Base module

k1lib.settings

This is actually an object of type Settings:

Settings:
- displayCutoff = 50                                                          ​cutoff length when displaying a Settings object
- svgScale      = 0.7                                                         ​default svg scales for clis that displays graphviz graphs
- wd            = /home/kelvin/repos/labs/k1lib/docs                          ​default working directory, will get from `os.getcwd()`. Will update using `os.chdir()` automatically when changed
- cli           = <Settings>                                                  ​from k1lib.cli module
  - jit           = True                                                      ​whether to enable automatic JIT compilation of cli tools. See `fastF` for more details
  - defaultDelim  =                                                           ​default delimiter used in-between columns when creating tables. Defaulted to tab character.
  - defaultIndent =                                                           ​default indent used for displaying nested structures
  - strict        = False                                                     ​turning it on can help you debug stuff, but could also be a pain to work with
  - inf           = inf                                                       ​infinity definition for many clis. Here because you might want to temporarily not loop things infinitely
  - quiet         = False                                                     ​whether to mute extra outputs from clis or not
  - smooth        = 10                                                        ​default smooth amount, used in utils.smooth
  - atomic        = <Settings>                                                ​classes/types that are considered atomic and specified cli tools should never try to iterate over them
    - baseAnd = (<class 'numbers.Number'>, <class 'numpy.number...            ​used by BaseCli.__and__
    - deref   = (<class 'numbers.Number'>, <class 'numpy.number...            ​used by deref
  - bio           = <Settings>                                                ​from k1lib.cli.bio module
    - blast      = None                                                       ​location of BLAST database
    - go         = None                                                       ​location of gene ontology file (.obo)
    - so         = None                                                       ​location of sequence ontology file
    - lookupImgs = True                                                       ​sort of niche. Whether to auto looks up extra gene ontology relationship images
    - phred      = !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJ                 ​Phred quality score
  - sam           = <Settings>                                                ​from k1lib.cli.sam module
    - flags  = ['PAIRED', 'PROPER_PAIR', 'UNMAP', 'MUNMAP', 'R...             ​list of flags
    - header = <Settings>                                                     ​sam headers
      - short = ['qname', 'flag', 'rname', 'pos', 'mapq', 'ciga...            ​
      - long  = ['Query template name', 'Flags', 'Reference seq...            ​
- eqn           = <Settings>                                                  ​from k1lib.eqn module
  - spaceBetweenValueSymbol = True                                            ​
  - eqnPrintExtras          = True                                            ​
- mo            = <Settings>                                                  ​from k1lib.mo module
  - overOctet = False                                                         ​whether to allow making bonds that exceeds the octet rule

Also, this is exposed automatically, so something like this works:

settings.svgScale = 0.6

Classes

• k1lib.Learner

• k1lib.Object

• k1lib.Range

• k1lib.Domain

• k1lib.AutoIncrement

• k1lib.Wrapper

• k1lib.Every

• k1lib.RunOnce

• k1lib.MaxDepth

• k1lib.MovingAvg

• k1lib.Absorber

• k1lib.Settings

class k1lib.Learner

Bases: object

property model

Set this to change the model to run

property data

Set this to change the data (list of 2 dataloader) to run against.

property opt

Set this to change the optimizer. If you’re making your own optimizers, beware to follow the PyTorch’s style guide as there are callbacks that modifies optimizer internals while training like k1lib.schedule.ParamScheduler.

property cbs

The Callbacks object. Initialized to include all the common callbacks. You can set a new one if you want to.

property css

The css selector string. Set this to select other parts of the network. After setting, you can access the selector like this: l.selector

See also: ModuleSelector

property lossF

Set this to specify a loss function.

evaluate()

Function to visualize quickly how the network is doing. Undefined by default, just placed here as a convention, so you have to do something like this:

l = k1lib.Learner()
def evaluate(self):
    xbs, ybs, ys = self.Recorder.record(1, 3)
    plt.plot(torch.vstack(xbs), torch.vstack(ys))
l.evaluate = partial(evaluate(l))

__call__(xb, yb=None)

Executes just a small batch. Convenience method to query how the network is doing.

