Provide support for conjugate complex numbers

[Klaus Iglberger]

Description

Blaze provides support for complex numbers, but is missing the feature to compute the conjugate of a complex number. Also, Blaze does not yet provide the feature to compute the conjugate of a vector or matrix of complex numbers. Conceptually, the conj operation should work like this:

using blaze::StaticMatrix;

typedef std::complex<double>  cplx;

// Creating the matrix
//    ( (1,0)  (-2,-1) )
//    ( (1,1)  ( 0, 1) )
StaticMatrix<cplx,2UL,2UL> A( cplx(1.0,0.0), cplx(-2.0,-1.0),
                              cplx(1.0,1.0), cplx( 0.0, 1.0) );

// Computing the matrix of complex conjugates
//    ( (1, 0)  (-2, 1) )
//    ( (1,-1)  ( 0,-1) )
StaticMatrix<cplx,2UL,2UL> B;
B = conj( A );

Tasks

• provide the conj operation for scalars, including complex numbers
• provide the conj operation for dense and sparse vectors
• provide the conj operation for dense and sparse matrices
• provide a full documentation of the operation
• ensure compatibility to all existing vector and matrix classes
• ensure compatibility to all existing vector and matrix expressions
• guarantee maximum performance for the operation
• extend existing test cases to also cover the conj operation

[Klaus Iglberger]

The operations should be named conj as the according function in the standard library:

std::complex<double> a( 2.0, -1.0 );
std::complex<double> b( conj( a ) );  // Results in (2,1)

[Klaus Iglberger]

The feature has been implemented, tested, optimized (including vectorization and parallelization) and documented as required. The following examples give an impression of the final feature:

using blaze::StaticVector;

typedef std::complex<double>  cplx;

// Creating the vector
//    ( (-2,-1) )
//    ( ( 1, 1) )
StaticVector<cplx,2UL> a( cplx(-2.0,-1.0), cplx(1.0,1.0) );

// Computing the vector of complex conjugates
//    ( (-2, 1) )
//    ( ( 1,-1) )
StaticVector<cplx,2UL> b;
b = conj( a );

using blaze::StaticMatrix;

typedef std::complex<double>  cplx;

// Creating the matrix
//    ( (1,0)  (-2,-1) )
//    ( (1,1)  ( 0, 1) )
StaticMatrix<cplx,2UL,2UL> A( cplx(1.0,0.0), cplx(-2.0,-1.0),
                              cplx(1.0,1.0), cplx( 0.0, 1.0) );

// Computing the matrix of conjugate values
//    ( (1, 0)  (-2, 1) )
//    ( (1,-1)  ( 0,-1) )
StaticMatrix<cplx,2UL,2UL> B;
B = conj( A );

The feature is immediately available via cloning the Blaze repository. It will be officially released in Blaze 2.5.