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<H2>NAME</H2>
<EM><B>r.mapcalc</B></EM>
<H2>DESCRIPTION</H2>
<EM>r.mapcalc</EM> 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.
<H2>PROGRAM USE</H2>
If used without command line arguments, <EM>r.mapcalc</EM> 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.
<EM>r.mapcalc</EM> expects its input to have the form:
<P>
<B>result=</B><EM>expression</EM>
<P>
where <EM>result</EM> is the name of a raster map layer
to contain the result of the calculation and
<EM>expression</EM> 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.
<EM>result</EM> will be created in the user's current mapset.
<P>
The formula entered to <EM>r.mapcalc</EM> by the user is recorded both in the
<EM>result</EM> map title (which appears in the category file for <EM>result</EM>)
and in the history file for <EM>result</EM>.
<P>
Some characters have special meaning to the command shell. If the user
is entering input to <EM>r.mapcalc</EM> on the command line, expressions
should be enclosed within single quotes. See NOTES, below.
<P>
<H2>OPERATORS AND ORDER OF PRECEDENCE</H2>
The following operators are supported:
<div class="code"><PRE>
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
</PRE></div>
(modulus is the remainder upon division)
<P>
[1] The &&& and ||| operators handle null values differently to other
operators. See the section entitled <b>NULL support</b> below for more
details.
<P>
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.
<P>
<P>
<H2>RASTER MAP LAYER NAMES</H2>
Anything in the expression which is not a number, operator, or function name
is taken to be a raster map layer name.
Examples:
<P>
<div class="code"><PRE>
elevation
x3
3d.his
</PRE></div>
<P>
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
<P>
<div class="code"><PRE>
x = a-b
</PRE></div>
<P>
would be interpreted as: x equals a minus b, whereas
<P>
<div class="code"><PRE>
x = "a-b"
</PRE></div>
<P>
would be interpreted as: x equals the raster map layer named <EM>a-b</EM>
<P>
Also
<P>
<div class="code"><PRE>
x = 3107
</PRE></div>
<P>
would create <EM>x</EM> filled with the number 3107, while
<P>
<div class="code"><PRE>
x = "3107"
</PRE></div>
<P>
would copy the raster map layer <EM>3107</EM> to the raster map layer <EM>x</EM>.
<P>
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.
<P>
<EM>r.mapcalc</EM> 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:
<P>
<div class="code"><PRE>
name@mapset
</PRE></div>
<P>
For example, the following is a legal expression:
<P>
<div class="code"><PRE>
result = x@PERMANENT / y@SOILS
</PRE></div>
<P>
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 <EM>r.mapcalc</EM>.)
<P>
<H2>THE NEIGHBORHOOD MODIFIER</H2>
Maps and images are data base files stored in raster format, i.e.,
two-dimensional matrices of integer values.
In <EM>r.mapcalc</EM>, maps may be followed by a <EM>neighborhood</EM> modifier that
specifies a relative offset from the current cell being evaluated. The format is
<EM>map[r,c]</EM>, where <EM>r</EM> is the row offset and <EM>c</EM> is the column offset.
For example, <EM>map[1,2]</EM> refers to the cell one row below and two columns
to the right of the current cell, <EM>map[-2,-1]</EM> refers to the cell
two rows above and one column to the left of the current cell,
and <EM>map[0,1]</EM> 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.
<P>
<H2>RASTER MAP LAYER VALUES FROM THE CATEGORY FILE</H2>
Sometimes it is desirable to use a value associated with a category's
<EM>label</EM> instead of the category value itself. If a raster
map layer name is preceded by the <B>@</B>
operator, then the labels in the category file for the raster map layer
are used in the expression instead of the category value.
<P>
For example, suppose that the raster map layer <EM>soil.ph</EM>
(representing soil pH values) has a category file with labels as follows:
<P>
<div class="code"><PRE>
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
</PRE></div>
<P>
Then the expression:
<P>
<div class="code"><PRE>
result = @soils.ph
</PRE></div>
<P>
would produce a result with category values
0, 1.4, 2.4, 3.5, 5.8, 7.2, 8.8 and 9.4.
<P>
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.
<H2>GREY SCALE EQUIVALENTS AND COLOR SEPARATES</H2>
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.
