Gaussian Filter (GAUSS)

// Licensed under the Apache License, Version 2.0
// © mihakralj
//@version=6
indicator("Gaussian Filter (GAUSS)", "GAUSS", overlay=true)

//@function Calculates Gaussian Filter using true convolution
//@param src Series to calculate Gaussian filter from
//@param sigma Standard deviation of the Gaussian kernel
//@returns Gaussian filter value
//@optimized Uses Gaussian kernel convolution with O(n) complexity per bar
gauss(series float src, simple float sigma) =>
    int kernel_size = 2 * math.ceil(3.0 * sigma) + 1
    var array<float> kernel = array.new_float(0)
    var array<float> norm_kernel = array.new_float(1, 1.0)
    var int last_kernel_size = 1
    if last_kernel_size != kernel_size
        float center = math.floor(kernel_size / 2.0)
        array.clear(kernel)
        float kernel_sum = 0.0
        for i = 0 to kernel_size - 1
            float x = i - center
            float weight = math.exp(-(x * x) / (2.0 * sigma * sigma))
            array.push(kernel, weight)
            kernel_sum += weight
        norm_kernel := array.copy(kernel)
        if kernel_sum != 0.0
            float inv_sum = 1.0 / kernel_sum
            for i = 0 to kernel_size - 1
                array.set(norm_kernel, i, array.get(kernel, i) * inv_sum)
        last_kernel_size := kernel_size
    int p = math.min(bar_index + 1, kernel_size)
    float sum = 0.0
    float weight_sum = 0.0
    for i = 0 to p - 1
        float price = src[i]
        if not na(price)
            float w = array.get(norm_kernel, i)
            sum += price * w
            weight_sum += w
    nz(sum / weight_sum, src)

// ---------- Main loop ----------

// Inputs
i_sigma = input.float(1.0, "Sigma", minval=0.1, maxval=10.0, step=0.1)
i_source = input.source(close, "Source")

// Calculation
gauss_val = gauss(i_source, i_sigma)

// Plot
plot(gauss_val, "Gaussian", color=color.yellow, linewidth=2)