PySpark : how to split data without randomnize - pyspark

there are function that can randomize spilt data
trainingRDD, validationRDD, testRDD = RDD.randomSplit([6, 2, 2], seed=0L)
I'm curious if there a way that we generate data the same partition ( train 60 / valid 20 / test 20 ) but without randommize ( let's just say use the current data to split first 60 = train, next 20 =valid and last 20 are for test data)
is there a possible way to split data similar way to split but not randomize?


The basic issue here is that unless you have an index column in your data, there is no concept of "first rows" and "next rows" in your RDD, it's just an unordered set. If you have an integer index column you could do something like this:
train = RDD.filter(lambda r: r['index'] % 5 <= 3)
validation = RDD.filter(lambda r: r['index'] % 5 == 4)
test = RDD.filter(lambda r: r['index'] % 5 == 5)

Related

Using a grouped z-score over a rolling window

I would like to calculate a z-score over a bin based on the data of a rolling look-back period.
Example
Todays visitor amount during [9:30-9:35) should be z-score normalized based off the (mean, std) of the last 3 days of visitors that visited during [9:30-9:35).
My current attempts both raise InvalidOperationError. Is there a way in polars to calculate this?
import polars as pl
def z_score(col: str, over: str, alias: str):
# calculate z-score normalized `col` over `over`
return (
(pl.col(col)-pl.col(col).over(over).mean()) / pl.col(col).over(over).std()
).alias(alias)
df = pl.from_dict(
{
"timestamp": pd.date_range("2019-12-02 9:30", "2019-12-02 12:30", freq="30s").union(
pd.date_range("2019-12-03 9:30", "2019-12-03 12:30", freq="30s")
),
"visitors": [(e % 2) + 1 for e in range(722)]
}
# 5 minute bins for grouping [9:30-9:35) -> 930
).with_column(
pl.col("timestamp").dt.truncate(every="5m").dt.strftime("%H%M").cast(pl.Int32).alias("five_minute_bin")
).with_column(
pl.col("timestamp").dt.truncate(every="3d").alias("daytrunc")
)
# normalize visitor amount for each 5 min bin over the rolling 3 day window using z-score.
# not rolling but also wont work (InvalidOperationError: window expression not allowed in aggregation)
# df.with_column(
# z_score("visitors", "five_minute_bin", "normalized").over("daytrunc")
# )
# won't work either (InvalidOperationError: window expression not allowed in aggregation)
#df.groupby_rolling(index_column="daytrunc", period="3i").agg(z_score("visitors", "five_minute_bin", "normalized"))
For an example of 4 days of data with four data-points each lying in two time-bins ({0,0} - {0,1}), ({1,0} - {1,1})
Input:
Day 0: x_d0_{0,0}, x_d0_{0,1}, x_d0_{1,0}, x_d0_{1,1}
Day 1: x_d1_{0,0}, x_d1_{0,1}, x_d1_{1,0}, x_d1_{1,1}
Day 2: x_d2_{0,0}, x_d2_{0,1}, x_d2_{1,0}, x_d2_{1,1}
Day 3: x_d3_{0,0}, x_d3_{0,1}, x_d3_{1,0}, x_d3_{1,1}
Output:
Day 0: norm_x_d0_{0,0} = nan, norm_x_d0_{0,1} = nan, norm_x_d0_{1,0} = nan, norm_x_d0_{1,1} = nan
Day 1: norm_x_d1_{0,0} = nan, norm_x_d1_{0,1} = nan, norm_x_d1_{1,0} = nan, norm_x_d1_{1,1} = nan
Day 2: norm_x_d2_{0,0} = nan, norm_x_d2_{0,1} = nan, norm_x_d2_{1,0} = nan, norm_x_d2_{1,1} = nan
Day 3: norm_x_d3_{0,0} = (x_d3_{0,0} - np.mean([x_d0_{0,0}, x_d0_{0,1}, X_d1_{0,0}, ..., x_d3_{0,1}]) / np.std([x_d0_{0,0}, x_d0_{0,1}, X_d1_{0,0}, ..., x_d3_{0,1}])) , ... ,

