KRON: Calculating Kronecker Products of Two Matrices with C++ and Fortran 90

Purpose

• The library "kron" provides generic C++ and Fortran 90 codes for calculating the Kronecker product of two matrices of any size. It does not require any installation of other libraries. In C++, matrices are stored as 'column major ordered' vectors. In Fortran 90, matrices are stored as 2-D arrays.

Specifications

• Name: kron.
• Author: Feng Chen.
• Version: 2.8
• Language: C++ and Fortran 90.

Simple Example

• Given matrices: \begin{equation} A = \left[ \begin{array}{ccc} 1 & 2 & 3 \\ 2 & 4 & 6 \end{array} \right], \quad B = \left[ \begin{array}{cc} 2 & 3 \\ 3 & 4 \end{array} \right] \end{equation}
• Results: \begin{equation} C = A \otimes B = \left[ \begin{array}{cccccc} 2 & 3 & 4 & 6 & 6 & 9 \\ 3 & 4 & 6 & 8 & 9 & 12 \\ 4 & 6 & 8 & 12 & 12 & 18 \\ 6 & 8 & 12 & 16 & 18 & 24 \end{array} \right] \end{equation}

Quick Start

• Compiling and running:

  gfortran tst_Kronecker.f90 Kronecker.f90
  

• Output:

   
   ---A---
   1.0     2.0     3.0    
   2.0     4.0     6.0    
   ---B---
   2.0     3.0    
   3.0     4.0    
   ---C---
   2.0     3.0     4.0     6.0     6.0     9.0    
   3.0     4.0     6.0     8.0     9.0     12.    
   4.0     6.0     8.0     12.     12.     18.    
   6.0     8.0     12.     16.     18.     24.    
  

• CPU: Genuine Intel(R) CPU T2060 @ 1.60GHz.
• OS: Ubuntu 10.10.
• Release: gcc version 4.4.5.

References

• Kronecker product. Link.

Code Highlights

//
// calculate the Kronecker product of two matrices of any size:
//     C = a*C + b*(A kron B);
//
// PARAMETERS:
//    ma - number of rows of A.
//    na - number of columns of A.
//    mb - number of rows of B.
//    nb - number of columns of B.
//    A - matrix 'A', column major ordering, stored as a 1-D vector.
//    B - matrix 'B', column major ordering, stored as a 1-D vector.
//    C - matrix 'a*C + b*(A kron B)', column major ordering, stored as a 1-D vector.
//
// WARNINGS:
//    1. Every matrix is stored in a column major fashion, in order to be compatible with Fortran.
//       For row major ordering vectors, users have to switch the row and column indicies.
//    2. Every matrix is stored as a 1-D vector instead of a pointer to pointers.
//

void Kronecker(const int ma, const int na, const int mb, const int nb,
 const double a, const double b, const double *A, const double *B, double *C){

 int i, j, I, J, M, N;
 double c;
 M = ma*mb;
 N = na*nb;
 for(j=0; j < na; j++){
  for(i=0; i < ma; i++){
   I = i*mb;
   J = j*nb;
   c = b*A[cm(i,j,ma)];
   assign_matrix_block(I, J, mb, nb, M, N, a, c, B, C);
  }
 }
}