def getWeights(X1D):
d = len(X1D)
''' puts the X values in their respective dimensions to use bsxfun for
evaluation'''
Xreshape = []
Xreshape.append(X1D[0].reshape(-1,1))
if d >= 2:
Xreshape.append(X1D[1].reshape([1,-1]))
for idx in range (2,d):
dims = [1]*idx
dims.append(-1)
Xreshape.append(reshape(X1D[idx], dims))
# to find and handle singleton dimensions
sizes = [X1D[ix].size for ix in range(0,d)]
Xlength = array(sizes)
''' calculate weights '''
#1) calculate mass/volume for each cuboid
weight = 1
for idx in range(0,d):
if Xlength[idx] > 1:
if idx > 1:
weight = multiply(weight[...,newaxis],diff(Xreshape[idx], axis=idx))
else:
weight = multiply(weight,diff(Xreshape[idx], axis=idx))
else:
weight = weight[...,newaxis]
#2) sum to get weight for each point
if d > 1:
dims = tile(2,[1,d])
dims[0,where(Xlength == 1)] = 1
d = sum(Xlength > 1)
weight = (2**(-d))*convn(weight, ones(dims.ravel()), mode='full')
else:
weight = (2**(-1))*convolve(weight, array([[1],[1]]))
return weight
def getWeights(X1D):
d = len(X1D)
''' puts the X values in their respective dimensions to use bsxfun for
evaluation'''
Xreshape = []
Xreshape.append(X1D[0].reshape(-1, 1))
if d >= 2:
Xreshape.append(X1D[1].reshape([1, -1]))
for idx in range(2, d):
dims = [1] * idx
dims.append(-1)
Xreshape.append(reshape(X1D[idx], dims))
# to find and handle singleton dimensions
sizes = [X1D[ix].size for ix in range(0, d)]
Xlength = array(sizes)
''' calculate weights '''
#1) calculate mass/volume for each cuboid
weight = 1
for idx in range(0, d):
if Xlength[idx] > 1:
if idx > 1:
weight = multiply(weight[..., newaxis],
diff(Xreshape[idx], axis=idx))
else:
weight = multiply(weight, diff(Xreshape[idx], axis=idx))
else:
weight = weight[..., newaxis]
#2) sum to get weight for each point
if d > 1:
dims = tile(2, [1, d])
dims[0, where(Xlength == 1)] = 1
d = sum(Xlength > 1)
weight = (2.**(-d)) * convn(weight, ones(dims.ravel()), mode='full')
else:
weight = (2.**(-1)) * convolve(weight, array([[1], [1]]))
return weight
def plotPrior(result,
lineWidth = 2,
lineColor = np.array([0,105,170])/255,
markerSize = 30):
"""
This function creates the plot illustrating the priors on the different
parameters
"""
data = result['data']
if np.size(result['options']['stimulusRange']) <= 1:
result['options']['stimulusRange'] = np.array([min(data[:,0]), max(data[:,0])])
stimRangeSet = False
else:
stimRangeSet = True
stimRange = result['options']['stimulusRange']
r = stimRange[1] - stimRange[0]
# get borders for width
# minimum = minimal difference of two stimulus levels
if len(np.unique(data[:,0])) > 1 and not(stimRangeSet):
widthmin = min(np.diff(np.sort(np.unique(data[:,0]))))
else:
widthmin = 100*np.spacing(stimRange[1])
# maximum = spread of the data
# We use the same prior as we previously used... e.g. we use the factor by
# which they differ for the cumulative normal function
Cfactor = (my_norminv(.95,0,1) - my_norminv(.05,0,1))/ \
(my_norminv(1-result['options']['widthalpha'], 0,1) - \
my_norminv(result['options']['widthalpha'], 0,1))
widthmax = r
steps = 10000
theta = np.empty(5)
for itheta in range(0,5):
if itheta == 0:
x = np.linspace(stimRange[0]-.5*r, stimRange[1]+.5*r, steps)
elif itheta == 1:
x = np.linspace(min(result['X1D'][itheta]), max(result['X1D'][1],),steps)
elif itheta == 2:
x = np.linspace(0,.5,steps)
elif itheta == 3:
x = np.linspace(0,.5,steps)
elif itheta == 4:
x = np.linspace(0,1,steps)
y = result['options']['priors'][itheta](x)
theta[itheta] = np.sum(x*y)/np.sum(y)
if result['options']['expType'] == 'equalAsymptote':
theta[3] = theta[2]
if result['options']['expType'] == 'nAFC':
theta[3] = 1/result['options']['expN']