They key here is to use over to restrict your calculations to the five minute bins and then use the rolling functions to get the rolling mean and standard deviation over days restricted by those five minute bin keys. five_minute_bin works as in your code and I believe that a truncated day_bin is necessary so that, for example, 9:33 on one day will include 9:31 both 9:34 on the same and 9:31 from 2 days ago.
days = 5
pl.DataFrame(
{
"timestamp": pl.concat(
[
pl.date_range(
datetime(2019, 12, d, 9, 30), datetime(2019, 12, d, 12, 30), "30s"
)
for d in range(2, days + 2)
]
),
"visitors": [(e % 2) + 1 for e in range(days * 361)],
}
).with_columns(
five_minute_bin=pl.col("timestamp").dt.truncate(every="5m").dt.strftime("%H%M"),
day_bin=pl.col("timestamp").dt.truncate(every="1d"),
).with_columns(
standardized_visitors=(
(
pl.col("visitors")
- pl.col("visitors").rolling_mean("3d", by="day_bin", closed="right")
)
/ pl.col("visitors").rolling_std("3d", by="day_bin", closed="right")
).over("five_minute_bin")
)
Now, that said, when trying out the code for this, I found polars doesn't handle non-unique values in the by-column in the rolling function correctly, so that the same values in the same 5-minute bin don't end up as the same standardized values. Opened bug report here: https://github.com/pola-rs/polars/issues/6691. For large amounts of real world data, this shouldn't actually matter that much, unless your data systematically differs in distribution within the 5 minute bins.

Decay chain simulation - with significantly different time scales

I would like to simulate a decay chain with Python. Normally, (in a loop over all nuclides) one calculates the number of decays per time step and updates the number of mother and daughter nuclei.
My problem is that the decay chain contains half-lives on very different time scales, i.e.
0.0001643 seconds for Po-214 and 307106512477175.9 seconds (= 1600 years) for Ra-226.
Using the same time step for all nuclides seems useless.
Is there a simulation method, preferably in Python, that can be used to handle this case?

