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):

r.mapcalc "foo = 1"

r.mapcalc 'foo = 1'

r.mapcalc 'foo=1'
Sorry, <foo> is not a valid parameter

r.mapcalc file=file

r.mapcalc file=- < file

r.mapcalc file=- <<EOF
foo = 1
EOF

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.

Computational regions in r.mapcalc

By default r.mapcalc uses the current region as computational region that was set with g.region for processing. Sometimes it is necessary to use a region that is derived from the raster maps in the expression to set the computational region. This is of high importance for modules that use r.mapcalc internally to process time series of satellite images that all have different spatial extents. A module that requires this feature is t.rast.algebra. The region option of r.mapcalc was implemented to address this requirement. It allows computing and using a region based on all raster maps in an expression. Three modes are supported:

• Setting the region parameter to current will result in the use of the current region as computational region. This is the default. The current region can be set with g.region.
• The parameter union will force r.mapcalc to compute the disjoint union of all regions from raster maps specified in the expression. This computed region will then be used as computational region at runtime. The region of the mapset will not be modified. The smallest spatial resolution of all raster maps will be used for processing.
• The parameter intersect will force r.mapcalc to compute the intersection of all regions from raster maps specified in the expression. This computed region will then be used as computational region at runtime. The region of the mapset will not be modified. The smallest spatial resolution of all raster maps will be used for processing.

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.

Raster map layer names

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.)

The neighborhood modifier

The neighborhood modifier cannot be used on maps generated within same r.mapcalc command run (see "KNOWN ISSUES" section).

Raster map layer values from the category file

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.

Grey scale equivalents and color separates

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

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
 nrows()                number of rows in computation region            I
 ncols()                number of columns in computation region         I
 x()                    current x-coordinate of moving window           F
 y()                    current y-coordinate of moving window           F
 ewres()                current east-west resolution                    F
 nsres()                current north-south 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():

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

Multiple computations

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"

use:

	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

as the latter will read each input map only once.

Backwards compatibility

r.mapcalc < file

r.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 r.mapcalc command will be valid also without quotes:

r.mapcalc elevation_A=1
r.mapcalc elevation.1=1

Interactive input in command line

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.

Raster MASK handling

r.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:

r.mapcalc "elevation_exaggerated = elevation * 3"

However, when creating a map which is not based on any map, e.g. a map from a constant:

r.mapcalc "base_height = 200.0"

If also in this case the MASK should be applied, an if() statement including the MASK should be used, e.g.:

r.mapcalc "base_height = if(MASK, 200.0, null())"

eval function

r.mapcalc << EOF
eval(elev_200 = elevation - 200, \
     elev_5 = 5 * elevation, \
     elev_p = pow(elev_5, 2))
elevation_result = (0.5 * elev_200) + 0.8 * elev_p
EOF

Note that the temporary variables (maps) are not created and thus it does not matter whether they exists or not. In the example above, if map elev_200 exists it will not be overwritten and no error will be generated. The reason is that the name elev_200 now denotes the temporary variable (map) and not the existing map. The following parts of the expression will use the temporary elev_200 and the existing elev_200 will be left intact and will not be used. If a user want to use the existing map, the name of the temporary variable (map) must be changed.

Using the same map for input and output results

r.mapcalc "newmap = oldmap + 1"
g.rename raster=newmap,oldmap

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

To form a weighted average:

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

To produce a binary representation of the raster map layer a so that category 0 remains 0 and all other categories become 1:

mapmask = a != 0

mapmask = if(a)

To mask raster map layer b by raster map layer a:

result = if(a,b)

To change all values below 5 to NULL:

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

To create a map with random values in a defined range (needs either the usage of -s flag or the seed parameter). The precision of the input values determines the output precision (the resulting raster map type):

# write result as integer map (CELL)
random_int   = rand(-100,100)

# write result as double precision floating point map (DCELL)
random_dcell = rand(-100.0,100.0)

# write result as single precision floating point map (FCELL)
random_fcell = float(rand(-100.0,100.0))

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)

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 r.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 r.mapcalc command run. Consequently, the following (strikethrough code) does not work:

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 r.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 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.

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)

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).

SEE ALSO

AUTHORS

Glynn Clements

SOURCE CODE

Available at: r.mapcalc source code (history)

Accessed: Sunday Jan 22 07:36:02 2023

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