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NAME

       r.mapcalc  - Raster map calculator.

KEYWORDS

       raster, algebra

SYNOPSIS

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

   Flags:
       -s
           Generate random seed (result is non-deterministic)

       -l
           List input and output maps

       --overwrite
           Allow output files to overwrite existing files

       --help
           Print usage summary

       --verbose
           Verbose module output

       --quiet
           Quiet module output

       --ui
           Force launching GUI dialog

   Parameters:
       expression=string
           Expression to evaluate

       region=string
           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=name
           File containing expression(s) to evaluate

       seed=integer
           Seed for rand() function

DESCRIPTION

       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.

   Program use
       r.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):
       r.mapcalc "foo = 1"
       or:
       r.mapcalc ’foo = 1’
       An unquoted expression (i.e. split over multiple arguments) won’t work, nor will  omitting
       the space before the = sign:
       r.mapcalc ’foo=1’
       Sorry, <foo> is not a valid parameter
       To read command from the file, use file= explicitly, e.g.:
       r.mapcalc file=file
       or:
       r.mapcalc file=- < file
       or:
       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
       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
       otherwise.

   Raster map layer names
       Anything  in  the expression which is not a number, operator, or function name is taken to
       be a raster map layer name.  Examples:

       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
       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.

   Raster map layer values from the category file
       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 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
       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
       black
       white

       To assign this map red colors type:

       r.colors map=red color=rules
       black
       red

   Functions
       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
       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                  *
       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
       Note, that the row() and col() 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():
             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
       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
       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
       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 *.

   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
       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.:
       r.mapcalc < file
       or:
       r.mapcalc <<EOF
       foo = 1
       EOF
       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 r.mapcalc command will be valid also without quotes:
       r.mapcalc elevation_A=1
       r.mapcalc elevation.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, 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.

   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"
       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:
       r.mapcalc "base_height = 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.:
       r.mapcalc "base_height = 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.

   eval function
       If the output of the computation should be only one map but the expression is  so  complex
       that it is better to split it to several expressions, the eval function can be used:
       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
       This example uses unix-like << EOF syntax to provide input to r.mapcalc.

       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
       A  map  cannot  be  used  both  as an input and as an output as in this invalid expression
       oldmap = oldmap + 1, instead a subsequent rename using g.rename is needed  when  the  same
       name is desired:
       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

       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:
       mapmask = a != 0
       This could also be accomplished by:
       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)
       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

KNOWN ISSUES

       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  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.

SEE ALSO

        g.region, r.bitpattern, r.blend, r.colors, r.fillnulls, r.mapcalc.simple

REFERENCES

       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).

AUTHORS

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

       Glynn Clements

       Last changed: $Date: 2018-12-14 22:43:04 +0100 (Fri, 14 Dec 2018) $

SOURCE CODE

       Available at: r.mapcalc source code (history)

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       © 2003-2019 GRASS Development Team, GRASS GIS 7.6.0 Reference Manual