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Pike Module Reference: module version 6, prepared
| MODULE module.ODE |
Methods
RungeKutta()
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-
Method RungeKutta
array module.ODE.RungeKutta(float x0, float xmax, float y0, float h, function f)
- Description
The Runge-Kutta method. Given the point (x0 , y0) / y0 = f(x0) and the step h, solves the differential equation dy / dt = f(x,y) ;
- Parameter x0
The point where the integration begins
- Parameter xmax
The point to finish the integration
- Parameter y0
The initial condition to y.
- Parameter f
The function which gives df/dt = f(x, y) ;
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| MODULE module.Statistics |
Methods
mean()
standarDeviation()
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-
Method mean
float module.Statistics.mean(array serie)
- Description
Computes the mean of a time series
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Method standarDeviation
float module.Statistics.standarDeviation(array serie)
- Description
Computes the standar deviation of a time series.
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| MODULE module.LinearAlgebra |
Classes
NMatrix
Methods
ColumnFromArray()
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-
Method ColumnFromArray
object(NMatrix) module.LinearAlgebra.ColumnFromArray(array a)
- Description
Returns a column Matrix from an array
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| CLASS module.LinearAlgebra.NMatrix |
Methods
LU()
`*()
`+()
`-()
backSubstitution()
columns()
create()
determinant()
dims()
get()
getColumn()
inverse()
mult()
productByScalar()
rows()
show()
solveLinearEquations()
sub()
sum()
swapRows()
transpose()
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- Description
A NMatrix object is a matrix.
-
Inherit Matrix
Math.Matrix
-
Method create
void module.LinearAlgebra.NMatrix()->create(int|array fst, void|int snd)
- Description
You can create a NMatrix object giving an array or two ints: the number of rows and columns.
-
Method get
float module.LinearAlgebra.NMatrix()->get(int i, int j)
- Description
Using get you obtain the element at row i, column j of the NMatrix.
-
Method dims
array(int) module.LinearAlgebra.NMatrix()->dims()
- Description
Returns an array ({ rows, columns })
-
Method rows
int module.LinearAlgebra.NMatrix()->rows()
- Description
Number of rows of a NMatrix
-
Method columns
int module.LinearAlgebra.NMatrix()->columns()
- Description
Number of columns of a NMatrix
-
Method show
void module.LinearAlgebra.NMatrix()->show()
- Description
Shows a NMatrix on the screen.
-
Method productByScalar
object(NMatrix) module.LinearAlgebra.NMatrix()->productByScalar(int|float n)
- Description
Multiplies a NMatrix by a scalar, multiplying all its elements by that scalar.
-
Method swapRows
object(NMatrix) module.LinearAlgebra.NMatrix()->swapRows(int i, int j)
- Description
Returns a new NMatrix, with rows i and j swapped.
-
Method mult
object(NMatrix) module.LinearAlgebra.NMatrix()->mult(object(NMatrix) b)
- Description
Multiplies two matrices.
-
Method `*
object(NMatrix) module.LinearAlgebra.NMatrix()->`*(object(NMatrix) a)
- Description
a * b
-
Method sub
object(NMatrix) module.LinearAlgebra.NMatrix()->sub(object(NMatrix) b)
- Description
a - b
-
Method sum
object(NMatrix) module.LinearAlgebra.NMatrix()->sum(object(NMatrix) b)
- Description
a + b
-
Method `+
object(NMatrix) module.LinearAlgebra.NMatrix()->`+(object(NMatrix) b)
- Description
a + b
-
Method `-
object(NMatrix) module.LinearAlgebra.NMatrix()->`-(object(NMatrix) b)
- Description
a - b
-
Method transpose
object(NMatrix) module.LinearAlgebra.NMatrix()->transpose()
- Description
Returns a new matrix, transposed of the original matrix.
-
Method getColumn
object(NMatrix) module.LinearAlgebra.NMatrix()->getColumn(int i)
- Description
Returns a NMatrix object, with the same content of the i column of the original matrix.
-
Method LU
array module.LinearAlgebra.NMatrix()->LU()
- Description
This does the LU decomposition of the matrix. Returns an array ({ L , U , permutation_matrix , signum })
-
Method backSubstitution
object(NMatrix) module.LinearAlgebra.NMatrix()->backSubstitution(object(NMatrix) L, object(NMatrix) U, object(NMatrix) P, object(NMatrix) w)
- Description
Given the LU decomposition of a NMatrix, solves the linear equations system AX = w
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Method solveLinearEquations
object(NMatrix) module.LinearAlgebra.NMatrix()->solveLinearEquations(object(NMatrix) w)
- Description
Solves the linear equations system AX = w
-
Method inverse
object(NMatrix) module.LinearAlgebra.NMatrix()->inverse()
- Description
Returns the inverse of the matrix.
