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MathSpecialFunctionsGammaLibrary "MathSpecialFunctionsGamma" Gamma Functions. GammaQ(index) Enumeration of the polynomial coefficients for the "GammaLn" approximation. Parameters: index : int, 0 => index => 10, index of coeficient. Returns: float GammaLn(z) Computes the logarithm of the Gamma function. Parameters: z : The argument of the gamma function. Returns: The logarithm of the gamma function. Gamma(z) Computes the Gamma function. Parameters: z : The argument of the gamma function. Returns: float, The logarithm of the gamma function. GammaLowerRegularized(a, x) Parameters: a : float, The argument for the gamma function. x : float, The upper integral limit. Returns: float, The lower incomplete gamma function. GammaUpperRegularized(a, x) Returns the upper incomplete regularized gamma function Parameters: a : float, The argument for the gamma function. x : float, The lower integral limit. Returns: float, The upper incomplete regularized gamma function. GammaUpperIncomplete(a, x) Returns the upper incomplete gamma function. Parameters: a : float, The argument for the gamma function. x : float, The lower integral limit. Returns: float, The upper incomplete gamma function. GammaLowerIncomplete(a, x) Parameters: a : float, The argument for the gamma function. x : float, The upper integral limit. Returns: float, The lower incomplete gamma function.
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ProbabilityLibrary "Probability" erf(value) Complementary error function Parameters: value : float, value to test. Returns: float ierf_mcgiles(value) Computes the inverse error function using the Mc Giles method, sacrifices accuracy for speed. Parameters: value : float, -1.0 >= _value >= 1.0 range, value to test. Returns: float ierf_double(value) computes the inverse error function using the Newton method with double refinement. Parameters: value : float, -1. > _value > 1. range, _value to test. Returns: float ierf(value) computes the inverse error function using the Newton method. Parameters: value : float, -1. > _value > 1. range, _value to test. Returns: float complement(probability) probability that the event will not occur. Parameters: probability : float, 0 >=_p >= 1, probability of event. Returns: float entropy_gini_impurity_single(probability) Gini Inbalance or Gini index for a given probability. Parameters: probability : float, 0>=x>=1, probability of event. Returns: float entropy_gini_impurity(events) Gini Inbalance or Gini index for a series of events. Parameters: events : float , 0>=x>=1, array with event probability's. Returns: float entropy_shannon_single(probability) Entropy information value of the probability of a single event. Parameters: probability : float, 0>=x>=1, probability value. Returns: float, value as bits of information. entropy_shannon(events) Entropy information value of a distribution of events. Parameters: events : float , 0>=x>=1, array with probability's. Returns: float inequality_chebyshev(n_stdeviations) Calculates Chebyshev Inequality. Parameters: n_stdeviations : float, positive over or equal to 1.0 Returns: float inequality_chebyshev_distribution(mean, std) Calculates Chebyshev Inequality. Parameters: mean : float, mean of a distribution std : float, standard deviation of a distribution Returns: float inequality_chebyshev_sample(data_sample) Calculates Chebyshev Inequality for a array of values. Parameters: data_sample : float , array of numbers. Returns: float intersection_of_independent_events(events) Probability that all arguments will happen when neither outcome is affected by the other (accepts 1 or more arguments) Parameters: events : float , 0 >= _p >= 1, list of event probabilities. Returns: float union_of_independent_events(events) Probability that either one of the arguments will happen when neither outcome is affected by the other (accepts 1 or more arguments) Parameters: events : float , 0 >= _p >= 1, list of event probabilities. Returns: float mass_function(sample, n_bins) Probabilities for each bin in the range of sample. Parameters: sample : float , samples to pool probabilities. n_bins : int, number of bins to split the range @return float cumulative_distribution_function(mean, stdev, value) Use the CDF to determine the probability that a random observation that is taken from the population will be less than or equal to a certain value. Or returns the area of probability for a known value in a normal distribution. Parameters: mean : float, samples to pool probabilities. stdev : float, number of bins to split the range value : float, limit at which to stop. Returns: float transition_matrix(distribution) Transition matrix for the suplied distribution. Parameters: distribution : float , array with probability distribution. ex:. Returns: float diffusion_matrix(transition_matrix, dimension, target_step) Probability of reaching target_state at target_step after starting from start_state Parameters: transition_matrix : float , "pseudo2d" probability transition matrix. dimension : int, size of the matrix dimension. target_step : number of steps to find probability. Returns: float state_at_time(transition_matrix, dimension, start_state, target_state, target_step) Probability of reaching target_state at target_step after starting from start_state Parameters: transition_matrix : float , "pseudo2d" probability transition matrix. dimension : int, size of the matrix dimension. start_state : state at which to start. target_state : state to find probability. target_step : number of steps to find probability.
