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       r3.mapcalc  performs  arithmetic on 3D grid volume data. New 3D grids can be created which
       are arithmetic  expressions  involving  existing  3D  grids,  integer  or  floating  point
       constants, and functions.


       If  used  without  command  line  arguments, r3.mapcalc will read its input, one line at a
       time, from standard input (which is the keyboard, unless redirected from a file or  across
       a  pipe).   Otherwise, the expression on the command line is evaluated. r3.mapcalc expects
       its input to have the form:


       where result is the name of a 3D grid  to  contain  the  result  of  the  calculation  and
       expression  is  any legal arithmetic expression involving existing 3D grid, 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

       The formula entered to r3.mapcalc by the user is recorded both in the  result  grid  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.


       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
            &&&amp;        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  &&&amp; 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


       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.)


       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
       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
        depth()                return current depth
        x()                    current x-coordinate of moving window
        y()                    current y-coordinate of moving window
        z()                    return current z value
        ewres()                current east-west resolution
        nsres()                current north-south resolution
        tbres()                current top-bottom resolution
        null()                 NULL value
        Note, that the row(), col() and depth() indexing starts with 1.


       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():
             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, &&&amp; and ||| are treated specially, as described below).

                           The &&&amp; 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.


       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:
       newmap = if(map<5, null(), 5)
         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.  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, 16.5
       2.9, 47.5
       4, 50
       100, 50


       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 = 'elevation * 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 *.

       If the input comes directly from the keyboard and the result 3D grid exists, the user will
       be asked if it can be overwritten. Otherwise, the result 3D  grid  will  automatically  be
       overwritten if it exists.

       Quoting  result is not allowed. However, it is never necessary to quote result since it is
       always taken to be a 3D grid 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 \e 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

       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 3D grids. Users should therefore
       take care to assign program outputs 3D grid file names that do  not  yet  exist  in  their
       current mapsets.

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


       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 important for the eval() function.

       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 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.

       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.


       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)



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

       Last changed: $Date: 2012-11-24 01:24:40 -0800 (Sat, 24 Nov 2012) $

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