User guide¶
PyQ lets you enjoy the power of kdb+ in a comfortable environment provided by a mainstream programming language. In this guide we will assume that the reader has a working knowledge of Python, but we will explain the q language concepts as we encounter them.
The q namespace¶
Meet q
– your portal to kdb+. Once you import q
from pyq
, you get access to over 170 functions:
>>> from pyq import q
>>> dir(q)
['abs', 'acos', 'aj', 'aj0', 'all', 'and_', 'any', 'asc', 'asin', ...]
These functions should be familiar to anyone who knows the q language and this is exactly what these functions are: q functions repackaged so that they can be called from Python. Some of the q functions are similar to Python builtins or math functions, which is not surprising because q, like Python, is a complete generalpurpose language. In the following sections we will systematically draw an analogy between q and Python functions and explain the differences between them.
The til
function¶
Since Python does not have language constructs to loop over integers, many Python tutorials introduce the range()
function early on. In the q language, the situation is similar and the function that produces a sequence of integers is called til
. Mnemonically, q.til(n)
means count from zero until n.
>>> q.til(10)
k('0 1 2 3 4 5 6 7 8 9')
The return value of a q function is always an instance of the class K
, which will be described in the next chapter. In the case of q.til(n)
, the result is a K
vector, which is similar to a Python list. In fact, you can get the Python list simply by calling the list()
constructor on the q vector.
>>> list(_)
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
While useful for illustrative purposes, you should avoid converting K
vectors to Python lists in real programs. It is often more efficient to manipulate K
objects directly. For example, unlike range()
, til()
does not have optional start or step arguments. This is not necessary because you can do arithmetic on the K
vectors to achieve a similar result.
>>> range(10, 20, 2) == 10 + 2 * q.til(5)
True
Many q functions are designed to ‘map’ themselves automatically over sequences passed as arguments. Those functions are called atomic and will be covered in the next section. The til()
function is not atomic, but it can be mapped explicitly.
>>> q.til.each(range(1,5)).show()
,0
0 1
0 1 2
0 1 2 3
The last example requires some explanation. First we have used the show()
method to provide a nice multiline display of a list of vectors. This method is available for all K
objects. Second, the first line in the display shows an empty list of type long. Note that, unlike Python lists, K
vectors come in different types, and til()
returns vectors of type long. Finally, the second line in the display starts with ,
to emphasize that this is a vector of length 1 rather than an atom.
The each()
adverb is similar to Python’s map()
, but is often much faster.
>>> q.til.each(range(5)) == map(q.til, range(5))
True
Atomic functions¶
As we mentioned in the previous section, atomic functions operate on numbers or lists of numbers. When given a number, an atomic function acts similarly to its Python analogue.
Compare
>>> q.exp(1)
k('2.718282')
to
>>> math.exp(1)
2.718281828459045
Want to see more digits? Set q
’s display precision using the system()
function:
>>> q.system(b"P 16")
k('::')
>>> q.exp(1)
k('2.718281828459045')
Unlike their native Python analogues, atomic q
functions can operate on sequences:
>>> q.exp(range(5))
k('1 2.718282 7.389056 20.08554 54.59815')
The result in this case is a K
vector whose elements are obtained by applying the function to each element of the given sequence.
Mathematical functions¶
As you can see in the table below, most of the mathematical functions provided by q are similar to the Python standard library functions in the math
module.
q  Python  Return 

neg() 
operator.neg() 
the negative of the argument 
abs() 
abs() 
the absolute value 
signum() 
±1 or 0 depending on the sign of the argument  
sqrt() 
math.sqrt() 
the square root of the argument 
exp() 
math.exp() 
e raised to the power of the argument 
log() ) 
math.log() 
the natural logarithm (base e) of the argument 
cos() 
math.cos() 
the cosine of the argument 
sin() 
math.sin() 
the sine of the argument 
tan() 
math.tan() 
the tangent of the argument 
acos() 
math.acos() 
the arc cosine of the argument 
asin() 
math.asin() 
the arc sine of the argument 
atan() 
math.atan() 
the arc tangent of the argument 
ceiling() 
math.ceil() 
the smallest integer ≥ the argument 
floor() 
math.floor() 
the largest integer ≤ the argument 
reciprocal() 
1 divided by the argument 
Other than being able to operate on lists of numbers, q functions differ from Python functions in the way they treat outofdomain errors.
Where Python functions raise an exception,
>>> math.log(0)
Traceback (most recent call last):
...
ValueError: math domain error
q functions return special values:
>>> q.log([1, 0, 1])
k('0n 0w 0')
The null function¶
Unlike Python, q allows division by zero. The reciprocal of zero is infinity, which shows up as 0w
or 0W
in displays.
>>> q.reciprocal(0)
k('0w')
Multiplying infinity by zero produces a null value that generally indicates missing data
>>> q.reciprocal(0) * 0
k('0n')
Null values and infinities can also appear as a result of applying a mathematical function to numbers outside of its domain:
>>> q.log([1, 0, 1])
k('0n 0w 0')
The null()
function returns 1b
(boolean true) when given a null value and 0b
otherwise. For example, when applied to the output of the log()
function from the previous example, it returns
>>> q.null(_)
k('100b')
Aggregation functions¶
Aggregation functions (also known as reduction functions) are functions that given a sequence of atoms produce an atom. For example,
>>> sum(range(10))
45
>>> q.sum(range(10))
k('45')
q  Python  Return 

