plot

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 Go to latest Published: Feb 27, 2022 License: MIT Imports: 13 Imported by: 0

README

plot

Go simple-to-use library for plotting and interpreting data, including the Gaussian distribution and Taylor series approximations as well as statistical computations of datasets, vector and matrix visualizations and more.

GoDoc

The plot package is easy to use and it offers a vast ammount of data methods. You can upload your own dataset to plot or use a dataset with the correspondant output. Looking forward to get some feedback!

Let's take a look at some functionality!

Installation

Pretty straightforward.

go get github.com/timothy102/plot

Import the library in your Go file.

import "github.com/timothy102/plot"

Usage

Let's look at a dataset using the cosine function. Second and third argument to the function invoke the starting and end point of iteration. You can adjust the iterations parameter to get a more dense distribution.

points := plot.DefineDataset(math.Cos, -10.0, 10.0, 500)
plot.PlotPoints(points, "Cosine.png", false)

alt text

That is how simple it is. If you would like to import your dataset externally, use the ReadFromDatafile function. The rest is the same.

points,err:=plot.ReadFromDatafile(filepath)
//error handling
if err:=PlotPoints(points,"Graph.png",false);err!=nil{
  log.Fatalf("could not plot data :%v",err)
}

Taylor series approximation for the Tan function and its error with the real deal. The last argument indicates the polynomial degree to which the function approximates.

points := plot.DefineDatasetWithPolynomial(TanEstimate, -2.0, 2.0, 250, 15)
e := EstimationError(math.Tan, points)
fmt.Printf("%.9f\n", e)

And the error is:

0.000000059

Taylor series approximation of the 15th degree polynomial of Sine and the difference between Sine.

points := plot.DefineDatasetWithPolynomial(plot.SinusEstimate, -5.0, 5.0, 250, 14)
plot.PlotPoints(points, "SinusEstimate.png", false)

p2 := plot.DefineDataset(math.Sin, -5.0, 5.0, 250)
plot.PlotPoints(p2, "Sinus.png", false)
	
e := plot.ErrorBetweenPoints(points, p2)
fmt.Printf("%.7f", e)

alt text alt text

With an average error of:

0.0000085

Let's take a look at creating a random dataset and then normalizing it so the data is centered and it has the standard deviation of 1 The DefineRandomPoints creates a 1000 points between 0 and 10.

pts := plot.DefineRandomPoints(1000, 0.0, 10.0)
pts = plot.Normalize(pts)
plot.PlotPoints(pts, "RandomPoints.png", true)

alt text alt text

And finally, the Gaussian distribution. First parameter is the mean value, the second is the standard deviation and the third is the number of iterations. Adjust these parameters for experimentation.

PlotGaussian(4.2,1.2,1000)

alt text

Contact

Please, feel free to reach out on LinkedIn, gmail. For more, check my medium article.

https://towardsdatascience.com/golang-as-the-new-machine-learning-powerforce-e1b74b10b83b

https://www.linkedin.com/in/tim-cvetko-32842a1a6/

License

Licensed under the MIT LICENSE

Documentation

Overview

Package plot implements plotting functionality for all kinds of data, including the Gaussian distribution, Taylor series approximations and more. It provides an insightful way to data representation and interpretation along with vector and matrix visualisations.

Index

Constants

This section is empty.

Variables

This section is empty.

Functions

func Absolute 

func Absolute(x float64) float64

Absolute returns absolute value of x

func ApplyProductRule 

func ApplyProductRule(f func(x float64) float64, base, power float64) func(float64) float64

ApplyProductRule returns the function via the productRule. Note that the input function should be of shape a*b**x

func AreDistant 

func AreDistant(a, b int) bool

AreDistant returns true if the largest common divider between a and b is 1, meaning they have no common dividers.

func AverageEuclidean 

func AverageEuclidean(pts Points) float64

AverageEuclidean returns the average euclidean distance by iteration through all Points.

func AverageX 

func AverageX(pts Points) float64

AverageX computes the average of x coordinates of the dataset

func AverageY 

func AverageY(pts Points) float64

AverageY computes the average of y coordinates of the dataset

func BiggestIndividualError 

func BiggestIndividualError(est, real Points) float64

BiggestIndividualError returns the highest error of individual Points.

