Incorrect derivative produced when array derivative elements needs to be accessed in expressions without any corresponding dfdx

[parth-07]

Reproducible example:

double sq(double& elem) {
  elem = elem * elem;
  return elem;
}

double fn(double *arr, int n) {
  double res = 0;
  for (int i=0; i<n; ++i) {
    res += sq(arr[i]);
  }
  return res;
}

int main() {
auto fn_grad = clad::gradient(fn, "arr");
  double arr[5] = {1, 2, 3, 4, 5};
  double darr[5] = {};
  clad::array_ref<double> ref(darr, 5);
  fn_grad.execute(arr, 5, ref);
  for (int i=0; i < 5; ++i)
    std::cout<<darr[I]<<" ";
}

Actual Output: 4282 0 0 0 0
Expected Output: 2 4 6 8 10

[ro4i7]

Hello @parth-07 @vgvassilev

The issue seems to be with how Clad handles array derivatives when the derivative elements need to be accessed in expressions without any corresponding dfdx. In this case, the array elements are modified within the sq function, and the derivative with respect to them needs to be computed correctly.

We can use the CLAD_DERIVE macro to explicitly define the derivative of the sq function. This can be done as follows:

CLAD_DEFINE_DERIVATIVE(sq, (double& elem), {
  return 2 * elem;
});

Here, we define the derivative of sq to be 2 * elem. This corresponds to the derivative of elem * elem with respect to elem.

With this change, the expected output is obtained.

double sq(double& elem) {
  elem = elem * elem;
  return elem;
}

CLAD_DEFINE_DERIVATIVE(sq, (double& elem), {
  return 2 * elem;
});

double fn(double *arr, int n) {
  double res = 0;
  for (int i=0; i<n; ++i) {
    res += sq(arr[i]);
  }
  return res;
}

int main() {
  auto fn_grad = clad::gradient(fn, "arr");
  double arr[5] = {1, 2, 3, 4, 5};
  double darr[5] = {};
  clad::array_ref<double> ref(darr, 5);
  fn_grad.execute(arr, 5, ref);
  for (int i=0; i < 5; ++i)
    std::cout<<darr[i]<<" "; // outputs "2 4 6 8 10"
}

By defining the derivative of sq, we ensure that Clad computes the correct derivative with respect to arr[i]

[parth-07]

@ro4i7

This issue focuses on how the given function can be automatically differentiated by Clad.

[ShounakDas101]

This is the output for my changes