/// This is an improved McGinleyDynamic to address the problem with the original.
/// See author ImmortalFreedom notes at the link below
/// @link https://www.tradingview.com/script/AKsKg1ih-McGinley-Dynamic-Improved-John-R-McGinley-Jr
///
/// An example of a problem - pick a stock that has gap down a lot and see what the functions oMD() and iMD() show.
_SECTION_BEGIN( "Price" );
SetChartOptions( 0, chartShowArrows | chartShowDates );
_N( Title = StrFormat( "{{NAME}} - {{INTERVAL}} {{DATE}} Open %g, Hi %g, Lo %g, Close %g (%.1f%%) Vol " + WriteVal( V, 1.0 ) + " {{VALUES}}", O, H, L, C, SelectedValue( ROC( C, 1 ) ) ) );
Plot( C, "Close", ParamColor( "Color", colorBlack ), styleNoTitle | ParamStyle( "Style" ) | GetPriceStyle() );
_SECTION_END();

// Original McGinleyDynamic
function oMD( array, period )
{
    local array, period;
    local i, j, MD;

    MD = Null;
    j = NullCount( array );
    MD[j] = array[j];

    for( i = j + 1; i < BarCount; i++ )
    {
        // The equation is: D = D1 + (I - D1) / ( N * (I/D1)^4)
        // where
        //		D1 = yesterday's Dynamic,
        //		I = today's price,
        //		N = smoothing factor.
        MD[ i ] = MD[ i - 1 ] + ( array[i] - MD[i - 1] ) / ( period * ( array[i] / MD[i - 1] ) ^ 4 );
    }

    return MD;
}

/// @link https://www.tradingview.com/script/AKsKg1ih-McGinley-Dynamic-Improved-John-R-McGinley-Jr
/// Improved McGinleyDynamic
function iMD( array, period, custom_k, custom_exp )
{
    local array, period, custom_k, custom_exp;
    local i, j, MD;

    period = max( 1.0, Period );
    MD = Null;
    j = NullCount( array );
    MD[j] = array[j];

    for( i = j + 1; i < BarCount; i++ )
    {
        // original MD
        // MD[ i ] = MD[ i - 1 ] + ( array[i] - MD[i - 1] ) / ( period * ( array[i] / MD[i - 1] ) ^ 4 );
        // author ImmortalFreedom came up with the formula
        // MD[ i ] = MD[ i - 1 ] + ( array[i] - MD[i - 1] ) / ( custom_k * period * ( array[i] / MD[i - 1] ) ^ custom_exp );
        // but author ImmortalFreedom finds Unconstrained McGinley Dynamic, susceptible to miscalculation
        // It required upgrading the formulation with two constraints.
        // MD[ i ] = MD[ i - 1 ] + ( array[i] - MD[i - 1] ) /  Min( period,  Max( 1.0, custom_k * period * ( array[i] / MD[i - 1] ) ^ custom_exp ))
        // so even with k = 1 and exponent = 4, MD will not give the calculation of the original md
        MD[ i ] = MD[ i - 1 ] + ( array[i] - MD[i - 1] ) / Min( period,  Max( 1.0, custom_k * period * ( array[i] / MD[i - 1] ) ^ custom_exp ) );
    }

    return MD;
}

_SECTION_BEGIN( "MD" );
source = ParamField( "Price field", -1 );
length = Param( "Length", 25, 1, 300, 0.5 );
Plot( oMD( source, length ), _DEFAULT_NAME(), ParamColor( "Color", colorCycle ), ParamStyle( "Style" ), Null, Null, 0, 1, 2 );
_SECTION_END();

_SECTION_BEGIN( "iMD" );
source = ParamField( "Price field", -1 );
_N( param_source = StrReplace( _PARAM_VALUES(), ")", "" ) );
length = Param( "Length", 25, 1, 300, 0.5 );
_N( formula  = ParamList( "Formulas k value", "Modern|Original|Custom k", 0 ) );
kCustom  = Param( "Custom k (tweak)", 0.5, 0.3, 1.0, 0.05 );
exponent = Param( "Exponent (tweak)", 4.0, 1.0, 5.0, 0.1 );

switch( formula )
{
case "Modern":
    k_value = 0.6;
    break;

case "Original":
    k_value = 1.0;
    break;

case "Custom k":
default:
    k_value = kCustom;
    break;
}

_N( Param_title = _SECTION_NAME() + Param_source + "," + length + "," + k_value + "," + exponent + ")" );
Plot( iMD( source, length, k_value, exponent ), _DEFAULT_NAME(), ParamColor( "Color", colorCycle ), ParamStyle( "Style" ), Null, Null, 0, 1, 2 );
_SECTION_END();