quad — Approximate finite scalar definite integrals with MATLAB's legacy quad interface.
q = quad(fun, a, b) approximates the definite integral of scalar integrand fun from a to b using adaptive Simpson quadrature. It supports the legacy MATLAB call forms with optional tolerance, trace output, forwarded parameters, and [q, fcnt] output.
Syntax
q = quad(fun, a, b)
q = quad(fun, a, b, tol, trace, p1, p2, ...)
[q, fcnt] = quad(fun, a, b)
[q, fcnt] = quad(fun, a, b, tol, trace, p1, p2, ...)Inputs
| Name | Type | Required | Default | Description |
|---|---|---|---|---|
fun | Any | Yes | — | Scalar integrand callback. |
a | Any | Yes | — | Lower integration bound. |
b | Any | Yes | — | Upper integration bound. |
tol | NumericScalar | No | 1e-6 | Absolute error tolerance. Empty uses the default. |
trace | Any | No | false | Nonzero value prints legacy [fcnEvals, a, b-a, Q] trace rows. |
p | Any | Variadic | — | Additional arguments forwarded to the integrand. |
Returns
| Name | Type | Description |
|---|---|---|
q | NumericScalar | Numerical integral estimate. |
fcnt | NumericScalar | Number of integrand evaluations. |
Returned values from quad depend on how many outputs the caller requests.
Errors
| Identifier | When | Message |
|---|---|---|
RunMat:quad:InvalidArgument | Tolerance, trace flag, or argument grammar is invalid. | quad: invalid argument |
RunMat:quad:InvalidInput | Bounds, integrand values, or adaptive solver semantics are invalid. | quad: invalid input |
RunMat:quad:TooManyOutputs | `quad` is called with more than two requested output arguments. | quad: too many output arguments |
How quad works
- The function may be a named function handle such as
@sin, an anonymous function such as@(x) x.^2, or a function-handle string. - The integration loop evaluates the integrand at scalar sample points and adapts subintervals using Simpson error estimates.
tolis an absolute positive scalar tolerance and defaults to1e-6; an emptytoluses the default.traceprints legacy adaptive subdivision rows as[fcnEvals, a, b-a, Q]when nonzero; an emptytracedisables tracing.- Arguments after
traceare forwarded to the integrand asfun(x, p1, p2, ...). - The integrand must return a finite real scalar. Array-valued and complex-valued integrands are not supported by
quad. - Finite reversed bounds are accepted and negate the result. Equal bounds return zero with a function count of zero.
- Requests for more than two outputs are rejected.
Examples
Integrate sine over one half-period
q = quad(@sin, 0, pi)Expected output:
q =
2.0000Return the function evaluation count
[q, fcnt] = quad(@(x) x.^2, 0, 1)Expected output:
q =
0.3333Forward an extra argument to the integrand
q = quad(@(x,a) a.*x, 0, 2, [], [], 3)Expected output:
q =
6.0000Using quad with coding agents
Open a RunMat example with live inputs, then ask the agent to explain how quad changes the result.
Run a small quad example, explain the result, then change one input and compare the output.
FAQ
Should new code use quad or integral?⌄
Use integral for new code when possible. quad exists for legacy MATLAB script compatibility.
Does quad support extra parameters?⌄
Yes. Values after trace are forwarded to the function handle after the scalar sample point.
Does quad run on the GPU?⌄
The adaptive solver runs on the host because it repeatedly invokes user code through function-handle dispatch. The callback itself may call GPU-aware builtins.
Related Math functions
Elementwise
abs · angle · complex · conj · double · exp · expm1 · factorial · gamma · heaviside · hypot · imag · ldivide · log · log10 · log1p · log2 · minus · nextpow2 · plus · pow2 · power · rdivide · real · sign · single · sqrt · times
Trigonometry
acos · acosh · asin · asinh · atan · atan2 · atanh · cos · cosd · cosh · deg2rad · rad2deg · sin · sind · sinh · tan · tand · tanh
Reduction
all · any · cummax · cummin · cumprod · cumsum · cumtrapz · diff · gradient · max · mean · median · min · nnz · prod · std · sum · trapz · var
Structure
Open-source implementation
Unlike proprietary runtimes, every RunMat function is open-source. Read exactly how quad is executed, line by line, in Rust.
- View the source for quad in Rust on GitHub
- Learn how the RunMat runtime works
- Found a bug? Open an issue with a minimal reproduction.
About RunMat
RunMat is an open-source runtime that executes MATLAB-syntax code blazing on any GPU. It is licensed under the Apache 2.0 license.
- RunMat automatically optimizes your math for GPU execution on Apple, Nvidia, and AMD hardware. No code changes needed. Simulations that took hours now take minutes.
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