Set intersection of two arrays (2024)

Set intersection of two arrays

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Syntax

C = intersect(A,B)

C = intersect(A,B,setOrder)

C = intersect(A,B,___,'rows')

C = intersect(A,B,'rows',___)

[C,ia,ib]= intersect(___)

[C,ia,ib]= intersect(A,B,'legacy')

[C,ia,ib]= intersect(A,B,'rows','legacy')

Description

example

C = intersect(A,B) returns the data common to both A and B, with no repetitions. C is in sorted order.

If A and B are tables or timetables, then intersect returns the set of rows common to both tables. For timetables, intersect takes row times into account to determine equality, and sorts the output timetable C by row times.

example

C = intersect(A,B,setOrder) returns C in a specific order. setOrder can be 'sorted' or 'stable'.

C = intersect(A,B,___,'rows') and C = intersect(A,B,'rows',___) treat each row of A and each row of B as single entities and return the rows common to both A and B, with no repetitions. You must specify A and B and optionally can specify setOrder.

The 'rows' option does not support cell arrays, unless one of the inputs is either a categorical array or a datetime array.

example

[C,ia,ib]= intersect(___) also returns index vectors ia and ib using any of the previous syntaxes.

Generally, C = A(ia) and C = B(ib).
If the 'rows' option is specified, then C = A(ia,:) and C = B(ib,:).
If A and B are tables or timetables, then C = A(ia,:) and C = B(ib,:).

example

[C,ia,ib]= intersect(A,B,'legacy') and [C,ia,ib]= intersect(A,B,'rows','legacy') preserve the behavior of the intersect function from R2012b and prior releases.

The 'legacy' option does not support categoricalarrays, datetime arrays, duration arrays, tables, or timetables.

Examples

collapse all

Intersection of Two Vectors

Open Live Script

Create two vectors that have some values in common.

A = [7 1 7 7 4]; B = [7 0 4 4 0];

Find the values common to both A and B.

C = intersect(A,B)

C = 1×2 4 7

Intersection of Two Tables

Open Live Script

Create two tables with rows in common.

A = table([1:5]',categorical({'A';'B';'C';'D';'E'}),logical([0;1;0;1;0]))

A=5×3 table Var1 Var2 Var3 ____ ____ _____ 1 A false 2 B true 3 C false 4 D true 5 E false

B = table([1:2:10]',categorical({'A';'C';'E';'G';'I'}),logical(zeros(5,1)))

B=5×3 table Var1 Var2 Var3 ____ ____ _____ 1 A false 3 C false 5 E false 7 G false 9 I false

Find the rows common to both A and B.

C = intersect(A,B)

C=3×3 table Var1 Var2 Var3 ____ ____ _____ 1 A false 3 C false 5 E false

Intersection of Two Vectors and Their Indices

Open Live Script

Create two vectors with values in common.

A = [7 1 7 7 4]; B = [7 0 4 4 0];

Find the values common to both A and B, as well as the index vectors ia and ib, such that C = A(ia) and C = B(ib).

[C,ia,ib] = intersect(A,B)

C = 1×2 4 7

ia = 2×1 5 1

ib = 2×1 3 1

Intersection of Two Tables and Their Indices

Open Live Script

Create a table, A, of gender, age, and height for five people.

A = table(categorical({'M';'M';'F';'M';'F'}),...[27;52;31;46;35],[74;68;64;61;64],...'VariableNames',{'Gender' 'Age' 'Height'},...'RowNames',{'Ted' 'Fred' 'Betty' 'Bob' 'Judy'})

A=5×3 table Gender Age Height ______ ___ ______ Ted M 27 74 Fred M 52 68 Betty F 31 64 Bob M 46 61 Judy F 35 64

Create a table, B, with rows in common with A.

B = table(categorical({'F';'M';'F';'F'}),...[31;47;35;23],[64;68;62;58],...'VariableNames',{'Gender' 'Age' 'Height'},...'RowNames',{'Meg' 'Joe' 'Beth' 'Amy'})

B=4×3 table Gender Age Height ______ ___ ______ Meg F 31 64 Joe M 47 68 Beth F 35 62 Amy F 23 58

Find the rows common to both A and B, as well as the index vectors ia and ib, such that C = A(ia,:) and C = B(ib,:).