func Bisection 

func Bisection(f func(float64) float64, down, upper float64, iter int) float64

Bisection method for finding null values of the polynom by disecting the interval given down and upper parameters in this case.

func ClosestToZero 

func ClosestToZero(pts Points) float64

ClosestToZero returns value closest to zero. You can use this function to see which approximation best estimates the actual function.

func Correlation 

func Correlation(pts Points)

Correlation prints the memo for how the X and Y of the dataset are correlated.

func CosineEstimate 

func CosineEstimate(x float64, polynomial int) float64

CosineEstimate returns the Taylor series cosine approximate of X.

func Cost 

func Cost(pts Points, k, n float64) float64

Cost returns the cost function.

func Covariance 

func Covariance(pts Points) float64

Covariance returns the covariance of a given dataset

func CovarianceMatrix 

func CovarianceMatrix(pts Points) matrix.Matrix

CovarianceMatrix returns the covariance matrix of the dataset.

func CrossEntropy 

func CrossEntropy(f func(x float64) float64, pts Points) float64

CrossEntropy returns the cross entropy loss

func DegreesToRadians 

func DegreesToRadians(x float64) float64

DegreesToRadians converts degrees to radians

func DisplayAllStats 

func DisplayAllStats(pts Points)

DisplayAllStats prints all the statistics considering the dataset.

func DistanceFromOrigin 

func DistanceFromOrigin(p Point) float64

DistanceFromOrigin returns the euclidean distance from origin.

func DoApproximation 

func DoApproximation(pts Points, learningRate float64, iterations int, file string) error

DoApproximation uses the ApproximateLine outputs to plot the approximation line.

func DrawApproximation 

func DrawApproximation(pts Points, k, n float64, file string) error

DrawApproximation draws a line of approximation based on k,n which should be the outputs of ApproximiateLine

func DrawLine 

func DrawLine(p1, p2 Point) (*plotter.Line, error)

DrawLine draws a line between p1 and p2.

func DrawStddev 

func DrawStddev(pl *plot.Plot, pts Points) error

DrawStddev plots the standard deviation

func ErrorBetweenPoints 

func ErrorBetweenPoints(est, real Points) float64

ErrorBetweenPoints returns the average error between est and real.

func EstimationError 

func EstimationError(f func(x float64) float64, pts Points) float64

EstimationError returns the average error between Points and the function f at same parameters.

func Euclidean 

func Euclidean(p1, p2 Point) float64

Euclidean returns the Euclidean distance between two Points.

func ExponentialEstimate 

func ExponentialEstimate(x float64, polynomial int) float64

ExponentialEstimate returns the Taylor series exponential approximate of X. E to the x.

func F1Score 

func F1Score(p1, p2 Points) int

F1Score based on the bool of Points, p1 should be the predicted value and p2 the actual values.

func Factorial 

func Factorial(n int) int

Factorial returns the factorial of n

func FalseNegatives 

func FalseNegatives(p1, p2 Points) int

FalseNegatives returns the number of false negative predicted values.

func FalsePositives 

func FalsePositives(p1, p2 Points) int

FalsePositives returns the number of false positive predicted values.

func FindMaxX 

func FindMaxX(pts Points) float64

FindMaxX returns the Point with the highest X value

func FindMaxY 

func FindMaxY(pts Points) float64

FindMaxY returns the Point with the highest Y value

func FindMinX 

func FindMinX(pts Points) float64

FindMinX returns the Point with the lowest X value

func FindMinY 

func FindMinY(pts Points) float64

FindMinY returns the Point with the lowest Y value

func FixDifferentPointSizes 

func FixDifferentPointSizes(p1, p2 Points) (Points, Points)

FixDifferentPointSizes equalizes Point sizes by shortening the longer one.

func Gaussian 

func Gaussian(x float64, mean float64, stddev float64) float64

Gaussian returns the Gaussian distribution function. For plotting, check PlotGaussian().

func GetEigenValues 

func GetEigenValues(m matrix.Matrix) ([]float64, error)

