docs: update docs

Author: YuLiu98

docs/advanced/elec_properties/hs_matrix.md

@@ -61,7 +61,10 @@ We also offer the option of only calculating the overlap matrix without running
 
 A file named `SR.csr` will be generated in the working directory, which contains the overlap matrix.
 
-> Note that the column of the overlap matrix when nspin=4 adopts the format of s(up) s(down) p(up) p(down) ... instead of s(up) p(up) ... s(down) p(down) ... 
+> When `nspin` is set to 1 or 2, the dimension of the overlap matrix is nlocal $\times$ nlocal, where nlocal is the total number of numerical atomic orbitals. 
+These numerical atomic orbitals are ordered from outer to inner loop as atom, angular  quantum number $l$, zeta, and magnetic quantum number $m$. 
+When `nspin` is set to 4, the dimension of the overlap matrix is (2 $\times$ nlocal) $\times$ (2 $\times$ nlocal). In this case, the numerical atomic orbitals are ordered from outer to inner loop as atom, angular  quantum number $l$, zeta, magnetic quantum number $m$, and npol (npol ranges from 0 to 1).
+
 
 ## examples
 We provide [examples](https://github.com/deepmodeling/abacus-develop/tree/develop/examples/matrix_hs) of outputting the matrices. There are four examples:

docs/advanced/elec_properties/position_matrix.md

@@ -18,4 +18,7 @@ Each file or each section of the appended file starts with "STEP: " followed by
 
 Each block here contains the matrix for the corresponding cell. There are three columns in each block, giving the matrix elements in x, y, z directions, respectively. There are altogether nbasis * nbasis lines in each block, which emulates the matrix elements.
 
-In molecular dynamics (MD) calculations, if [out_app_flag](../input_files/input-main.md#out_app_flag) is set to true, then `data-rR-tr` is written in an append manner. Otherwise, output files will be put in a separate directory, `matrix`, and named as `$x`_data-rR-tr, where `$x` is the number of MD step. In addition, The output frequency is controlled by [out_interval](../input_files/input-main.md#out_interval). For example, if we are running a 10-step MD with out_interval = 3, then `$x` will be 0, 3, 6, and 9.
+In molecular dynamics (MD) calculations, if [out_app_flag](../input_files/input-main.md#out_app_flag) is set to true, then `data-rR-tr` is written in an append manner. Otherwise, output files will be put in a separate directory, `matrix`, and named as `$x`_data-rR-tr, where `$x` is the number of MD step. In addition, The output frequency is controlled by [out_interval](../input_files/input-main.md#out_interval). For example, if we are running a 10-step MD with out_interval = 3, then `$x` will be 0, 3, 6, and 9.
+
+## get_S
+We also offer the option of only calculating the position matrix without running SCF. For that purpose, in `INPUT` file we need to set the value keyword [calculation](../input_files/input-main.md#calculation) to be `get_S`.

docs/advanced/input_files/input-main.md

@@ -1717,7 +1717,7 @@ These variables are used to control the output of properties.
 
 - **Type**: Boolean
 - **Availability**: Numerical atomic orbital basis (not gamma-only algorithm)
-- **Description**: Whether to print the matrix representation of the position matrix (in Bohr) into a file named `data-rR-tr` in the directory `OUT.${suffix}`. For more information, please refer to [position_matrix.md](../elec_properties/position_matrix.md#extracting-position-matrices).
+- **Description**: Whether to print the matrix representation of the position matrix (in Bohr) into a file named `data-rR-tr` in the directory `OUT.${suffix}`. If [calculation](#calculation) is set to `get_S`, the position matrix can be obtained without scf iterations. For more information, please refer to [position_matrix.md](../elec_properties/position_matrix.md#extracting-position-matrices).
 - **Default**: False
 
 ### out_mat_hs2