Merge branch 'develop' of https://github.com/deepmodeling/abacus-develop into develop

Author: caic99

source/Makefile.Objects

@@ -21,8 +21,6 @@ run_lcao.o\
 
 OBJS_PW=xc_type.o \
 xc_functional.o\
-xc_1.o\
-xc_2.o\
 xc_3.o \
 vdwd2.o\
 vdwd2_parameters.o\

source/module_base/complexmatrix.h

@@ -48,16 +48,20 @@ class ComplexMatrix
 	ComplexMatrix& operator*=(const std::complex<double> &s);
 	ComplexMatrix& operator+=(const ComplexMatrix &m);
 	ComplexMatrix& operator-=(const ComplexMatrix &m);
+	//return a matrix whose element is the real part of element of the ComplexMatrix.
 	matrix real() const;						// Peize Lin add 2017-03-29
 
 	//==================
 	// member function:
 	//==================
+	//set all elements to be complex<double> {0.0,0.0}
 	void zero_out(void);
+	//set to be a unit matrix,
 	void set_as_identity_matrix(void);
 
 	std::ostream & print( std::ostream & os, const double threshold_abs=0.0, const double threshold_imag=0.0 ) const;		// Peize Lin add 2021.09.08
 
+	// check if all the elements are real
 	bool checkreal(void);
 };
 
@@ -68,35 +72,47 @@ ComplexMatrix operator*(const std::complex<double> &s, const ComplexMatrix &m);
 ComplexMatrix operator*(const ComplexMatrix &m,   const std::complex<double> &s);
 ComplexMatrix operator*(const double &s,          const ComplexMatrix &m);
 ComplexMatrix operator*(const ComplexMatrix &m,   const double &s);
-	
+
+//calculate the trace	
 std::complex<double> trace(const ComplexMatrix &m);
 
-double abs2_row(const ComplexMatrix &m,const int ir);		// mohan add 2008-7-1
-double abs2_column(const ComplexMatrix &m,const int ic);	// mohan add 2008-7-1
+//calculate the sum of the square of the modulus of the elements in ir row.
+double abs2_row(const ComplexMatrix &m,const int ir);		// mohan add 2008-7-1	
+
+//calculate the sum of the square of the modulus of the elements in ic-th column.
+double abs2_column(const ComplexMatrix &m,const int ic);	// mohan add 2008-7-1 
+
+// calculate the sum of the square of the modulus of all elements.
 double abs2(const ComplexMatrix &m);
+
+// calculate the sum of the square of the modulus of all elements of an array of ComplexMatrix.
 double abs2(const int nmat, ComplexMatrix **m);
 
 ComplexMatrix transpose(const ComplexMatrix &m, const bool &conjugate);
 ComplexMatrix conj(const ComplexMatrix &m);						// Peize Lin add 2019-05-13
 
+//do mout += s*min
 void scale_accumulate(
 		const std::complex<double> &s, 
 		const ComplexMatrix &min, 
 		ComplexMatrix &mout);
 
+//do (*mout[i]) += s * (*min[i]); int i<nmat
 void scale_accumulate(
 		const int &nmat, 
 		const std::complex<double> &s, 
 		ComplexMatrix **min, 
 		ComplexMatrix **mout);
 
+// Do mout = s1*m1 + s2*m2
 void scaled_sum(
 		const std::complex<double> &s1, 
 		const ComplexMatrix &m1, 
 		const std::complex<double> &s2, 
 		const ComplexMatrix &m2, 
 		ComplexMatrix &mout);
 
+// Do (*mout[i]) = s1 * (*m1[i]) + s2 * (*m2[i])
 void scaled_sum(
 		const int &nmat,
 		const std::complex<double> &s1, 

source/module_base/math_integral.h

@@ -13,35 +13,72 @@ class Integral
     Integral();
     ~Integral();
 
-	// Peize Lin accelerate 2017-10-02
-    static void Simpson_Integral
-    (
+    /**
+     * @brief simpson integral.
+     * 
+     * @param mesh [in] number of grid points (should be odd)
+     * @param func [in] function to be integrated
+     * @param rab [in] a list of interval
+     * @param asum [out] the final integral value
+     * @author Peize Lin
+     * @date 2017-10-02
+     */
+    static void Simpson_Integral 
+    (    
         const int mesh,
         const double * const func,
         const double * const rab,
         double &asum
     );
 
-	// Peize Lin accelerate 2017-10-02
-	static void Simpson_Integral
+    /**
+     * @brief simpson integral. 
+     * 
+     * @param mesh [in] number of grid points (should be odd)
+     * @param func [in] function to be integrated
+     * @param dr [in] interval
+     * @param asum [out] the final integral value
+     * @author Peize Lin
+     * @date 2017-10-02
+     */
+	static void Simpson_Integral 
 	(
 		const int mesh,
 		const double * const func,
 		const double dr,
 		double &asum
 	);
 
-    // Peize Lin add 2016-02-14
-    static void Simpson_Integral_0toall
+    /**
+     * @brief simpson integral. 
+     *  
+     * 
+     * @param mesh [in] number of grid points 
+     * @param func [in] function to be integrated
+     * @param rab [in] a list of interval
+     * @param asum [out] a list of integral value. asum[i] = integral from 0 to i. The max index of asum is an even (mesh-1 or mesh).
+     * @author Peize Lin
+     * @date 2016-02-14
+     */
+    static void Simpson_Integral_0toall 
     (
         const int mesh,
         const double * const func,
         const double * const rab,
         double * const asum
     );
 
-    // Peize Lin add 2016-02-14
-    static void Simpson_Integral_alltoinf
+    /**
+     * @brief simpson integral. 
+     * 
+     * @param mesh [in] number of grid points 
+     * @param func [in] function to be integrated 
+     * @param rab [in] r(i) * dr(i)/di * di or (b-a)/2n 
+     * @param asum [out] a list of integral value. sum[i] = integral from i to mesh-1. 
+     * @author Peize Lin
+     * @date 2016-02-14
+     */
+    static void Simpson_Integral_alltoinf 
     (
         const int mesh,
         const double * const func,