GetEigenValues returns the eigenvalues. Inputs should be eigenvectors.

func GetIndex 

func GetIndex(pts Points, p Point) (x int)

GetIndex returns the index of p in Points

func GetValueX 

func GetValueX(pts Points, index int) float64

GetValueX returns the X coordinate of Point at index.

func GetValueY 

func GetValueY(pts Points, index int) float64

GetValueY returns the Y coordinate of Point at index.

func GradientAt 

func GradientAt(f func(x float64) float64, x float64) float64

GradientAt returns the gradient of f at x

func GradientLines 

func GradientLines(f func(float64) float64, stPoint, endPoint float64, step float64, file string) error

GradientLines plots the tangents based on the gradients of the function f, given the starting and end point and the step

func Gradients 

func Gradients(f func(x float64) float64, startPoint, endPoint float64) []float64

Gradients returns the gradients from startPoint to endPoint See GradientAt for gradient at a specific Point.

func IndexAtClosestToValue 

func IndexAtClosestToValue(pts Points, value float64) int

IndexAtClosestToValue returns the index of the Point that is closest to the value on the Y axis.

func IndexAtClosestToZero 

func IndexAtClosestToZero(pts Points) int

IndexAtClosestToZero returns the index of the value within Points that is closest to zero.

func IndexAtMedianX 

func IndexAtMedianX(pts Points) int

IndexAtMedianX returns the index of the median x value of the dataset.

func IndexAtMedianY 

func IndexAtMedianY(pts Points) int

IndexAtMedianY returns the index of the median y value of the dataset.

func Integral 

func Integral(f func(x float64) float64, a, b float64, n int) float64

Integral defines a definite integral between the Points a and b for function f. N represents the number to which you want to divide the space from a and b into. You should be getting better approximations for the area under the curve by increasing n.

func IntegralByTrapezoid 

func IntegralByTrapezoid(f func(x float64) float64, a, b float64, n int) float64

IntegralByTrapezoid defines a definite integral between the Points a and b for function f. N represents the number of trapezoids you want to divide the space between a and b into. You should be getting better approximations for the area under the curve by increasing n.

func Intercept 

func Intercept(p1, p2 Point) float64

Intercept returns the intercept or the value of the linear function at Point 0.

func JaccardIndex 

func JaccardIndex(p1, p2 Points) int

JaccardIndex returns the Jaccard index.

func LargestCommonDivider 

func LargestCommonDivider(a, b int) int

LargestCommonDivider returns the largest common divider between a and b

func LassoRegression 

func LassoRegression(actual, pred []float64, lambda float64) float64

LassoRegression returns the LassoRegression or the l1 regularization to the loss function.

func LinearRegression 

func LinearRegression(pts Points, lr float64, iterations int) (k, c float64)

LinearRegression returns the optimal line via gradient descent and returns the coefficient and the intercept.

func MaclaurinFor1Over1MinusX 

func MaclaurinFor1Over1MinusX(x float64, polynomial int) float64

MaclaurinFor1Over1MinusX is designed to estimate 1/(1-x) function via Maclaurin series

func MedianX 

func MedianX(pts Points) float64

MedianX returns the median x value of the dataset.

func MedianY 

func MedianY(pts Points) float64

MedianY returns the median y value of the dataset.

func Mse 

func Mse(f func(x float64) float64, pts Points) float64

Mse returns the mean squared error between the function f and Points

func OutOfRange 

func OutOfRange(pts Points, index int) bool

OutOfRange returns true if index is out of range.

func PartialsForLinReg 

func PartialsForLinReg(pts Points, k, c float64) (dk, dc float64)

PartialsForLinReg returns the

func PlotEigen 

func PlotEigen(m matrix.Matrix, file string) error

PlotEigen plots m's eigenvectors

func PlotGaussian 

func PlotGaussian(mean, stddev float64, iterations int) error

PlotGaussian plots the Gaussian distribution with the default filename of "Gaussian"

func PlotMatrix 

func PlotMatrix(m matrix.Matrix, file string) error

PlotMatrix returns the input matrix plotted to a file.

