math

Library "math"
It's a library of discrete aproximations of a price or Series float it uses Fourier Discrete transform, Laplace Discrete Original and Modified transform and Euler's Theoreum for Homogenus White noice operations. Calling functions without source value it automatically take close as the default source value.

Here is a picture of Laplace and Fourier approximated close prices from this library:

Copy this indicator and try it yourself:

import AutomatedTradingAlgorithms/math/1 as math

//@version=5
indicator("Close Price with Aproximations", shorttitle="Close and Aproximations", overlay=false)

// Sample input data (replace this with your own data)
inputData = close

// Plot Close Price
plot(inputData, color=color.blue, title="Close Price")


ltf32_result = math.LTF32(a=0.01)
plot(ltf32_result, color=color.green, title="LTF32 Aproximation")

fft_result = math.FFT()
plot(fft_result, color=color.red, title="Fourier Aproximation")

wavelet_result = math.Wavelet()
plot(wavelet_result, color=color.orange, title="Wavelet Aproximation")

wavelet_std_result = math.Wavelet_std()
plot(wavelet_std_result, color=color.yellow, title="Wavelet_std Aproximation")

DFT3(xval, _dir)
Discrete Fourier Transform with last 3 points
  Parameters:
    xval (float): Source series
    _dir (int): Direction parameter
  Returns: Aproxiated source value

DFT2(xval, _dir)
Discrete Fourier Transform with last 2 points
  Parameters:
    xval (float): Source series
    _dir (int): Direction parameter
  Returns: Aproxiated source value

FFT(xval)
Fast Fourier Transform once. It aproximates usig last 3 points.
  Parameters:
    xval (float): Source series
  Returns: Aproxiated source value

DFT32(xval)
Combined Discrete Fourier Transforms of DFT3 and DTF2 it aproximates last point by first
aproximating last 3 ponts and than using last 2 points of the previus.
  Parameters:
    xval (float): Source series
  Returns: Aproxiated source value

DTF32(xval)
Combined Discrete Fourier Transforms of DFT3 and DTF2 it aproximates last point by first
aproximating last 3 ponts and than using last 2 points of the previus.
  Parameters:
    xval (float): Source series
  Returns: Aproxiated source value

LFT3(xval, _dir, a)
Discrete Laplace Transform with last 3 points
  Parameters:
    xval (float): Source series
    _dir (int): Direction parameter
    a (float): laplace coeficient
  Returns: Aproxiated source value

LFT2(xval, _dir, a)
Discrete Laplace Transform with last 2 points
  Parameters:
    xval (float): Source series
    _dir (int): Direction parameter
    a (float): laplace coeficient
  Returns: Aproxiated source value

LFT(xval, a)
Fast Laplace Transform once. It aproximates usig last 3 points.
  Parameters:
    xval (float): Source series
    a (float): laplace coeficient
  Returns: Aproxiated source value

LFT32(xval, a)
Combined Discrete Laplace Transforms of LFT3 and LTF2 it aproximates last point by first
aproximating last 3 ponts and than using last 2 points of the previus.
  Parameters:
    xval (float): Source series
    a (float): laplace coeficient
  Returns: Aproxiated source value

LTF32(xval, a)
Combined Discrete Laplace Transforms of LFT3 and LTF2 it aproximates last point by first
aproximating last 3 ponts and than using last 2 points of the previus.
  Parameters:
    xval (float): Source series
    a (float): laplace coeficient
  Returns: Aproxiated source value

whitenoise(indic_, _devided, minEmaLength, maxEmaLength, src)
Ehler's Universal Oscillator with White Noise, without extra aproximated src.
It uses dinamic EMA to aproximate indicator and thus reducing noise.
  Parameters:
    indic_ (float): Input series for the indicator values to be smoothed
    _devided (int): Divisor for oscillator calculations
    minEmaLength (int): Minimum EMA length
    maxEmaLength (int): Maximum EMA length
    src (float): Source series
  Returns: Smoothed indicator value

whitenoise(indic_, dft1, _devided, minEmaLength, maxEmaLength, src)
Ehler's Universal Oscillator with White Noise and DFT1.
It uses src and sproxiated src (dft1) to clearly define white noice.
It uses dinamic EMA to aproximate indicator and thus reducing noise.
  Parameters:
    indic_ (float): Input series for the indicator values to be smoothed
    dft1 (float): Aproximated src value for white noice calculation
    _devided (int): Divisor for oscillator calculations
    minEmaLength (int): Minimum EMA length
    maxEmaLength (int): Maximum EMA length
    src (float): Source series
  Returns: Smoothed indicator value

smooth(dft1, indic__, _devided, minEmaLength, maxEmaLength, src)
Smoothing source value with help of indicator series and aproximated source value
It uses src and sproxiated src (dft1) to clearly define white noice.
It uses dinamic EMA to aproximate src and thus reducing noise.
  Parameters:
    dft1 (float): Value to be smoothed.
    indic__ (float): Optional input for indicator to help smooth dft1 (default is FFT)
    _devided (int): Divisor for smoothing calculations
    minEmaLength (int): Minimum EMA length
    maxEmaLength (int): Maximum EMA length
    src (float): Source series
  Returns: Smoothed source (src) series

smooth(indic__, _devided, minEmaLength, maxEmaLength, src)
Smoothing source value with help of indicator series
It uses dinamic EMA to aproximate src and thus reducing noise.
  Parameters:
    indic__ (float): Optional input for indicator to help smooth dft1 (default is FFT)
    _devided (int): Divisor for smoothing calculations
    minEmaLength (int): Minimum EMA length
    maxEmaLength (int): Maximum EMA length
    src (float): Source series
  Returns: Smoothed src series

vzo_ema(src, len)
Volume Zone Oscillator with EMA smoothing
  Parameters:
    src (float): Source series
    len (simple int): Length parameter for EMA
  Returns: VZO value

vzo_sma(src, len)
Volume Zone Oscillator with SMA smoothing
  Parameters:
    src (float): Source series
    len (int): Length parameter for SMA
  Returns: VZO value

vzo_wma(src, len)
Volume Zone Oscillator with WMA smoothing
  Parameters:
    src (float): Source series
    len (int): Length parameter for WMA
  Returns: VZO value

alma2(series, windowsize, offset, sigma)
Arnaud Legoux Moving Average 2 accepts sigma as series float
  Parameters:
    series (float): Input series
    windowsize (int): Size of the moving average window
    offset (float): Offset parameter
    sigma (float): Sigma parameter
  Returns: ALMA value