Don't use time steps for this. Use event scheduling.
Half lives can be expressed as exponential decay, and the conversion between half life and rate of decay is straightforward. Start with the number of both types of nuclei, and schedule exponential inter-event times to figure out when the next decay of each type will occur. Whichever type has the lower time, decrement the corresponding number of nuclei and schedule the next decay for that type (and if need be, increment the count of whatever it decays into).
This can easily be generalized to multiple distinct event types by using a priority queue ordered by time of occurrence to determine which event will be the next one performed. This is the underlying principle behind discrete event simulation.
Update
This approach works with individual decay events, but we can leverage two important properties when we have exponential inter-event times.
The first is to note that exponentially distributed inter-event times means these are Poisson processes. The superposition property tells us that the union of two independent Poisson processes, each having rate λ, is a Poisson process with rate 2λ. Simple induction shows that if we have n independent Poisson properties with the same rate, their superposition is a Poisson process with rate nλ.
The second property is that the exponential distribution is memoryless. This means that when a Poisson event occurs, we can generate the time to the next event by generating a new exponentially distributed time at the current rate and adding it to the current time.
You haven't provided any information about what you want in the way of output, so I arbitrarily decided to print a report showing the time and the current numbers of nuclides whenever that number was halved. I also printed a report every 10 years, given the long half-life of Po-214.
I converted half-lifes to rates using the link provided at the top of the post, and then to means since that's what
Python numpy's exponential generator is parameterized to use. That's an easy conversion, since means and rates are inverses of each other.
Here's a Python implementation with comments:
from numpy.random import default_rng
from math import log
rng = default_rng()
# This creates a list of entries of quantities that will trigger a report.
# I've chosen to go with successive halvings of the original quantity.
def generate_report_qtys(n0):
report_qty = []
divisor = 2
while divisor < n0:
report_qty.append(n0 // divisor) # append next half-life qty to array
divisor *= 2
return report_qty
seconds_per_year = 365.25 * 24 * 60 * 60
po_214_half_life = 0.0001643 # seconds
ra_226_half_life = 1590 * seconds_per_year
log_2 = log(2)
po_mean = po_214_half_life / log_2 # per-nuclide decay rate for po_214
ra_mean = ra_226_half_life / log_2 # ditto for ra_226
po_n = po_n0 = 1_000_000_000
ra_n = ra_n0 = 1_000_000_000
time = 0.0
# Generate a report when the following sets of half-lifes are reached
po_report_qtys = generate_report_qtys(po_n0)
ra_report_qtys = generate_report_qtys(ra_n0)
# Initialize first event times for each type of event:
# - first entry is polonium next event time
# - second entry is radium next event time
# - third entry is next ten year report time
next_event_time = [
rng.exponential(po_mean / po_n),
rng.exponential(ra_mean / ra_n),
10 * seconds_per_year
]
# Print column labels and initial values
print("time,po_214,ra_226,time_in_years")
print(f"{time},{po_n},{ra_n},{time / seconds_per_year}")
while time < ra_226_half_life:
# Find the index of the next event time. Index tells us the event type.
min_index = next_event_time.index(min(next_event_time))
if min_index == 0:
po_n -= 1 # decrement polonium count
