brainsatplay-math

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.