This is the command r.mapcalcgrass that can be run in the OnWorks free hosting provider using one of our multiple free online workstations such as Ubuntu Online, Fedora Online, Windows online emulator or MAC OS online emulator

**PROGRAM:**

**NAME**

**r.mapcalc**- Raster map calculator.

**KEYWORDS**

raster, algebra

**SYNOPSIS**

**r.mapcalc**

**r.mapcalc**

**--help**

**r.mapcalc**[-

**s**] [

**expression**=

__string__] [

**file**=

__name__] [

**seed**=

__integer__] [--

**overwrite**]

[--

**help**] [--

**verbose**] [--

**quiet**] [--

**ui**]

**Flags:**

**-s**

Generate random seed (result is non-deterministic)

**--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

**file**=

__name__

File containing expression(s) to evaluate

**seed**=

__integer__

Seed for rand() function

**DESCRIPTION**

__r.mapcalc__performs arithmetic on raster map layers. New raster map layers can be created

which are arithmetic expressions involving existing raster map layers, integer or floating

point constants, and functions.

**Program**

**use**

__r.mapcalc__expression have the form:

**result**

**=**

__expression__

where

__result__is the name of a raster map layer to contain the result of the calculation

and

**expression**is any legal arithmetic expression involving existing raster map layers

(except

__result__itself), integer or floating point constants, and functions known to the

calculator. Parentheses are allowed in the expression and may be nested to any depth.

__result__will be created in the user’s current mapset.

As

**expression=**is the first option, it is the default. This means that passing an

expression on the command line is possible as long as the expression is quoted and a space

is included before the first

__=__sign. Example (’foo’ is the resulting map):

r.mapcalc "foo = 1"

or:

r.mapcalc ’foo = 1’

An unquoted expression (i.e. split over multiple arguments) won’t work, nor will omitting

the space before the = sign:

r.mapcalc ’foo=1’

Sorry, <foo> is not a valid parameter

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

r.mapcalc file=file

or:

r.mapcalc file=- < file

or:

r.mapcalc file=- <<EOF

foo = 1

EOF

The formula entered to

__r.mapcalc__by the user is recorded both in the

__result__map title

(which appears in the category file for

__result__) and in the history file for

__result__.

Some characters have special meaning to the command shell. If the user is entering input

to

__r.mapcalc__on the command line, expressions should be enclosed within single quotes.

See NOTES, below.

**Operators**

**and**

**order**

**of**

**precedence**

The following operators are supported:

Operator Meaning Type Precedence

--------------------------------------------------------------

- negation Arithmetic 12

~ one’s complement Bitwise 12

! not Logical 12

^ exponentiation Arithmetic 11

% modulus Arithmetic 10

/ division Arithmetic 10

* multiplication Arithmetic 10

+ addition Arithmetic 9

- subtraction Arithmetic 9

<< left shift Bitwise 8

>> right shift Bitwise 8

>>> right shift (unsigned) Bitwise 8

> greater than Logical 7

>= greater than or equal Logical 7

< less than Logical 7

<= less than or equal Logical 7

== equal Logical 6

!= not equal Logical 6

& bitwise and Bitwise 5

| bitwise or Bitwise 4

&& logical and Logical 3

&&& logical and[1] Logical 3

|| logical or Logical 2

||| logical or[1] Logical 2

?: conditional Logical 1

(modulus is the remainder upon division)

[1] The &&& and ||| operators handle null values differently to other operators. See the

section entitled

**NULL**

**support**below for more details.

The operators are applied from left to right, with those of higher precedence applied

before those with lower precedence. Division by 0 and modulus by 0 are acceptable and

give a NULL result. The logical operators give a 1 result if the comparison is true, 0

otherwise.

**Raster**

**map**

**layer**

**names**

Anything in the expression which is not a number, operator, or function name is taken to

be a raster map layer name. Examples:

elevation

x3

3d.his

Most GRASS raster map layers meet this naming convention. However, if a raster map layer

has a name which conflicts with the above rule, it should be quoted. For example, the

expression

x = a-b

would be interpreted as: x equals a minus b, whereas

x = "a-b"

would be interpreted as: x equals the raster map layer named

__a-b__

Also

x = 3107

would create

__x__filled with the number 3107, while

x = "3107"

would copy the raster map layer

__3107__to the raster map layer

__x__.

Quotes are not required unless the raster map layer names look like numbers or contain

operators, OR unless the program is run non-interactively. Examples given here assume the

program is run interactively. See NOTES, below.