Wavelet(src, len, offset, sigma)
Aproxiates srt using Discrete wavelet transform.
  Parameters:
    src (float): Source series
    len (int): Length parameter for ALMA
    offset (simple float)
    sigma (simple float)
  Returns: Wavelet-transformed series

Wavelet_std(src, len, offset, mag)
Aproxiates srt using Discrete wavelet transform with standard deviation as a magnitude.
  Parameters:
    src (float): Source series
    len (int): Length parameter for ALMA
    offset (float): Offset parameter for ALMA
    mag (int): Magnitude parameter for standard deviation
  Returns: Wavelet-transformed series

LaplaceTransform(xval, N, a)
Original Laplace Transform over N set of close prices
  Parameters:
    xval (float): series to aproximate
    N (int): number of close prices in calculations
    a (float): laplace coeficient
  Returns: Aproxiated source value


NLaplaceTransform(xval, N, a, repeat)
Y repetirions on Original Laplace Transform over N set of close prices, each time N-k set of close prices
  Parameters:
    xval (float): series to aproximate
    N (int): number of close prices in calculations
    a (float): laplace coeficient
    repeat (int): number of repetitions
  Returns: Aproxiated source value

LaplaceTransformsum(xval, N, a, b)
Sum of 2 exponent coeficient of Laplace Transform over N set of close prices
  Parameters:
    xval (float): series to aproximate
    N (int): number of close prices in calculations
    a (float): laplace coeficient
    b (float): second laplace coeficient
  Returns: Aproxiated source value

NLaplaceTransformdiff(xval, N, a, b, repeat)
Difference of 2 exponent coeficient of Laplace Transform over N set of close prices
  Parameters:
    xval (float): series to aproximate
    N (int): number of close prices in calculations
    a (float): laplace coeficient
    b (float): second laplace coeficient
    repeat (int): number of repetitions
  Returns: Aproxiated source value

N_divLaplaceTransformdiff(xval, N, a, b, repeat)
N repetitions of Difference of 2 exponent coeficient of Laplace Transform over N set of close prices, with dynamic rotation
  Parameters:
    xval (float): series to aproximate
    N (int): number of close prices in calculations
    a (float): laplace coeficient
    b (float): second laplace coeficient
    repeat (int): number of repetitions
  Returns: Aproxiated source value

LaplaceTransformdiff(xval, N, a, b)
Difference of 2 exponent coeficient of Laplace Transform over N set of close prices
  Parameters:
    xval (float): series to aproximate
    N (int): number of close prices in calculations
    a (float): laplace coeficient
    b (float): second laplace coeficient
  Returns: Aproxiated source value

NLaplaceTransformdiffFrom2(xval, N, a, b, repeat)
N repetitions of Difference of 2 exponent coeficient of Laplace Transform over N set of close prices, second element has for 1 higher exponent factor
  Parameters:
    xval (float): series to aproximate
    N (int): number of close prices in calculations
    a (float): laplace coeficient
    b (float): second laplace coeficient
    repeat (int): number of repetitions
  Returns: Aproxiated source value

N_divLaplaceTransformdiffFrom2(xval, N, a, b, repeat)
N repetitions of Difference of 2 exponent coeficient of Laplace Transform over N set of close prices, second element has for 1 higher exponent factor, dynamic rotation
  Parameters:
    xval (float): series to aproximate
    N (int): number of close prices in calculations
    a (float): laplace coeficient
    b (float): second laplace coeficient
    repeat (int): number of repetitions
  Returns: Aproxiated source value

LaplaceTransformdiffFrom2(xval, N, a, b)
Difference of 2 exponent coeficient of Laplace Transform over N set of close prices, second element has for 1 higher exponent factor
  Parameters:
    xval (float): series to aproximate
    N (int): number of close prices in calculations
    a (float): laplace coeficient
    b (float): second laplace coeficient
  Returns: Aproxiated source value

Release Notes:

v2

Added:
calculateParameters(src, n)
  calculateParameter: aproximates parrameters for a * e^k + b * e^l
  Parameters:
    src (float): series price Source
    n (int)
  Returns: a k b l parameters for a * e^k + b * e^l

LaplaceTransformv1(xval, N, a, b, c, d, repeat)
  LaplaceTransformv1: My version 1 of laplace transform with 4 parrameters
  Parameters:
    xval (float): series to aproximate
    N (int): number of close prices in calculations
    a (float): laplace coeficient
    b (float): second laplace coeficient
    c (float): laplace multyply
    d (float): second laplace multiply
    repeat (int): number of repetitions
  Returns: Aproxiated source value

LaplaceTransformv2(xval, N, a, b, c, d, repeat)
  LaplaceTransformv1: My version 1 of laplace transform with 4 parrameters
  Parameters:
    xval (float): series to aproximate
    N (int): number of close prices in calculations
    a (float): laplace coeficient
    b (float): second laplace coeficient
    c (float): laplace multyply
    d (float): second laplace multiply
    repeat (int): number of repetitions
  Returns: Aproxiated source value