Parameters

• xb – x batch

• yb – y batch. If specified, return (y, loss), else return y alone

static load(fileName: Optional[str] = None)

Loads a Learner from a file. See also: save()

Parameters

fileName – if empty, then will prompt for file name

run(epochs: int, batches: Optional[int] = None)

Main run function.

Parameters

• epochs – number of epochs to run. 1 epoch is the length of the dataset

• batches – if set, then cancels the epoch after reaching the specified batch

static sample() → k1lib._learner.Learner

Creates an example learner, just for simple testing stuff anywhere. The network tries to learn the function y=x. Only bare minimum callbacks are included.

save(fileName: Optional[str] = None)

Saves this Learner to file. See also: load(). Does not save the data object, because that’s potentially very big.

Parameters

fileName – if empty, then will save as “learner-0.pth”, with 0 changeable to avoid conflicts. If resave this exact Learner, then use the old name generated before

class k1lib.Object

Bases: object

Convenience class that acts like defaultdict. You can use it like a normal object:

a = k1lib.Object()
a.b = 3
print(a.b) # outputs "3"

__repr__() output is pretty nice too:

<class '__main__.Object'>, with attrs:
- b

You can instantiate it from a dict:

a = k1lib.Object.fromDict({"b": 3, "c": 4})
print(a.c) # outputs "4"

And you can specify a default value, just like defaultdict:

a = k1lib.Object().withAutoDeclare(lambda: [])
a.texts.extend(["factorio", "world of warcraft"])
print(a.texts[0]) # outputs "factorio"

Warning

Default values only work with variables that don’t start with an underscore “_”.

Treating it like defaultdict is okay too:

a = k1lib.Object().withAutoDeclare(lambda: [])
a["movies"].append("dune")
print(a.movies[0]) # outputs "dune" 

static fromDict(_dict: Dict[str, Any])

Creates an object with attributes from a dictionary

property state

Essentially __dict__, but only outputs the fields you defined. If your framework intentionally set some attributes, those will be reported too, so beware

withAutoDeclare(defaultValueGenerator)

Sets this Object up so that if a field doesn’t exist, it will automatically create it with a default value.

withRepr(_repr: str)

Specify output of __repr__(). Legacy code. You can just monkey patch it instead.

class k1lib.Range(start=0, stop=None)

Bases: object

A range of numbers. It’s just 2 numbers really: start and stop

This is essentially a convenience class to provide a nice, clean abstraction and to eliminate errors. You can transform values:

Range(10, 20).toUnit(13) # returns 0.3
Range(10, 20).fromUnit(0.3) # returns 13
Range(10, 20).toRange(Range(20, 10), 13) # returns 17

You can also do random math operations on it:

(Range(10, 20) * 2 + 3) == Range(23, 43) # returns True
Range(10, 20) == ~Range(20, 10) # returns True

__getitem__(index)

0 for start, 1 for stop

You can also pass in a slice object, in which case, a range subset will be returned. Code kinda looks like this:

range(start, stop)[index]

__init__(start=0, stop=None)

Creates a new Range.

There are different __init__ functions for many situations:

• Range(2, 11.1): create range [2, 11.1]

• Range(15.2): creates range [0, 15.2]

• Range(Range(2, 3)): create range [2, 3]. This serves as sort of a catch-all

• Range(slice(2, 5, 2)): creates range [2, 5]. Can also be a range

• Range(slice(2, -1), 10): creates range [2, 9]

• Range([1, 2, 7, 5]): creates range [1, 5]. Can also be a tuple

fixOrder() → k1lib._baseClasses.Range

If start greater than stop, switch the 2, else do nothing

intIter(step: int = 1) → Iterator[int]

Returns integers within this Range

toUnit(x)

