# Cartesian2polar.m

From Spinach Documentation Wiki

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

[A,phi,df_dA,df_dphi]=cartesian2polar(x,y,df_dx,df_dy)

Parameters:

x - vector of waveform amplitudes along X

y - vector of waveform amplitudes along Y

df_dx - optional vector of derivatives of a scalar function with respect to the waveform amplitudes along X

df_dy - optional vector of derivatives of a scalar function with respect to the waveform amplitudes along Y

d2f_dx2 - optional matrix of second derivatives of a scalar function with respect to the waveform amplitudes along X

d2f_dxdy- optional matrix of second derivatives of a scalar function with respect to the waveform amplitudes along X and Y

d2f_dy2 - optional matrix of second derivatives of a scalar function with respect to the waveform amplitudes along Y

Outputs:

A - vector of waveform amplitudes

phi - vector of waveform phases

df_dA - vector of derivatives of the function with respect to the waveform amplitudes.

df_dphi - vector of derivatives of the function with respect to the waveform phases.

d2f_dA2 - matrix of second derivatives of the function with respect to the waveform amplitudes.

d2f_dAdphi- matrix of second derivatives of the function with respect to the waveform amplitudes and phases.

d2f_dphi2- matrix of second derivatives of the function with respect to the waveform phases.