<P>
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.
<P>
<div class="code"><PRE>
result = #map
</PRE></div>
<P>
converts each category value in <EM>map</EM> 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:
<P>
<div class="code"><PRE>
0.10 * red + 0.81 * green + 0.01 * blue
</PRE></div>
<P>
Alternatively, you can use:
<P>
<div class="code"><PRE>
result = y#map
</PRE></div>
<P>
to use the NTSC weightings:
<P>
<div class="code"><PRE>
0.30 * red + 0.59 * green + 0.11 * blue
</PRE></div>
<P>
Or, you can use:
<P>
<div class="code"><PRE>
result = i#map
</PRE></div>
<P>
to use equal weightings:
<P>
<div class="code"><PRE>
0.33 * red + 0.33 * green + 0.33 * blue
</PRE></div>
<P>
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 <EM><A HREF="r.blend.html">r.blend</A></EM> 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 <EM>map</EM>
and store it in the new 0-255 map layer <EM>red</EM>,
the user could type:
<P>
<div class="code"><PRE>
red = r#map
</PRE></div>
<P>
To assign this map grey colors type:
<P>
<div class="code"><PRE>
<A HREF="r.colors.html">r.colors</A> map=red color=rules
black
white
</PRE></div>
<P>
To assign this map red colors type:
<P>
<div class="code"><PRE>
<A HREF="r.colors.html">r.colors</A> map=red color=rules
black
red
</PRE></div>
<P>
<H2>FUNCTIONS</H2>
The functions currently supported are listed in the table below.
The type of the result is indicated in the last column.
<EM>F</EM>
means that the functions always results in a floating point value,
<EM>I</EM>
means that the function gives an integer result, and
<EM>*</EM>
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.
<P>
<div class="code"><PRE>
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
</PRE></div>
<div class="code"><PRE>
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
</PRE></div>
Note, that the row() and col() indexing starts with 1.
<H2>FLOATING POINT VALUES IN THE EXPRESSION</H2>
Floating point numbers are allowed in the expression. A floating point
number is a number which contains a decimal point:
<div class="code"><PRE>
2.3 12.0 12. .81
</PRE></div>
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.
<P>
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).
<P>
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():
<div class="code"><PRE>
r.mapcalc "ndvi=float(lsat.4 - lsat.3) / (lsat.4 + lsat.3)"
</PRE></div>
<H2>NULL support</H2>
<menu>
<li>Division by zero should result in NULL.
<li>Modulus by zero should result in NULL.
<li> NULL-values in any arithmetic or logical operation should result
in NULL. (however, &&& and ||| are treated specially, as described below).
<li> The &&& and ||| operators observe the following axioms even when x is NULL:
<div class="code"><PRE>
x &&& false == false
false &&& x == false
x ||| true == true
true ||| x == true
</PRE></div>
<li> NULL-values in function arguments should result in NULL (however,
if(), eval() and isnull() are treated specially, as described below).
<li> The eval() function always returns its last argument
<li> The situation for if() is:
<div class="code"><PRE>
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
</PRE></div>
<li> 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.
<li>Non-NULL, but invalid, arguments to functions should result in NULL.
<div class="code"><PRE>
Examples:
log(-2)
sqrt(-2)
pow(a,b) where a is negative and b is not an integer
</PRE></div>
</menu>
<P>
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.
<p>
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:<p>
<div class="code"><PRE>
C=A + if(isnull(B),0,B)
</PRE></div>
<p>
<b>NULL and conditions:</b>
<p>
For the one argument form:
<div class="code"><PRE>
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).
</PRE></div>
<p>
For the two argument form:
<div class="code"><PRE>
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).
</PRE></div>
<p>
For the three argument form:
<div class="code"><PRE>
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).
</PRE></div>
<p>
For the four argument form:
<div class="code"><PRE>
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
</PRE></div>
More generally, all operators and most functions return NULL if *any*
of their arguments are NULL.
<br>
The functions if(), isnull() and eval() are exceptions.
<br>
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.
<p>
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.:
<div class="code"><PRE>
if(0,a,b) = b regardless of whether a is NULL
if(1,a,b) = a regardless of whether b is NULL
</pre></div>
eval() always returns its last argument, so it only returns NULL if
the last argument is NULL.