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MathStatisticsKernelDensityEstimationLibrary "MathStatisticsKernelDensityEstimation" (KDE) Method for Kernel Density Estimation kde(observations, kernel, bandwidth, nsteps) Parameters: observations : float array, sample data. kernel : string, the kernel to use, default='gaussian', options='uniform', 'triangle', 'epanechnikov', 'quartic', 'triweight', 'gaussian', 'cosine', 'logistic', 'sigmoid'. bandwidth : float, bandwidth to use in kernel, default=0.5, range=(0, +inf), less will smooth the data. nsteps : int, number of steps in range of distribution, default=20, this value is connected to how many line objects you can display per script. Returns: tuple with signature: (float array, float array) draw_horizontal(distribution_x, distribution_y, distribution_lines, graph_lines, graph_labels) Draw a horizontal distribution at current location on chart. Parameters: distribution_x : float array, distribution points x value. distribution_y : float array, distribution points y value. distribution_lines : line array, array to append the distribution curve lines. graph_lines : line array, array to append the graph lines. graph_labels : label array, array to append the graph labels. Returns: void, updates arrays: distribution_lines, graph_lines, graph_labels. draw_vertical(distribution_x, distribution_y, distribution_lines, graph_lines, graph_labels) Draw a vertical distribution at current location on chart. Parameters: distribution_x : float array, distribution points x value. distribution_y : float array, distribution points y value. distribution_lines : line array, array to append the distribution curve lines. graph_lines : line array, array to append the graph lines. graph_labels : label array, array to append the graph labels. Returns: void, updates arrays: distribution_lines, graph_lines, graph_labels. style_distribution(lines, horizontal, to_histogram, line_color, line_style, linewidth) Style the distribution lines. Parameters: lines : line array, distribution lines to style. horizontal : bool, default=true, if the display is horizontal(true) or vertical(false). to_histogram : bool, default=false, if graph style should be switched to histogram. line_color : color, default=na, if defined will change the color of the lines. line_style : string, defaul=na, if defined will change the line style, options=('na', line.style_solid, line.style_dotted, line.style_dashed, line.style_arrow_right, line.style_arrow_left, line.style_arrow_both) linewidth : int, default=na, if defined will change the line width. Returns: void. style_graph(lines, lines, horizontal, line_color, line_style, linewidth) Style the graph lines and labels Parameters: lines : line array, graph lines to style. lines : labels array, graph labels to style. horizontal : bool, default=true, if the display is horizontal(true) or vertical(false). line_color : color, default=na, if defined will change the color of the lines. line_style : string, defaul=na, if defined will change the line style, options=('na', line.style_solid, line.style_dotted, line.style_dashed, line.style_arrow_right, line.style_arrow_left, line.style_arrow_both) linewidth : int, default=na, if defined will change the line width. Returns: void.