sum() 
sum() 
the sum of the elements 
prd() 
the product of the elements  
all() 
all() 
1b if all elements are nonzero, 0b otherwise 
any() 
any() 
1b if any of the elements is nonzero, 0b otherwise 
min() 
min() 
the smallest element 
max() 
max() 
the largest element 
avg() 
statistics.mean() 
the arithmetic mean 
var() 
statistics.pvariance() 
the population variance 
dev() 
statistics.pstdev() 
the square root of the population variance 
svar() 
statistics.variance() 
the sample variance 
sdev() 
statistics.stdev() 
the square root of the sample variance 
Accumulation functions¶
Given a sequence of numbers, one may want to compute not just the sum total, but all the intermediate sums as well. In q, this can be achieved by applying the sums
function to the sequence:
>>> q.sums(range(10))
k('0 1 3 6 10 15 21 28 36 45')
q  Return 

sums() 
the cumulative sums of the elements 
prds() 
the cumulative products of the elements 
maxs() 
the maximums of the prefixes of the argument 
mins() 
the minimums of the prefixes of the argument 
There are no direct analogues of these functions in the Python standard library, but the itertools.accumulate()
function provides similar functionality:
>>> list(itertools.accumulate(range(10)))
[0, 1, 3, 6, 10, 15, 21, 28, 36, 45]
Passing operator.mul()
, max()
or min()
as the second optional argument to itertools.accumulate()
, one can get analogues of q.prds()
, q.maxs()
and q.mins()
.
Sliding window statistics¶
mavg()
mcount()
mdev()
mmax()
mmin()
msum()
Uniform functions¶
Uniform functions are functions that take a list and return another list of the same size.
reverse()
ratios()
deltas()
differ()
next()
prev()
fills()
Set operations¶
except_()
inter()
union()
Sorting and searching¶
Functions asc()
and desc()
sort lists in ascending and descending order respectively:
>>> a = [9, 5, 7, 3, 1]
>>> q.asc(a)
k('`s#1 3 5 7 9')
>>> q.desc(a)
k('9 7 5 3 1')
Sorted attribute
The s#
prefix that appears in the display of the output for the asc()
function indicates that the resulting vector has a sorted attribute set. An attribute can be queried by calling the attr()
function or accessing the attr
property of the result:
>>> s = q.asc(a) >>> q.attr(s) k('s')
>>> s.attr
k('s')
When theasc()
function gets a vector with the s
attribute set, it skips sorting and immediately returns the same vector.
Functions iasc()
and idesc()
return the indices indicating the order in which the items of the incoming list should be arranged to be sorted.
>>> q.iasc(a)
k('4 3 1 2 0')
Sorted lists can be searched efficiently using the bin()
and binr()
functions. As their names suggest, both use binary search to locate the position of an item equal to the search key; but where there is more than one such element, binr()
returns the index of the first match while bin()
returns the index of the last.
>>> q.binr([10, 20, 20, 20, 30], 20)
k('1')
>>> q.bin([10, 20, 20, 20, 30], 20)
k('3')
When no item matches, binr()
(bin()
) returns the index of the position before (after) which the key can be inserted so that the list remains sorted.
>>> q.binr([10, 20, 20, 20, 30], [5, 15, 20, 25, 35])
k('0 1 1 4 5')
>>> q.bin([10, 20, 20, 20, 30], [5, 15, 20, 25, 35])
k('1 0 3 3 4')
In the Python standard library similar functionality is provided by the bisect
module.
>>> [bisect.bisect_left([10, 20, 20, 20, 30], key) for key in [5, 15, 20, 25, 35]]
[0, 1, 1, 4, 5]
>>> [1 + bisect.bisect_right([10, 20, 20, 20, 30], key) for key in [5, 15, 20, 25, 35]]
[1, 0, 3, 3, 4]
Note that while binr()
and bisect.bisect_left()
return the same values, bin()
and bisect.bisect_right()
are off by 1.
Q does not have a named function for searching an unsorted list because it uses the ?
operator for that. We can easily expose this functionality in PyQ as follows:
>>> index = q('?')
>>> index([10, 30, 20, 40], [20, 25])
k('2 4')
Note that our homebrewed index
function resembles the list.index()
method, but it returns the oneafterlast index when the key is not found, where list.index()
raises an exception.
>>> list.index([10, 30, 20, 40], 20)
2
>>> list.index([10, 30, 20, 40], 25)
Traceback (most recent call last):
...
ValueError: 25 is not in list
If you are not interested in the index, but want to know only whether the keys can be found in a list, you can use the in_()
function:
>>> q.in_([20, 25], [10, 30, 20, 40])
k('10b')
Trailing underscore
The q.in_
function has a trailing underscore because otherwise it would conflict with the Python keyword in
.
From Python to kdb+¶
You can pass data from Python to kdb+ by assigning to q
attributes. For example,
>>> q.i = 42
>>> q.a = [1, 2, 3]
>>> q.t = ('Python', 3.5)
>>> q.d = {'date': date(2012, 12, 12)}
>>> q.value.each(['i', 'a', 't', 'd']).show()
42
1 2 3
(`Python;3.5)
(,`date)!,2012.12.12