[C,ia,ib] = intersect(A,B)

C=1×3 table Gender Age Height ______ ___ ______ Betty F 31 64

ia = 3

ib = 1

Two rows that have the same values, but different names, are considered equal. Therefore, we discover that Betty, A(3,:), and Meg, B(1,:) have the same gender, age, and height.

Intersection of Rows in Two Matrices

Open Live Script

Create two matrices with rows in common.

A = [2 2 2; 0 0 1; 1 2 3; 1 1 1];B = [1 2 3; 2 2 2; 2 2 0];

Find the rows common to both A and B as well as the index vectors ia and ib, such that C = A(ia,:) and C = B(ib,:).

[C,ia,ib] = intersect(A,B,'rows')

C = 2×3 1 2 3 2 2 2

ia = 2×1 3 1

ib = 2×1 1 2

A and B do not need to have the same number of rows, but they must have the same number of columns.

Intersection with Specified Output Order

Open Live Script

Use the setOrder argument to specify the ordering of the values in C.

Specify 'stable' if you want the values in C to have the same order as in A.

A = [7 1 7 7 4]; B = [7 0 4 4 0];[C,ia,ib] = intersect(A,B,'stable')

C = 1×2 7 4

ia = 2×1 1 5

ib = 2×1 1 3

Alternatively, you can specify 'sorted' order.

[C,ia,ib] = intersect(A,B,'sorted')

C = 1×2 4 7

ia = 2×1 5 1

ib = 2×1 3 1

Intersection of Vectors Containing NaNs

Open Live Script

Create two vectors containing NaN.

A = [5 NaN NaN]; B = [5 NaN NaN];

Find the values common to both A and B.

C = intersect(A,B)

C = 5

intersect treats NaN values as distinct.

Cell Array of Character Vectors with Trailing White Space

Open Live Script

Create a cell array of character vectors, A.

A = {'dog','cat','fish','horse'};

Create a cell array of character vectors, B, where some of the vectors have trailing white space.

B = {'dog ','cat','fish ','horse'};

Find the character vectors common to both A and B.

[C,ia,ib] = intersect(A,B)

C = 1x2 cell {'cat'} {'horse'}

ia = 2×1 2 4

ib = 2×1 2 4

intersect treats trailing white space in cell arrays of character vectors as distinct characters.

Intersection of Arrays of Different Classes and Shapes

Open Live Script

Create a column vector character array.

A = ['A';'B';'C'], class(A)

A = 3x1 char array 'A' 'B' 'C'

ans = 'char'

Create a 2-by-3 matrix containing elements of numeric type double.

B = [65 66 67;68 69 70], class(B)

B = 2×3 65 66 67 68 69 70

ans = 'double'

Find the values common to both A and B.

[C,ia,ib] = intersect(A,B)

C = 3x1 char array 'A' 'B' 'C'

ia = 3×1 1 2 3

ib = 3×1 1 3 5

intersect interprets B as a character array and returns a character array, C.

class(C)

ans = 'char'

Intersection of Char and Cell Array of Character Vectors

Open Live Script

Create a character vector containing animal names that have three letters.

A = ['dog';'cat';'fox';'pig'];class(A)

ans = 'char'

Create a cell array of character vectors containing animal names of varying lengths.

B = {'cat','dog','fish','horse'};class(B)

ans = 'cell'

Find the character vectors common to both A and B.

C = intersect(A,B)

C = 2x1 cell {'cat'} {'dog'}

The result, C, is a cell array of character vectors.

class(C)

ans = 'cell'

Preserve Legacy Behavior of intersect

Open Live Script

Use the 'legacy' flag to preserve the behavior of intersect from R2012b and prior releases in your code.

Find the intersection of A and B with the current behavior.

A = [7 1 7 7 4]; B = [7 0 4 4 0];[C1,ia1,ib1] = intersect(A,B)

C1 = 1×2 4 7

ia1 = 2×1 5 1

ib1 = 2×1 3 1

Find the unique elements of A and preserve the legacy behavior.

[C2,ia2,ib2] = intersect(A,B,'legacy')

C2 = 1×2 4 7

ia2 = 1×2 5 4

ib2 = 1×2 4 1

Input Arguments

collapse all

`setOrder` — Order flag
`'sorted'` (default) | `'stable'`

Order flag, specified as 'sorted' or 'stable', indicates the order of the values (or rows) in C.

