Fix: unify DAV subspace diagonalization to use lapack_hegvx

[Cstandardlib]

Summary

• Unify GPU and CPU serial subspace diagonalization to use container::kernels::lapack_hegvx, computing only the needed nband eigenpairs instead of all nbase eigenvalues
• Remove ~30 lines of manual matrix save/restore code in CPU path (now handled internally by lapack_hegvx)
• Add lapack_hegvx<T, DEVICE_GPU> GPU specialization for ROCm using CPU fallback, following the existing lapack_heevd pattern

Motivation

The DAV subspace diagonalization had inconsistent eigensolver calls:

• GPU: lapack_hegvd (divide-and-conquer, ALL eigenvalues)
• CPU: hegvx_op (expert driver, subset eigenvalues)

This caused wasted computation on GPU (computing all eigenvalues when only nband were needed) and inconsistent semantics. Now both paths explicitly request only the first nband eigenpairs.

Changes

File	Change
rocm/lapack.hip.cu	+33 lines: add lapack_hegvx GPU specialization with CPU fallback
diago_dav_subspace.cpp	+8/-45 lines: unify both paths to lapack_hegvx, remove save/restore boilerplate

Test Results

• MODULE_HSOLVER_dav (double): 3/3 PASSED
• MODULE_HSOLVER_dav_float (single): 3/3 PASSED
• GPU integration scf_dav: 7/7 PASSED
• GPU integration scf_dav_sub: 7/7 PASSED

[Copilot]

Pull request overview

This PR unifies DAV subspace diagonalization across CPU and GPU to use container::kernels::lapack_hegvx, so only the required nband eigenpairs are computed (instead of all nbase), and adds an ROCm lapack_hegvx<T, DEVICE_GPU> specialization via a CPU fallback.

Changes:

• Switch DAV subspace diagonalization (CPU + GPU) to lapack_hegvx with nband subset selection.
• Remove CPU-side manual save/restore boilerplate around hegvx.
• Add ROCm lapack_hegvx<T, DEVICE_GPU> specialization that falls back to CPU LAPACK by copying data host<->device.

Reviewed changes

Copilot reviewed 2 out of 2 changed files in this pull request and generated 1 comment.

File	Description
source/source_hsolver/diago_dav_subspace.cpp	Uses lapack_hegvx for both CPU and GPU paths; removes manual matrix save/restore in CPU serial path.
source/source_base/module_container/ATen/kernels/rocm/lapack.hip.cu	Adds ROCm lapack_hegvx GPU specialization implemented via CPU fallback and host/device copies.

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[Copilot]

In this ROCm GPU specialization, the host buffers and memcpy sizes for outputs should match what lapack_hegvx actually produces: eigen_val is length m (see lapack_hegvx<T, DEVICE_CPU> usage in lapack_test.cpp), and eigen_vec is lda * m (Z is n-by-m). Copying n eigenvalues and n*lda eigenvector elements back can write past the caller’s allocated buffers when they size them to m (e.g., the hegvx unit test allocates E with neig entries). Please resize H_eigen_val to m and copy back only m values; likewise allocate/copy H_eigen_vec as lda * m (or at least only memcpy that many elements).

Suggested change

	std::vector<Real> H_eigen_val(n);
	std::vector<T> H_eigen_vec(n * lda);
	hipErrcheck(hipMemcpy(H_A.data(), A, sizeof(T) * n * lda, hipMemcpyDeviceToHost));
	hipErrcheck(hipMemcpy(H_B.data(), B, sizeof(T) * n * lda, hipMemcpyDeviceToHost));
	lapack_hegvx<T, DEVICE_CPU>()(n, lda, H_A.data(), H_B.data(), m, H_eigen_val.data(), H_eigen_vec.data());
	hipErrcheck(hipMemcpy(eigen_val, H_eigen_val.data(), sizeof(Real) * n, hipMemcpyHostToDevice));
	hipErrcheck(hipMemcpy(eigen_vec, H_eigen_vec.data(), sizeof(T) * n * lda, hipMemcpyHostToDevice));
	std::vector<Real> H_eigen_val(m);
	std::vector<T> H_eigen_vec(lda * m);
	hipErrcheck(hipMemcpy(H_A.data(), A, sizeof(T) * n * lda, hipMemcpyDeviceToHost));
	hipErrcheck(hipMemcpy(H_B.data(), B, sizeof(T) * n * lda, hipMemcpyDeviceToHost));
	lapack_hegvx<T, DEVICE_CPU>()(n, lda, H_A.data(), H_B.data(), m, H_eigen_val.data(), H_eigen_vec.data());
	hipErrcheck(hipMemcpy(eigen_val, H_eigen_val.data(), sizeof(Real) * m, hipMemcpyHostToDevice));
	hipErrcheck(hipMemcpy(eigen_vec, H_eigen_vec.data(), sizeof(T) * lda * m, hipMemcpyHostToDevice));