Note that Python objects are automatically converted to kdb+ form when they are assigned in the q
namespace, but when they are retrieved, Python gets a ‘handle’ to kdb+ data.
For example, passing an int
to q
results in
>>> q.i
k('42')
If you want a Python integer instead, you have to convert explicitly.
>>> int(q.i)
42
This will be covered in more detail in the next section.
You can also create kdb+ objects by calling q
functions that are also accessible as q
attributes. For example,
>>> q.til(5)
k('0 1 2 3 4')
Some q functions don’t have names because q uses special characters. For example, to generate random data in q you should use the ?
operator. While PyQ does not supply a Python name for ?
, you can easily add it to your own toolkit:
>>> rand = q('?')
And use it as you would any other Python function
>>> x = rand(10, 2) # generates 10 random 0s or 1s (coin toss)
From kdb+ to Python¶
In many cases your data is already stored in kdb+, and PyQ philosophy is that it should stay there. Rather than converting kdb+ objects to Python, manipulating Python objects and converting them back to kdb+, PyQ lets you work directly with kdb+ data as if it were already in Python.
For example, let us retrieve the release date from kdb+:
>>> d1 = q('.z.k')
add 30 days to get another date
>>> d2 = d1 + 30
and find the difference in whole weeks
>>> (d2  d1) % 7
k('2')
Note that the result of operations are (handles to) kdb+ objects. The only exceptions to this rule are indexing and iteration over simple kdb+ vectors. These operations produce Python scalars
>>> list(q.a)
[1, 2, 3]
>>> q.a[1]
3
In addition to Python operators, one invokes q functions on kdb+ objects directly from Python using the convenient attribute access / method call syntax.
For example
>>> q.i.neg.exp.log.mod(5)
k('3f')
Note that the above is equivalent to
>>> q.mod(q.log(q.exp(q.neg(q.i))), 5)
k('3f')
but shorter and closer to q
syntax
>>> q('(log exp neg i)mod 5')
k('3f')
The difference being that in q, functions are applied right to left, but in PyQ left to right.
Finally, if q does not provide the function you need, you can unleash the full power of numpy or scipy on your kdb+ data.
>>> numpy.log2(q.a)
array([ 0. , 1. , 1.5849625])
Note that the result is a numpy array, but you can redirect the output back to kdb+. To illustrate this, create a vector of 0s in kdb+
>>> b = q.a * 0.0
and call a numpy function on one kdb+ object, redirecting the output to another:
>>> numpy.log2(q.a, out=numpy.asarray(b))
The result of a numpy function is now in the kdb+ object.
>>> b
k('0 1 1.584963')
Working with files¶
Kdb+ uses the unmodified host file system to store data and therefore q has excellent support for working with files. Recall that we can send Python objects to kdb+ simply by assigning them to a q
attribute:
>>> q.data = range(10)
This code saves 10 integers in kdb+ memory and makes a global variable data
available to kdb+ clients, but it does not save the data in any persistent storage. To save data
as a file data
, we can simply call the pyq.q.save
function as follows:
>>> q.save('data')
k(':data')
Note that the return value of the pyq.q.save
function is a K
symbol that is formed by prepending :
to the file name. Such symbols are known as file handles in q. Given a file handle, the kdb+ object stored in the file can be obtained by accessing the value
property of the file handle.
>>> _.value
k('0 1 2 3 4 5 6 7 8 9')
Now we can delete the data from memory
>>> del q.data
and load it back from the file using the pyq.q.load
function:
>>> q.load('data')
k('data')
>>> q.data
k('0 1 2 3 4 5 6 7 8 9')
pyq.q.save
and pyq.q.load
functions can also take a pathlib.Path
object
>>> data_path = pathlib.Path('data')
>>> q.save(data_path)
k('`:data')
>>> q.load(data_path)
k('`data')
>>> data_path.unlink()
It is not necessary to assign data to a global variable before saving it to a file. We can save our 10 integers directly to a file using the pyq.q.set
function
>>> q.set(':09', range(10))
k(':09')
and read it back using the pyq.q.set
function
>>> q.get(_)
k('0 1 2 3 4 5 6 7 8 9')
>>> pathlib.Path('09').unlink()
K objects¶
The q language has has atoms (scalars), lists, dictionaries, tables and functions. In PyQ, kdb+ objects of any type appear as instances of class K
. To tell the underlying kdb+ type, one can access the type
property to obtain a type code. For example,
>>> vector = q.til(5); scalar = vector.first
>>> vector.type
k('7h')
>>> scalar.type
k('7h')
Basic vector types have type codes in the range 1 through 19 and their elements have the type code equal to the negative of the vector type code. For the basic vector types, one can also get a humanreadable type name by accessing the key
property.
>>> vector.key k('long')
To get the same from a scalar, convert it to a vector first.
>>> scalar.enlist.key
k('long')
code  kdb+ type  Python type 

