r3.mapcalc(1grass) GRASS GIS User's Manual r3.mapcalc(1grass)
NAME
r3.mapcalc - Raster map calculator.
KEYWORDS
raster, algebra
SYNOPSIS
r3.mapcalc
r3.mapcalc --help
r3.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
r3.mapcalc performs arithmetic on raster map layers. New raster map
layers can be created which are arithmetic expressions involving exist-
ing raster map layers, integer or floating point constants, and func-
tions.
Program use
r3.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 in-
volving 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):
r3.mapcalc "foo = 1"
or:
r3.mapcalc ’foo = 1’
An unquoted expression (i.e. split over multiple arguments) won’t work,
nor will omitting the space before the = sign:
r3.mapcalc ’foo=1’
Sorry, <foo> is not a valid parameter
If no options are given, it manufactures "file=-" (which reads from
stdin), so you can continue to use e.g.:
r3.mapcalc < file
or:
r3.mapcalc <<EOF
foo = 1
EOF
But unless you need compatibility with previous versions, use file= ex-
plicitly, e.g.:
r3.mapcalc file=file
or:
r3.mapcalc file=- <<EOF
foo = 1
EOF
The formula entered to r3.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 r3.mapcalc on the command line, expressions should
be enclosed within single quotes. See NOTES, below.
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 de-
tails.
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.
3D Grid names
Anything in the expression which is not a number, operator, or function
name is taken to be a 3D grid name. Examples:
volume
x3
3d.his
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
x = a-b
would be interpreted as: x equals a minus b, whereas
x = "a-b"
would be interpreted as: x equals the 3D grid named a-b
Also
x = 3107
would create x filled with the number 3107, while
x = "3107"
would copy the 3D grid 3107 to the 3D grid x.
Quotes are not required unless the 3D grid names look like numbers or
contain operators, OR unless the program is run non-interactively. Ex-
amples given here assume the program is run interactively. See NOTES,
below.
r3.mapcalc will look for the 3D grids according to the user’s current
mapset search path. It is possible to override the search path and
specify the mapset from which to select the 3D grid. This is done by
specifying the 3D grid name in the form:
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 r3.mapcalc.)
The neighborhood modifier
3D grids are data base files stored in voxel format, i.e., three-dimen-
sional matrices of float/double values. In r3.mapcalc, 3D grids may be
followed by a neighborhood modifier that specifies a relative offset
from the current cell being evaluated. The format is map[r,c,d], where
r is the row offset, c is the column offset and d is the depth offset.
For example, map[1,2,3] refers to the cell one row below, two columns
to the right and 3 levels below of the current cell, map[-3,-2,-1]
refers to the cell three rows above, two columns to the left and one
level below of the current cell, and map[0,1,0] refers to the cell one
column to the right of the current cell. This syntax permits the devel-
opment of neighborhood-type filters within a single 3D grid or across
multiple 3D grids.
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 *
mod(x,y) return the modulus (the remainder) of x/y *
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
depth() return current depth I
nrows() number of rows in computation region I
ncols() number of columns in computation region I
ndepths() number of depth levels in computation region I
x() current x-coordinate of moving window F
y() current y-coordinate of moving window F
z() return current z value F
ewres() current east-west resolution F
nsres() current north-south resolution F
tbres() current top-bottom resolution F
area() area of current cell in square meters F
null() NULL value
Note, that the row(), col() and depth() 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 (trun-
cated) integer, while division of floats results in an accurate float-
ing point value. With functions of type * (see table above), the re-
sult 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 pro-
duce a floating-point result, as will using float():
r3.mapcalc "ratio = float(soil.4 - soil.3) / soil.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 re-
sult 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 (how-
ever, if(), eval() and isnull() are treated specially, as de-
scribed 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 other-
wise. The (new) function null() (which has no arguments) re-
turns 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 al-
ways 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 ze-
ros. 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 other-
wise. If the user wants the opposite, the ! operator, e.g. "!is-
null(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 re-
turns 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 val-
ues, 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 = volume * 2’
Without the quotes, the *, which has special meaning to the UNIX shell,
would be altered and r3.mapcalc would see something other than the *.
Multiple computations
In general, it’s preferable to do as much as possible in each r3.map-
calc command using multi-line input.
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.:
r3.mapcalc < file
or:
r3.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 r3.mapcalc command will be
valid also without quotes:
r3.mapcalc volume_A=1
r3.mapcalc volume.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, r3.mapcalc assumes that
the formula being entered by the user continues on to the next input
line. There is no limit to the possible number of input lines or to
the length of a formula.
If the r3.mapcalc formula entered by the user is very long, the map ti-
tle will contain only some of it, but most (if not all) of the formula
will be placed into the history file for the result map.
When the user enters input to r3.mapcalc non-interactively on the com-
mand 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.
3D GRID MASK handling
r3.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:
r3.mapcalc "volume_amplified = volume * 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:
r3.mapcalc "volume_const = 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 men-
tioned 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 in-
cluding the MASK should be used, e.g.:
r3.mapcalc "volume_const = 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.
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 3D grids a and b:
ave = (a + b)/2
To form a weighted average:
ave = (5*a + 3*b)/8.0
To produce a binary representation of 3D grid a so that category 0 re-
mains 0 and all other categories become 1:
mask = a != 0
This could also be accomplished by:
mask = if(a)
To mask 3D grid b by 3D grid a:
result = if(a,b)
To change all values below 5 to NULL, keep otherwise:
newmap = if(map < 5, null(), map)
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 rep-
resented 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 r3.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 r3.mapcalc command run.
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 con-
tinuation lines, the error messages produced by r3.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 r3.mapcalc. Perhaps adding
a capability that would cause the entire line to be ignored when the
user inserted a # at the start of a line as if it were not present,
would do the trick.
The function should require the user to type "end" or "exit" instead of
simply a blank line. This would make separation of multiple scripts
separable by white space.
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.
SEE ALSO
g.region, r3.colors, r.mapcalc
REFERENCES
r.mapcalc: An Algebra for GIS and Image Processing, by Michael Shapiro
and Jim Westervelt, U.S. Army Construction Engineering Research Labora-
tory (March/1991).
Performing Map Calculations on GRASS Data: r.mapcalc Program Tutorial,
by Marji Larson, Michael Shapiro and Scott Tweddale, U.S. Army Con-
struction Engineering Research Laboratory (December 1991)
Neteler, M. (2001): Volume modelling of soils using GRASS GIS 3D tools.
- in: Brovelli, M. (ed.)(2001): The Geomatics Workbook N. 2. Politec-
nico di Milano, Italy (ISSN 1591-092X) (PDF)
AUTHORS
Tomas Paudits & Jaro Hofierka, funded by GeoModel s.r.o., Slovakia
tpaudits@mailbox.sk, hofierka@geomodel.sk
Glynn Clements
SOURCE CODE
Available at: r3.mapcalc source code (history)
Accessed: unknown
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