diff --git a/docs/advanced/input_files/input-main.md b/docs/advanced/input_files/input-main.md
index 6e58330990..9e87b52dcc 100644
--- a/docs/advanced/input_files/input-main.md
+++ b/docs/advanced/input_files/input-main.md
@@ -343,6 +343,8 @@
     - [td\_heavi\_amp](#td_heavi_amp)
     - [out\_dipole](#out_dipole)
     - [out\_efield](#out_efield)
+    - [out\_vecpot](#out_vecpot)
+    - [init\_vecpot\_file](#init_vecpot_file)
     - [ocp](#ocp)
     - [ocp\_set](#ocp_set)
   - [Variables useful for debugging](#variables-useful-for-debugging)
@@ -1836,6 +1838,14 @@ Warning: this function is not robust enough for the current version. Please try
 - **Note**: A trained, traced model file is needed.
 - **Default**: False
 
+### deepks_equiv
+
+- **Type**: Boolean
+- **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
@@ -3254,6 +3264,22 @@ These variables are used to control berry phase and wannier90 interface paramete
   - False: do not output efield.
 - **Default**: False
 
+### out_vecpot
+
+- **Type**: Boolean
+- **Description**: output TDDFT Vector potential or not(a.u.)
+  - True: output Vector potential in file "OUT.suffix/At.dat"
+  - False: do not output Vector potential.
+- **Default**: False
+
+### init_vecpot_file
+
+- **Type**: Boolean
+- **Description**: Init vector potential through file or not
+  - True: init vector potential from file "At.dat".(a.u.) It consists of four columns, representing istep and vector potential on each direction.
+  - False: calculate vector potential by integral of Efield
+- **Default**: False
+
 ### ocp
 
 - **Type**: Boolean
diff --git a/examples/interface_wannier90/ABACUS_towannier90_lcao/INPUT-nscf b/examples/interface_wannier90/ABACUS_towannier90_lcao/INPUT-nscf
index b2c769166d..1dbecf0753 100644
--- a/examples/interface_wannier90/ABACUS_towannier90_lcao/INPUT-nscf
+++ b/examples/interface_wannier90/ABACUS_towannier90_lcao/INPUT-nscf
@@ -8,9 +8,11 @@ nbands                  12
 calculation             nscf
 scf_nmax                50
 pw_diag_thr             1.0e-12
-scf_thr                 1.0e-15
+scf_thr                 1.0e-13
 init_chg                file
 symmetry                0
 towannier90             1
 nnkpfile                diamond.nnkp
-basis_type		lcao
+basis_type		        lcao
+wannier_method          2
+out_wannier_unk         0
diff --git a/examples/interface_wannier90/ABACUS_towannier90_lcao/INPUT-scf b/examples/interface_wannier90/ABACUS_towannier90_lcao/INPUT-scf
index 9aefe7c367..89c777e981 100644
--- a/examples/interface_wannier90/ABACUS_towannier90_lcao/INPUT-scf
+++ b/examples/interface_wannier90/ABACUS_towannier90_lcao/INPUT-scf
@@ -7,4 +7,4 @@ ecutwfc                 50
 calculation             scf
 scf_thr                 1e-13
 out_chg                 1
-basis_type		lcao
+basis_type              lcao
diff --git a/examples/interface_wannier90/ABACUS_towannier90_lcao/diamond.win b/examples/interface_wannier90/ABACUS_towannier90_lcao/diamond.win
index 675745083d..816324eb2e 100644
--- a/examples/interface_wannier90/ABACUS_towannier90_lcao/diamond.win
+++ b/examples/interface_wannier90/ABACUS_towannier90_lcao/diamond.win
@@ -1,15 +1,17 @@
 num_bands         =   12
 num_wann          =   8 
 
-Begin Projections
-C:s;px;py;pz
-End Projections  
+dis_win_min       =  -7.2
+dis_win_max       =  45
+dis_froz_min      =  -7.2
+dis_froz_max      =  20
+dis_num_iter      =  200
 
-dis_num_iter      = 5000
-num_iter          = 5000
-num_print_cycles  = 50 
+begin projections
+C:s;px;py;pz
+end projections 
 
-wannier_plot=.true.
+wannier_plot=.false.
 wannier_plot_supercell = 3
 wvfn_formatted = .true.
 
@@ -26,6 +28,14 @@ begin unit_cell_cart
 -1.613990   1.613990   0.000000
 end unit_cell_cart
 
+bands_plot = true
+
+begin kpoint_path
+G 0.0000000000  0.0000000000    0.0000000000     L 0.5000000000 0.5000000000    0.5000000000
+L 0.5000000000  0.5000000000    0.5000000000     W 0.5000000000 0.2500000000    0.7500000000
+W 0.5000000000  0.2500000000    0.7500000000     X 0.5000000000 0.0000000000    0.5000000000
+end kpoint_path
+
 mp_grid : 4 4 4
 
 begin kpoints
diff --git a/examples/interface_wannier90/ABACUS_towannier90_lcao_in_pw/INPUT-nscf b/examples/interface_wannier90/ABACUS_towannier90_lcao_in_pw/INPUT-nscf
index bd326e7944..f39b37ab96 100644
--- a/examples/interface_wannier90/ABACUS_towannier90_lcao_in_pw/INPUT-nscf
+++ b/examples/interface_wannier90/ABACUS_towannier90_lcao_in_pw/INPUT-nscf
@@ -8,11 +8,12 @@ nbands                  12
 calculation             nscf
 scf_nmax                50
 pw_diag_thr             1.0e-12
-scf_thr                 1.0e-15
+scf_thr                 1.0e-13
 init_chg                file
 symmetry                0
 towannier90             1
-wannier_method 1
 nnkpfile                diamond.nnkp
-basis_type		lcao
+basis_type              lcao
+wannier_method          1
+out_wannier_unk         0
 
diff --git a/examples/interface_wannier90/ABACUS_towannier90_lcao_in_pw/INPUT-scf b/examples/interface_wannier90/ABACUS_towannier90_lcao_in_pw/INPUT-scf
index 91d87fa7e0..50eb2f10c0 100644
--- a/examples/interface_wannier90/ABACUS_towannier90_lcao_in_pw/INPUT-scf
+++ b/examples/interface_wannier90/ABACUS_towannier90_lcao_in_pw/INPUT-scf
@@ -7,5 +7,5 @@ ecutwfc                 50
 calculation             scf
 scf_thr                 1e-13
 out_chg                 1
-basis_type		lcao_in_pw
+basis_type              lcao_in_pw
 ks_solver               lapack
diff --git a/examples/interface_wannier90/ABACUS_towannier90_lcao_in_pw/diamond.win b/examples/interface_wannier90/ABACUS_towannier90_lcao_in_pw/diamond.win
index 675745083d..816324eb2e 100644
--- a/examples/interface_wannier90/ABACUS_towannier90_lcao_in_pw/diamond.win
+++ b/examples/interface_wannier90/ABACUS_towannier90_lcao_in_pw/diamond.win
@@ -1,15 +1,17 @@
 num_bands         =   12
 num_wann          =   8 
 
-Begin Projections
-C:s;px;py;pz
-End Projections  
+dis_win_min       =  -7.2
+dis_win_max       =  45
+dis_froz_min      =  -7.2
+dis_froz_max      =  20
+dis_num_iter      =  200
 
-dis_num_iter      = 5000
-num_iter          = 5000
-num_print_cycles  = 50 
+begin projections
+C:s;px;py;pz
+end projections 
 
-wannier_plot=.true.
+wannier_plot=.false.
 wannier_plot_supercell = 3
 wvfn_formatted = .true.
 
@@ -26,6 +28,14 @@ begin unit_cell_cart
 -1.613990   1.613990   0.000000
 end unit_cell_cart
 
+bands_plot = true
+
+begin kpoint_path
+G 0.0000000000  0.0000000000    0.0000000000     L 0.5000000000 0.5000000000    0.5000000000
+L 0.5000000000  0.5000000000    0.5000000000     W 0.5000000000 0.2500000000    0.7500000000
+W 0.5000000000  0.2500000000    0.7500000000     X 0.5000000000 0.0000000000    0.5000000000
+end kpoint_path
+
 mp_grid : 4 4 4
 
 begin kpoints
diff --git a/examples/interface_wannier90/ABACUS_towannier90_pw/INPUT-nscf b/examples/interface_wannier90/ABACUS_towannier90_pw/INPUT-nscf
index 9010e1527f..d58eb06007 100644
--- a/examples/interface_wannier90/ABACUS_towannier90_pw/INPUT-nscf
+++ b/examples/interface_wannier90/ABACUS_towannier90_pw/INPUT-nscf
@@ -5,11 +5,14 @@ orbital_dir             ../../../tests/PP_ORB
 ntype                   1
 ecutwfc                 50
 nbands                  4
+smearing_method         fixed
 calculation             nscf
 scf_nmax                50
 pw_diag_thr             1.0e-12
-scf_thr                 1.0e-15
+scf_thr                 1.0e-13
 init_chg                file
 symmetry                0
 towannier90             1
 nnkpfile                diamond.nnkp
+basis_type		        pw
+out_wannier_unk         0
\ No newline at end of file
diff --git a/examples/interface_wannier90/ABACUS_towannier90_pw/diamond.win b/examples/interface_wannier90/ABACUS_towannier90_pw/diamond.win
index 321f3058e0..69225b0213 100644
--- a/examples/interface_wannier90/ABACUS_towannier90_pw/diamond.win
+++ b/examples/interface_wannier90/ABACUS_towannier90_pw/diamond.win
@@ -1,7 +1,7 @@
 num_wann        =  4 
 num_iter        = 20
 
-wannier_plot=.true.
+wannier_plot=.false.
 wannier_plot_supercell = 3
 wvfn_formatted = .true.
 
diff --git a/source/Makefile.Objects b/source/Makefile.Objects
index 6209241fa5..3415ccb7b4 100644
--- a/source/Makefile.Objects
+++ b/source/Makefile.Objects
@@ -226,7 +226,6 @@ OBJS_ESOLVER_LCAO=esolver_ks_lcao.o\
       io_npz.o\
 
 OBJS_GINT=gint.o\
-      gint_gamma.o\
       gint_gamma_env.o\
       gint_gamma_vl.o\
       gint_fvl.o\
@@ -298,7 +297,7 @@ OBJS_HSOLVER=diago_cg.o\
     dngvd_op.o\
     
 OBJS_HSOLVER_LCAO=hsolver_lcao.o\
-      diago_blas.o\
+      diago_scalapack.o\
       diago_elpa.o\
       elpa_new.o\
       elpa_new_real.o\
diff --git a/source/module_base/global_variable.cpp b/source/module_base/global_variable.cpp
index 9c27000423..250739b6de 100644
--- a/source/module_base/global_variable.cpp
+++ b/source/module_base/global_variable.cpp
@@ -207,6 +207,8 @@ bool deepks_scf = false; // caoyu add 2021-10-16 for DeePKS, wenfei 2022-1-16
 bool deepks_bandgap = false; // for bandgap label. QO added 2021-12-15
 bool deepks_out_unittest = false;
 
+bool deepks_equiv = false;
+
 bool deepks_setorb = false;
 
 bool out_element_info = false; // added by zhengdy 2021-11-26
diff --git a/source/module_base/global_variable.h b/source/module_base/global_variable.h
index b9168664f1..06f2cf9771 100644
--- a/source/module_base/global_variable.h
+++ b/source/module_base/global_variable.h
@@ -231,6 +231,8 @@ extern bool
     deepks_scf; //(need libnpy and libtorch) if set 1, a trained model would be needed to cal V_delta and F_delta
 extern bool deepks_bandgap; // for bandgap label. QO added 2021-12-15
 
+extern bool deepks_equiv; //whether to use equviariant version of DeePKS
+
 extern bool deepks_setorb;
 
 extern bool deepks_out_unittest; // if set 1, prints intermediate quantities that shall be used for making unit test
diff --git a/source/module_base/test/timer_test.cpp b/source/module_base/test/timer_test.cpp
index f90454ea16..59c206b110 100644
--- a/source/module_base/test/timer_test.cpp
+++ b/source/module_base/test/timer_test.cpp
@@ -118,10 +118,10 @@ TEST_F(TimerTest, PrintAll)
 	EXPECT_THAT(output,testing::HasSubstr("TIME STATISTICS"));
 	EXPECT_THAT(output,testing::HasSubstr("CLASS_NAME"));
 	EXPECT_THAT(output,testing::HasSubstr("NAME"));
-	EXPECT_THAT(output,testing::HasSubstr("TIME(Sec)"));
+	EXPECT_THAT(output,testing::HasSubstr("TIME/s"));
 	EXPECT_THAT(output,testing::HasSubstr("CALLS"));
-	EXPECT_THAT(output,testing::HasSubstr("AVG(Sec)"));
-	EXPECT_THAT(output,testing::HasSubstr("PER(%)"));
+	EXPECT_THAT(output,testing::HasSubstr("AVG/s"));
+	EXPECT_THAT(output,testing::HasSubstr("PER/%"));
 	// check output in file
 	ifs.open("tmp");
 	std::cout << "Capture contents line by line from output file: \n" << std::endl;
@@ -131,10 +131,10 @@ TEST_F(TimerTest, PrintAll)
 	getline(ifs,output);
 	EXPECT_THAT(output,testing::HasSubstr("CLASS_NAME"));
 	EXPECT_THAT(output,testing::HasSubstr("NAME"));
-	EXPECT_THAT(output,testing::HasSubstr("TIME(Sec)"));
+	EXPECT_THAT(output,testing::HasSubstr("TIME/s"));
 	EXPECT_THAT(output,testing::HasSubstr("CALLS"));
-	EXPECT_THAT(output,testing::HasSubstr("AVG(Sec)"));
-	EXPECT_THAT(output,testing::HasSubstr("PER(%)"));
+	EXPECT_THAT(output,testing::HasSubstr("AVG/s"));
+	EXPECT_THAT(output,testing::HasSubstr("PER/%"));
 	ifs.close();
 	remove("time.json");
 }
@@ -162,10 +162,10 @@ TEST_F(TimerTest, Finish)
 	EXPECT_THAT(output,testing::HasSubstr("TIME STATISTICS"));
 	EXPECT_THAT(output,testing::HasSubstr("CLASS_NAME"));
 	EXPECT_THAT(output,testing::HasSubstr("NAME"));
-	EXPECT_THAT(output,testing::HasSubstr("TIME(Sec)"));
+	EXPECT_THAT(output,testing::HasSubstr("TIME/s"));
 	EXPECT_THAT(output,testing::HasSubstr("CALLS"));
-	EXPECT_THAT(output,testing::HasSubstr("AVG(Sec)"));
-	EXPECT_THAT(output,testing::HasSubstr("PER(%)"));
+	EXPECT_THAT(output,testing::HasSubstr("AVG/s"));
+	EXPECT_THAT(output,testing::HasSubstr("PER/%"));
 	// check output in file
 	ifs.open("tmp");
 	std::cout << "Capture contents line by line from output file: \n" << std::endl;
@@ -175,10 +175,10 @@ TEST_F(TimerTest, Finish)
 	getline(ifs,output);
 	EXPECT_THAT(output,testing::HasSubstr("CLASS_NAME"));
 	EXPECT_THAT(output,testing::HasSubstr("NAME"));
-	EXPECT_THAT(output,testing::HasSubstr("TIME(Sec)"));
+	EXPECT_THAT(output,testing::HasSubstr("TIME/s"));
 	EXPECT_THAT(output,testing::HasSubstr("CALLS"));
-	EXPECT_THAT(output,testing::HasSubstr("AVG(Sec)"));
-	EXPECT_THAT(output,testing::HasSubstr("PER(%)"));
+	EXPECT_THAT(output,testing::HasSubstr("AVG/s"));
+	EXPECT_THAT(output,testing::HasSubstr("PER/%"));
 	ifs.close();
 }
 
diff --git a/source/module_base/timer.cpp b/source/module_base/timer.cpp
index cede14041f..c47d58f2a9 100644
--- a/source/module_base/timer.cpp
+++ b/source/module_base/timer.cpp
@@ -275,7 +275,7 @@ void timer::print_all(std::ofstream &ofs)
 	assert(class_names.size() == calls.size());
 	assert(class_names.size() == avgs.size());
 	assert(class_names.size() == pers.size());
-	std::vector<std::string> titles = {"CLASS_NAME", "NAME", "TIME(Sec)", "CALLS", "AVG(Sec)", "PER(%)"};
+	std::vector<std::string> titles = {"CLASS_NAME", "NAME", "TIME/s", "CALLS", "AVG/s", "PER/%"};
 	std::vector<std::string> formats = {"%-10s", "%-10s", "%6.2f", "%8d", "%6.2f", "%6.2f"};
 	FmtTable time_statistics(titles, pers.size(), formats, {FmtTable::Align::LEFT, FmtTable::Align::CENTER});
 	time_statistics << class_names << names << times << calls << avgs << pers;
diff --git a/source/module_elecstate/elecstate_print.cpp b/source/module_elecstate/elecstate_print.cpp
index b57c5f2712..4ce3b4c246 100644
--- a/source/module_elecstate/elecstate_print.cpp
+++ b/source/module_elecstate/elecstate_print.cpp
@@ -10,6 +10,78 @@
 #include "module_base/formatter.h"
 namespace elecstate
 {
+	/**
+	 * Notes on refactor of ESolver's functions
+	 * 
+	 * the print of SCF iteration on-the-fly information.
+	 * 1. Previously it is expected for nspin 1, 2, and 4, also with xc_type 3/5 or not, the information will organized in different ways.
+	 * This brings inconsistencies between patterns of print and make it hard to vectorize information.
+	 * 2. the function print_etot actually do two kinds of things, 1) print information into running_*.log, 2) print information onto 
+	 * screen. These two tasks are, in no way should be placed/implemented in one function directly
+	 * 3. there are information redundance: the istep of SCF can provide information determing whether print out the SCF iteration info.
+	 * table header or not, rather than dividing into two functions and hard code the format.
+	 * 
+	 * For nspin 1, print: ITER, ETOT, EDIFF, DRHO, TIME
+	 * 	   nspin 2, print: ITER, TMAG, AMAG, ETOT, EDIFF, DRHO, TIME
+	 * 	   nspin 4 with nlcc, print: ITER, TMAGX, TMAGY, TMAGZ, AMAG, ETOT, EDIFF, DRHO, TIME
+	 * xc type_id 3/5: DKIN 
+	 * 
+	 * Based on summary above, there are several groups of info:
+	 * 1. counting: ITER
+	 * 2. (optional) magnetization: TMAG or TMAGX-TMAGY-TMAGZ, AMAG
+	 * 3. energies: ETOT, EDIFF
+	 * 4. densities: DRHO, DKIN(optional)
+	 * 5. time: TIME
+	 */
+	void print_scf_iterinfo(const std::string& ks_solver, const int& istep, const int& witer,
+							const std::vector<double>& mag, const int& wmag,
+							const double& etot, const double& ediff, const int& wener,
+							const std::vector<double>& drho, const int& wrho,
+							const double& time, const int& wtime)
+	{
+		std::map<std::string, std::string> iter_header_dict = {
+			{"cg", "CG"}, {"cg_in_lcao", "CG"}, {"lapack", "LA"}, {"genelpa", "GE"},
+			{"dav", "DA"}, {"dav_subspace", "DS"}, {"scalapack_gvx", "GV"}, {"cusolver", "CU"},
+			{"bpcg", "BP"}, {"pexsi", "PE"}
+		}; // I change the key of "cg_in_lcao" to "CG" because all the other are only two letters
+		// ITER column
+		std::vector<std::string> th_fmt = {" %-" + std::to_string(witer) + "s"}; 		 // table header: th: ITER
+		std::vector<std::string> td_fmt = {" " + iter_header_dict[ks_solver] + "%-" + std::to_string(witer - 2) + ".0f"}; // table data: td: GE10086
+		// magnetization column, might be non-exist, but size of mag can only be 0, 2 or 4
+		for(int i = 0; i < mag.size(); i++) {th_fmt.emplace_back("%" + std::to_string(wmag) + "s");}
+		for(int i = 0; i < mag.size(); i++) {td_fmt.emplace_back("%" + std::to_string(wmag) + ".4e");} // hard-code precision here
+		// energies
+		for(int i = 0; i < 2; i++) {th_fmt.emplace_back("%" + std::to_string(wener) + "s");}
+		for(int i = 0; i < 2; i++) {td_fmt.emplace_back("%" + std::to_string(wener) + ".8e");}
+		// densities column, size can be 1 or 2, DRHO or DRHO, DKIN
+		for(int i = 0; i < drho.size(); i++) {th_fmt.emplace_back("%" + std::to_string(wrho) + "s");}
+		for(int i = 0; i < drho.size(); i++) {td_fmt.emplace_back("%" + std::to_string(wrho) + ".8e");}
+		// time column, trivial
+		th_fmt.emplace_back("%" + std::to_string(wtime) + "s\n");
+		td_fmt.emplace_back("%" + std::to_string(wtime) + ".2f\n");
+		// contents
+		std::vector<std::string> titles; std::vector<double> values;
+		switch (mag.size())
+		{
+			case 2: 
+			titles = {"ITER", FmtCore::center("TMAG", wmag), FmtCore::center("AMAG", wmag), 
+                      FmtCore::center("ETOT/eV", wener), FmtCore::center("EDIFF/eV", wener), FmtCore::center("DRHO", wrho)}; 
+			values = {double(istep), mag[0], mag[1], etot, ediff, drho[0]}; break;
+			case 4:
+			titles = {"ITER", FmtCore::center("TMAGX", wmag), FmtCore::center("TMAGY", wmag), FmtCore::center("TMAGZ", wmag), 
+                      FmtCore::center("AMAG", wmag), FmtCore::center("ETOT/eV", wener), FmtCore::center("EDIFF/eV", wener), FmtCore::center("DRHO", wrho)}; 
+			values = {double(istep), mag[0], mag[1], mag[2], mag[3], etot, ediff, drho[0]}; break;
+			default:
+			titles = {"ITER", FmtCore::center("ETOT/eV", wener), FmtCore::center("EDIFF/eV", wener), FmtCore::center("DRHO", wrho)};
+			values = {double(istep), etot, ediff, drho[0]}; break;
+		}
+		if(drho.size() > 1) {titles.push_back(FmtCore::center("DKIN", wrho)); values.push_back(drho[1]);}
+		titles.push_back(FmtCore::center("TIME/s", wtime)); values.push_back(time);
+		std::string buf;
+		if(istep == 1) { for(int i = 0; i < titles.size(); i++) {buf += FmtCore::format(th_fmt[i].c_str(), titles[i]);} }
+		for(int i = 0; i < values.size(); i++) {buf += FmtCore::format(td_fmt[i].c_str(), values[i]);}
+		std::cout << buf;
+	}
 /// @brief print and check for band energy and occupations
 /// @param ofs
 void ElecState::print_eigenvalue(std::ofstream& ofs)
@@ -259,144 +331,21 @@ void ElecState::print_etot(const bool converged,
         this->f_en.etot_old = this->f_en.etot;
     }
     this->f_en.etot_delta = this->f_en.etot - this->f_en.etot_old;
-
-    // mohan update 2011-02-26
-    std::stringstream ss;
-
-    // xiaohui add 2013-09-02, Peize Lin update 2020.11.14
-    std::string label;
-    std::string ks_solver_type = get_ks_solver_type();
-    if (ks_solver_type == "cg")
-    {
-        label = "CG";
-    }
-    else if (ks_solver_type == "cg_in_lcao")
-    {
-        label = "CGAO";
-    }
-    else if (ks_solver_type == "lapack")
-    {
-        label = "LA";
-    }
-    else if (ks_solver_type == "genelpa")
-    {
-        label = "GE";
-    }
-    else if (ks_solver_type == "dav")
-    {
-        label = "DA";
-    }
-    else if (ks_solver_type == "dav_subspace")
-    {
-        label = "DS";
-    }
-    else if (ks_solver_type == "scalapack_gvx")
-    {
-        label = "GV";
-    }
-    else if (ks_solver_type == "cusolver")
-    {
-        label = "CU";
-    }
-    else if (ks_solver_type == "bpcg")
-    {
-        label = "BP";
-    }
-    else if (ks_solver_type == "pexsi")
-    {
-        label = "PE";
-    }
-    else
-    {
-        ModuleBase::WARNING_QUIT("Energy", "print_etot found unknown ks_solver_type");
-    }
-    ss << label << iter;
-    // xiaohui add 2013-09-02
-
-    bool scientific = true;
-    int prec = 6;
-
-    if (!print)
-        return;
-
     if (GlobalV::OUT_LEVEL == "ie" || GlobalV::OUT_LEVEL == "m") // xiaohui add 'm' option, 2015-09-16
     {
-        std::cout << " " << std::setw(7) << ss.str();
-        // std::cout << std::setiosflags(ios::fixed);
-        // std::cout << std::setiosflags(ios::showpos);
-        if (scientific)
-        {
-            std::cout << std::scientific;
-        }
-
-        if (GlobalV::COLOUR)
-        {
-            if (GlobalV::MY_RANK == 0)
-            {
-                printf("\e[36m%-15f\e[0m", this->f_en.etot);
-                if (GlobalV::NSPIN == 2)
-                {
-                    std::cout << std::setprecision(2);
-                    std::cout << std::setw(10) << get_ucell_tot_magnetization();
-                    std::cout << std::setw(10) << get_ucell_abs_magnetization();
-                }
-                else if (GlobalV::NSPIN == 4 && GlobalV::NONCOLIN)
-                {
-                    std::cout << std::setprecision(2);
-                    std::cout << std::setw(10) << get_ucell_tot_magnetization_nc_x() << std::setw(10)
-                              << get_ucell_tot_magnetization_nc_y() << std::setw(10)
-                              << get_ucell_tot_magnetization_nc_z();
-                    std::cout << std::setw(10) << get_ucell_abs_magnetization();
-                }
-                if (scf_thr > 1.0)
-                {
-                    // 31 is red
-                    printf("\e[31m%-14e\e[0m", scf_thr);
-                    // printf( "[31m%-14e[0m", scf_thr);
-                }
-                else
-                {
-                    // 32 is green
-                    printf("\e[32m%-14e\e[0m", scf_thr);
-                    // printf( "[32m%-14e[0m", scf_thr);
-                }
-                // 34 is blue
-                printf("\e[36m%-15f\e[0m", this->f_en.etot * ModuleBase::Ry_to_eV);
-                std::cout << std::setprecision(3);
-                std::cout << std::resetiosflags(std::ios::scientific);
-
-                std::cout << std::setw(11) << duration;
-                std::cout << std::endl;
-            }
-        }
-        else
+        std::vector<double> mag; 
+        switch (GlobalV::NSPIN)
         {
-            std::cout << std::setprecision(prec);
-            if (GlobalV::NSPIN == 2)
-            {
-                std::cout << std::setprecision(2);
-                std::cout << std::setw(10) << get_ucell_tot_magnetization();
-                std::cout << std::setw(10) << get_ucell_abs_magnetization();
-            }
-            std::cout << std::setprecision(6);
-            std::cout << std::setw(15) << this->f_en.etot * ModuleBase::Ry_to_eV;
-            std::cout << std::setw(15) << this->f_en.etot_delta * ModuleBase::Ry_to_eV;
-            std::cout << std::setprecision(3);
-            std::cout << std::setw(11) << scf_thr;
-            if (elecstate::get_xc_func_type() == 3 || elecstate::get_xc_func_type() == 5)
-            {
-                std::cout << std::setprecision(3);
-                std::cout << std::setw(11) << scf_thr_kin;
-            }
-            std::cout << std::setprecision(3);
-            std::cout << std::setw(11) << duration;
-            std::cout << std::endl;
+        case 2: mag = {get_ucell_tot_magnetization(), get_ucell_abs_magnetization()}; break;
+        case 4: mag = {get_ucell_tot_magnetization_nc_x(), get_ucell_tot_magnetization_nc_y(),
+        get_ucell_tot_magnetization_nc_z(), get_ucell_abs_magnetization()}; break;
+        default: mag = {}; break;
         }
+        std::vector<double> drho = {scf_thr};
+        if(elecstate::get_xc_func_type() == 3 || elecstate::get_xc_func_type() == 5) {drho.push_back(scf_thr_kin);}
+        elecstate::print_scf_iterinfo(get_ks_solver_type(), iter, 6, mag, 12, this->f_en.etot * ModuleBase::Ry_to_eV,
+        this->f_en.etot_delta * ModuleBase::Ry_to_eV, 16, drho, 16, duration, 6);
     }
-    else
-    {
-    }
-
     this->f_en.etot_old = this->f_en.etot;
     return;
 }
@@ -414,5 +363,4 @@ void ElecState::print_format(const std::string& name, const double& value)
     GlobalV::ofs_running << std::resetiosflags(std::ios::showpos);
     return;
 }
-
 } // namespace elecstate
\ No newline at end of file
diff --git a/source/module_elecstate/potentials/H_TDDFT_pw.cpp b/source/module_elecstate/potentials/H_TDDFT_pw.cpp
index 93601bac40..6f37cd87d3 100644
--- a/source/module_elecstate/potentials/H_TDDFT_pw.cpp
+++ b/source/module_elecstate/potentials/H_TDDFT_pw.cpp
@@ -38,7 +38,7 @@ double H_TDDFT_pw::lcut1;
 double H_TDDFT_pw::lcut2;
 
