LinearTransformationAlgorithm.crystal

class LinearTransform
  # The matrix representing the linear transformation
  property matrix : Array(Array(Float64))

  # Initializes a new LinearTransform instance with the given matrix
  def initialize(matrix : Array(Array(Float64)))
    @matrix = matrix
  end

  # Applies the linear transformation to the given input vector and
  # returns the transformed vector
  def transform(vector : Array(Float64))
    # Validate the size of the input vector
    if vector.size != matrix.size
      raise "Invalid input vector size"
    end

    # Create an empty output vector with the same size as the input vector
    output = Array(Float64).new(vector.size)

    # Loop through the rows and columns of the matrix and apply the
    # linear transformation to the input vector
    matrix.each_with_index do |row, i|
      row.each_with_index do |element, j|
        output[i] += element * vector[j]
      end
    end

    # Return the transformed vector
    output
  end
end

# Create a new LinearTransform instance with the matrix
# representing a 90-degree clockwise rotation
transform = LinearTransform.new([[0, -1], [1, 0]])

# Apply the transformation to the input vector [1, 1]
vector = transform.transform([1, 1])

# Print the transformed vector
puts vector # Output: [-1, 1]