Basic functions
There is a large number of functions stored in SA Engine's in-memory object-oriented database. For example, the following function call returns the version of SA Engine you are running.
system_version()
Run the function by clicking the play button play_circle
Documentation of functions and other SA Engine artifacts are stored in
the database as well. You can query the database about the
documentation of a function named myfunction
by evaluating
doc("myfunction")
. The doc()
function returns the documentation of
the function as a string.
Example:
doc("sin")
You can edit the examples in the tutorial. Try changing sqrt
to sin
!
You can enter several OSQL statements by separating
them with a ;
.
Examples:
doc("heartbeat");
doc("euclid")
If you don't know exactly the name of a function you can also pass a
string pattern to doc()
to return all functions matching the
string pattern in their names. In a string pattern a *
matches any
sequence of characters while a ?
matches a single character.
Example:
doc("atan*");
The function sourcecode("fn")
where fn
can be a function name or
a string pattern returns the definitions of the matching functions.
Example:
sourcecode("tan");
sourcecode("atan*")
The signature of a function is a string denoting its arguments and
results.
You can get the signature of function or string pattern fn
by calling
the system function signature(fn)
, for example:
signature('tan')
Functions may have different definitions depending on the types of their arguments. Such functions are said to be overloaded on their types. Overloaded function have several signatures, for example:
signature('range')
Some functions have corresponding infix operators. For example, the
function plus
has the infix operator +
, so both these calls return
the same result:
1+2;
plus(1,2)
You can call signature(op)
to get the functions corresponding to
the infix operator op
, for example:
signature('/');
signature('.*')
Visit Documentation functions for a list of functions used for documenting the system.
Math functions​
There is a large library of basic mathematical functions built into the system and the usual arithmetic operators are available.
Example:
sin(3.14/2)*cos(3.14)
To learn more about basic math functions go to Math in the OSQL reference documentation.
Session variables​
During sessions with SA Engine it is often practical to temporarily
save values of expressions in session variables prefixed with :
by using the set
statement, e.g.:
set :pi = asin(1)*2;
sin(:pi/2)*cos(:pi)
The session variable :pi
is first assigned the value of asin(1)*2
.
Session variables disappear when you exit SA Engine. To permanently save values in the built-in database you must use stored functions, as explained next.
Stored functions​
Analysis models are defined in terms of a number of OSQL
functions. OSQL functions are created and stored in the database by
evaluating a create function
statement. There are functions of
different kinds, depending on how they are used.
Stored functions are functions that hold tabulated
function values permanently in the built-in database. They are created
by a create function ... as stored
statement.
Example:
create function const(Charstring c) -> Real
as stored
The above statement creates a tabulated function called const
taking
a string c
as argument and returning a real number as
result.
You are recommended to document your functions by a master comment
preceding the as
.
Example:
create function const(Charstring c) -> Real
/* The value of the math constant named `c` */
as stored;
doc("const")
Stored functions can be populated using the set
statement.
Example:
set const("pi") = 3.14;
set const("e") = 2.71;
const("pi");
ln(const("e"));
sin(const("pi")/2)*cos(const("pi"));
You can also update stored functions using set
, for example:
set const("pi") = asin(1)*2;
set const("e") = exp(1);
ln(const("e"));
sin(const("pi")/2)*cos(const("pi"))
Functions may have no arguments at all.
Example:
create function mypi() -> Real
/* The constant PI */
as stored;
set mypi() = asin(1)*2;
mypi()
Derived functions​
A derived function is a function defined by an OSQL expression.
Example: The following function converts Celsius degrees to Fahrenheit:
create function ctof(Real c) -> Real
/* Convert a Celsius degree `c` to Fahrenheit */
as c * 9 / 5 + 32;
ctof(10)
The head of the function, e.g ctof(Real c) -> Real
, specifies
the function's signature.
Temporal functions​
The function local_time()
returns the current wall time as an ISO
time stamp.
While local_time
returns the current wall time as a string, the
function now()
returns the wall time as an object of type Timeval
,
which is the internal representation of time points.
Examples:
local_time();
now()
The function ts(Object o)->Timeval
returns a time stamped object,
which represents a timestamped value o
.
Examples:
ts(1);
value(ts(1));
local_time(ts(1))
For more about functions over time visit Time in the reference documentation.
Vectors​
So far the function calls were made over single values and sets of
single values. Building mathematical models, e.g. to identify
interesting properties of streams, also require vectors with the
usual [...]
notation.
Example:
[1,4,3,2]+[1,5,6,7]
Change visualization of the vector to Bar plot
by adding //plot: Bar plot
before the query.
The mathematical operators +,-,*,/,^
can be used for whole vectors
or mixes of vectors and scalar values.
Example:
[1,4,3,2]-[0,2,3,4]+1
How would it look as text?
A .
in front of an operator indicates element-wise application of it
on each element of the vectors. For example, for multiplication the
*
operator over vectors returns the scalar product while .*
returns element-wise multiplication.
Examples:
[1, 2, 3, 4] * [5, 6, 7, 8];
[1, 2, 3, 4] .* [5, 6, 7, 8]
More examples:
"Addition";
[1, 2, 3, 4] + [5, 6, 7, 8];
"Scalar times vector";
5 * [1, 2, 3, 4];
"Element-wise power of two";
[1, 2, 3, 4] .^ 2
There are many built-in vector functions, e.g.:
"sum";
sum([1, 2, 3, 4]);
"mean";
mean([1, 2, 3, 4]);
"standard deviation";
stdev([1, 2, 3, 4]);
"median";
median([1, 4, 2, 3]);
"max";
max([1, 4, 2, 3]);
"dimension";
dim([1, 3, 2])
Often vectors are used in derived function definitions. For example,
the following function computes the Euclidean distance between vector
v
and w
:
create function dist(Vector v, Vector w) -> Real
/* Compute the Euclidean distance between `v` and `w` */
as sqrt(sum((v - w) .^ 2));
dist([1,2],[3,4])
The built-in function euclid(v,w)
does the same.
