ADX and DI (SMA+Wilder) - Technical Guide

Computes ADX, DI+ and DI- lines with a choice of SMA or Wilder smoothing for ADX.

Overview

This indicator measures both the direction (DI+/DI-) and the absolute strength (ADX) of a trend. It is a port of the TradingView “ADX and DI” by BeikabuOyaji, extended with a user-selectable ADX smoothing method (SMA or Wilder).

The chart displays four lines: a green DI+ line, a red DI- line, a navy ADX line, and a black horizontal threshold line (default at 20). The ADX line can be computed either with a simple moving average (SMA) or with Wilder’s classic exponential-style smoothing, chosen in the settings.

How it works

1. Compute the Directional Movement Index (DMI) components using the built-in Adx.new algorithm, which returns minus_di, classic_adx, and plus_di series.
2. Calculate the Directional Index (DX) from the current DI+ and DI- values, with zero-division protection.
3. Store the DX value in a MutSeriesF to make it available as a series for SMA computation.
4. Compute an SMA of the DX series over the given length to obtain the original (SMA-smoothed) ADX.
5. Select the final ADX value: use the SMA-smoothed ADX if the user chose ‘SMA (Original)’, otherwise use the classic ADX from Adx.new (Wilder smoothing).
6. Return the current DI+, DI-, final ADX, and the threshold value as a constant line.

Mathematical model

Parameters

Code walkthrough

Indicator declaration and parameters

Lines 7-14 of ADX and DI (SMA+Wilder).indie5:

@indicator('ADX and DI', format=format.PRICE)
@param.int('length', default=14, min=1, title='Length')
@param.int('th', default=20, min=1, title='Threshold')
@param.str('adx_smoothing', default='SMA (Original)', options=['SMA (Original)', 'Wilder (Classic)'], title='ADX Smoothing Method')
@plot.line(color=color.GREEN, title='DI+')
@plot.line(color=color.RED, title='DI-')
@plot.line(color=color.NAVY, title='ADX')
@plot.line(color=color.BLACK, title='Threshold')

The @indicator decorator sets the name and price format. Three @param decorators define the length, threshold, and ADX smoothing method as user-configurable settings. The @plot.line decorators assign colors and titles to the four output lines.

Core DMI computation via Adx.new

Lines 15-16 of ADX and DI (SMA+Wilder).indie5:

def Main(self, length, th, adx_smoothing):
    minus_di, classic_adx, plus_di = Adx.new(length, length)

The Main function receives the parameters. Adx.new(length, length) computes the minus_di, classic_adx, and plus_di series. The classic_adx uses Wilder’s smoothing internally.

DX calculation with zero-division protection

Lines 18-19 of ADX and DI (SMA+Wilder).indie5:

    denom = plus_di[0] + minus_di[0]
    dx_val = 0.0 if (isnan(denom) or denom == 0.0) else abs(plus_di[0] - minus_di[0]) / denom * 100

The denominator is the sum of DI+ and DI-. If it is zero or NaN, DX is set to 0.0 to avoid division errors. Otherwise, DX is the absolute difference divided by the sum, multiplied by 100.

SMA smoothing and final ADX selection

Lines 21-24 of ADX and DI (SMA+Wilder).indie5:

    dx_series = MutSeriesF.new(dx_val)
    original_adx = Sma.new(dx_series, length)

    final_adx_val = original_adx[0] if adx_smoothing == 'SMA (Original)' else classic_adx[0]

The DX value is wrapped in a MutSeriesF so it can be passed to Sma.new. The SMA of DX over length bars gives the original ADX. The final ADX is chosen based on the user’s adx_smoothing parameter: either the SMA-smoothed or the classic (Wilder) ADX.

Return values for plotting

Lines 26-26 of ADX and DI (SMA+Wilder).indie5:

    return plus_di[0], minus_di[0], final_adx_val, float(th)

The function returns a tuple of four values: plus_di[0], minus_di[0], final_adx_val, and the threshold as a float. These are plotted as lines according to the @plot.line decorators.

Pine Script vs Indie

The original Pine Script v4 by BeikabuOyaji computes the DMI manually and uses sma() for ADX. The Indie port uses the built-in Adx.new algorithm and adds a choice of smoothing methods.

DMI calculation

Pine Script, lines 21-25 of ADX and DI (SMA+Wilder).pinescript4:

TrueRange = max(max(high-low, abs(high-nz(close[1]))), abs(low-nz(close[1])))

DirectionalMovementPlus = high-nz(high[1]) > nz(low[1])-low ? max(high-nz(high[1]), 0): 0

DirectionalMovementMinus = nz(low[1])-low > high-nz(high[1]) ? max(nz(low[1])-low, 0): 0

Indie, lines 15-16 of ADX and DI (SMA+Wilder).indie5:

def Main(self, length, th, adx_smoothing):
    minus_di, classic_adx, plus_di = Adx.new(length, length)

The Pine script manually computes True Range and Directional Movements. The Indie script delegates all of this to the built-in Adx.new algorithm, which returns the DI+ and DI- series directly.