Flag Description

Flag	Description
`'sorted'`	The values (or rows) in `C` return in sorted order as returned by sort. Example C = intersect([7 0 1 5],[0 2 7 5],'sorted') C = 0 5 7
`'stable'`	The values (or rows) in `C` return in the same order as they appear in `A`. Example C = intersect([7 0 1 5],[0 2 7 5],'stable') C = 7 0 5

'sorted'

The values (or rows) in C return in sorted order as returned by sort.

Example

C = intersect([7 0 1 5],[0 2 7 5],'sorted')

C = 0 5 7

'stable'

The values (or rows) in C return in the same order as they appear in A.

Example

C = intersect([7 0 1 5],[0 2 7 5],'stable')

C = 7 0 5

Data Types: char | string

Output Arguments

collapse all

`C` — Data common to `A` and `B`
vector | matrix | table | timetable

Data common to A and B, returned as a vector, matrix, or table. If the inputs A and B are tables or timetables, then the order of the variables in C is the same as the order of the variables in A.

The following describes the shape of C when the inputs are vectors or matrices and when the 'legacy' flag is not specified:

If the 'rows' flag is not specified, then C is a column vector unless both A and B are row vectors, in which case C is a row vector.
If the 'rows' flag is specified, then C is a matrix containing the rows in common from A and B.

The class of the inputs A and B determinesthe class of C:

If the class of A and B arethe same, then C is the same class.
If you combine a char or nondoublenumeric class with double, then C isthe same class as the nondouble input.
If you combine a logical classwith double, then C is double.
If you combine a cell array of character vectors with char,then C is a cell array of character vectors.
If you combine a categorical array with a charactervector, cell array of character vectors, or string, then C isa categorical array.
If you combine a datetime array with a cell arrayof date character vectors or single date character vector, then C isa datetime array.
If you combine a string array with a character vectoror cell array of character vectors, then C is astring array.

`ia` — Index to `A`
column vector

Index to A, returned as a column vector when the 'legacy' flag is not specified. ia identifies the values (or rows) in A that are common to B. If there is a repeated value (or row) in A, then ia contains the index to the first occurrence of the value (or row).

`ib` — Index to `B`
column vector

Index to B, returned as a column vector when the 'legacy' flag is not specified. ib identifies the values (or rows) in B that are common to A. If there is a repeated value (or row) in B, then ib contains the index to the first occurrence of the value (or row).

Tips

To find the intersection with respect to a subset of variables from a table or timetable, you can use column subscripting. For example, you can use intersect(A(:,vars),B(:,vars)), where vars is a positive integer, a vector of positive integers, a variable name, a cell array of variable names, or a logical vector. Alternatively, you can use vartype to create a subscript that selects variables of a specified type.

Extended Capabilities

Tall Arrays
Calculate with arrays that have more rows than fit in memory.

Usage notes and limitations:

The 'legacy' flag is not supported.
The 'stable' flag is not supported when both inputs are tall arrays.
Inputs of type 'char' are not supported when both inputs are tall arrays.
Ordinal categorical arrays are not supported.

For more information, see Tall Arrays.

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

Code generation does not support cell arrays for the first or second arguments.
When you do not specify the 'rows' option:
- Inputs A and B must be vectors. If you specify the 'legacy' option, inputs A and B must be row vectors.
- The first dimension of a variable-size row vector must have fixed length 1. The second dimension of a variable-size column vector must have fixed length 1.
- The input [] is not supported. Use a 1-by-0 or 0-by-1 input, for example, zeros(1,0), to represent the empty set.
- If you specify the 'legacy' option, then empty outputs are row vectors, 1-by-0. They are never 0-by-0.
When you specify both the 'legacy' option and the 'rows' option, the outputs ia and ib are column vectors. If these outputs are empty, they are 0-by-1. They are never 0-by-0, even if the output C is 0-by-0.
When the setOrder is 'sorted' or when you specify the 'legacy' option, the inputs must already be sorted in ascending order. The first output, C, is sorted in ascending order.
Complex inputs must be single or double.
When one input is complex and the other input is real, do one of the following:
- Set setOrder to 'stable'.
- Sort the real input in complex ascending order (by absolute value). Suppose the real input is x. Use sort(complex(x))or sortrows(complex(x)).
See Code Generation for Complex Data with Zero-Valued Imaginary Parts (MATLAB Coder).