1  boolean 
bool 
2  guid 
uuid.UUID 
4  byte 

5  short 

6  int 

7  long 
int 
8  real 

9  float 
float 
10  char 
bytes (*) 
11  symbol 
str 
12  timestamp 

13  month 

14  date 
datetime.date 
16  timespan 
datetime.timedelta 
17  minute 

18  second 

19  time 
datetime.time 
(*) Unlike other Python types mentioned in the table above, bytes
instances get converted to a vector type.
>>> K(b'x')
k(',"x"')
>>> q.type(_)
k('10h')
There is no scalar character type in Python, so to create a K
character scalar, use a typed constructor:
>>> K.char(b'x')
k('"x"')
Typed constructors are discussed in the next section.
Constructors and casts¶
As we have seen in the previous chapter, it is seldom necessary to construct K
objects explicitly, because they are created automatically whenever a Python object is passed to a q function. This is done by passing the Python object to the default K
constructor.
For example, if you need to pass a long atom to a q function, you can use a Python int instead, but if a different integer type is required, you will need to create it explicitly.
>>> K.short(1)
k('1h')
Since an empty list does not know its type, passing []
to the default K
constructor produces a generic (type 0h
) list.
>>> K([])
k('()')
>>> q.type(_)
k('0h')
To create an empty list of a specific type, pass []
to one of the named constructors.
>>> K.time([])
k('`time$()')
constructor  accepts  description 

K.boolean() 
int , bool 
logical type 0b is false and 1b is true 
byte() 
int , bytes 
8bit bytes 
short() 
int 
16bit integers 
int() 
int 
32bit integers 
long() 
int 
64bit integers 
real() 
int , float 
32bit floating point numbers 
float() 
int , float 
32bit floating point numbers 
char() 
str , bytes 
8bit characters 
symbol() 
str , bytes 
interned strings 
timestamp() 
int (nanoseconds), datetime 
date and time 
month() 
int (months), date 
year and month 
date() 
int (days), date 
year, month and day 
datetime() 
(deprecated)  
timespan() 
int (nanoseconds), timedelta 
duration in nanoseconds 
minute() 
int (minutes), time 
duration or time of day in minutes 
second() 
int (seconds), time 
duration or time of day in seconds 
time() 
int (milliseconds), time 
duration or time of day in milliseconds 
The typed constructors can also be used to access infinities and missing values of the given type.
>>> K.real.na, K.real.inf
(k('0Ne'), k('0we'))
If you already have a K
object and want to convert it to a different type, you can access the property named after the type name. For example,
>>> x = q.til(5)
>>> x.date
k('2000.01.01 2000.01.02 2000.01.03 2000.01.04 2000.01.05')
Operators¶
Both Python and q provide a rich system of operators. In PyQ, K
objects can appear in many Python expressions where they often behave as native Python objects.
Most operators act on K
instances as namesake q functions. For example:
>>> K(1) + K(2)
k('3')
The if statement and boolean operators¶
Python has three boolean operators or
, and
and not
and K
objects can appear in boolean expressions. The result of a boolean expression depends on how the objects are tested in Python ifstatements.
All K
objects can be tested for ‘truth’. Similarly to the Python numeric types and sequences, K
atoms of numeric types are true if they are not zero, and vectors are true if they are nonempty.
Atoms of nonnumeric types follow different rules. Symbols test true except for the empty symbol; characters and bytes tested true except for the null character/byte; guid, timestamp, and (deprecated) datetime types always test as true.
Functions test as true, except for the monadic passthrough function:
>>> q('::') or q('+') or 1
k('+')
Dictionaries and tables are treated as sequences: they are true if nonempty.
Note that in most cases how the object test does not change when Python native types are converted to K
:
>>> objects = [None, 1, 0, True, False, 'x', '', {1:2}, {}, date(2000, 1, 1)]
>>> [bool(o) for o in objects]
[False, True, False, True, False, True, False, True, False, True]
>>>[bool(K(o)) for o in objects]
[False, True, False, True, False, True, False, True, False, True]
One exception is the Python time
type. Starting with version 3.5 all time
instances test as true, but time(0)
converts to k('00:00:00.000')
which tests false:
>>> [bool(o) for o in (time(0), K(time(0)))]
[True, False]
Info
Python changed the rule for time(0)
because time
instances can be timezoneaware and because they do not support addition, making 0 less than special. Neither of those arguments apply to q
time, second or minute data types which behave more like timedelta
.
Arithmetic operations¶
Python has the four familiar arithmetic operators +
, 
, *
and /
as well as less common **
(exponentiation), %
(modulo) and //
(floor division). PyQ maps those to q operators as follows
operation  Python  q 