func PlotPoints 

func PlotPoints(pts Points, file string, showStddev bool) error

PlotPoints plots the Points onto the file. By default it shows the standard deviation on the graph.

func PlotSinusApproximation 

func PlotSinusApproximation(iterations, polynomial int, file string) error

PlotSinusApproximation plots the sinus approximation onto file

func PlotTangents 

func PlotTangents(f func(x float64) float64, startingPoint, endPoint float64, iterations int) error

PlotTangents plots the tangent via gradient to the plot

func PlotVector 

func PlotVector(v matrix.Vector, file string) error

PlotVector plots the vector onto file.

func PlotVectorAfterMatrixTransformation 

func PlotVectorAfterMatrixTransformation(v matrix.Vector, mat matrix.Matrix, file string) error

PlotVectorAfterMatrixTransformation plots vector before and after matrix transorfmation

func PlotVectors 

func PlotVectors(vectors []matrix.Vector, file string) error

PlotVectors plots vectors

func PlotsineAndCosine 

func PlotsineAndCosine(file string) error

PlotsineAndCosine plots all four derivates.

func PointInDataset 

func PointInDataset(pts Points, p Point) bool

PointInDataset returns a bool if a Point belongs to the dataset

func PointToVector 

func PointToVector(pts Points) []matrix.Vector

PointToVector is a helper function

func PointToXYs 

func PointToXYs(pts Points) plotter.XYs

PointToXYs is a helper function

func Precision 

func Precision(p1, p2 Points) int

Precision returns the precision.

func PrintMetrics 

func PrintMetrics(p1, p2 Points)

PrintMetrics prints the evaluation metrics.

func PrintPoints 

func PrintPoints(pts Points)

PrintPoints prints Points by line.

func RadiansToDegrees 

func RadiansToDegrees(x float64) float64

RadiansToDegrees converts radians to degrees

func Recall 

func Recall(p1, p2 Points) int

Recall returns the recall.

func RidgeRegression 

func RidgeRegression(actual, pred []float64, lambda float64) float64

RidgeRegression returns the RidgeRegression or the l2 regularization to the loss function.

func Rmse 

func Rmse(f func(x float64) float64, pts Points) float64

Rmse returns the root mean squared error between the function f and Points

func SamePoints 

func SamePoints(p1, p2 Points) bool

SamePoints returns true if p1 dataset is the same as the p2 dataset.

func SameSign 

func SameSign(f func(float64) float64, a, b float64) bool

SameSign returns true if for f(a) and f(b) the values are on the side of the x axis. Either both positive or both negative.

func Seasonality 

func Seasonality(time, amplitude float64, period, phase int) float64

Seasonality returns the amplitude* seasonalPattern

func Sensitivity 

func Sensitivity(p1, p2 Points) int

Sensitivity returns the sensitivity

func Series 

func Series(i Season, x float64) float64

Series returns a seasonal plot defined by 5 parameters. X is the actual input, time and slope define the gradient, amplitude is the frequency and noiseLevel is a constant You can use the SeasonalPattern,Seasonality and trend to define this function, but this has been taken care of for you.

func Sigmoid 

func Sigmoid(x float64) float64

Sigmoid returns the sigmoid of x

func SigmoidPrime 

func SigmoidPrime(x float64) float64

SigmoidPrime returns the derivative of sigmoid.

func SinusEstimate 

func SinusEstimate(x float64, polynomial int) float64

SinusEstimate returns the Taylor series sinus approximate of X.

func Slope 

func Slope(p1, p2 Point) float64

Slope returns the coeffcient for linear regression

func SmallestIndividualError 

func SmallestIndividualError(est, real Points) float64

SmallestIndividualError returns the smallest error of individual Points.

func Specificity 

func Specificity(p1, p2 Points) int

Specificity returns the specificity

func StddevX 

func StddevX(pts Points) float64

StddevX returns the standard devation of X coordinates

func StddevY 

func StddevY(pts Points) float64

StddevY returns the standard devation of Y coordinates

func TanEstimate 

func TanEstimate(x float64, polynomial int) float64

TanEstimate returns the Taylor series approximation with polynomial accuracy.