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MathStatisticsKernelFunctionsLibrary "MathStatisticsKernelFunctions" TODO: add library description here uniform(distance, bandwidth) Uniform kernel. Parameters: distance : float, distance to kernel origin. bandwidth : float, default=1.0, bandwidth limiter to weight the kernel. Returns: float. triangular(distance, bandwidth) Triangular kernel. Parameters: distance : float, distance to kernel origin. bandwidth : float, default=1.0, bandwidth limiter to weight the kernel. Returns: float. epanechnikov(distance, bandwidth) Epanechnikov kernel. Parameters: distance : float, distance to kernel origin. bandwidth : float, default=1.0, bandwidth limiter to weight the kernel. Returns: float. quartic(distance, bandwidth) Quartic kernel. Parameters: distance : float, distance to kernel origin. bandwidth : float, default=1.0, bandwidth limiter to weight the kernel. Returns: float. triweight(distance, bandwidth) Triweight kernel. Parameters: distance : float, distance to kernel origin. bandwidth : float, default=1.0, bandwidth limiter to weight the kernel. Returns: float. tricubic(distance, bandwidth) Tricubic kernel. Parameters: distance : float, distance to kernel origin. bandwidth : float, default=1.0, bandwidth limiter to weight the kernel. Returns: float. gaussian(distance, bandwidth) Gaussian kernel. Parameters: distance : float, distance to kernel origin. bandwidth : float, default=1.0, bandwidth limiter to weight the kernel. Returns: float. cosine(distance, bandwidth) Cosine kernel. Parameters: distance : float, distance to kernel origin. bandwidth : float, default=1.0, bandwidth limiter to weight the kernel. Returns: float. logistic(distance, bandwidth) logistic kernel. Parameters: distance : float, distance to kernel origin. bandwidth : float, default=1.0, bandwidth limiter to weight the kernel. Returns: float. sigmoid(distance, bandwidth) Sigmoid kernel. Parameters: distance : float, distance to kernel origin. bandwidth : float, default=1.0, bandwidth limiter to weight the kernel. Returns: float. select(kernel, distance, bandwidth) Kernel selection method. Parameters: kernel : string, kernel to select. (options="uniform", "triangle", "epanechnikov", "quartic", "triweight", "tricubic", "gaussian", "cosine", "logistic", "sigmoid") distance : float, distance to kernel origin. bandwidth : float, default=1.0, bandwidth limiter to weight the kernel. Returns: float.
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MathTransformsHartleyLibrary "MathTransformsHartley" implementation of the Fast Discrete Hartley Transform(DHT). naive(samples) Generic naive transform for the (DHT). Parameters: samples : float array, 1d data. Returns: float array. fdht(samples) Fast Discrete Hartley Transform (DHT). Parameters: samples : float array, data samples. Returns: float array. idht(samples, asymmetric_scaling) Inverse Discrete Hartley Transform (DHT). Parameters: samples : float array, data samples. asymmetric_scaling : bool, default=true, scaling option. Returns: float array.
