def random_simulations(no,bvals,gradients,d=0.0015,fractions=[100,0,0],snr=None):
sticks=random_uniform_on_sphere(n=no,coords='xyz')
fractions=[f/100. for f in fractions]
f0=1-np.sum(fractions)
S=np.zeros(len(gradients)-1)
for (i,g) in enumerate(gradients[1:]):
S[i]=f0*np.exp(-bvals[i+1]*d)+ np.sum([fractions[j]*np.exp(-bvals[i+1]*d*np.dot(s,g)**2) for (j,s) in enumerate(sticks)])
if snr!=None:
std=S/snr
S=S+np.random.randn(len(S))*std
return S,sticks
orientations = bvecs101[1:,:]
templates = [signal_1_stick(S0,bvals64[1:],d,orientation,gradients)
for i, orientation in enumerate(orientations)]
# add isotropic component as last column
templates += [np.ones(gradients.shape[0])]
design = np.array(templates).T
# Make pure fiber data to test against
#test_direction = np.array([1,2,3])/np.sqrt(14.)
#print np.sum(test_direction**2)
#unit vector for test signal direction
#test_direction = gradients[15,:]
test_directions = sphere_tools.random_uniform_on_sphere(10**2)
sparsity = []
lambd = 2.**18.1
for test_direction in test_directions:
sparsity += [qpfit1(design, S0,bvals,d,test_direction,gradients,lambd)]
angles =[np.abs(np.dot(s['actual'],gradients[s['top']].T)) for s in sparsity]
max_angles =[np.max(np.abs(np.dot(s['actual'],gradients[s['top']].T))) for s in sparsity]
lengths = np.bincount([len(s['top']) for s in sparsity])
'''
Y = signal_1_stick(S0,bvals[1:],d,test_direction,gradients)
# Set up model according to Jonathan's recipe
n, m = design.shape
'''