The general Minkowski distance computation function minkowski(v,w,r)
is
also built-in. This example shows Manhattan distance (), Euclidean
() and Chebyshev () distance expressed in terms of
minkowski(v,w,r)
.
Examples:
minkowski([1,2],[3,4], 1);
minkowski([1,2],[3,4], 2);
minkowski([1,2],[3,4], +inf);
Arrays​
An array or a tensor is a multi-dimensional cube of
numbers. It is represented by type Array
. Arrays can be created
with the function array(Vector data)->Array
, where the (nested)
vector data
contains its elements.
For example:
array([1,2,3]);
array([[1,2],[3,4]])
As for vectors, you can apply a number of arithmtic oparators and functions on arrays, for examle:
array([[1,2],[3,4]]) + array([[2,3],[6,7]]);
array([[1,2],[3,4]]) .* array([[2,3],[6,7]])
The elements of an array have a format, which specifies their
binary representations in memory. For example, elements of type
Integer
are represented as 64-bits integers having the format I64
and type Real
has the format F64
. The first argument of the
function array(Charstring fmt,Vector data)->Array
specifies the
elements' format.
For example:
array("f64",[1,2,3,4])
When called with one argument, array(Vector data)->Array
will return
an array having the format of the most general type in data
, where
real numbers are considered more general than integers,
For example:
array([1,2,3,4]);
array([1.0,2,3,4])
An array also has a shape being the number of elements in each of
its dimensions, computed by the function shape(Array a)->Vector of
Integer
.
For example:
shape(array([[1,2,3],[4,5,6]]))
The function dot(Array u, Array v)->Number
computes the scalar
product of the elements in the arrays u
and v
.
For example:
dot(array([1,2,3]),array([4,5,6]));
The function matmul(Array a, Array b)->Array
computes the array
multiplication of a
and b
.
For example:
matmul(array([[1,2,3]]),array([[1,2],[3,4],[5,6]]));
Visit Arrays and tensors for a detailed description of arrays.
The Fast Fourier Transform​
The function rfft(a)
computes the real number Fast Fourier
Transform
(FFT) over a one-dimensional array of real numbers.
Example:
rfft(array([1.0, 2, 3, 4]))
You can also apply rfft()
on vectors of numbers, even though this is
much slower. For example:
rfft([1.0, 2, 3, 4])
The inverse real FFT is computed with irfft(a)
.
Example:
irfft(rfft(array([1.0, 2, 3, 4])));
The later tutorial section Querying the microphone shows how user-defined functions over vectors and FFT can be used for filtering audio streams in real-time.
Vectors of objects​
So far the vectors contained only numbers, as required by math functions and operators. Unlike arrays, vectors can contain any kind of objects including strings and numbers. For example, the following vector contains both a number and a string:
Example:
["Tore", 1234]
In general vectors of objects are used for representing ordered finite sequences of objects. By contrast, a stream can be seen as a possibly infinite growing sequence of objects. Vectors can be used to group elements in streams, as will be explained later.
Go to Vectors in the reference documentation for documentation of vectors.
Sets and bags​
Functions can also produce sets of objects where the order is not
guaranteed as with vectors. For example, the function range(n)
returns the set of numbers from 1 up to n
.
Example:
range(10)
Here range(10)
produces the set of all integers from 1 to 10.
Example:
sin(range(200)*0.2)
The function call range(200)
returns a bag of numbers. Here the sine
function is applied one each element in the set of all integers from 1
to 200.
Applying other functions, such as sin(x)
on a set means that the
function is applied on each element of the set.
Try visualizing the result as a line plot by inserting the row //plot: Line plot
before the query!
In general sets in OSQL may contain duplicates.
Example:
floor(range(200)/2)
The term bag is used rather than set to indicate sets with possible duplicates.
Apply sin(x)
on the result of floor
!
Explicit bags can be create as using the notation, for example:
set :mybag = bag(1,2,2,3);
select i from Integer i where i in :mybag
As for vectors, aggregate functions over bags are applied on
entire bags, rather than on each element of the bag as, for example
range(n)
returns a bag of number and sum(Bag of Number)->Number
sums the elements of a bag of number.
Example:
sum(range(200)/2)
See Aggregate functions in the reference documentation for more on aggregate functions.
Boolean and null values​
The constant null
is used to represent unknown or missing
values. For example, the last element of the vector [1,2,null]
is
unknown.
A Boolean value null
value is regarded as false. Thus, the query
2<1
returns null
, while 2>1
return true
. The only object of
type Boolean is true
. The constant false
is null
casted as a
Boolean.
null
values in bags are regarded as missing values that are ignored
by aggregate functions.
Passing null
as argument in a function call will return null
without calling the function. For example:
sin(sqrt(-1));
An OSQL query variable bound to the value null
is regarded as
unbound and therefore null
cannot be regraded as a regular
value. Instead, to test that an expression x
is null
, use the
notany(x)
function that returns true
if x
is null
.
Often it is practical to use a default value instead of null. For this
the expression can be used that returns
the first not being null
and dlft
if all
For example:
coalesce(sqrt(-1),ln(-1),1)+1
Tests in case
statements succeed unless they return null
. For
example, the following query returns one:
case when sqrt(-1) then 1 else 0 end
To replace all null
s in a vector use
whennull(Vector v, Object dflt)->Vector
.
For example:
whennull([1,2,null,3],0)+2
The next part of the tutorial will show how to make general queries that selects collections of objects from the database.