Converts x from current range to [0, 1] range. Example:

r = Range(2, 10)
r.toUnit(5) # will return 0.375, as that is (5-2)/(10-2)

You can actually pass in a lot in place of x:

r = Range(0, 10)
r.toUnit([5, 3, 6]) # will be [0.5, 0.3, 0.6]. Can also be a tuple
r.toUnit(slice(5, 6)) # will be slice(0.5, 0.6). Can also be a range, or Range

Note

In the last case, if start is None, it gets defaulted to 0, and if end is None, it gets defaulted to 1

fromUnit(x)

Converts x from [0, 1] range to this range. Example:

r = Range(0, 10)
r.fromUnit(0.3) # will return 3

x can be a lot of things, see toUnit() for more

toRange(_range: k1lib._baseClasses.Range, x)

Converts x from current range to another range. Example:

r = Range(0, 10)
r.toRange(Range(0, 100), 6) # will return 60

x can be a lot of things, see toUnit() for more.

fromRange(_range: k1lib._baseClasses.Range, x)

Reverse of toRange(), effectively.

property range_

Returns a range object with start and stop values rounded off

property slice_

Returns a slice object with start and stop values rounded off

static proportionalSlice(r1, r2, r1Slice: slice) → Tuple[k1lib._baseClasses.Range, k1lib._baseClasses.Range]

Slices r1 and r2 proportionally. Best to explain using an example. Let’s say you have 2 arrays created from a time-dependent procedure like this:

a = []; b = []
for t in range(100):
    if t % 3 == 0: a.append(t)
    if t % 5 == 0: b.append(1 - t)
len(a), len(b) # returns (34, 20)

a and b are of different lengths, but you want to plot both from 30% mark to 50% mark (for a, it’s elements 10 -> 17, for b it’s 6 -> 10), as they are time-dependent. As you can probably tell, to get the indicies 10, 17, 6, 10 is messy. So, you can do something like this instead:

r1, r2 = Range.proportionalSlice(Range(len(a)), Range(len(b)), slice(10, 17))

This will return the Ranges [10, 17] and [5.88, 10]

Then, you can plot both of them side by side like this:

fig, axes = plt.subplots(ncols=2)
axes[0].plot(r1.range_, a[r1.slice_])
axes[1].plot(r2.range_, a[r2.slice_])

bound(rs: Union[range, slice]) → Union[range, slice]

If input range|slice’s stop and start is missing, then use this range’s start and stop instead.

copy()

__invert__()

class k1lib.Domain(*ranges, dontCheck: bool = False)

Bases: object

__init__(*ranges, dontCheck: bool = False)

Creates a new domain.

Parameters

• ranges – each element is a Range, although any format will be fine as this selects for that

• dontCheck – don’t sanitize inputs, intended to boost perf internally only

A domain is just an array of Range that represents what intervals on the real number line is chosen. Some examples:

inf = float("inf") # shorthand for infinity
Domain([5, 7.5], [2, 3]) # represents "[2, 3) U [5, 7.5)"
Domain([2, 3.2], [3, 8]) # represents "[2, 8)" as overlaps are merged
-Domain([2, 3]) # represents "(-inf, 2) U [3, inf)", so essentially R - d, with R being the set of real numbers
-Domain([-inf, 3]) # represents "[3, inf)"
Domain.fromInts(2, 3, 6) # represents "[2, 4) U [6, 7)"

You can also do arithmetic on them, and check “in” oeprator:

Domain([2, 3]) + Domain([4, 5]) # represents "[2, 3) U [4, 5)"
Domain([2, 3]) + Domain([2.9, 5]) # represents "[2, 5)", also merges overlaps
3 in Domain([2, 3]) # returns False
2 in Domain([2, 3]) # returns True

static fromInts(*ints: List[int])

Returns a new Domain which has ranges [i, i+1] for each int given.

copy()

intIter(step: int = 1, start: int = 0)

