Step by Step solution about How to resolve the algorithm Deconvolution/1D step by step in the C++ programming language

The provided C++ code snippet is an implementation of deconvolution, which is a mathematical operation that reverses the effects of convolution.

• print_vector:

  This is a utility function that prints a vector of int32_t values in a formatted manner, enclosing them in square brackets and separating them by commas. The last element is printed without a trailing comma.

• deconvolution:

  This is the main function that performs deconvolution. It takes two vectors, a and b, as input and returns a new vector that is the result of deconvolving a by b.

  • The function initializes a result vector result with a size equal to a.size() - b.size() + 1 and initializes all its elements to 0.

  • It then iterates through the result vector, with result[n] representing the nth element, and performs the following steps:

    • Sets result[n] to a[n].
    • Calculates the start index as std::max((int) (n - b.size() + 1), 0) to ensure it doesn't go below 0.
    • Iterates through the range [start, n) and subtracts result[i] * b[n - i] from result[n].

  • Finally, it divides result[n] by b[0] and returns the result vector.

• main:

  This is the entry point of the program.

  • It defines three constant vectors: h, f, and g with pre-populated values.
  • It then calls deconvolution with g and f as arguments and prints the result by passing it to print_vector.
  • It follows by calling deconvolution again with g and h as arguments and prints the result.

#include <algorithm>
#include <cstdint>
#include <iostream>
#include <vector>

void print_vector(const std::vector<int32_t>& list) {
	std::cout << "[";
	for ( uint64_t i = 0; i < list.size() - 1; ++i ) {
		std::cout << list[i] << ", ";
	}
	std::cout << list.back() << "]" << std::endl;
}

std::vector<int32_t> deconvolution(const std::vector<int32_t>& a, const std::vector<int32_t>& b) {
	std::vector<int32_t> result(a.size() - b.size() + 1, 0);
	for ( uint64_t n = 0; n < result.size(); n++ ) {
		result[n] = a[n];
		uint64_t start = std::max((int) (n - b.size() + 1), 0);
		for ( uint64_t i = start; i < n; i++ ) {
			result[n] -= result[i] * b[n - i];
		}
		result[n] /= b[0];
	}
	return result;
}

int main() {
	const std::vector<int32_t> h = { -8, -9, -3, -1, -6, 7 };
	const std::vector<int32_t> f = { -3, -6, -1, 8, -6, 3, -1, -9, -9, 3, -2, 5, 2, -2, -7, -1 };
	const std::vector<int32_t> g = { 24, 75, 71, -34, 3, 22, -45, 23, 245, 25, 52,
                                     25, -67, -96, 96, 31, 55, 36, 29, -43, -7 };

    std::cout << "h =                   "; print_vector(h);
	std::cout << "deconvolution(g, f) = "; print_vector(deconvolution(g, f));
	std::cout << "f =                   "; print_vector(f);
	std::cout << "deconvolution(g, h) = "; print_vector(deconvolution(g, h));
}