stable-diffusion-webui/extensions-builtin/Lora/lyco_helpers.py

import torch


def make_weight_cp(t, wa, wb):
    temp = torch.einsum('i j k l, j r -> i r k l', t, wb)
    return torch.einsum('i j k l, i r -> r j k l', temp, wa)


def rebuild_conventional(up, down, shape, dyn_dim=None):
    up = up.reshape(up.size(0), -1)
    down = down.reshape(down.size(0), -1)
    if dyn_dim is not None:
        up = up[:, :dyn_dim]
        down = down[:dyn_dim, :]
    return (up @ down).reshape(shape)


def rebuild_cp_decomposition(up, down, mid):
    up = up.reshape(up.size(0), -1)
    down = down.reshape(down.size(0), -1)
    return torch.einsum('n m k l, i n, m j -> i j k l', mid, up, down)


# copied from https://github.com/KohakuBlueleaf/LyCORIS/blob/dev/lycoris/modules/lokr.py
def factorization(dimension: int, factor:int=-1) -> tuple[int, int]:
    '''
    return a tuple of two value of input dimension decomposed by the number closest to factor
    second value is higher or equal than first value.

    In LoRA with Kroneckor Product, first value is a value for weight scale.
    secon value is a value for weight.

    Becuase of non-commutative property, A⊗B ≠ B⊗A. Meaning of two matrices is slightly different.

    examples)
    factor
        -1               2                4               8               16               ...
    127 -> 1, 127   127 -> 1, 127    127 -> 1, 127   127 -> 1, 127   127 -> 1, 127
    128 -> 8, 16    128 -> 2, 64     128 -> 4, 32    128 -> 8, 16    128 -> 8, 16
    250 -> 10, 25   250 -> 2, 125    250 -> 2, 125   250 -> 5, 50    250 -> 10, 25
    360 -> 8, 45    360 -> 2, 180    360 -> 4, 90    360 -> 8, 45    360 -> 12, 30
    512 -> 16, 32   512 -> 2, 256    512 -> 4, 128   512 -> 8, 64    512 -> 16, 32
    1024 -> 32, 32  1024 -> 2, 512   1024 -> 4, 256  1024 -> 8, 128  1024 -> 16, 64
    '''

    if factor > 0 and (dimension % factor) == 0:
        m = factor
        n = dimension // factor
        if m > n:
            n, m = m, n
        return m, n
    if factor < 0:
        factor = dimension
    m, n = 1, dimension
    length = m + n
    while m<n:
        new_m = m + 1
        while dimension%new_m != 0:
            new_m += 1
        new_n = dimension // new_m
        if new_m + new_n > length or new_m>factor:
            break
        else:
            m, n = new_m, new_n
    if m > n:
        n, m = m, n
    return m, n

# from https://github.com/KohakuBlueleaf/LyCORIS/blob/dev/lycoris/modules/boft.py
def butterfly_factor(dimension: int, factor: int = -1) -> tuple[int, int]:
    """
    m = 2k
    n = 2**p
    m*n = dim
    """

    # Find the first solution and check if it is even doable
    m = n = 0
    while m <= factor:
        m += 2
        while dimension % m != 0 and m < dimension:
            m += 2
        if m > factor:
            break
        if sum(int(i) for i in f"{dimension//m:b}") == 1:
            n = dimension // m

    if n == 0:
        raise ValueError(
            f"It is impossible to decompose {dimension} with factor {factor} under BOFT constrains."
        )

    #log_butterfly_factorize(dimension, factor, (dimension // n, n))
    return dimension // n, n