__r.mapcalc__will look for the raster map layers according to the user’s current mapset

search path. It is possible to override the search path and specify the mapset from which

to select the raster map layer. This is done by specifying the raster map layer name in

the form:

name@mapset

For example, the following is a legal expression:

result = x@PERMANENT / y@SOILS

The mapset specified does not have to be in the mapset search path. (This method of

overriding the mapset search path is common to all GRASS commands, not just

__r.mapcalc__.)

**The**

**neighborhood**

**modifier**

Maps and images are data base files stored in raster format, i.e., two-dimensional

matrices of integer values. In

__r.mapcalc__, maps may be followed by a

__neighborhood__modifier

that specifies a relative offset from the current cell being evaluated. The format is

__map[r,c]__, where

__r__is the row offset and

__c__is the column offset. For example,

__map[1,2]__

refers to the cell one row below and two columns to the right of the current cell,

__map[-2,-1]__refers to the cell two rows above and one column to the left of the current

cell, and

__map[0,1]__refers to the cell one column to the right of the current cell. This

syntax permits the development of neighborhood-type filters within a single map or across

multiple maps.

**Raster**

**map**

**layer**

**values**

**from**

**the**

**category**

**file**

Sometimes it is desirable to use a value associated with a category’s

__label__instead of the

category value itself. If a raster map layer name is preceded by the

**@**operator, then the

labels in the category file for the raster map layer are used in the expression instead of

the category value.

For example, suppose that the raster map layer

__soil.ph__(representing soil pH values) has a

category file with labels as follows:

cat label

------------------

0 no data

1 1.4

2 2.4

3 3.5

4 5.8

5 7.2

6 8.8

7 9.4

Then the expression:

result = @soils.ph

would produce a result with category values 0, 1.4, 2.4, 3.5, 5.8, 7.2, 8.8 and 9.4.

Note that this operator may only be applied to raster map layers and produces a floating

point value in the expression. Therefore, the category label must start with a valid

number. If the category label is integer, it will be represented by a floating point

number. I the category label does not start with a number or is missing, it will be

represented by NULL (no data) in the resulting raster map.

**Grey**

**scale**

**equivalents**

**and**

**color**

**separates**

It is often helpful to manipulate the colors assigned to map categories. This is

particularly useful when the spectral properties of cells have meaning (as with imagery

data), or when the map category values represent real quantities (as when category values

reflect true elevation values). Map color manipulation can also aid visual recognition,

and map printing.

The # operator can be used to either convert map category values to their grey scale

equivalents or to extract the red, green, or blue components of a raster map layer into

separate raster map layers.

result = #map

converts each category value in

__map__to a value in the range 0-255 which represents the

grey scale level implied by the color for the category. If the map has a grey scale color

table, then the grey level is what #map evaluates to. Otherwise, it is computed as:

0.10 * red + 0.81 * green + 0.01 * blue

Alternatively, you can use:

result = y#map

to use the NTSC weightings:

0.30 * red + 0.59 * green + 0.11 * blue

Or, you can use:

result = i#map

to use equal weightings:

0.33 * red + 0.33 * green + 0.33 * blue

The # operator has three other forms: r#map, g#map, b#map. These extract the red, green,

or blue components in the named raster map, respectively. The GRASS shell script

__r.blend__

extracts each of these components from two raster map layers, and combines them by a

user-specified percentage. These forms allow color separates to be made. For example, to

extract the red component from

__map__and store it in the new 0-255 map layer

__red__, the user

could type:

red = r#map

To assign this map grey colors type:

r.colors map=red color=rules

black

white

To assign this map red colors type:

r.colors map=red color=rules

black

red

**Functions**

The functions currently supported are listed in the table below. The type of the result

is indicated in the last column.

__F__means that the functions always results in a floating

point value,

__I__means that the function gives an integer result, and

__*__indicates that the

result is float if any of the arguments to the function are floating point values and

integer if all arguments are integer.

function description type

---------------------------------------------------------------------------

abs(x) return absolute value of x *

acos(x) inverse cosine of x (result is in degrees) F

asin(x) inverse sine of x (result is in degrees) F

atan(x) inverse tangent of x (result is in degrees) F

atan(x,y) inverse tangent of y/x (result is in degrees) F

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

graph2(x,x1[,x2,..],y1[,y2..])