ADX smoothing

Pine Script, lines 51-53 of ADX and DI (SMA+Wilder).pinescript4:

DX = abs(DIPlus-DIMinus) / (DIPlus+DIMinus)*100

ADX = sma(DX, len)

Indie, lines 21-24 of ADX and DI (SMA+Wilder).indie5:

    dx_series = MutSeriesF.new(dx_val)
    original_adx = Sma.new(dx_series, length)

    final_adx_val = original_adx[0] if adx_smoothing == 'SMA (Original)' else classic_adx[0]

Pine uses sma(DX, len) for ADX. Indie computes both an SMA-based ADX and the classic ADX from Adx.new, then selects one based on the user’s adx_smoothing parameter. This adds the flexibility of choosing between SMA and Wilder smoothing.

Reading the chart

• DI+ (green line): When above DI-, bullish momentum is dominant.
• DI- (red line): When above DI+, bearish momentum is dominant.
• ADX (navy line): Values above the threshold (default 20) indicate a strong trend; values below suggest a weak or ranging market.
• Threshold (black line): A horizontal reference line at the user-set level (default 20) to help filter out weak trends.
• Crossovers: A DI+ crossing above DI- can signal a bullish move; a DI- crossing above DI+ can signal a bearish move.

Implementation notes

• The Adx.new algorithm internally handles the Wilder smoothing for the classic ADX, so no manual Wilder smoothing is needed in this code.
• Zero-division protection is applied only to the DX calculation; the built-in Adx.new already handles its own edge cases.
• The threshold line is drawn as a constant value across all bars; it does not change over time.
• The MutSeriesF wrapper is necessary because Sma.new expects a series input, but dx_val is a scalar per bar.

FAQ

What is the difference between ‘SMA (Original)’ and ‘Wilder (Classic)’ smoothing?

SMA (Original) computes ADX as a simple moving average of the DX values, matching the original BeikabuOyaji script. Wilder (Classic) uses Wilder’s exponential-style smoothing, which is the traditional method from J. Welles Wilder’s original ADX.

How should I set the threshold value?

The threshold (default 20) is a horizontal line used to filter out weak trends. ADX values above the threshold indicate a strong trend; values below suggest a ranging market. You can adjust it based on the asset’s typical ADX range.

Does this indicator repaint?

No, the indicator does not repaint. All calculations use current and past bar data only, and the output for a given bar is fixed once the bar closes.

License and attribution

This Indie script is a derivative work of ADX and DI by BeikabuOyaji on TradingView. The Pine Script original carries a Mozilla Public License 2.0 notice in its header. A modified version of MPL-2.0 code must stay under MPL-2.0, so this file is distributed under that license (the notice is appended to the end of the source file). The original author keeps the credit for the algorithm; this page is not affiliated with or endorsed by them.

Full source code

Indie Script v5, as published on TakeProfit. Copy it into the platform’s script editor or open the live script.

# indie:lang_version = 5
from math import isnan
from indie import indicator, format, param, plot, color, MutSeriesF
from indie.algorithms import Adx, Sma


@indicator('ADX and DI', format=format.PRICE)
@param.int('length', default=14, min=1, title='Length')
@param.int('th', default=20, min=1, title='Threshold')
@param.str('adx_smoothing', default='SMA (Original)', options=['SMA (Original)', 'Wilder (Classic)'], title='ADX Smoothing Method')
@plot.line(color=color.GREEN, title='DI+')
@plot.line(color=color.RED, title='DI-')
@plot.line(color=color.NAVY, title='ADX')
@plot.line(color=color.BLACK, title='Threshold')
def Main(self, length, th, adx_smoothing):
    minus_di, classic_adx, plus_di = Adx.new(length, length)

    denom = plus_di[0] + minus_di[0]
    dx_val = 0.0 if (isnan(denom) or denom == 0.0) else abs(plus_di[0] - minus_di[0]) / denom * 100

    dx_series = MutSeriesF.new(dx_val)
    original_adx = Sma.new(dx_series, length)

    final_adx_val = original_adx[0] if adx_smoothing == 'SMA (Original)' else classic_adx[0]

    return plus_di[0], minus_di[0], final_adx_val, float(th)

# ---------------------------------------------------------------------------
# This Source Code Form is subject to the terms of the Mozilla Public
# License, v. 2.0. If a copy of the MPL was not distributed with this
# file, You can obtain one at https://mozilla.org/MPL/2.0/
# Derived from "ADX and DI by BeikabuOyaji" (TradingView).
# ---------------------------------------------------------------------------