# An overview of the Math toolset in Image Analyst

The Math toolset contains tools that perform mathematical operations on rasters.

The tools are grouped into four main categories:

• Math

The tools at the top level of the math toolset perform basic mathematical operations on rasters in the following categories: Arithmetic, Power, Exponential, and Logarithmic. Also included are tools that alter the sign of the raster values, as well as those involved in converting the values between integer and floating point.

• Conditional

The Conditional math toolset allows you to control the output values based on the conditions placed on the input values.

• Logical

The Logical math toolset contains tools for performing logical evaluations on rasters in the following categories: Bitwise, Boolean, Combinatorial, Relational, and Conditional.

• Trigonometric

The Trigonometric math toolset contains tools for trigonometric calculations in several categories: Regular, Inverse, Hyperbolic, and Inverse Hyperbolic.

The Math tools are also available if you have a Spatial Analyst extension license.

Certain Math tools are also available with a 3D Analyst extension license. These tools are: Divide, Float, Int, Minus, Plus, and Times.

The following table lists the available Math toolsets and provides a brief description of each.

ToolDescription

General Math toolset

The general Math tools apply a mathematical function to the input. These tools fall into several categories. The arithmetic tools perform basic mathematical operations, such as addition and multiplication. There are tools that perform various types of exponentiation operations, which includes exponentials and logarithms in addition to the basic power operations. The remaining tools are used either for sign conversion or for conversion between integer and floating point data types.

Conditional Math toolset

The Conditional Math tools allow you to control the output values based on the conditions placed on the input values. The conditions that can be applied are of two types, those being either queries on the attributes or a condition based on the position of the conditional statement in a list.

Logical Math toolset

The Logical Math tools evaluate the values of the inputs and determine the output values based on a defined logic. The tools are grouped into four main categories: Bitwise, Boolean, Combinatorial, Logical, and Relational.

Trigonometric Math toolset

Trigonometric Math tools perform various trigonometric calculations on the values in an input raster.

The Math toolsets

## The general Math tools

The following applies only to the tools at the top level of this toolset. For more details on the others, go to the appropriate sections for the Conditional, Logical and Trigonometric mathematical operations.

The general Math tools apply a mathematical function to the input. These tools fall into several categories. The arithmetic tools perform basic mathematical operations, such as addition and multiplication. There are tools that perform various types of exponentiation operations, which includes exponentials and logarithms in addition to the basic power operations. The remaining tools are used either for sign conversion or for conversion between integer and floating point data types.

Certain tools require two inputs:

• Arithmetic: Plus, Minus, Times, Divide, Mod (modulus)
• Power: Power

While other tools only need a single input:

• Exponential: Exp, Exp2, Exp10
• Logarithmic: Ln, Log2, Log10
• Power: Square, Square Root
• Sign: Abs, Negate
• Type conversion: Float, Int, Round Down, Round Up

The following table lists the available general Math tools and provides a brief description of each:

ToolDescription

Abs

Calculates the absolute value of the cells in a raster.

Divide

Divides the values of two rasters on a cell-by-cell basis.

Exp

Calculates the base e exponential of the cells in a raster.

Exp10

Calculates the base 10 exponential of the cells in a raster.

Exp2

Calculates the base 2 exponential of the cells in a raster.

Float

Converts each cell value of a raster into a floating-point representation.

Int

Converts each cell value of a raster to an integer by truncation.

Ln

Calculates the natural logarithm (base e) of cells in a raster.

Log10

Calculates the base 10 logarithm of cells in a raster.

Log2

Calculates the base 2 logarithm of cells in a raster.

Minus

Subtracts the value of the second input raster from the value of the first input raster on a cell-by-cell basis.

Mod

Finds the remainder (modulo) of the first raster when divided by the second raster on a cell-by-cell basis.

Negate

Changes the sign (multiplies by -1) of the cell values of the input raster on a cell-by-cell basis.

Plus

Adds (sums) the values of two rasters on a cell-by-cell basis.

Power

Raises the cell values in a raster to the power of the values found in another raster.

Round Down

Returns the next lower integer value, just represented as a floating point, for each cell in a raster.

Round Up

Returns the next higher integer value, just represented as a floating point, for each cell in a raster.

Square

Calculates the square of the cell values in a raster.

Square Root

Calculates the square root of the cell values in a raster.

Times

Multiplies the values of two rasters on a cell-by-cell basis.

Tools in the general Math toolset

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1. The general Math tools