alternative form of graph() F

if decision options: *

if(x) 1 if x not zero, 0 otherwise

if(x,a) a if x not zero, 0 otherwise

if(x,a,b) a if x not zero, b otherwise

if(x,a,b,c) a if x > 0, b if x is zero, c if x < 0

int(x) convert x to integer [ truncates ] I

isnull(x) check if x = NULL

log(x) natural log of x F

log(x,b) log of x base b F

max(x,y[,z...]) largest value of those listed *

median(x,y[,z...]) median value of those listed *

min(x,y[,z...]) smallest value of those listed *

mode(x,y[,z...]) mode value of those listed *

nmax(x,y[,z...]) largest value of those listed, excluding NULLs *

nmedian(x,y[,z...]) median value of those listed, excluding NULLs *

nmin(x,y[,z...]) smallest value of those listed, excluding NULLs *

nmode(x,y[,z...]) mode value of those listed, excluding NULLs *

not(x) 1 if x is zero, 0 otherwise

pow(x,y) x to the power y *

rand(a,b) random value x : a <= x < b *

round(x) round x to nearest integer I

round(x,y) round x to nearest multiple of y

round(x,y,z) round x to nearest y*i+z for some integer i

sin(x) sine of x (x is in degrees) F

sqrt(x) square root of x F

tan(x) tangent of x (x is in degrees) F

xor(x,y) exclusive-or (XOR) of x and y I

Internal variables:

row() current row of moving window

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

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

**Floating**

**point**

**values**

**in**

**the**

**expression**

Floating point numbers are allowed in the expression. A floating point number is a number

which contains a decimal point:

2.3 12.0 12. .81

Floating point values in the expression are handled in a special way. With arithmetic and

logical operators, if either operand is float, the other is converted to float and the

result of the operation is float. This means, in particular that division of integers

results in a (truncated) integer, while division of floats results in an accurate floating

point value. With functions of type * (see table above), the result is float if any

argument is float, integer otherwise.

Note: If you calculate with integer numbers, the resulting map will be integer. If you

want to get a float result, add the decimal point to integer number(s).

If you want floating point division, at least one of the arguments has to be a floating

point value. Multiplying one of them by 1.0 will produce a floating-point result, as will

using float():

r.mapcalc "ndvi = float(lsat.4 - lsat.3) / (lsat.4 + lsat.3)"

**NULL**

**support**

· Division by zero should result in NULL.

· Modulus by zero should result in NULL.

· NULL-values in any arithmetic or logical operation should result in NULL.

(however, &&& and ||| are treated specially, as described below).

· The &&& and ||| operators observe the following axioms even when x is NULL:

x &&& false == false

false &&& x == false

x ||| true == true

true ||| x == true

· NULL-values in function arguments should result in NULL (however, if(), eval() and

isnull() are treated specially, as described below).

· The eval() function always returns its last argument

· The situation for if() is:

if(x)

NULL if x is NULL; 0 if x is zero; 1 otherwise

if(x,a)

NULL if x is NULL; a if x is non-zero; 0 otherwise

if(x,a,b)

NULL if x is NULL; a if x is non-zero; b otherwise

if(x,n,z,p)

NULL if x is NULL; n if x is negative;

z if x is zero; p if x is positive

· The (new) function isnull(x) returns: 1 if x is NULL; 0 otherwise. The (new)

function null() (which has no arguments) returns an integer NULL.

· Non-NULL, but invalid, arguments to functions should result in NULL.

Examples:

log(-2)

sqrt(-2)

pow(a,b) where a is negative and b is not an integer

NULL support: Please note that any math performed with NULL cells always results in a NULL

value for these cells. If you want to replace a NULL cell on-the-fly, use the isnull()

test function in a if-statement.

Example: The users wants the NULL-valued cells to be treated like zeros. To add maps A and

B (where B contains NULLs) to get a map C the user can use a construction like:

C = A + if(isnull(B),0,B)

**NULL**

**and**

**conditions:**

For the one argument form:

if(x) = NULL if x is NULL

if(x) = 0 if x = 0

if(x) = 1 otherwise (i.e. x is neither NULL nor 0).

For the two argument form:

if(x,a) = NULL if x is NULL

if(x,a) = 0 if x = 0

if(x,a) = a otherwise (i.e. x is neither NULL nor 0).

For the three argument form:

if(x,a,b) = NULL if x is NULL

if(x,a,b) = b if x = 0

if(x,a,b) = a otherwise (i.e. x is neither NULL nor 0).

For the four argument form:

if(x,a,b,c) = NULL if x is NULL

if(x,a,b,c) = a if x > 0

if(x,a,b,c) = b if x = 0

if(x,a,b,c) = c if x < 0

More generally, all operators and most functions return NULL if *any* of their arguments

are NULL.