 //velocity gauge
-double H_TDDFT_pw::At[3]={0.0,0.0,0.0};
+ModuleBase::Vector3<double> H_TDDFT_pw::At;
 
 // time domain parameters
 
diff --git a/source/module_elecstate/potentials/H_TDDFT_pw.h b/source/module_elecstate/potentials/H_TDDFT_pw.h
index ea6b4f0ef9..8b3ffcaf42 100644
--- a/source/module_elecstate/potentials/H_TDDFT_pw.h
+++ b/source/module_elecstate/potentials/H_TDDFT_pw.h
@@ -54,7 +54,7 @@ class H_TDDFT_pw : public PotBase
     static double lcut2;
 
     //velocity gauge, vector magnetic potential
-    static double At[3];
+    static ModuleBase::Vector3<double> At;
 
     // time domain parameters
 
diff --git a/source/module_elecstate/test/elecstate_print_test.cpp b/source/module_elecstate/test/elecstate_print_test.cpp
index 69f93df393..555103b473 100644
--- a/source/module_elecstate/test/elecstate_print_test.cpp
+++ b/source/module_elecstate/test/elecstate_print_test.cpp
@@ -392,36 +392,36 @@ TEST_F(ElecStatePrintTest, PrintEtotColorS4)
     elecstate.print_etot(converged, iter, scf_thr, scf_thr_kin, duration, printe, pw_diag_thr, avg_iter, print);
 }
 
-TEST_F(ElecStatePrintTest, PrintEtotWarning)
-{
-    GlobalV::ofs_running.open("test.dat", std::ios::out);
-    bool converged = false;
-    int iter = 1;
-    double scf_thr = 0.1;
-    double scf_thr_kin = 0.0;
-    double duration = 2.0;
-    int printe = 0;
-    double pw_diag_thr = 0.1;
-    int avg_iter = 2;
-    bool print = true;
-    elecstate.charge = new Charge;
-    elecstate.charge->nrxx = 100;
-    elecstate.charge->nxyz = 1000;
-    GlobalV::imp_sol = true;
-    GlobalV::EFIELD_FLAG = true;
-    GlobalV::GATE_FLAG = true;
-    GlobalV::TWO_EFERMI = false;
-    GlobalV::out_bandgap = true;
-    GlobalV::COLOUR = false;
-    GlobalV::MY_RANK = 0;
-    GlobalV::BASIS_TYPE = "pw";
-    GlobalV::SCF_NMAX = 100;
-    elecstate::tmp_ks_solver = "unknown";
-    testing::internal::CaptureStdout();
-    EXPECT_EXIT(elecstate.print_etot(converged, iter, scf_thr, scf_thr_kin, duration, printe, pw_diag_thr, avg_iter, print), ::testing::ExitedWithCode(0), "");
-    output = testing::internal::GetCapturedStdout();
-    EXPECT_THAT(output, testing::HasSubstr("print_etot found unknown ks_solver_type"));
-    GlobalV::ofs_running.close();
-    delete elecstate.charge;
-    std::remove("test.dat");
-}
+// TEST_F(ElecStatePrintTest, PrintEtotWarning)
+// {
+//     GlobalV::ofs_running.open("test.dat", std::ios::out);
+//     bool converged = false;
+//     int iter = 1;
+//     double scf_thr = 0.1;
+//     double scf_thr_kin = 0.0;
+//     double duration = 2.0;
+//     int printe = 0;
+//     double pw_diag_thr = 0.1;
+//     int avg_iter = 2;
+//     bool print = true;
+//     elecstate.charge = new Charge;
+//     elecstate.charge->nrxx = 100;
+//     elecstate.charge->nxyz = 1000;
+//     GlobalV::imp_sol = true;
+//     GlobalV::EFIELD_FLAG = true;
+//     GlobalV::GATE_FLAG = true;
+//     GlobalV::TWO_EFERMI = false;
+//     GlobalV::out_bandgap = true;
+//     GlobalV::COLOUR = false;
+//     GlobalV::MY_RANK = 0;
+//     GlobalV::BASIS_TYPE = "pw";
+//     GlobalV::SCF_NMAX = 100;
+//     elecstate::tmp_ks_solver = "unknown";
+//     testing::internal::CaptureStdout();
+//     EXPECT_EXIT(elecstate.print_etot(converged, iter, scf_thr, scf_thr_kin, duration, printe, pw_diag_thr, avg_iter, print), ::testing::ExitedWithCode(0), "");
+//     output = testing::internal::GetCapturedStdout();
+//     EXPECT_THAT(output, testing::HasSubstr("print_etot found unknown ks_solver_type"));
+//     GlobalV::ofs_running.close();
+//     delete elecstate.charge;
+//     std::remove("test.dat");
+// }
diff --git a/source/module_esolver/esolver_ks.cpp b/source/module_esolver/esolver_ks.cpp
index cb608a142f..d0f63bf67f 100644
--- a/source/module_esolver/esolver_ks.cpp
+++ b/source/module_esolver/esolver_ks.cpp
@@ -455,16 +455,17 @@ void ESolver_KS<T, Device>::runner(const int istep, UnitCell& ucell)
 		ModuleBase::GlobalFunc::DONE(GlobalV::ofs_running, "INIT SCF");
 
         // 3) print head
-		if(this->maxniter > 0)  
-		{
-			this->print_head(); //print the headline on the screen.
-		}
+		// if(this->maxniter > 0)  
+		// {
+		// 	this->print_head(); //print the headline on the screen.
+		// }
 
 		bool firstscf = true;
 		this->conv_elec = false;
 		this->niter = this->maxniter;
 
         // 4) SCF iterations
+		std::cout << " * * * * * *\n << Start SCF iteration." << std::endl;
 		for (int iter = 1; iter <= this->maxniter; ++iter)
 		{
             // 5) write head
@@ -622,7 +623,7 @@ void ESolver_KS<T, Device>::runner(const int istep, UnitCell& ucell)
 				std::cout<<" SCF restart after this step!"<<std::endl;
 			}
 		}// end scf iterations
-
+		std::cout << " >> Leave SCF iteration.\n * * * * * *" << std::endl;
 
 #ifdef __RAPIDJSON
 		// 14) add Json of efermi energy converge
diff --git a/source/module_esolver/esolver_ks.h b/source/module_esolver/esolver_ks.h
index bfd3fd2e63..b63fea304c 100644
--- a/source/module_esolver/esolver_ks.h
+++ b/source/module_esolver/esolver_ks.h
@@ -16,7 +16,6 @@
 #include "module_io/cal_test.h"
 #include "module_io/output_potential.h"
 #include "module_io/output_rho.h"
-
 namespace ModuleESolver
 {
 
@@ -101,7 +100,6 @@ class ESolver_KS : public ESolver_FP
 				const double duration, 
 				const double ethr);
 
-
 		// Write the headline in the running_log file
 		// "PW/LCAO" ALGORITHM --------------- ION=   1  ELEC=   1--------------------------------
 		void write_head(
@@ -140,7 +138,6 @@ class ESolver_KS : public ESolver_FP
 		std::string basisname; //PW or LCAO
 
 		void print_wfcfft(Input& inp, std::ofstream &ofs);
-};
-
+};	
 } // end of namespace
 #endif
diff --git a/source/module_hamilt_lcao/hamilt_lcaodft/FORCE_STRESS.cpp b/source/module_hamilt_lcao/hamilt_lcaodft/FORCE_STRESS.cpp
index 4e98f79458..022b87e269 100644
--- a/source/module_hamilt_lcao/hamilt_lcaodft/FORCE_STRESS.cpp
+++ b/source/module_hamilt_lcao/hamilt_lcaodft/FORCE_STRESS.cpp
@@ -396,28 +396,29 @@ void Force_Stress_LCAO<T>::getForceStress(const bool isforce,
             {
                 GlobalC::ld.save_npy_f(fcs - GlobalC::ld.F_delta, "f_base.npy", GlobalC::ucell.nat); // Ry/Bohr, F_base
 
-                if (GlobalV::GAMMA_ONLY_LOCAL)
+                if(!GlobalV::deepks_equiv) //training with force label not supported by equivariant version now
                 {
-                    const std::vector<std::vector<double>>& dm_gamma
-                        = dynamic_cast<const elecstate::ElecStateLCAO<double>*>(pelec)->get_DM()->get_DMK_vector();
-                    GlobalC::ld.cal_gdmx(dm_gamma[0], GlobalC::ucell, GlobalC::ORB, GlobalC::GridD, isstress);
-                }
-                else
-                {
-                    const std::vector<std::vector<std::complex<double>>>& dm_k
-                        = dynamic_cast<const elecstate::ElecStateLCAO<std::complex<double>>*>(pelec)
-                              ->get_DM()
-                              ->get_DMK_vector();
-                    GlobalC::ld
-                        .cal_gdmx_k(dm_k, GlobalC::ucell, GlobalC::ORB, GlobalC::GridD, kv.nks, kv.kvec_d, isstress);
-                }
-                if (GlobalV::deepks_out_unittest)
-                    GlobalC::ld.check_gdmx(GlobalC::ucell.nat);
-                GlobalC::ld.cal_gvx(GlobalC::ucell.nat);
+                    if (GlobalV::GAMMA_ONLY_LOCAL)
+                    {
+                        const std::vector<std::vector<double>>& dm_gamma
+                            = dynamic_cast<const elecstate::ElecStateLCAO<double>*>(pelec)->get_DM()->get_DMK_vector();
+                        GlobalC::ld.cal_gdmx(dm_gamma[0], GlobalC::ucell, GlobalC::ORB, GlobalC::GridD, isstress);
+                    }
+                    else
+                    {
+                        const std::vector<std::vector<std::complex<double>>>& dm_k
+                            = dynamic_cast<const elecstate::ElecStateLCAO<std::complex<double>>*>(pelec)
+                                ->get_DM()
+                                ->get_DMK_vector();
+                        GlobalC::ld
+                            .cal_gdmx_k(dm_k, GlobalC::ucell, GlobalC::ORB, GlobalC::GridD, kv.nks, kv.kvec_d, isstress);
+                    }
+                    if (GlobalV::deepks_out_unittest) { GlobalC::ld.check_gdmx(GlobalC::ucell.nat); }
+                    GlobalC::ld.cal_gvx(GlobalC::ucell.nat);
 
-                if (GlobalV::deepks_out_unittest)
-                    GlobalC::ld.check_gvx(GlobalC::ucell.nat);
-                GlobalC::ld.save_npy_gvx(GlobalC::ucell.nat); //  /Bohr, grad_vx
+                    if (GlobalV::deepks_out_unittest) { GlobalC::ld.check_gvx(GlobalC::ucell.nat); }
+                    GlobalC::ld.save_npy_gvx(GlobalC::ucell.nat); //  /Bohr, grad_vx
+                }
             }
             else
             {
@@ -606,8 +607,11 @@ void Force_Stress_LCAO<T>::getForceStress(const bool isforce,
                 GlobalC::ld.save_npy_s(scs,
                                        "s_tot.npy",
                                        GlobalC::ucell.omega); // change to energy unit Ry when printing, S_tot, w/ model
-                GlobalC::ld.cal_gvepsl(GlobalC::ucell.nat);
-                GlobalC::ld.save_npy_gvepsl(GlobalC::ucell.nat); //  unitless, grad_vepsl
+                if(!GlobalV::deepks_equiv) //training with stress label not supported by equivariant version now
+                {
+                    GlobalC::ld.cal_gvepsl(GlobalC::ucell.nat);
+                    GlobalC::ld.save_npy_gvepsl(GlobalC::ucell.nat); //  unitless, grad_vepsl
+                }
             }
             else
             {
diff --git a/source/module_hamilt_lcao/hamilt_lcaodft/operator_lcao/deepks_lcao.cpp b/source/module_hamilt_lcao/hamilt_lcaodft/operator_lcao/deepks_lcao.cpp
index 577475f6d8..f75e0e9d85 100644
--- a/source/module_hamilt_lcao/hamilt_lcaodft/operator_lcao/deepks_lcao.cpp
+++ b/source/module_hamilt_lcao/hamilt_lcaodft/operator_lcao/deepks_lcao.cpp
@@ -337,7 +337,7 @@ void hamilt::DeePKS<hamilt::OperatorLCAO<TK, TR>>::calculate_HR()
         std::vector<int> trace_alpha_row;
         std::vector<int> trace_alpha_col;
         std::vector<double> gedms;
-        if(!GlobalC::ld.get_if_equiv())
+        if(!GlobalV::deepks_equiv)
         {
             int ib=0;
             for (int L0 = 0; L0 <= orb.Alpha[0].getLmax();++L0)
diff --git a/source/module_hamilt_lcao/hamilt_lcaodft/operator_lcao/td_ekinetic_lcao.cpp b/source/module_hamilt_lcao/hamilt_lcaodft/operator_lcao/td_ekinetic_lcao.cpp
index 4102aae997..03bfdfdda5 100644
--- a/source/module_hamilt_lcao/hamilt_lcaodft/operator_lcao/td_ekinetic_lcao.cpp
+++ b/source/module_hamilt_lcao/hamilt_lcaodft/operator_lcao/td_ekinetic_lcao.cpp
@@ -60,7 +60,7 @@ void TDEkinetic<OperatorLCAO<std::complex<double>, double>>::td_ekinetic_scalar(
 template <typename TK, typename TR>
 void TDEkinetic<OperatorLCAO<TK, TR>>::td_ekinetic_grad(std::complex<double>* Hloc, int nnr, ModuleBase::Vector3<double> grad_overlap){
 	std::complex<double> tmp= {0, grad_overlap*cart_At};
-	Hloc[nnr] += tmp;
+	Hloc[nnr] -= tmp;
 	return;
 }
 
@@ -193,10 +193,9 @@ void TDEkinetic<OperatorLCAO<TK, TR>>::init_td(void)
 {
     TD_Velocity::td_vel_op = &td_velocity;
     //calculate At in cartesian coorinates.
-	double l_norm[3]={this->ucell->a1.norm() ,this->ucell->a2.norm() ,this->ucell->a3.norm()};
-    double (&A)[3] = elecstate::H_TDDFT_pw::At;
-	cart_At = this->ucell->a1*A[0]/l_norm[0] + this->ucell->a2*A[1]/l_norm[1] + this->ucell->a3*A[2]/l_norm[2];
-    std::cout << "cart_At: " << cart_At[0] << " " <<cart_At[1]<< " " << cart_At[2] << std::endl;
+    td_velocity.cal_cart_At(this->ucell->a1, this->ucell->a2, this->ucell->a3, elecstate::H_TDDFT_pw::At);
+    this->cart_At = td_velocity.cart_At;
+    std::cout<<"cart_At: "<<cart_At[0]<< " "<<cart_At[1]<< " "<<cart_At[2]<<std::endl;
 
     //init MOT,MGT
     const LCAO_Orbitals& orb = LCAO_Orbitals::get_const_instance();
diff --git a/source/module_hamilt_lcao/hamilt_lcaodft/operator_lcao/td_nonlocal_lcao.cpp b/source/module_hamilt_lcao/hamilt_lcaodft/operator_lcao/td_nonlocal_lcao.cpp
index e1e0bcede9..5905b022a0 100644
--- a/source/module_hamilt_lcao/hamilt_lcaodft/operator_lcao/td_nonlocal_lcao.cpp
+++ b/source/module_hamilt_lcao/hamilt_lcaodft/operator_lcao/td_nonlocal_lcao.cpp
@@ -47,10 +47,7 @@ template <typename TK, typename TR>
 void hamilt::TDNonlocal<hamilt::OperatorLCAO<TK, TR>>::init_td(void)
 {
     //calculate At in cartesian coorinates.
-	double l_norm[3]={this->ucell->a1.norm() ,this->ucell->a2.norm() ,this->ucell->a3.norm()};
-    double (&A)[3] = elecstate::H_TDDFT_pw::At;
-	cart_At = -(this->ucell->a1*A[0]/l_norm[0] + this->ucell->a2*A[1]/l_norm[1] + this->ucell->a3*A[2]/l_norm[2]);
-    std::cout << "cart_At: " << cart_At[0] << " " <<cart_At[1]<< " " << cart_At[2] << std::endl;
+	this->cart_At=TD_Velocity::td_vel_op->cart_At;
 }
 // initialize_HR()
 template <typename TK, typename TR>
@@ -207,7 +204,7 @@ void hamilt::TDNonlocal<hamilt::OperatorLCAO<TK, TR>>::calculate_HR()
                                             atom1->iw2n[iw1],
                                             tau0 * this->ucell->lat0,
                                             T0,
-                                            -cart_At,
+                                            -cart_At/2.0,
                                             0);
 #else
                 uot.snap_psibeta_half_tddft(orb,
@@ -220,7 +217,7 @@ void hamilt::TDNonlocal<hamilt::OperatorLCAO<TK, TR>>::calculate_HR()
                                             atom1->iw2n[iw1],
                                             tau0 * this->ucell->lat0,
                                             T0,
-                                            -cart_At,
+                                            -cart_At/2.0,
                                             0);
 #endif
                 nlm_tot[ad].insert({all_indexes[iw1l], nlm[0]});
diff --git a/source/module_hamilt_lcao/hamilt_lcaodft/spar_hsr.cpp b/source/module_hamilt_lcao/hamilt_lcaodft/spar_hsr.cpp
index 8829bef774..162f7857e5 100644
--- a/source/module_hamilt_lcao/hamilt_lcaodft/spar_hsr.cpp
+++ b/source/module_hamilt_lcao/hamilt_lcaodft/spar_hsr.cpp
@@ -376,4 +376,4 @@ void sparse_format::clear_zero_elements(
     }
 
     return;
-}
+}
\ No newline at end of file
diff --git a/source/module_hamilt_lcao/hamilt_lcaodft/spar_hsr.h b/source/module_hamilt_lcao/hamilt_lcaodft/spar_hsr.h
index d7b36f397f..d46a0304d3 100644
--- a/source/module_hamilt_lcao/hamilt_lcaodft/spar_hsr.h
+++ b/source/module_hamilt_lcao/hamilt_lcaodft/spar_hsr.h
@@ -46,4 +46,4 @@ namespace sparse_format
 
 }
 
-#endif
+#endif
\ No newline at end of file
diff --git a/source/module_hamilt_lcao/module_deepks/LCAO_deepks.cpp b/source/module_hamilt_lcao/module_deepks/LCAO_deepks.cpp
index a8b3d8cfcd..1b32601a27 100644
--- a/source/module_hamilt_lcao/module_deepks/LCAO_deepks.cpp
+++ b/source/module_hamilt_lcao/module_deepks/LCAO_deepks.cpp
@@ -89,7 +89,7 @@ void LCAO_Deepks::init(
     
     int tot_inl = tot_inl_per_atom * nat;
 
-    if(if_equiv) tot_inl = nat;
+    if(GlobalV::deepks_equiv) tot_inl = nat;
 
     this->lmaxd = lm;
     this->nmaxd = nm;
@@ -99,7 +99,7 @@ void LCAO_Deepks::init(
 
     int pdm_size = 0;
     this->inlmax = tot_inl;
-    if(!if_equiv)
+    if(!GlobalV::deepks_equiv)
     {
         GlobalV::ofs_running << " total basis (all atoms) for descriptor= " << std::endl;
 
@@ -125,7 +125,7 @@ void LCAO_Deepks::init(
     }
 
     // cal n(descriptor) per atom , related to Lmax, nchi(L) and m. (not total_nchi!)
-    if(!if_equiv)
+    if(!GlobalV::deepks_equiv)
     {
         this->des_per_atom=0; // mohan add 2021-04-21
         for (int l = 0; l <= this->lmaxd; l++)
@@ -215,7 +215,7 @@ void LCAO_Deepks::init_gdmx(const int nat)
     this->gdmy = new double** [nat];
     this->gdmz = new double** [nat];
     int pdm_size = 0;
-    if(!if_equiv)
+    if(!GlobalV::deepks_equiv)
     {
         pdm_size = (this->lmaxd * 2 + 1) * (this->lmaxd * 2 + 1);
     }
@@ -269,7 +269,7 @@ void LCAO_Deepks::init_gdmepsl()
     this->gdm_epsl = new double** [6];
     
     int pdm_size = 0;
-    if(!if_equiv)
+    if(!GlobalV::deepks_equiv)
     {
         pdm_size = (this->lmaxd * 2 + 1) * (this->lmaxd * 2 + 1);
     }
@@ -328,7 +328,7 @@ void LCAO_Deepks::allocate_V_delta(const int nat, const int nks)
 
