Conditional total

Question

I am looking for a way to calculate the total amount using numpy, but I do not want to retell the value (or set it to zero) if the cumulative sum is very close to zero and negative.

for example

a = np.asarray([0, 4999, -5000, 1000])
np.cumsum(a)

returns [0, 4999, -1, 999]

but I would like to set the [2]-value (-1) value to zero during calculation. The problem is that this solution can only be performed in the calculation, since the intermediate result is not known a priori.

Expected Array: [0, 4999, 0, 1000]

The reason for this is that I get very small values ​​(with a floating point, not integers, as in the example), which are due to floating point calculations, which should actually be zero. Calculation of the total sum connects those values ​​that lead to errors.

Answer 1

Kach summation algorithm can solve the problem. Unfortunately, this is not implemented in numpy . This means that a special implementation is required:

def kahan_cumsum(x):
    x = np.asarray(x)
    cumulator = np.zeros_like(x)
    compensation = 0.0

    cumulator[0] = x[0]    
    for i in range(1, len(x)):
        y = x[i] - compensation
        t = cumulator[i - 1] + y
        compensation = (t - cumulator[i - 1]) - y
        cumulator[i] = t
    return cumulator

I must admit that this is not exactly what was asked in the question. (Example value -1 on the 3rd output of cumsum is correct in the example). However, I hope this solves the actual problem behind the issue, which is related to floating point precision.

Answer 2

I wonder if rounding will do what you ask for:

np.cumsum(np.around(a,-1))
# the -1 means it rounds to the nearest 10

gives

array([   0, 5000,    0, 1000])

, , around, , decimals 0, , .

Answer 3

, - Cython ( cumsum_eps.pyx):

cimport numpy as cnp
import numpy as np

cdef inline _cumsum_eps_f4(float *A, int ndim, int dims[], float *out, float eps):
    cdef float sum
    cdef size_t ofs

    N = 1
    for i in xrange(0, ndim - 1):
        N *= dims[i]
    ofs = 0
    for i in xrange(0, N):
        sum = 0
        for k in xrange(0, dims[ndim-1]):
            sum += A[ofs]
            if abs(sum) < eps:
                sum = 0
            out[ofs] = sum
            ofs += 1

def cumsum_eps_f4(cnp.ndarray[cnp.float32_t, mode='c'] A, shape, float eps):
    cdef cnp.ndarray[cnp.float32_t] _out
    cdef cnp.ndarray[cnp.int_t] _shape
    N = np.prod(shape)
    out = np.zeros(N, dtype=np.float32)
    _out = <cnp.ndarray[cnp.float32_t]> out
    _shape = <cnp.ndarray[cnp.int_t]> np.array(shape, dtype=np.int)
    _cumsum_eps_f4(&A[0], len(shape), <int*> &_shape[0], &_out[0], eps)
    return out.reshape(shape)


def cumsum_eps(A, axis=None, eps=np.finfo('float').eps):
    A = np.array(A)
    if axis is None:
        A = np.ravel(A)
    else:
        axes = list(xrange(len(A.shape)))
        axes[axis], axes[-1] = axes[-1], axes[axis]
        A = np.transpose(A, axes)
    if A.dtype == np.float32:
        out = cumsum_eps_f4(np.ravel(np.ascontiguousarray(A)), A.shape, eps)
    else:
        raise ValueError('Unsupported dtype')
    if axis is not None: out = np.transpose(out, axes)
    return out

(Windows, Visual ++ 2008 Command Line):

\Python27\Scripts\cython.exe cumsum_eps.pyx
cl /c cumsum_eps.c /IC:\Python27\include /IC:\Python27\Lib\site-packages\numpy\core\include
F:\Users\sadaszew\Downloads>link /dll cumsum_eps.obj C:\Python27\libs\python27.lib /OUT:cumsum_eps.pyd

(Linux .so/Cygwin .dll, gcc):

cython cumsum_eps.pyx
gcc -c cumsum_eps.c -o cumsum_eps.o -I/usr/include/python2.7 -I/usr/lib/python2.7/site-packages/numpy/core/include
gcc -shared cumsum_eps.o -o cumsum_eps.so -lpython2.7

:

from cumsum_eps import *
import numpy as np
x = np.array([[1,2,3,4], [5,6,7,8]], dtype=np.float32)

>>> print cumsum_eps(x)
[  1.   3.   6.  10.  15.  21.  28.  36.]
>>> print cumsum_eps(x, axis=0)
[[  1.   2.   3.   4.]
 [  6.   8.  10.  12.]]
>>> print cumsum_eps(x, axis=1)
[[  1.   3.   6.  10.]
 [  5.  11.  18.  26.]]
>>> print cumsum_eps(x, axis=0, eps=1)
[[  1.   2.   3.   4.]
 [  6.   8.  10.  12.]]
>>> print cumsum_eps(x, axis=0, eps=2)
[[  0.   2.   3.   4.]
 [  5.   8.  10.  12.]]
>>> print cumsum_eps(x, axis=0, eps=3)
[[  0.   0.   3.   4.]
 [  5.   6.  10.  12.]]
>>> print cumsum_eps(x, axis=0, eps=4)
[[  0.   0.   0.   4.]
 [  5.   6.   7.  12.]]
>>> print cumsum_eps(x, axis=0, eps=8)
[[ 0.  0.  0.  0.]
 [ 0.  0.  0.  8.]]
>>> print cumsum_eps(x, axis=1, eps=3)
[[  0.   0.   3.   7.]
 [  5.  11.  18.  26.]]

.., , eps , / .

double, _f8 , cumsum_eps().

, setup.py - Cython setup.py

Update # 1: if you have good compiler support in the runtime, you can try [Theano] [3] to implement a compensation algorithm or your original idea:

import numpy as np
import theano
import theano.tensor as T
from theano.ifelse import ifelse

A=T.vector('A')

sum=T.as_tensor_variable(np.asarray(0, dtype=np.float64))

res, upd=theano.scan(fn=lambda cur_sum, val: ifelse(T.lt(cur_sum+val, 1.0), np.asarray(0, dtype=np.float64), cur_sum+val), outputs_info=sum, sequences=A)

f=theano.function(inputs=[A], outputs=res)

f([0.9, 2, 3, 4])

will give [0 2 3 4] output. In either Cython or this, you get at least +/- native code performance.