Add deepks_out_freq_elec for outputting deepks labels during electronic steps (#6325)

* add parameter "deepks_out_freq_elec"

* set global_deepks_label_elec_dir, make the directory named "DeePKS_Label_Elec" when needed

* output files during electronic steps, add function get_filename to simplify the process

* modify get_filename

* change the output process of deepks_dm_eig.npy, making it consistent with other outputs

* support output deepks labels during electronic steps

* add test for deepks_out_freq_elec > 0

* optimize LCAO_deepks_interface

* modify test script for deepks

* add doc for deepks_out_freq_elec

* Update input-main.md

Author: xuan112358

docs/advanced/input_files/input-main.md

@@ -188,6 +188,7 @@
     - [bessel\_nao\_sigma](#bessel_nao_sigma)
   - [DeePKS](#deepks)
     - [deepks\_out\_labels](#deepks_out_labels)
+    - [deepks\_out\_freq\_elec](#deepks_out_freq_elec)
     - [deepks\_scf](#deepks_scf)
     - [deepks\_equiv](#deepks_equiv)
     - [deepks\_model](#deepks_model)
@@ -2141,7 +2142,7 @@ Warning: this function is not robust enough for the current version. Please try
 ### deepks_out_labels
 
 - **Type**: Integer
-- **Availability**: numerical atomic orbital basis
+- **Availability**: Numerical atomic orbital basis
 - **Description**: Print labels and descriptors for DeePKS in OUT.${suffix}. The names of these files start with "deepks".
   - 0 : No output.
   - 1 : Output intermediate files needed during DeePKS training.
@@ -2159,26 +2160,33 @@ Warning: this function is not robust enough for the current version. Please try
   This is not needed when `deepks_out_labels` equals 2. 
 - **Default**: 0
 
+### deepks_out_freq_elec
+
+- **Type**: Integer
+- **Availability**: Numerical atomic orbital basis
+- **Description**: When `deepks_out_freq_elec` is greater than 0, print labels and descriptors for DeePKS in OUT.${suffix}/DeePKS_Labels_Elec per `deepks_out_freq_elec` electronic iterations, with suffix `_e*` to distinguish different steps. Often used with `deepks_out_labels` equals 1.
+- **Default**: 0
+
 ### deepks_scf
 
 - **Type**: Boolean
-- **Availability**: numerical atomic orbital basis
+- **Availability**: Numerical atomic orbital basis
 - **Description**: perform self-consistent field iteration in DeePKS method
 - **Note**: A trained, traced model file is needed.
 - **Default**: False
 
 ### deepks_equiv
 
 - **Type**: Boolean
-- **Availability**: numerical atomic orbital basis
+- **Availability**: Numerical atomic orbital basis
 - **Description**: whether to use equivariant version of DeePKS
 - **Note**: the equivariant version of DeePKS-kit is still under development, so this feature is currently only intended for internal usage.
 - **Default**: False
 
 ### deepks_model
 
 - **Type**: String
-- **Availability**: numerical atomic orbital basis and `deepks_scf` is true
+- **Availability**: Numerical atomic orbital basis and `deepks_scf` is true
 - **Description**: the path of the trained, traced neural network model file generated by [deepks-kit](https://github.com/deepmodeling/deepks-kit)
 - **Default**: None
 
@@ -2231,7 +2239,7 @@ Warning: this function is not robust enough for the current version. Please try
 ### deepks_bandgap
 
 - **Type**: Int
-- **Availability**: numerical atomic orbital basis and `deepks_scf` is true
+- **Availability**: Numerical atomic orbital basis and `deepks_scf` is true
 - **Description**: include bandgap label for DeePKS training
   - 0: Don't include bandgap label
   - 1: Include target bandgap label (see [deepks\_band\_range](#deepks_band_range) for more details)
@@ -2242,7 +2250,7 @@ Warning: this function is not robust enough for the current version. Please try
 ### deepks_band_range
 
 - **Type**: Int*2
-- **Availability**: numerical atomic orbital basis, `deepks_scf` is true, and `deepks_bandgap` is 1 or 2
+- **Availability**: Numerical atomic orbital basis, `deepks_scf` is true, and `deepks_bandgap` is 1 or 2
 - **Description**: The first value should not be larger than the second one and the meaning differs in different cases below
   - `deepks_bandgap` is 1: Bandgap label is the energy between `LUMO + deepks_band_range[0]` and `LUMO + deepks_band_range[1]`. If not set, it will calculate energy between HOMO and LUMO states.
   - `deepks_bandgap` is 2: Bandgap labels are energies between HOMO and all states in range [`LUMO + deepks_band_range[0]`, `LUMO + deepks_band_range[1]`] (Thus there are `deepks_band_range[1] - deepks_band_range[0] + 1` bandgaps in total). If HOMO is included in the setting range, it will be ignored since it will always be zero and has no valuable messages (`deepks_band_range[1] - deepks_band_range[0]` bandgaps in this case). *NOTICE: The set range can be greater than, less than, or include the value of HOMO. In the bandgap label, we always calculate the energy of the state in the set range minus the energy of HOMO state, so the bandgap can be negative if the state is lower than HOMO.*
@@ -2251,7 +2259,7 @@ Warning: this function is not robust enough for the current version. Please try
 ### deepks_v_delta
 
 - **Type**: int
-- **Availability**: numerical atomic orbital basis
+- **Availability**: Numerical atomic orbital basis
 - **Description**: Include V_delta/V_delta_R (Hamiltonian in k/real space) label for DeePKS training. When `deepks_out_labels` is true and `deepks_v_delta` > 0 (k space), ABACUS will output `deepks_hbase.npy`, `deepks_vdelta.npy` and `deepks_htot.npy`(htot=hbase+vdelta). When `deepks_out_labels` is true and `deepks_v_delta` < 0 (real space), ABACUS will output `deepks_hrtot.csr`, `deepks_hrdelta.csr`. Some more files output for different settings.
   - `deepks_v_delta` = 1: `deepks_vdpre.npy`, which is used to calculate V_delta during DeePKS training.
   - `deepks_v_delta` = 2: `deepks_phialpha.npy` and `deepks_gevdm.npy`, which can be used to calculate `deepks_vdpre.npy`. A recommanded method for memory saving.