     //init gedm**
     int pdm_size = 0;
-    if(!if_equiv)
+    if(!GlobalV::deepks_equiv)
     {
         pdm_size = (this->lmaxd * 2 + 1) * (this->lmaxd * 2 + 1);
     }
diff --git a/source/module_hamilt_lcao/module_deepks/LCAO_deepks.h b/source/module_hamilt_lcao/module_deepks/LCAO_deepks.h
index 1b9c4a668e..481a8612d7 100644
--- a/source/module_hamilt_lcao/module_deepks/LCAO_deepks.h
+++ b/source/module_hamilt_lcao/module_deepks/LCAO_deepks.h
@@ -82,7 +82,6 @@ class LCAO_Deepks
     int get_inl(const int& T0, const int& I0, const int& L0, const int& N0) { return inl_index[T0](I0, L0, N0); }
     const double* get_gedms(const int& inl){ return gedm[inl]; }
 
-    bool get_if_equiv(){return if_equiv;}
     int get_lmaxd(){return lmaxd;}
 //-------------------
 // private variables
@@ -96,8 +95,6 @@ class LCAO_Deepks
     int nks_V_delta = 0;
 
     bool init_pdm = false; //for DeePKS NSCF calculation
-
-    bool if_equiv = false; //equivariant version
     
 	// deep neural network module that provides corrected Hamiltonian term and
 	// related derivatives.
diff --git a/source/module_hamilt_lcao/module_deepks/LCAO_deepks_fdelta.cpp b/source/module_hamilt_lcao/module_deepks/LCAO_deepks_fdelta.cpp
index 3bdafecf04..5adf7f5195 100644
--- a/source/module_hamilt_lcao/module_deepks/LCAO_deepks_fdelta.cpp
+++ b/source/module_hamilt_lcao/module_deepks/LCAO_deepks_fdelta.cpp
@@ -133,7 +133,7 @@ void LCAO_Deepks::cal_f_delta_gamma(const std::vector<std::vector<double>>& dm,
 
                             assert(nlm1.size()==nlm2[0].size());
 
-                            if(!if_equiv)
+                            if(!GlobalV::deepks_equiv)
                             {
                                 int ib=0;
                                 for (int L0 = 0; L0 <= orb.Alpha[0].getLmax();++L0)
@@ -196,7 +196,7 @@ void LCAO_Deepks::cal_f_delta_gamma(const std::vector<std::vector<double>>& dm,
 
                                 assert(nlm1.size()==nlm2[0].size());                                
 
-                                if(!if_equiv)
+                                if(!GlobalV::deepks_equiv)
                                 {
                                     int ib=0;
                                     for (int L0 = 0; L0 <= orb.Alpha[0].getLmax();++L0)
@@ -378,7 +378,7 @@ void LCAO_Deepks::cal_f_delta_k(const std::vector<std::vector<std::complex<doubl
 
                             assert(nlm1.size()==nlm2[0].size());
 
-                            if(!if_equiv)
+                            if(!GlobalV::deepks_equiv)
                             {
                                 int ib=0;
                                 for (int L0 = 0; L0 <= orb.Alpha[0].getLmax();++L0)
@@ -441,7 +441,7 @@ void LCAO_Deepks::cal_f_delta_k(const std::vector<std::vector<std::complex<doubl
 
                                 assert(nlm1.size()==nlm2[0].size());                                
 
-                                if(!if_equiv)
+                                if(!GlobalV::deepks_equiv)
                                 {
                                     int ib=0;
                                     for (int L0 = 0; L0 <= orb.Alpha[0].getLmax();++L0)
diff --git a/source/module_hamilt_lcao/module_deepks/LCAO_deepks_io.cpp b/source/module_hamilt_lcao/module_deepks/LCAO_deepks_io.cpp
index 150e7a5f9d..1726132db5 100644
--- a/source/module_hamilt_lcao/module_deepks/LCAO_deepks_io.cpp
+++ b/source/module_hamilt_lcao/module_deepks/LCAO_deepks_io.cpp
@@ -102,7 +102,7 @@ void LCAO_Deepks::save_npy_d(const int nat)
     ModuleBase::TITLE("LCAO_Deepks", "save_npy_d");
     if(GlobalV::MY_RANK!=0) return;
     //save descriptor in .npy format
-    if(!if_equiv)
+    if(!GlobalV::deepks_equiv)
     {
         vector<double> npy_des;
         for (int inl = 0;inl < inlmax;++inl)
diff --git a/source/module_hamilt_lcao/module_deepks/LCAO_deepks_pdm.cpp b/source/module_hamilt_lcao/module_deepks/LCAO_deepks_pdm.cpp
index 47da26b27f..be06283cd9 100644
--- a/source/module_hamilt_lcao/module_deepks/LCAO_deepks_pdm.cpp
+++ b/source/module_hamilt_lcao/module_deepks/LCAO_deepks_pdm.cpp
@@ -35,7 +35,7 @@ void LCAO_Deepks::cal_projected_DM(const elecstate::DensityMatrix<double, double
     ModuleBase::TITLE("LCAO_Deepks", "cal_projected_DM");
 
     int pdm_size = 0;
-    if(!if_equiv)
+    if(!GlobalV::deepks_equiv)
     {
         pdm_size = (this->lmaxd * 2 + 1) * (this->lmaxd * 2 + 1);
     }
@@ -93,7 +93,7 @@ void LCAO_Deepks::cal_projected_DM(const elecstate::DensityMatrix<double, double
             //trace alpha orbital
             std::vector<int> trace_alpha_row;
             std::vector<int> trace_alpha_col;
-            if(!if_equiv)
+            if(!GlobalV::deepks_equiv)
             {
                 int ib=0;
                 for (int L0 = 0; L0 <= orb.Alpha[0].getLmax();++L0)
@@ -231,7 +231,7 @@ void LCAO_Deepks::cal_projected_DM(const elecstate::DensityMatrix<double, double
                         &row_size);
 				}//ad2
                 // do dot of g_1dmt and s_1t to get orbital_pdm_shell
-                if(!if_equiv)
+                if(!GlobalV::deepks_equiv)
                 {
                     int ib=0, index=0, inc=1;
                     for (int L0 = 0; L0 <= orb.Alpha[0].getLmax();++L0)
@@ -291,7 +291,7 @@ void LCAO_Deepks::cal_projected_DM_k(const elecstate::DensityMatrix<std::complex
 {
 
     int pdm_size = 0;
-    if(!if_equiv)
+    if(!GlobalV::deepks_equiv)
     {
         pdm_size = (this->lmaxd * 2 + 1) * (this->lmaxd * 2 + 1);
     }
@@ -350,7 +350,7 @@ void LCAO_Deepks::cal_projected_DM_k(const elecstate::DensityMatrix<std::complex
             //trace alpha orbital
             std::vector<int> trace_alpha_row;
             std::vector<int> trace_alpha_col;
-            if(!if_equiv)
+            if(!GlobalV::deepks_equiv)
             {
                 int ib=0;
                 for (int L0 = 0; L0 <= orb.Alpha[0].getLmax();++L0)
@@ -495,7 +495,7 @@ void LCAO_Deepks::cal_projected_DM_k(const elecstate::DensityMatrix<std::complex
                         &row_size);
 				}//ad2
                 // do dot of g_1dmt and s_1t to get orbital_pdm_shell
-                if(!if_equiv)
+                if(!GlobalV::deepks_equiv)
                 {
                     int ib=0, index=0, inc=1;
                     for (int L0 = 0; L0 <= orb.Alpha[0].getLmax();++L0)
diff --git a/source/module_hamilt_lcao/module_deepks/LCAO_deepks_torch.cpp b/source/module_hamilt_lcao/module_deepks/LCAO_deepks_torch.cpp
index 0126d20acc..cb731ee32c 100644
--- a/source/module_hamilt_lcao/module_deepks/LCAO_deepks_torch.cpp
+++ b/source/module_hamilt_lcao/module_deepks/LCAO_deepks_torch.cpp
@@ -58,7 +58,7 @@ void LCAO_Deepks::cal_descriptor(const int nat)
     ModuleBase::TITLE("LCAO_Deepks", "cal_descriptor");
     ModuleBase::timer::tick("LCAO_Deepks", "cal_descriptor");
 
-    if(if_equiv)
+    if(GlobalV::deepks_equiv)
     {
         this->cal_descriptor_equiv(nat);
         return;
@@ -113,7 +113,7 @@ void LCAO_Deepks::check_descriptor(const UnitCell &ucell)
     if(GlobalV::MY_RANK!=0) return;
     std::ofstream ofs("descriptor.dat");
     ofs<<std::setprecision(10);
-    if(!if_equiv)
+    if(!GlobalV::deepks_equiv)
     {
         for (int it = 0; it < ucell.ntype; it++)
         {
@@ -471,7 +471,7 @@ void LCAO_Deepks::cal_gedm_equiv(const int nat)
 //obtain from the machine learning model dE_delta/dDescriptor
 void LCAO_Deepks::cal_gedm(const int nat)
 {
-    if(if_equiv)
+    if(GlobalV::deepks_equiv)
     {
         this->cal_gedm_equiv(nat);
         return;
diff --git a/source/module_hamilt_lcao/module_gint/CMakeLists.txt b/source/module_hamilt_lcao/module_gint/CMakeLists.txt
index e0fb786318..5cd0ca654e 100644
--- a/source/module_hamilt_lcao/module_gint/CMakeLists.txt
+++ b/source/module_hamilt_lcao/module_gint/CMakeLists.txt
@@ -2,7 +2,6 @@
 
 list(APPEND objects
     gint.cpp
-    gint_gamma.cpp
     gint_gamma_env.cpp
     gint_gamma_vl.cpp
     gint_fvl.cpp
@@ -25,13 +24,23 @@ list(APPEND objects
 if(USE_CUDA)
   list(APPEND objects
       kernels/cuda/cuda_tools.cu
-      kernels/cuda/vbatch_matrix_mul.cu
       kernels/cuda/gint_vl.cu
       kernels/cuda/gint_rho.cu
       kernels/cuda/gint_force.cu
       gint_vl_gpu.cu
       gint_rho_gpu.cu
       gint_force_gpu.cu
+      kernels/cuda/gemm_selector.cu
+      kernels/cuda/code_gen_00.cu
+      kernels/cuda/code_gen_01.cu
+      kernels/cuda/code_gen_02.cu
+      kernels/cuda/code_gen_03.cu
+      kernels/cuda/code_gen_04.cu
+      kernels/cuda/code_gen_05.cu
+      kernels/cuda/code_gen_06.cu
+      kernels/cuda/code_gen_07.cu
+      kernels/cuda/code_gen_08.cu
+      kernels/cuda/code_gen_09.cu
       gtask_vl.cpp
       gtask_rho.cpp
       gtask_force.cpp
diff --git a/source/module_hamilt_lcao/module_gint/gint_gamma.cpp b/source/module_hamilt_lcao/module_gint/gint_gamma.cpp
deleted file mode 100644
index 7b2683d807..0000000000
--- a/source/module_hamilt_lcao/module_gint/gint_gamma.cpp
+++ /dev/null
@@ -1,74 +0,0 @@
-#include "gint_gamma.h"
-#include "module_hamilt_pw/hamilt_pwdft/global.h"
-#include "module_base/ylm.h"
-#include "module_cell/module_neighbor/sltk_atom_arrange.h"
-#include "module_base/timer.h"
-#ifdef _OPENMP
-#include <omp.h>
-#endif
-
-#ifdef __MKL
-#include <mkl_service.h>
-#endif
-
-Gint_Gamma::Gint_Gamma()
-{
-   
-    sender_index_size = 1;
-	sender_local_index = nullptr;
-    sender_size_process = nullptr;
-    sender_displacement_process = nullptr;
-    sender_size=1;
-    sender_buffer=nullptr;
-
-    receiver_index_size=1;
-    receiver_global_index = nullptr;
-    receiver_size_process = nullptr;
-    receiver_displacement_process = nullptr;
-    receiver_size=1;
-    receiver_buffer=nullptr;
-}
-
-Gint_Gamma::~Gint_Gamma()
-{
-    // mohan add if 2024-04-09
-	if(sender_local_index != nullptr)
-	{
-		delete[] sender_local_index;
-	}
-
-	if(sender_size_process != nullptr)
-	{
-		delete[] sender_size_process;
-	}
-
-	if(sender_displacement_process != nullptr)
-	{
-		delete[] sender_displacement_process;
-	}
-
-	if(sender_buffer != nullptr)
-	{
-		delete[] sender_buffer;
-	}
-
-    if(receiver_global_index != nullptr)
-	{
-		delete[] receiver_global_index;
-	}
-
-    if(receiver_size_process != nullptr)
-	{
-		delete[] receiver_size_process;
-	}
-
-    if(receiver_displacement_process != nullptr)
-	{
-		delete[] receiver_displacement_process;
-	}
-
-    if(receiver_buffer != nullptr)
-	{
-		delete[] receiver_buffer;
-	}
-}
diff --git a/source/module_hamilt_lcao/module_gint/gint_gamma.h b/source/module_hamilt_lcao/module_gint/gint_gamma.h
index 7ed700828f..275b8cebe0 100644
--- a/source/module_hamilt_lcao/module_gint/gint_gamma.h
+++ b/source/module_hamilt_lcao/module_gint/gint_gamma.h
@@ -24,8 +24,8 @@ class Gint_Gamma : public Gint
 {
 	public:
 
-	Gint_Gamma();
-	~Gint_Gamma();
+	// Gint_Gamma();
+	// ~Gint_Gamma();
 
     //------------------------------------------------------
     // in gint_gamma_vl.cpp 
@@ -51,37 +51,6 @@ class Gint_Gamma : public Gint
 
     double*** DM = nullptr;   //pointer to LOC.DM
 
-    ///------------------------------------------------------
-    /// in gint_gamma_vl.cpp 
-    ///------------------------------------------------------
-    /// method for redistributing the Hamiltonian
-    /// from grid to 2D format
-    /// pass a setter function to customize row/col major and outputs
-    void vl_grid_to_2D(const double* vl_grid,
-        const Parallel_2D& p2d,
-        const int loc_grid_dim,
-        const bool new_e_iteration,
-        double* vl_2d,
-        std::function<void(const int&, const int&, const double&, double*)> setfunc);
-
-    ///===============================
-    /// Use MPI_Alltoallv to convert a grid distributed matrix
-    /// to 2D - block cyclic distributed matrix.
-    ///===============================
-    int sender_index_size;
-    int *sender_local_index;
-    int sender_size;
-    int *sender_size_process;
-    int *sender_displacement_process;
-    double* sender_buffer;
-
-    int receiver_index_size;
-    int *receiver_global_index;
-    int receiver_size;
-    int *receiver_size_process;
-    int *receiver_displacement_process;
-    double* receiver_buffer;
-
 };
 
 #endif
diff --git a/source/module_hamilt_lcao/module_gint/gint_gamma_vl.cpp b/source/module_hamilt_lcao/module_gint/gint_gamma_vl.cpp
index 5177036c11..ce135db9b1 100644
--- a/source/module_hamilt_lcao/module_gint/gint_gamma_vl.cpp
+++ b/source/module_hamilt_lcao/module_gint/gint_gamma_vl.cpp
@@ -44,247 +44,6 @@ void Gint_Gamma::cal_vlocal(Gint_inout* inout,bool new_e_iteration)
 	}
 }
 
-#ifdef __MPI
-//------------------------------------------------------------------
-// mohan add notes: 2021-03-11
-// this subroutine is used to transform data from grid integrals
-// to 2D-block distribution
-// s stands for 'sender' and r stands for 'receiver'
-//------------------------------------------------------------------
-inline int setBufferParameter(
-    const Grid_Technique& gt,
-	MPI_Comm comm_2D,
-	int blacs_ctxt,
-	int nblk,
-	int& s_index_siz,
-	int*& s_local_index,
-	int*& s_siz_pro,
-	int*& s_dis_pro,
-	int& s_siz,
-	double*& s_buffer,
-	int& r_index_siz,
-	int*& r_global_index,
-	int*& r_siz_pro,
-	int*& r_dis_pro,
-	int& r_siz,
-	double*& r_buffer)
-{
-    const int nlocal = GlobalV::NLOCAL;
-
-	//-----------------------------------------
-    // setup blacs parameters
-	//-----------------------------------------
-    int nprows=0;
-    int npcols=0;
-    int nprocs=0;
-
-    int myprow=0;
-    int mypcol=0;
-    int myproc=0;
-
-    Cblacs_gridinfo(blacs_ctxt, &nprows, &npcols, &myprow, &mypcol);
-
-	//-----------------------------------------
-	// set index of current proor: myproc
-	// set number of total proors: nprocs
-	//-----------------------------------------
-    Cblacs_pinfo(&myproc, &nprocs);
-
-    // initialize data arrays
-    delete[] s_siz_pro;
-    delete[] s_dis_pro;
-    delete[] r_siz_pro;
-    delete[] r_dis_pro;
-
-    s_siz_pro=new int[nprocs];
-    s_dis_pro=new int[nprocs];
-    r_siz_pro=new int[nprocs];
-    r_dis_pro=new int[nprocs];
-
-	//---------------------------------------------------------------------
-    // build the local index to be sent to other pro (s_local_index),
-    // the global index to be received from other pro (r_global_index),
-    // the send/receive siz/dis for data exchange by MPI_Alltoall
-	//---------------------------------------------------------------------
-    s_index_siz=gt.lgd*gt.lgd*2;
-
-    delete[] s_local_index;
-    s_local_index=new int[s_index_siz];
-
-    int *s_global_index=new int[s_index_siz];
-
-    int pos=0;
-    s_siz_pro[0]=0;
-    for(int iproc=0; iproc<nprocs; ++iproc)
-    {
-        s_dis_pro[iproc]=pos;
-
-        int iprow=0;
-		int ipcol=0;
-        Cblacs_pcoord(blacs_ctxt, iproc, &iprow, &ipcol);
-
-        // find out the global index and local index of elements
-		// in each pro based on 2D block cyclic distribution
-        for(int irow=0, grow=0; grow<nlocal; ++irow)
-        {
-            grow=Local_Orbital_wfc::globalIndex(irow, nblk, nprows, iprow);
-			if (grow >= nlocal)
-			{
-				continue;
-			}
-			int lrow = gt.trace_lo[grow];
-			if (lrow < 0)
-			{
-				continue;
-			}
-
-            for(int icol=0, gcol=0; gcol<nlocal; ++icol)
-            {
-                gcol=Local_Orbital_wfc::globalIndex(icol,nblk, npcols, ipcol);
-				if (gcol >= nlocal)
-				{
-					continue;
-				}
-                int lcol = gt.trace_lo[gcol];
-				if (lcol < 0)
-				{
-					continue;
-				}
-                s_global_index[pos]=grow;
-                s_global_index[pos+1]=gcol;
-                s_local_index[pos]=lrow;
-                s_local_index[pos+1]=lcol;
-                pos+=2;
-            }
-        }
-        s_siz_pro[iproc]=pos-s_dis_pro[iproc];
-    }
-
-    MPI_Alltoall(s_siz_pro, 1, MPI_INT,
-                 r_siz_pro, 1, MPI_INT, comm_2D);
-
-    r_index_siz=r_siz_pro[0];
-    r_dis_pro[0]=0;
-    for(int i=1; i<nprocs; ++i)
-    {
-        r_index_siz+=r_siz_pro[i];
-        r_dis_pro[i]=r_dis_pro[i-1]+r_siz_pro[i-1];
-    }
-
-	delete[] r_global_index;
-	r_global_index=new int[r_index_siz];
-
-    // send the global index in sendBuffer to recvBuffer
-    MPI_Alltoallv(s_global_index, s_siz_pro, s_dis_pro, MPI_INT,
-                  r_global_index, r_siz_pro, r_dis_pro, MPI_INT, comm_2D);
-
-    delete [] s_global_index;
-
-    // the s_siz_pro, s_dis_pro, r_siz_pro,
-    // and r_dis_pro will be used in transfer s_buffer, which
-    // is half siz of s_global_index
-    // we have to rebuild the siz and dis for each pro
-    for (int iproc=0; iproc < nprocs; ++iproc)
-    {
-        s_siz_pro[iproc]=s_siz_pro[iproc]/2;
-        s_dis_pro[iproc]=s_dis_pro[iproc]/2;
-        r_siz_pro[iproc]=r_siz_pro[iproc]/2;
-        r_dis_pro[iproc]=r_dis_pro[iproc]/2;
-    }
-
-    s_siz=s_index_siz/2;
-	delete[] s_buffer;
-	s_buffer=new double[s_siz];
-
-    r_siz=r_index_siz/2;
-	delete[] r_buffer;
-	r_buffer=new double[r_siz];
-
-    return 0;
-}
-#endif
-
-
-void Gint_Gamma::vl_grid_to_2D(
-		const double* vl_grid, 
-		const Parallel_2D& p2d, 
-		const int loc_grid_dim, 
-		const bool new_e_iteration, 
-		double* vl_2d,
-		std::function<void(const int&, const int&, const double&, double*)> setfunc)
-{
-    ModuleBase::timer::tick("Gint_Gamma","distri_vl");
-    // setup send buffer and receive buffer size
-    // OUT(GlobalV::ofs_running, "Start transforming vlocal from grid distribute to 2D block");
-    if(new_e_iteration)
-    {
-        ModuleBase::timer::tick("Gint_Gamma","distri_vl_index");
-#ifdef __MPI
-		setBufferParameter(*this->gridt, p2d.comm_2D, p2d.blacs_ctxt, p2d.nb,
-				this->sender_index_size, this->sender_local_index,
-				this->sender_size_process, this->sender_displacement_process,
-				this->sender_size, this->sender_buffer,
-				this->receiver_index_size, this->receiver_global_index,
-				this->receiver_size_process, this->receiver_displacement_process,
-				this->receiver_size, this->receiver_buffer);
-#endif
-#ifdef __DEBUG
-        ModuleBase::GlobalFunc::OUT(GlobalV::ofs_running, "vlocal exchange index is built");
-        ModuleBase::GlobalFunc::OUT(GlobalV::ofs_running, "buffer size(M):", 
-        (this->sender_size+this->receiver_size)*sizeof(double)/1024/1024);
-        ModuleBase::GlobalFunc::OUT(GlobalV::ofs_running, "buffer index size(M):", 
-        (this->sender_index_size+this->receiver_index_size)*sizeof(int)/1024/1024);
-#endif
-        ModuleBase::timer::tick("Gint_Gamma","distri_vl_index");
-    }
-
-    ModuleBase::timer::tick("Gint_Gamma","distri_vl_value");
-
-    // put data to send buffer
-    for(int i=0; i<this->sender_index_size; i+=2)
-    {
-        const int irow=this->sender_local_index[i];
-        const int icol=this->sender_local_index[i+1];
-        if(irow<=icol)
-		{
-            this->sender_buffer[i / 2] = vl_grid[irow * loc_grid_dim + icol];
-		}
-        else
-		{
-            this->sender_buffer[i / 2] = vl_grid[icol * loc_grid_dim + irow];
-		}
-    }
-
-#ifdef __DEBUG
-    ModuleBase::GlobalFunc::OUT(GlobalV::ofs_running, 
-    "vlocal data are put in sender_buffer, size(M):", 
-    this->sender_size*8/1024/1024);
-#endif
-
-	// use mpi_alltoall to get local data
-#ifdef __MPI
-	MPI_Alltoallv(this->sender_buffer, this->sender_size_process, this->sender_displacement_process, MPI_DOUBLE,
-			this->receiver_buffer, this->receiver_size_process,
-			this->receiver_displacement_process, MPI_DOUBLE, p2d.comm_2D);
-#endif
-
-#ifdef __DEBUG
-    ModuleBase::GlobalFunc::OUT(GlobalV::ofs_running, 
-    "vlocal data are exchanged, received size(M):", 
-    this->receiver_size*8/1024/1024);
-#endif
-
-    // put local data to H matrix
-    for(int i=0; i<this->receiver_index_size; i+=2)
-    {
-        const int g_row = this->receiver_global_index[i];
-        const int g_col = this->receiver_global_index[i + 1];
-        setfunc(g_row, g_col, this->receiver_buffer[i / 2], vl_2d);
-    }
-
-    ModuleBase::timer::tick("Gint_Gamma","distri_vl_value");
-    ModuleBase::timer::tick("Gint_Gamma","distri_vl");
-}
 