Yields ints in all ranges of this domain. If first range’s domain is \((-\inf, a)\), then starts at the specified integer

class k1lib.AutoIncrement(initialValue: int = - 1, n: int = inf, prefix: Optional[str] = None)

Bases: object

__init__(initialValue: int = - 1, n: int = inf, prefix: Optional[str] = None)

Creates a new AutoIncrement object. Every time the object is called it gets incremented by 1 automatically. Example:

a = k1lib.AutoIncrement()
a() # returns 0
a() # returns 1
a() # returns 2
a.value # returns 2
a.value # returns 2
a() # returns 3

a = AutoIncrement(n=3, prefix="cluster_")
a() # returns "cluster_0"
a() # returns "cluster_1"
a() # returns "cluster_2"
a() # returns "cluster_0"

Parameters

• n – if specified, then will wrap around to 0 when hit this number

• prefix – if specified, will yield strings with specified prefix

static random() → k1lib._baseClasses.AutoIncrement

Creates a new AutoIncrement object that has a random integer initial value

property value

Get the value as-is, without auto incrementing it

__call__()

Increments internal counter, and return it.

class k1lib.Wrapper(value)

Bases: object

__init__(value)

Creates a wrapper for some value and get it by calling it. Example:

a = k1lib.Wrapper(list(range(int(1e7))))
# returns [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
a()[:10]

This exists just so that Jupyter Lab’s contextual help won’t automatically display the (possibly humongous) value. Could be useful if you want to pass a value by reference everywhere like this:

o = k1lib.Wrapper(None)
def f(obj):
    obj.value = 3
f(o)
o() # returns 3

value: Any

Internal value of this Wrapper

class k1lib.Every(n)

Bases: object

__init__(n)

Returns True every interval. Example:

e = k1lib.Every(4)
e() # returns True
e() # returns False
e() # returns False
e() # returns False
e() # returns True

__call__() → bool

Returns True or False based on internal count.

property value

class k1lib.RunOnce

Bases: object

__init__()

Returns False first time only. Example:

r = k1lib.RunOnce()
r.done() # returns False
r.done() # returns True
r.done() # returns True
r.revert()
r.done() # returns False
r.done() # returns True
r.done() # returns True

May be useful in situations like:

class A:
    def __init__(self):
        self.ro = k1lib.RunOnce()
    def f(self, x):
        if self.ro.done(): return 3 + x
        return 5 + x
a = A()
a.f(4) # returns 9
a.f(4) # returns 7

done()

Whether this has been called once before.

revert()

class k1lib.MaxDepth(maxDepth: int, depth: int = 0)

Bases: object

__init__(maxDepth: int, depth: int = 0)

Convenience utility to check for graph max depth. Example:

def f(d):
    print(d.depth)
    if d: f(d.enter())
# prints "0\n1\n2\n3"
f(k1lib.MaxDepth(3))

Of course, this might look unpleasant to the end user, so this is more likely for internal tools.

enter() → k1lib._baseClasses.MaxDepth

class k1lib.MovingAvg(initV: float = 0, alpha=0.9, debias=False)

Bases: object

__init__(initV: float = 0, alpha=0.9, debias=False)

Smoothes out sequential data using momentum. Example:

a = k1lib.MovingAvg(5)
a(3).value # returns 4.8, because 0.9*5 + 0.1*3 = 4.8
a(3).value # returns 4.62

Difference between normal and debias modes:

x = torch.linspace(0, 10, 100); y = torch.cos(x) | op().item().all() | deref()
plt.plot(x, y);
a = k1lib.MovingAvg(debias=False); plt.plot(x, y | apply(lambda y: a(y).value) | deref())
a = k1lib.MovingAvg(debias=True); plt.plot(x, y | apply(lambda y: a(y).value) | deref())
plt.legend(["Signal", "Normal", "Debiased"])

As you can see, normal mode still has the influence of the initial value at 0 and can’t rise up fast, whereas the debias mode will ignore the initial value and immediately snaps to the first saved value.

