lsqnonlin
lsqnonlin minimizes the squared 2-norm of a vector-valued residual callback fun(x) using RunMat's shared finite-difference Levenberg-Marquardt least-squares solver. Scalar, vector, and matrix x0 inputs are supported and the returned solution preserves the shape of x0.
Syntax
x = lsqnonlin(r, [0; 0])GPU memory and residency
lsqnonlin gathers residuals and bounds to the host for iterative solving. Callback bodies can still use GPU-aware builtins; provider-native nonlinear least-squares is deferred to the GPU fast-path audit.
Examples
r = @(x) [x(1)-2; x(2)-3; x(1)+x(2)-5];
x = lsqnonlin(r, [0; 0])Expected output:
x = [2; 3]x = lsqnonlin(@(x) [x-2, x-2], 0, -1, 1)Expected output:
x = 1opts = optimoptions("lsqnonlin", "Algorithm", "levenberg-marquardt", "Display", "off");
[x, resnorm, residual, exitflag, output, lambda, jacobian] = lsqnonlin(@(x) [x(1)-1, 2*x(2)-4], [0 0], [], [], opts)Expected output:
x approaches [1 2], resnorm approaches 0, and jacobian is 2-by-2.Using lsqnonlin with coding agents
Open a RunMat example with live inputs, then ask the agent to explain how lsqnonlin changes the result.
Run a small lsqnonlin example, explain the result, then change one input and compare the output.
FAQ
Does lsqnonlin support linear or nonlinear constraints?⌄
Not yet. Empty A, b, Aineq, bineq, Aeq, beq, and nonlcon placeholders are accepted so common option-forwarding scripts run, but non-empty constraints are rejected because RunMat does not yet have the interior-point constrained least-squares infrastructure.
Does lsqnonlin run on the GPU?⌄
The solver is host iterative work. Callback code may call GPU-aware builtins, but residuals and bounds are gathered for the solver. Provider-native nonlinear least-squares execution belongs to the queued GPU fast-path audit rather than this compatibility slice.
Related Math functions
Optim
coneprog · fminbnd · fminunc · fsolve · fzero · integral · linprog · lsqcurvefit · 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 lsqnonlin is executed, line by line, in Rust.
- View the source for lsqnonlin 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.