Working with operators

In Map Algebra, operators apply a mathematical operation on input rasters and numbers.

Operators are generally placed between two inputs to perform a mathematical operation (for example, outVar = 3 + 7). In Map Algebra, operators have been overloaded, allowing operators to be used with Raster objects. To utilize an operator with a raster dataset, the dataset name must be cast as a Raster object, indicating that the Spatial Analyst implementation of the operator should be used.

The table below provides a quick reference indicating how current Map Algebra operators have been implemented in relation to Python operators and previous 9.x Map Algebra operators.

Operation	Python operator	Map Algebra operator	9.x Map Algebra operator *	Spatial Analyst GP tool
Arithmetic
Addition	+	+	+	Plus
Division	/	/	/, div	Divide
Integer Division	//	//	N/A	N/A
Modulo	%	%	Mod	Mod
Multiplication	*	*	*	Times
Power	**	**	N/A	Power
Subtraction	-	-	-	Minus
Unary Minus	-	-	-	Negate
Unary Plus	+	+	N/A	N/A
Boolean
Boolean And	N/A	&	&, and	Boolean And
Boolean Complement	N/A	~	^, not	Boolean Not
Boolean Exclusive Or	N/A	^	!, xor	Boolean XOr
Boolean Or	N/A	|	|, or	Boolean Or
Relational
Equal To	==	==	==, eq	Equal To
Greater Than	>	>	>, gt	Greater Than
Greater Than And Equal To	>=	>=	>=, ge	Greater Than Equal
Less Than	<	<	<, lt	Less Than
Less Than And Equal To	<=	<=	<=, le	Less Than Equal
Not Equal To	!=	!=	^=, <>, ne	Not Equal
Bitwise
Bitwise And	&	N/A	&&	Bitwise And
Bitwise Complement	~	N/A	^^	Bitwise Not
Bitwise Exclusive Or	^	N/A	!!	Bitwise XOr
Bitwise Left Shift	<<	<<	<<	Bitwise Left Shift
Bitwise Or	|	N/A	||	Bitwise Or
Bitwise Right Shift	>>	>>	>>	Bitwise Right Shift

* 9.x Map Algebra operator refers to the operator symbol you would have used in the Single Output Map Algebra tool or the Raster Calculator in the Spatial Analyst toolbar in ArcGIS versions 9.x and prior.

Operator rules

• When operators are only used with numbers, then the Python operator is used and acts accordingly. As shown below, the following operation will return a number.

  # outVar will be assigned 10
  outVar = 3 + 7 

• When applying an operator to rasters, the dataset names must be cast by calling the Raster class constructor to identify that the statement should use the Spatial Analyst operator to process the spatial datasets. As shown below, the operation will return a Raster object.

  outRas = Raster("inraster1") + Raster("inraster2")

• If a raster is to be used in conjunction with a number, the Spatial Analyst operator will be used.

  # In the following statement 4 is added to each cell value in inraster1
  outRas = Raster("inraster1") + 4  

• Some Spatial Analyst operators can precede the input dataset.

  outRas = -Raster("inraster")

• Python constants can be used with operators in Map Algebra statements.

  from arcpy.sa import *
  import math
  outRas = Raster("inraster") + math.pi

  In the above statement, pi is used from the Python math module. The math module also includes the base of the natural logarithm, math.e, which can also be used in a Map Algebra statement.

Tools and operators can be nested to create complex statements.

Learn more about building complex statements

Tip:

Spaces are not necessary between operators but are recommended for readability.

Operator precedence

The precedence value determines the order in which operators are executed. The operator with the higher precedence will be processed first. You can use parentheses to override the precedence priority, with the operation in the deepest parentheses being processed first no matter what operator is specified.

The following table identifies the precedence value defining the priority order for processing each operator.

Map Algebra operator	Description	Precedence
Arithmetic
- (Subtraction)	Subtraction	11
- (Negate)	Unary minus	14
% (Modulo)	Modulus	13
* (Multiplication)	Multiplication	13
/ (Division)	Division	13
// (Integer Division)	Integer divide	13
+ (Addition)	Addition	12
+ (Unary Plus)	Unary plus	14
** (Power)	Power	16
Bitwise
>> (Bitwise Right Shift)	Bitwise right shift	11
<< (Bitwise Left Shift)	Bitwise left shift	11
Boolean
~ (Boolean Not)	Boolean complement	4
& (Boolean And)	Boolean and	3
^ (Boolean XOr)	Boolean exclusive	2
| (Boolean Or)	Boolean or	2
Relational
< (Less Than)	Less than	7
<= (Less Than Equal)	Less than or equal to	7
> (Greater Than)	Greater than	7
>= (Greater Than Equal)	Greater than or equal to	7
== (Equal To)	Equal to	7
!= (Not Equal)	Not equal to	7