brainsatplay-math

Brains@Play math stuff. Math2 contains all static methods. These get assigned to the main Math object as well as an extension.

This repo will be deprecated at some point when I know where to put all this stuff (if it's even worth keeping later)

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