fsolve — Solve nonlinear equation systems in MATLAB and RunMat.
x = fsolve(fun, x0) solves fun(x) = 0 starting from binary64 initial guess x0 using finite-difference Levenberg-Marquardt iterations. Scalar guesses return scalars, and vector/matrix guesses return solutions with the same shape as x0.
Syntax
x = fsolve(fun, x0)
x = fsolve(fun, x0, options)
[x,fval] = fsolve(fun, x0)
[x,fval] = fsolve(fun, x0, options)
[x,fval,exitflag] = fsolve(fun, x0)
[x,fval,exitflag] = fsolve(fun, x0, options)All supported fsolve forms
x = fsolve(fun, x0)
x = fsolve(fun, x0, options)
[x,fval] = fsolve(fun, x0)
[x,fval] = fsolve(fun, x0, options)
[x,fval,exitflag] = fsolve(fun, x0)
[x,fval,exitflag] = fsolve(fun, x0, options)
[x,fval,exitflag,output] = fsolve(fun, x0)
[x,fval,exitflag,output] = fsolve(fun, x0, options)
[x,fval,exitflag,output,jacobian] = fsolve(fun, x0)
[x,fval,exitflag,output,jacobian] = fsolve(fun, x0, options)Inputs
| Name | Type | Required | Default | Description |
|---|---|---|---|---|
fun | Any | Yes | — | System residual callback. |
x0 | Any | Yes | — | Initial guess scalar/vector. |
options | Any | No | — | Options struct from optimset. |
Returns
| Name | Type | Description |
|---|---|---|
x | NumericArray | Approximate solution vector/scalar. |
x | NumericArray | Approximate solution. |
fval | NumericArray | Function value at x. |
exitflag | NumericScalar | Convergence status code. |
output | Any | Solver diagnostics. |
jacobian | NumericArray | Jacobian at x. |
Returned values from fsolve depend on how many outputs the caller requests.
Errors
| Identifier | When | Message |
|---|---|---|
RunMat:fsolve:InvalidArgument | Argument grammar/options configuration is invalid. | fsolve: invalid argument |
RunMat:fsolve:InvalidInput | Initial guess/callback/iteration semantics are invalid. | fsolve: invalid input |
How fsolve works
- The function handle must return a finite real scalar or vector.
- Strict compatibility mode rejects typed-integer or logical initial guesses and residuals. RunMat extension mode accepts those values when every integer converts exactly to binary64.
- Typed-integer option controls are a separately gated RunMat extension. Structural counts such as
MaxIterandMaxFunEvalsare validated as exact nonnegative integers rather than rounded through floating point. - Jacobians are estimated with forward finite differences.
- The step is chosen with a Levenberg-Marquardt damping parameter and accepted only when it reduces the residual norm.
- Options are supplied as a struct, usually created with
optimset.TolX,TolFun,MaxIter,MaxFunEvals, andDisplayare accepted. - Up to five outputs are supported:
x,fval,exitflag,output, and the final Jacobian. A stationary non-root or exhausted budget is returned with a nonpositive convergence status instead of being raised as an evaluation error.
Examples
Solve a two-variable nonlinear system
F = @(x) [x(1)^2 + x(2)^2 - 4; x(1)*x(2) - 1];
x = fsolve(F, [1; 1])Expected output:
x =
1.9319
0.5176Solve a scalar equation
x = fsolve(@sin, 3)Expected output:
x =
3.1416Using fsolve with coding agents
Open a RunMat example with live inputs, then ask the agent to explain how fsolve changes the result.
Run a small fsolve example, explain the result, then change one input and compare the output.
Related Math functions
Optim
coneprog · fminbnd · fminunc · fzero · integral · linprog · lsqcurvefit · lsqnonlin · optimoptions · optimset · quad · 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 fsolve is executed, line by line, in Rust.
- View the source for fsolve 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.