-Added Hermitian and symmetric matrices multiplication

-Fixed imaginary numbers printing by removing excess "+" when imaginary
part is negative
-

include/internal/LapackAdapters.h

@@ -30,8 +30,15 @@ extern "C" int  cheevd_( char* jobz, char* uplo, lapack_int* n, lapack_complex_f
 extern "C" int  zheevd_( char* jobz, char* uplo, lapack_int* n, lapack_complex_double* a, lapack_int* lda, double* w, lapack_complex_double* work, lapack_int* lwork, double* rwork, lapack_int* lrwork, lapack_int* iwork, lapack_int* liwork, lapack_int *info );
 extern "C" void sgemm_(char * transa, char * transb, lapack_int * m, lapack_int * n, lapack_int * k, float* alpha, float * A, lapack_int * lda, float * B, lapack_int * ldb, float * beta, float *, lapack_int * ldc);
 extern "C" void dgemm_(char * transa, char * transb, lapack_int * m, lapack_int * n, lapack_int * k, double * alpha, double * A, lapack_int * lda, double * B, lapack_int * ldb, double * beta, double *, lapack_int * ldc);
-extern "C" void cgemm_(char*,char*,lapack_int*,lapack_int*,lapack_int*, lapack_complex_float*, lapack_complex_float*, lapack_int*, lapack_complex_float*,lapack_int*, lapack_complex_float*, lapack_complex_float*,lapack_int*);
-extern "C" void zgemm_(char*, char*, lapack_int*, lapack_int*, lapack_int*, lapack_complex_double*, lapack_complex_double*,lapack_int*, lapack_complex_double*,lapack_int*, lapack_complex_double*,lapack_complex_double*,lapack_int*);
+extern "C" void cgemm_(char*     , char*     , lapack_int*  ,lapack_int*   , lapack_int*  , lapack_complex_float*, lapack_complex_float*, lapack_int*, lapack_complex_float*,lapack_int*, lapack_complex_float*, lapack_complex_float*,lapack_int*);
+extern "C" void zgemm_(char*     , char*     , lapack_int*  , lapack_int*  , lapack_int*  , lapack_complex_double*, lapack_complex_double*,lapack_int*, lapack_complex_double*,lapack_int*, lapack_complex_double*,lapack_complex_double*,lapack_int*);
+extern "C" int  ssymm_(char *side, char *uplo, lapack_int *m, lapack_int *n, float  *alpha, float  *a, lapack_int *lda, float  *b, lapack_int *ldb, float  *beta, float  *c__, lapack_int *ldc);
+extern "C" int  dsymm_(char *side, char *uplo, lapack_int *m, lapack_int *n, double *alpha, double *a, lapack_int *lda, double *b, lapack_int *ldb, double *beta, double *c__, lapack_int *ldc);
+extern "C" int  csymm_(char *side, char *uplo, lapack_int *m, lapack_int *n, lapack_complex_float  *alpha, lapack_complex_float  *a, lapack_int *lda, lapack_complex_float  *b, lapack_int *ldb, lapack_complex_float  *beta, lapack_complex_float  *c__, lapack_int *ldc);
+extern "C" int  zsymm_(char *side, char *uplo, lapack_int *m, lapack_int *n, lapack_complex_double *alpha, lapack_complex_double *a, lapack_int *lda, lapack_complex_double *b, lapack_int *ldb, lapack_complex_double *beta, lapack_complex_double *c__, lapack_int *ldc);
+extern "C" int  chemm_(char *side, char *uplo, lapack_int *m, lapack_int *n, lapack_complex_float  *alpha, lapack_complex_float  *a, lapack_int *lda, lapack_complex_float  *b, lapack_int *ldb, lapack_complex_float  *beta, lapack_complex_float  *c__, lapack_int *ldc);
+extern "C" int  zhemm_(char *side, char *uplo, lapack_int *m, lapack_int *n, lapack_complex_double *alpha, lapack_complex_double *a, lapack_int *lda, lapack_complex_double *b, lapack_int *ldb, lapack_complex_double *beta, lapack_complex_double *c__, lapack_int *ldc);
+
 //#endif
 