time = next_event_time[0] # update clock to the event time
if po_n > 0:
next_event_time[0] += rng.exponential(po_mean / po_n) # determine next event time for po
else:
next_event_time[0] = float('Inf')
# print report if this is a half-life occurrence
if len(po_report_qtys) > 0 and po_n == po_report_qtys[0]:
po_report_qtys.pop(0) # remove this occurrence from the list
print(f"{time},{po_n},{ra_n},{time / seconds_per_year}")
elif min_index == 1:
# same as above, but for radium
ra_n -= 1
time = next_event_time[1]
if ra_n > 0:
next_event_time[1] += rng.exponential(ra_mean / ra_n)
else:
next_event_time[1] = float('Inf')
if len(ra_report_qtys) > 0 and ra_n == ra_report_qtys[0]:
ra_report_qtys.pop(0)
print(f"{time},{po_n},{ra_n},{time / seconds_per_year}")
else:
# update clock, print ten year report
time = next_event_time[2]
next_event_time[2] += 10 * seconds_per_year
print(f"{time},{po_n},{ra_n},{time / seconds_per_year}")
Run times are proportional to the number of nuclides. Running with a billion of each took 831.28s on my M1 MacBook Pro, versus 2.19s for a million of each. I also ported this to Crystal, a compiled Ruby-like language, which produced comparable results in 32 seconds for a billion of each nuclide. I would recommend using a compiled language if you intend to run larger sized problems, but I will also point out that if you use half-life reporting as I did the results are virtually identical for smaller population sizes but are obtained much more rapidly.
I would also suggest that if you want to use this approach for a more complex model, you should use a priority queue of tuples containing time and type of event to store the set of pending future events rather than a simple list.
Last but not least, here's some sample output:
time,po_214,ra_226,time_in_years
0.0,1000000000,1000000000,0.0
0.0001642985647308265,500000000,1000000000,5.20630734690935e-12
0.0003286071415481526,250000000,1000000000,1.0412931957694901e-11
0.0004929007624958987,125000000,1000000000,1.5619082645571865e-11
0.0006571750701843468,62500000,1000000000,2.082462133319222e-11
0.0008214861652253772,31250000,1000000000,2.6031325741671646e-11
0.0009858208114474198,15625000,1000000000,3.1238776442043114e-11
0.0011502417677631668,7812500,1000000000,3.6448962144243124e-11
0.0013145712145548718,3906250,1000000000,4.165624808460947e-11
0.0014788866075394896,1953125,1000000000,4.686308868670272e-11
0.0016432124609700412,976562,1000000000,5.2070260760325286e-11
0.001807832817519779,488281,1000000000,5.728676507465013e-11
0.001972981254301889,244140,1000000000,6.252000324175124e-11
0.0021372947080755688,122070,1000000000,6.772678239395799e-11
0.002301139510796509,61035,1000000000,7.29187108904514e-11
0.0024642826956509244,30517,1000000000,7.808840645837847e-11
0.0026302282280720344,15258,1000000000,8.33469030620844e-11
0.0027944471221414947,7629,1000000000,8.855068579808016e-11
0.002954014120737834,3814,1000000000,9.3607058861822e-11
0.0031188370035748177,1907,1000000000,9.882998084692174e-11
0.003282466175503322,953,1000000000,1.0401507641592902e-10
0.003457552492113242,476,1000000000,1.0956322699169905e-10
0.003601851131916978,238,1000000000,1.1413577496124477e-10
0.0037747824699194033,119,1000000000,1.1961563838566314e-10
0.0039512825256332275,59,1000000000,1.252085876503038e-10
0.004124330529803301,29,1000000000,1.3069214800248755e-10
0.004337121375518753,14,1000000000,1.3743508300754027e-10
0.004535068261934763,7,1000000000,1.437076413268044e-10
0.004890820999020369,3,1000000000,1.5498076529965425e-10
0.004909065046898487,1,1000000000,1.555588842908994e-10
315576000.0,0,995654793,10.0
631152000.0,0,991322602,20.0
946728000.0,0,987010839,30.0
1262304000.0,0,982711723,40.0