 #ifdef __MPI
 #include "module_hamilt_lcao/module_hcontainer/hcontainer_funcs.h"
diff --git a/source/module_hamilt_lcao/module_gint/gint_rho_gpu.cu b/source/module_hamilt_lcao/module_gint/gint_rho_gpu.cu
index a598720c8c..13ffe9b2d2 100644
--- a/source/module_hamilt_lcao/module_gint/gint_rho_gpu.cu
+++ b/source/module_hamilt_lcao/module_gint/gint_rho_gpu.cu
@@ -1,5 +1,4 @@
 #include "kernels/cuda/cuda_tools.cuh"
-#include "kernels/cuda/vbatch_matrix_mul.cuh"
 #include "module_base/ylm.h"
 #include "module_hamilt_lcao/module_gint/gint_rho.h"
 #include "module_hamilt_lcao/module_gint/gint_tools.h"
diff --git a/source/module_hamilt_lcao/module_gint/gint_vl_gpu.cu b/source/module_hamilt_lcao/module_gint/gint_vl_gpu.cu
index 2c3d5b3922..73d6c8d201 100644
--- a/source/module_hamilt_lcao/module_gint/gint_vl_gpu.cu
+++ b/source/module_hamilt_lcao/module_gint/gint_vl_gpu.cu
@@ -1,7 +1,6 @@
 #include <omp.h>
 
 #include "kernels/cuda/cuda_tools.cuh"
-#include "kernels/cuda/vbatch_matrix_mul.cuh"
 #include "module_base/ylm.h"
 #include "module_hamilt_lcao/module_gint/gint_tools.h"
 #include "module_hamilt_lcao/module_gint/gint_vl.h"
diff --git a/source/module_hamilt_lcao/module_gint/grid_technique.h b/source/module_hamilt_lcao/module_gint/grid_technique.h
index 03cca8e924..898b0ffb51 100644
--- a/source/module_hamilt_lcao/module_gint/grid_technique.h
+++ b/source/module_hamilt_lcao/module_gint/grid_technique.h
@@ -11,7 +11,7 @@
 #include <cuda_runtime.h>
 
 #include "kernels/cuda/cuda_tools.cuh"
-#include "kernels/cuda/vbatch_matrix_mul.cuh"
+#include "kernels/cuda/gemm_selector.cuh"
 #endif
 
 // Author: mohan
diff --git a/source/module_hamilt_lcao/module_gint/kernels/cuda/code_gen.cpp b/source/module_hamilt_lcao/module_gint/kernels/cuda/code_gen.cpp
index 4edfce05cb..42e8c4f0c5 100644
--- a/source/module_hamilt_lcao/module_gint/kernels/cuda/code_gen.cpp
+++ b/source/module_hamilt_lcao/module_gint/kernels/cuda/code_gen.cpp
@@ -1,6 +1,3 @@
-// Generate and test the efficiency of matrix multiplication functions with different parameters
-// This file takes a long time to compile
-
 gemm_time_measure<double, 2, 16, 16, 32, 2, 2, 16, 2, 16>(max_m,
                                                           max_n,
                                                           d_m,
@@ -4181,25 +4178,6 @@ gemm_time_measure<double, 16, 32, 64, 64, 32, 16, 32, 16, 32>(max_m,
                                                               h_global_C,
                                                               d_global_C);
 
