Contents

# Auxiliary Data Transformations

This section presents C 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
}```

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