1577880000.0,0,978442651,50.0
1893456000.0,0,974185269,60.0
2209032000.0,0,969948418,70.0
2524608000.0,0,965726762,80.0
2840184000.0,0,961524848,90.0
3155760000.0,0,957342148,100.0
3471336000.0,0,953178898,110.0
3786912000.0,0,949029294,120.0
4102488000.0,0,944898063,130.0
4418064000.0,0,940790494,140.0
4733640000.0,0,936699123,150.0
5049216000.0,0,932622334,160.0
5364792000.0,0,928565676,170.0
5680368000.0,0,924523267,180.0
5995944000.0,0,920499586,190.0
6311520000.0,0,916497996,200.0
6627096000.0,0,912511030,210.0
6942672000.0,0,908543175,220.0
7258248000.0,0,904590364,230.0
7573824000.0,0,900656301,240.0
7889400000.0,0,896738632,250.0
8204976000.0,0,892838664,260.0
8520552000.0,0,888956681,270.0
8836128000.0,0,885084855,280.0
9151704000.0,0,881232862,290.0
9467280000.0,0,877401861,300.0
9782856000.0,0,873581425,310.0
10098432000.0,0,869785364,320.0
10414008000.0,0,866002042,330.0
10729584000.0,0,862234212,340.0
11045160000.0,0,858485627,350.0
11360736000.0,0,854749939,360.0
11676312000.0,0,851032010,370.0
11991888000.0,0,847329028,380.0
12307464000.0,0,843640016,390.0
12623040000.0,0,839968529,400.0
12938616000.0,0,836314000,410.0
13254192000.0,0,832673999,420.0
13569768000.0,0,829054753,430.0
13885344000.0,0,825450233,440.0
14200920000.0,0,821859757,450.0
14516496000.0,0,818284787,460.0
14832072000.0,0,814727148,470.0
15147648000.0,0,811184419,480.0
15463224000.0,0,807655470,490.0
15778800000.0,0,804139970,500.0
16094376000.0,0,800643280,510.0
16409952000.0,0,797159389,520.0
16725528000.0,0,793692735,530.0
17041104000.0,0,790239221,540.0
17356680000.0,0,786802135,550.0
17672256000.0,0,783380326,560.0
17987832000.0,0,779970864,570.0
18303408000.0,0,776576174,580.0
18618984000.0,0,773197955,590.0
18934560000.0,0,769836170,600.0
19250136000.0,0,766488931,610.0
19565712000.0,0,763154778,620.0
19881288000.0,0,759831742,630.0
20196864000.0,0,756528400,640.0
20512440000.0,0,753237814,650.0
20828016000.0,0,749961747,660.0
21143592000.0,0,746699940,670.0
21459168000.0,0,743450395,680.0
21774744000.0,0,740219531,690.0
22090320000.0,0,736999181,700.0
22405896000.0,0,733793266,710.0
22721472000.0,0,730602000,720.0
23037048000.0,0,727427544,730.0
23352624000.0,0,724260327,740.0
23668200000.0,0,721110260,750.0
23983776000.0,0,717973915,760.0
24299352000.0,0,714851218,770.0
24614928000.0,0,711740161,780.0
24930504000.0,0,708645945,790.0
25246080000.0,0,705559170,800.0
25561656000.0,0,702490991,810.0
25877232000.0,0,699436919,820.0
26192808000.0,0,696394898,830.0
26508384000.0,0,693364883,840.0
26823960000.0,0,690348242,850.0
27139536000.0,0,687345934,860.0
27455112000.0,0,684354989,870.0
27770688000.0,0,681379178,880.0
28086264000.0,0,678414567,890.0
28401840000.0,0,675461363,900.0
28717416000.0,0,672522494,910.0
29032992000.0,0,669598412,920.0
29348568000.0,0,666687807,930.0
29664144000.0,0,663787671,940.0
29979720000.0,0,660901676,950.0
30295296000.0,0,658027332,960.0
30610872000.0,0,655164886,970.0
30926448000.0,0,652315268,980.0
31242024000.0,0,649481821,990.0
31557600000.0,0,646656096,1000.0
31873176000.0,0,643841377,1010.0
32188752000.0,0,641041609,1020.0
32504328000.0,0,638253759,1030.0
32819904000.0,0,635479981,1040.0
33135480000.0,0,632713706,1050.0
33451056000.0,0,629962868,1060.0
33766632000.0,0,627223350,1070.0
34082208000.0,0,624494821,1080.0
34397784000.0,0,621778045,1090.0
34713360000.0,0,619076414,1100.0
35028936000.0,0,616384399,1110.0
35344512000.0,0,613702920,1120.0
35660088000.0,0,611035112,1130.0
35975664000.0,0,608376650,1140.0
36291240000.0,0,605729994,1150.0
36606816000.0,0,603093946,1160.0
36922392000.0,0,600469403,1170.0
37237968000.0,0,597854872,1180.0
37553544000.0,0,595254881,1190.0
37869120000.0,0,592663681,1200.0
