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       r.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.

       If used without command line arguments, r.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.  r.mapcalc expects its
       input to have the form:


       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.

       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 raster map layer name.  Examples:


       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

       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


       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:


       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.)

       Maps and images are data  base  files  stored  in  raster  format,  i.e.,  two-dimensional
       matrices of integer values.  In r.mapcalc, maps may be followed by a neighborhood modifier
       that specifies a relative offset from the current cell being  evaluated.   The  format  is
       map[r,c],  where  r  is  the row offset and c is the column offset.  For example, map[1,2]
       refers to the cell one row below and two  columns  to  the  right  of  the  current  cell,
       map[-2,-1]  refers  to  the  cell two rows above and one column to the left of the current
       cell, and map[0,1] 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 map or across
       multiple maps.

       Sometimes it is desirable to use a value associated with a category's label instead of the
       category value itself.  If a raster map layer name is preceded by the @ operator, then the
       labels in the category file for the raster map layer are used in the expression instead of
       the category value.

       For example, suppose that the raster map layer (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 =

       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.

       It is often helpful to  manipulate  the  colors  assigned  to  map  categories.   This  is
       particularly  useful  when  the spectral properties of cells have meaning (as with imagery
       data), or when the map category values represent real quantities (as when category  values
       reflect  true  elevation values).  Map color manipulation can also aid visual recognition,
       and map printing.

       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

       To assign this map red colors type:

       r.colors map=red color=rules

       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
        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
        Note, that the row() and col() 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.


       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 r.mapcalc would see something other than the *.

       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  *  .$GIS_OPT_PERCENT  + (1.0 -
               r.mapcalc "$GIS_OPT_OUTPUT.g =  g#$GIS_OPT_FIRST  *  .$GIS_OPT_PERCENT  +  (1.0  -
               r.mapcalc  "$GIS_OPT_OUTPUT.b  =  b#$GIS_OPT_FIRST  *  .$GIS_OPT_PERCENT  + (1.0 -
                 r.mapcalc <<EOF
               $GIS_OPT_OUTPUT.r   =   r#$GIS_OPT_FIRST   *   .$GIS_OPT_PERCENT    +    (1.0    -
               $GIS_OPT_OUTPUT.g    =    g#$GIS_OPT_FIRST    *   .$GIS_OPT_PERCENT   +   (1.0   -
               $GIS_OPT_OUTPUT.b   =   b#$GIS_OPT_FIRST   *   .$GIS_OPT_PERCENT    +    (1.0    -
         as  the latter will read each input map only once.  If the input comes directly from the
       keyboard and the result raster map layer exists, the user will  be  asked  if  it  can  be
       overwritten.   Otherwise, the result raster map layer 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 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

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


       To compute the average of two raster map layers 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 the raster map layer 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 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)
         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


       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 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.


       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)

       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


       Michael Shapiro, U.S.Army Construction Engineering Research Laboratory

       Glynn Clements

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

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