ahwillia

# The MIT License (MIT)
# 
# Copyright (c) Alex H. Williams
#
# Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation
# files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy,
# modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the
# Software is furnished to do so, subject to the following conditions:
#
# The above copyright notice and this permission notice shall be included in all copies or substantial portions of the

ahwillia

import numpy as np
import numpy.random as npr
from functools import reduce

# Goal
# ----
# Compute (As[0] kron As[1] kron ... As[-1]) @ v

# ==== HELPER FUNCTIONS ==== #

ahwillia

"""
Python code to generate M-splines.

References
----------
Ramsay, J. O. (1988). Monotone regression splines in action.
Statistical science, 3(4), 425-441.
"""

import numpy as np

ahwillia

"""
NOTE: This code has not been rigorously tested.
"""
import matplotlib.pyplot as plt
import jax.numpy as jnp
import jax
from tqdm import trange


def elliptical_slice_update(x, log_density, sigmas, key):

ahwillia

import numpy as np
from numpy.random import randn, rand
from scipy.optimize import minimize
import matplotlib.pyplot as plt
from nnls import nnlsm_blockpivot as nnlstsq
import itertools
from scipy.spatial.distance import cdist

def censored_lstsq(A, B, M):
    """Solves least squares problem with missing data in B

ahwillia

import matplotlib.pyplot as plt
import numpy as np

def raised_cos(t, loc, scale, amp):
    """
    Raised, 1d-cosine basis functions tiling [0, 2 * pi)
    These functions have the property of summing to a
    constant amplitude at all points (i.e. uniform
    tiling of space).

ahwillia

import numba
import numpy as np
from scipy.spatial.distance import pdist, squareform
from math import comb

@numba.jit(nopython=True)
def index(n, i, j):
    """
    Computes linear index of (i, j) from the (n x n) distance matrix.
    """

ahwillia

from pca_crossval import * 
from tqdm import tqdm
import itertools
np.random.seed(1111)

m, n, r = 100, 101, 3
Utrue, Vtrue = rand(m,r), rand(r,n)
data = np.dot(Utrue, Vtrue) + .25*randn(m,n)
data[data < 0] = 0
ranks = []

ahwillia

from sklearn.datasets import make_biclusters
import numpy as np
import matplotlib.pyplot as plt
%matplotlib inline

def resort_rows_hclust(U):
    """Sorts the rows of a matrix by hierarchical clustering

    Parameters:
        U (ndarray) : matrix of data

ahwillia

import numpy as np
from scipy.spatial.distance import cdist, pdist

def mmd_two_sample_test(X, Y):
    """
    Implements Gretton's test for equality of
    distributions in high-dimensional settings
    using concentration bounds on the maximum
    mean discrepancy (MMD). This function uses
    the unbiased estimator of the MMD (see