Python for kdb+¶
Introduction¶
Kdb+, a high-performance database system comes with a programming language (q) that may be unfamiliar to many programmers. 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
general purpose 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 a 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 ‘til 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 Python list. In fact, you can get
the Python list by simply 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(5)).show()
`long$()
,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 multi-line display of a list of vectors. This method is
available for all K objects. Second, the first line in the display shows
and 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 size
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')
and
>>> math.exp(1)
2.718281828459045
Note
Want to see more digits? Set q 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 of numbers, q functions differ from Python functions in a way they treat out of domain 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 that 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, wen 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
total sum, 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 |
|---|---|
pyq.q.sums() |
the cumulative sums of the elements |
pyq.q.prds() |
the cumulative products of the elements |
pyq.q.maxs() |
the maximums of the prefixes of the argument |
pyq.q.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 pyq.q.prds(), pyq.q.maxs() and pyq.q.mins().
Uniform functions¶
Uniform functions are functions that take a list and return another list of the same size.
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')
Note
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 the asc() 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 elements of the incoming list should be taken to make them
sorted:
>>> q.iasc(a)
k('4 3 1 2 0')
Sorted lists can be efficiently searched using bin() and
binr() functions. As the names suggest, both use binary search to
locate the position the element that is equal to the search key, but in the
case when 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 matching element can be found, 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 in 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 home-brew index function is similar to the list.index() method, but
it returns the one after last index when the key is not found while 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 only want to know 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')
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 ?
function (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 0's or 1's (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 was 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 invoke q functions on kdb+ objects directly from Python using 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, by in PyQ left to right.
Finally, if q does not provide the function that 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 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+ by simply 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 is 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')
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(':0-9', range(10))
k('`:0-9')
and read it back using the pyq.q.set function
>>> q.get(_)
k('0 1 2 3 4 5 6 7 8 9')
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 human readable 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 in order to create a K character scalar,
one will need to use a typed constructor:
>>> K.char(b'x')
k('"x"')
Typed constructors are discussed in the next section.
Constructors and casts¶
As we’ve seen in the previous chapter, it is often not necessary to construct K
objects explicitly because they are automatically created 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 type 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 empty list does not know the element 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 |
8-bit bytes |
short() |
int |
16-bit integers |
int() |
int |
32-bit integers |
long() |
int |
64-bit integers |
real() |
int, float |
32-bit floating point numbers |
float() |
int, float |
32-bit floating point numbers |
char() |
str, bytes |
8-bit 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 an 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 boolean expressions depends
on how the objects are tested in Python if statements.
All K objects can be tested for “truth”. Similarly to
the Python numeric types and sequences, K atoms of numeric types are true
is they are not zero and vectors are true if they are non-empty.
Atoms of non-numeric 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 pass-through function:
>>> q('::') or q('+') or 1
k('+')
Dictionaries and tables are treated as sequences: they are true if non-empty.
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]
Arithmetic operations¶
Python has the four familiar arithmetic operators +, -, * and / as well as
less common ** (exponentiation), % (modulo) and // (floor division). PyQ
maps those operators to q “verbs” 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 similar to atoms: arithmetic
operations act element-wise 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 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 | Notes |
|---|---|---|
x | y |
element-wise maximum of x and y | |
x ^ y |
y with null elements filled with x | |
x & y |
element-wise minimum of x and y | |
x << n |
x shifted left by n elements | |
x >> n |
x shifted right by n elements | |
~x |
a boolean vector with 1’s for zero elements of x |
Notes:
- For boolean vectors,
|and&are also element-wise or and and operations. - For Python integers, the result of
x ^ yis 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 >> -nis the same asx << n.
Minimum and maximum¶
Minimum and maximum operators are & and | in q. PyQ maps similar
looking 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¶
Python 3.5 introduced the @ operator that can be used by user types. Unlike
numpy that defines @ as the matrix multiplication 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() |
': |
each-prior |
K.sv() |
/: |
each-right or scalar from vector |
K.vs() |
\: |
each-left 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 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 follow:
>>> r = q('{(y+z-x)%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 turns the vector v into an
n-ary 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')
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, f.over and f.scan adverbs 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, let’s 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’ve seen before:
>>> q.ratios(_)
k('0 0w 1 2 1.5 1.666667 1.6 1.625 1.615385 1.619048 1.617647')
Each previous¶
In the previous section we’ve seen a function ratios() that takes
a vector and produces the ratios of the adjacent elements. A similar function
called deltas() produces the differences between the adjacent
elements:
>>> 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¶
Of all adverbs, these two have the most cryptic names and offer some non-obvious features.
To illustrate how vs and sv modify binary functions, lets 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”. 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:`x`y)')
>>> sum(q.t.a)
3
>>> del q.t
Numeric Computing¶
NumPy is the fundamental package for scientific computing in Python. NumPy shares
common APL ancestry with q and can often operate directly on K objects.
Primitive data types¶
There are eighteen primitive data types in kdb+, eight of those 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 are dealing with 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 16-byte identifier |
| 4 | byte | uint8 | uint8 | Byte (0 to 255) |
| 5 | short | int16 | int16 | Signed 16-bit integer |
| 6 | int | int32 | int32 | Signed 32-bit integer |
| 7 | long | int64 | int64 | Signed 64-bit integer |
| 8 | real | float32 | float32 | Single precision 32-bit float |
| 9 | float | float64 | float64 | Double precision 64-bit 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 1-dimensional 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¶
An age old 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 a more practical choice for date 0 to be 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 at midnight of the day 0
>>> K.timestamp(0)
k('2000.01.01D00:00:00.000000000')
NumPy, however the third choice was made. Kowtowing to the UNIX tradition, NumPy took midnight of January 1, 1970 as the zero mark on its timescales.
>>> numpy.array([0], 'datetime64[D]')
array(['1970-01-01'], dtype='datetime64[D]')
>>> numpy.array([0], 'datetime64[ns]')
array(['1970-01-01T00:00:00.000000000'], dtype='datetime64[ns]')
PyQ will automatically adjust 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(['2000-01-01', '2000-01-02'], dtype='datetime64[D]')
>>> K(a)
k('2000.01.01 2000.01.02')
This convenience comes at a cost of copying the data
>>> a[0] = 0
>>> a
array(['1970-01-01', '2000-01-02'], 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 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 NumPy array a:
>>> a[:] = 'x'
>>> x
k('"xxx"')
Nested lists¶
Kdb+ does not have a data type representing multi-dimensional contiguous arrays.
In PyQ, a multi-dimensional 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 multi-dimensional 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 column-wise tables. Instead it has record arrays that can store table-like data row by row. PyQ supports two-way 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
For a better experience, load pyq.magic extension:
In [1]: %load_ext pyq.magic
This makes K objects display nicely in the output and gives you access to the PyQ-specific 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:
q) prompt¶
While in PyQ, you can drop to emulated kdb+ Command Line 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 shell:
q)\\
$
Calling Python from KDB+¶
KDB+ is designed as a platform for multiple programming languages. Out of the box, it comes with q and K distributes variant of ANSI SQL as the “s)” language. Installing pyq gives access to the “p)” language, where “p” obviously 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 follow with the Python statement(s). Since the standard q)
prompt does not allow multi-line 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, multi-line
python statements can be used as long as 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 top level entry points imported and called in q scripts.
Exporting Python functions to q¶
As we’ve 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 monadic 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"
Python functions exported to q should return a K object or an instance
of one of the simple scalar types: None, bool, int,
float or str which are automatically converted to q ::, boolean,
long, float or symbol respectively.
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.
Note
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