def build_ft_regress(xdata,
ydata,
nparam=2,
init_rank=5,
adaptrank=1,
verbose=0):
dim = xdata.shape[1]
ndata = xdata.shape[0]
ft = c3py.FunctionTrain(dim)
for ii in range(dim):
ft.set_dim_opts(ii, "legendre", LB, UB, nparam)
ranks = [init_rank] * (dim + 1)
ranks[0] = 1
ranks[dim] = 1
ft.set_ranks(ranks)
ft.build_data_model(ndata,
xdata,
ydata,
alg="AIO",
obj="LS",
adaptrank=adaptrank,
kickrank=1,
roundtol=1e-10,
verbose=verbose)
return ft
def build_ft_adapt(dim):
ft = c3py.FunctionTrain(dim)
for ii in range(dim):
ft.set_dim_opts(ii, "legendre", LB, UB, NPARAM)
verbose = 0
init_rank = 2
adapt = 0
ft.build_approximation(func1, None, init_rank, verbose, adapt)
return ft
def gen_results(alpha):
lb = -1 # lower bounds of features
ub = 1 # upper bounds of features
nparam = 3 # number of parameters per univariate function
## Run a rank-adaptive regression routine to approximate the first function
ft = c3py.FunctionTrain(dim)
for ii in range(dim):
ft.set_dim_opts(ii, "legendre", lb, ub, nparam)
verbose = 0
init_rank = 2
adapt = 1
ft.build_approximation(func2, alpha, init_rank, verbose, adapt)
print("Computing Sobol Indices")
SI = c3py.SobolIndices(ft, order=2)
print("done")
var = SI.get_variance()
names = []
mains = np.zeros((dim, ))
totals = np.zeros((dim, ))
for ii in range(dim):
mains[ii] = SI.get_main_sensitivity(ii)
totals[ii] = SI.get_total_sensitivity(ii)
names.append(str(ii))
# print("totals = ", totals)
# print("Sum totals = ", np.sum(totals))
# print("Mains = ", mains)
# print("Sum mains = ", np.sum(mains))
inter = []
for ii in range(dim):
for jj in range(ii + 1, dim):
val = SI.get_interaction([ii, jj])
names.append(str(ii) + str(jj))
inter.append(val)
inter = np.array(inter)
# print("sum = ", np.sum(mains) + np.sum(inter))
left_over = var - np.sum(mains) - np.sum(inter)
# print("leftover = ", left_over)
names.append("other")
all_sizes = list(mains / var) + list(inter / var) + [left_over / var]
return names, all_sizes
def build_ft_regress(dim):
ft = c3py.FunctionTrain(dim)
for ii in range(dim):
ft.set_dim_opts(ii, "legendre", LB, UB, NPARAM)
ranks = [5]*(DIM+1)
ranks[0] = 1
ranks[DIM] = 1
ft.set_ranks(ranks)
verbose = 0
adaptrank = 1
ft.build_data_model(NDATA, X, Y,
alg="AIO", obj="LS", adaptrank=adaptrank,
kickrank=1, roundtol=1e-10, verbose=verbose)
return ft
def func2_grad(x):
return np.cos(np.sum(x, axis=1))
dim = 2 # number of features
ndata = 100 # number of data points
x = np.random.rand(ndata, dim) * 2.0 - 1.0 # training samples
y1 = func1(x) # function values
y2 = func2(x) # ditto
lb = -1 # lower bounds of features
ub = 1 # upper bounds of features
nparam = 2 # number of parameters per univariate function
## Run a rank-adaptive regression routine to approximate the first function
ft = c3py.FunctionTrain(dim)
for ii in range(dim):
ft.set_dim_opts(ii, "legendre", lb, ub, nparam)
ft.build_data_model(ndata,
x,
y1,
alg="AIO",
obj="LS",
adaptrank=1,
kickrank=1,
roundtol=1e-10,
verbose=0,
store_opt_info=False)
## Run a fixed-rank regression routine to approximate the second function with stochastic gradient descent
ft_sgd = c3py.FunctionTrain(dim)
dim = 3 # number of features
def func2(x,param=None):
if (param is not None):
print("param = ", param)
out = np.sin(2*np.pi*np.sum(x,axis=1))
return out
if __name__ == "__main__":
lb = -1 # lower bounds of features
ub = 1 # upper bounds of features
nparam = 3 # number of parameters per univariate function
## Run a rank-adaptive regression routine to approximate the first function
ft = c3py.FunctionTrain(dim)
for ii in range(dim):
ft.set_dim_opts(ii,"legendre",lb,ub,nparam)
verbose=0
init_rank=2
adapt=1
ft.build_approximation(func2,None,init_rank,verbose,adapt)
# collect functions
ranks = ft.get_ranks()
funcs = [[]]*dim
for ii in range(dim):
funcs[ii] = [None]*ranks[ii]
f, axis = plt.subplots(ranks[ii],ranks[ii+1])
for row in range(ranks[ii]):
# print(x[:, 2])
# print("\n\n\n\n\n")
out = np.sin(np.sum(x, axis=1))
return out
if __name__ == "__main__":
lb = [-1] * DIM # lower bounds of features
ub = [1] * DIM # upper bounds of features
# number of parameters per univariate function
nparam = [3] * DIM
## Run a rank-adaptive regression routine to approximate the first function
ft = c3py.FunctionTrain(DIM)
for ii in range(DIM):
ft.set_dim_opts(ii, "legendre", lb[ii], ub[ii], nparam[ii])
verbose = 1
init_rank = 2
adapt = 1
maxrank = 10
kickrank = 2
roundtol = 1e-8
maxiter = 5
scales = [2] * DIM
scales[2] = 0.2
ft.build_approximation(func2,
scales,
init_rank,