From 0e2e2c13063a3f11cd62a6f2d674b196dd9cf118 Mon Sep 17 00:00:00 2001
From: wqzhou <33364058+WHUweiqingzhou@users.noreply.github.com>
Date: Mon, 5 Aug 2024 16:48:26 +0800
Subject: [PATCH] Try I: replace dsytrf & dsytri & gemv by dsysv in
 `Broyden_mixing` (#4842)

* replace dsytrf & dsytri & gemv by dsysv

* fix a bug
---
 source/module_base/lapack_connector.h         |  4 ++
 .../module_mixing/broyden_mixing.cpp          | 41 ++++++-------------
 2 files changed, 16 insertions(+), 29 deletions(-)

diff --git a/source/module_base/lapack_connector.h b/source/module_base/lapack_connector.h
index 653bc6428a..0b0b822bfb 100644
--- a/source/module_base/lapack_connector.h
+++ b/source/module_base/lapack_connector.h
@@ -174,6 +174,10 @@ extern "C"
 
     // solve a tridiagonal linear system
     void dgtsv_(int* N, int* NRHS, double* DL, double* D, double* DU, double* B, int* LDB, int* INFO);
+
+    // solve Ax = b 
+    void dsysv_(const char* uplo, const int* n, const int* m, double * a, const int* lda,
+                 int *ipiv, double * b, const int* ldb, double *work, const int* lwork ,int *info);
 }
 
 #ifdef GATHER_INFO
diff --git a/source/module_base/module_mixing/broyden_mixing.cpp b/source/module_base/module_mixing/broyden_mixing.cpp
index ba42ff4029..3b0f53d19d 100644
--- a/source/module_base/module_mixing/broyden_mixing.cpp
+++ b/source/module_base/module_mixing/broyden_mixing.cpp
@@ -137,41 +137,24 @@ void Broyden_Mixing::tem_cal_coef(const Mixing_Data& mdata, std::function<double
                 }
             }
         }
-        double* work = new double[ndim_cal_dF];
-        int* iwork = new int[ndim_cal_dF];
+        double* work = new double[ndim_cal_dF];   // workspace
+        int* iwork = new int[ndim_cal_dF];   // ipiv
         char uu = 'U';
         int info;
-        dsytrf_(&uu, &ndim_cal_dF, beta_tmp.c, &ndim_cal_dF, iwork, work, &ndim_cal_dF, &info);
-        if (info != 0)
-            ModuleBase::WARNING_QUIT("Charge_Mixing", "Error when factorizing beta.");
-        dsytri_(&uu, &ndim_cal_dF, beta_tmp.c, &ndim_cal_dF, iwork, work, &info);
-        if (info != 0)
-            ModuleBase::WARNING_QUIT("Charge_Mixing", "Error when DSYTRI beta.");
-        for (int i = 0; i < ndim_cal_dF; ++i)
-        {
-            for (int j = i + 1; j < ndim_cal_dF; ++j)
-            {
-                beta_tmp(i, j) = beta_tmp(j, i);
-            }
-        }
+        int m = 1;
+        // gamma means the coeficients for mixing
+        // but now gamma store <dFi|Fm>, namely c
+        std::vector<double> gamma(ndim_cal_dF);
         for (int i = 0; i < ndim_cal_dF; ++i)
         {
             FPTYPE* dFi = FP_dF + i * length;
-            work[i] = inner_product(dFi, FP_F);
+            gamma[i] = inner_product(dFi, FP_F);
         }
-        // gamma[i] = \sum_j beta_tmp(i,j) * work[j]
-        std::vector<double> gamma(ndim_cal_dF);
-        container::BlasConnector::gemv('N',
-                                       ndim_cal_dF,
-                                       ndim_cal_dF,
-                                       1.0,
-                                       beta_tmp.c,
-                                       ndim_cal_dF,
-                                       work,
-                                       1,
-                                       0.0,
-                                       gamma.data(),
-                                       1);
+        // solve aG = c 
+        dsysv_(&uu, &ndim_cal_dF, &m, beta_tmp.c, &ndim_cal_dF, iwork, gamma.data(), &ndim_cal_dF, work, &ndim_cal_dF, &info);
+        if (info != 0)
+            ModuleBase::WARNING_QUIT("Charge_Mixing", "Error when DSYSV.");
+        // after solving, gamma store the coeficients for mixing
         coef[mdata.start] = 1 + gamma[dFindex_move(0)];
         for (int i = 1; i < ndim_cal_dF; ++i)
         {