-gemm_time_measure<double, 16, 32, 64, 64, 32, 16, 32, 16, 32>(max_m,
-                                                              max_n,
-                                                              d_m,
-                                                              d_n,
-                                                              d_k,
-                                                              d_global_A_array,
-                                                              d_global_lda,
-                                                              d_global_B_array,
-                                                              d_global_ldb,
-                                                              d_global_C_array,
-                                                              d_global_ldc,
-                                                              batchCount,
-                                                              temp_stream,
-                                                              fastest_time,
-                                                              fastest_algo,
-                                                              cpu_result,
-                                                              h_global_C,
-                                                              d_global_C);
-
 gemm_time_measure<double, 20, 8, 40, 24, 20, 20, 8, 20, 8>(max_m,
                                                            max_n,
                                                            d_m,
diff --git a/source/module_hamilt_lcao/module_gint/kernels/cuda/code_gen.cuh b/source/module_hamilt_lcao/module_gint/kernels/cuda/code_gen.cuh
new file mode 100644
index 0000000000..a4b1a75916
--- /dev/null
+++ b/source/module_hamilt_lcao/module_gint/kernels/cuda/code_gen.cuh
@@ -0,0 +1,473 @@
+#ifndef CODE_GEN_CUH
+#define CODE_GEN_CUH
+
+#include "gemm_selector.cuh"
+#include <cuda_runtime.h>
+
+extern template void gemm_time_measure<double, 2, 16, 16, 32, 2, 2, 16, 2, 16>(int, int, int*, int*, int*, double**, int*, double**, int*, double**, int*, int, cudaStream_t, float&, matrix_multiple_func_type&, double*, double*, double*);
+
+extern template void gemm_time_measure<double, 2, 16, 16, 32, 4, 2, 16, 2, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 2, 16, 16, 32, 6, 2, 16, 2, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 2, 16, 16, 32, 8, 2, 16, 2, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 2, 16, 16, 48, 2, 2, 16, 2, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 2, 16, 16, 48, 4, 2, 16, 2, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 2, 16, 16, 48, 6, 2, 16, 2, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 4, 8, 8, 24, 4, 4, 8, 4, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 4, 8, 8, 24, 8, 4, 8, 4, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 4, 8, 8, 24, 12, 4, 8, 4, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 4, 8, 8, 32, 4, 4, 8, 4, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 4, 8, 8, 32, 8, 4, 8, 4, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 4, 8, 8, 40, 4, 4, 8, 4, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 4, 8, 8, 40, 8, 4, 8, 4, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 4, 8, 8, 48, 4, 4, 8, 4, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 4, 8, 8, 56, 4, 4, 8, 4, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 4, 8, 8, 64, 4, 4, 8, 4, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 4, 8, 16, 16, 4, 4, 8, 4, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 4, 8, 16, 16, 8, 4, 8, 4, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 4, 8, 16, 16, 12, 4, 8, 4, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 4, 8, 16, 24, 4, 4, 8, 4, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 4, 8, 16, 24, 8, 4, 8, 4, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 4, 8, 16, 32, 4, 4, 8, 4, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 4, 8, 16, 32, 8, 4, 8, 4, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 4, 8, 16, 40, 4, 4, 8, 4, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 4, 8, 16, 48, 4, 4, 8, 4, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 4, 8, 16, 56, 4, 4, 8, 4, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 4, 8, 24, 16, 4, 4, 8, 4, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 4, 8, 24, 16, 8, 4, 8, 4, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 4, 8, 24, 24, 4, 4, 8, 4, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 4, 8, 24, 24, 8, 4, 8, 4, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 4, 8, 24, 32, 4, 4, 8, 4, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 4, 8, 24, 40, 4, 4, 8, 4, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 4, 8, 32, 16, 4, 4, 8, 4, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 4, 8, 32, 16, 8, 4, 8, 4, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 4, 8, 32, 24, 4, 4, 8, 4, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 4, 8, 40, 16, 4, 4, 8, 4, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 4, 8, 40, 24, 4, 4, 8, 4, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 4, 8, 48, 16, 4, 4, 8, 4, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 4, 8, 56, 16, 4, 4, 8, 4, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 4, 16, 16, 32, 4, 4, 16, 4, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 4, 16, 16, 32, 8, 4, 16, 4, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 4, 16, 16, 32, 12, 4, 16, 4, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 4, 16, 16, 32, 16, 4, 16, 4, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 4, 16, 16, 48, 4, 4, 16, 4, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 4, 16, 16, 48, 8, 4, 16, 4, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 4, 16, 16, 48, 12, 4, 16, 4, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 4, 16, 16, 64, 4, 4, 16, 4, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 4, 16, 16, 64, 8, 4, 16, 4, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 4, 16, 32, 32, 4, 4, 16, 4, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 4, 16, 32, 32, 8, 4, 16, 4, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 4, 16, 32, 32, 12, 4, 16, 4, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 4, 16, 32, 48, 4, 4, 16, 4, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 4, 16, 32, 48, 8, 4, 16, 4, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 4, 16, 48, 32, 4, 4, 16, 4, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 4, 16, 48, 32, 8, 4, 16, 4, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 4, 24, 24, 48, 4, 4, 24, 4, 24>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 4, 24, 24, 48, 8, 4, 24, 4, 24>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 4, 24, 24, 48, 12, 4, 24, 4, 24>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 4, 24, 48, 48, 4, 4, 24, 4, 24>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 4, 24, 48, 48, 8, 4, 24, 4, 24>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 4, 32, 32, 64, 4, 4, 32, 4, 32>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 4, 32, 32, 64, 8, 4, 32, 4, 32>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 4, 32, 32, 64, 12, 4, 32, 4, 32>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 4, 32, 32, 64, 16, 4, 32, 4, 32>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 6, 16, 48, 32, 6, 6, 16, 6, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 6, 16, 48, 32, 12, 6, 16, 6, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 6, 16, 48, 48, 6, 6, 16, 6, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 4, 16, 12, 8, 8, 4, 8, 4>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 4, 16, 16, 8, 8, 4, 8, 4>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 4, 16, 20, 8, 8, 4, 8, 4>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 4, 16, 24, 8, 8, 4, 8, 4>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 4, 16, 28, 8, 8, 4, 8, 4>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 4, 16, 32, 8, 8, 4, 8, 4>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 4, 24, 8, 8, 8, 4, 8, 4>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 4, 24, 12, 8, 8, 4, 8, 4>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 4, 24, 16, 8, 8, 4, 8, 4>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 4, 24, 20, 8, 8, 4, 8, 4>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 4, 24, 24, 8, 8, 4, 8, 4>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 4, 32, 8, 8, 8, 4, 8, 4>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 4, 32, 12, 8, 8, 4, 8, 4>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 4, 32, 16, 8, 8, 4, 8, 4>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 4, 40, 8, 8, 8, 4, 8, 4>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 8, 16, 24, 8, 8, 8, 8, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 8, 16, 24, 16, 8, 8, 8, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 8, 16, 32, 8, 8, 8, 8, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 8, 16, 32, 16, 8, 8, 8, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 8, 16, 40, 8, 8, 8, 8, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 8, 16, 48, 8, 8, 8, 8, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 8, 16, 56, 8, 8, 8, 8, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 8, 16, 64, 8, 8, 8, 8, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 8, 24, 16, 8, 8, 8, 8, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 8, 24, 16, 16, 8, 8, 8, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 8, 24, 24, 8, 8, 8, 8, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 8, 24, 24, 16, 8, 8, 8, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 8, 24, 32, 8, 8, 8, 8, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 8, 24, 40, 8, 8, 8, 8, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 8, 24, 48, 8, 8, 8, 8, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 8, 24, 56, 8, 8, 8, 8, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 8, 24, 64, 8, 8, 8, 8, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 8, 32, 16, 8, 8, 8, 8, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 8, 32, 16, 16, 8, 8, 8, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 8, 32, 24, 8, 8, 8, 8, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 8, 32, 32, 8, 8, 8, 8, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 8, 32, 40, 8, 8, 8, 8, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 8, 32, 48, 8, 8, 8, 8, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 8, 32, 56, 8, 8, 8, 8, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 8, 40, 16, 8, 8, 8, 8, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 8, 40, 24, 8, 8, 8, 8, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 8, 40, 32, 8, 8, 8, 8, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 8, 40, 40, 8, 8, 8, 8, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 8, 40, 48, 8, 8, 8, 8, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 8, 48, 16, 8, 8, 8, 8, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 8, 48, 24, 8, 8, 8, 8, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 8, 48, 32, 8, 8, 8, 8, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 8, 48, 40, 8, 8, 8, 8, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 8, 56, 16, 8, 8, 8, 8, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 8, 56, 24, 8, 8, 8, 8, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 8, 56, 32, 8, 8, 8, 8, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 8, 64, 16, 8, 8, 8, 8, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 8, 64, 24, 8, 8, 8, 8, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 12, 24, 24, 8, 8, 12, 8, 12>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 12, 24, 24, 16, 8, 12, 8, 12>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 12, 24, 36, 8, 8, 12, 8, 12>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 12, 24, 36, 16, 8, 12, 8, 12>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 12, 24, 48, 8, 8, 12, 8, 12>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 12, 24, 60, 8, 8, 12, 8, 12>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 12, 48, 24, 8, 8, 12, 8, 12>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 12, 48, 36, 8, 8, 12, 8, 12>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 12, 48, 48, 8, 8, 12, 8, 12>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 12, 48, 60, 8, 8, 12, 8, 12>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 16, 16, 48, 8, 8, 16, 8, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 16, 16, 48, 16, 8, 16, 8, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 16, 16, 48, 24, 8, 16, 8, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 16, 16, 64, 8, 8, 16, 8, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 16, 16, 64, 16, 8, 16, 8, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 16, 32, 32, 8, 8, 16, 8, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 16, 32, 32, 16, 8, 16, 8, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 16, 32, 32, 24, 8, 16, 8, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 16, 32, 48, 8, 8, 16, 8, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 16, 32, 48, 16, 8, 16, 8, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 16, 32, 64, 8, 8, 16, 8, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 16, 32, 64, 16, 8, 16, 8, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 16, 48, 32, 8, 8, 16, 8, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 16, 48, 32, 16, 8, 16, 8, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 16, 48, 48, 8, 8, 16, 8, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 16, 48, 48, 16, 8, 16, 8, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 16, 48, 64, 8, 8, 16, 8, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 16, 64, 32, 8, 8, 16, 8, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 16, 64, 32, 16, 8, 16, 8, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 16, 64, 48, 8, 8, 16, 8, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 20, 40, 40, 8, 8, 20, 8, 20>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 20, 40, 40, 16, 8, 20, 8, 20>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 20, 40, 60, 8, 8, 20, 8, 20>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 24, 24, 48, 8, 8, 24, 8, 24>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 24, 24, 48, 16, 8, 24, 8, 24>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 24, 24, 48, 24, 8, 24, 8, 24>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 24, 48, 48, 8, 8, 24, 8, 24>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 24, 48, 48, 16, 8, 24, 8, 24>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 28, 56, 56, 8, 8, 28, 8, 28>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 28, 56, 56, 16, 8, 28, 8, 28>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 32, 32, 64, 8, 8, 32, 8, 32>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 32, 32, 64, 16, 8, 32, 8, 32>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 32, 32, 64, 24, 8, 32, 8, 32>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 32, 32, 64, 32, 8, 32, 8, 32>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 32, 64, 64, 8, 8, 32, 8, 32>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 32, 64, 64, 16, 8, 32, 8, 32>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 8, 32, 64, 64, 24, 8, 32, 8, 32>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 12, 8, 24, 24, 12, 12, 8, 12, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 12, 8, 24, 32, 12, 12, 8, 12, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 12, 8, 24, 40, 12, 12, 8, 12, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 12, 8, 24, 48, 12, 12, 8, 12, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 12, 8, 24, 56, 12, 12, 8, 12, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 12, 8, 48, 16, 12, 12, 8, 12, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 12, 8, 48, 24, 12, 12, 8, 12, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 12, 8, 48, 32, 12, 12, 8, 12, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 12, 16, 48, 32, 12, 12, 16, 12, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 12, 16, 48, 32, 24, 12, 16, 12, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 12, 16, 48, 48, 12, 12, 16, 12, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 12, 16, 48, 64, 12, 12, 16, 12, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 12, 24, 48, 48, 12, 12, 24, 12, 24>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 12, 24, 48, 48, 24, 12, 24, 12, 24>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 16, 4, 32, 12, 16, 16, 4, 16, 4>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 16, 4, 32, 16, 16, 16, 4, 16, 4>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 16, 6, 48, 12, 16, 16, 6, 16, 6>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 16, 8, 32, 24, 16, 16, 8, 16, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 16, 8, 32, 32, 16, 16, 8, 16, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 16, 8, 32, 40, 16, 16, 8, 16, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 16, 8, 32, 48, 16, 16, 8, 16, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 16, 8, 32, 56, 16, 16, 8, 16, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 16, 8, 32, 64, 16, 16, 8, 16, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 16, 8, 48, 16, 16, 16, 8, 16, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 16, 8, 48, 24, 16, 16, 8, 16, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 16, 8, 48, 32, 16, 16, 8, 16, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 16, 8, 48, 40, 16, 16, 8, 16, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 16, 8, 48, 48, 16, 16, 8, 16, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 16, 8, 64, 16, 16, 16, 8, 16, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 16, 8, 64, 24, 16, 16, 8, 16, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 16, 8, 64, 32, 16, 16, 8, 16, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 16, 12, 48, 24, 16, 16, 12, 16, 12>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 16, 12, 48, 36, 16, 16, 12, 16, 12>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 16, 12, 48, 48, 16, 16, 12, 16, 12>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 16, 12, 48, 60, 16, 16, 12, 16, 12>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 16, 16, 32, 48, 16, 16, 16, 16, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 16, 16, 32, 48, 32, 16, 16, 16, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 16, 16, 32, 64, 16, 16, 16, 16, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 16, 16, 32, 64, 32, 16, 16, 16, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 16, 16, 48, 32, 16, 16, 16, 16, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 16, 16, 48, 32, 32, 16, 16, 16, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 16, 16, 48, 48, 16, 16, 16, 16, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 16, 16, 48, 48, 32, 16, 16, 16, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 16, 16, 48, 64, 16, 16, 16, 16, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 16, 16, 64, 32, 16, 16, 16, 16, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 16, 16, 64, 32, 32, 16, 16, 16, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 16, 16, 64, 48, 16, 16, 16, 16, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 16, 16, 64, 64, 16, 16, 16, 16, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 16, 24, 48, 48, 16, 16, 24, 16, 24>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 16, 24, 48, 48, 32, 16, 24, 16, 24>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 16, 32, 64, 64, 16, 16, 32, 16, 32>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 16, 32, 64, 64, 32, 16, 32, 16, 32>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 20, 8, 40, 24, 20, 20, 8, 20, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 20, 8, 40, 32, 20, 20, 8, 20, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 24, 8, 48, 24, 24, 24, 8, 24, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 24, 8, 48, 32, 24, 24, 8, 24, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 24, 12, 48, 36, 24, 24, 12, 24, 12>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 24, 12, 48, 48, 24, 24, 12, 24, 12>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 24, 12, 48, 60, 24, 24, 12, 24, 12>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 24, 16, 48, 48, 24, 24, 16, 24, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 24, 16, 48, 64, 24, 24, 16, 24, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 32, 8, 64, 24, 32, 32, 8, 32, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 32, 8, 64, 32, 32, 32, 8, 32, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 32, 16, 64, 48, 32, 32, 16, 32, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+extern template void gemm_time_measure<double, 32, 16, 64, 64, 32, 32, 16, 32, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+#endif
\ No newline at end of file
diff --git a/source/module_hamilt_lcao/module_gint/kernels/cuda/code_gen_00.cu b/source/module_hamilt_lcao/module_gint/kernels/cuda/code_gen_00.cu
new file mode 100644
index 0000000000..a07c411485
--- /dev/null
+++ b/source/module_hamilt_lcao/module_gint/kernels/cuda/code_gen_00.cu
@@ -0,0 +1,48 @@
+#include "vbatch_matrix_mul.cuh"
+
+template void gemm_time_measure<double, 2, 16, 16, 32, 2, 2, 16, 2, 16>(int, int, int*, int*, int*, double**, int*, double**, int*, double**, int*, int, cudaStream_t, float&, matrix_multiple_func_type&, double*, double*, double*);
+
+template void gemm_time_measure<double, 2, 16, 16, 32, 4, 2, 16, 2, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 2, 16, 16, 32, 6, 2, 16, 2, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 2, 16, 16, 32, 8, 2, 16, 2, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 2, 16, 16, 48, 2, 2, 16, 2, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 2, 16, 16, 48, 4, 2, 16, 2, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 2, 16, 16, 48, 6, 2, 16, 2, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 4, 8, 8, 24, 4, 4, 8, 4, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 4, 8, 8, 24, 8, 4, 8, 4, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 4, 8, 8, 24, 12, 4, 8, 4, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 4, 8, 8, 32, 4, 4, 8, 4, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 4, 8, 8, 32, 8, 4, 8, 4, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 4, 8, 8, 40, 4, 4, 8, 4, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 4, 8, 8, 40, 8, 4, 8, 4, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 4, 8, 8, 48, 4, 4, 8, 4, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 4, 8, 8, 56, 4, 4, 8, 4, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 4, 8, 8, 64, 4, 4, 8, 4, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 4, 8, 16, 16, 4, 4, 8, 4, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 4, 8, 16, 16, 8, 4, 8, 4, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 4, 8, 16, 16, 12, 4, 8, 4, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 4, 8, 16, 24, 4, 4, 8, 4, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 4, 8, 16, 24, 8, 4, 8, 4, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 4, 8, 16, 32, 4, 4, 8, 4, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
diff --git a/source/module_hamilt_lcao/module_gint/kernels/cuda/code_gen_01.cu b/source/module_hamilt_lcao/module_gint/kernels/cuda/code_gen_01.cu
new file mode 100644
index 0000000000..9f725c23c6
--- /dev/null
+++ b/source/module_hamilt_lcao/module_gint/kernels/cuda/code_gen_01.cu
@@ -0,0 +1,48 @@
+#include "vbatch_matrix_mul.cuh"
+
+template void gemm_time_measure<double, 4, 8, 16, 32, 8, 4, 8, 4, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 4, 8, 16, 40, 4, 4, 8, 4, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 4, 8, 16, 48, 4, 4, 8, 4, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 4, 8, 16, 56, 4, 4, 8, 4, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 4, 8, 24, 16, 4, 4, 8, 4, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 4, 8, 24, 16, 8, 4, 8, 4, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 4, 8, 24, 24, 4, 4, 8, 4, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 4, 8, 24, 24, 8, 4, 8, 4, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 4, 8, 24, 32, 4, 4, 8, 4, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 4, 8, 24, 40, 4, 4, 8, 4, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 4, 8, 32, 16, 4, 4, 8, 4, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 4, 8, 32, 16, 8, 4, 8, 4, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 4, 8, 32, 24, 4, 4, 8, 4, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 4, 8, 40, 16, 4, 4, 8, 4, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 4, 8, 40, 24, 4, 4, 8, 4, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 4, 8, 48, 16, 4, 4, 8, 4, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 4, 8, 56, 16, 4, 4, 8, 4, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 4, 16, 16, 32, 4, 4, 16, 4, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 4, 16, 16, 32, 8, 4, 16, 4, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 4, 16, 16, 32, 12, 4, 16, 4, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 4, 16, 16, 32, 16, 4, 16, 4, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 4, 16, 16, 48, 4, 4, 16, 4, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 4, 16, 16, 48, 8, 4, 16, 4, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
diff --git a/source/module_hamilt_lcao/module_gint/kernels/cuda/code_gen_02.cu b/source/module_hamilt_lcao/module_gint/kernels/cuda/code_gen_02.cu
new file mode 100644
index 0000000000..090eab0709
--- /dev/null
+++ b/source/module_hamilt_lcao/module_gint/kernels/cuda/code_gen_02.cu
@@ -0,0 +1,48 @@
+#include "vbatch_matrix_mul.cuh"
+
+template void gemm_time_measure<double, 4, 16, 16, 48, 12, 4, 16, 4, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 4, 16, 16, 64, 4, 4, 16, 4, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 4, 16, 16, 64, 8, 4, 16, 4, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 4, 16, 32, 32, 4, 4, 16, 4, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 4, 16, 32, 32, 8, 4, 16, 4, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 4, 16, 32, 32, 12, 4, 16, 4, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 4, 16, 32, 48, 4, 4, 16, 4, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 4, 16, 32, 48, 8, 4, 16, 4, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 4, 16, 48, 32, 4, 4, 16, 4, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 4, 16, 48, 32, 8, 4, 16, 4, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 4, 24, 24, 48, 4, 4, 24, 4, 24>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 4, 24, 24, 48, 8, 4, 24, 4, 24>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 4, 24, 24, 48, 12, 4, 24, 4, 24>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 4, 24, 48, 48, 4, 4, 24, 4, 24>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 4, 24, 48, 48, 8, 4, 24, 4, 24>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 4, 32, 32, 64, 4, 4, 32, 4, 32>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 4, 32, 32, 64, 8, 4, 32, 4, 32>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 4, 32, 32, 64, 12, 4, 32, 4, 32>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 4, 32, 32, 64, 16, 4, 32, 4, 32>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 6, 16, 48, 32, 6, 6, 16, 6, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 6, 16, 48, 32, 12, 6, 16, 6, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 6, 16, 48, 48, 6, 6, 16, 6, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 8, 4, 16, 12, 8, 8, 4, 8, 4>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
diff --git a/source/module_hamilt_lcao/module_gint/kernels/cuda/code_gen_03.cu b/source/module_hamilt_lcao/module_gint/kernels/cuda/code_gen_03.cu
new file mode 100644
index 0000000000..046d0e5063
--- /dev/null
+++ b/source/module_hamilt_lcao/module_gint/kernels/cuda/code_gen_03.cu
@@ -0,0 +1,48 @@
+#include "vbatch_matrix_mul.cuh"
+
+template void gemm_time_measure<double, 8, 4, 16, 16, 8, 8, 4, 8, 4>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 8, 4, 16, 20, 8, 8, 4, 8, 4>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 8, 4, 16, 24, 8, 8, 4, 8, 4>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 8, 4, 16, 28, 8, 8, 4, 8, 4>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 8, 4, 16, 32, 8, 8, 4, 8, 4>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 8, 4, 24, 8, 8, 8, 4, 8, 4>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 8, 4, 24, 12, 8, 8, 4, 8, 4>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 8, 4, 24, 16, 8, 8, 4, 8, 4>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 8, 4, 24, 20, 8, 8, 4, 8, 4>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 8, 4, 24, 24, 8, 8, 4, 8, 4>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 8, 4, 32, 8, 8, 8, 4, 8, 4>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 8, 4, 32, 12, 8, 8, 4, 8, 4>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 8, 4, 32, 16, 8, 8, 4, 8, 4>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 8, 4, 40, 8, 8, 8, 4, 8, 4>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 8, 8, 16, 24, 8, 8, 8, 8, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 8, 8, 16, 24, 16, 8, 8, 8, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 8, 8, 16, 32, 8, 8, 8, 8, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 8, 8, 16, 32, 16, 8, 8, 8, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 8, 8, 16, 40, 8, 8, 8, 8, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 8, 8, 16, 48, 8, 8, 8, 8, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 8, 8, 16, 56, 8, 8, 8, 8, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 8, 8, 16, 64, 8, 8, 8, 8, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 8, 8, 24, 16, 8, 8, 8, 8, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
diff --git a/source/module_hamilt_lcao/module_gint/kernels/cuda/code_gen_04.cu b/source/module_hamilt_lcao/module_gint/kernels/cuda/code_gen_04.cu
new file mode 100644
index 0000000000..f74209d829
--- /dev/null
+++ b/source/module_hamilt_lcao/module_gint/kernels/cuda/code_gen_04.cu
@@ -0,0 +1,48 @@
+#include "vbatch_matrix_mul.cuh"
+
+template void gemm_time_measure<double, 8, 8, 24, 16, 16, 8, 8, 8, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 8, 8, 24, 24, 8, 8, 8, 8, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 8, 8, 24, 24, 16, 8, 8, 8, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 8, 8, 24, 32, 8, 8, 8, 8, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 8, 8, 24, 40, 8, 8, 8, 8, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 8, 8, 24, 48, 8, 8, 8, 8, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 8, 8, 24, 56, 8, 8, 8, 8, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 8, 8, 24, 64, 8, 8, 8, 8, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 8, 8, 32, 16, 8, 8, 8, 8, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 8, 8, 32, 16, 16, 8, 8, 8, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 8, 8, 32, 24, 8, 8, 8, 8, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 8, 8, 32, 32, 8, 8, 8, 8, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 8, 8, 32, 40, 8, 8, 8, 8, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 8, 8, 32, 48, 8, 8, 8, 8, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 8, 8, 32, 56, 8, 8, 8, 8, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 8, 8, 40, 16, 8, 8, 8, 8, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 8, 8, 40, 24, 8, 8, 8, 8, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 8, 8, 40, 32, 8, 8, 8, 8, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 8, 8, 40, 40, 8, 8, 8, 8, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 8, 8, 40, 48, 8, 8, 8, 8, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 8, 8, 48, 16, 8, 8, 8, 8, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 8, 8, 48, 24, 8, 8, 8, 8, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 8, 8, 48, 32, 8, 8, 8, 8, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
diff --git a/source/module_hamilt_lcao/module_gint/kernels/cuda/code_gen_05.cu b/source/module_hamilt_lcao/module_gint/kernels/cuda/code_gen_05.cu
new file mode 100644
index 0000000000..c9cb81bd7c
--- /dev/null
+++ b/source/module_hamilt_lcao/module_gint/kernels/cuda/code_gen_05.cu
@@ -0,0 +1,48 @@
+#include "vbatch_matrix_mul.cuh"
+
+template void gemm_time_measure<double, 8, 8, 48, 40, 8, 8, 8, 8, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 8, 8, 56, 16, 8, 8, 8, 8, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 8, 8, 56, 24, 8, 8, 8, 8, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 8, 8, 56, 32, 8, 8, 8, 8, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 8, 8, 64, 16, 8, 8, 8, 8, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 8, 8, 64, 24, 8, 8, 8, 8, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 8, 12, 24, 24, 8, 8, 12, 8, 12>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 8, 12, 24, 24, 16, 8, 12, 8, 12>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 8, 12, 24, 36, 8, 8, 12, 8, 12>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 8, 12, 24, 36, 16, 8, 12, 8, 12>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 8, 12, 24, 48, 8, 8, 12, 8, 12>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 8, 12, 24, 60, 8, 8, 12, 8, 12>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 8, 12, 48, 24, 8, 8, 12, 8, 12>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 8, 12, 48, 36, 8, 8, 12, 8, 12>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 8, 12, 48, 48, 8, 8, 12, 8, 12>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 8, 12, 48, 60, 8, 8, 12, 8, 12>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 8, 16, 16, 48, 8, 8, 16, 8, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 8, 16, 16, 48, 16, 8, 16, 8, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 8, 16, 16, 48, 24, 8, 16, 8, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 8, 16, 16, 64, 8, 8, 16, 8, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 8, 16, 16, 64, 16, 8, 16, 8, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 8, 16, 32, 32, 8, 8, 16, 8, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 8, 16, 32, 32, 16, 8, 16, 8, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
diff --git a/source/module_hamilt_lcao/module_gint/kernels/cuda/code_gen_06.cu b/source/module_hamilt_lcao/module_gint/kernels/cuda/code_gen_06.cu
new file mode 100644
index 0000000000..f5fac39df2
--- /dev/null
+++ b/source/module_hamilt_lcao/module_gint/kernels/cuda/code_gen_06.cu
@@ -0,0 +1,48 @@
+#include "vbatch_matrix_mul.cuh"
+
+template void gemm_time_measure<double, 8, 16, 32, 32, 24, 8, 16, 8, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 8, 16, 32, 48, 8, 8, 16, 8, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 8, 16, 32, 48, 16, 8, 16, 8, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 8, 16, 32, 64, 8, 8, 16, 8, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 8, 16, 32, 64, 16, 8, 16, 8, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 8, 16, 48, 32, 8, 8, 16, 8, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 8, 16, 48, 32, 16, 8, 16, 8, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 8, 16, 48, 48, 8, 8, 16, 8, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 8, 16, 48, 48, 16, 8, 16, 8, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 8, 16, 48, 64, 8, 8, 16, 8, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 8, 16, 64, 32, 8, 8, 16, 8, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 8, 16, 64, 32, 16, 8, 16, 8, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 8, 16, 64, 48, 8, 8, 16, 8, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 8, 20, 40, 40, 8, 8, 20, 8, 20>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 8, 20, 40, 40, 16, 8, 20, 8, 20>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 8, 20, 40, 60, 8, 8, 20, 8, 20>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 8, 24, 24, 48, 8, 8, 24, 8, 24>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 8, 24, 24, 48, 16, 8, 24, 8, 24>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 8, 24, 24, 48, 24, 8, 24, 8, 24>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 8, 24, 48, 48, 8, 8, 24, 8, 24>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 8, 24, 48, 48, 16, 8, 24, 8, 24>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 8, 28, 56, 56, 8, 8, 28, 8, 28>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 8, 28, 56, 56, 16, 8, 28, 8, 28>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
diff --git a/source/module_hamilt_lcao/module_gint/kernels/cuda/code_gen_07.cu b/source/module_hamilt_lcao/module_gint/kernels/cuda/code_gen_07.cu
new file mode 100644
index 0000000000..971c6eb0c0
--- /dev/null
+++ b/source/module_hamilt_lcao/module_gint/kernels/cuda/code_gen_07.cu
@@ -0,0 +1,48 @@
+#include "vbatch_matrix_mul.cuh"
+
+template void gemm_time_measure<double, 8, 32, 32, 64, 8, 8, 32, 8, 32>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 8, 32, 32, 64, 16, 8, 32, 8, 32>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 8, 32, 32, 64, 24, 8, 32, 8, 32>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 8, 32, 32, 64, 32, 8, 32, 8, 32>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 8, 32, 64, 64, 8, 8, 32, 8, 32>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 8, 32, 64, 64, 16, 8, 32, 8, 32>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 8, 32, 64, 64, 24, 8, 32, 8, 32>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 12, 8, 24, 24, 12, 12, 8, 12, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 12, 8, 24, 32, 12, 12, 8, 12, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 12, 8, 24, 40, 12, 12, 8, 12, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 12, 8, 24, 48, 12, 12, 8, 12, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 12, 8, 24, 56, 12, 12, 8, 12, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 12, 8, 48, 16, 12, 12, 8, 12, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 12, 8, 48, 24, 12, 12, 8, 12, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 12, 8, 48, 32, 12, 12, 8, 12, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 12, 16, 48, 32, 12, 12, 16, 12, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 12, 16, 48, 32, 24, 12, 16, 12, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 12, 16, 48, 48, 12, 12, 16, 12, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 12, 16, 48, 64, 12, 12, 16, 12, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 12, 24, 48, 48, 12, 12, 24, 12, 24>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 12, 24, 48, 48, 24, 12, 24, 12, 24>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 16, 4, 32, 12, 16, 16, 4, 16, 4>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 16, 4, 32, 16, 16, 16, 4, 16, 4>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
diff --git a/source/module_hamilt_lcao/module_gint/kernels/cuda/code_gen_08.cu b/source/module_hamilt_lcao/module_gint/kernels/cuda/code_gen_08.cu
new file mode 100644
index 0000000000..8643faae70
--- /dev/null
+++ b/source/module_hamilt_lcao/module_gint/kernels/cuda/code_gen_08.cu
@@ -0,0 +1,48 @@
+#include "vbatch_matrix_mul.cuh"
+
+template void gemm_time_measure<double, 16, 6, 48, 12, 16, 16, 6, 16, 6>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 16, 8, 32, 24, 16, 16, 8, 16, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 16, 8, 32, 32, 16, 16, 8, 16, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 16, 8, 32, 40, 16, 16, 8, 16, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 16, 8, 32, 48, 16, 16, 8, 16, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 16, 8, 32, 56, 16, 16, 8, 16, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 16, 8, 32, 64, 16, 16, 8, 16, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 16, 8, 48, 16, 16, 16, 8, 16, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 16, 8, 48, 24, 16, 16, 8, 16, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 16, 8, 48, 32, 16, 16, 8, 16, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 16, 8, 48, 40, 16, 16, 8, 16, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 16, 8, 48, 48, 16, 16, 8, 16, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 16, 8, 64, 16, 16, 16, 8, 16, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 16, 8, 64, 24, 16, 16, 8, 16, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 16, 8, 64, 32, 16, 16, 8, 16, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 16, 12, 48, 24, 16, 16, 12, 16, 12>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 16, 12, 48, 36, 16, 16, 12, 16, 12>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 16, 12, 48, 48, 16, 16, 12, 16, 12>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 16, 12, 48, 60, 16, 16, 12, 16, 12>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 16, 16, 32, 48, 16, 16, 16, 16, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 16, 16, 32, 48, 32, 16, 16, 16, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 16, 16, 32, 64, 16, 16, 16, 16, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 16, 16, 32, 64, 32, 16, 16, 16, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
diff --git a/source/module_hamilt_lcao/module_gint/kernels/cuda/code_gen_09.cu b/source/module_hamilt_lcao/module_gint/kernels/cuda/code_gen_09.cu
new file mode 100644
index 0000000000..8cf333bf6f
--- /dev/null
+++ b/source/module_hamilt_lcao/module_gint/kernels/cuda/code_gen_09.cu
@@ -0,0 +1,53 @@
+#include "vbatch_matrix_mul.cuh"
+
+template void gemm_time_measure<double, 16, 16, 48, 32, 16, 16, 16, 16, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 16, 16, 48, 32, 32, 16, 16, 16, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 16, 16, 48, 48, 16, 16, 16, 16, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 16, 16, 48, 48, 32, 16, 16, 16, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 16, 16, 48, 64, 16, 16, 16, 16, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 16, 16, 64, 32, 16, 16, 16, 16, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 16, 16, 64, 32, 32, 16, 16, 16, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 16, 16, 64, 48, 16, 16, 16, 16, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 16, 16, 64, 64, 16, 16, 16, 16, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 16, 24, 48, 48, 16, 16, 24, 16, 24>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 16, 24, 48, 48, 32, 16, 24, 16, 24>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 16, 32, 64, 64, 16, 16, 32, 16, 32>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 16, 32, 64, 64, 32, 16, 32, 16, 32>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 20, 8, 40, 24, 20, 20, 8, 20, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 20, 8, 40, 32, 20, 20, 8, 20, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 24, 8, 48, 24, 24, 24, 8, 24, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 24, 8, 48, 32, 24, 24, 8, 24, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 24, 12, 48, 36, 24, 24, 12, 24, 12>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 24, 12, 48, 48, 24, 24, 12, 24, 12>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 24, 12, 48, 60, 24, 24, 12, 24, 12>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 24, 16, 48, 48, 24, 24, 16, 24, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 24, 16, 48, 64, 24, 24, 16, 24, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 32, 8, 64, 24, 32, 32, 8, 32, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 32, 8, 64, 32, 32, 32, 8, 32, 8>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 32, 16, 64, 48, 32, 32, 16, 32, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
+
+template void gemm_time_measure<double, 32, 16, 64, 64, 32, 32, 16, 32, 16>(int,int,int*,int*,int*,double**,int*,double**,int*,double**,int*,int,cudaStream_t,float&,matrix_multiple_func_type&,double*,double*,double*);
\ No newline at end of file
diff --git a/source/module_hamilt_lcao/module_gint/kernels/cuda/gemm_selector.cu b/source/module_hamilt_lcao/module_gint/kernels/cuda/gemm_selector.cu
new file mode 100644
index 0000000000..cfad7440f3
--- /dev/null
+++ b/source/module_hamilt_lcao/module_gint/kernels/cuda/gemm_selector.cu
@@ -0,0 +1,138 @@
+#include <iostream>
+
+#include "gemm_selector.cuh"
+#include "vbatch_matrix_mul.cuh"
+#include "cuda_tools.cuh"
+#include "module_base/blas_connector.h"
+#include "code_gen.cuh"
+
+/*
+ * Here we have utilized a very straightforward and brute-force method to select
+ * the optimal matrix multiplication kernel for a given scale of computation: we
+ * compute with all scales of kernels under the current computational task to
+ * find the fastest parameter combination. This approach can lead to an increase
+ * in compilation time.
+ */
+void gemm_algo_selector(int matrix_k, matrix_multiple_func_type& fastest_algo,const UnitCell& ucell)
+{
+    int batchCount_per_type = 32;
+    int batchCount
+        = batchCount_per_type * ucell.ntype * ucell.ntype;
+
+    Cuda_Mem_Wrapper<int> m(batchCount);
+    Cuda_Mem_Wrapper<int> n(batchCount);
+    Cuda_Mem_Wrapper<int> k(batchCount);
+
+    int max_m = ucell.nwmax, max_n = ucell.nwmax;
+
+    Cuda_Mem_Wrapper<double> A(batchCount * max_m * matrix_k);
+    Cuda_Mem_Wrapper<double> B(batchCount * max_n * matrix_k);
+    Cuda_Mem_Wrapper<double> C(batchCount * max_m * max_n);
+
+    Cuda_Mem_Wrapper<int> lda(batchCount);
+    Cuda_Mem_Wrapper<int> ldb(batchCount);
+    Cuda_Mem_Wrapper<int> ldc(batchCount);
+
+    Cuda_Mem_Wrapper<double*> A_array(batchCount);
+    Cuda_Mem_Wrapper<double*> B_array(batchCount);
+    Cuda_Mem_Wrapper<double*> C_array(batchCount);
+
+    for (int i = 0; i < batchCount * max_m * matrix_k; ++i)
+    {
+        A.get_host_pointer()[i] = i * 0.001;
+    }
+    for (int i = 0; i < batchCount * max_n * matrix_k; ++i)
+    {
+        B.get_host_pointer()[i] = i * 0.002;
+    }
+
+    double* cpu_result = new double[batchCount * max_m * max_n];
+    memset(cpu_result, 0, batchCount * max_m * max_n * sizeof(double));
+    int index = 0;
+    for (int i = 0; i < batchCount_per_type; ++i)
+    {
+        for (int j = 0; j < ucell.ntype; j++)
+        {
+            for (int l = 0; l < ucell.ntype; l++)
+            {
+                m.get_host_pointer()[index] = ucell.atoms[j].nw;
+                n.get_host_pointer()[index] = ucell.atoms[l].nw;
+                k.get_host_pointer()[index] = matrix_k;
+
+                lda.get_host_pointer()[index] = matrix_k;
+                ldb.get_host_pointer()[index] = matrix_k;
+                ldc.get_host_pointer()[index] = ucell.atoms[l].nw;
+
+                A_array.get_host_pointer()[index]
+                    = &A.get_device_pointer()[index * max_m * matrix_k];
+                B_array.get_host_pointer()[index]
+                    = &B.get_device_pointer()[index * max_n * matrix_k];
+                C_array.get_host_pointer()[index]
+                    = &C.get_device_pointer()[index * max_n
+                                              * max_m]; // test atom add
+                BlasConnector::gemm(
+                    'N',
+                    'T',
+                    m.get_host_pointer()[index],
+                    n.get_host_pointer()[index],
+                    matrix_k,
+                    1.0,
+                    &A.get_host_pointer()[index * max_m * matrix_k],
+                    matrix_k,
+                    &B.get_host_pointer()[index * max_n * matrix_k],
+                    matrix_k,
+                    1.0,
+                    &cpu_result[index * max_m * max_n],
+                    n.get_host_pointer()[index]);
+                index++;
+            }
+        }
+    }
+
+    m.copy_host_to_device_sync();
+    n.copy_host_to_device_sync();
+    k.copy_host_to_device_sync();
+
+    lda.copy_host_to_device_sync();
+    ldb.copy_host_to_device_sync();
+    ldc.copy_host_to_device_sync();
+
+    A.copy_host_to_device_sync();
+    B.copy_host_to_device_sync();
+    A_array.copy_host_to_device_sync();
+    B_array.copy_host_to_device_sync();
+    C_array.copy_host_to_device_sync();
+
+    cudaStream_t temp_stream;
+    checkCuda(cudaStreamCreate(&temp_stream));
+
+    float fastest_time = 1000000;
+    fastest_algo = vbatched_gemm_impl<double, 16, 4, 32, 16, 16, 16, 4, 16, 4>;
+
+    int* d_m = m.get_device_pointer();
+    int* d_n = n.get_device_pointer();
+    int* d_k = k.get_device_pointer();
+
+    double** d_global_A_array = A_array.get_device_pointer();
+    double** d_global_B_array = B_array.get_device_pointer();
+    double** d_global_C_array = C_array.get_device_pointer();
+
+    double* h_global_C = C.get_host_pointer();
+    double* d_global_C = C.get_device_pointer();
+
+    int* d_global_lda = lda.get_device_pointer();
+    int* d_global_ldb = ldb.get_device_pointer();
+    int* d_global_ldc = ldc.get_device_pointer();
+
+/*
+ * Please do not manually modify the code in the following file;
+ * it should simply be generated through a loop using a short Python program.
+ */
+#include "code_gen.cpp"
+    checkCuda(cudaStreamDestroy(temp_stream));
+    std::cout << " gemm_algo_selector::Fastest time: " << fastest_time << " ms"
+              << std::endl;
+    // fastest_algo = vbatched_gemm_impl<double, 16, 4, 32, 16, 16, 16, 4, 16,
+    // 4>;
+    delete[] cpu_result;
+}
\ No newline at end of file
diff --git a/source/module_hamilt_lcao/module_gint/kernels/cuda/gemm_selector.cuh b/source/module_hamilt_lcao/module_gint/kernels/cuda/gemm_selector.cuh
new file mode 100644
index 0000000000..380a16c842
--- /dev/null
+++ b/source/module_hamilt_lcao/module_gint/kernels/cuda/gemm_selector.cuh
@@ -0,0 +1,24 @@
+#ifndef GEMM_SELECTOR_H
+#define GEMM_SELECTOR_H
+
+#include "module_cell/unitcell.h"
+
+typedef std::function<void(int,
+                           int,
+                           int*,
+                           int*,
+                           int*,
+                           double**,
+                           int*,
+                           double**,
+                           int*,
+                           double**,
+                           int*,
+                           int,
+                           cudaStream_t,
+                           double* alpha)>
+matrix_multiple_func_type;
+
+void gemm_algo_selector(int k, matrix_multiple_func_type& func,const UnitCell& ucell);
+
+#endif
\ No newline at end of file
diff --git a/source/module_hamilt_lcao/module_gint/kernels/cuda/vbatch_matrix_mul.cu b/source/module_hamilt_lcao/module_gint/kernels/cuda/vbatch_matrix_mul.cu
deleted file mode 100644
index b84b76a840..0000000000
--- a/source/module_hamilt_lcao/module_gint/kernels/cuda/vbatch_matrix_mul.cu
+++ /dev/null
@@ -1,659 +0,0 @@
-#include <functional>
-
-#include "cuda_tools.cuh"
-#include "module_base/blas_connector.h"
-#include "module_hamilt_pw/hamilt_pwdft/global.h"
-#include "vbatch_matrix_mul.cuh"
-
-#define sA(i, j) sA[(j)*slda + (i)]
-#define sB(i, j) sB[(j)*sldb + (i)]
-#define fetch(A, m, n, bound) offs_d##A[min(n * LD##A + m, bound)]
-
-template <typename T,
-          int DIM_X,
-          int DIM_Y,
-          int BLK_M,
-          int BLK_N,
-          int BLK_K,
-          int DIM_XA,
-          int DIM_YA,
-          int DIM_XB,
-          int DIM_YB,
-          int THR_M,
-          int THR_N>
-static __device__ void vbatched_gemm_device(int M,
-                                            int N,
-                                            int K,
-                                            T* __restrict__ A,
-                                            int LDA,
-                                            T* __restrict__ B,
-                                            int LDB,
-                                            T* __restrict__ C,
-                                            int LDC,
-                                            T* sA,
-                                            int slda,
-                                            T* sB,
-                                            int sldb,
-                                            T alpha)
-{
-    int idx = threadIdx.x; // thread's m dimension
-    int idy = threadIdx.y; // thread's n dimension
-
-    int idt = DIM_X * idy + idx; // thread's global number
-
-    int idxA = idt % DIM_XA; // idx within A
-    int idyA = idt / DIM_XA; // idy within A
-
-    int idxB = idt % DIM_XB; // idx within B
-    int idyB = idt / DIM_XB; // idy within B
-
-    int blx = blockIdx.x; // block's m dimension
-    int bly = blockIdx.y; // block's n dimension
-
-    // Registers for the innermost loop
-    T rC[THR_N][THR_M];
-    T rA[THR_M];
-    T rB[THR_N];
-
-    // Registers for the dev->shmem copy
-    T ra[BLK_M / DIM_YA][BLK_K / DIM_XA];
-    T rb[BLK_N / DIM_YB][BLK_K / DIM_XB];
-
-    // bound is the correction to offs_d in order to not get out of memory bound
-    // so bound could be negative value since offs_d could be out of bound
-    T* offs_dA = A + blx * BLK_M * LDA + idyA * LDA + idxA;
-    int boundA
-        = (LDA * (M - 1) + K) - (blx * BLK_M * LDA + idyA * LDA + idxA) - 1;
-
-    T* offs_dB = B + bly * BLK_N * LDB + idyB * LDB + idxB;
-    int boundB
-        = (LDB * (N - 1) + K) - (bly * BLK_N * LDB + idyB * LDB + idxB) - 1;
-
-    int m, n, k, kk;
-
-// Zero C
-#pragma unroll
-    for (n = 0; n < THR_N; n++)
-    {
-#pragma unroll
-        for (m = 0; m < THR_M; m++)
-        {
-            rC[n][m] = 0.0;
-        }
-    }
-
-// Load A dev->shmem
-#pragma unroll
-    for (n = 0; n < BLK_M; n += DIM_YA)
-    {
-#pragma unroll
-        for (m = 0; m < BLK_K; m += DIM_XA)
-        {
-            sA(n + idyA, m + idxA) = fetch(A, m, n, boundA);
-        }
-    }
-
-#pragma unroll
-    for (n = 0; n < BLK_N; n += DIM_YB)
-    {
-#pragma unroll
-        for (m = 0; m < BLK_K; m += DIM_XB)
-        {
-            sB(m + idxB, n + idyB) = fetch(B, m, n, boundB);
-        }
-    }
-
-    __syncthreads();
-
-    for (kk = 0; kk < K - BLK_K; kk += BLK_K)
-    {
-        offs_dA += BLK_K;
-        boundA -= BLK_K;
-
-        offs_dB += BLK_K;
-        boundB -= BLK_K;
-
-// Load A dev->regs
-#pragma unroll
-        for (n = 0; n < BLK_M / DIM_YA; n++)
-        {
-#pragma unroll
-            for (m = 0; m < BLK_K / DIM_XA; m++)
-            {
-                ra[n][m] = fetch(A, m * DIM_XA, n * DIM_YA, boundA);
-            }
-        }
-
-// Load B dev->regs
-#pragma unroll
-        for (n = 0; n < BLK_N / DIM_YB; n++)
-        {
-#pragma unroll
-            for (m = 0; m < BLK_K / DIM_XB; m++)
-            {
-                rb[n][m] = fetch(B, m * DIM_XB, n * DIM_YB, boundB);
-            }
-        }
-
-// Multiply
-#pragma unroll
-        for (k = 0; k < BLK_K; k++)
-        {
-// Load A shmem->regs
-#pragma unroll
-            for (m = 0; m < THR_M; m++)
-            {
-                rA[m] = sA(m * DIM_X + idx, k);
-            }
-
-// Load B shmem->regs
-#pragma unroll
-            for (n = 0; n < THR_N; n++)
-            {
-                rB[n] = sB(k, n * DIM_Y + idy);
-            }
-
-// Compute
-#pragma unroll
-            for (n = 0; n < THR_N; n++)
-            {
-#pragma unroll
-                for (m = 0; m < THR_M; m++)
-                {
-                    rC[n][m] += rA[m] * rB[n];
-                }
-            }
-        }
-
-        __syncthreads();
-
-// Load A regs->shmem
-#pragma unroll
-        for (n = 0; n < BLK_M / DIM_YA; n++)
-        {
-#pragma unroll
-            for (m = 0; m < BLK_K / DIM_XA; m++)
-            {
-                sA(n * DIM_YA + idyA, m * DIM_XA + idxA) = ra[n][m];
-            }
-        }
-
-// Load B regs->shmem
-#pragma unroll
-        for (n = 0; n < BLK_N / DIM_YB; n++)
-        {
-#pragma unroll
-            for (m = 0; m < BLK_K / DIM_XB; m++)
-            {
-                sB(m * DIM_XB + idxB, n * DIM_YB + idyB) = rb[n][m];
-            }
-        }
-        __syncthreads();
-    }
-
-    // Multiply last full (BLK_K) or partial block of
-    // columns of op(A) and rows of op(B).
-    // It's okay that m,n exceed matrix bounds as all work is in registers
-    // or shared memory, and out-of-bounds rC[n][m] will not be saved later.
-    kk = K - kk;
-#pragma unroll
-    for (k = 0; k < kk; k++)
-    {
-// Load A shmem->regs
-#pragma unroll
-        for (m = 0; m < THR_M; m++)
-        {
-            rA[m] = sA(m * DIM_X + idx, k);
-        }
-
-// Load B shmem->regs
-#pragma unroll
-        for (n = 0; n < THR_N; n++)
-        {
-            rB[n] = sB(k, n * DIM_Y + idy);
-        }
-
-// Compute
-#pragma unroll
-        for (n = 0; n < THR_N; n++)
-        {
-#pragma unroll
-            for (m = 0; m < THR_M; m++)
-            {
-                rC[n][m] += rA[m] * rB[n];
-            }
-        }
-    }
-
-// Store C regs->dev
-#pragma unroll
-    for (n = 0; n < THR_N; n++)
-    {
-        int coord_dCn = bly * BLK_N + n * DIM_Y + idy;
-#pragma unroll
-        for (m = 0; m < THR_M; m++)
-        {
-            int coord_dCm = blx * BLK_M + m * DIM_X + idx;
-            if (coord_dCm < M && coord_dCn < N)
-            {
-                int offsC = coord_dCn * LDC + coord_dCm;
-
-                atomicAdd(C + offsC, rC[n][m] * alpha);
-            }
-        }
-    }
-}
-
-/******************************************************************************/
-template <typename T,
-          int DIM_X,
-          int DIM_Y,
-          int BLK_M,
-          int BLK_N,
-          int BLK_K,
-          int DIM_XA,
-          int DIM_YA,
-          int DIM_XB,
-          int DIM_YB>
-static __global__ void vbatched_gemm_kernel(int* M,
-                                            int* N,
-                                            int* K,
-                                            T** global_A_array,
-                                            int* global_lda,
-                                            T** global_B_array,
-                                            int* global_ldb,
-                                            T** global_C_array,
-                                            int* global_ldc,
-                                            T* alpha)
-{
-    extern __shared__ __align__(sizeof(T)) unsigned char smem[];
-    T* shared_mem = reinterpret_cast<T*>(smem);
-
-    int batchid = blockIdx.z;
-    int local_M = (int)M[batchid];
-    int local_N = (int)N[batchid];
-    int local_K = (int)K[batchid];
-
-    if (blockIdx.x >= (local_M + BLK_M - 1) / BLK_M)
-        return;
-    if (blockIdx.y >= (local_N + BLK_N - 1) / BLK_N)
-        return;
-
-    int shared_lda = BLK_M + 1;
-    int shared_ldb = BLK_K + 1;
-    T* shared_A = (T*)shared_mem;
-    T* shared_B = shared_A + shared_lda * BLK_K;
-    double alpha_tmp = 1.0;
-    if (alpha != nullptr)
-    {
-        alpha_tmp = alpha[batchid];
-    }
-    vbatched_gemm_device<T,
-                         DIM_X,
-                         DIM_Y,
-                         BLK_M,
-                         BLK_N,
-                         BLK_K,
-                         DIM_XA,
-                         DIM_YA,
-                         DIM_XB,
-                         DIM_YB,
-                         (BLK_M / DIM_X),
-                         (BLK_N / DIM_Y)>(local_M,
-                                          local_N,
-                                          local_K,
-                                          global_A_array[batchid],
-                                          (int)global_lda[batchid],
-                                          global_B_array[batchid],
-                                          (int)global_ldb[batchid],
-                                          global_C_array[batchid],
-                                          (int)global_ldc[batchid],
-                                          shared_A,
-                                          shared_lda,
-                                          shared_B,
-                                          shared_ldb,
-                                          alpha_tmp);
-}
-
-static inline int ceildiv(int x, int y)
-{
-    return (x + y - 1) / y;
-}
-
-template <typename T,
-          int DIM_X,
-          int DIM_Y,
-          int BLK_M,
-          int BLK_N,
-          int BLK_K,
-          int DIM_XA,
-          int DIM_YA,
-          int DIM_XB,
-          int DIM_YB>
-void vbatched_gemm_impl(int max_m,
-                        int max_n,
-                        int* m,
-                        int* n,
-                        int* k,
-                        T** global_A_array,
-                        int* global_lda,
-                        T** global_B_array,
-                        int* global_ldb,
-                        T** global_C_array,
-                        int* global_ldc,
-                        int batchCount,
-                        cudaStream_t stream,
-                        T* alpha)
-{
-    // The positions of A and B have been swapped here.
-    // This is because the original code is for column-major matrices.
-    // We use row-major matrices, so we need to swap A and B.
-    // The vbatched_gemm_impl is for C = trans(A) * B + C, but we need trans(C).
-    // Which means: trans(C) = trans(trans(A)*B + C) = trans(B) * A + trans(C)
-    // Then, ldc should be N, lda and ldb should be K
-
-    size_t shared_mem_size = 0;
-    shared_mem_size += (BLK_M + 1) * BLK_K * sizeof(T);
-    shared_mem_size += (BLK_K + 1) * BLK_N * sizeof(T);
-    dim3 dimBlock(DIM_X, DIM_Y);
-    const int max_batch_count = 32768;
-    const int loop_num = batchCount / max_batch_count;
-    const int remain_num = batchCount % max_batch_count;
-
-    for (int i = 0; i < loop_num; ++i)
-    {
-        dim3 dimGrid(ceildiv(max_n, BLK_M),
-                     ceildiv(max_m, BLK_N),
-                     max_batch_count);
-        T* alpha_tmp = nullptr;
-        if (alpha != nullptr)
-        {
-            alpha_tmp = alpha + i * max_batch_count;
-        }
-
-        vbatched_gemm_kernel<T,
-                             DIM_X,
-                             DIM_Y,
-                             BLK_M,
-                             BLK_N,
-                             BLK_K,
-                             DIM_XA,
-                             DIM_YA,
-                             DIM_XB,
-                             DIM_YB>
-            <<<dimGrid, dimBlock, shared_mem_size, stream>>>(
-                n + i * max_batch_count,
-                m + i * max_batch_count,
-                k + i * max_batch_count,
-                global_B_array + i * max_batch_count,
-                global_ldb + i * max_batch_count,
-                global_A_array + i * max_batch_count,
-                global_lda + i * max_batch_count,
-                global_C_array + i * max_batch_count,
-                global_ldc + i * max_batch_count,
-                alpha_tmp);
-        checkCudaLastError();
-    }
-    if (remain_num > 0)
-    {
-        dim3 dimGrid(ceildiv(max_n, BLK_M), ceildiv(max_m, BLK_N), remain_num);
-        T* alpha_tmp = nullptr;
-        if (alpha != nullptr)
-        {
-            alpha_tmp = alpha + loop_num * max_batch_count;
-        }
-        vbatched_gemm_kernel<T,
-                             DIM_X,
-                             DIM_Y,
-                             BLK_M,
-                             BLK_N,
-                             BLK_K,
-                             DIM_XA,
-                             DIM_YA,
-                             DIM_XB,
-                             DIM_YB>
-            <<<dimGrid, dimBlock, shared_mem_size, stream>>>(
-                n + loop_num * max_batch_count,
-                m + loop_num * max_batch_count,
-                k + loop_num * max_batch_count,
-                global_B_array + loop_num * max_batch_count,
-                global_ldb + loop_num * max_batch_count,
-                global_A_array + loop_num * max_batch_count,
-                global_lda + loop_num * max_batch_count,
-                global_C_array + loop_num * max_batch_count,
-                global_ldc + loop_num * max_batch_count,
-                alpha_tmp);
-        checkCudaLastError();
-    }
-}
-
-template <typename T,
-          int DIM_X,
-          int DIM_Y,
-          int BLK_M,
-          int BLK_N,
-          int BLK_K,
-          int DIM_XA,
-          int DIM_YA,
-          int DIM_XB,
-          int DIM_YB>
-void gemm_time_measure(int max_m,
-                       int max_n,
-                       int* m,
-                       int* n,
-                       int* k,
-                       T** global_A_array,
-                       int* global_lda,
-                       T** global_B_array,
-                       int* global_ldb,
-                       T** global_C_array,
-                       int* global_ldc,
-                       int batchCount,
-                       cudaStream_t stream,
-                       float& fast_time,
-                       matrix_multiple_func_type& fastest_algo,
-                       double* cpu_result,
-                       double* h_global_C,
-                       double* d_global_C)
-{
-    cudaEvent_t start, stop;
-    checkCuda(
-        cudaMemset(d_global_C, 0, batchCount * max_m * max_n * sizeof(double)));
-    checkCuda(cudaEventCreate(&start));
-    checkCuda(cudaEventCreate(&stop));
-    checkCuda(cudaEventRecord(start, stream));
-    vbatched_gemm_impl<T,
-                       DIM_X,
-                       DIM_Y,
-                       BLK_M,
-                       BLK_N,
-                       BLK_K,
-                       DIM_XA,
-                       DIM_YA,
-                       DIM_XB,
-                       DIM_YB>(max_m,
-                               max_n,
-                               m,
-                               n,
-                               k,
-                               global_A_array,
-                               global_lda,
-                               global_B_array,
-                               global_ldb,
-                               global_C_array,
-                               global_ldc,
-                               batchCount,
-                               stream);
-    checkCuda(cudaEventRecord(stop, stream));
-    cudaError_t cuda_status = cudaGetLastError();
-    checkCuda(cudaStreamSynchronize(stream));
-    float milliseconds = 0;
-    checkCuda(cudaEventElapsedTime(&milliseconds, start, stop));
-
-    // WARNING !!!!! Here we assume that all m and n are the same
-    checkCuda(cudaMemcpy(h_global_C,
-                         d_global_C,
-                         batchCount * max_m * max_n * sizeof(double),
-                         cudaMemcpyDeviceToHost));
-    bool check_result = true;
-    for (int i = 0; i < batchCount * max_m * max_n; ++i)
-    {
-        if (abs(cpu_result[i] - h_global_C[i]) > 0.001)
-        {
-            check_result = false;
-            break;
-        }
-    }
-    if (milliseconds < fast_time && cuda_status == cudaSuccess && check_result)
-    {
-        fast_time = milliseconds;
-        fastest_algo = vbatched_gemm_impl<T,
-                                          DIM_X,
-                                          DIM_Y,
-                                          BLK_M,
-                                          BLK_N,
-                                          BLK_K,
-                                          DIM_XA,
-                                          DIM_YA,
-                                          DIM_XB,
-                                          DIM_YB>;
-#ifdef __DEBUG
-        std::cout << "found! fastest time: " << fast_time << std::endl;
-        std::cout << DIM_X << "," << DIM_Y << "," << BLK_M << "," << BLK_N
-                  << "," << BLK_K << "," << DIM_XA << "," << DIM_YA << ","
-                  << DIM_XB << "," << DIM_YB << std::endl;
-#endif
-    }
-}
-
-/*
- * Here we have utilized a very straightforward and brute-force method to select
- * the optimal matrix multiplication kernel for a given scale of computation: we
- * compute with all scales of kernels under the current computational task to
- * find the fastest parameter combination. This approach can lead to an increase
- * in compilation time (TODO: so in the future, it will be necessary to split
- * this large section of code into multiple files, multiple compilation units).
- */
-void gemm_algo_selector(int matrix_k, matrix_multiple_func_type& fastest_algo,const UnitCell& ucell)
-{
-    int batchCount_per_type = 32;
-    int batchCount
-        = batchCount_per_type * ucell.ntype * ucell.ntype;
-
-    Cuda_Mem_Wrapper<int> m(batchCount);
-    Cuda_Mem_Wrapper<int> n(batchCount);
-    Cuda_Mem_Wrapper<int> k(batchCount);
-
-    int max_m = ucell.nwmax, max_n = ucell.nwmax;
-
-    Cuda_Mem_Wrapper<double> A(batchCount * max_m * matrix_k);
-    Cuda_Mem_Wrapper<double> B(batchCount * max_n * matrix_k);
-    Cuda_Mem_Wrapper<double> C(batchCount * max_m * max_n);
-
-    Cuda_Mem_Wrapper<int> lda(batchCount);
-    Cuda_Mem_Wrapper<int> ldb(batchCount);
-    Cuda_Mem_Wrapper<int> ldc(batchCount);
-
-    Cuda_Mem_Wrapper<double*> A_array(batchCount);
-    Cuda_Mem_Wrapper<double*> B_array(batchCount);
-    Cuda_Mem_Wrapper<double*> C_array(batchCount);
-
-    for (int i = 0; i < batchCount * max_m * matrix_k; ++i)
-    {
-        A.get_host_pointer()[i] = i * 0.001;
-    }
-    for (int i = 0; i < batchCount * max_n * matrix_k; ++i)
-    {
-        B.get_host_pointer()[i] = i * 0.002;
-    }
-
-    double* cpu_result = new double[batchCount * max_m * max_n];
-    memset(cpu_result, 0, batchCount * max_m * max_n * sizeof(double));
-    int index = 0;
-    for (int i = 0; i < batchCount_per_type; ++i)
-    {
-        for (int j = 0; j < ucell.ntype; j++)
-        {
-            for (int l = 0; l < ucell.ntype; l++)
-            {
-                m.get_host_pointer()[index] = ucell.atoms[j].nw;
-                n.get_host_pointer()[index] = ucell.atoms[l].nw;
-                k.get_host_pointer()[index] = matrix_k;
-
-                lda.get_host_pointer()[index] = matrix_k;
-                ldb.get_host_pointer()[index] = matrix_k;
-                ldc.get_host_pointer()[index] = ucell.atoms[l].nw;
-
-                A_array.get_host_pointer()[index]
-                    = &A.get_device_pointer()[index * max_m * matrix_k];
-                B_array.get_host_pointer()[index]
-                    = &B.get_device_pointer()[index * max_n * matrix_k];
-                C_array.get_host_pointer()[index]
-                    = &C.get_device_pointer()[index * max_n
-                                              * max_m]; // test atom add
-                BlasConnector::gemm(
-                    'N',
-                    'T',
-                    m.get_host_pointer()[index],
-                    n.get_host_pointer()[index],
-                    matrix_k,
-                    1.0,
-                    &A.get_host_pointer()[index * max_m * matrix_k],
-                    matrix_k,
-                    &B.get_host_pointer()[index * max_n * matrix_k],
-                    matrix_k,
-                    1.0,
-                    &cpu_result[index * max_m * max_n],
-                    n.get_host_pointer()[index]);
-                index++;
-            }
-        }
-    }
-
-    m.copy_host_to_device_sync();
-    n.copy_host_to_device_sync();
-    k.copy_host_to_device_sync();
-
-    lda.copy_host_to_device_sync();
-    ldb.copy_host_to_device_sync();
-    ldc.copy_host_to_device_sync();
-
-    A.copy_host_to_device_sync();
-    B.copy_host_to_device_sync();
-    A_array.copy_host_to_device_sync();
-    B_array.copy_host_to_device_sync();
-    C_array.copy_host_to_device_sync();
-
-    cudaStream_t temp_stream;
-    checkCuda(cudaStreamCreate(&temp_stream));
-
-    float fastest_time = 1000000;
-    fastest_algo = vbatched_gemm_impl<double, 16, 4, 32, 16, 16, 16, 4, 16, 4>;
-
-    int* d_m = m.get_device_pointer();
-    int* d_n = n.get_device_pointer();
-    int* d_k = k.get_device_pointer();
-
-    double** d_global_A_array = A_array.get_device_pointer();
-    double** d_global_B_array = B_array.get_device_pointer();
-    double** d_global_C_array = C_array.get_device_pointer();
-
-    double* h_global_C = C.get_host_pointer();
-    double* d_global_C = C.get_device_pointer();
-
-    int* d_global_lda = lda.get_device_pointer();
-    int* d_global_ldb = ldb.get_device_pointer();
-    int* d_global_ldc = ldc.get_device_pointer();
-
-/*
- * Please do not manually modify the code in the following file;
- * it should simply be generated through a loop using a short Python program.
- */
-#include "code_gen.cpp"
-    checkCuda(cudaStreamDestroy(temp_stream));
-    std::cout << " gemm_algo_selector::Fastest time: " << fastest_time << " ms"
-              << std::endl;
-    // fastest_algo = vbatched_gemm_impl<double, 16, 4, 32, 16, 16, 16, 4, 16,
-    // 4>;
-    delete[] cpu_result;
-}
\ No newline at end of file
diff --git a/source/module_hamilt_lcao/module_gint/kernels/cuda/vbatch_matrix_mul.cuh b/source/module_hamilt_lcao/module_gint/kernels/cuda/vbatch_matrix_mul.cuh
index ea4e42e521..24e8ba91e1 100644
--- a/source/module_hamilt_lcao/module_gint/kernels/cuda/vbatch_matrix_mul.cuh
+++ b/source/module_hamilt_lcao/module_gint/kernels/cuda/vbatch_matrix_mul.cuh
@@ -1,13 +1,333 @@
-#ifndef VBATCH_MATRIX_MUL_H
-#define VBATCH_MATRIX_MUL_H
+#ifndef VBATCH_MATRIX_MUL_CUH
+#define VBATCH_MATRIX_MUL_CUH
 #include <assert.h> // for assert
 #include <cublas_v2.h>
 #include <cuda.h> // for CUDA_VERSION
 #include <cuda_runtime.h>
 #include <stdio.h> // for fprintf and stderr
 
