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Math2 contains all static methods. These get assigned to the main Math object as well as an extension.\r\n\r\n This repo will be deprecated at some point when I know where to put all this stuff (if it's even worth keeping later)\r\n\r\n * Math2: Advanced Mathematical Utilities\r\n *\r\n * This class provides a comprehensive set of mathematical and statistical functions,\r\n * vector operations, matrix manipulations, and various utility methods.\r\n * The methods are static and can be used without instantiating the class.\r\n *\r\n * Note: When importing this script, these methods are also assigned to the Math object without conflict.\r\n *\r\n * --- Constants ---\r\n * - TWO_PI: Represents 2π.\r\n * - C, G, h, R, Ra, H, kbar, kB, ke, me, mp, mn, P0, T0, p0, Na, y, M0, g0, Re, B, S, Sigma: Various mathematical and physical constants.\r\n *\r\n * --- Vector Operations ---\r\n * - vecadd(...vectors): Element-wise addition of vectors.\r\n * - vecmul(...vectors): Element-wise multiplication of vectors.\r\n * - vecsub(vec1, vec2): Subtract vec2 from vec1.\r\n * - vecdiv(numvec, denvec): Element-wise division of numvec by denvec.\r\n * - vecscale(vec, scalar): Scale a vector by a scalar.\r\n * - dot(vec1, vec2): Dot product of two vectors.\r\n * - cross3D(vec1, vec2): Cross product for 3D vectors.\r\n * - magnitude(vec): Compute the magnitude of a vector.\r\n * - distance(point1, point2): Compute the distance between two points.\r\n * - normalize(vec): Normalize a vector.\r\n * - project(vec1, vec2): Project vec1 onto vec2.\r\n * - angleBetween(vec1, vec2): Compute the angle (in radians) between two vectors.\r\n * - sphericalToCartesian(r, theta, phi): Convert spherical coordinates to Cartesian.\r\n * - cartesianToSpherical(x, y, z): Convert Cartesian coordinates to spherical.\r\n * - makeVec(point1, point2): Create a vector from two points.\r\n * - vecaddScalar, vecmulScalar, vecsubScalar, vecdivScalar: Perform operations between a vector and a scalar.\r\n * - midpoint: Compute the midpoint between two points.\r\n * - normalizeSeries: Normalize a series of numbers.\r\n *\r\n * --- Matrix Operations ---\r\n * - transpose(mat): Transpose a 2D matrix.\r\n * - matmul(A, B): Multiply two matrices.\r\n * - matscale(mat, scalar): Scale a matrix by a scalar.\r\n * - matadd(A, B): Add two matrices.\r\n * - matsub(A, B): Subtract matrix B from A.\r\n * - inverse(matrix): Compute the inverse of a square matrix.\r\n * - diagonalMatrix(values): Create a diagonal matrix with given values.\r\n * - identityMatrix(size): Create an identity matrix of a given size.\r\n * - getColumn(matrix, col): Extract a column from a matrix.\r\n * - clone(mat): Create a deep copy of a matrix.\r\n * - qrDecomposition(matrix): Perform QR decomposition on a matrix.\r\n * - householderMatrix: Generate a Householder matrix from a vector.\r\n * - inverse: Compute the inverse of a matrix.\r\n * - column: Extract a column from a matrix.\r\n * - flatten_vector: Flatten a vector.\r\n * - squared_difference: Compute the squared difference between two vectors.\r\n * - shift_deflate: Perform shift deflate operation on a matrix.\r\n * - eigenvalue_of_vector: Compute the eigenvalue of a vector for a matrix.\r\n * - svdSimultaneousPowerIteration: Compute the SVD using simultaneous power iteration.\r\n * - reshape: Reshape an array to a given shape.\r\n *\r\n * --- Statistical Functions ---\r\n * - mean(arr): Compute the mean of an array.\r\n * - median(data): Compute the median of an array.\r\n * - mode(arr): Compute the mode of an array.\r\n * - std(arr, mean): Compute the standard deviation of an array.\r\n * - variance(arr): Compute the variance of an array.\r\n * - coeffVariation(arr, populationMean): Compute the coefficient of variance.\r\n * - skewness(arr): Compute the skewness of an array.\r\n * - kurtosis(arr): Compute the kurtosis of an array.\r\n * - chiSquareTest(observed, expected): Perform a chi-square goodness of fit test.\r\n * - percentile(arr, p): Compute the p-th percentile of an array.\r\n * - interquartileRange(arr): Compute the interquartile range of an array.\r\n * - range(data): Compute the range (max - min) of an array.\r\n * - relError(actual, forecast): Compute the relative error between actual and forecast values.\r\n * - zscore(arr): Compute the z-scores of an array.\r\n * - covariance(arr1, arr2): Compute the covariance between two arrays.\r\n * - correlationCoeff(arr1, arr2): Compute the correlation coefficient between two arrays.