38184696000.0,0,590085028,1210.0
38500272000.0,0,587517782,1220.0
38815848000.0,0,584961743,1230.0
39131424000.0,0,582420312,1240.0
39447000000.0,0,579886455,1250.0
39762576000.0,0,577362514,1260.0
40078152000.0,0,574849251,1270.0
40393728000.0,0,572346625,1280.0
40709304000.0,0,569856166,1290.0
41024880000.0,0,567377753,1300.0
41340456000.0,0,564908008,1310.0
41656032000.0,0,562450828,1320.0
41971608000.0,0,560005832,1330.0
42287184000.0,0,557570018,1340.0
42602760000.0,0,555143734,1350.0
42918336000.0,0,552729893,1360.0
43233912000.0,0,550326162,1370.0
43549488000.0,0,547932312,1380.0
43865064000.0,0,545550017,1390.0
44180640000.0,0,543178924,1400.0
44496216000.0,0,540814950,1410.0
44811792000.0,0,538462704,1420.0
45127368000.0,0,536123339,1430.0
45442944000.0,0,533792776,1440.0
45758520000.0,0,531469163,1450.0
46074096000.0,0,529157093,1460.0
46389672000.0,0,526854383,1470.0
46705248000.0,0,524564196,1480.0
47020824000.0,0,522282564,1490.0
47336400000.0,0,520011985,1500.0
47651976000.0,0,517751635,1510.0
47967552000.0,0,515499791,1520.0
48283128000.0,0,513257373,1530.0
48598704000.0,0,511022885,1540.0
48914280000.0,0,508798440,1550.0
49229856000.0,0,506582663,1560.0
49545432000.0,0,504379227,1570.0
49861008000.0,0,502186693,1580.0
50176584000.0,0,500000869,1590.0
Expanded for More than 2 Nuclides
I mentioned that for more than a couple of nuclides you'd want to use a priority queue to track which decays occur next. I reorganized the code around functions, but that allowed greater flexibility in expanding the scope of the problem. Here you go:
#!/usr/bin/env python3
from numpy.random import default_rng
from math import log
import heapq
SECONDS_PER_YEAR = 365.25 * 24 * 60 * 60
LOG_2 = log(2)
rng = default_rng()
def generate_report_qtys(n0):
report_qty = []
divisor = 2
while divisor < n0:
report_qty.append(n0 // divisor) # append next half-life qty to array
divisor *= 2
return report_qty
po_n0 = 10_000_000
ra_n0 = 10_000_000
mu_n0 = 10_000_000
# mean is half-life / LOG_2
properties = dict(
po_214 = dict(
mean = 0.0001643 / LOG_2,
qty = po_n0,
report_qtys = generate_report_qtys(po_n0)
),
ra_226 = dict(
mean = 1590 * SECONDS_PER_YEAR / LOG_2,
qty = ra_n0,
report_qtys = generate_report_qtys(ra_n0)
),
made_up = dict(
mean = 75 * SECONDS_PER_YEAR / LOG_2,
qty = mu_n0,
report_qtys = generate_report_qtys(mu_n0)
)
)
nuclide_names = [name for name in properties.keys()]
def population_mean(nuclide):
return properties[nuclide]['mean'] / properties[nuclide]['qty']
def report(): # isolate as single point of maintenance even though it's a one-liner
nuc_qtys = [str(properties[nuclide]['qty']) for nuclide in nuclide_names]
print(f"{time},{time / SECONDS_PER_YEAR}," + ','.join(nuc_qtys))
def decay_event(nuclide):
properties[nuclide]['qty'] -= 1
current_qty = properties[nuclide]['qty']
if current_qty > 0:
heapq.heappush(event_q, (time + rng.exponential(population_mean(nuclide)), nuclide))
rep_qty = properties[nuclide]['report_qtys']
if len(rep_qty) > 0 and current_qty == rep_qty[0]:
rep_qty.pop(0) # remove this occurrence from the list
report()
def report_event():
heapq.heappush(event_q, (time + 10 * SECONDS_PER_YEAR, 'report_event'))
report()
event_q = [(rng.exponential(population_mean(nuclide)), nuclide) for nuclide in nuclide_names]
event_q.append((0.0, "report_event"))
heapq.heapify(event_q)
time = 0.0 # simulated time
print("time(seconds),time(years)," + ','.join(nuclide_names)) # column labels
while time < 1600 * SECONDS_PER_YEAR:
time, event_id = heapq.heappop(event_q)
if event_id == 'report_event':
report_event()
else:
decay_event(event_id)
To add more nuclides, add more entries to the properties dictionary, following the template of the current entries.