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MathSpecialFunctionsTestFunctionsLibrary "MathSpecialFunctionsTestFunctions" Methods for test functions. rosenbrock(input_x, input_y) Valley-shaped Rosenbrock function for 2 dimensions: (x,y) -> (1-x)^2 + 100*(y-x^2)^2. Parameters: input_x : float, common range within (-5.0, 10.0) or (-2.048, 2.048). input_y : float, common range within (-5.0, 10.0) or (-2.048, 2.048). Returns: float rosenbrock_mdim(samples) Valley-shaped Rosenbrock function for 2 or more dimensions. Parameters: samples : float array, common range within (-5.0, 10.0) or (-2.048, 2.048). Returns: float himmelblau(input_x, input_y) Himmelblau, a multi-modal function: (x,y) -> (x^2+y-11)^2 + (x+y^2-7)^2 Parameters: input_x : float, common range within (-6.0, 6.0 ). input_y : float, common range within (-6.0, 6.0 ). Returns: float rastrigin(samples) Rastrigin, a highly multi-modal function with many local minima. Parameters: samples : float array, common range within (-5.12, 5.12 ). Returns: float drop_wave(input_x, input_y) Drop-Wave, a multi-modal and highly complex function with many local minima. Parameters: input_x : float, common range within (-5.12, 5.12 ). input_y : float, common range within (-5.12, 5.12 ). Returns: float ackley(input_x) Ackley, a function with many local minima. It is nearly flat in outer regions but has a large hole at the center. Parameters: input_x : float array, common range within (-32.768, 32.768 ). Returns: float bohachevsky1(input_x, input_y) Bowl-shaped first Bohachevsky function. Parameters: input_x : float, common range within (-100.0, 100.0 ). input_y : float, common range within (-100.0, 100.0 ). Returns: float matyas(input_x, input_y) Plate-shaped Matyas function. Parameters: input_x : float, common range within (-10.0, 10.0 ). input_y : float, common range within (-10.0, 10.0 ). Returns: float six_hump_camel(input_x, input_y) Valley-shaped six-hump camel back function. Parameters: input_x : float, common range within (-3.0, 3.0 ). input_y : float, common range within (-2.0, 2.0 ). Returns: float
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MathGeometryCurvesChaikinLibrary "MathGeometryCurvesChaikin" Implements the chaikin algorithm to create a curved path, from assigned points. chaikin(points_x, points_y, closed) Chaikin algorithm method, uses provided points to generate a smoothed path. Parameters: points_x : float array, the x value of points. points_y : float array, the y value of points. closed : bool, default=false, is the path closed or not. Returns: tuple with 2 float arrays. smooth(points_x, points_y, iterations, closed) Iterate the chaikin algorithm, to smooth a sample of points into a curve path. Parameters: points_x : float array, the x value of points. points_y : float array, the y value of points. iterations : int, number of iterations to apply the smoothing. closed : bool, default=false, is the path closed or not. Returns: array of lines. draw(path_x, path_y, closed) Draw the path. Parameters: path_x : float array, the x value of the path. path_y : float array, the y value of the path. closed : bool, default=false, is the path closed or not. Returns: array of lines.
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Double_Triple_EMALibrary "Double_Triple_EMA" Provides the functions to calculate Double and Triple Exponentional Moving Averages (DEMA & TEMA). dema(_source, _length) Calculates Double Exponentional Moving Averages (DEMA) Parameters: _source : -> Open, Close, High, Low, etc ('close' is used if no argument is supplied) _length : -> DEMA length Returns: Double Exponential Moving Average (DEMA) of an input source at the specified input length tema(_source, _length) Calculates Triple Exponentional Moving Averages (TEMA) Parameters: _source : -> Open, Close, High, Low, etc ('close' is used if no argument is supplied) _length : -> TEMA length Returns: Triple Exponential Moving Average (TEMA) of an input source at the specified input length
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MathTrigonometryLibrary "MathTrigonometry" Trigonometric methods. sinc(value) Normalized sinc function. Parameters: value : float, value. Returns: float. cot(value) Cotangent of value. Parameters: value : float, value. Returns: float. csc(value) Cosecant of value. Parameters: value : float, value. Returns: float. sec(value) Secant of value. Parameters: value : float, value. Returns: float. acot(value) Arc cotangent of value. Parameters: value : float, adjacent value. Returns: float. asec(value) Arc secant of value. Parameters: value : float, hypotenuse value. Returns: float. acsc(value) Arc cosecant of value. Parameters: value : float, hipotenuse value. Returns: float. sinh(angle) Hyperbolic sine of angle. Parameters: angle : float, value. Returns: float. cosh(angle) Hyperbolic cosine of angle. Parameters: angle : float, value. Returns: float. tanh(angle) Hyperbolic tangent of angle. Parameters: angle : float, value. Returns: float. coth(angle) Hyperbolic cotangent of angle. Parameters: angle : float, value. Returns: float. sech(angle) Hyperbolic secant of angle. Parameters: angle : float, value. Returns: float. csch(angle) Hyperbolic cosecant of angle. Parameters: angle : float, value. Returns: float. asinh(value) Hyperbolic area sine. Parameters: value : float, value. Returns: float. acosh(value) Hyperbolic area cosine. Parameters: value : float, value. Returns: float. atanh(value) Hyperbolic area tangent. Parameters: value : float, value. Returns: float. acoth(value) Hyperbolic area cotangent. Parameters: value : float, value. Returns: float. asech(value) Hyperbolic area secant. Parameters: value : float, value. Returns: float. acsch(value) Hyperbolic area cosecant. Parameters: value : float, value. Returns: float.