<p>
<b>Note</b>: 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.
<br>
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.
<H2>EXAMPLES</H2>
To compute the average of two raster map layers
<EM>a</EM> and <EM>b</EM>:
<div class="code"><PRE>
ave = (a + b)/2
</pre></div>
To form a weighted average:
<div class="code"><PRE>
ave = (5*a + 3*b)/8.0
</pre></div>
To produce a binary representation of the raster map layer
<EM>a</EM> so that category 0 remains 0 and all other categories become 1:
<div class="code"><PRE>
mask = a != 0
</pre></div>
This could also be accomplished by:
<div class="code"><PRE>
mask = if(a)
</pre></div>
To mask raster map layer <EM>b</EM> by raster map layer <EM>a</EM>:
<div class="code"><PRE>
result = if(a,b)
</pre></div>
To change all values below 5 to NULL:
<div class="code"><PRE>
newmap = if(map<5, null(), 5)
</pre></div>
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:
<div class="code"><PRE>
newmap = graph(map, 1,10, 2,25, 3,50)
</pre></div>
X (map) values supplied and y (newmap) values returned:
<div class="code"><PRE>
0, 10
1, 10,
1.5, 16.5
2.9, 47.5
4, 50
100, 50
</pre></div>
<H2>NOTES</H2>
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:
<P>
* ( ) > & |
<P>
It is advisable to put single quotes around the expression; e.g.:
<div class="code"><PRE>
result = 'elevation * 2'
</pre></div>
Without the quotes, the *, which has special meaning to the UNIX shell,
would be altered and <EM>r.mapcalc</EM> would see something other than the *.
<P>
If the input comes directly from the keyboard and the <EM>result</EM> raster
map layer exists, the user will be asked if it can be overwritten.
Otherwise, the <EM>result</EM> raster map layer will automatically be
overwritten if it exists.
<P>
Quoting <EM>result</EM> is not allowed.
However, it is never necessary to quote <EM>result</EM> since
it is always taken to be a raster map layer name.
<P>
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, <EM>r.mapcalc</EM> 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.
<P>
If the <EM>r.mapcalc</EM> 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 <EM>result</EM> map.
<P>
When the user enters input to <EM>r.mapcalc</EM> 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.
<P>
The environment variable GRASS_RND_SEED is read to initialise the
random number generator.
<H2>BUGS</H2>
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 <EM>r.mapcalc</EM> will
be meaningless and the equation will not work as the user intended.
This is important for the eval() function.
<P>
Error messages produced by <EM>r.mapcalc</EM> are almost useless.
In future, <EM>r.mapcalc</EM> should make some attempt
to point the user to the offending section of the equation, e.g.:
<div class="code"><PRE>
x = a * b ++ c
ERROR: somewhere in line 1: ... b ++ c ...
</pre></div>
<P>
Currently, there is no comment mechanism in <EM>r.mapcalc</EM>.
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.
<P>
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.
<P>
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.
<H2>SEE ALSO</H2>
<B><A HREF="http://grass.itc.it/gdp/raster/mapcalc-algebra.pdf">r.mapcalc: An Algebra for GIS and Image
Processing</A></B>, by Michael Shapiro and Jim Westervelt, U.S. Army
Construction Engineering Research Laboratory (March/1991).
<P>
<B><A HREF="http://grass.itc.it/gdp/raster/mapcalc.pdf">Performing Map Calculations on GRASS Data:
r.mapcalc Program Tutorial</A></B>, by Marji Larson, Michael Shapiro and Scott
Tweddale, U.S. Army Construction Engineering Research Laboratory (December
1991)
<p>
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).
<P>
<EM>
<A HREF="g.region.html">g.region</A>,
<A HREF="r.bitpattern.html">r.bitpattern</A>,
<A HREF="r.blend.html">r.blend</A>,
<A HREF="r.colors.html">r.colors</A>,
<A HREF="r.fillnulls.html">r.fillnulls</A>
</EM>
<H2>AUTHORS</H2>
Michael Shapiro, U.S.Army Construction Engineering
Research Laboratory
<P>
Glynn Clements
<p><i>Last changed: $Date: 2007-08-24 06:13:51 +0200 (Fri, 24 Aug 2007) $</i>
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