# Utility functions¶

.ml Utility functions arange Evenly-spaced values within a range combs n linear combinations of k numbers df2tab kdb+ table from a pandas dataframe df2tabTimezone Pandas dataframe to kdb+ conversion handling dates/times/timezones eye Identity matrix iMax Index of maximum element of a list iMin Index of minimum element of a list linearSpace List of evenly-spaced values range Range of values shape Shape of a matrix tab2df Pandas dataframe from a q table trainTestSplit Split into training and test sets

The toolkit contains utility functions, used in many applications and not limited to categories such as statistics or preprocessing.

## .ml.arange¶

Evenly-spaced values

.ml.arange[start;end;step]

Where

• start is the start of the interval (inclusive)
• end is the end of the interval (non-inclusive)
• step is the spacing between values

returns a vector of evenly-spaced values between start and end in steps of length step

q).ml.arange[1;10;1]
1 2 3 4 5 6 7 8 9
q).ml.arange[6.25;10.5;0.05]
6.25 6.3 6.35 6.4 6.45 6.5 6.55 6.6 6.65 6.7 6.75 6.8 6.85 6.9 6.95 7 7.05 7...

## .ml.combs¶

Unique combinations of a vector or matrix

.ml.combs[n;degree]

Where

• n is the integer number of values required for combinations
• degree is the degree of the combinations to be produced

returns the unique combinations of values from the data.

q).ml.combs[3;2]
0 1
0 2
1 2
q)show k:5?1
pjeob
q)k .ml.combs[count k;4]    / display values in combinations
p j e o
p j e b
p j o b
p e o b
j e o b
q)show m:(0 1 2;2 3 4;4 5 6;6 7 8)
0 1 2
2 3 4
4 5 6
6 7 8
q)m .ml.combs[count m;3]
0 1 2 2 3 4 4 5 6
0 1 2 2 3 4 6 7 8
0 1 2 4 5 6 6 7 8
2 3 4 4 5 6 6 7 8

## .ml.df2tab¶

Convert pandas dataframe to q table

.ml.df2tab[tab]

Where

• tab is an embedPy representation of a Pandas dataframe

returns tab as a q table.

q)p)import pandas as pd
q)print t:.p.eval"pd.DataFrame({'fcol':[0.1,0.2,0.3,0.4,0.5],'jcol':[10,20,30,40,50]})"
fcol  jcol
0   0.1    10
1   0.2    20
2   0.3    30
3   0.4    40
4   0.5    50
q).ml.df2tab t
fcol jcol
---------
0.1  10
0.2  20
0.3  30
0.4  40
0.5  50
q)print kt:t[:set_index]jcol
fcol
jcol
10     0.1
20     0.2
30     0.3
40     0.4
50     0.5
q).ml.df2tab kt
jcol| fcol
----| ----
10  | 0.1
20  | 0.2
30  | 0.3
40  | 0.4
50  | 0.5

Index columns This function assumes a single unnamed Python index column is to be removed. It returns an unkeyed table. All other variants of Python index columns map to q key columns. For example any instance with two or more indexes will map to two or more Python keys, while any named single-index Python column be associated with a q key in a keyed table.

Note

This function is a wrapper around .ml.df2tabTimezone, conversions within this function will default to convert datetime.date and datetime.time types to foreign objects, numpy timezone types are converted to their UTC representation. These conversion choices have been made due to python related computational inefficiencies in converting to native q types and local-time representations respectively.

## .ml.df2tabTimezone¶

Convert a pandas dataframe containing datetime objects to a q table

.ml.df2tabTimezone[tab;local;qObj]

Where:

• tab is an embedPy representation of a Pandas dataframe
• local is a boolean indicating if timezone(tz) objects are to be converted to local time (1b) or UTC (0b)
• qObj is a boolean indicating if python datetime.date/datetime.time objects are returned as q (1b) or foreign objects (0b)

