import numpy as np
import holoviews as hv
hv.extension('bokeh')
%opts Curve Area [width=600]

def fm_modulation(f_carrier=110, f_mod=110, mod_index=1, length=0.1, sampleRate=3000):
    x = np.arange(0, length, 1.0/sampleRate)
    y = np.sin(2*np.pi*f_carrier*x + mod_index*np.sin(2*np.pi*f_mod*x))
    return hv.Curve((x, y), kdims=['Time'], vdims=['Amplitude'])

fm_modulation()

carrier_frequencies = [10, 20, 110, 220, 330]
modulation_frequencies = [110, 220, 330]

hmap = hv.HoloMap({(fc, fm): fm_modulation(fc, fm) for fc in carrier_frequencies
                   for fm in modulation_frequencies}, kdims=['fc', 'fm'])
hmap

# Exercise: Try changing the function below to return an ``Area`` or ``Scatter`` element,
# in the same way `fm_modulation` returned a ``Curve`` element.
def fm_modulation2(f_carrier=220, f_mod=110, mod_index=1, length=0.1, sampleRate=3000):
    x = np.arange(0,length, 1.0/sampleRate)
    y = np.sin(2*np.pi*f_carrier*x + mod_index*np.sin(2*np.pi*f_mod*x))

# Then declare a HoloMap like above and assign it to a ``exercise_hmap`` variable and display that


%%opts Curve (color='red')
dmap = hv.DynamicMap(fm_modulation, kdims=['f_carrier', 'f_mod', 'mod_index'])
dmap = dmap.redim.range(f_carrier=((10, 110)), f_mod=(10, 110), mod_index=(0.1, 2))
dmap

# Exercise: Declare a DynamicMap using the function from the previous exercise and name it ``exercise_dmap``


# Exercise (Optional): Use the ``.redim.step`` method and a floating point range to modify the slider step


%%opts Curve [width=150]
hv.GridSpace(hmap).opts()

# Exercise: Try casting your ``exercise_hmap`` HoloMap from the first exercise to an ``NdLayout`` or 
# ``NdOverlay``, guessing from the name what the resulting organization will be before testing it.


hmap.overlay('fm')

%%opts Curve [width=150]
dmap.redim.values(f_mod=[10, 20, 30], f_carrier=[10, 20, 30]).overlay('f_mod').grid('f_carrier').opts()

# Exercise: Facet the ``exercise_dmap`` DynamicMap using ``.overlay`` and ``.grid``
# Hint: Use the .redim.values method to set discrete values for ``f_mod`` and ``f_carrier`` dimensions


%%opts Curve [width=300]
hmap[10, 110] + hmap[10, 200:].overlay() + hmap[[10, 110], 110].overlay()

(hmap.select(fc=10, fm=110) +
 hmap.select(fc=10, fm=(200, None)).overlay() +
 hmap.select(fc=[10, 110], fm=110).overlay())

# Exercise: Try selecting two carrier frequencies and two modulation frequencies on the ``exercise_hmap``