+#include "cuda_tools.cuh"
 #include <functional>
 #include "module_cell/unitcell.h"
+#include "module_hamilt_pw/hamilt_pwdft/global.h"
+#include <module_base/module_device/device.h>
+
+
+#define sA(i, j) sA[(j)*slda + (i)]
+#define sB(i, j) sB[(j)*sldb + (i)]
+#define fetch(A, m, n, bound) offs_d##A[min(n * LD##A + m, bound)]
+
+template <typename T,
+          int DIM_X,
+          int DIM_Y,
+          int BLK_M,
+          int BLK_N,
+          int BLK_K,
+          int DIM_XA,
+          int DIM_YA,
+          int DIM_XB,
+          int DIM_YB,
+          int THR_M,
+          int THR_N>
+static __device__ void vbatched_gemm_device(int M,
+                                            int N,
+                                            int K,
+                                            T* __restrict__ A,
+                                            int LDA,
+                                            T* __restrict__ B,
+                                            int LDB,
+                                            T* __restrict__ C,
+                                            int LDC,
+                                            T* sA,
+                                            int slda,
+                                            T* sB,
+                                            int sldb,
+                                            T alpha)
+{
+    int idx = threadIdx.x; // thread's m dimension
+    int idy = threadIdx.y; // thread's n dimension
+
+    int idt = DIM_X * idy + idx; // thread's global number
+
+    int idxA = idt % DIM_XA; // idx within A
+    int idyA = idt / DIM_XA; // idy within A
+
+    int idxB = idt % DIM_XB; // idx within B
+    int idyB = idt / DIM_XB; // idy within B
+
+    int blx = blockIdx.x; // block's m dimension
+    int bly = blockIdx.y; // block's n dimension
+
+    // Registers for the innermost loop
+    T rC[THR_N][THR_M];
+    T rA[THR_M];
+    T rB[THR_N];
+
+    // Registers for the dev->shmem copy
+    T ra[BLK_M / DIM_YA][BLK_K / DIM_XA];
+    T rb[BLK_N / DIM_YB][BLK_K / DIM_XB];
+
+    // bound is the correction to offs_d in order to not get out of memory bound
+    // so bound could be negative value since offs_d could be out of bound
+    T* offs_dA = A + blx * BLK_M * LDA + idyA * LDA + idxA;
+    int boundA
+        = (LDA * (M - 1) + K) - (blx * BLK_M * LDA + idyA * LDA + idxA) - 1;
+
+    T* offs_dB = B + bly * BLK_N * LDB + idyB * LDB + idxB;
+    int boundB
+        = (LDB * (N - 1) + K) - (bly * BLK_N * LDB + idyB * LDB + idxB) - 1;
+
+    int m, n, k, kk;
+
+// Zero C
+#pragma unroll
+    for (n = 0; n < THR_N; n++)
+    {
+#pragma unroll
+        for (m = 0; m < THR_M; m++)
+        {
+            rC[n][m] = 0.0;
+        }
+    }
+
+// Load A dev->shmem
+#pragma unroll
+    for (n = 0; n < BLK_M; n += DIM_YA)
+    {
+#pragma unroll
+        for (m = 0; m < BLK_K; m += DIM_XA)
+        {
+            sA(n + idyA, m + idxA) = fetch(A, m, n, boundA);
+        }
+    }
+
+#pragma unroll
+    for (n = 0; n < BLK_N; n += DIM_YB)
+    {
+#pragma unroll
+        for (m = 0; m < BLK_K; m += DIM_XB)
+        {
+            sB(m + idxB, n + idyB) = fetch(B, m, n, boundB);
+        }
+    }
+
+    __syncthreads();
+
+    for (kk = 0; kk < K - BLK_K; kk += BLK_K)
+    {
+        offs_dA += BLK_K;
+        boundA -= BLK_K;
+
+        offs_dB += BLK_K;
+        boundB -= BLK_K;
+
+// Load A dev->regs
+#pragma unroll
+        for (n = 0; n < BLK_M / DIM_YA; n++)
+        {
+#pragma unroll
+            for (m = 0; m < BLK_K / DIM_XA; m++)
+            {
+                ra[n][m] = fetch(A, m * DIM_XA, n * DIM_YA, boundA);
+            }
+        }
+
+// Load B dev->regs
+#pragma unroll
+        for (n = 0; n < BLK_N / DIM_YB; n++)
+        {
+#pragma unroll
+            for (m = 0; m < BLK_K / DIM_XB; m++)
+            {
+                rb[n][m] = fetch(B, m * DIM_XB, n * DIM_YB, boundB);
+            }
+        }
+
+// Multiply
+#pragma unroll
+        for (k = 0; k < BLK_K; k++)
+        {
+// Load A shmem->regs
+#pragma unroll
+            for (m = 0; m < THR_M; m++)
+            {
+                rA[m] = sA(m * DIM_X + idx, k);
+            }
+
+// Load B shmem->regs
+#pragma unroll
+            for (n = 0; n < THR_N; n++)
+            {
+                rB[n] = sB(k, n * DIM_Y + idy);
+            }
+
+// Compute
+#pragma unroll
+            for (n = 0; n < THR_N; n++)
+            {
+#pragma unroll
+                for (m = 0; m < THR_M; m++)
+                {
+                    rC[n][m] += rA[m] * rB[n];
+                }
+            }
+        }
+
+        __syncthreads();
+
+// Load A regs->shmem
+#pragma unroll
+        for (n = 0; n < BLK_M / DIM_YA; n++)
+        {
+#pragma unroll
+            for (m = 0; m < BLK_K / DIM_XA; m++)
+            {
+                sA(n * DIM_YA + idyA, m * DIM_XA + idxA) = ra[n][m];
+            }
+        }
+
+// Load B regs->shmem
+#pragma unroll
+        for (n = 0; n < BLK_N / DIM_YB; n++)
+        {
+#pragma unroll
+            for (m = 0; m < BLK_K / DIM_XB; m++)
+            {
+                sB(m * DIM_XB + idxB, n * DIM_YB + idyB) = rb[n][m];
+            }
+        }
+        __syncthreads();
+    }
+
+    // Multiply last full (BLK_K) or partial block of
+    // columns of op(A) and rows of op(B).
+    // It's okay that m,n exceed matrix bounds as all work is in registers
+    // or shared memory, and out-of-bounds rC[n][m] will not be saved later.
+    kk = K - kk;
+#pragma unroll
+    for (k = 0; k < kk; k++)
+    {
+// Load A shmem->regs
+#pragma unroll
+        for (m = 0; m < THR_M; m++)
+        {
+            rA[m] = sA(m * DIM_X + idx, k);
+        }
+
+// Load B shmem->regs
+#pragma unroll
+        for (n = 0; n < THR_N; n++)
+        {
+            rB[n] = sB(k, n * DIM_Y + idy);
+        }
+
+// Compute
+#pragma unroll
+        for (n = 0; n < THR_N; n++)
+        {
+#pragma unroll
+            for (m = 0; m < THR_M; m++)
+            {
+                rC[n][m] += rA[m] * rB[n];
+            }
+        }
+    }
+
+// Store C regs->dev
+#pragma unroll
+    for (n = 0; n < THR_N; n++)
+    {
+        int coord_dCn = bly * BLK_N + n * DIM_Y + idy;
+#pragma unroll
+        for (m = 0; m < THR_M; m++)
+        {
+            int coord_dCm = blx * BLK_M + m * DIM_X + idx;
+            if (coord_dCm < M && coord_dCn < N)
+            {
+                int offsC = coord_dCn * LDC + coord_dCm;
+
+                atomicAdd(C + offsC, rC[n][m] * alpha);
+            }
+        }
+    }
+}
+
+/******************************************************************************/
+template <typename T,
+          int DIM_X,
+          int DIM_Y,
+          int BLK_M,
+          int BLK_N,
+          int BLK_K,
+          int DIM_XA,
+          int DIM_YA,
+          int DIM_XB,
+          int DIM_YB>
+static __global__ void vbatched_gemm_kernel(int* M,
+                                            int* N,
+                                            int* K,
+                                            T** global_A_array,
+                                            int* global_lda,
+                                            T** global_B_array,
+                                            int* global_ldb,
+                                            T** global_C_array,
+                                            int* global_ldc,
+                                            T* alpha)
+{
+    extern __shared__ __align__(sizeof(T)) unsigned char smem[];
+    T* shared_mem = reinterpret_cast<T*>(smem);
+
+    int batchid = blockIdx.z;
+    int local_M = (int)M[batchid];
+    int local_N = (int)N[batchid];
+    int local_K = (int)K[batchid];
+
+    if (blockIdx.x >= (local_M + BLK_M - 1) / BLK_M)
+        return;
+    if (blockIdx.y >= (local_N + BLK_N - 1) / BLK_N)
+        return;
+
+    int shared_lda = BLK_M + 1;
+    int shared_ldb = BLK_K + 1;
+    T* shared_A = (T*)shared_mem;
+    T* shared_B = shared_A + shared_lda * BLK_K;
+    double alpha_tmp = 1.0;
+    if (alpha != nullptr)
+    {
+        alpha_tmp = alpha[batchid];
+    }
+    vbatched_gemm_device<T,
+                         DIM_X,
+                         DIM_Y,
+                         BLK_M,
+                         BLK_N,
+                         BLK_K,
+                         DIM_XA,
+                         DIM_YA,
+                         DIM_XB,
+                         DIM_YB,
+                         (BLK_M / DIM_X),
+                         (BLK_N / DIM_Y)>(local_M,
+                                          local_N,
+                                          local_K,
+                                          global_A_array[batchid],
+                                          (int)global_lda[batchid],
+                                          global_B_array[batchid],
+                                          (int)global_ldb[batchid],
+                                          global_C_array[batchid],
+                                          (int)global_ldc[batchid],
+                                          shared_A,
+                                          shared_lda,
+                                          shared_B,
+                                          shared_ldb,
+                                          alpha_tmp);
+}
+
+static inline int ceildiv(int x, int y)
+{
+    return (x + y - 1) / y;
+}
+
 /**
  * Performs a batched matrix multiplication using the vbatched_gemm_impl
  * function.
@@ -81,35 +401,198 @@ template <typename T,
           int DIM_XB,
           int DIM_YB>
 void vbatched_gemm_impl(int max_m,
-                        int max_n,
-                        int* m,
-                        int* n,
-                        int* k,
-                        T** global_A_array,
-                        int* global_lda,
-                        T** global_B_array,
-                        int* global_ldb,
-                        T** global_C_array,
-                        int* global_ldc,
-                        int batchCount,
-                        cudaStream_t stream,
-                        T* alpha = nullptr);
-
-typedef std::function<void(int,
-                           int,
-                           int*,
-                           int*,
-                           int*,
-                           double**,
-                           int*,
-                           double**,
-                           int*,
-                           double**,
-                           int*,
-                           int,
-                           cudaStream_t,
-                           double* alpha)>
-    matrix_multiple_func_type;
-
-void gemm_algo_selector(int k, matrix_multiple_func_type& func,const UnitCell& ucell);
-#endif // VBATCH_MATRIX_MUL_H
\ No newline at end of file
+                               int max_n,
+                               int* m,
+                               int* n,
+                               int* k,
+                               T** global_A_array,
+                               int* global_lda,
+                               T** global_B_array,
+                               int* global_ldb,
+                               T** global_C_array,
+                               int* global_ldc,
+                               int batchCount,
+                               cudaStream_t stream,
+                               T* alpha = nullptr)
+{
+    // The positions of A and B have been swapped here.
+    // This is because the original code is for column-major matrices.
+    // We use row-major matrices, so we need to swap A and B.
+    // The vbatched_gemm_impl is for C = trans(A) * B + C, but we need trans(C).
+    // Which means: trans(C) = trans(trans(A)*B + C) = trans(B) * A + trans(C)
+    // Then, ldc should be N, lda and ldb should be K
+
+    size_t shared_mem_size = 0;
+    shared_mem_size += (BLK_M + 1) * BLK_K * sizeof(T);
+    shared_mem_size += (BLK_K + 1) * BLK_N * sizeof(T);
+    dim3 dimBlock(DIM_X, DIM_Y);
+    const int max_batch_count = 32768;
+    const int loop_num = batchCount / max_batch_count;
+    const int remain_num = batchCount % max_batch_count;
+
+    for (int i = 0; i < loop_num; ++i)
+    {
+        dim3 dimGrid(ceildiv(max_n, BLK_M),
+                     ceildiv(max_m, BLK_N),
+                     max_batch_count);
+        T* alpha_tmp = nullptr;
+        if (alpha != nullptr)
+        {
+            alpha_tmp = alpha + i * max_batch_count;
+        }
+
+        vbatched_gemm_kernel<T,
+                             DIM_X,
+                             DIM_Y,
+                             BLK_M,
+                             BLK_N,
+                             BLK_K,
+                             DIM_XA,
+                             DIM_YA,
+                             DIM_XB,
+                             DIM_YB>
+            <<<dimGrid, dimBlock, shared_mem_size, stream>>>(
+                n + i * max_batch_count,
+                m + i * max_batch_count,
+                k + i * max_batch_count,
+                global_B_array + i * max_batch_count,
+                global_ldb + i * max_batch_count,
+                global_A_array + i * max_batch_count,
+                global_lda + i * max_batch_count,
+                global_C_array + i * max_batch_count,
+                global_ldc + i * max_batch_count,
+                alpha_tmp);
+        checkCudaLastError();
+    }
+    if (remain_num > 0)
+    {
+        dim3 dimGrid(ceildiv(max_n, BLK_M), ceildiv(max_m, BLK_N), remain_num);
+        T* alpha_tmp = nullptr;
+        if (alpha != nullptr)
+        {
+            alpha_tmp = alpha + loop_num * max_batch_count;
+        }
+        vbatched_gemm_kernel<T,
+                             DIM_X,
+                             DIM_Y,
+                             BLK_M,
+                             BLK_N,
+                             BLK_K,
+                             DIM_XA,
+                             DIM_YA,
+                             DIM_XB,
+                             DIM_YB>
+            <<<dimGrid, dimBlock, shared_mem_size, stream>>>(
+                n + loop_num * max_batch_count,
+                m + loop_num * max_batch_count,
+                k + loop_num * max_batch_count,
+                global_B_array + loop_num * max_batch_count,
+                global_ldb + loop_num * max_batch_count,
+                global_A_array + loop_num * max_batch_count,
+                global_lda + loop_num * max_batch_count,
+                global_C_array + loop_num * max_batch_count,
+                global_ldc + loop_num * max_batch_count,
+                alpha_tmp);
+        checkCudaLastError();
+    }
+}
+
+template <typename T,
+          int DIM_X,
+          int DIM_Y,
+          int BLK_M,
+          int BLK_N,
+          int BLK_K,
+          int DIM_XA,
+          int DIM_YA,
+          int DIM_XB,
+          int DIM_YB>
+void gemm_time_measure(int max_m,
+                       int max_n,
+                       int* m,
+                       int* n,
+                       int* k,
+                       T** global_A_array,
+                       int* global_lda,
+                       T** global_B_array,
+                       int* global_ldb,
+                       T** global_C_array,
+                       int* global_ldc,
+                       int batchCount,
+                       cudaStream_t stream,
+                       float& fast_time,
+                       matrix_multiple_func_type& fastest_algo,
+                       double* cpu_result,
+                       double* h_global_C,
+                       double* d_global_C)
+{
+    cudaEvent_t start, stop;
+    checkCuda(
+        cudaMemset(d_global_C, 0, batchCount * max_m * max_n * sizeof(double)));
+    checkCuda(cudaEventCreate(&start));
+    checkCuda(cudaEventCreate(&stop));
+    checkCuda(cudaEventRecord(start, stream));
+    vbatched_gemm_impl<T,
+                       DIM_X,
+                       DIM_Y,
+                       BLK_M,
+                       BLK_N,
+                       BLK_K,
+                       DIM_XA,
+                       DIM_YA,
+                       DIM_XB,
+                       DIM_YB>(max_m,
+                               max_n,
+                               m,
+                               n,
+                               k,
+                               global_A_array,
+                               global_lda,
+                               global_B_array,
+                               global_ldb,
+                               global_C_array,
+                               global_ldc,
+                               batchCount,
+                               stream);
+    checkCuda(cudaEventRecord(stop, stream));
+    cudaError_t cuda_status = cudaGetLastError();
+    checkCuda(cudaStreamSynchronize(stream));
+    float milliseconds = 0;
+    checkCuda(cudaEventElapsedTime(&milliseconds, start, stop));
+
+    // WARNING !!!!! Here we assume that all m and n are the same
+    checkCuda(cudaMemcpy(h_global_C,
+                         d_global_C,
+                         batchCount * max_m * max_n * sizeof(double),
+                         cudaMemcpyDeviceToHost));
+    bool check_result = true;
+    for (int i = 0; i < batchCount * max_m * max_n; ++i)
+    {
+        if (abs(cpu_result[i] - h_global_C[i]) > 0.001)
+        {
+            check_result = false;
+            break;
+        }
+    }
+    if (milliseconds < fast_time && cuda_status == cudaSuccess && check_result)
+    {
+        fast_time = milliseconds;
+        fastest_algo = vbatched_gemm_impl<T,
+                                          DIM_X,
+                                          DIM_Y,
+                                          BLK_M,
+                                          BLK_N,
+                                          BLK_K,
+                                          DIM_XA,
+                                          DIM_YA,
+                                          DIM_XB,
+                                          DIM_YB>;
+#ifdef __DEBUG
+        std::cout << "found! fastest time: " << fast_time << std::endl;
+        std::cout << DIM_X << "," << DIM_Y << "," << BLK_M << "," << BLK_N
+                  << "," << BLK_K << "," << DIM_XA << "," << DIM_YA << ","
+                  << DIM_XB << "," << DIM_YB << std::endl;
+#endif
+    }
+}
+#endif // VBATCH_MATRIX_MUL_CUH
\ No newline at end of file
diff --git a/source/module_hamilt_lcao/module_hcontainer/base_matrix.cpp b/source/module_hamilt_lcao/module_hcontainer/base_matrix.cpp
index ff02d7744a..a7531a1245 100644
--- a/source/module_hamilt_lcao/module_hcontainer/base_matrix.cpp
+++ b/source/module_hamilt_lcao/module_hcontainer/base_matrix.cpp
@@ -109,8 +109,11 @@ assert(this->value_begin != nullptr);
 template <typename T>
 void BaseMatrix<T>::add_array(T* array)
 {
-    // if allocated, save data from array into matrix
-    // if whole matrix and 2d-block format, save data from array into matrix either
+#ifdef __DEBUG
+assert(this->value_begin != nullptr);
+#endif
+    // if allocated, add data from array into matrix
+    // if whole matrix and 2d-block format, add data from array into matrix either
     for (int i = 0; i < nrow_local * ncol_local; ++i)
     {
         value_begin[i] += array[i];
@@ -120,6 +123,9 @@ void BaseMatrix<T>::add_array(T* array)
 template <typename T>
 void BaseMatrix<T>::add_element(int mu, int nu, const T& value)
 {
+#ifdef __DEBUG
+assert(this->value_begin != nullptr);
+#endif
     int index = mu * this->ncol_local + nu;
     value_begin[index] += value;
 }
@@ -127,6 +133,9 @@ void BaseMatrix<T>::add_element(int mu, int nu, const T& value)
 template <typename T>
 T& BaseMatrix<T>::get_value(const size_t& i_row, const size_t& j_col) const
 {
+#ifdef __DEBUG
+assert(this->value_begin != nullptr);
+#endif
     int index = i_row * this->ncol_local + j_col;
     return value_begin[index];
 }
@@ -145,6 +154,12 @@ BaseMatrix<T>& BaseMatrix<T>::operator=(const BaseMatrix<T>& other)
     {
         this->nrow_local = other.nrow_local;
         this->ncol_local = other.ncol_local;
+
+        if (this->allocated)
+        {
+            delete[] this->value_begin;
+        }
+
         if (other.allocated)
         {
             this->value_begin = new T[nrow_local * ncol_local];
@@ -172,6 +187,12 @@ BaseMatrix<T>& BaseMatrix<T>::operator=(BaseMatrix<T>&& other) noexcept
     {
         this->nrow_local = other.nrow_local;
         this->ncol_local = other.ncol_local;
+
+        if (this->allocated)
+        {
+            delete[] this->value_begin;
+        }
+
         this->value_begin = other.value_begin;
         this->allocated = other.allocated;
         if (other.allocated)
diff --git a/source/module_hamilt_lcao/module_hcontainer/base_matrix.h b/source/module_hamilt_lcao/module_hcontainer/base_matrix.h
index d866c6f67f..ef591546a1 100644
--- a/source/module_hamilt_lcao/module_hcontainer/base_matrix.h
+++ b/source/module_hamilt_lcao/module_hcontainer/base_matrix.h
@@ -39,11 +39,12 @@ class BaseMatrix
     void set_zero();
 
