nnz

Number of nonzero matrix elements

Syntax

N = nnz(X)

Description

N = nnz(X) returns the number of nonzero elements in matrix X.

Examples

Number of Nonzeros

Create an identity matrix and determine the number of nonzeros it contains.

X = eye(4)

X = 4×4

     1     0     0     0
     0     1     0     0
     0     0     1     0
     0     0     0     1

N = nnz(X)

N = 
4

Number of Elements Meeting a Condition

Use nnz in conjunction with a relational operator to determine how many matrix elements meet a condition. Since relational operators produce logical matrices of 1s and 0s, the nnz function counts the 1s where the condition is true.

Create a matrix and determine how many elements are greater than 10.

X = magic(5)

X = 5×5

    17    24     1     8    15
    23     5     7    14    16
     4     6    13    20    22
    10    12    19    21     3
    11    18    25     2     9

nnz(X>10)

ans = 
15

Density of Sparse Matrix

The density of a matrix is the ratio of nonzeros to the total number of elements, nnz(X)/numel(X).

Create a sparse matrix representing the finite difference Laplacian on an L-shaped domain and calculate its density.

X = delsq(numgrid('L',20));
spy(X)

d = nnz(X)/numel(X)

d = 
0.0194

The result indicates that only about 2% of the elements in the matrix are nonzero.

Input Arguments

X — Input matrix

matrix

Input matrix.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | logical | duration | calendarDuration
Complex Number Support: Yes

Extended Capabilities

Tall Arrays

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

The nnz function fully supports tall arrays. For more information, see Tall Arrays.

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

GPU Code Generation
Generate CUDA® code for NVIDIA® GPUs using GPU Coder™.

Thread-Based Environment

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

This function fully supports thread-based environments. For more information, see Run MATLAB Functions in Thread-Based Environment.

GPU Arrays

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

The nnz function fully supports GPU arrays. To run the function on a GPU, specify the input data as a gpuArray (Parallel Computing Toolbox). 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™.

This function fully supports distributed arrays. For more information, see Run MATLAB Functions with Distributed Arrays (Parallel Computing Toolbox).

Version History

Introduced before R2006a