Numpy time based vector operations where state of preceding elements matters - are for loops appropriate?

What do numpy arrays provide when performing time based calculations where state matters. In other words, where what has occurred in earlier or later in a sequence is important.

Consider the following time based vectors,

TIME = np.array([0.,   10.,  20.,  30.,  40.,  50.,  60.,  70.,  80.,  90.])
FLOW = np.array([100., 75.,  60.,  20.0, 60.0, 50.0, 20.0, 30.0, 20.0, 10.0])
TEMP = np.array([300., 310., 305., 300., 310., 305., 310., 305., 300., 295.0])

Let's say that an exponential decay in TEMP should be applied once the FLOW falls below 30 without raising again above 50. In the data above, a function would be applied at TIME=60 above and the last two values of TEMP would be updated by this secondary function which would began with the corresponding TEMP value.

There is a need to "look ahead" to determine if the FLOW rises above 50 in the elements after the <30 condition is requested. It does not seem that the numpy functions are aimed at time based vectors where state is important and the traditional method of nested for 开发者_开发知识库loops perhaps remains the way to go. But given given my newness to numpy and the fact that I have to perform alot of these types of state based manipulations, I would appreciate direction or affirmation.

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While Joe Kington's answer is certainly correct (and quite flexible), it is rather more circuitous than need be. For someone trying to learn Numpy, I think a more direct route might be easier to understand.

As I noted under your question (and as Joe also noticed), there seems to be an inconsistency between your description of the code's behaviour and your example. Like Joe, I'm also going to assume you describe the correct behaviour.

A couple notes:

1. Numpy works well with filter arrays to specify to which elements an operation should be applied. I make use of them several times.
2. The np.flatnonzero function returns an array of indices specifying the locations at which the given array is non-zero (or True).

The code uses the example arrays you provided.

import numpy as np

TIME = np.array([0.,   10.,  20.,  30.,  40.,  50.,  60.,  70.,  80.,  90.])
FLOW = np.array([100., 75.,  60.,  20.0, 60.0, 50.0, 20.0, 30.0, 20.0, 10.0])
TEMP = np.array([300., 310., 305., 300., 310., 305., 310., 305., 300., 295.0])

last_high_flow_index = np.flatnonzero(FLOW > 50)[-1]
low_flow_indices = np.flatnonzero(FLOW < 30)
acceptable_low_flow_indices = low_flow_indices[low_flow_indices > last_high_flow_index]
apply_after_index = acceptable_low_flow_indices[0]

We now have the index after which the function should be applied to TEMP. If I am reading your question correctly, you would like the temperature to begin decaying once your condition is met. This can be done as follows:

time_delta = TIME[apply_after_index:] - TIME[apply_after_index]
TEMP[apply_after_index:] = TEMP[apply_after_index:] * np.exp(-0.05 * time_delta)

TEMP has been updated, so print TEMP outputs

[ 300.          310.          305.          300.          310.          305.
  310.          184.99185121  110.36383235   65.82339724]

Alternatively, you can apply an arbitrary Python function to the appropriate elements by first vectorizing the function:

def myfunc(x):
    ''' a normal python function that acts on individual numbers'''
    return x + 3

myfunc_v = np.vectorize(myfunc)

and then updating the TEMP array:

TEMP[apply_after:] = myfunc_v(TEMP[apply_after:])

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You can certainly do this without nested loops in numpy. If you want to get really fancy, you could probably vectorize the entire thing, but it's probably the most readable to just vectorize it to the point that you only need one loop.

Generally speaking, try to vectorize things unless it becomes excessively clunky/unreadable or you're having memory usage issues. Then do it another way.

In some cases loops are more readable, and they'll commonly use less memory than vectorized expressions, but they're generally slower than vectorized expressions.

You'd probably be surprised at how flexible the various indexing tricks are, though. It's rare that you have to use loops to do a calculation, but they often wind up being more readable in complex cases.

However, I'm slightly confused by what you state as the correct case... You say that you want to apply a function to portions of temp where the flow falls below 30 without rising above 50. By this logic, the function should be applied to the last 4 elements of the temp array. However, you state that it should only be applied to the last two... I'm confused! I'm going to go with my reading of things and have it applied to the last 4 elements of the array...

Here's how I would do it. This uses random data rather than your data so that there are multiple regions...

Note that there aren't any nested loops, and we're only iterating over the number of contiguous regions in the array where your "asymmetric" threshold conditions are met (i.e. there's only one iteration, in this case).

import numpy as np
import matplotlib.pyplot as plt

def main():
    num = 500
    flow = np.cumsum(np.random.random(num) - 0.5)
    temp = np.cumsum(np.random.random(num) - 0.5)
    temp -= temp.min() - 10
    time = np.linspace(0, 10, num)

    low, high = -1, 1 
    # For regions of "flow" where flow drops below low and thereafter 
    # stays below high...
    for start, stop in asymmetric_threshold_regions(flow, low, high):
        # Apply an exponential decay function to temp...
        t = time[start:stop+1] - time[start]
        temp[start:stop+1] = temp[start] * np.exp(-0.5 * t)

    plot(flow, temp, time, low, high)

def contiguous_regions(condition):
    """Finds contiguous True regions of the boolean array "condition". Returns
    a 2D array where the first column is the start index of the region and the
    second column is the end index."""

    # Find the indicies of changes in "condition"
    d = np.diff(condition)
    idx, = d.nonzero()

    if condition[0]:
        # If the start of condition is True prepend a 0
        idx = np.r_[0, idx]

    if condition[-1]:
        # If the end of condition is True, append the length of the array
        idx = np.r_[idx, len(condition)-1]

    # Reshape the result into two columns
    idx.shape = (-1,2)
    return idx

def asymmetric_threshold_regions(x, low, high):
    """Returns an iterator over regions where "x" drops below "low" and 
    doesn't rise above "high"."""

    # Start with contiguous regions over the high threshold...
    for region in contiguous_regions(x < high):
        start, stop = region

        # Find where "x" drops below low within these
        below_start, = np.nonzero(x[start:stop] < low)

        # If it does, start at where "x" drops below "low" instead of where
        # it drops below "high"
        if below_start.size > 0:
            start += below_start[0]
            yield start, stop

def plot(flow, temp, time, low, high):
    fig = plt.figure()
    ax1 = fig.add_subplot(2,1,1)
    ax1.plot(time, flow, 'g-')
    ax1.set_ylabel('Flow')

    ax1.axhline(y=low, color='b')
    ax1.axhline(y=high, color='g')
    ax1.text(time.min()+1, low, 'Low Threshold', va='top')
    ax1.text(time.min()+1, high, 'High Threshold', va='bottom')

    ax2 = fig.add_subplot(2,1,2, sharex=ax1)
    ax2.plot(time, temp, 'b-')
    ax2.set_ylabel('Temp')
    ax2.set_xlabel('Time (s)')

    for start, stop in asymmetric_threshold_regions(flow, low, high):
        ax1.axvspan(time[start], time[stop], color='r', alpha=0.5)
        ax2.axvspan(time[start], time[stop], color='r', alpha=0.5)

    plt.setp(ax1.get_xticklabels(), visible=False)
    plt.show()

if __name__ == '__main__':
    main()