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# Author: Nelle Varoquaux, Andrew Tulloch, Antony Lee
# Uses the pool adjacent violators algorithm (PAVA), with the
# enhancement of searching for the longest decreasing subsequence to
# pool at each step.
import numpy as np
cimport numpy as np
cimport cython
ctypedef np.float64_t DOUBLE
@cython.boundscheck(False)
@cython.wraparound(False)
@cython.cdivision(True)
def _inplace_contiguous_isotonic_regression(DOUBLE[::1] y, DOUBLE[::1] w):
cdef:
Py_ssize_t n = y.shape[0], i, k
DOUBLE prev_y, sum_wy, sum_w
Py_ssize_t[::1] target = np.arange(n, dtype=np.intp)
# target describes a list of blocks. At any time, if [i..j] (inclusive) is
# an active block, then target[i] := j and target[j] := i.
# For "active" indices (block starts):
# w[i] := sum{w_orig[j], j=[i..target[i]]}
# y[i] := sum{y_orig[j]*w_orig[j], j=[i..target[i]]} / w[i]
with nogil:
i = 0
while i < n:
k = target[i] + 1
if k == n:
break
if y[i] < y[k]:
i = k
continue
sum_wy = w[i] * y[i]
sum_w = w[i]
while True:
# We are within a decreasing subsequence.
prev_y = y[k]
sum_wy += w[k] * y[k]
sum_w += w[k]
k = target[k] + 1
if k == n or prev_y < y[k]:
# Non-singleton decreasing subsequence is finished,
# update first entry.
y[i] = sum_wy / sum_w
w[i] = sum_w
target[i] = k - 1
target[k - 1] = i
if i > 0:
# Backtrack if we can. This makes the algorithm
# single-pass and ensures O(n) complexity.
i = target[i - 1]
# Otherwise, restart from the same point.
break
# Reconstruct the solution.
i = 0
while i < n:
k = target[i] + 1
y[i + 1 : k] = y[i]
i = k
@cython.boundscheck(False)
@cython.wraparound(False)
@cython.cdivision(True)
def _make_unique(np.ndarray[dtype=np.float64_t] X,
np.ndarray[dtype=np.float64_t] y,
np.ndarray[dtype=np.float64_t] sample_weights):
"""Average targets for duplicate X, drop duplicates.
Aggregates duplicate X values into a single X value where
the target y is a (sample_weighted) average of the individual
targets.
Assumes that X is ordered, so that all duplicates follow each other.
"""
unique_values = len(np.unique(X))
if unique_values == len(X):
return X, y, sample_weights
cdef np.ndarray[dtype=np.float64_t] y_out = np.empty(unique_values)
cdef np.ndarray[dtype=np.float64_t] x_out = np.empty(unique_values)
cdef np.ndarray[dtype=np.float64_t] weights_out = np.empty(unique_values)
cdef np.float64_t current_x = X[0]
cdef np.float64_t current_y = 0
cdef np.float64_t current_weight = 0
cdef np.float64_t y_old = 0
cdef int i = 0
cdef int current_count = 0
cdef int j
cdef np.float64_t x
cdef int n_samples = len(X)
for j in range(n_samples):
x = X[j]
if x != current_x:
# next unique value
x_out[i] = current_x
weights_out[i] = current_weight
y_out[i] = current_y / current_weight
i += 1
current_x = x
current_weight = sample_weights[j]
current_y = y[j] * sample_weights[j]
current_count = 1
else:
current_weight += sample_weights[j]
current_y += y[j] * sample_weights[j]
current_count += 1
x_out[i] = current_x
weights_out[i] = current_weight
y_out[i] = current_y / current_weight
return x_out, y_out, weights_out