Geografic-Information-System/raster/r.mapcalc/r3.mapcalc.html

<h2>DESCRIPTION</h2>
<em>r3.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>

<em>r3.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>
As <em>expression=</em> 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 <em>=</em> sign.

Example ('foo' is the resulting map):
<div class="code"><pre>
r3.mapcalc "foo = 1"
</pre></div>
or:
<div class="code"><pre>
r3.mapcalc 'foo = 1'
</pre></div>

An unquoted expression (i.e. split over multiple arguments) won't
work, nor will omitting the space before the = sign:

<div class="code"><pre>
r3.mapcalc 'foo=1'
Sorry, &lt;foo&gt; is not a valid parameter
</pre></div>

If no options are given, it manufactures "input=-" (which reads from
stdin), so you can continue to use e.g.:

<div class="code"><pre>
r3.mapcalc &lt; file
</pre></div>
or:
<div class="code"><pre>
r3.mapcalc &lt;&lt;EOF
foo = 1
EOF
</pre></div>
But unless you need compatibility with previous versions, use input=
explicitly, e.g.:

<div class="code"><pre>
r3.mapcalc input=file
</pre></div>
or:
<div class="code"><pre>
r3.mapcalc input=- &lt;&lt;EOF
foo = 1
EOF
</pre></div>

<p>The formula entered to <em>r3.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>r3.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
     &lt;&lt;         left shift                 Bitwise      8
     &gt;&gt;         right shift                Bitwise      8
     &gt;&gt;&gt;        right shift (unsigned)     Bitwise      8
     &gt;          greater than               Logical      7
     &gt;=         greater than or equal      Logical      7
     &lt;          less than                  Logical      7
     &lt;=         less than or equal         Logical      7
     ==         equal                      Logical      6
     !=         not equal                  Logical      6
     &amp;          bitwise and                Bitwise      5
     |          bitwise or                 Bitwise      4
     &amp;&amp;         logical and                Logical      3
     &amp;&amp;&amp;        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 &amp;&amp;&amp; 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>3D GRID NAMES</h2>
Anything in the expression which is not a number, operator, or function
name is taken to be a 3D grid name. Examples:
<p><div class="code"><pre>
volume
x3
3d.his
</pre></div>
<p>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 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 3D grid 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 3D grid <em>3107</em> to the 3D grid <em>x</em>.

<p>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.
<p><em>r3.mapcalc</em> 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:
<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>r3.mapcalc</em>.)
<p>

<h2>THE NEIGHBORHOOD MODIFIER</h2>
3D grids are data base files stored in voxel format, i.e., three-dimensional
matrices of float/double values. In <em>r3.mapcalc</em>, 3D grids 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,d]</em>,
where <em>r</em> is the row offset, <em>c</em> is the column offset and <em>d</em>
is the depth offset. For example, <em>map[1,2,3]</em> refers to the cell
one row below, two columns to the right and 3 levels below of the current
cell, <em>map[-3,-2,-1]</em> refers to the cell three rows above, two columns
to the left and one level below of the current cell, and <em>map[0,1,0]</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 3D
grid or across multiple 3D grids.

<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 &gt; 0, b if x is zero, c if x &lt; 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 &lt;= x &lt; 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
 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
</pre></div>
Note, that the row(), col() and depth() 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>
      r3.mapcalc "ratio = float(soil.4 - soil.3) / soil.3)"
</pre></div>


<h2>NULL support</h2>
<ul>
<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, &amp;&amp;&amp; and ||| are treated specially, as described below).
<li>The &amp;&amp;&amp; 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>
</ul>
<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 &lt; 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 3D grids
<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 3D grid
<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 3D grid <em>b</em> by 3D grid <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&lt;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>* ( ) &gt; &amp; |
<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>r3.mapcalc</em> would see something other than the *.
<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>r3.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>r3.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>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>r3.mapcalc</em> will
be meaningless and the equation will not work as the user intended.
This is important for the eval() function.
<p><!-- STILL TRUE ??-->
Currently, there is no comment mechanism in <em>r3.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>r3.mapcalc does not print a warning in case of operations on NULL cells.
It is left to the user to utilize the isnull() function.


<h2>SEE ALSO</h2>
<b><a href="http://grass.osgeo.org/uploads/grass/history_docs/mapcalc-algebra.pdf">r3.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.osgeo.org/uploads/grass/history_docs/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><em><a href="r.mapcalc.html">r.mapcalc</a></em>


<h2>AUTHORS</h2>
Tomas Paudits &amp; Jaro Hofierka, funded by GeoModel s.r.o., Slovakia
<br><a href="mailto:tpaudits@mailbox.sk">tpaudits@mailbox.sk</a>,
<a href="MAILTO:hofierka@geomodel.sk">hofierka@geomodel.sk</a>

<p><i>Last changed: $Date$</i>