Auxiliary Data Transformations

This section presents code examples for conversion from the Cartesian to polar representation of complex data and vice versa.

Conversion from Cartesian to polar representation of complex data

// Cartesian->polar conversion of complex data
// Cartesian representation: z = re + I*im
// Polar representation: z = r * exp( I*phi )
#include <mkl_vml.h>
 
void 
variant1_Cartesian2Polar(int n,const double *re,const double *im,
                         double *r,double *phi)
{
    vdHypot(n,re,im,r);         // compute radii r[]
    vdAtan2(n,im,re,phi);       // compute phases phi[]
}
 
void 
variant2_Cartesian2Polar(int n,const MKL_Complex16 *z,double *r,double *phi,
                         double *temp_re,double *temp_im)
{
    vzAbs(n,z,r);               // compute radii r[]
    vdPackI(n, (double*)z + 0, 2, temp_re);
    vdPackI(n, (double*)z + 1, 2, temp_im);
    vdAtan2(n,temp_im,temp_re,phi); // compute phases phi[]
}

Conversion from polar to Cartesian representation of complex data

// Polar->Cartesian conversion of complex data.
// Polar representation: z = r * exp( I*phi )
// Cartesian representation: z = re + I*im
#include <mkl_vml.h>
 
void
variant1_Polar2Cartesian(int n,const double *r,const double *phi,
                         double *re,double *im)
{
    vdSinCos(n,phi,im,re);      // compute direction, i.e. z[]/abs(z[])
    vdMul(n,r,re,re);           // scale real part
    vdMul(n,r,im,im);           // scale imaginary part
}
 
void
variant2_Polar2Cartesian(int n,const double *r,const double *phi,
                         MKL_Complex16 *z,
                         double *temp_re,double *temp_im)
{
    vdSinCos(n,phi,temp_im,temp_re); // compute direction, i.e. z[]/abs(z[])
    vdMul(n,r,temp_im,temp_im); // scale imaginary part
    vdMul(n,r,temp_re,temp_re); // scale real part
    vdUnpackI(n,temp_re,(double*)z + 0, 2); // fill in result.re
    vdUnpackI(n,temp_im,(double*)z + 1, 2); // fill in result.im
}