Is the function nnet adapted for neural network with a text?

I am trying to make a neural network model to predict sentiment about a text.
I have a data frame BDD with 3 columns:
1) there are adjectives. The name of the column is "ADJ"
2) there are nouns. The name of the column is "NOUN"
3) It's 1 if adj+noun is positive, -1 if negative and 0 if neutral. The name of the column is "V3"
BDD is divided with BDD_train and BDD_test. I succeeded to make my model, but the problem is when I make prediction.
This is the result of the model with BDD_train:
# weights: 476
initial value 133.618585
iter 10 value 18.334323
iter 20 value 15.922404
iter 30 value 15.823113
iter 40 value 15.816471
iter 50 value 15.811491
iter 60 value 15.811371
iter 60 value 15.811371
iter 60 value 15.811371
final value 15.811371
converged
nn_model <- nnet(V3~.,data = BDD_train,size = 5,decay = 1,linout = TRUE, maxit = 500)
pred2 <- predict(nn_model,newdata = BDD_test)
My error message is :
"Error in model.frame.default(Terms, newdata, na.action = na.omit, xlev = object$xlevels) :
le facteur ADJ a des nouveaux niveaux accommodative, Annual, Apparent, aware, definitive, federal, Good, greater, healthy, Monthly, more"

Table sort by month

I have a table in MATLAB with attributes in the first three columns and data from the fourth column onwards. I was trying to sort the entire table based on the first three columns. However, one of the columns (Column C) contains months ('January', 'February' ...etc). The sortrows function would only let me choose 'ascend' or 'descend' but not a custom option to sort by month. Any help would be greatly appreciated. Below is the code I used.
sortrows(Table, {'Column A','Column B','Column C'} , {'ascend' , 'ascend' , '???' } )

As #AnonSubmitter85 suggested, the best thing you can do is to convert your month names to numeric values from 1 (January) to 12 (December) as follows:
c = {
7 1 'February';
1 0 'April';
2 1 'December';
2 1 'January';
5 1 'January';
};
t = cell2table(c,'VariableNames',{'ColumnA' 'ColumnB' 'ColumnC'});
t.ColumnC = month(datenum(t.ColumnC,'mmmm'));
This will facilitate the access to a standard sorting criterion for your ColumnC too (in this example, ascending):
t = sortrows(t,{'ColumnA' 'ColumnB' 'ColumnC'},{'ascend', 'ascend', 'ascend'});
If, for any reason that is unknown to us, you are forced to keep your months as literals, you can use a workaround that consists in sorting a clone of the table using the approach described above, and then applying to it the resulting indices:
c = {
7 1 'February';
1 0 'April';
2 1 'December';
2 1 'January';
5 1 'January';
};
t_original = cell2table(c,'VariableNames',{'ColumnA' 'ColumnB' 'ColumnC'});
t_clone = t_original;
t_clone.ColumnC = month(datenum(t_clone.ColumnC,'mmmm'));
[~,idx] = sortrows(t_clone,{'ColumnA' 'ColumnB' 'ColumnC'},{'ascend', 'ascend', 'ascend'});
t_original = t_original(idx,:);

How to use GroupByKey in Spark to calculate nonlinear-groupBy task

I have a table looks like
Time ID Value1 Value2
1 a 1 4
2 a 2 3
3 a 5 9
1 b 6 2
2 b 4 2
3 b 9 1
4 b 2 5
1 c 4 7
2 c 2 0
Here is the tasks and requirements:
I want to set the column ID as the key, not the column Time, but I don't want to delete the column Time. Is there a way in Spark to set Primary Key?
The aggregation function is non-linear, which means you can not use "reduceByKey". All the data must be shuffled to one single node before calculation. For example, the aggregation function may looks like root N of the sum values, where N is the number of records (count) for each ID :
output = root(sum(value1), count(*)) + root(sum(value2), count(*))
To make it clear, for ID="a", the aggregated output value should be
output = root(1 + 2 + 5, 3) + root(4 + 3 + 9, 3)
the later 3 is because we have 3 record for a. For ID='b', it is:
output = root(6 + 4 + 9 + 2, 4) + root(2 + 2 + 1 + 5, 4)
The combination is non-linear. Therefore, in order to get correct results, all the data with the same "ID" must be in one executor.
I checked UDF or Aggregator in Spark 2.0. Based on my understanding, they all assume "linear combination"
Is there a way to handle such nonlinear combination calculation? Especially, taking the advantage of parallel computing with Spark?

Function you use doesn't require any special treatment. You can use plain SQL with join
import org.apache.spark.sql.Column
import org.apache.spark.sql.functions.{count, lit, sum, pow}
def root(l: Column, r: Column) = pow(l, lit(1) / r)
val out = root(sum($"value1"), count("*")) + root(sum($"value2"), count("*"))
df.groupBy("id").agg(out.alias("outcome")).join(df, Seq("id"))
or window functions:
import org.apache.spark.sql.expressions.Window
val w = Window.partitionBy("id")
val outw = root(sum($"value1").over(w), count("*").over(w)) +
root(sum($"value2").over(w), count("*").over(w))
df.withColumn("outcome", outw)