Module sample_func: random sampling from the functional TT-tensor

Package teneva, module sample_func: sampling from functional TT-tensor.

This module contains the function “sample_func” for sampling from the functional TT-tensor (i.e., the tensor of interpolation coefficients).

---

teneva.sample_func.sample_func(A, seed=None, cores_are_prepared=False)

Sample random points according to given functional probability TT-tensor.

Parameters:

• A (list) – TT-tensor, which represents the interpolation coeeficients for the probability distribution.

• cores_are_prepared (bool) – special flag for inner usage.

• seed (int) – random seed. It should be an integer number or a numpy Generator class instance.

Returns:

generated point for the tensor in the form of array of the shape [d], where d is the dimension.

Return type:

np.ndarray

Examples:

Y = np.array([            # We generate 2D tensor for demo
    [0.1, 0.2, 0.3],
    [0. , 0. , 0. ],
    [0.2, 0.2, 0. ],
    [0. , 0. , 0. ],
])
Y = teneva.svd(Y)         # We compute its TT-representation
print(teneva.sum(Y))      # We print the sum of tensor elements

A = teneva.func_int(Y)    # We build TT-tensor of interpolation coefficients
x = teneva.sample_func(A) # And now we generate the sample
print(x)

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

# 1.0000000000000002
# [-0.27512534  0.73238222]
#

And now let check this function for big random TT-tensor:

# 5-dim random TT-tensor with TT-rank 5:
Y = teneva.rand([4]*5, 5)

# Compute the square of Y:
Y = teneva.mul(Y, Y)

# Normalize the tensor:
p = teneva.sum(Y)
Y = teneva.mul(Y, 1./p)

# Print the resulting TT-tensor:
teneva.show(Y)

# Build TT-tensor of interpolation coefficients:
A = teneva.func_int(Y)

# Generate the sample:

x = teneva.sample_func(A)
print('\n--- Result:', x)

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

# TT-tensor     5D : |4|  |4|  |4|  |4|  |4|
# <rank>  =   25.0 :   \25/ \25/ \25/ \25/
#
# --- Result: [-0.42474031 -0.69073916  0.78832627 -0.87249403  0.73524451]
#

Note that we can also set a random seed value:

x = teneva.sample_func(A, seed=42)
print('\n--- Result:', x)

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

#
# --- Result: [ 0.2085743  -0.24040686  0.90514291 -0.18823296  0.0276718 ]
#

We can also check the generated distribution (note that matplotlib is used below):

import matplotlib.pyplot as plt

samples = int(1.E+4)

A = teneva.rand([4]*2, 2)

X = np.array([teneva.sample_func(A, seed=s) for s in range(samples)])

N = 512
X_m = np.linspace(-1, 1, N)
x, y = np.meshgrid(X_m, X_m)
x = x.reshape(-1)
y = y.reshape(-1)
y = teneva.func_get(np.array([x, y]).T, A, -1, 1)

fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(16, 8))
plt.subplots_adjust(wspace=0.3)
im = ax1.scatter(X[:, 0], X[:, 1], s=[.5]*samples)
im = ax2.imshow(y.reshape(N, -1)**2, origin='lower')
plt.colorbar(im, fraction=0.046, pad=0.04)
ax1.set_xticks([])
ax1.set_yticks([])
ax2.set_xticks([])
ax2.set_yticks([])
plt.show()

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

# <Figure size 1600x800 with 3 Axes>
#

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

# Display of images is not supported in the docs. See related ipynb file.