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5.1 Complex numbers

Complex numbers are represented using the type gsl_complex. The internal representation of this type may vary across platforms and should not be accessed directly. The functions and macros described below allow complex numbers to be manipulated in a portable way.

For reference, the default form of the gsl_complex type is given by the following struct, 

     typedef struct
     {
       double dat[2];
     } gsl_complex;

The real and imaginary part are stored in contiguous elements of a two element array. This eliminates any padding between the real and imaginary parts, dat[0] and dat[1], allowing the struct to be mapped correctly onto packed complex arrays.

— Function: gsl_complex gsl_complex_rect (double x, double y)

This function uses the rectangular cartesian components (x,y) to return the complex number z = x + i y.

— Function: gsl_complex gsl_complex_polar (double r, double theta)

This function returns the complex number z = r \exp(i \theta) = r (\cos(\theta) + i \sin(\theta)) from the polar representation (r,theta).

— Macro: GSL_REAL (z)
— Macro: GSL_IMAG (z)

These macros return the real and imaginary parts of the complex number z.

— Macro: GSL_SET_COMPLEX (zp, x, y)

This macro uses the cartesian components (x,y) to set the real and imaginary parts of the complex number pointed to by zp. For example, 

          GSL_SET_COMPLEX(&z, 3, 4)

sets z to be 3 + 4i.

— Macro: GSL_SET_REAL (zp,x)
— Macro: GSL_SET_IMAG (zp,y)

These macros allow the real and imaginary parts of the complex number pointed to by zp to be set independently.