Pine-Script normalize() 和 rescale() 函数有计算或输入错误？

Question

(Sorry, I wrote this question as an answer. So, I ask a new question.)

I have two problems with the normalize()-function:

1) Is there a tiny calculation error? Compared to the standard MACD with same parameters there is a small difference of the MACD-Histogram values. Especially with small values. I did a lot adjustments onto the function formula, but I haven't fixed it so far. I lifted the histbase (the zero-line of histogram) to 50 and the normalize spread between min to max is 0 to 100.

2) Pretty rare, I have stocks where the normalized MACD Histogram is showing completely red (throughout negative values). It seems there is a zero-line error in the formular.

Check the pics I've added. They should explane it pretty good.

Here the code:

// MACD ################################################

//Inputs MACD
fast_length     = input(title="MACD Fast Length", type=input.integer, defval=10)
slow_length     = input(title="MACD Slow Length", type=input.integer, defval=35)
src             = input(type=input.source, defval=close)
signal_length   = input(title="MACD Signal Smoothing", type=input.integer, minval = 1, maxval = 50, defval = 5)
sma_source      = input(title="Simple MA(Oscillator)", type=input.bool, defval=false)
sma_signal      = input(title="Simple MA(Signal Line)", type=input.bool, defval=false)


//Calculating MACD, Signal + Histogram
fast_ma = sma_source ? sma(src, fast_length) : ema(src, fast_length)
slow_ma = sma_source ? sma(src, slow_length) : ema(src, slow_length)
macd    = fast_ma - slow_ma
signal  = sma_signal ? sma(macd, signal_length) : ema(macd, signal_length)


//Reference Declaration
hist    = (macd-signal) // true reference historgram


//Normalize Function when min/max unknown
normalize(_src, _min, _max) => 
    // Normalizes series with unknown min/max using historical min/max.
    // _src: series to rescale.
    // _min: minimum value of rescaled series.
    // _max: maximum value of rescaled series.
    var _historicMin = +10e10
    var _historicMax = -10e10
    _historicMin := min(nz(_src, _historicMin), _historicMin)
    _historicMax := max(nz(_src, _historicMax), _historicMax)
    _min + (_max - _min) * (_src - _historicMin) / max(_historicMax - _historicMin, 10e-10)


//Histogram Colors
col_grow_above  = #26A69A
col_grow_below  = #FFCDD2
col_fall_above  = #B2DFDB
col_fall_below  = #EF5350
col_macd        = #0094ff
col_signal      = #ff6a00
ma_color = normalize(hist, 0,100) // Coloring of histo-bars


//Plot MACD
plot(normalize(hist, 0,100), title="Histogram", style=plot.style_columns, color=color.red, histbase=50.0, color=(ma_color>=50? (ma_color[1] < ma_color ? col_grow_above : col_fall_above) : (ma_color[1] < ma_color ? col_grow_below : col_fall_below)),transp=50)


//END RSI/MACD/MFI ####################################################

1) Calculation Errors

2) Negative bars only

Answer 1

Just wanted to add to the answer, to continue from what LucF said. I didn't have the permission to make comments on his answer.

I used your code and it worked great, I managed to get it to sit on the zero line everytime by doing this: _historicMax:= _historicMin - (_historicMin * 2)

So what I am doing is completely not bothering to calculate the historicMax and instead use the historicMin value and convert it into a negative.

Its because I noticed that on the chart the predicted max and min were at random ranges apart. So if you lock them so they mirror each other, then that means the center will always be zero.

I guess doing this could cut off one of the ranges? so maybe first check which is bigger, like if min was -45 and max was +40, then you could lock them both to min's range, eg -45 and +45, which means the middle is 0.

Answer 2

You are normalizing an unbounded signal into new coordinates, so nothing guarantees that a negative value will be above or below the centerline once normalized. The best way to visualize it is that the normalized centerline is moving, as bars progress. Different original signal values can map to 100 in your normalized value, as new original signal historical highs are discovered with the progressive discovery of history.