 

include/internal/Matrix.h

@@ -106,7 +106,7 @@ to_string(const T& a_value, int precision)
 {
     std::ostringstream out;
     out << std::setprecision(precision) << a_value.real();
-    out << "+";
+    out << (a_value.imag() < 0 ? "" : "+"); //"-" comes from the number itself
     out << std::setprecision(precision) << a_value.imag();
     out << Poly::ComplexUnit;
     return out.str();
@@ -133,9 +133,9 @@ const static EIGENS_METHOD METHOD_DIVIDE_CONQUER = 1;
 
 
 template <typename T, int M>
-void MultiplyMatrices(const Matrix<T,M> &matrixLHS, const Matrix<T,M> &matrixRHS, Matrix<T,M> &result);
+void MultiplyMatrices(const Matrix<T,M> &matrixLHS, const Matrix<T,M> &matrixRHS, Matrix<T,M> &result, const MATRIX_TYPE& lhs_type = MATRIX_GENERAL, const MATRIX_TYPE& rhs_type = MATRIX_GENERAL);
 template <typename T, int M>
-void MultiplyMatrices(const Matrix<T,M>& lhs, const Matrix<T,M>& rhs, Matrix<T,M> &to_add_then_result, T alpha, T beta);
+void MultiplyMatrices(const Matrix<T,M>& lhs, const Matrix<T,M>& rhs, Matrix<T,M> &to_add_then_result, T alpha, T beta, const MATRIX_TYPE& lhs_type = MATRIX_GENERAL, const MATRIX_TYPE& rhs_type = MATRIX_GENERAL);
 template <typename T, int M>
 Matrix<T,M> IdentityMatrix(const typename Matrix<T,M>::size_type& size);
 template <typename T, typename U, int M>
@@ -558,7 +558,6 @@ Matrix<std::complex<T>,M> operator*(const T& lhs, const Matrix<std::complex<T>,M
     return result;
 }
 
-
 template <typename T, int M>
 Matrix<T,M> operator*(const Matrix<T,M>& lhs, const Matrix<T,M>& rhs)
 {
@@ -1498,6 +1497,93 @@ std::string _lapack_eigens_exception_converge_error(int info);
 std::string _lapack_unsupported_type();
 std::string _unsupported_type(const std::string& function_name);
 
