Decompose Data

HDMR

import numpy as np
from hdmrlib import HDMR

X = np.random.rand(10, 10)

hdmr = HDMR(X, order=2)

HDMR uses the same top-level call pattern.

HDMR Weight and Support Options

hdmr = HDMR(X, order=2, weight="avg", supports="ones")

Supported weight modes:

• "avg" or "average"

• "gaussian"

• "chebyshev"

• "custom"

Supported support modes:

• "das"

• "ones"

• "custom"

Use custom_weights when weight="custom" and custom_supports when supports="custom".

custom_weights = [
    np.ones((10, 1)),
    np.ones((10, 1)),
]

custom_supports = [
    np.ones((10, 1)),
    np.ones((10, 1)),
]

hdmr = HDMR(
    X,
    order=2,
    weight="custom",
    custom_weights=custom_weights,
    supports="custom",
    custom_supports=custom_supports,
)

EMPR

import numpy as np
from hdmrlib import EMPR

X = np.random.rand(10, 10)

empr = EMPR(X, order=2)

EMPR takes the input tensor as the first argument and the decomposition order as order.

EMPR Support Options

empr = EMPR(X, order=2, supports="das")

Supported support modes:

• "das"

• "ones"

• "custom"

Use custom_supports when supports="custom".

custom_supports = [
    np.ones((10, 1)),
    np.ones((10, 1)),
]

empr = EMPR(
    X,
    order=2,
    supports="custom",
    custom_supports=custom_supports,
)

What You Get Back

Both calls return decomposition objects. The next steps are typically:

• inspect component terms

• reconstruct lower-order approximations

• compare different decomposition orders