## table of contents

r.mapcalc(1grass) | GRASS GIS User's Manual | r.mapcalc(1grass) |

# 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:¶

## 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 parameterTo read command from the file, use file= explicitly, e.g.:

r.mapcalc file=fileor:

r.mapcalc file=- < fileor:

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.

The neighborhood modifier cannot be used on maps generated within
same *r.mapcalc* command run (see "KNOWN ISSUES"
section).

## 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:Note, that the row() and col() indexing starts with 1.

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

## 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 < 0More 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 NULLeval() 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=1However, 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

# SOURCE CODE¶

Available at: r.mapcalc source code (history)

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© 2003-2020 GRASS Development Team, GRASS GIS 7.8.5 Reference Manual

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