The functions if(), isnull() and eval() are exceptions.

The function isnull() returns 1 if its argument is NULL and 0 otherwise. If the user

wants the opposite, the ! operator, e.g. "!isnull(x)" must be used.

All forms of if() return NULL if the first argument is NULL. The 2, 3 and 4 argument forms

of if() return NULL if the "selected" argument is NULL, e.g.:

if(0,a,b) = b regardless of whether a is NULL

if(1,a,b) = a regardless of whether b is NULL

eval() always returns its last argument, so it only returns NULL if the last argument is

NULL.

**Note**: The user cannot test for NULL using the == operator, as that returns NULL if either

or both arguments are NULL, i.e. if x and y are both NULL, then "x == y" and "x != y" are

both NULL rather than 1 and 0 respectively.

The behaviour makes sense if the user considers NULL as representing an unknown quantity.

E.g. if x and y are both unknown, then the values of "x == y" and "x != y" are also

unknown; if they both have unknown values, the user doesn’t know whether or not they both

have the same value.

**NOTES**

**Usage**

**from**

**command**

**line**

Extra care must be taken if the expression is given on the command line. Some characters

have special meaning to the UNIX shell. These include, among others:

* ( ) > & |

It is advisable to put single quotes around the expression; e.g.:

’result = elevation * 2’

Without the quotes, the *, which has special meaning to the UNIX shell, would be altered

and

__r.mapcalc__would see something other than the *.

**Multiple**

**computations**

In general, it’s preferable to do as much as possible in each r.mapcalc command. E.g.

rather than:

r.mapcalc "$GIS_OPT_OUTPUT.r = r#$GIS_OPT_FIRST * .$GIS_OPT_PERCENT + (1.0 - .$GIS_OPT_PERCENT) * r#$GIS_OPT_SECOND"

r.mapcalc "$GIS_OPT_OUTPUT.g = g#$GIS_OPT_FIRST * .$GIS_OPT_PERCENT + (1.0 - .$GIS_OPT_PERCENT) * g#$GIS_OPT_SECOND"

r.mapcalc "$GIS_OPT_OUTPUT.b = b#$GIS_OPT_FIRST * .$GIS_OPT_PERCENT + (1.0 - .$GIS_OPT_PERCENT) * b#$GIS_OPT_SECOND"

use:

r.mapcalc <<EOF

$GIS_OPT_OUTPUT.r = r#$GIS_OPT_FIRST * .$GIS_OPT_PERCENT + (1.0 - .$GIS_OPT_PERCENT) * r#$GIS_OPT_SECOND

$GIS_OPT_OUTPUT.g = g#$GIS_OPT_FIRST * .$GIS_OPT_PERCENT + (1.0 - .$GIS_OPT_PERCENT) * g#$GIS_OPT_SECOND

$GIS_OPT_OUTPUT.b = b#$GIS_OPT_FIRST * .$GIS_OPT_PERCENT + (1.0 - .$GIS_OPT_PERCENT) * b#$GIS_OPT_SECOND

EOF

as the latter will read each input map only once.

**Backwards**

**compatibility**

For the backwards compatibility with GRASS 6, if no options are given, it manufactures

file=- (which reads from stdin), so you can continue to use e.g.:

r.mapcalc < file

or:

r.mapcalc <<EOF

foo = 1

EOF

But unless you need compatibility with previous GRASS GIS versions, use file= explicitly,

as stated above.

When the map name contains uppercase letter(s) or a dot which are not allowed to be in

module option names, the

__r.mapcalc__command will be valid also without quotes:

r.mapcalc elevation_A=1

r.mapcalc elevation.1=1

However, this syntax is not recommended as quotes as stated above more safe. Using quotes

is both backwards compatible and valid in future.

**Interactive**

**input**

**in**

**command**

**line**

For formulas that the user enters from standard input (rather than from the command line),

a line continuation feature now exists. If the user adds a backslash to the end of an

input line,

__r.mapcalc__assumes that the formula being entered by the user continues on to

the next input line. There is no limit to the possible number of input lines or to the

length of a formula.

If the

__r.mapcalc__formula entered by the user is very long, the map title will contain only

some of it, but most (if not all) of the formula will be placed into the history file for

the

__result__map.

When the user enters input to

__r.mapcalc__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.

**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.

**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:

mask = a != 0

This could also be accomplished by:

mask = 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)

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**

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.

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