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MathSearchDijkstraLibrary "MathSearchDijkstra" Shortest Path Tree Search Methods using Dijkstra Algorithm. min_distance(distances, flagged_vertices) Find the lowest cost/distance. Parameters: distances : float array, data set with distance costs to start index. flagged_vertices : bool array, data set with visited vertices flags. Returns: int, lowest cost/distance index. dijkstra(matrix_graph, dim_x, dim_y, start) Dijkstra Algorithm, perform a greedy tree search to calculate the cost/distance to selected start node at each vertex. Parameters: matrix_graph : int array, matrix holding the graph adjacency list and costs/distances. dim_x : int, x dimension of matrix_graph. dim_y : int, y dimension of matrix_graph. start : int, the vertex index to start search. Returns: int array, set with costs/distances to each vertex from start vertexs. shortest_path(start, end, matrix_graph, dim_x, dim_y) Retrieves the shortest path between 2 vertices in a graph using Dijkstra Algorithm. Parameters: start : int, the vertex index to start search. end : int, the vertex index to end search. matrix_graph : int array, matrix holding the graph adjacency list and costs/distances. dim_x : int, x dimension of matrix_graph. dim_y : int, y dimension of matrix_graph. Returns: int array, set with vertex indices to the shortest path.
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MathGaussFunctionLibrary "MathGaussFunction" Implements multiple gauss methods. f_1d(point_x, sigma) 1-D Gaussian function. Parameters: point_x : float, x value. sigma : float, sigma value, default=1.0. Returns: float, function's value at point_x. f_2d(point_x, point_y, sigma) 2-D Gaussian function. Parameters: point_x : float, x value. point_y : float, y value. sigma : float, sigma value, default=1.0. Returns: float, function's value at (point_x, point_y). kernel_1d(size, sigma) 1-D Gaussian kernel. Parameters: size : int, Kernel size (should be odd), . sigma : float, sigma value, default=1.0. Returns: float array, Returns 1-D Gaussian kernel of the specified size. kernel_2d(size, sigma) 2-D Gaussian kernel. Parameters: size : int, Kernel size (should be odd), . sigma : float, sigma value, default=1.0. Returns: float array, Returns 2-D Gaussian kernel of the specified size.
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MathFinancialAbsoluteRiskMeasuresLibrary "MathFinancialAbsoluteRiskMeasures" Financial Absolute Risk Measures. gain_stdev(sample) Standard deviation of gains in a data sample. Parameters: sample : float array, data sample. Returns: float. loss_stdev(sample) Standard deviation of losses in a data sample. Parameters: sample : float array, data sample. Returns: float. downside_stdev(sample, minimal_acceptable_return) Downside standard deviation in a data sample. Parameters: sample : float array, data sample. minimal_acceptable_return : float, minimum gain value. Returns: float. semi_stdev(sample) Standard deviation of less than average returns in a data sample. Parameters: sample : float array, data sample. Returns: float. gain_loss_ratio(sample) ratio of average gains of average losses in a data sample. Parameters: sample : float array, data sample. Returns: float. compound_risk_score(source, length) Compound Risk Score Parameters: source : float, input data, default=close. length : int, period of observation, default=12) Returns: float.
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