# polar2cartesian.m

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Converts [RF_amplitude, RF_phase] representation of a pulse waveform and the derivatives of any function with respect to those amplitudes and phases into the [RF_x, RF_y] representation and the derivatives of the function with respect to those X and Y RF values.

## Syntax

    [x,y,Dx,Dy,Dxx,Dxy,Dyx,Dyy]=polar2cartesian(r,p,Dr,Dp,Drr,Drp,Dpr,Dpp)


## Arguments

   r    - vector of waveform amplitudes

p    - vector of waveform phases

Dr   - optional vector of derivatives of some scalar function
with respect to the waveform amplitudes.

Dp   - optional vector of derivatives of some scalar function
with respect to the waveform phases.

Drr  - matrix of second derivatives of the function with respect
to the waveform amplitudes.

Drp  - matrix of second derivatives of the function with respect
to the waveform amplitudes and phases.

Dpr  - matrix of second derivatives of the function with respect
to the waveform phases and amplitudes.

Dpp  - matrix of second derivatives of the function with respect
to the waveform phases.


## Outputs

   x    - vector of waveform amplitudes along X

y    - vector of waveform amplitudes along Y

Dx   - vector of derivatives of the function with respect to
the waveform amplitudes along X

Dy   - vector of derivatives of the function with respect to
the waveform amplitudes along Y

Dxx  - optional matrix of second derivatives of a scalar function
with respect to the waveform amplitudes along X

Dxy  - optional matrix of second derivatives of a scalar function
with respect to the waveform amplitudes along X and Y

Dyx  - optional matrix of second derivatives of a scalar function
with respect to the waveform amplitudes along Y and X

Dyy  - optional matrix of second derivatives of a scalar function
with respect to the waveform amplitudes along Y


## See also

Version 2.4, authors: David Goodwin, Ilya Kuprov