ismembertol — Test numeric membership within tolerance in MATLAB and RunMat.

ismembertol(A, B) returns logical membership flags for real numeric values in A that are within tolerance of values in B. Optional outputs return first or all matching one-based indices into B.

Syntax

LIA = ismembertol(A, B)
LIA = ismembertol(A, B, tol, Name, Value)
[LIA, LocB] = ismembertol(A, B)
[LIA, LocB] = ismembertol(A, B, tol, Name, Value)

Inputs

Returns

Returned values from ismembertol depend on how many outputs the caller requests.

Errors

How ismembertol works

• Without an explicit tolerance, RunMat uses MATLAB-compatible defaults: 1e-12 for double inputs and 1e-6 when either input is single precision.
• Element comparisons use abs(A-B) <= tol * max(abs([A(:); B(:)])) unless DataScale is supplied.
• DataScale, when scalar, changes the tolerance test to abs(A-B) <= tol * DataScale.
• ByRows, true compares complete rows and returns outputs of size size(A,1) x 1; A and B must have the same number of columns.
• In row mode, vector DataScale supplies one scale per column. A scale of Inf ignores that column during matching.
• The optional second output LocB contains the first one-based index in B for each match and 0 when absent.
• OutputAllIndices, true makes LocB a cell array whose cells contain all matching one-based indices, or [0] when no match exists.
• NaN values do not match. Exact equalities, including equal infinities, match before tolerance subtraction is considered.
• Complex, sparse, string, character, cell, struct, and object inputs are rejected. The documented host data and tolerance domains are single and double; RunMat mode additionally accepts host integer/logical data and typed integer/logical tolerance controls through declared compatibility extensions.

Does RunMat run ismembertol on the GPU?

ismembertol is registered as a sink builtin. When either input tensor lives on the GPU the runtime gathers authoritative typed storage to host memory and performs tolerance matching there.

Documented ordinary logical and double-index outputs are restored to the first resident input handle's owning provider. Integer gpuArray inputs through 32 bits retain their documented support across the fallback.

Resident 64-bit integer input and enabled ByRows or OutputAllIndices are RunMat-only extensions checked before gather. The extended all-indices cell result remains host materialized because the public GPU form excludes that output.

Examples

Testing approximate membership with default scaling

A = [0.1 1e10];
B = [0.1 + 1e-14, 1e10 + 5e-3];
LIA = ismembertol(A, B)

Expected output:

LIA =
  1x2 logical array
   1   1

Returning first matching indices

A = [1 2 4];
B = [2.01 2.02 4.2];
[LIA, LocB] = ismembertol(A, B, 0.05)

Expected output:

LIA =
  1x3 logical array
   0   1   1
LocB =
     0     1     3

Using absolute tolerance with DataScale

A = 1e10;
B = 1e10 + 5e-3;
LIA = ismembertol(A, B, 1e-6, 'DataScale', 1)

Expected output:

LIA =
     0

Comparing rows and ignoring one column

A = [0 0.5; 10 20];
B = [0.05 999; 10.2 -999];
[LIA, LocB] = ismembertol(A, B, 0.1, 'ByRows', true, 'DataScale', [1 Inf])

Expected output:

LIA =
  2x1 logical array
   1
   0
LocB =
     1
     0

Returning all matching locations

A = 2;
B = [1.99 2.01 9.5];
[LIA, LocB] = ismembertol(A, B, 0.01, 'OutputAllIndices', true)

Expected output:

LIA =
     1
LocB =
  1x1 cell array
    {[1; 2]}

Using gpuArray inputs

G = gpuArray([1; 2]);
H = gpuArray([1 + 1e-13; 3]);
LIA = ismembertol(G, H)

Expected output:

LIA =
  2x1 logical array
   1
   0

Using ismembertol with coding agents

Open a RunMat example with live inputs, then ask the agent to explain how ismembertol changes the result.

FAQ

Related Array functions

Open-source implementation

Unlike proprietary runtimes, every RunMat function is open-source. Read exactly how ismembertol is executed, line by line, in Rust.

• View the source for ismembertol in Rust on GitHub
• Learn how the RunMat runtime works
• Found a bug? Open an issue with a minimal reproduction.

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