func TriangleArea 

func TriangleArea(p1, p2, p3 Point) float64

TriangleArea returns the area of a triangle via the determinant.

func TrueNegatives 

func TrueNegatives(p1, p2 Points) int

TrueNegatives returns the number of true negative predicted values.

func TruePositivies 

func TruePositivies(p1, p2 Points) int

TruePositivies returns the number of true positive predicted values.

func VarianceX 

func VarianceX(pts Points) float64

VarianceX returns the variance of X coordinates

func VarianceY 

func VarianceY(pts Points) float64

VarianceY returns the variance of Y coordinates

func VectorToXYs 

func VectorToXYs(vectors []matrix.Vector) plotter.XYs

VectorToXYs is a helper function

func Xs 

func Xs(pts Points) []float64

Xs returns all x coordinates of the dataset.

func Ys 

func Ys(pts Points) []float64

Ys returns all y coordinates of the dataset.

Types

type Category 

type Category struct {
	// contains filtered or unexported fields
}

Category used with KNN algorithm

func Knn 

func Knn(k int, p Point, pts []Point) Category

Knn is the K-Nearest-Neighbour classifiCation algorithm. You can vary the parameter k for k nearest neighbours to be selected as an estimation. Knn is implemented with the help of the struct Category.

type Point 

type Point struct {
	X, Y float64
	Is   bool
	Cat  Category
}

Point struct Use the boolean is and categories only if needed.

func GetPoint 

func GetPoint(pts Points, index int) Point

GetPoint returns Point at index.

func HighestAccuracyPolynomial 

func HighestAccuracyPolynomial(f func(x float64, polynomial int) float64, fa func(x float64) float64, stPoint, endPoint float64, iterations, uptopolynomial int) ([]Point, int)

HighestAccuracyPolynomial plots the best polynomial approximation of f regarding fa->which should be the actual function. Function returns Points and the polynomial accuracy index.

func NewPoint 

func NewPoint(x, y float64) Point

NewPoint returns a new Point object.

func PointNearestValue 

func PointNearestValue(pts Points, value float64) Point

PointNearestValue returns the Point which is closest to value on the Y axis

func RandomPoint 

func RandomPoint() Point

RandomPoint returns a random Point

func TopKEuclideans 

func TopKEuclideans(p Point, pts []Point, k int) []Point

TopKEuclideans returns the closest k points to the point p. Which Points have the shortest Euclidean distance to the Point p. It is used with KNN Algorithm.

type Points 

type Points []Point

Points is a slice of Points.

func DefineDataset 

func DefineDataset(f func(x float64) float64, stPoint, endPoint float64, iterations int) Points

DefineDataset returns Points given the inputs. The function will iterate from stPoint to endPoint producing iterations number of Points.

func DefineDatasetPolynomial 

func DefineDatasetPolynomial(f func(x float64, polynomial int) float64, stPoint, endPoint float64, iterations, polynomial int) Points

DefineDatasetPolynomial returns an array of Points given the inputs. The function will iterate from stPoint to endPoint with iterations.

func DefineDatasetQuadratic 

func DefineDatasetQuadratic(f func(x, a, b, c float64) float64, a, b, c float64, stPoint, endPoint float64, iterations int) Points

DefineDatasetQuadratic defines a quadratic dataset

func DefineDatasetToPower 

func DefineDatasetToPower(n float64, stPoint, endPoint float64, iterations int) Points

DefineDatasetToPower is designed to plot Points to the power datasets.

func DefineLinearDataset 

func DefineLinearDataset(k, n, min, max float64, iterations int) Points

DefineLinearDataset returns points given k=slope and n=the intercept from min to max with iterations.

func DefineNormalDistribution 

func DefineNormalDistribution(n int, min, max, mean, stddev float64) Points

DefineNormalDistribution defines the normal distribution via n which is the number of points, min and max, and the mean and the standard deviaton.

func DefineRandomPoints 

func DefineRandomPoints(number int, min, max float64) Points

DefineRandomPoints returns 'number' of Points between min and max

func DefineWithRandomNoise 

func DefineWithRandomNoise(f func(x float64) float64, stPoint, endPoint float64, iterations int) Points

