add tests & docs

Author: jieli-matrix

docs/advanced/input_files/input-main.md

@@ -38,6 +38,7 @@
     - [pw\_seed](#pw_seed)
     - [pw\_diag\_thr](#pw_diag_thr)
     - [diago\_smooth\_ethr](#diago_smooth_ethr)
+    - [use\_k\_continuity](#use_k_continuity)
     - [pw\_diag\_nmax](#pw_diag_nmax)
     - [pw\_diag\_ndim](#pw_diag_ndim)
     - [diag\_subspace](#diag_subspace)
@@ -820,6 +821,18 @@ These variables are used to control the plane wave related parameters.
 - **Description**: If `TRUE`, the smooth threshold strategy, which applies a larger threshold (10e-5) for the empty states, will be implemented in the diagonalization methods. (This strategy should not affect total energy, forces, and other ground-state properties, but computational efficiency will be improved.) If `FALSE`, the smooth threshold strategy will not be applied.
 - **Default**: false
 
+### use_k_continuity
+
+- **Type**: Boolean
+- **Availability**: Used only for plane wave basis set.
+- **Description**: Whether to use k-point continuity for initializing wave functions. When enabled, this strategy exploits the similarity between wavefunctions at neighboring k-points by propagating the wavefunction from a previously initialized k-point to a new k-point, significantly reducing the computational cost of the initial guess.
+
+  **Important constraints:**
+  - Must be used together with `diago_smooth_ethr = 1` for optimal performance
+
+  This feature is particularly useful for calculations with dense k-point sampling where the computational cost of wavefunction initialization becomes significant.
+- **Default**: false
+
 ### pw_diag_nmax
 
 - **Type**: Integer

tests/01_PW/001_PW_UPF100_Al/INPUT

@@ -23,3 +23,5 @@ smearing_sigma	0.002
 #Parameters (5.Mixing)
 mixing_type		broyden
 mixing_beta		0.7
+diago_smooth_ethr 1
+use_k_continuity 1

tests/11_PW_GPU/001_PW_BPCG_GPU/INPUT

@@ -35,3 +35,5 @@ mixing_beta         0.4
 mixing_gg0          1.5
 
 pw_seed   1
+diago_smooth_ethr 1
+use_k_continuity 1