1. Improve output accuracy of Exx_Opt_Orb (#6509)

* Refactor: change cal_proj() to cal_mul() in Exx_Opt_Orb

* 1. Improve output accuracy of Exx_Opt_Orb
2. Change default value of exx_opt_orb_tolerence

---------

Co-authored-by: linpz <[email protected]>

Author: linpeize

docs/advanced/input_files/input-main.md

@@ -2977,7 +2977,7 @@ These variables are relevant when using hybrid functionals with *[basis_type](#b
 - **Type**: Real
 - **Availability**: *[calculation](#calculation)==gen_opt_abfs*
 - **Description**: The threshold when solving for the zeros of spherical Bessel functions. A reasonable choice is 1e-12.
-- **Default**: 0
+- **Default**: 1E-12
 
 ### exx_real_number
 

source/source_hamilt/module_xc/exx_info.h

@@ -81,7 +81,7 @@ struct Exx_Info
     {
         int abfs_Lmax = 0; // tmp
         double ecut_exx = 60;
-        double tolerence = 1E-2;
+        double tolerence = 1E-12;
         double kmesh_times = 4;
     };
     Exx_Info_Opt_ABFs info_opt_abfs;

source/source_io/module_parameter/input_parameter.h

@@ -546,7 +546,7 @@ struct Input_para
                                                  ///< calculating Columb potential is to that of atomic orbitals
     int exx_opt_orb_lmax = 0;                    ///< the maximum l of the spherical Bessel functions for opt ABFs
     double exx_opt_orb_ecut = 0.0;               ///< the cut-off of plane wave expansion for opt ABFs
-    double exx_opt_orb_tolerence = 0.0;          ///< the threshold when solving for the zeros of spherical Bessel
+    double exx_opt_orb_tolerence = 1E-12;        ///< the threshold when solving for the zeros of spherical Bessel
                                                  ///< functions for opt ABFs
     bool exx_symmetry_realspace
         = true; ///< whether to reduce the real-space sector in when using symmetry=1 in EXX calculation

source/source_io/test/read_input_ptest.cpp

@@ -296,7 +296,7 @@ TEST_F(InputParaTest, ParaRead)
     EXPECT_DOUBLE_EQ(param.inp.rpa_ccp_rmesh_times, 10.0);
     EXPECT_EQ(param.inp.exx_opt_orb_lmax, 0);
     EXPECT_DOUBLE_EQ(param.inp.exx_opt_orb_ecut, 0.0);
-    EXPECT_DOUBLE_EQ(param.inp.exx_opt_orb_tolerence, 0.0);
+    EXPECT_DOUBLE_EQ(param.inp.exx_opt_orb_tolerence, 1E-12);
     EXPECT_FALSE(param.inp.noncolin);
     EXPECT_FALSE(param.inp.lspinorb);
     EXPECT_DOUBLE_EQ(param.inp.soc_lambda, 1.0);

source/source_io/test/support/INPUT

@@ -291,7 +291,7 @@ exx_v_grad_r_threshold         0 #
 exx_ccp_rmesh_times            default #
 exx_opt_orb_lmax               0 #
 exx_opt_orb_ecut               0 #
-exx_opt_orb_tolerence          0 #
+exx_opt_orb_tolerence          1E-12 #
 
 #Parameters (16.tddft)
 td_vext                        0 #add extern potential or not

source/source_lcao/module_ri/exx_opt_orb-print.cpp

@@ -1,6 +1,7 @@
 #include "exx_opt_orb.h"
 #include "../../source_pw/module_pwdft/global.h"
 #include "exx_abfs-jle.h"
+#include <iomanip>
 
 void Exx_Opt_Orb::print_matrix(
 	const Exx_Info::Exx_Info_Opt_ABFs &info,
@@ -204,6 +205,7 @@ void Exx_Opt_Orb::print_matrix(
 
 	std::ofstream ofs(file_name+"_"+std::to_string(TA)+"_"+std::to_string(IA)+"_"+std::to_string(TB)+"_"+std::to_string(IB));
 	print_header(ofs);
+	ofs<<std::setprecision(15);
 	print_Q(ofs);
 	print_S(ofs);
 	print_V(ofs);