# get limits for the psychometric function plots
xLimit = [stimRange[0] - .5*r , stimRange[1] +.5*r]
""" threshold """
xthresh = np.linspace(xLimit[0], xLimit[1], steps )
ythresh = result['options']['priors'][0](xthresh)
wthresh = convn(np.diff(xthresh), .5*np.array([1,1]))
cthresh = np.cumsum(ythresh*wthresh)
plt.subplot(2,3,1)
plt.plot(xthresh,ythresh, lw = lineWidth, c= lineColor)
plt.hold(True)
plt.xlim(xLimit)
plt.title('Threshold', fontsize = 18)
plt.ylabel('Density', fontsize = 18)
plt.subplot(2,3,4)
plt.plot(data[:,0], np.zeros(data[:,0].shape), 'k.', ms = markerSize*.75 )
plt.hold(True)
plt.ylabel('Percent Correct', fontsize = 18)
plt.xlim(xLimit)
for idot in range(0,5):
if idot == 0:
xcurrent = theta[0]
color = 'k'
elif idot == 1:
xcurrent = min(xthresh)
color = [1,200/255,0]
elif idot == 2:
tix = cthresh[cthresh >=.25].size
xcurrent = xthresh[-tix]
color = 'r'
elif idot == 3:
tix = cthresh[cthresh >= .75].size
xcurrent = xthresh[-tix]
color = 'b'
elif idot == 4:
xcurrent = max(xthresh)
color = 'g'
y = 100*(theta[3]+(1-theta[2])-theta[3])*result['options']['sigmoidHandle'](x,xcurrent, theta[1])
plt.subplot(2,3,4)
plt.plot(x,y, '-', lw=lineWidth,c=color )
plt.subplot(2,3,1)
plt.plot(xcurrent, result['options']['priors'][0](xcurrent), '.',c=color, ms = markerSize)
""" width"""
xwidth = np.linspace(widthmin, 3/Cfactor*widthmax, steps)
ywidth = result['options']['priors'][1](xwidth)
wwidth = convn(np.diff(xwidth), .5*np.array([1,1]))
cwidth = np.cumsum(ywidth*wwidth)
plt.subplot(2,3,2)
plt.plot(xwidth,ywidth,lw=lineWidth,c=lineColor)
plt.hold(True)
plt.xlim([widthmin,3/Cfactor*widthmax])
plt.title('Width',fontsize=18)
plt.subplot(2,3,5)
plt.plot(data[:,0],np.zeros(data[:,0].size),'k.',ms =markerSize*.75)
plt.hold(True)
plt.xlim(xLimit)
plt.xlabel('Stimulus Level',fontsize=18)
x = np.linspace(xLimit[0],xLimit[1],steps)
for idot in range(0,5):
if idot == 0:
xcurrent = theta[1]
color = 'k'
elif idot == 1:
xcurrent = min(xwidth)
color = [1,200/255,0]
elif idot == 2:
wix = cwidth[cwidth >= .25].size
xcurrent = xwidth[-wix]
color = 'r'
elif idot == 3:
wix = cwidth[cwidth >= .75].size
xcurrent = xwidth[-wix]
color = 'b'
elif idot ==4:
xcurrent = max(xwidth)
color = 'g'
y = 100*(theta[3]+ (1-theta[2] -theta[3])* result['options']['sigmoidHandle'](x,theta[0],xcurrent))
plt.subplot(2,3,5)
plt.plot(x,y,'-',lw = lineWidth, c= color)
plt.subplot(2,3,2)
plt.plot(xcurrent,result['options']['priors'][1](xcurrent),'.',c = color,ms=markerSize)
""" lapse """
xlapse = np.linspace(0,.5,steps)
ylapse = result['options']['priors'][2](xlapse)
wlapse = convn(np.diff(xlapse),.5*np.array([1,1]))
clapse = np.cumsum(ylapse*wlapse)
plt.subplot(2,3,3)
plt.plot(xlapse,ylapse,lw=lineWidth,c=lineColor)
plt.hold(True)
plt.xlim([0,.5])
plt.title('\lambda',fontsize=18)
plt.subplot(2,3,6)
plt.plot(data[:,0],np.zeros(data[:,0].size),'k.',ms=markerSize*.75)
plt.hold(True)
plt.xlim(xLimit)
x = np.linspace(xLimit[0],xLimit[1],steps)
for idot in range(0,5):
if idot == 0:
xcurrent = theta[2]
color = 'k'
elif idot == 1:
xcurrent = 0
color = [1,200/255,0]
elif idot == 2:
lix = clapse[clapse >= .25].size
xcurrent = xlapse[-lix]
color = 'r'
elif idot == 3:
lix = clapse[clapse >= .75].size
xcurrent = xlapse[-lix]
color = 'b'
elif idot ==4:
xcurrent = .5
color = 'g'
y = 100*(theta[3]+ (1-xcurrent-theta[3])*result['options']['sigmoidHandle'](x,theta[0],theta[1]))
plt.subplot(2,3,6)
plt.plot(x,y,'-',lw=lineWidth,c=color)
plt.subplot(2,3,3)
plt.plot(xcurrent,result['options']['priors'][2](xcurrent),'.',c=color,ms=markerSize)
a_handle = plt.gca()
a_handle.set_position([200,300,1000,600])
fig, ax = plt.subplots()
for item in [fig, ax]:
item.patch.set_visible(False)
