Components of Complex Matrices

SourcePro : Linear Algebra Module User’s Guide : Vectors and Matrices : Accessing Data : Components of Complex Matrices

The real and imaginary parts of complex matrices are also easy to access. The member functions real() and imag() return a matrix containing the real or imaginary part. For example, consider the following code:

#include <rw/lapack/hermmat.h>

#include <rw/lapack/symmat.h>

#include <rw/lapack/skewmat.h>

int main()

{

RWHermMat<DComplex> H(5, 5); // 1

RWSymMat<double> Hreal = real(H); // 2

RWSkewMat<double> Himag = imag(H); // 3

return 0;

}

//1 In //1 the matrix H is defined to be a 5 x 5 Hermitian matrix. A Hermitian matrix is equal to its complex conjugate transpose; this implies that its real part is symmetric, and its imaginary part is skew symmetric.

//2 Here we extract the real part of H. Note that the global function real() is an overloaded function. The compiler selects the function with prototype:

RWSymMat<double> real(const RWHermMat<DComplex>&);

Note that this function returns a symmetric matrix.

//3 Now the imaginary part of H is extracted. The function imag() has prototype:

RWSkewMat<double> imag(const RWHermMat<DComplex>&);

and returns a skew symmetric matrix, just as the mathematics implies it must.

In this example, the matrices Hreal and Himag actually refer to the data of H; that is, they present different views of the same data as H. You can use this fact to conveniently modify the real and imaginary parts of a complex matrix in the following example:

#include <rw/cgenmat.h>

#include <rw/dgenmat.h>

int main()

{

RWGenMat<DComplex> A(5,5, rwUninitialized); // 1

real(A) = 1; // 2

imag(A) = -1; // 3

return 0;

}

//1 This line defines a 5 x 5 general complex matrix with double precision.

//2 The real parts of the matrix are set to 1.

//3 The imaginary parts of the matrix are set to –1.