addition  + 
+ 
subtraction   
 
multiplication  * 
* 
true division  / 
% 
exponentiation  ** 
xexp 
floor division  // 
div 
modulo  % 
mod 
K
objects can be freely mixed with Python native types in arithmetic expressions and the result is a K
object in most cases:
>>> q.til(10) % 3
k('0 1 2 0 1 2 0 1 2 0')
A notable exception occurs when the modulo operator is used for string formatting.
>>> "%.5f" % K(3.1415)
'3.14150'
Unlike Python sequences, K
lists behave very similarly to atoms: arithmetic operations act itemwise on them.
Compare
>>> [1, 2] * 5
[1, 2, 1, 2, 1, 2, 1, 2, 1, 2]
and
>>> K([1, 2]) * 5
k('5 10')
or
>>> [1, 2] + [3, 4]
[1, 2, 3, 4]
and
>>> K([1, 2]) + [3, 4]
k('4 6')
The flip (+
) operator¶
The unary +
operator acts as the flip()
function on K
objects. Applied to atoms, it has no effect:
>>> +K(0)
k('0')
but it can be used to transpose a matrix:
>>> m = K([[1, 2], [3, 4]])
>>> m.show()
1 2
3 4
>>> (+m).show()
1 3
2 4
or turn a dictionary into a table:
>>> d = q('!', ['a', 'b'], m)
>>> d.show()
a 1 2
b 3 4
>>> (+d).show()
a b

1 3
2 4
Bitwise operators¶
Python has six bitwise operators: 
, ^
, &
, <<
, >>
, and ~
. Since there are no bitwise operations in q, PyQ redefines them as follows:
operation  result  note 

x  y 
elementwise maximum of x and y 
1 
x ^ y 
y with null elements filled with x 
2 
x & y 
elementwise minimum of x and y 
1 
x << n 
x shifted left by n elements 
3 
x >> n 
x shifted right by n elements 
3 
~x 
a boolean vector with 1s for zero elements of x 
Notes:

For boolean vectors,

and&
are also itemwise or and and operations. 
For Python integers, the result of
x^y
is the bitwise exclusive or. There is no similar operation inq
, but for boolean vectors exclusive or is equivalent to q<>
(not equal). 
Negative shift counts result in a shift in the opposite direction to that indicated by the operator:
x >> n
is the same asx << n
.
Minimum and maximum¶
Minimum and maximum operators are &
and 
in q. PyQ maps similarlooking Python bitwise operators to the corresponding q ones:
>>> q.til(10)  5
k('5 5 5 5 5 5 6 7 8 9')
>>> q.til(10) & 5
k('0 1 2 3 4 5 5 5 5 5')
The ^
operator¶
Unlike Python, where caret (^
) is the binary xor operator, q defines it to denote the fill operation that replaces null values in the right argument with the left argument. PyQ follows the q definition:
>>> x = q('1 0N 2') >>> 0 ^ x
k('1 0 2')
The @
operator¶
Python 3.5 introduced the @
operator, which can be used by user types. Unlike NumPy that defines @
as the matrixmultiplication operator, PyQ uses @
for function application and composition:
>>> q.log @ q.exp @ 1
k('1f')
Adverbs¶
Adverbs in q are somewhat similar to Python decorators. They act on functions and produce new functions. The six adverbs are summarized in the table below.
PyQ  q  description 