+template <typename T, int M>
+void _Lapack_multiply_matrix_symmetric(const Matrix<T,M>& lhs_i, const Matrix<T,M>& rhs_i, bool sym_mat_matrix_is_left, Matrix<T,M> &to_add_then_result, T alpha, T beta)
+{
+    char sym_mat_is_left_or_right = (sym_mat_matrix_is_left ? 'L' : 'R');
+    const Matrix<T,M> *lhs, *rhs;
+    //whether the first matrix is on the left or right is determined by the first parameter in the LAPACK call
+    if(sym_mat_matrix_is_left)
+    {
+        lhs = &lhs_i;
+        rhs = &rhs_i;
+    }
+    else
+    {
+        lhs = &rhs_i;
+        rhs = &lhs_i;
+    }
+    char uplo = 'U';
+    int m = static_cast<int>(lhs->rows());
+    int n = static_cast<int>(rhs->columns());
+    int k = static_cast<int>(lhs->columns());
+    int lda = std::max({1,k});
+    int ldb = std::max({1,n});
+    int ldc = std::max({1,m});
+    if(std::is_same<T,double>::value)
+    {
+        typedef double TP;
+        dsymm_(&sym_mat_is_left_or_right, &uplo, &m, &n, (TP*)&alpha, (TP*)&lhs->front(), &lda, (TP*)&rhs->front(), &ldb, (TP*)&beta, (TP*)&to_add_then_result.front(), &ldc);
+    }
+    else if(std::is_same<T,lapack_complex_double>::value)
+    {
+        typedef lapack_complex_double TP;
+        zsymm_(&sym_mat_is_left_or_right, &uplo, &m, &n, (TP*)&alpha, (TP*)&lhs->front(), &lda, (TP*)&rhs->front(), &ldb, (TP*)&beta, (TP*)&to_add_then_result.front(), &ldc);
+    }
+    else if(std::is_same<T,float>::value)
+    {
+        typedef float TP;
+        ssymm_(&sym_mat_is_left_or_right, &uplo, &m, &n, (TP*)&alpha, (TP*)&lhs->front(), &lda, (TP*)&rhs->front(), &ldb, (TP*)&beta, (TP*)&to_add_then_result.front(), &ldc);
+    }
+    else if(std::is_same<T,lapack_complex_float>::value)
+    {
+        typedef lapack_complex_float TP;
+        csymm_(&sym_mat_is_left_or_right, &uplo, &m, &n, (TP*)&alpha, (TP*)&lhs->front(), &lda, (TP*)&rhs->front(), &ldb, (TP*)&beta, (TP*)&to_add_then_result.front(), &ldc);
+    }
+    else
+    {
+        throw std::logic_error(_lapack_unsupported_type());
+    }
+}
+
+template <typename T, int M>
+void _Lapack_multiply_matrix_hermitian(const Matrix<T,M>& lhs_i, const Matrix<T,M>& rhs_i, bool herm_mat_matrix_is_left, Matrix<T,M> &to_add_then_result, T alpha, T beta)
+{
+    char herm_mat_is_left_or_right = (herm_mat_matrix_is_left ? 'L' : 'R');
+    const Matrix<T,M> *lhs, *rhs;
+    //whether the first matrix is on the left or right is determined by the first parameter in the LAPACK call
+    if(herm_mat_matrix_is_left)
+    {
+        lhs = &lhs_i;
+        rhs = &rhs_i;
+    }
+    else
+    {
+        lhs = &rhs_i;
+        rhs = &lhs_i;
+    }
+    char uplo = 'U';
+    int m = static_cast<int>(lhs->rows());
+    int n = static_cast<int>(rhs->columns());
+    int k = static_cast<int>(lhs->columns());
+    int lda = std::max({1,k});
+    int ldb = std::max({1,n});
+    int ldc = std::max({1,m});
+    if(std::is_same<T,lapack_complex_double>::value)
+    {
+        typedef lapack_complex_double TP;
+        zhemm_(&herm_mat_is_left_or_right, &uplo, &m, &n, (TP*)&alpha, (TP*)&lhs->front(), &lda, (TP*)&rhs->front(), &ldb, (TP*)&beta, (TP*)&to_add_then_result.front(), &ldc);
+    }
+    else if(std::is_same<T,lapack_complex_float>::value)
+    {
+        typedef lapack_complex_float TP;
+        chemm_(&herm_mat_is_left_or_right, &uplo, &m, &n, (TP*)&alpha, (TP*)&lhs->front(), &lda, (TP*)&rhs->front(), &ldb, (TP*)&beta, (TP*)&to_add_then_result.front(), &ldc);
+    }
+    else
+    {
+        throw std::logic_error(_lapack_unsupported_type());
+    }
+}
 
 template <typename T, int M>
 void _Lapack_multiply_matrix_general(const Matrix<T,M>& lhs, const Matrix<T,M>& rhs, Matrix<T,M> &to_add_then_result, T alpha, T beta)
@@ -1541,7 +1627,13 @@ void _Lapack_multiply_matrix_general(const Matrix<T,M>& lhs, const Matrix<T,M>&
 }
 