Thread-Based Environment
Run code in the background using MATLAB® `backgroundPool` or accelerate code with Parallel Computing Toolbox™ `ThreadPool`.

GPU Arrays
Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

Usage notes and limitations:

The 'legacy' flag is not supported.
64-bit integers are not supported.

For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).

Distributed Arrays
Partition large arrays across the combined memory of your cluster using Parallel Computing Toolbox™.

Usage notes and limitations:

The 'legacy' flag is not supported.
Table, timetable, categorical, datetime and duration inputs are not supported.
Inputs of type char and string are not supported when A or B is a cell array of character vectors. Convert cell arrays of character vectors input arguments to string arrays instead.

For more information, see Run MATLAB Functions with Distributed Arrays (Parallel Computing Toolbox).

Version History

Introduced before R2006a

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Set intersection of two arrays (2024)

Syntax

Description

Examples

Intersection of Two Vectors

Intersection of Two Tables

Intersection of Two Vectors and Their Indices

Intersection of Two Tables and Their Indices

Intersection of Rows in Two Matrices

Intersection with Specified Output Order

Intersection of Vectors Containing NaNs

Cell Array of Character Vectors with Trailing White Space

Intersection of Arrays of Different Classes and Shapes

Intersection of Char and Cell Array of Character Vectors

Preserve Legacy Behavior of intersect

Input Arguments

`setOrder` — Order flag
`'sorted'` (default) | `'stable'`

Output Arguments

`C` — Data common to `A` and `B`
vector | matrix | table | timetable

`ia` — Index to `A`
column vector

`ib` — Index to `B`
column vector

Tips

Extended Capabilities

Tall Arrays
Calculate with arrays that have more rows than fit in memory.

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

Thread-Based Environment
Run code in the background using MATLAB® `backgroundPool` or accelerate code with Parallel Computing Toolbox™ `ThreadPool`.

GPU Arrays
Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

Distributed Arrays
Partition large arrays across the combined memory of your cluster using Parallel Computing Toolbox™.

Version History

See Also

Topics

MATLAB Command

Americas

Europe

Asia Pacific

References

Set intersection of two arrays (2024)

Syntax

Description

Examples

Intersection of Two Vectors

Intersection of Two Tables

Intersection of Two Vectors and Their Indices

Intersection of Two Tables and Their Indices

Intersection of Rows in Two Matrices

Intersection with Specified Output Order

Intersection of Vectors Containing NaNs

Cell Array of Character Vectors with Trailing White Space

Intersection of Arrays of Different Classes and Shapes

Intersection of Char and Cell Array of Character Vectors

Preserve Legacy Behavior of intersect

Input Arguments

setOrder — Order flag 'sorted' (default) | 'stable'

Output Arguments

C — Data common to A and B vector | matrix | table | timetable

ia — Index to A column vector

ib — Index to B column vector

Tips

Extended Capabilities

Tall Arrays Calculate with arrays that have more rows than fit in memory.

C/C++ Code Generation Generate C and C++ code using MATLAB® Coder™.

Thread-Based Environment Run code in the background using MATLAB® backgroundPool or accelerate code with Parallel Computing Toolbox™ ThreadPool.

GPU ArraysAccelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

Distributed ArraysPartition large arrays across the combined memory of your cluster using Parallel Computing Toolbox™.

Version History

See Also

Topics

MATLAB Command

Americas

Europe

Asia Pacific

References

`setOrder` — Order flag
`'sorted'` (default) | `'stable'`

`C` — Data common to `A` and `B`
vector | matrix | table | timetable

`ia` — Index to `A`
column vector

`ib` — Index to `B`
column vector

Tall Arrays
Calculate with arrays that have more rows than fit in memory.

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

Thread-Based Environment
Run code in the background using MATLAB® `backgroundPool` or accelerate code with Parallel Computing Toolbox™ `ThreadPool`.

GPU Arrays
Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

Distributed Arrays
Partition large arrays across the combined memory of your cluster using Parallel Computing Toolbox™.