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Asencio","email":"maasencioh@gmail.com"},"license":"MIT","homepage":"https://github.com/mljs/levenberg-marquardt#readme","keywords":["machine","learning","data","mining","datamining","levenberg","marquardt"],"repository":{"type":"git","url":"git+https://github.com/mljs/levenberg-marquardt.git"},"description":"Curve fitting method in javascript","maintainers":[{"name":"stropitek","email":"kostro.d@gmail.com"},{"name":"targos","email":"npm@secmail.targos.dev"},{"name":"lpatiny","email":"luc@patiny.com"},{"name":"mljs-bot","email":"bot+npm-mljs@zakodium.com"},{"name":"maasencioh","email":"maasencioh@gmail.com"},{"name":"jeffersonh44","email":"jeffersonh44@gmail.com"},{"name":"andcastillo","email":"andcastillo@gmail.com"}],"readme":"# ml-levenberg-marquardt\n\n[![NPM version](https://img.shields.io/npm/v/ml-levenberg-marquardt.svg)](https://www.npmjs.com/package/ml-levenberg-marquardt)\n[![npm download](https://img.shields.io/npm/dm/ml-levenberg-marquardt.svg)](https://www.npmjs.com/package/ml-levenberg-marquardt)\n[![test coverage](https://img.shields.io/codecov/c/github/mljs/levenberg-marquardt.svg)](https://codecov.io/gh/mljs/levenberg-marquardt)\n[![license](https://img.shields.io/npm/l/ml-levenberg-marquardt.svg)](https://github.com/mljs/levenberg-marquardt/blob/main/LICENSE)\n\nCurve fitting method in javascript.\n\n## [API Documentation](https://mljs.github.io/levenberg-marquardt/)\n\nThis algorithm is based on the article [Brown, Kenneth M., and J. E. Dennis. \"Derivative free analogues of the Levenberg-Marquardt and Gauss algorithms for nonlinear least squares approximation.\" Numerische Mathematik 18.4 (1971): 289-297.](https://doi.org/10.1007/BF01404679) and [http://people.duke.edu/~hpgavin/ce281/lm.pdf](http://people.duke.edu/~hpgavin/ce281/lm.pdf)\n\nTo get a general idea of the problem, you could also check the [Wikipedia article](https://en.wikipedia.org/wiki/Levenberg%E2%80%93Marquardt_algorithm).\n\n## Installation\n\n```console\nnpm i ml-levenberg-marquardt\n```\n\n## Usage\n\n```js\nimport { levenbergMarquardt } from 'ml-levenberg-marquardt';\n\nconst result = levenbergMarquardt(data, parameterizedFunction, options);\n```\n\n- `data` — an object `{ x, y }` where `x` and `y` are arrays (or typed arrays) of the same length.\n- `parameterizedFunction` — takes an array of parameters and returns a function of the independent variable.\n- `options` — see below. `initialValues` is mandatory.\n\nThe returned object has `parameterValues` (the fitted parameters), `parameterError` (the sum of squared weighted residuals) and `iterations` (the number of iterations performed).\n\n## Options\n\n| Option                 | Default | Description                                                                                                       |\n| ---------------------- | ------- | ----------------------------------------------------------------------------------------------------------------- |\n| `initialValues`        | —       | Array of initial parameter values. Mandatory.                                                                     |\n| `weights`              | `1`     | Weighting vector. If its length does not match the number of data points, it is rebuilt from the first value.     |\n| `damping`              | `1e-2`  | Levenberg-Marquardt parameter λ; small values give a Gauss-Newton update, large values a gradient descent update. |\n| `dampingStepDown`      | `9`     | Factor used to reduce the damping when an update improves the fit.                                                |\n| `dampingStepUp`        | `11`    | Factor used to increase the damping when an update does not improve the fit.                                      |\n| `improvementThreshold` | `1e-3`  | Threshold defining what counts as an improvement.                                                                 |\n| `gradientDifference`   | `10e-2` | Step size used to approximate the jacobian. See below.                                                            |\n| `centralDifference`    | `false` | Approximate the jacobian by central differences instead of forward differences. See below.                        |\n| `jacobianFunction`     | —       | Analytical jacobian of the model. See below.                                                                      |\n| `minValues`            | —       | Minimum allowed values for the parameters.                                                                        |\n| `maxValues`            | —       | Maximum allowed values for the parameters.                                                                        |\n| `maxIterations`        | `100`   | Maximum number of iterations.                                                                                     |\n| `errorTolerance`       | `10e-3` | Stop as soon as the error drops below this value.                                                                 |\n| `timeout`              | —       | Maximum running time in seconds; throws when exceeded.                                                            |\n\n### centralDifference\n\nThe jacobian matrix is approximated by finite difference; forward differences or central differences (one additional function evaluation). The option centralDifference select one of them, by default the jacobian is calculated by forward difference.\n\n### gradientDifference\n\nThe jacobian matrix is approximated as mentioned above, the gradientDifference option is the step size (dp) to calculate the difference between the function with the current parameter state and the perturbation added. It could be a number (same step size for all parameters) or an array with different values for each parameter, if the gradientDifference is zero, the derive will be zero, and the parameter will hold fixed\n\n### jacobianFunction\n\nInstead of approximating the jacobian by finite differences, you can provide it analytically. Like `parameterizedFunction`, it takes the parameter array and returns a function of the independent variable, but that function returns the partial derivatives of the model with respect to every parameter, in the same order as the parameters.\n\nProviding it avoids the extra model evaluation per parameter and is more accurate, so the fit usually converges in fewer iterations. When it is set, `centralDifference` and `gradientDifference` are ignored.\n\n```js\nimport { levenbergMarquardt } from 'ml-levenberg-marquardt';\n\n// y = slope * x + intercept\nfunction line([slope, intercept]) {\n  return (x) => slope * x + intercept;\n}\n\n// [dy/dslope, dy/dintercept]\nfunction lineJacobian() {\n  return (x) => [x, 1];\n}\n\nconst x = [0, 1, 2, 3, 4, 5, 6];\nconst y = [-2, 0, 2, 4, 6, 8, 10];\n\nconst result = levenbergMarquardt({ x, y }, line, {\n  initialValues: [1, 0],\n  jacobianFunction: lineJacobian,\n});\nconsole.log(result);\n// {\n//   parameterValues: [1.9999986750084098, -1.9999943899435104],\n//   parameterError: 6.78713215849927e-11,\n//   iterations: 2\n// }\n```\n\n## Examples\n\n### Linear regression\n\n```js\nimport { levenbergMarquardt } from 'ml-levenberg-marquardt';\n\n// Creates linear function using the provided slope and intercept parameters\nfunction line([slope, intercept]) {\n  return (x) => slope * x + intercept;\n}\n\n// Input points (x,y)\nconst x = [0, 1, 2, 3, 4, 5, 6];\nconst y = [-2, 0, 2, 4, 6, 8, 10];\n\n// Parameter values to use for first iteration\nconst initialValues = [1, 0]; // i.e., y = x\n\nconst result = levenbergMarquardt({ x, y }, line, { initialValues });\nconsole.log(result);\n// {\n//   parameterValues: [1.9999986750084096, -1.9999943899435104]\n//   parameterError: 6.787132159723697e-11\n//   iterations: 2\n// }\n```\n\n### Sine fit\n\n```js\nimport { levenbergMarquardt } from 'ml-levenberg-marquardt';\n\n// function that receives the parameters and returns\n// a function with the independent variable as a parameter\nfunction sinFunction([a, b]) {\n  return (t) => a * Math.sin(b * t);\n}\n\n// array of points to fit\nconst data = {\n  x: [/* x1, x2, ... */],\n  y: [/* y1, y2, ... */],\n};\n\n// array of initial parameter values (must be provided)\nconst initialValues = [/* a, b, c, ... */];\n\n// Optionally, restrict parameters to minimum & maximum values\nconst minValues = [/* a_min, b_min, c_min, ... */];\nconst maxValues = [/* a_max, b_max, c_max, ... */];\n\nconst options = {\n  damping: 1.5,\n  initialValues,\n  minValues,\n  maxValues,\n  gradientDifference: 10e-2,\n  maxIterations: 100,\n  errorTolerance: 10e-3,\n};\n\nconst result = levenbergMarquardt(data, sinFunction, options);\n```\n\n## License\n\n[MIT](./LICENSE)\n","readmeFilename":"README.md","users":{"marciofpa":true}}