\r\n * - informationEntropy: Compute the information entropy of an array.\r\n * - coeffDetermination: Compute the coefficient of determination between observed and expected values.\r\n * - simpleLinearRegression: Perform simple linear regression on x and y coordinates.\r\n * - expectedValue: Compute the expected value of samples.\r\n * - originMoment: Compute the origin moment of samples.\r\n * - centralMoment: Compute the central moment of samples.\r\n * - linearDiscriminantAnalysis: Perform linear discriminant analysis on samples.\r\n * - decompose: Decompose a signal.\r\n * - idwt: Inverse discrete wavelet transform.\r\n * - dwtMaxLevel: Compute the maximum level of discrete wavelet transform.\r\n * - minMaxScaler: Scale data to a min-max range.\r\n * - garroteThreshold: Apply garrote thresholding to data.\r\n * - covVec: Compute the covariance of two vectors.\r\n * - cov1d, cov2d, cov3d, covNd: Compute the covariance for 1D, 2D, 3D, and N-dimensional data.\r\n * - eigens2x2, eigenvectors2x2: Compute the eigenvalues and eigenvectors for a 2x2 matrix.\r\n * - fastpca2d: Perform fast PCA for 2D data.\r\n * - crosscorrelation, autocorrelation, autocorrelation2d, autocorrelation2dNormalized, crosscorrelation2d, crosscorrelation2dNormalized, correlograms: Various correlation methods.\r\n * - sma: Compute the simple moving average.\r\n * - reduceArrByFactor: Reduce an array by a given factor.\r\n * - makeArr: Create an array with linearly spaced values.\r\n * - autoscale: Autoscale an array.\r\n * - absmax: Compute the absolute maximum of an array.\r\n * - downsample, upsample, dyadicUpsample, resample: Various sampling methods.\r\n * - isExtrema, isCriticalPoint: Check for extrema or critical points in an array.\r\n * - peakDetect: Detect peaks in an array.\r\n * - getPeakThreshold: Compute the threshold for peak detection.\r\n * - circularBuffer: Implement a circular buffer.\r\n *\r\n * --- Utility Methods ---\r\n * - HSLToRGB(h, s, l, scalar): Convert HSL to RGB.\r\n * - genSineWave(): Generate a sine wave.\r\n * - linspace(start, end, num): Generate linearly spaced values between start and end.\r\n * - lerp(v0, v1, t): Linear interpolation between v0 and v1.\r\n * - pad(arr, pad, padValue): Pad an array with a given value.\r\n * - flatten(arr): Flatten a multi-dimensional array.\r\n * - sum(arr): Compute the sum of an array's elements.\r\n * - histogram(arr, binSize): Compute a histogram of an array.\r\n * - normalDistribution(samples, normalize): Generate a normal distribution from samples.\r\n *\r\n * --- Advanced Mathematical Methods ---\r\n * - eigens(mat): Compute the eigenvalues of a matrix.\r\n * - pca(mat): Principal Component Analysis.\r\n * - dft(arr): Discrete Fourier Transform.\r\n * - svd(A): Singular Value Decomposition of a matrix.\r\n * - power_iteration(A): Power iteration method for eigenvalue computation.\r\n * - quadraticFormula(a, b, c): Solve a quadratic equation.\r\n * - newtonsMethod1D(foo): Newton's method for root finding in 1D.\r\n * - integral(func, range): Compute the integral of a function over a range.\r\n * - dintegral(func, range, stepx, stepy): Approximate the double integral (volume under a surface) in 3D space using the provided function and range.\r\n * - tintegral(func, range, stepx, stepy, stepz): Approximate the triple integral in 4D space using the provided function and range.\r\n * - pintegral(func, range, stepx): Approximate the path integral (length of a curve) in 2D space using the provided function and range.\r\n * - pathIntegral2D(xFunc, yFunc, range, stepx, stepy): Approximate the path integral (length of a curve) in 2D space using parametric functions for x and y.\r\n * - pathIntegral3D(xFunc, yFunc, zFunc, range, stepx, stepy, stepz): Approximate the path integral (length of a curve) in 3D space using parametric functions for x, y, and z.\r\n *\r\n * --- Filters and Kernels ---\r\n * - imgkernels: Collection of image processing kernels.\r\n * - conv1D(s, kernel): 1D convolution.\r\n * - conv2D(matrix, kernel): 2D convolution.\r\n * - convN(matrix, kernel): N-dimensional convolution\r\n * - p300: Compute the P300 component of event-related potentials.\r\n * - waveletFiltering: Filter a signal using wavelets.\r\n * - dec_lo,dec_hi,rec_lo,rec_hi: sym4 wavelet lowpass/highpass filters prepicked for motion artifacts\r\n *\r\n * For detailed parameter descriptions and usage, refer to the individual method documentation.\r\n ","readmeFilename":"README.md"}