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, ...). - Integer bounds and tolerance are gated RunMat extensions and must be exactly representable in the double quadrature domain.
- Integer trace values are documented structural controls tested for exact zero/nonzero state without floating conversion. Integer forwarded parameters are documented callback payloads and retain exact native storage.
- Integer integrand results are a gated RunMat extension and must be exactly representable before adaptive Simpson arithmetic.
- 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
Optim
coneprog · fminbnd · fminunc · fsolve · fzero · integral · linprog · lsqcurvefit · lsqnonlin · optimoptions · optimset · secondordercone
Elementwise
abs · angle · bsxfun · complex · conj · double · erf · erfcinv · exp · expm1 · factorial · flintmax · gamma · gammaln · heaviside · hypot · idivide · imag · intmax · intmin · ldivide · log · log10 · log1p · log2 · minus · nextpow2 · plus · pow2 · power · rdivide · real · realmax · realmin · realsqrt · rescale · sign · single · sqrt · swapbytes · times · typecast · uint16 · uint32 · uint8
Trigonometry
acos · acosh · asin · asinh · atan · atan2 · atanh · cos · cosd · cosh · cospi · deg2rad · pol2cart · rad2deg · sin · sind · sinh · sinpi · tan · tand · tanh
Reduction
all · any · bounds · cummax · cummin · cumprod · cumsum · cumtrapz · diff · gradient · max · maxk · mean · median · min · mink · movmax · movmean · movmedian · movmin · movprod · movstd · movsum · movvar · nnz · prod · rms · std · sum · trapz · var
Structure
bandwidth · isdiag · ishermitian · issymmetric · istril · istriu · symrcm
Signal
blackman · butter · buttord · cheb2ord · conv · conv2 · deconv · downsample · envelope · filter · filtfilt · fir1 · freqz · gauspuls · hamming · hann · hilbert · periodogram · pulstran · pwelch · rectpuls · resample · sawtooth · sinc · spectrogram · square · tripuls · unwrap · upsample · zplane
Ops
cross · ctranspose · dot · mldivide · mpower · mrdivide · mtimes · pagemtimes · pagetranspose · trace · transpose
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.
- Start running code in seconds. RunMat runs in the browser, on the desktop, or from the CLI. No license server, no IT ticket.