K.each() 
' 
map or case 
K.over() 
/ 
reduce 
K.scan() 
\ 
accumulate 
K.prior() 
': 
eachprior 
K.sv() 
/: 
eachright or scalar from vector 
K.vs() 
\: 
eachleft or vector from scalar 
The functionality provided by the first three adverbs is similar to functional programming features scattered throughout Python standard library.
Thus each
is similar to map()
.
For example, given a list of lists of numbers
>>> data = [[1, 2], [1, 2, 3]]
One can do
>>> q.sum.each(data)
k('3 6')
or
>>> list(map(sum, [[1, 2], [1, 2, 3]]))
[3, 6]
and get similar results.
The over
adverb is similar to the functools.reduce()
function. Compare
>>> q(',').over(data)
k('1 2 1 2 3')
and
>>> functools.reduce(operator.concat, data)
[1, 2, 1, 2, 3]
Finally, the scan
adverb is similar to the itertools.accumulate()
function.
>>> q(',').scan(data).show()
1 2
1 2 1 2 3
>>> for x in itertools.accumulate(data, operator.concat):
... print(x)
...
[1, 2] [1, 2, 1, 2, 3]
Each¶
The each
adverb serves double duty in q. When it is applied to a function, it returns a new derivative function that expects lists as arguments and maps the original function over those lists. For example, we can write a ‘daily return’ function in q that takes yesterday’s price as the first argument x
, today’s price as the second y
, and dividend as the third z
as follows:
>>> r = q('{(y+zx)%x}') # Recall that % is the division operator in q.
and use it to compute returns from a series of prices and dividends using r.each
:
>>> p = [50.5, 50.75, 49.8, 49.25]
>>> d = [.0, .0, 1.0, .0]
>>> r.each(q.prev(p), p, d)
k('0n 0.004950495 0.0009852217 0.01104418')
When the each
adverb is applied to an integer vector, it returns a nary derivative function that for each i
^{th} argument selects its v[i]
^{th} element. For example,
>>> v = q.til(3)
>>> v.each([1, 2, 3], 100, [10, 20, 30])
k('1 100 30')
case adverb
Note that scalars passed to v.each
are treated as infinitely repeated values. Vector arguments must all be of the same length.
Over and scan¶
Given a function f
, the derivatives f.over
and f.scan
are similar as both apply f
repeatedly, but f.over
only returns the final result, while f.scan
returns all intermediate values as well.
For example, recall that the Golden Ratio can be written as a continued fraction as follows:
or equivalently as the limit of the sequence that can be obtained by starting with 1 and repeatedly applying the function
The numerical value of the Golden Ratio can be found as
>>> phi = (1+math.sqrt(5)) / 2
>>> phi
1.618033988749895
Function f can be written in q as follows:
>>> f = q('{1+reciprocal x}')
and
>>> f.over(1.)
k('1.618034')
indeed yields a number recognizable as the Golden Ratio. If instead of f.over
, we compute f.scan
, we will get the list of all convergents.
>>> x = f.scan(1.)
>>> len(x)
32
Note that f.scan
(and f.over
) stop calculations when the next iteration yields the same value and indeed f
applied to the last value returns the same value:
>>> f(x.last) == x.last
True
which is close to the value computed using the exact formula
>>> math.isclose(x.last, phi)
True
The number of iterations can be given explicitly by passing two arguments to f.scan
or f.over
:
>>> f.scan(10, 1.)
k('1 2 1.5 1.666667 1.6 1.625 1.615385 1.619048 1.617647 1.618182 1.617978')
>>> f.over(10, 1.)
k('1.617978')
This is useful when you need to iterate a function that does not converge.
Continuing with the Golden Ratio theme, define a function
>>> f = q('{(last x;sum x)}')
that, given a pair of numbers, returns another pair made out of the last and the sum of the numbers in the original pair. Iterating this function yields the Fibonacci sequence
>>> x = f.scan(10,[0, 1])
>>> q.first.each(x)
k('0 1 1 2 3 5 8 13 21 34 55')
and the ratios of consecutive Fibonacci numbers form the sequence of Golden Ratio convergents that we have seen before:
>>> q.ratios(_)
k('0 0w 1 2 1.5 1.666667 1.6 1.625 1.615385 1.619048 1.617647')
Eachprior¶
In the previous section we saw a function ratios()
that takes a vector and returns the ratios between adjacent items. A similar function deltas()
returns the differences between adjacent items.
>>> q.deltas([1, 3, 2, 5])
k('1 2 1 3')
These functions are in fact implemented in q by applying the prior
adverb to the division (%
) and subtraction functions respectively.
>>> q.ratios == q('%').prior and q.deltas == q('').prior
True
In general, for any binary function f and a vector v
Adverbs vs
and sv
¶
vs
and sv
K.vs
and K.sv
correspond to q’s vs
and sv
and also behave as the adverbs eachleft and eachright.
Of all adverbs, these two have the most cryptic names and offer some nonobvious features.
To illustrate how vs
and sv
modify binary functions, let’s give a Python name to the q ,
operator:
>>> join = q(',')
Suppose you have a list of file names
>>> name = K.string(['one', 'two', 'three'])
and an extension
>>> ext = K.string(".py")
You want to append the extension to each name on your list. If you naively call join
on name
and ext
, the result will not be what you might expect:
>>> join(name, ext)
k('("one";"two";"three";".";"p";"y")')
This happened because join
treated ext
as a list of characters rather than an atomic string and created a mixed list of three strings followed by three characters. What we need is to tell join
to treat its first argument as a vector and the second as a scalar and this is exactly what the vs
adverb will achieve:
>>> join.vs(name, ext)
k('("one.py";"two.py";"three.py")')
The mnemonic rule is "vs" = "vector, scalar". (Scalar is a synonym for atom.) Now, if you want to prepend a directory name to each resulting file, you can use the sv
attribute:
>>> d = K.string("/tmp/")
>>> join.sv(d, _)
k('("/tmp/one.py";"/tmp/two.py";"/tmp/three.py")')
Input/output¶
>>> import os
>>> r, w = os.pipe()
>>> h = K(w)(kp("xyz"))
>>> os.read(r, 100)
b'xyz'
>>> os.close(r); os.close(w)
Q variables can be accessed as attributes of the q
object:
>>> q.t = q('([]a:1 2i;b:xy)')
>>> sum(q.t.a)
3
>>> del q.t
Numeric computing¶
NumPy is the fundamental package for scientific computing in Python. NumPy shares APL ancestry with q and can often operate directly on K
objects.
Primitive data types¶
There are eighteen primitive data types in kdb+. Eight closely match their NumPy analogues and will be called simple types in this section. Simple types consist of booleans, bytes, characters, integers of three different sizes, and floating point numbers of two sizes. Seven kdb+ types represent dates, times and durations. Similar data types are available in recent versions of NumPy, but they differ from kdb+ types in many details. Finally, kdb+ symbol, enum and guid types have no direct analogue in NumPy.
No  kdb+ type  array type  raw  description 