Parameters

• initV – initial value

• alpha – number in [0, 1]. Basically how much to keep old value?

• debias – whether to debias the initial value

class k1lib.Absorber(initDict: dict = {})

Bases: object

Creates an object that absorbes every operation done on it. Could be useful in some scenarios:

ab = k1lib.Absorber()
# absorbs all operations done on the object
abs(ab[::3].sum(dim=1))

t = torch.randn(5, 3, 3)
# returns transformed tensor of size [2, 3]
ab.ab_operate(t)

Another:

ab = Absorber()
ab[2] = -50
# returns [0, 1, -50, 3, 4]
ab.ab_operate(list(range(5)))

Because this object absorbs every operation done on it, you have to be gentle with it, as any unplanned disturbances might throw your code off. Best to create a new one on the fly, and pass them immediately to functions, because if you’re in a notebook environment like Jupyter, it might poke at variables.

For extended code example that utilizes this, check over k1lib.cli.modifier.op source code.

__init__(initDict: dict = {})

Creates a new Absorber.

Parameters

initDict – initial variables to set, as setattr operation is normally absorbed

ab_operate(x)

Special method to actually operate on an object and get the result. Not absorbed. Example:

# returns 6
(op() * 2).ab_operate(3)

ab_fastF()

Returns a function that operates on the input (just like ab_operate()), but much faster, suitable for high performance tasks. Example:

f = (k1lib.Absorber() * 2).ab_fastF()
# returns 6
f(3)

__ror__(o)

__invert__()

ab_int()

Replacement for int(ab), as that requires returning an actual int.

ab_float()

Replacement for float(ab), as that requires returning an actual float.

ab_str()

Replacement for str(ab), as that requires returning an actual str.

ab_len()

Replacement for len(ab), as that requires returning an actual int.

ab_contains(key)

Replacement for key in ab, as that requires returning an actual int.

class k1lib.Settings(**kwargs)

Bases: object

__init__(**kwargs)

Creates a new settings object. Basically fancy version of dict. Example:

s = k1lib.Settings(a=3, b="42")
s.c = k1lib.Settings(d=8)

s.a # returns 3
s.b # returns "42"
s.c.d # returns 8
print(s) # prints nested settings nicely

context(**kwargs)

Context manager to temporarily modify some settings. Applies to all sub-settings. Example:

s = k1lib.Settings(a=3, b="42", c=k1lib.Settings(d=8))
with s.context(a=4):
    s.c.d = 20
    s.a # returns 4
    s.c.d # returns 20
s.a # returns 3
s.c.d # returns 8

add(k: str, v: Any, docs: str = '', cb: Optional[Callable[[k1lib._baseClasses.Settings, Any], None]] = None) → k1lib._baseClasses.Settings

Long way to add a variable. Advantage of this is that you can slip in extra documentation for the variable. Example:

s = k1lib.Settings()
s.add("a", 3, "some docs")
print(s) # displays the extra docs

Parameters

cb – callback that takes in (settings, new value) if any property changes

class k1lib.wrapMod(m, moduleName=None)

Bases: object

__init__(m, moduleName=None)

Wraps around a module, and only suggest symbols in __all__ list defined inside the module. Example:

from . import randomModule
randomModule = wrapMod(randomModule)

Parameters

• m – the imported module

• moduleName – optional new module name for elements (their __module__ attr)

Context managers

• k1lib.captureStdout

• k1lib.ignoreWarnings

• k1lib.timer

• k1lib.attrContext

class k1lib.captureStdout

Captures every print() statement. Taken from https://stackoverflow.com/questions/16571150/how-to-capture-stdout-output-from-a-python-function-call. Example:

with k1lib.captureStdout() as outer:
    print("something")
    with k1lib.captureStdout() as inner:
        print("inside inner")
    print("else")
# prints "['something', 'else']"
print(outer.value)
# prints "['inside inner']"
print(inner.value)