DefineWithRandomNoise generates a dataset based on a function and random noise

func DiscludeNan 

func DiscludeNan(pts Points) Points

DiscludeNan gets rid of every NaN dataPoint

func FlipOverXAxis 

func FlipOverXAxis(pts Points) Points

FlipOverXAxis flips Points over the X axis.

func FlipOverYAxis 

func FlipOverYAxis(pts Points) Points

FlipOverYAxis flips Points over the Y axis.

func LimitTo 

func LimitTo(pts Points, xUpper, xDown, yUpper, yDown float64) Points

LimitTo limits Points to x and y limits

func LimitToXDown 

func LimitToXDown(pts Points, xDown float64) Points

LimitToXDown limits Points to an upper X limit.

func LimitToXUpper 

func LimitToXUpper(pts Points, xUpper float64) Points

LimitToXUpper limits Points to an upper X limit.

func LimitToYDown 

func LimitToYDown(pts Points, yDown float64) Points

LimitToYDown limits Points to an upper X limit.

func LimitToYUpper 

func LimitToYUpper(pts Points, yUpper float64) Points

LimitToYUpper limits Points to an upper X limit.

func Normalize 

func Normalize(pts Points) Points

Normalize normalizes data so that it is between the interval of 0 and 1

func PointsFromArrays 

func PointsFromArrays(xs, ys []float64) Points

PointsFromArrays returns Points from arrays of x and y coordiantes.

func Randomize 

func Randomize(pts Points) Points

Randomize randomizes Points to random values.

func ReadFromDatafile 

func ReadFromDatafile(filepath string) (Points, error)

ReadFromDatafile reads from the filepath and returns an array of Points.

func RemoveFromIndexDownwards 

func RemoveFromIndexDownwards(pts Points, index int) Points

RemoveFromIndexDownwards removes all Points from index Points downwards from the array

func RemoveFromIndexUpwards 

func RemoveFromIndexUpwards(pts Points, index int) Points

RemoveFromIndexUpwards removes all Points from index Points upwards from the array

func RemoveFromPoints 

func RemoveFromPoints(pts Points, p Point) Points

RemoveFromPoints removes p from Points

func RemovePointAt 

func RemovePointAt(pts Points, index int) Points

RemovePointAt removes Point at index from Points.

func ReverseIndexes 

func ReverseIndexes(pts Points) Points

ReverseIndexes flips the array indices.

func RoundPointstoDecimals 

func RoundPointstoDecimals(pts Points, decimals int) Points

RoundPointstoDecimals rounds all Points to decimals accuracy.

func SeriesDataset 

func SeriesDataset(s Season, iterations int) Points

SeriesDataset returns Points from inputs and iterations.

func ShiftDatasetOnX 

func ShiftDatasetOnX(pts Points, scalar float64) Points

ShiftDatasetOnX shifts the x coordinates by the scalar

func ShiftDatasetOnY 

func ShiftDatasetOnY(pts Points, scalar float64) Points

ShiftDatasetOnY shifts the y coordinates by the scalar

func SortPointsByX 

func SortPointsByX(pts Points) Points

SortPointsByX bubble sorts Points, so the Point with the highest X value is the last element of the array.

func SortPointsByY 

func SortPointsByY(pts Points) Points

SortPointsByY bubble sorts Points, so the Point with the highest Y value is the last element of the array.

func Standardize 

func Standardize(pts Points) Points

Standardize standardizes Points so that they are centered and the standard deviation is 1.

func StretchByFactorX 

func StretchByFactorX(pts Points, factor float64) Points

StretchByFactorX streches the x coordinates by the factor. Check how mean and variance change.

func StretchByFactorY 

func StretchByFactorY(pts Points, factor float64) Points

StretchByFactorY streches the x coordinates by the factor. Check how mean and variance change.

func VectorToPoints 

func VectorToPoints(vectors []matrix.Vector) Points

VectorToPoints is a helper function

type Season 

type Season struct {
	// contains filtered or unexported fields
}

Season struct is used with the MessyDataset function to generate a seasonal plot. Start and end are defining an interval where your seasonality would like to occur.

Source Files

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