1  boolean  bool_  bool_  Boolean (True or False) stored as a byte 
2  guid  uint8 (x16)  uint8 (x16)  Globally unique 16byte identifier 
4  byte  uint8  uint8  Byte (0 to 255) 
5  short  int16  int16  Signed 16bit integer 
6  int  int32  int32  Signed 32bit integer 
7  long  int64  int64  Signed 64bit integer 
8  real  float32  float32  Singleprecision 32bit float 
9  float  float64  float64  Doubleprecision 64bit float 
10  char  S1  S1  (byte)string 
11  symbol  str  P  Strings from a pool 
12  timestamp  datetime64[ns]  int64  Date and time with nanosecond resolution 
13  month  datetime64[M]  int32  Year and month 
14  date  datetime64[D]  int32  Date (year, month, day) 
16  timespan  timedelta64[ns]  int64  Time duration in nanoseconds 
17  minute  datetime64[m]  int32  Time duration (or time of day) in minutes 
18  second  datetime64[s]  int32  Time duration (or time of day) in seconds 
19  time  datetime64[ms]  int32  Time duration (or time of day) in milliseconds 
20+  enum  str  int32  Enumerated strings 
Simple types¶
Kdb+ atoms and vectors of the simple types (booleans, characters, integers and floats) can be viewed as 0 or 1dimensional NumPy arrays. For example,
>>> x = K.real([10, 20, 30])
>>> a = numpy.asarray(x)
>>> a.dtype
dtype('float32')
Note that a
in the example above is not a copy of x
. It is an array view into the same data:
>>> a.base.obj
k('10 20 30e')
If you modify a
, you modify x
as well:
>>> a[:] = 88
>>> x
k('88 88 88e')
Dates, times and durations¶
The ageold question of when to start counting calendar years did not get any easier in the computer age. Python standard date
starts at
>>> date.min
datetime.date(1, 1, 1)
more commonly known as
>>> date.min.strftime('%B %d, %Y')
'January 01, 0001'
and this date is considered to be day 1
>>> date.min.toordinal()
1
Note that, according to the Python calendar, the world did not exist before that date:
>>> date.fromordinal(0)
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
ValueError: ordinal must be >= 1
At the time of this writing,
>>> date.today().toordinal()
736335
The designer of kdb+ made the more practical choice: date 0 is January 1, 2000. As a result, in PyQ we have
>>> K.date(0)
k('2000.01.01')
and
>>> (2 + q.til(5)).date
k('1999.12.30 1999.12.31 2000.01.01 2000.01.02 2000.01.03')
Similarly, the 0 timestamp was chosen to be midnight of the day 0
>>> K.timestamp(0)
k('2000.01.01D00:00:00.000000000')
With NumPy, however the third choice was made. Bowing to the UNIX tradition, NumPy took midnight of January 1, 1970 as the zero mark on its timescales.
>>> numpy.array([0], 'datetime64[D]')
array(['19700101'], dtype='datetime64[D]')
>>> numpy.array([0], 'datetime64[ns]')
array(['19700101T00:00:00.000000000'], dtype='datetime64[ns]')
PyQ automatically adjusts the epoch when converting between NumPy arrays and K
objects.
>>> d = q.til(2).date
>>> a = numpy.array(d)
>>> d
k('2000.01.01 2000.01.02')
>>> a
array(['20000101', '20000102'], dtype='datetime64[D]')
>>> K(a)
k('2000.01.01 2000.01.02')
This convenience comes at the cost of copying the data.
>>> a[0] = 0
>>> a array(['19700101', '20000102'], dtype='datetime64[D]')
>>> d
k('2000.01.01 2000.01.02')
To avoid such copying, K
objects can expose their raw data to numpy
.
>>> b = numpy.asarray(d.data)
>>> b.tolist()
[0, 1]
Arrays created this way share their data with the underlying K
objects. Any change to the array is reflected in kdb+.
>>> b[:] += 42
>>> d
k('2000.02.12 2000.02.13')
Characters, strings and symbols¶
Text data appears in kdb+ as character atoms and strings or as symbols and enumerations. Character strings are compatible with the NumPy "bytes" type:
>>> x = K.string("abc")
>>> a = numpy.asarray(x)
>>> a.dtype.type
<class 'numpy.bytes_'>
In the example above, data is shared between the kdb+ string x
and the NumPy array a
:
>>> a[:] = 'x'
>>> x
k('"xxx"')
Nested lists¶
Kdb+ does not have a datatype representing multidimensional contiguous arrays. In PyQ, a multidimensional NumPy array becomes a nested list when passed to q
functions or converted to K
objects. For example,
>>> a = numpy.arange(12, dtype=float).reshape((2,2,3))
>>> x = K(a)
>>> x
k('((0 1 2f;3 4 5f);(6 7 8f;9 10 11f))')
Similarly, kdb+ nested lists of regular shape, become multidimensional NumPy arrays when passed to numpy.array()
:
>>> numpy.array(x)
array([[[ 0., 1., 2.],
[ 3., 4., 5.]],
[[ 6., 7., 8.],
[ 9., 10., 11.]]])
Moreover, many NumPy functions can operate directly on kdb+ nested lists, but they internally create a contiguous copy of the data
>>> numpy.mean(x, axis=2)
array([[ 1., 4.],
[ 7., 10.]])
Tables and dictionaries¶
Unlike kdb+, NumPy does not implement columnwise tables. Instead it has record arrays that can store tablelike data row by row. PyQ supports twoway conversion between kdb+ tables and NumPy record arrays:
>>> trades.show()
sym time size