-
Method determinant
float module.LinearAlgebra.NMatrix()->determinant()
- Description
Returns the determinant of a matrix.
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| MODULE module.Minimization |
Classes
Simplex
Methods
SimpleQuestWith1stDerivatives()
|
- Import
-
Method SimpleQuestWith1stDerivatives
float module.Minimization.SimpleQuestWith1stDerivatives(function df, array range, int NITER, float tol_rel)
- Description
Finds the minimum of a function using the first derivative of a function
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| CLASS module.Minimization.Simplex |
Methods
create()
minimize()
|
- Description
A simplex is a set of N + 1 points in a N dimensional space. It's one of the most beautiful methods to minimize a function of more than 1 variable.
-
Method create
void module.Minimization.Simplex()->create(function function2minimize, array points)
- Description
To create a Simplex, we give a function to minimize and an array of points. Exemple: if we want to minimize a function of two variables, f(x,y), we must call Simplex with f(x,y) and an array of 3 elements: ({ ({x1, y1 }) , ({x2, y2}) , ({x3, y3}) })
-
Method minimize
array module.Minimization.Simplex()->minimize(int NITER, float tol_rel)
- Description
To minimize a Simplex, we can do NITER iterations and tolerate a relative error of tol_rel.
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| MODULE module.Derivatives |
Methods
derive()
derive2()
|
-
Method derive
function module.Derivatives.derive(function f, float h)
- Description
This function returns the derivative of f calculated simply applying the definition, with step h
-
Method derive2
function module.Derivatives.derive2(function f, float h)
- Description
This function returns the derivative of f calculated by a better algorhytm.
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| MODULE module.Fourier |
Methods
DiscreteFourierTransformation()
InverseDiscreteFourierTransformation()
PowerSpectrum()
|
- Import
- Import
-
Method DiscreteFourierTransformation
array module.Fourier.DiscreteFourierTransformation(array data, int max)
- Description
Does the discrete fourier transformation of some data.
-
Method InverseDiscreteFourierTransformation
array module.Fourier.InverseDiscreteFourierTransformation(array data, int max)
- Description
Does the inverse discrete fourier transformation of data.
-
Method PowerSpectrum
array module.Fourier.PowerSpectrum(array data, int max)
- Description
Power spectrum of data. This first does a discreteFourierTransformation of data, them computes the powerSpectrum.
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| MODULE module.Roots |
Methods
Bisection()
NewtonRaphson()
RegulaFalsi()
Steffensen()
|
-
Method Bisection
float module.Roots.Bisection(function f, array range, float error_p, int iterations)
- Description
This function tries to find a root of f , given the interval (a,b) where you think that It's fitted.
- Parameter f
The function that we are tryint to find a root.
- Parameter range
The interval ({ a, b }) where we think that the root is fitted.
- Parameter error_p
The relative error that It's allowed to the solution.
- Parameter iterations
The maxim number of iterations that the method can do trying to find the root.
-
Method NewtonRaphson
float module.Roots.NewtonRaphson(function f, function df, float point, float error_abs, int iterations)
- Description
This function tries to find a root of f using the Newton-Raphson method.
- Parameter f
The function
- Parameter df
The derivative of f
- Parameter point
A point to start the method from x = point
- Parameter error_abs
The absolute error that we tolerate to the solution
- Parameter iterations
The maximum number of iterations that we can do trying to find the root.
-
Method Steffensen
float module.Roots.Steffensen(function f, float point, float error_abs, int iterations)
- Description
This function tries to find a root of f using the Newton-Raphson method.
- Parameter f
The function
- Parameter point
A point to start the method from x = point
- Parameter error_abs
The absolute error that we tolerate to the solution
-
Method RegulaFalsi
float module.Roots.RegulaFalsi(function f, array range, float error_p, int iterations)
- Description
This function tries to find a root of f , given the interval (a,b) where you think that It's fitted. It uses the Regula-Falsi method. The paramethers have the same meaning than in Bisection.
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| MODULE module.Functions |
Methods
Weierstrass()
|
-
Method Weierstrass
function module.Functions.Weierstrass(float lamda, float s, void|int iterations)
- Description
The Weierstrass function. s is the fractal dimension, lamda must be greather than one.
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| MODULE module.Integration |
Methods
SimpleMontecarlo()
|
- Import
-
Method SimpleMontecarlo
array module.Integration.SimpleMontecarlo(function f, array interval, int points)
- Description
Uses a simple Montecarlo algorithm to integrate f in the interval .
- Parameter f
The function to integrate
- Parameter interval
The interval ({ a, b }) where we wish to do the integral.
- Parameter points
The number of points that the montecarlo algorithm has to use.
