def showmap(a, fmt='png'):
a = np.uint8(np.clip(a, 0, 255))
f = StringIO()
PIL.Image.fromarray(a).save(f, fmt)
display(Image(data=f.getvalue()))
#def checkparam(param):
# octave = param['octave']
# starting_range = param['starting_range']
# ending_range = param['ending_range']
# assert starting_range <= ending_range, 'starting ratio should <= ending ratio'
# assert octave >= 1, 'octave should >= 1'
# return starting_range, ending_range, octave
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