     /**
-     * @brief save an array to the matrix
+     * @brief add an array to the matrix
      *
-     * @param array array to be saved
+     * @param array array to be added
      */
     void add_array(T* array);
+
     /**
      * @brief add a single element to the matrix
      *
@@ -52,6 +53,7 @@ class BaseMatrix
      * @param value value to be added
      */
     void add_element(int mu, int nu, const T& value);
+
     // for inside matrix
     /**
      * @brief get value from a whole matrix
@@ -61,6 +63,7 @@ class BaseMatrix
      * @return T&
      */
     T& get_value(const size_t& i_row, const size_t& j_col) const;
+
     /**
      * @brief get pointer of value from a submatrix
      */
diff --git a/source/module_hamilt_lcao/module_tddft/td_velocity.cpp b/source/module_hamilt_lcao/module_tddft/td_velocity.cpp
index 5de3d35209..3056c3d414 100644
--- a/source/module_hamilt_lcao/module_tddft/td_velocity.cpp
+++ b/source/module_hamilt_lcao/module_tddft/td_velocity.cpp
@@ -1,24 +1,145 @@
-#include "module_base/timer.h"
 #include "td_velocity.h"
 
+#include "module_base/timer.h"
+#include "module_elecstate/potentials/H_TDDFT_pw.h"
 
 bool TD_Velocity::tddft_velocity = false;
 bool TD_Velocity::out_mat_R = false;
+bool TD_Velocity::out_vecpot = false;
+bool TD_Velocity::init_vecpot_file = false;
+
 TD_Velocity* TD_Velocity::td_vel_op = nullptr;
 
+int TD_Velocity::istep = -1;
+int TD_Velocity::max_istep = -1;
+std::vector<ModuleBase::Vector3<double>> TD_Velocity::At_from_file;
+
 TD_Velocity::TD_Velocity()
 {
-  return;
+    if (init_vecpot_file && istep == -1)
+    {
+        this->read_cart_At();
+    }
+    return;
 }
 TD_Velocity::~TD_Velocity()
 {
-  this->destroy_HS_R_td_sparse();
+    this->destroy_HS_R_td_sparse();
+}
+
+void TD_Velocity::output_cart_At(const std::string& out_dir)
+{
+    if (GlobalV::MY_RANK == 0)
+    {
+        std::string out_file;
+        // generate the output file name
+        out_file = out_dir + "At.dat";
+        std::ofstream ofs;
+        // output title
+        if (istep == 0)
+        {
+            ofs.open(out_file.c_str(), std::ofstream::out);
+            ofs << std::left << std::setw(8) << "#istep" << std::setw(15) << "A_x" << std::setw(15) << "A_y"
+                << std::setw(15) << "A_z" << std::endl;
+        }
+        else
+        {
+            ofs.open(out_file.c_str(), std::ofstream::app);
+        }
+        // output the vector potential
+        ofs << std::left << std::setw(8) << istep;
+        // divide by 2.0 to get the atomic unit
+        for (int i = 0; i < 3; i++)
+        {
+            ofs << std::scientific << std::setprecision(4) << std::setw(15) << cart_At[i] / 2.0;
+        }
+        ofs << std::endl;
+        ofs.close();
+    }
+    return;
 }
 
+void TD_Velocity::cal_cart_At(const ModuleBase::Vector3<double>& a0,
+                              const ModuleBase::Vector3<double>& a1,
+                              const ModuleBase::Vector3<double>& a2,
+                              const ModuleBase::Vector3<double>& At)
+{
+    istep++;
+    if (init_vecpot_file)
+    {
+        this->cart_At = At_from_file[istep > max_istep ? max_istep : istep];
+    }
+    else
+    {
+        const double l_norm[3] = {a0.norm(), a1.norm(), a2.norm()};
+        this->cart_At = a0 * At[0] / l_norm[0] + a1 * At[1] / l_norm[1] + a2 * At[2] / l_norm[2];
+    }
+    // output the vector potential if needed
+    if (out_vecpot == true)
+    {
+        this->output_cart_At(GlobalV::global_out_dir);
+    }
+}
+
+void TD_Velocity::read_cart_At(void)
+{
+    std::string in_file;
+    // generate the input file name
+    in_file = "At.dat";
+    std::ifstream ifs(in_file.c_str());
+    // check if the file is exist
+    if (!ifs)
+    {
+        ModuleBase::WARNING_QUIT("TD_Velocity::read_cart_At", "Cannot open Vector potential file!");
+    }
+    std::string line;
+    std::vector<std::string> str_vec;
+    // use tmp to skip the istep number
+    int tmp = 0;
+    while (std::getline(ifs, line))
+    {
+        // A tmporary vector3 to store the data of this line
+        ModuleBase::Vector3<double> At;
+        if (line[0] == '#')
+        {
+            continue;
+        }
+        std::istringstream iss(line);
+        // skip the istep number
+        if (!(iss >> tmp))
+        {
+            ModuleBase::WARNING_QUIT("TD_Velocity::read_cart_At", "Error reading istep!");
+        }
+        // read the vector potential
+        double component = 0;
+        // Read three components
+        for (int i = 0; i < 3; i++)
+        {
+            if (!(iss >> component))
+            {
+                ModuleBase::WARNING_QUIT("TD_Velocity::read_cart_At",
+                                         "Error reading component " + std::to_string(i + 1) + " for istep "
+                                             + std::to_string(tmp) + "!");
+            }
+            At[i] = component;
+        }
+        // unit transform ,change unit into Ry/bohr/e*t_a.u.
+        At *= 2.0;
+        // add the tmporary vector3 to the vector potential vector
+        At_from_file.push_back(At);
+    }
+    // set the max_istep
+    max_istep = At_from_file.size() - 1;
+    ifs.close();
+
+    return;
+}
 void TD_Velocity::destroy_HS_R_td_sparse(void)
 {
-  std::map<Abfs::Vector3_Order<int>, std::map<size_t, std::map<size_t, std::complex<double>>>> empty_HR_sparse_td_vel_up;
-  std::map<Abfs::Vector3_Order<int>, std::map<size_t, std::map<size_t, std::complex<double>>>> empty_HR_sparse_td_vel_down;
-  HR_sparse_td_vel[0].swap(empty_HR_sparse_td_vel_up);
-  HR_sparse_td_vel[1].swap(empty_HR_sparse_td_vel_down);
-}
\ No newline at end of file
+    std::map<Abfs::Vector3_Order<int>, std::map<size_t, std::map<size_t, std::complex<double>>>>
+        empty_HR_sparse_td_vel_up;
+    std::map<Abfs::Vector3_Order<int>, std::map<size_t, std::map<size_t, std::complex<double>>>>
+        empty_HR_sparse_td_vel_down;
+    HR_sparse_td_vel[0].swap(empty_HR_sparse_td_vel_up);
+    HR_sparse_td_vel[1].swap(empty_HR_sparse_td_vel_down);
+}
diff --git a/source/module_hamilt_lcao/module_tddft/td_velocity.h b/source/module_hamilt_lcao/module_tddft/td_velocity.h
index 0d274228dd..ddfaaf87cf 100644
--- a/source/module_hamilt_lcao/module_tddft/td_velocity.h
+++ b/source/module_hamilt_lcao/module_tddft/td_velocity.h
@@ -1,17 +1,19 @@
 #ifndef TD_VELOCITY_H
 #define TD_VELOCITY_H
-#include <map>
-
-#include "module_base/timer.h"
 #include "module_base/abfs-vector3_order.h"
-//Class to store TDDFT velocity gague infos.
+#include "module_base/timer.h"
+
+#include <map>
+// Class to store TDDFT velocity gague infos.
 class TD_Velocity
 {
   public:
     TD_Velocity();
     ~TD_Velocity();
 
-    /// @brief Judge if in tddft calculation or not 
+    void init();
+
+    /// @brief Judge if in tddft calculation or not
     static bool tddft_velocity;
 
     /// @brief switch to control the output of HR
@@ -20,15 +22,42 @@ class TD_Velocity
     /// @brief pointer to the only TD_Velocity object itself
     static TD_Velocity* td_vel_op;
 
-    //For TDDFT velocity gague, to fix the output of HR
-    std::map<Abfs::Vector3_Order<int>, std::map<size_t, std::map<size_t, std::complex<double>>>> HR_sparse_td_vel[2];
+    /// @brief switch to control the output of At
+    static bool out_vecpot;
+
+    /// @brief switch to control the source of At
+    static bool init_vecpot_file;
 
+    /// @brief Store the vector potential for tddft calculation
+    ModuleBase::Vector3<double> cart_At;
+
+    /// @brief calculate the At in cartesian coordinate
+    void cal_cart_At(const ModuleBase::Vector3<double>& a0,
+                     const ModuleBase::Vector3<double>& a1,
+                     const ModuleBase::Vector3<double>& a2,
+                     const ModuleBase::Vector3<double>& At);
+
+    // For TDDFT velocity gague, to fix the output of HR
+    std::map<Abfs::Vector3_Order<int>, std::map<size_t, std::map<size_t, std::complex<double>>>> HR_sparse_td_vel[2];
 
   private:
+    /// @brief read At from output file
+    void read_cart_At(void);
+
+    /// @brief output cart_At to output file
+    void output_cart_At(const std::string& out_dir);
+
+    /// @brief store isteps now
+    static int istep;
+
+    /// @brief total steps of read in At
+    static int max_istep;
+
+    /// @brief store the read in At_data
+    static std::vector<ModuleBase::Vector3<double>> At_from_file;
 
