bollinger bands in ruby programming language

To calculate and visualize Bollinger Bands in a Ruby program, you can use the `Numo::NArray` library for numerical computations and the `Numo::Gnuplot` library for plotting. If you haven't already installed these libraries, you can do so using the following commands:

```bash
gem install numo-narray
gem install numo-gnuplot
```

Here's a sample Ruby program that calculates and plots Bollinger Bands for a set of price data:

```ruby
require 'numo/narray'
require 'numo/gnuplot'

# Sample price data (replace this with your own price data)
price_data = [100, 102, 104, 105, 103, 101, 99, 98, 97, 95, 93, 91]

# Bollinger Bands parameters
window_size = 10
num_standard_deviations = 2

# Calculate the moving average (middle band)
sma = Numo::NArray[
  (price_data[0, window_size - 1] + price_data[window_size - 1, -1].sum) / window_size
]

(1..price_data.size - window_size).each do |i|
  sma = Numo::NArray.hstack(
    sma,
    (sma[i - 1] * window_size - price_data[i - 1] + price_data[i + window_size - 1]) / window_size
  )
end

# Calculate the standard deviation
std_dev = []
(0..price_data.size - window_size).each do |i|
  slice = price_data[i, window_size]
  std_dev << Math.sqrt(slice.var)
end

# Calculate the upper and lower Bollinger Bands
upper_band = sma + num_standard_deviations * std_dev
lower_band = sma - num_standard_deviations * std_dev

# Create a time array for plotting
time = Numo::NArray[*(1..price_data.size)]

# Plot the price data and Bollinger Bands
Numo::Gnuplot::Splot.new do |plot|
  plot.data << Numo::Gnuplot::DataSet.new([time, price_data]) { |ds|
    ds.with = 'lines'
    ds.title = 'Price Data'
  }

  plot.data << Numo::Gnuplot::DataSet.new([time[window_size - 1..-1], sma]) { |ds|
    ds.with = 'lines'
    ds.title = 'SMA (Middle Band)'
  }

  plot.data << Numo::Gnuplot::DataSet.new([time[window_size - 1..-1], upper_band]) { |ds|
    ds.with = 'lines'
    ds.title = 'Upper Band'
  }

  plot.data << Numo::Gnuplot::DataSet.new([time[window_size - 1..-1], lower_band]) { |ds|
    ds.with = 'lines'
    ds.title = 'Lower Band'
  }

  plot.title = 'Bollinger Bands'
  plot.xlabel = 'Time'
  plot.ylabel = 'Price'
end
```

This program calculates the Bollinger Bands (SMA, upper band, and lower band) and plots them using the `Numo::Gnuplot` library. You can replace the `price_data` array with your own price data, and adjust the `window_size` and `num_standard_deviations` variables according to your preferences.