Refactor: update assignment logic of ecutwfc and ecutrho (#5907)

Author: YuLiu98

docs/advanced/input_files/input-main.md

@@ -771,6 +771,7 @@ These variables are used to control the plane wave related parameters.
 
 - **Type**: Real
 - **Description**: Energy cutoff for plane wave functions, the unit is **Rydberg**. Note that even for localized orbitals basis, you still need to setup an energy cutoff for this system. Because our local pseudopotential parts and the related force are calculated from plane wave basis set, etc. Also, because our orbitals are generated by matching localized orbitals to a chosen set of wave functions from a certain energy cutoff, this set of localize orbitals is most accurate under this same plane wave energy cutoff.
+> `ecutwfc` and `ecutrho` can be set simultaneously. Besides, if only one parameter is set, abacus will automatically set another parameter based on the 4-time relationship. If both parameters are not set, the default values will be employed.
 - **Default**: 50 Ry (PW basis), 100 Ry (LCAO basis)
 
 ### ecutrho

source/module_io/read_input_item_system.cpp

@@ -285,8 +285,13 @@ void ReadInput::item_system()
         item.annotation = "energy cutoff for wave functions";
         read_sync_double(input.ecutwfc);
         item.reset_value = [](const Input_Item& item, Parameter& para) {
-            if (para.input.ecutwfc == 0){ // 0 means no input value
-                if (para.input.basis_type == "lcao")
+            if (para.input.ecutwfc == 0)
+            { // 0 means no input value
+                if (para.input.ecutrho > 0)
+                {
+                    para.input.ecutwfc = para.input.ecutrho / 4.0;
+                }
+                else if (para.input.basis_type == "lcao")
                 {
                     para.input.ecutwfc = 100;
                 }
@@ -324,6 +329,10 @@ void ReadInput::item_system()
             {
                 ModuleBase::WARNING_QUIT("ReadInput", "ecutrho/ecutwfc must >= 4");
             }
+            if (para.sys.double_grid == true && para.input.basis_type == "lcao")
+            {
+                ModuleBase::WARNING_QUIT("ReadInput", "ecutrho/ecutwfc must = 4 for lcao calculation");
+            }
         };
         this->add_item(item);
     }