     /// @brief destory HSR data stored
     void destroy_HS_R_td_sparse(void);
-
 };
 
-#endif
\ No newline at end of file
+#endif
diff --git a/source/module_hamilt_pw/hamilt_pwdft/kernels/cuda/force_op.cu b/source/module_hamilt_pw/hamilt_pwdft/kernels/cuda/force_op.cu
index 81a0e176c3..5a1cdeecac 100644
--- a/source/module_hamilt_pw/hamilt_pwdft/kernels/cuda/force_op.cu
+++ b/source/module_hamilt_pw/hamilt_pwdft/kernels/cuda/force_op.cu
@@ -7,6 +7,7 @@
 #include <thrust/complex.h>
 #include <cuda_runtime.h>
 #include <base/macros/macros.h>
+#include <module_base/module_device/device.h>
 
 #define THREADS_PER_BLOCK 256
 
diff --git a/source/module_hamilt_pw/hamilt_pwdft/kernels/cuda/stress_op.cu b/source/module_hamilt_pw/hamilt_pwdft/kernels/cuda/stress_op.cu
index 01c9f18175..91ac04ebc0 100644
--- a/source/module_hamilt_pw/hamilt_pwdft/kernels/cuda/stress_op.cu
+++ b/source/module_hamilt_pw/hamilt_pwdft/kernels/cuda/stress_op.cu
@@ -4,6 +4,7 @@
 #include <complex>
 #include <thrust/complex.h>
 #include <base/macros/macros.h>
+#include <module_base/module_device/device.h>
 
 #include <cuda_runtime.h>
 
diff --git a/source/module_hsolver/CMakeLists.txt b/source/module_hsolver/CMakeLists.txt
index c4e7410da5..3c0b35383e 100644
--- a/source/module_hsolver/CMakeLists.txt
+++ b/source/module_hsolver/CMakeLists.txt
@@ -13,7 +13,7 @@ list(APPEND objects
 if(ENABLE_LCAO)
   list(APPEND objects
       hsolver_lcao.cpp
-      diago_blas.cpp
+      diago_scalapack.cpp
   )
   if (USE_ELPA)
     list(APPEND objects
diff --git a/source/module_hsolver/diago_blas.cpp b/source/module_hsolver/diago_scalapack.cpp
similarity index 94%
rename from source/module_hsolver/diago_blas.cpp
rename to source/module_hsolver/diago_scalapack.cpp
index 1b9183520f..3a1432dee7 100644
--- a/source/module_hsolver/diago_blas.cpp
+++ b/source/module_hsolver/diago_scalapack.cpp
@@ -5,7 +5,7 @@
 // DATE : 2022-04-14
 //=====================
 
-#include "diago_blas.h"
+#include "diago_scalapack.h"
 
 #include <cassert>
 #include <cstring>
@@ -21,9 +21,9 @@ typedef hamilt::MatrixBlock<std::complex<double>> matcd;
 namespace hsolver
 {
     template<>
-    void DiagoBlas<double>::diag(hamilt::Hamilt<double>* phm_in, psi::Psi<double>& psi, Real* eigenvalue_in)
+    void DiagoScalapack<double>::diag(hamilt::Hamilt<double>* phm_in, psi::Psi<double>& psi, Real* eigenvalue_in)
 {
-    ModuleBase::TITLE("DiagoElpa", "diag");
+    ModuleBase::TITLE("DiagoScalapack", "diag");
     matd h_mat, s_mat;
     phm_in->matrix(h_mat, s_mat);
     assert(h_mat.col == s_mat.col && h_mat.row == s_mat.row && h_mat.desc == s_mat.desc);
@@ -33,9 +33,9 @@ namespace hsolver
     BlasConnector::copy(GlobalV::NBANDS, eigen.data(), inc, eigenvalue_in, inc);
 }
     template<>
-    void DiagoBlas<std::complex<double>>::diag(hamilt::Hamilt<std::complex<double>>* phm_in, psi::Psi<std::complex<double>>& psi, Real* eigenvalue_in)
+    void DiagoScalapack<std::complex<double>>::diag(hamilt::Hamilt<std::complex<double>>* phm_in, psi::Psi<std::complex<double>>& psi, Real* eigenvalue_in)
 {
-    ModuleBase::TITLE("DiagoElpa", "diag");
+    ModuleBase::TITLE("DiagoScalapack", "diag");
     matcd h_mat, s_mat;
     phm_in->matrix(h_mat, s_mat);
     assert(h_mat.col == s_mat.col && h_mat.row == s_mat.row && h_mat.desc == s_mat.desc);
@@ -46,7 +46,7 @@ namespace hsolver
 }
 
     template<typename T>
-    std::pair<int, std::vector<int>> DiagoBlas<T>::pdsygvx_once(const int* const desc,
+    std::pair<int, std::vector<int>> DiagoScalapack<T>::pdsygvx_once(const int* const desc,
                                                          const int ncol,
                                                          const int nrow,
                                                          const double *const h_mat,
@@ -169,7 +169,7 @@ namespace hsolver
                                  + ModuleBase::GlobalFunc::TO_STRING(__LINE__));
 }
     template<typename T>
-    std::pair<int, std::vector<int>> DiagoBlas<T>::pzhegvx_once(const int* const desc,
+    std::pair<int, std::vector<int>> DiagoScalapack<T>::pzhegvx_once(const int* const desc,
                                                          const int ncol,
                                                          const int nrow,
                                                          const std::complex<double> *const h_mat,
@@ -303,7 +303,7 @@ namespace hsolver
                                  + ModuleBase::GlobalFunc::TO_STRING(__LINE__));
 }
     template<typename T>
-    void DiagoBlas<T>::pdsygvx_diag(const int* const desc,
+    void DiagoScalapack<T>::pdsygvx_diag(const int* const desc,
                              const int ncol,
                              const int nrow,
                              const double *const h_mat,
@@ -321,7 +321,7 @@ namespace hsolver
 }
 
     template<typename T>
-    void DiagoBlas<T> ::pzhegvx_diag(const int* const desc,
+    void DiagoScalapack<T> ::pzhegvx_diag(const int* const desc,
                              const int ncol,
                              const int nrow,
                              const std::complex<double> *const h_mat,
@@ -339,7 +339,7 @@ namespace hsolver
 }
 
     template<typename T>
-    void DiagoBlas<T>::post_processing(const int info, const std::vector<int>& vec)
+    void DiagoScalapack<T>::post_processing(const int info, const std::vector<int>& vec)
 {
     const std::string str_info = "info = " + ModuleBase::GlobalFunc::TO_STRING(info) + ".\n";
     const std::string str_FILE
diff --git a/source/module_hsolver/diago_blas.h b/source/module_hsolver/diago_scalapack.h
similarity index 96%
rename from source/module_hsolver/diago_blas.h
rename to source/module_hsolver/diago_scalapack.h
index b445f0cc12..92f557de75 100644
--- a/source/module_hsolver/diago_blas.h
+++ b/source/module_hsolver/diago_scalapack.h
@@ -5,8 +5,8 @@
 // DATE : 2022-04-14
 //=====================
 
-#ifndef DIAGOBLAS_H
-#define DIAGOBLAS_H
+#ifndef DIAGO_SCALAPACK_H
+#define DIAGO_SCALAPACK_H
 
 #include <complex>
 #include <utility>
@@ -20,7 +20,7 @@
 namespace hsolver
 {
     template<typename T>
-    class DiagoBlas : public DiagH<T>
+    class DiagoScalapack : public DiagH<T>
 {
 private:
     using Real = typename GetTypeReal<T>::type;
diff --git a/source/module_hsolver/hsolver_lcao.cpp b/source/module_hsolver/hsolver_lcao.cpp
index 0c3a787607..eb573c7cb4 100644
--- a/source/module_hsolver/hsolver_lcao.cpp
+++ b/source/module_hsolver/hsolver_lcao.cpp
@@ -1,6 +1,6 @@
 #include "hsolver_lcao.h"
 
-#include "diago_blas.h"
+#include "diago_scalapack.h"
 #include "diago_cg.h"
 #include <ATen/core/tensor.h>
 #include <ATen/core/tensor_types.h>
@@ -49,7 +49,7 @@ void HSolverLCAO<T, Device>::solveTemplate(hamilt::Hamilt<T>* pHamilt,
         }
         if (this->pdiagh == nullptr)
         {
-            this->pdiagh = new DiagoBlas<T>();
+            this->pdiagh = new DiagoScalapack<T>();
             this->pdiagh->method = this->method;
         }
     }
diff --git a/source/module_hsolver/test/CMakeLists.txt b/source/module_hsolver/test/CMakeLists.txt
index cb785e83bb..9889d33de4 100644
--- a/source/module_hsolver/test/CMakeLists.txt
+++ b/source/module_hsolver/test/CMakeLists.txt
@@ -84,13 +84,13 @@ if(ENABLE_LCAO)
   AddTest(
     TARGET HSolver_LCAO
     LIBS ${math_libs} ELPA::ELPA base genelpa psi device
-    SOURCES diago_lcao_test.cpp ../diago_elpa.cpp ../diago_blas.cpp 
+    SOURCES diago_lcao_test.cpp ../diago_elpa.cpp ../diago_scalapack.cpp 
   )
   else()
     AddTest(
       TARGET HSolver_LCAO
       LIBS ${math_libs} base psi device
-      SOURCES diago_lcao_test.cpp ../diago_blas.cpp 
+      SOURCES diago_lcao_test.cpp ../diago_scalapack.cpp 
     )
   endif()
 
@@ -106,7 +106,7 @@ if (USE_CUDA)
 AddTest(
   TARGET HSolver_LCAO_cusolver
   LIBS ${math_libs}  base psi device 
-  SOURCES diago_lcao_cusolver_test.cpp ../diago_cusolver.cpp ../diago_blas.cpp 
+  SOURCES diago_lcao_cusolver_test.cpp ../diago_cusolver.cpp ../diago_scalapack.cpp 
   ../kernels/math_kernel_op.cpp
   ../kernels/dngvd_op.cpp
   ../kernels/cuda/diag_cusolver.cu
diff --git a/source/module_hsolver/test/diago_lcao_cusolver_test.cpp b/source/module_hsolver/test/diago_lcao_cusolver_test.cpp
index 3f29d823d4..8139c8e07e 100644
--- a/source/module_hsolver/test/diago_lcao_cusolver_test.cpp
+++ b/source/module_hsolver/test/diago_lcao_cusolver_test.cpp
@@ -1,7 +1,7 @@
 #include <vector>
 
 #include "gtest/gtest.h"
-#include "module_hsolver/diago_blas.h"
+#include "module_hsolver/diago_scalapack.h"
 #include "module_hsolver/test/diago_elpa_utils.h"
 #include "mpi.h"
 #include "string.h"
@@ -24,7 +24,7 @@
 /**
  * Tested function:
  *  - hsolver::DiagoElpa::diag (for ELPA)
- *  - hsolver::DiagoBlas::diag (for Scalapack)
+ *  - hsolver::DiagoScalapack::diag (for Scalapack)
  *
  * The 2d block cyclic distribution of H/S matrix is done by
  * self-realized functions in module_hsolver/test/diago_elpa_utils.h
@@ -76,7 +76,7 @@ class DiagoPrepare
         MPI_Comm_rank(MPI_COMM_WORLD, &myrank);
 
         if (ks_solver == "scalapack_gvx")
-            dh = new hsolver::DiagoBlas<T>;
+            dh = new hsolver::DiagoScalapack<T>;
 #ifdef __CUDA
         else if (ks_solver == "cusolver")
             dh = new hsolver::DiagoCusolver<T>;
diff --git a/source/module_hsolver/test/diago_lcao_test.cpp b/source/module_hsolver/test/diago_lcao_test.cpp
index 487820a9d5..d9ac6429a4 100644
--- a/source/module_hsolver/test/diago_lcao_test.cpp
+++ b/source/module_hsolver/test/diago_lcao_test.cpp
@@ -1,5 +1,5 @@
 #include "module_hsolver/test/diago_elpa_utils.h"
-#include "module_hsolver/diago_blas.h"
+#include "module_hsolver/diago_scalapack.h"
 #include "mpi.h"
 #include "string.h"
 #include "gtest/gtest.h"
@@ -20,7 +20,7 @@
 /**
  * Tested function:
  *  - hsolver::DiagoElpa::diag (for ELPA)
- *  - hsolver::DiagoBlas::diag (for Scalapack)
+ *  - hsolver::DiagoScalapack::diag (for Scalapack)
  *
  * The 2d block cyclic distribution of H/S matrix is done by 
  * self-realized functions in module_hsolver/test/diago_elpa_utils.h
@@ -60,7 +60,7 @@ template<class T> class DiagoPrepare
         MPI_Comm_rank(MPI_COMM_WORLD, &myrank);
 
         if (ks_solver == "scalapack_gvx")
-            dh = new hsolver::DiagoBlas<T>;
+            dh = new hsolver::DiagoScalapack<T>;
 #ifdef __ELPA
         else if(ks_solver == "genelpa")
             dh = new hsolver::DiagoElpa<T>;
diff --git a/source/module_io/input.cpp b/source/module_io/input.cpp
index 19bbe5deb8..64fae37c81 100644
--- a/source/module_io/input.cpp
+++ b/source/module_io/input.cpp
@@ -338,6 +338,7 @@ void Input::Default(void)
     deepks_scf = 0;
     deepks_bandgap = 0;
     deepks_out_unittest = 0;
+    deepks_equiv = 0;
 
     out_pot = 0;
     out_wfc_pw = 0;
@@ -469,6 +470,8 @@ void Input::Default(void)
     out_dipole = false;
     out_efield = false;
     out_current = false;
+    out_vecpot = false;
+    init_vecpot_file = false;
 
     td_print_eij = -1.0;
     td_edm = 0;
@@ -1412,6 +1415,10 @@ bool Input::Read(const std::string& fn)
         {
             read_bool(ifs, deepks_scf);
         }
+        else if (strcmp("deepks_equiv", word) == 0)
+        {
+            read_bool(ifs, deepks_equiv);
+        }
         else if (strcmp("deepks_bandgap", word) == 0) // caoyu added 2020-11-24, mohan modified 2021-01-03
         {
             read_bool(ifs, deepks_bandgap);
@@ -1808,6 +1815,14 @@ bool Input::Read(const std::string& fn)
         {
             read_value(ifs, out_efield);
         }
+        else if (strcmp("out_vecpot", word) == 0)
+        {
+            read_value(ifs, out_vecpot);
+        }
+        else if (strcmp("init_vecpot_file", word) == 0)
+        {
+            read_value(ifs, init_vecpot_file);
+        }
         else if (strcmp("td_print_eij", word) == 0)
         {
             read_value(ifs, td_print_eij);
@@ -3578,6 +3593,7 @@ void Input::Bcast()
     Parallel_Common::bcast_bool(deepks_bandgap);
     Parallel_Common::bcast_bool(deepks_out_unittest);
     Parallel_Common::bcast_string(deepks_model);
+    Parallel_Common::bcast_bool(deepks_equiv);
 
     Parallel_Common::bcast_int(out_pot);
     Parallel_Common::bcast_int(out_wfc_pw);
@@ -3746,6 +3762,8 @@ void Input::Bcast()
     Parallel_Common::bcast_bool(out_dipole);
     Parallel_Common::bcast_bool(out_efield);
     Parallel_Common::bcast_bool(out_current);
+    Parallel_Common::bcast_bool(out_vecpot);
+    Parallel_Common::bcast_bool(init_vecpot_file);
     Parallel_Common::bcast_double(td_print_eij);
     Parallel_Common::bcast_int(td_edm);
     Parallel_Common::bcast_bool(test_skip_ewald);
diff --git a/source/module_io/input.h b/source/module_io/input.h
index fb1b79f3ef..3aad48b7ce 100644
--- a/source/module_io/input.h
+++ b/source/module_io/input.h
@@ -416,6 +416,8 @@ class Input
     bool out_dipole; // output the dipole or not
     bool out_efield; // output the efield or not
     bool out_current; //output the current or not
+    bool out_vecpot; // output the vector potential or not
+    bool init_vecpot_file; // initialize the vector potential, though file or integral
 
     double td_print_eij; // threshold to output Eij elements
     int td_edm; //0: new edm method   1: old edm method
@@ -517,7 +519,7 @@ class Input
                             // 2022-1-12
     bool deepks_scf; //(need libnpy and libtorch) if set 1, a trained model would be needed to cal V_delta and F_delta
     bool deepks_bandgap; // for bandgap label. QO added 2021-12-15
-
+    bool deepks_equiv;
     bool deepks_out_unittest; // if set 1, prints intermediate quantities that shall be used for making unit test
 
     std::string deepks_model; // needed when deepks_scf=1
diff --git a/source/module_io/input_conv.cpp b/source/module_io/input_conv.cpp
index 8f6aaf256a..b2685ed702 100644
--- a/source/module_io/input_conv.cpp
+++ b/source/module_io/input_conv.cpp
@@ -550,6 +550,8 @@ void Input_Conv::Convert(void)
     module_tddft::Evolve_elec::out_current = INPUT.out_current;
     module_tddft::Evolve_elec::td_print_eij = INPUT.td_print_eij;
     module_tddft::Evolve_elec::td_edm = INPUT.td_edm;
+    TD_Velocity::out_vecpot = INPUT.out_vecpot;
+    TD_Velocity::init_vecpot_file = INPUT.init_vecpot_file;
     read_td_efield();
 #endif
 
@@ -769,6 +771,12 @@ void Input_Conv::Convert(void)
     GlobalV::deepks_bandgap = INPUT.deepks_bandgap; // QO added for bandgap label 2021-12-15
     GlobalV::deepks_out_unittest = INPUT.deepks_out_unittest;
     GlobalV::deepks_out_labels = INPUT.deepks_out_labels;
+    GlobalV::deepks_equiv = INPUT.deepks_equiv;
+
+    if(GlobalV::deepks_equiv && GlobalV::deepks_bandgap)
+    {
+        ModuleBase::WARNING_QUIT("Input_conv", "deepks_equiv and deepks_bandgap cannot be used together");
+    }
     if (GlobalV::deepks_out_unittest)
     {
         GlobalV::deepks_out_labels = 1;
diff --git a/source/module_io/parameter_pool.cpp b/source/module_io/parameter_pool.cpp
index c51eced6d7..f1f2a21ef3 100644
--- a/source/module_io/parameter_pool.cpp
+++ b/source/module_io/parameter_pool.cpp
@@ -1529,6 +1529,10 @@ void input_parameters_set(std::map<std::string, InputParameter> input_parameters
     {
         INPUT.deepks_scf = *static_cast<bool*>(input_parameters["deepks_scf"].get());
     }
+    else if (input_parameters.count("deepks_equiv") != 0)
+    {
+        INPUT.deepks_equiv = *static_cast<bool*>(input_parameters["deepks_equiv"].get());
+    }
     else if (input_parameters.count("deepks_bandgap") != 0)
     {
         INPUT.deepks_bandgap = *static_cast<bool*>(input_parameters["deepks_bandgap"].get());
diff --git a/source/module_io/test/for_testing_input_conv.h b/source/module_io/test/for_testing_input_conv.h
index d4449bdbf1..02d8c59484 100644
--- a/source/module_io/test/for_testing_input_conv.h
+++ b/source/module_io/test/for_testing_input_conv.h
@@ -16,6 +16,7 @@
 #include "module_hamilt_lcao/hamilt_lcaodft/local_orbital_charge.h"
 #include "module_hamilt_lcao/module_dftu/dftu.h"
 #include "module_hamilt_lcao/module_tddft/evolve_elec.h"
+#include "module_hamilt_lcao/module_tddft/td_velocity.h"
 #include "module_hamilt_pw/hamilt_pwdft/VNL_in_pw.h"
 #include "module_hamilt_pw/hamilt_pwdft/structure_factor.h"
 #include "module_hamilt_pw/hamilt_pwdft/wavefunc.h"
@@ -41,6 +42,8 @@ std::vector<int> module_tddft::Evolve_elec::td_vext_dire_case;
 bool module_tddft::Evolve_elec::out_dipole;
 bool module_tddft::Evolve_elec::out_efield;
 bool module_tddft::Evolve_elec::out_current;
+bool TD_Velocity::out_vecpot;
+bool TD_Velocity::init_vecpot_file;
 double module_tddft::Evolve_elec::td_print_eij;
 int module_tddft::Evolve_elec::td_edm;
 double elecstate::Gatefield::zgate = 0.5;
diff --git a/source/module_io/test/input_test.cpp b/source/module_io/test/input_test.cpp
index 547178db88..e92bc2e9ab 100644
--- a/source/module_io/test/input_test.cpp
+++ b/source/module_io/test/input_test.cpp
@@ -170,6 +170,7 @@ TEST_F(InputTest, Default)
         EXPECT_EQ(INPUT.out_dm1,0);
         EXPECT_EQ(INPUT.deepks_out_labels,0);
         EXPECT_EQ(INPUT.deepks_scf,0);
+		EXPECT_EQ(INPUT.deepks_equiv,0);
         EXPECT_EQ(INPUT.deepks_bandgap,0);
         EXPECT_EQ(INPUT.deepks_out_unittest,0);
         EXPECT_EQ(INPUT.out_pot,0);
@@ -537,6 +538,7 @@ TEST_F(InputTest, Read)
         EXPECT_EQ(INPUT.out_dm1,0);
         EXPECT_EQ(INPUT.deepks_out_labels,0);
         EXPECT_EQ(INPUT.deepks_scf,0);
+		EXPECT_EQ(INPUT.deepks_equiv,0);
         EXPECT_EQ(INPUT.deepks_bandgap,0);
         EXPECT_EQ(INPUT.deepks_out_unittest,0);
         EXPECT_EQ(INPUT.out_pot,2);
diff --git a/source/module_io/test/input_test_para.cpp b/source/module_io/test/input_test_para.cpp
index 5a6490551a..8246e057bd 100644
--- a/source/module_io/test/input_test_para.cpp
+++ b/source/module_io/test/input_test_para.cpp
@@ -177,6 +177,7 @@ TEST_F(InputParaTest, Bcast)
     EXPECT_EQ(INPUT.out_dm1, 0);
     EXPECT_EQ(INPUT.deepks_out_labels, 0);
     EXPECT_EQ(INPUT.deepks_scf, 0);
+    EXPECT_EQ(INPUT.deepks_equiv, 0);
     EXPECT_EQ(INPUT.deepks_bandgap, 0);
     EXPECT_EQ(INPUT.deepks_out_unittest, 0);
     EXPECT_EQ(INPUT.out_pot, 0);
diff --git a/source/module_io/write_HS_sparse.cpp b/source/module_io/write_HS_sparse.cpp
index c7e7d5475a..2ca1d58049 100644
--- a/source/module_io/write_HS_sparse.cpp
+++ b/source/module_io/write_HS_sparse.cpp
@@ -849,4 +849,4 @@ template void ModuleIO::save_sparse<std::complex<double>>(
     const Parallel_Orbitals&,
     const std::string&,
     const int&,
-    const bool&);
+    const bool&);
\ No newline at end of file
diff --git a/source/module_io/write_input.cpp b/source/module_io/write_input.cpp
index 91a04201ab..73f3ca345c 100644
--- a/source/module_io/write_input.cpp
+++ b/source/module_io/write_input.cpp
@@ -210,6 +210,7 @@ ModuleBase::GlobalFunc::OUTP(ofs, "out_bandgap", out_bandgap, "if true, print ou
     // for deepks
     ModuleBase::GlobalFunc::OUTP(ofs, "deepks_out_labels", deepks_out_labels, ">0 compute descriptor for deepks");
     ModuleBase::GlobalFunc::OUTP(ofs, "deepks_scf", deepks_scf, ">0 add V_delta to Hamiltonian");
+    ModuleBase::GlobalFunc::OUTP(ofs, "deepks_equiv", deepks_equiv, "whether to use equivariant version of DeePKS");
     ModuleBase::GlobalFunc::OUTP(ofs, "deepks_bandgap", deepks_bandgap, ">0 for bandgap label");
     ModuleBase::GlobalFunc::OUTP(ofs,
                                  "deepks_out_unittest",
diff --git a/source/version.h b/source/version.h
index 087959a258..3ada3d837e 100644
--- a/source/version.h
+++ b/source/version.h
@@ -1,3 +1,3 @@
 #ifndef VERSION
-#define VERSION "v3.6.3"
+#define VERSION "v3.6.4"
 #endif