Returns a q table

q)p)import pandas as pd
q)p)import datetime
q)p)import numpy as np
q)p)dtdf=pd.DataFrame(
{'time':[datetime.time(12, 10, 30,500),datetime.time(12, 13, 30,200)],
'timed':[datetime.timedelta(hours=-5),datetime.timedelta(seconds=1000)],
'datetime':[np.datetime64('2005-02-25T03:30'),np.datetime64('2015-12-22')]})
q)p)dtdf['dt_with_tz']=dtdf.datetime.dt.tz_localize('CET')

q)print dttab:.p.get[dtdf]
time             timed            datetime                dt_with_tz
0  12:10:30.000500 -1 days +19:00:00 2005-02-25 03:30:00 2005-02-25 03:30:00+01:00
1  12:13:30.000200          00:16:40 2015-12-22 00:00:00 2015-12-22 00:00:00+01:00

/ default behavior (tz -> UTC, time -> foreign)
q).ml.df2tabTimezone[dttab;0b;0b]
time    timed                 datetime                      dt_with_tz
-----------------------------------------------------------------------------------------
foreign -0D05:00:00.000000000 2005.02.25D03:30:00.000000000 2005.02.25D02:30:00.000000000
foreign 0D00:16:40.000000000  2015.12.22D00:00:00.000000000 2015.12.21D23:00:00.000000000

/ default time conversion, local tz conversion
q).ml.df2tabTimezone[dttab;1b;0b]
time    timed                 datetime                      dt_with_tz
-----------------------------------------------------------------------------------------
foreign -0D05:00:00.000000000 2005.02.25D03:30:00.000000000 2005.02.25D03:30:00.000000000
foreign 0D00:16:40.000000000  2015.12.22D00:00:00.000000000 2015.12.22D00:00:00.000000000

/ default tz conversion and conversion to q time
q).ml.df2tabTimezone[dttab;0b;1b]
time                 timed                 datetime                      dt_with_tz
------------------------------------------------------------------------------------------------------
0D12:10:30.000500000 -0D05:00:00.000000000 2005.02.25D03:30:00.000000000 2005.02.25D02:30:00.000000000
0D12:13:30.000200000 0D00:16:40.000000000  2015.12.22D00:00:00.000000000 2015.12.21D23:00:00.000000000

.ml.df2tab_tz deprecated

The above function was previously defined as .ml.df2tab_tz. It is still callable but will be deprecated after version 3.0.

## .ml.eye¶

Create identity matrix

.ml.eye[n]

Where

• n is the width/height of identity matrix

returns an identity matrix of height/width n.

q).ml.eye 5
1 0 0 0 0
0 1 0 0 0
0 0 1 0 0
0 0 0 1 0
0 0 0 0 1

## .ml.iMax¶

Index of maximum element of a list

.ml.iMax[array]

Where

• array is a numerical array of values

returns the index of the maximum element of the array

q)show a:8?5.
3.883438 4.96977 2.447749 3.253555 4.246108 4.54695 1.381171 2.273137
q).ml.iMax a
1
q)show b:8?100
23 8 12 24 6 36 68 37
q).ml.iMax b
6

.ml.imax deprecated

The above function was previously defined as .ml.imax. It is still callable but will be deprecated after version 3.0.

## .ml.iMin¶

Index of maximum element of a list

.ml.iMin[array]

Where

• array is a numerical array of values

returns the index of the minimum element of the array

q)show a:8?10.
0.6916353 8.045142 7.619755 4.599266 0.3341879 6.43216 6.177459 4.751895
q).ml.iMin a
4
q)show b:8?50
22 45 3 22 3 5 40 26
q).ml.iMin b
2

.ml.imin deprecated

The above function was previously defined as .ml.imin. It is still callable but will be deprecated after version 3.0.

## .ml.linearSpace¶

Array of evenly-spaced values

.ml.linearSpace[start;end;n]

Where

• start is the start of the interval (inclusive)
• end is the end of the interval (inclusive)
• n indicates how many spaces are to be created

returns a vector of n evenly-spaced values between start and end.

q).ml.linearSpace[10;20;9]
10 11.25 12.5 13.75 15 16.25 17.5 18.75 20
q).ml.linearSpace[0.5;15.25;12]
0.5 1.840909 3.181818 4.522727 5.863636 7.204545 8.545455 9.886364 11.22727 1..

