Minor gradcheck update to reduce computations (#45757)

Summary: Pull Request resolved: #45757

Test Plan: Imported from OSS

Reviewed By: glaringlee

Differential Revision: D24137143

Pulled By: anjali411

fbshipit-source-id: e0174ec03d93b1fedf27baa72c3542dac0b70058

torch/autograd/gradcheck.py

@@ -102,13 +102,11 @@ def fn_out():
             d[d_idx] = grad_out.conjugate() * conj_w_d + grad_out * w_d.conj()
         elif ds_dx.is_complex():  # R -> C
             # w_d = conj_w_d = 0.5 * ds_dx
-            dL_dz_conj = 0.5 * (grad_out.conjugate() * ds_dx + grad_out * ds_dx.conj())
-            # The above formula is derived for a C -> C function that's a part of
-            # bigger function with real valued output. From separate calculations,
-            # it can be verified that the gradient for R -> C function
-            # equals to real value of the result obtained from the generic formula for
-            # C -> C functions used above.
-            d[d_idx] = torch.real(dL_dz_conj)
+            # dL_dz_conj = 0.5 * [grad_out.conj() * ds_dx + grad_out * ds_dx.conj()]
+            #            = 0.5 * [grad_out.conj() * ds_dx + (grad_out.conj() * ds_dx).conj()]
+            #            = 0.5 * 2 * real(grad_out.conj() * ds_dx)
+            #            = real(grad_out.conj() * ds_dx)
+            d[d_idx] = torch.real(grad_out.conjugate() * ds_dx)
         else:   # R -> R
             d[d_idx] = ds_dx * grad_out