Note that internally, this replaces sys.stdout as io.StringIO, so might not work property if you have fancy bytes stuff going on. Also, carriage return (\r) will erase the line, so multi-line overlaps might not show up correctly.

class k1lib.ignoreWarnings

Context manager to ignore every warning. Example:

import warnings
with k1lib.ignoreWarnings():
    warnings.warn("some random stuff") # will not show anything

class k1lib.timer

Times generic code. Example:

with k1lib.timer() as t:
    time.sleep(1.1)
# prints out float close to 1.1
print(t())

The with- statement will actually return a Wrapper with value None. The correct time will be deposited into it after the code block ends.

class k1lib.attrContext(var, **kwargs)

Temporarily sets variable’s attribute to something else. Example:

class A: pass
a = A()
a.b = 3
print(a.b) # prints "3"
with k1lib.attrContext(a, b=4, c=5):
    print(a.b, a.c) # prints "4 5"
print(a.b, a.c) # prints "3 None"

Exceptions

These exceptions are used within Learner to cancel things early on. If you raise CancelBatchException while passing through the model, the Learner will catch it, run cleanup code (including checkpoint endBatch ), then proceeds as usual.

If you raise something more major, like CancelRunException, Learner will first catch it at batch level, run clean up code, then rethrow it. Learner will then recatch it at the epoch level, run clean up code, then rethrow again. Same deal at the run level.

exception k1lib.CancelRunException

Used in core training loop, to skip the run entirely

exception k1lib.CancelEpochException

Used in core training loop, to skip to next epoch

exception k1lib.CancelBatchException

Used in core training loop, to skip to next batch

Functions

k1lib.textToHtml(text: str) → str

Transform a string so that it looks the same on browsers as in print()

k1lib.clearLine()

Prints a character that clears the current line

k1lib.tab(text: Union[list, str], pad='    ') → Union[list, str]

Adds a tab before each line. str in, str out. List in, list out

k1lib.isNumeric(x) → bool

Returns whether object is actually a number

k1lib.close(a, b)

Returns whether 2 values are really close to each other

k1lib.patch(_class: type, name: Optional[str] = None, docs: Optional[Union[str, Any]] = None, static=False)

Patches a function to a class/object.

Parameters

• _class – object to patch function. Can also be a type

• name – name of patched function, if different from current

• docs – docs of patched function. Can be object with defined __doc__ attr

• static – whether to wrap this inside staticmethod or not

Returns

modified function just before patching

Intended to be used like this:

class A:
    def methA(self):
        return "inside methA"

@k1lib.patch(A)
def methB(self):
    return "inside methB"

a = A()
a.methB() # returns "inside methB"

You can do @property attributes like this:

class A: pass

@k1lib.patch(A, "propC")
@property
def propC(self): return self._propC

@k1lib.patch(A, "propC")
@propC.setter
def propC(self, value): self._propC = value

a = A(); a.propC = "abc"
a.propC # returns "abc"

The attribute name unfortunately has to be explicitly declared, as I can’t really find a way to extract the original name. You can also do static methods like this:

class A: pass

@k1lib.patch(A, static=True)
def staticD(arg1): return arg1

A.staticD("def") # returns "def"

k1lib.wraps(ogF)

Kinda like functools.wraps(), but don’t update __annotations__.

k1lib.squeeze(_list: Union[list, tuple, torch.Tensor, Any], hard=False)

If list only has 1 element, returns that element, else returns original list.

