fix: use real-only initial wavefunctions in PPCG unit test

H and S are real symmetric operators whose eigenvectors are real.
The previous complex random initialization produced complex
off-diagonal elements in the H-gram matrix (max |Im| ~ 0.5 for
nband=3), causing Re(<psi_i|H|psi_j>) != <psi_i|H|psi_j>.  The
gamma_dot function only returns the real part, so all subspace
Gram matrices (built via gram()) computed wrong off-diagonals,
leading to incorrect eigenvalues from sygvd.

With real-only psi all inner products are real and gamma_dot is
exact, so both BLOCK_SUBSPACE and CONJUGATE_GRADIENT strategies
should now converge to the correct eigenvalues.

Author: cheerly-pku

source/source_hsolver/test/diago_ppcg_test.cpp

@@ -75,10 +75,14 @@ class DiagoPPCGTest : public ::testing::Test
         std::mt19937 rng(42);
         std::uniform_real_distribution<Real> dist(-1.0, 1.0);
 
+        // Use real-only initial guess.  H and S are real symmetric, so the
+        // exact eigenvectors are real and any imaginary component can only
+        // slow convergence.  Keeping psi real also avoids the need for
+        // complex-Hermitian Gram matrices in the subspace eigenvalue solves.
         psi.assign(ld * nband, T(0));
         for (int j = 0; j < nband; ++j)
             for (int i = 0; i < n_dim; ++i)
-                psi[i + j * ld] = T(dist(rng), dist(rng));
+                psi[i + j * ld] = T(dist(rng), 0.0);
 
         // Gram-Schmidt orthonormalisation (S = I)
         for (int j = 0; j < nband; ++j) {