Module optima_func: estimate max for function

Package teneva, module optima_func: estimate max for function.

This module contains the novel algorithm for computation of minimum and maximum element of the multivariate function presented as the TT-tensor of Chebyshev coefficients.



teneva.optima_func.optima_func_tt_beam(A, k, k_loc=None)[source]

Find maximum modulo points in the functional TT-tensor.

Parameters:

  • A (list) – d-dimensional TT-tensor of interpolation coefficients.

  • k (int) – number of selected items (candidates for the optimum) for each tensor mode.

  • k_loc (int) – optional number of local maximum to take.

Returns:

the set of k_loc best multidimensional points (array of the shape [k, d]).

Return type:

np.ndarray

Examples:

n = [20, 18, 16, 14, 12]  # Shape of the tensor
Y = teneva.rand(n, r=4)   # Random TT-tensor with rank 4
A = teneva.func_int(Y)    # TT-tensor of interpolation coefficients

x_opt = teneva.optima_func_tt_beam(A, k=3)
y_opt = teneva.func_get(x_opt, A, -1, 1)

print(f'x opt appr :', x_opt)
print(f'y opt appr : {y_opt}')

# >>> ----------------------------------------
# >>> Output:

# x opt appr : [[-0.32574766  0.60650301  0.8935902   0.57796563 -0.94833635]
#  [-0.32574766  0.60650301  0.8935902   0.57796563  0.15852408]
#  [-0.32574766  0.60650301  0.74642396 -0.9809905  -0.64170661]]
# y opt appr : [-16.60387436  15.62801787  14.50242635]
#