcalc* should make some attempt
to point the user to the offending section of the equation, e.g.:

x = a * b ++ c ERROR: somewhere in line 1: ... b ++ c ...

Currently, there is no comment mechanism in *r.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.

r.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)

Grey scale conversion is based on the C.I.E. x,y,z system where y represents luminance. See "Fundamentals of Digital Image Processing," by Anil K. Jain (Prentice Hall, NJ, 1989; p 67).

*
g.region,
r.bitpattern,
r.blend,
r.colors,
r.fillnulls
*

Glynn Clements

*Last changed: $Date$*

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