.ml.linspace deprecated

The above function was previously defined as .ml.linspace. It is still callable but will be deprecated after version 3.0.

## .ml.range¶

Range of values

.ml.range[array]

Where

• array is a numerical array

returns the range of its values.

q).ml.range 1000?100000f
99742.37
q)show mat:(2 2#4?1f)
0.04492896 0.1786355
0.9694828  0.8964098
q).ml.range mat
0.9245539 0.7177742

## .ml.shape¶

Shape of a matrix

.ml.shape[matrix]

Where

• matrix is a matrix of values

returns its shape as a list of dimensions.

q).ml.shape 10
long\$()
q).ml.shape enlist 10
,1
q).ml.shape til 10
,10
q).ml.shape enlist til 10
1 10
q).ml.shape 2 5#til 10
2 5
q).ml.shape 2 3 4#til 24
2 3 4
q).ml.shape ([]c1:til 10;c2:0)
10 2

Behavior of .ml.shape is undefined for ragged/jagged arrays.

## .ml.tab2df¶

Convert q table to Pandas dataframe

.ml.tab2df[tab]

Where tab is a table

returns a Pandas dataframe.

q)n:5
/ q table for input
q)table:([]x:n?10000f;x1:1+til n;x2:reverse til n;x3:n?100f)
x        x1 x2 x3
-----------------------
2631.44  1  4  78.71917
1118.109 2  3  80.09356
3250.627 3  2  16.71013
// Convert to pandas dataframe and show it is an embedPy object
q)show pdf:.ml.tab2df[table]
{[f;x]embedPy[f;x]}[foreign]enlist
// Display the Python form of the dataframe
q)print pdf
x  x1  x2         x3
0  2631.439704   1   4  78.719172
1  1118.109056   2   3  80.093563
2  3250.627243   3   2  16.710134

## .ml.trainTestSplit¶

Split into training and test sets

.ml.trainTestSplit[data;target;size]

Where

• data is a matrix, table or list
• target is a vector of target values the same count as data
• size is the percentage size of the testing set

returns a dictionary containing the data matrix and target values, split into a training and testing set according to the percentage size of the data to be contained in the test set.

q)mat:(30 20)#1000?10f
q)target:rand each 30#0b
q).ml.trainTestSplit[mat;target;0.2] / split the data such that 20% is contained in the test set
xtrain| (2.02852 2.374546 1.083376 2.59378 6.698505 6.675959 4.120228 2.63468..
ytrain| 110010100101111001110000b
xtest | (8.379916 8.986609 7.06074 2.067817 5.468488 4.103195 0.1590803 0.259..
ytest | 000001b

q)tab:([]30?1f;30?1;30?10)
q).ml.trainTestSplit[tab;target;0.2]
xtrain| +xx1x2!(0.1659182 0.5316555 0.9658597 0.6659117 0.4921318 0.580703..
ytrain| 0.4449418 0.6637015 0.77852 0.8229043 0.5678825 0.9534722 0.2448434 0..
xtest | +xx1x2!(0.6913239 0.3921862 0.2904501 0.6536423 0.6517715 0.961030..
ytest | 0.9861457 0.752895 0.2695986 0.122979 0.4412847 0.4952119

q)list:asc 30?1f
q).ml.trainTestSplit[list;target;0.2]
xtrain| 0.4251052 0.6419072 0.5701215 0.4231011 0.327041 0.1573152 0.3414573 ..
ytrain| 0.5029018 0.05230331 0.628313 0.5766565 0.6314705 0.3266584 0.9624403..
xtest | 0.3692275 0.4192985 0.1573064 0.9121564 0.28237 0.07992544
ytest | 0.3821462 0.9177309 0.3572827 0.1110881 0.9807582 0.5132051

.ml.traintestsplit deprecated

The above function was previously defined as .ml.traintestsplit`. It is still callable but will be deprecated after version 3.0.