Complex Vectors and Matrices

When you are working with complex vectors and matrices dealing with real and imaginary parts is a common task. The following is supported in FLENS:

For complex valued dense vectors you can create real valued dense vectors that reference the real or imaginary vector parts. This is possible as as a dense vector reference can reference elements that are separated by a constant stride.
For complex valued matrices of type GeMatrix we support copying the real and imaginary parts to a real valued matrix and vice versa. Note that it is not possible that a GeMatrix view can be used to reference the real or imaginary part of a complex valued GeMatrix:
- If a GeMatrix stores elements in row major order then row elements must be contiguously in memory. However, complete rows can be separated by a constant stride.
- If a GeMatrix stores elements in col major order then column elements must be contiguously in memory. However, complete columns can be separated by a constant stride.
If you have complex elements and want to reference only the real or imaginary part there always will be gaps. So a new matrix type is defined for this case. However, BLAS functionality for this type is limited to copy.

Complex Vectors

flens/examples/complex-densevector-views.cc

#include <complex>

#include <iostream>

#include <flens/flens.cxx>

using namespace flens;

using namespace std;

int

main()

{

    typedef complex<double>        Complex;

    DenseVector<Array<Complex> >   z(5);

    z = Complex(1,2), Complex(3,4), Complex(5,6), Complex(7,8), Complex(9,10);

    Underscore<int> _;

    auto x = real(z);

    auto y = imag(z);

    cout << "z = " << z << endl;

    cout << "real(z) = " << x << endl;

    cout << "imag(z) = " << y << endl;

    x = 2, 9, 4, 7, 6;

    y(_(1,2,5)) = 666, -666, 666;

    cout << "z = " << z << endl;

    blas::swap(x,y);

    cout << "z = " << z << endl;

}

So some notes about what is going on :import: flens/examples/complex-densevector-views.cc [brief]

So let's compile and run the example:

$shell> cd flens/examples                                                         
$shell> g++ -Wall -std=c++11 -I../.. complex-densevector-views.cc                 
$shell> ./a.out                                                                   
z = 
                       (1,2)                         (3,4)                         (5,6)                         (7,8)                        (9,10) 
real(z) = 
            1              3              5              7              9 
imag(z) = 
            2              4              6              8             10 
z = 
                     (2,666)                         (9,4)                      (4,-666)                         (7,8)                       (6,666) 
z = 
                     (666,2)                         (4,9)                      (-666,4)                         (8,7)                       (666,6)

Complex Matrices

flens/examples/complex-gematrix-views.cc

#include <complex>

#include <iostream>

#include <flens/flens.cxx>

using namespace flens;

using namespace std;

int

main()

{

   typedef GeMatrix<FullStorage<complex<double> > >    ComplexGeMatrix;

   typedef GeMatrix<FullStorage<double> >              RealGeMatrix;

    const int m = 5;

    const int n = 4;

    ComplexGeMatrix  Z(m,n);

    ComplexGeMatrix::IndexVariable  i,j;

    Z(i,j) = Complex(i+j,j-i);

    RealGeMatrix X = real(Z);

    RealGeMatrix  Y;

    Y = imag(Z);

    cout << "Z = " << Z << endl;

    cout << "real(Z) = " << X << endl;

    cout << "imag(Z) = " << Y << endl;

    real(Z) = Y;

    imag(Z) = X;

    cout << "Z = " << Z << endl;

}

So some notes about what is going on :import: flens/examples/complex-gematrix-views.cc [brief]

So let's compile and run the example:

$shell> cd flens/examples                                                         
$shell> g++ -Wall -std=c++11 -I../.. complex-gematrix-views.cc                    
$shell> ./a.out                                                                   
Z = 
                       (2,0)                        (3,1)                        (4,2)                        (5,3) 
                      (3,-1)                        (4,0)                        (5,1)                        (6,2) 
                      (4,-2)                       (5,-1)                        (6,0)                        (7,1) 
                      (5,-3)                       (6,-2)                       (7,-1)                        (8,0) 
                      (6,-4)                       (7,-3)                       (8,-2)                       (9,-1) 
real(Z) = 
            2             3             4             5 
            3             4             5             6 
            4             5             6             7 
            5             6             7             8 
            6             7             8             9 
imag(Z) = 
            0             1             2             3 
           -1             0             1             2 
           -2            -1             0             1 
           -3            -2            -1             0 
           -4            -3            -2            -1 
Z = 
                       (0,2)                        (1,3)                        (2,4)                        (3,5) 
                      (-1,3)                        (0,4)                        (1,5)                        (2,6) 
                      (-2,4)                       (-1,5)                        (0,6)                        (1,7) 
                      (-3,5)                       (-2,6)                       (-1,7)                        (0,8) 
                      (-4,6)                       (-3,7)                       (-2,8)                       (-1,9)