sprandn

Sparse normally distributed random matrix

Syntax

R = sprandn(S)

R = sprandn(m,n,density)

R = sprandn(m,n,density,rc)

Description

R = sprandn(S) creates a sparse matrix that has the same sparsity pattern as the matrix S, but with normally distributed random entries with mean 0 and variance 1.

example

R = sprandn(m,n,density) creates a random m-by-n sparse matrix with approximately density*m*n normally distributed nonzero entries for density in the interval [0,1].

example

R = sprandn(m,n,density,rc) creates a matrix that also has reciprocal condition number approximately equal to rc. The matrix R is constructed from a sum of matrices of rank one.

example

Examples

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Create Sparse Matrices with Same Sparsity Pattern

Open Live Script

Create the 60-by-60 sparse adjacency matrix of the connectivity graph of the Buckminster Fuller geodesic dome. Plot the sparsity pattern of the matrix S.

S = bucky;
spy(S)

Figure contains an axes object. The axes object with xlabel nz = 180 contains a line object which displays its values using only markers.

Create another sparse matrix R that has the same sparsity pattern as the matrix S, but with normally distributed random entries. Plot the sparsity pattern of R.

R = sprandn(S);
spy(R)

Figure contains an axes object. The axes object with xlabel nz = 180 contains a line object which displays its values using only markers.

Specify Density

Open Live Script

Create a random 500-by-1000 sparse matrix with density 0.1. The matrix has approximately 0.1*500*1000 = 50000 normally distributed nonzero entries.

R = sprandn(500,1000,0.1);

Show the exact number of nonzero elements in the matrix R.

n = nnz(R)

n = 
47663

Specify Reciprocal Condition Number

Open Live Script

Create a random 50-by-100 sparse matrix with approximately 0.2*50*100 = 1000 normally distributed nonzero entries. Specify the reciprocal condition number of the matrix to be 0.25.

R = sprandn(50,100,0.2,0.25);

Show that the condition number of the matrix R is equal to 1/0.25 = 4.

cond(full(R))

ans = 
4.0000

Input Arguments

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`S` — Input matrix
full matrix | sparse matrix

Input matrix, specified as a full or sparse matrix.

`m` — Number of matrix rows
nonnegative integer

Number of matrix rows, specified as a nonnegative integer.

`n` — Number of matrix columns
nonnegative integer

Number of matrix columns, specified as a nonnegative integer.

`density` — Density of nonzero elements
scalar

Density of nonzero elements, specified as a scalar. density must be in the interval [0,1].

Data Types: double

`rc` — Reciprocal condition number
scalar | vector

Reciprocal condition number, specified as a scalar or vector. rc must be in the interval [0,1].

If rc is a vector of length lr, where lr <= min(m,n), then R = sprandn(m,n,density,rc) has rc as its first lr singular values and all others are zero. In this case, R is generated by random plane rotations applied to a diagonal matrix with the given singular values. It has a great deal of topological and algebraic structure.

Data Types: double

Limitations

sprandn is designed to produce large matrices with small density and will generate significantly fewer nonzero values than requested if m*n is small or density is large.

Tips

sprandn uses the same random number generator as the rand, randi, and randn functions. You can control this generator with the rng function.

Extended Capabilities

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

The sprandn function supports GPU array input with these usage notes and limitations:

The rc argument is 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:

See distributed.sprandn (Parallel Computing Toolbox).

Version History

Introduced before R2006a

expand all

R2022a: Improved performance when generating random sparse matrices

The sprand and sprandn functions show improved performance when generating random sparse matrices if the number of nonzero elements in the output is larger than the number of rows.

For example, generating a 10,000-by-10,000 matrix with 10% density of nonzero elements is about 2.5x faster than in the previous release.

function timingSprand
n = 1e4;
d = 0.1; 
rng default

tic
sprand(n,n,d);
toc
end

The approximate execution times are:

R2021b: 2.7 s

R2022a: 1.1 s

The code was timed on a Windows^® 10, Intel^® Xeon^® CPU W-2133 @ 3.60 GHz test system by calling the timingSprand function.

sprandn

Syntax

Description

Examples

Create Sparse Matrices with Same Sparsity Pattern

Specify Density

Specify Reciprocal Condition Number

Input Arguments

S — Input matrix full matrix | sparse matrix

m — Number of matrix rows nonnegative integer

n — Number of matrix columns nonnegative integer

density — Density of nonzero elements scalar

rc — Reciprocal condition number scalar | vector

Limitations

Tips

Extended Capabilities

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

R2022a: Improved performance when generating random sparse matrices

See Also

`S` — Input matrix
full matrix | sparse matrix

`m` — Number of matrix rows
nonnegative integer

`n` — Number of matrix columns
nonnegative integer

`density` — Density of nonzero elements
scalar

`rc` — Reciprocal condition number
scalar | vector

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™.