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Jakob Lass 2025-04-10 10:47:05 +02:00
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.gitignore vendored
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tests/__pycache__/* tests/__pycache__/*
*.pyc *.pyc
build/*
src/AMBER.egg-info/*

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src/graph_laplacian.py
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# tools
import numpy as np
import scipy
import torch
from scipy.sparse import lil_matrix, block_diag, csr_array, diags, csr_matrix
def create_laplacian_matrix(nx, ny=None):
"""
Helper method to create the laplacian matrix for the laplacian
regularization
Parameters
----------
:param nx: height of the original image
:param ny: width of the original image
Returns
-------
:rtype: scipy.sparse.csr_matrix
:return:the n x n laplacian matrix, where n = nx*ny
"""
if ny is None:
ny = nx
assert (nx > 1)
assert (ny > 1)
# Blocks corresponding to the corner of the image (linking row elements)
top_block = lil_matrix((ny, ny), dtype=np.float32)
top_block.setdiag([2] + [3] * (ny - 2) + [2])
top_block.setdiag(-1, k=1)
top_block.setdiag(-1, k=-1)
# Blocks corresponding to the middle of the image (linking row elements)
mid_block = lil_matrix((ny, ny), dtype=np.float32)
mid_block.setdiag([3] + [4]*(ny - 2) + [3])
mid_block.setdiag(-1, k=1)
mid_block.setdiag(-1, k=-1)
# Construction of the diagonal of blocks
list_blocks = [top_block] + [mid_block]*(nx-2) + [top_block]
blocks = block_diag(list_blocks)
# Diagonals linking different rows
blocks.setdiag(-1, k=ny)
return blocks
def delete_from_csr(mat, row_indices=[], col_indices=[]):
"""
Remove the rows (denoted by ``row_indices``) and columns (denoted by ``col_indices``) from the CSR sparse matrix ``mat``.
WARNING: Indices of altered axes are reset in the returned matrix
"""
if not isinstance(mat, csr_matrix):
raise ValueError("works only for CSR format -- use .tocsr() first")
rows = []
cols = []
if row_indices:
rows = list(row_indices)
if col_indices:
cols = list(col_indices)
if len(rows) > 0 and len(cols) > 0:
row_mask = np.ones(mat.shape[0], dtype=bool)
row_mask[rows] = False
col_mask = np.ones(mat.shape[1], dtype=bool)
col_mask[cols] = False
return mat[row_mask][:, col_mask]
elif len(rows) > 0:
mask = np.ones(mat.shape[0], dtype=bool)
mask[rows] = False
return mat[mask]
elif len(cols) > 0:
mask = np.ones(mat.shape[1], dtype=bool)
mask[cols] = False
return mat[:, mask]
else:
return mat
def remove_vertex(L, lst_rows=[], lst_cols=[]):
"""
Function that removes a vertex and adjust the graph laplacian matrix.
"""
L_cut = delete_from_csr(L.tocsr(), row_indices=lst_rows, col_indices=lst_cols)
L_cut = L_cut - diags(L_cut.diagonal())
L_cut = L_cut - diags(L_cut.sum(axis=1).A1)
assert (L_cut.sum(axis=1).A1 == np.zeros(L_cut.shape[0])).all()
return L_cut
def laplacian(Y, nx, ny=None):
"""
Function that removes the vertices corresponding to Nan locations of tensor Y.
Args:
- Y: torch.tensor of the observations (Float64)
- nx,ny: dimensions of the image (Int64)
"""
# find Nan indices
Nan_indices = torch.where(torch.isnan(Y.ravel()) is True)[0]
# get list of indices
list_idx = list(Nan_indices.detach().numpy())
# create Laplacian
L = create_laplacian_matrix(nx, ny=ny)
L = remove_vertex(L, list_idx, list_idx)
return L
def unnormalized_laplacian(y, nx, ny=None, method='inverse'):
"""Construct numpy array with non zeros weights and non zeros indices.
Args:
- y: np.array for observations of size (size_x*size_y)
- method: str indicating how to compute the weight of the unnormalized laplacian
"""
# create laplacian matrix
lapl_tmp = laplacian(y, nx, ny)
lapl_tmp.setdiag(np.zeros(nx*ny))
# select the non nan indices
y_tmp = y[torch.isnan(y) is False]
# store non zero indices
idx_rows = np.array(lapl_tmp.nonzero()[0])
idx_cols = np.array(lapl_tmp.nonzero()[1])
# construct the set of weights
nnz_w = np.zeros_like(idx_rows, dtype=np.float32)
# construction of the non zeros weights
if method == 'inverse':
nnz_w = 1/(np.abs(y_tmp[idx_rows] - y_tmp[idx_cols]) + 1e-4)
else:
nnz_w = np.exp(-np.abs(y_tmp[idx_rows] - y_tmp[idx_cols]))
# construct the non diagonal terms of the Laplacian
lapl_nondiag = csr_array((nnz_w, (idx_rows, idx_cols)), shape=(lapl_tmp.shape[0], lapl_tmp.shape[0]), dtype=np.float32)
# construct the diagonal terms of the Laplacian
lapl_diag = diags(lapl_nondiag.sum(axis=0))
# construct the Laplacian
L = lapl_diag - lapl_nondiag
return L
def laplacian_chain(nb_vertices):
"""
Construct the Laplacian matrix of a chain.
"""
L = np.zeros((nb_vertices, nb_vertices))
# First vertex
L[0, 0] = 1
L[0, 1] = -1
# Toeplitz matrix
if nb_vertices > 2:
first_row = torch.zeros(nb_vertices)
first_row[0] = -1
first_row[1] = 2
first_row[2] = -1
first_col = torch.zeros(nb_vertices-2)
first_col[0] = -1
D = scipy.linalg.toeplitz(first_col, r=first_row)
L[1:nb_vertices-1, :] = D
# Last vertex
L[-1, -2] = -1
L[-1, -1] = 1
return L
def unnormalized_laplacian_chain(y, nx, method='inverse'):
"""Construct numpy array with non zeros weights and non zeros indices.
Args:
- y: np.array for aggregated observations of size (nb_bins)
- method: str indicating how to compute the weight of the unnormalized laplacian
"""
# create laplacian matrix
lapl_tmp = csr_matrix(laplacian_chain(nx))
lapl_tmp.setdiag(np.zeros(nx*nx))
# select the non nan indices
y_tmp = np.nan_to_num(y)
# store non zero indices
idx_rows = np.array(lapl_tmp.nonzero()[0])
idx_cols = np.array(lapl_tmp.nonzero()[1])
# construct the set of weights
nnz_w = np.zeros_like(idx_rows, dtype=np.float32)
# construction of the non zeros weights
if method == 'inverse':
nnz_w = 1/(np.abs(y_tmp[idx_rows] - y_tmp[idx_cols]))
else:
nnz_w = np.exp(-np.abs(y_tmp[idx_rows] - y_tmp[idx_cols]))
# construct the non diagonal terms of the Laplacian
lapl_nondiag = csr_array((nnz_w, (idx_rows, idx_cols)), shape=(lapl_tmp.shape[0], lapl_tmp.shape[0]), dtype=np.float32)
# construct the diagonal terms of the Laplacian
lapl_diag = diags(lapl_nondiag.sum(axis=0))
# construct the Laplacian
L = lapl_diag - lapl_nondiag
return L