Provided by: grass-doc_7.6.0-1_all bug


       r3.mapcalc  - Raster map calculator.


       raster, algebra


       r3.mapcalc --help
       r3.mapcalc  [-sl]   [expression=string]    [region=string]    [file=name]   [seed=integer]
       [--overwrite]  [--help]  [--verbose]  [--quiet]  [--ui]

           Generate random seed (result is non-deterministic)

           List input and output maps

           Allow output files to overwrite existing files

           Print usage summary

           Verbose module output

           Quiet module output

           Force launching GUI dialog

           Expression to evaluate

           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 containing expression(s) to evaluate

           Seed for rand() function


       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"
       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 parameter
       If  no  options  are  given, it manufactures "file=-" (which reads from stdin), so you can
       continue to use e.g.:
       r3.mapcalc < file
       r3.mapcalc <<EOF
       foo = 1
       But unless you need compatibility with previous versions, use file= explicitly, e.g.:
       r3.mapcalc file=file
       r3.mapcalc file=- <<EOF
       foo = 1

       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

   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:


       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

       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


       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:


       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.

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

   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:
                    NULL if x is NULL; 0 if x is zero; 1 otherwise
                    NULL if x is NULL; a if x is non-zero; 0 otherwise
                    NULL if x is NULL; a if x is non-zero; b otherwise
                    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.
               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
       More 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 NULL
       eval()  always  returns its last argument, so it only returns NULL if the last argument is

       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.


   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
       r3.mapcalc <<EOF
       foo = 1
       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=1
       However, 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
       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

       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

       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.


       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


       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.


        g.region, r3.colors, r.mapcalc


       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)


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

       Glynn Clements

       Last changed: $Date: 2018-07-01 23:03:44 +0200 (Sun, 01 Jul 2018) $


       Available at: r3.mapcalc source code (history)

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