Parameters

hard – If True, then if list/tuple, filters out None, and takes the first element out even if that list/tuple has more than 1 element

k1lib.raiseEx(ex: Exception)

Raises a specific exception. May be useful in lambdas

k1lib.numDigits(num) → int

Get the number of digits/characters of this number/object

k1lib.limitLines(s: str, limit: int = 10) → str

If input string is too long, truncates it and adds ellipsis

k1lib.limitChars(s: str, limit: int = 50)

If input string is too long, truncates to first limit characters of the first line

k1lib.showLog(loggerName: str = '', level: int = 10)

Prints out logs of a particular logger at a particular level

k1lib.beep()

Plays a beeping sound, may be useful as notification for long-running tasks

k1lib.dontWrap()

Don’t wrap horizontally when in a notebook. Normally, if you’re displaying something long, like the output of print('a'*1000) in a notebook, it will display it in multiple lines. This may be undesirable, so this solves that by displaying some HTML with css styles so that the notebook doesn’t wrap.

k1lib.debounce(wait, threading=False)

Decorator that will postpone a function’s execution until after wait seconds have elapsed since the last time it was invoked. Taken from ipywidgets. Example:

import k1lib, time; value = 0

@k1lib.debounce(0.5, True)
def f(x): global value; value = x**2

f(2); time.sleep(0.3); f(3)
print(value) # prints "0"
time.sleep(0.7)
print(value) # prints "9"

Parameters

• wait – wait time in seconds

• threading – if True, use multiple threads, else just use async stuff

k1lib.scaleSvg(svg: str, scale: Optional[float] = None) → str

Scales an svg xml string by some amount.

k1lib.pValue(zScore)

2-sided p value of a particular z score. Requires scipy.

k1lib.perlin3d(shape=(100, 100, 100), res=(2, 2, 2), tileable=(False, False, False), interpolant=<function interpolant>)

Generate a 3D numpy array of perlin noise. Not my code! All credits go to the author of this library: https://github.com/pvigier/perlin-numpy

Parameters

• shape – The shape of the generated array (tuple of three ints). This must be a multiple of res.

• res – The number of periods of noise to generate along each axis (tuple of three ints). Note shape must be a multiple of res.

• tileable – If the noise should be tileable along each axis (tuple of three bools). Defaults to (False, False, False).

• interpolant – The interpolation function, defaults to t*t*t*(t*(t*6 - 15) + 10).

Returns

A numpy array of shape shape with the generated noise.

Raises

ValueError – If shape is not a multiple of res.

k1lib.graph()

Convenience method for creating a new graphviz Graph. See also: digraph()

k1lib.digraph()

Convenience method for creating a new graphviz Digraph. Example:

g = k1lib.graph()
g("a", "b", "c")
g # displays arrows from "a" to "b" and "a" to "c"

Higher order functions

k1lib.polyfit(x: List[float], y: List[float], deg: int = 6) → Callable[[float], float]

Returns a function that approximate \(f(x) = y\).

Parameters

deg – degree of the polynomial of the returned function

k1lib.derivative(f: Callable[[float], float], delta: float = 1e-06) → Callable[[float], float]

Returns the derivative of a function. Example:

f = lambda x: x**2
df = k1lib.derivative(f)
df(3) # returns roughly 6 

k1lib.optimize(f: Callable[[float], float], v: float = 1, threshold: float = 1e-06) → float

Given \(f(x) = 0\), solves for x using Newton’s method with initial value v. Example:

f = lambda x: x**2-2
# returns 1.4142 (root 2)
k1lib.optimize(f)
# returns -1.4142 (negative root 2)
k1lib.optimize(f, -1)

Interestingly, for some reason, result of this is more accurate than derivative().

k1lib.inverse(f: Callable[[float], float]) → Callable[[float], float]

Returns the inverse of a function. Example:

f = lambda x: x**2
fInv = k1lib.inverse(f)
# returns roughly 3
fInv(9)

Warning

The inverse function takes a long time to run, so don’t use this where you need lots of speed. Also, as you might imagine, the inverse function isn’t really airtight. Should work well with monotonic functions, but all bets are off with other functions.

k1lib.integrate(f: Callable[[float], float], _range: k1lib._baseClasses.Range) → float

Integrates a function over a range. Example:

f = lambda x: x**2
# returns roughly 9
k1lib.integrate(f, [0, 3])