 template <typename T, int M>
-void MultiplyMatrices(const Matrix<T,M>& lhs, const Matrix<T,M>& rhs, Matrix<T,M> &to_add_then_result, T alpha, T beta)
+void MultiplyMatrices(const Matrix<T,M>& lhs,
+                      const Matrix<T,M>& rhs,
+                      Matrix<T,M> &to_add_then_result,
+                      T alpha,
+                      T beta,
+                      const MATRIX_TYPE& lhs_type,
+                      const MATRIX_TYPE& rhs_type)
 {
 //    std::cout<<"multiplication: "<<lhs.columns()<<"\t"<<rhs.rows()<<std::endl;
 #ifdef POLYMATH_DEBUG
@@ -1556,7 +1648,19 @@ void MultiplyMatrices(const Matrix<T,M>& lhs, const Matrix<T,M>& rhs, Matrix<T,M
        std::is_same<T,lapack_complex_double>::value ||
        std::is_same<T,lapack_complex_float>::value)
     {
-        _Lapack_multiply_matrix_general(lhs,rhs,to_add_then_result,alpha,beta);
+        if(lhs_type == MATRIX_SYMMETRIC || rhs_type == MATRIX_SYMMETRIC)
+        {
+            _Lapack_multiply_matrix_symmetric(lhs,rhs,(lhs_type == MATRIX_SYMMETRIC ? true : false),to_add_then_result,alpha,beta);
+        }
+        else if((lhs_type == MATRIX_HERMITIAN || rhs_type == MATRIX_HERMITIAN) &&
+            (std::is_same<T,lapack_complex_float>::value || std::is_same<T,lapack_complex_double>::value))
+        {
+            _Lapack_multiply_matrix_hermitian(lhs,rhs,(lhs_type == MATRIX_HERMITIAN ? true : false),to_add_then_result,alpha,beta);
+        }
+        else
+        {
+            _Lapack_multiply_matrix_general(lhs,rhs,to_add_then_result,alpha,beta);
+        }
     }
     else
     {
@@ -1579,9 +1683,11 @@ void MultiplyMatrices(const Matrix<T,M>& lhs, const Matrix<T,M>& rhs, Matrix<T,M
 template <typename T, int M>
 void MultiplyMatrices(const Matrix<T,M> &matrixLHS,
                       const Matrix<T,M> &matrixRHS,
-                      Matrix<T,M> &result)
+                      Matrix<T,M> &result,
+                      const MATRIX_TYPE& lhs_type,
+                      const MATRIX_TYPE& rhs_type)
 {
-    Poly::MultiplyMatrices(matrixLHS,matrixRHS,result,T(1),T(0));
+    Poly::MultiplyMatrices(matrixLHS,matrixRHS,result,T(1),T(0),lhs_type,rhs_type);
 }
 
 template <typename T, int M = ColMaj>
@@ -1594,24 +1700,20 @@ RandomMatrix(const typename Matrix<T,M>::size_type& rows,
              const MATRIX_TYPE& type = Poly::MATRIX_GENERAL)
 {   
     Matrix<T,M> result(rows,columns);
-    if(std::is_integral<T>::value)
-    {
+    if(std::is_integral<T>::value) {
         std::uniform_int_distribution<T> distribution(min,max);
         std::default_random_engine generator(seed);
         std::generate(result.begin(), result.end(), [&]() { return distribution(generator); });
     }
 
-    if(type == MATRIX_SYMMETRIC || type == MATRIX_HERMITIAN)
-    {
+    if(type == MATRIX_SYMMETRIC || type == MATRIX_HERMITIAN) {
         result = result/T(2) + Poly::Transpose<T,M>(result/T(2));
     }
-    else if(type == MATRIX_ANTISYMMETRIC || type == MATRIX_ANTIHERMITIAN)
-    {
+    else if(type == MATRIX_ANTISYMMETRIC || type == MATRIX_ANTIHERMITIAN) {
         result = result/T(2) - Poly::Transpose<T,M>(result/T(2));
     }
     else if(type == MATRIX_GENERAL) {}
-    else
-    {
+    else {
         throw std::logic_error(_unsupported_type(__func__).c_str());
     }
     return result;