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| MODULE module.Fractal |
Methods
BurlagaKlein()
GenerateHiguchiData()
GenerateLinearData()
GenerateLogisticData()
GeneratePowerSpectrumExponentData()
GenerateSinusoidalData()
GenerateWeierstrassData()
Higuchi()
PowerSpectrumExponent()
SimpleFractalDimension()
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- Import
- Import
- Import
- Import
- Import
-
Method Higuchi
array module.Fractal.Higuchi(array serie, int kmin, int kmax, float error_percent, void|function stepper)
- Description
This function computes the Higuchi fractal dimension of a time serie.
- Parameter serie
The time serie we want to analize.
- Parameter kmin
Minimum value of the paramether we have to use to compute the fractal dimension
- Parameter kmax
Maximum value of the paramether we have to use to compute the fractal dimension
- Parameter error_percent
Percentual error of each point in serie
- Parameter stepper
A function which, given a value of k, returns the next value of k to use.
-
Method GenerateLinearData
array module.Fractal.GenerateLinearData(float a, float b, int n)
- Description
Generates n points following a linear distribucion y = a x + b ;
-
Method GenerateSinusoidalData
array module.Fractal.GenerateSinusoidalData(int n)
- Description
Generates n points following a sinusoidal function. Only one period.
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Method GenerateLogisticData
array module.Fractal.GenerateLogisticData(float r, float x0, int n, int transitori)
- Description
Generates n points from the logistic map x -> r x (1-x)
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Method GenerateHiguchiData
array module.Fractal.GenerateHiguchiData(int n)
- Description
Generates n points from a random walk (also called Fractional Brownian Function ), with fractal dimension 1.5 .
-
Method BurlagaKlein
array module.Fractal.BurlagaKlein(array serie, int kmin, int kmax, float error_percent, void|function stepper)
- Description
This function computes the Burlaga and Klein's fractal dimension of a time serie.
- Parameter serie
The time serie we want to analize.
- Parameter kmin
Minimum value of the paramether we have to use to compute the fractal dimension
- Parameter kmax
Maximum value of the paramether we have to use to compute the fractal dimension
- Parameter error_percent
Percentual error of each point in serie
- Parameter stepper
A function which, given a value of k, returns the next value of k to use.
-
Method SimpleFractalDimension
array module.Fractal.SimpleFractalDimension(array serie, int kmin, int kmax, float error_percent, void|function stepper)
- Description
This function computes the fractal dimension of a time serie simply using as the curve length abs( y1 - y2 ). Very primitive method, It's here only to compare with BK and Higuchi methods.
- Parameter serie
The time serie we want to analize.
- Parameter kmin
Minimum value of the paramether we have to use to compute the fractal dimension
- Parameter kmax
Maximum value of the paramether we have to use to compute the fractal dimension
- Parameter error_percent
Percentual error of each point in serie
- Parameter stepper
A function which, given a value of k, returns the next value of k to use.
-
Method GenerateWeierstrassData
array module.Fractal.GenerateWeierstrassData(int n, float xmin, float xmax, float lamda, float s)
- Description
Generates n points from the Weierstrass function. s is the fractal dimension of the graph. lamda must be greather than 1.
-
Method GeneratePowerSpectrumExponentData
array module.Fractal.GeneratePowerSpectrumExponentData(int n, float exponent, float angle_max)
- Description
Generates points following an exponential power expectrum law, where P(k) ~ k^(-exponent). The angle is picked from a Uniform distribution between 0 and angle_max (in degree).
-
Method PowerSpectrumExponent
array module.Fractal.PowerSpectrumExponent(array serie, int kmax, float error_p)
- Description
Tries to do a log-log adjust to get the exponent from a power spectrum which follows an exponential law.
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| MODULE module.Complex |
Classes
Complex
Methods
Exp()
|
-
Variable i
object(Complex) module.Complex.i
- Description
The imaginary unit.
-
Method Exp
object(Complex) module.Complex.Exp(object(Complex) a)
- Description
Exponential of a Complex number.
|
| CLASS module.Complex.Complex |
Methods
`-()
cast()
conjugate()
create()
imPart()
module()
realPart()
|
- Description
A complex number x = a + ib
-
Method create
void module.Complex.Complex()->create(float|int real, float|int imaginari)
- Description
We can create a complex given Its real and imaginary part, or only with one argument: an array.
-
Method realPart
float|int module.Complex.Complex()->realPart()
- Description
Returns the real part of the complex number.
-
Method imPart
float|int module.Complex.Complex()->imPart()
- Description
Returns the imaginary part of the complex number.
-
Method `-
object(Complex) module.Complex.Complex()->`-(object(Complex) a)
- Description
a - b
-
Method cast
string module.Complex.Complex()->cast(string what)
- Description
We can cast a Complex number to a string in a form Real + i * Imaginary
-
Method module
float module.Complex.Complex()->module()
- Description
Returns the module of a complex number.
-
Method conjugate
object(Complex) module.Complex.Complex()->conjugate()
- Description
Given a + ib, returns a -ib
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