[misc] Ensure succeeded variable is properly initialized in matrix-fr…

…ee solvers (#8484)

The `succeeded` variable was not properly initialized in the
`MatrixFreeCG` and `MatrixFreeBICGSTAB` functions, leading to potential
issues with the convergence check. By initializing the `succeeded`
variable at the beginning of the `solve` function, we ensure that the
variable is correctly set and returned at the end of the function,
improving the reliability of the solvers.

Issue: #

### Brief Summary

copilot:summary

### Walkthrough

copilot:walkthrough

python/taichi/linalg/matrixfree_cg.py

@@ -64,7 +64,6 @@ def MatrixFreeCG(A, b, x, tol=1e-6, maxiter=5000, quiet=True):
     beta = ti.field(dtype=solver_dtype)
     scalar_builder.place(alpha, beta)
     scalar_snode_tree = scalar_builder.finalize()
-    succeeded = True
 
     @ti.kernel
     def init():
@@ -96,6 +95,7 @@ def update_p():
             p[I] = r[I] + beta[None] * p[I]
 
     def solve():
+        succeeded = True
         A._matvec(x, Ax)
         init()
         initial_rTr = reduce(r, r)
@@ -129,8 +129,9 @@ def solve():
                     f">>> Conjugate Gradient method failed to converge in {maxiter} iterations: Residual = {sqrt(new_rTr):e}"
                 )
             succeeded = False
+        return succeeded
 
-    solve()
+    succeeded = solve()
     vector_fields_snode_tree.destroy()
     scalar_snode_tree.destroy()
     return succeeded
@@ -252,6 +253,7 @@ def update_r():
             r[I] = s[I] - omega[None] * t[I]
 
     def solve():
+        succeeded = True
         A._matvec(x, Ax)
         init()
         initial_rTr = reduce(r, r)
@@ -296,8 +298,9 @@ def solve():
             if not quiet:
                 print(f">>> BICGSTAB failed to converge in {maxiter} iterations: Residual = {sqrt(rTr):e}")
             succeeded = False
+        return succeeded
 
-    solve()
+    succeeded = solve()
     vector_fields_snode_tree.destroy()
     scalar_snode_tree.destroy()
     return succeeded