a 09:31 100
a 09:33 300
b 09:32 200
b 09:35 100
>>> numpy.array(trades)
array([('a', datetime.timedelta(0, 34260), 100),
('a', datetime.timedelta(0, 34380), 300),
('b', datetime.timedelta(0, 34320), 200),
('b', datetime.timedelta(0, 34500), 100)],
dtype=[('sym', 'O'), ('time', '<m8[m]'), ('size', '<i8')])
Enhanced shell¶
If you have IPython installed in your environment, you can run an interactive IPython shell as follows:
$ pyq m IPython
or use the ipyq
script.
For a better experience, load the pyq.magic
extension:
In [1]: %load_ext pyq.magic
This makes K objects display nicely in the output and gives you access to the PyQspecific IPython magic commands:
Line magic %q
:
In [2]: %q ([]a:til 3;b:10*til 3)
Out[2]:
a b

0 0
1 10
2 20
Cell magic %%q
:
In [4]: %%q
....: a: exec a from t where b=20
....: b: exec b from t where a=2
....: a+b
....:
Out[4]: ,22
You can pass following options to the %%q
cell magic:
option  effect 

l (dirscript) 
preload database or script 
h host:port 
execute on the given host 
o var 
send output to a variable named var 
i var1, .., varN 
input variables 
1 
redirect stdout 
2 
redirect stderr 
q) prompt¶
While in PyQ, you can drop in to an emulated kdb+ CommandLine Interface (CLI). Here is how:
Start PyQ:
$ pyq
>>> from pyq import q
Enter kdb+ CLI:
>>> q()
q)t:([]a:til 5; b:10*til 5)
q)t
a b

0 0
1 10
2 20
3 30
4 40
Exit back to Python:
q)\
>>> print("Back to Python")
Back to Python
Or you can exit back to the shell:
q)\\
$
Calling Python from kdb+¶
Kdb+ is designed as a platform for multiple programming languages. Out of the box, it comes with q, k, and a variant of ANSI SQL: the s language. Installing PyQ gives access to the p language, where "p" stands for "Python". In addition, PyQ provides a mechanism for exporting Python functions to q where they can be called as native q functions.
The p language¶
To access Python from the q)
prompt, simply start the line with the p)
prefix and continue with the Python statement/s. Since the standard q)
prompt does not allow multiline entries, you are limited to what can be written in one line and need to separate Python statements with semicolons.
q)p)x = 42; print(x)
42
The p)
prefix can also be used in q scripts. In this case, multiline Python statements can be used provided additional lines start with one or more spaces. For example, with the following code in hello.q
p)def f():
print('Hello')
p)f()
we get
$ q hello.q q
Hello
If your script contains more Python code than q, you can avoid sprinkling it with p)
s by placing the code in a file with .p
extension. Thus instead of hello.q
described above, we can write the following code in hello.p
def f():
print('Hello')
f()
q.exit(0)
and run it the same way:
$ q hello.p q
Hello
It is recommended that any substantial amount of Python code be placed in regular Python modules or packages, with only toplevel entry points imported and called in q scripts.
Exporting Python functions to q¶
As we have seen in the previous section, calling Python by evaluating p)
expressions has several limitations. For tighter integration between q and Python, PyQ supports exporting Python functions to q. Once exported, Python functions appear in q as unary functions that take a single argument that should be a list. For example, we can make Python’s %
formatting available in q as follows:
>>> def fmt(f, x):
... return K.string(str(f) % x)
>>> q.fmt = fmt
Now, calling the fmt
function from q will pass the argument list to Python and return the result back to q:
q)fmt("%10.6f";acos 1)
" 3.141593"
When a Python function is called from q, the returned Python objects are automatically converted to q. Any type accepted by the K()
constructor can be successfully converted. For example, the numpy.eye
function returns a 2D array with 1s on the diagonal and 0s elsewhere. It can be called from q as follows:
q)p)import numpy
q)p)q.eye = numpy.eye
q)eye 3 4 1
0 1 0 0
0 0 1 0
0 0 0 1
Exported functions are called from q by supplying a single argument that contains a list of objects to be passed to the Python functions as K
valued arguments.
To pass a single argument to an exported function, it has to be enlisted. For example,
q)p)q.erf = math.erf
q)erf enlist 1
0.8427008