How to do a scatter plot with empty circles in Python?

circle | StackOverflow

In Python, with Matplotlib, how can a scatter plot with empty circles be plotted? The goal is to draw empty circles around some of the colored disks already plotted by scatter(), so as to highlight them, ideally without having to redraw the colored circles.

I tried facecolors=None, to no avail.

Answer rating: 292

From the documentation for scatter:

Optional kwargs control the Collection properties; in particular:

    edgecolors:
        The string ‘none’ to plot faces with no outlines
    facecolors:
        The string ‘none’ to plot unfilled outlines

Try the following:

import matplotlib.pyplot as plt 
import numpy as np 

x = np.random.randn(60) 
y = np.random.randn(60)

plt.scatter(x, y, s=80, facecolors="none", edgecolors="r")
plt.show()

example image

Note: For other types of plots see this post on the use of markeredgecolor and markerfacecolor.





How to do a scatter plot with empty circles in Python?: StackOverflow Questions

How to do a scatter plot with empty circles in Python?

In Python, with Matplotlib, how can a scatter plot with empty circles be plotted? The goal is to draw empty circles around some of the colored disks already plotted by scatter(), so as to highlight them, ideally without having to redraw the colored circles.

I tried facecolors=None, to no avail.

plot a circle with pyplot

surprisingly I didn"t find a straight-forward description on how to draw a circle with matplotlib.pyplot (please no pylab) taking as input center (x,y) and radius r. I tried some variants of this:

import matplotlib.pyplot as plt
circle=plt.Circle((0,0),2)
# here must be something like circle.plot() or not?
plt.show()

... but still didn"t get it working.

Answer #1

The golden spiral method

You said you couldn’t get the golden spiral method to work and that’s a shame because it’s really, really good. I would like to give you a complete understanding of it so that maybe you can understand how to keep this away from being “bunched up.”

So here’s a fast, non-random way to create a lattice that is approximately correct; as discussed above, no lattice will be perfect, but this may be good enough. It is compared to other methods e.g. at BendWavy.org but it just has a nice and pretty look as well as a guarantee about even spacing in the limit.

Primer: sunflower spirals on the unit disk

To understand this algorithm, I first invite you to look at the 2D sunflower spiral algorithm. This is based on the fact that the most irrational number is the golden ratio (1 + sqrt(5))/2 and if one emits points by the approach “stand at the center, turn a golden ratio of whole turns, then emit another point in that direction,” one naturally constructs a spiral which, as you get to higher and higher numbers of points, nevertheless refuses to have well-defined ‘bars’ that the points line up on.(Note 1.)

The algorithm for even spacing on a disk is,

from numpy import pi, cos, sin, sqrt, arange
import matplotlib.pyplot as pp

num_pts = 100
indices = arange(0, num_pts, dtype=float) + 0.5

r = sqrt(indices/num_pts)
theta = pi * (1 + 5**0.5) * indices

pp.scatter(r*cos(theta), r*sin(theta))
pp.show()

and it produces results that look like (n=100 and n=1000):

enter image description here

Spacing the points radially

The key strange thing is the formula r = sqrt(indices / num_pts); how did I come to that one? (Note 2.)

Well, I am using the square root here because I want these to have even-area spacing around the disk. That is the same as saying that in the limit of large N I want a little region R ∈ (r, r + dr), Θ ∈ (θ, θ + dθ) to contain a number of points proportional to its area, which is r dr dθ. Now if we pretend that we are talking about a random variable here, this has a straightforward interpretation as saying that the joint probability density for (R, Θ) is just c r for some constant c. Normalization on the unit disk would then force c = 1/π.

Now let me introduce a trick. It comes from probability theory where it’s known as sampling the inverse CDF: suppose you wanted to generate a random variable with a probability density f(z) and you have a random variable U ~ Uniform(0, 1), just like comes out of random() in most programming languages. How do you do this?

  1. First, turn your density into a cumulative distribution function or CDF, which we will call F(z). A CDF, remember, increases monotonically from 0 to 1 with derivative f(z).
  2. Then calculate the CDF’s inverse function F-1(z).
  3. You will find that Z = F-1(U) is distributed according to the target density. (Note 3).

Now the golden-ratio spiral trick spaces the points out in a nicely even pattern for θ so let’s integrate that out; for the unit disk we are left with F(r) = r2. So the inverse function is F-1(u) = u1/2, and therefore we would generate random points on the disk in polar coordinates with r = sqrt(random()); theta = 2 * pi * random().

Now instead of randomly sampling this inverse function we’re uniformly sampling it, and the nice thing about uniform sampling is that our results about how points are spread out in the limit of large N will behave as if we had randomly sampled it. This combination is the trick. Instead of random() we use (arange(0, num_pts, dtype=float) + 0.5)/num_pts, so that, say, if we want to sample 10 points they are r = 0.05, 0.15, 0.25, ... 0.95. We uniformly sample r to get equal-area spacing, and we use the sunflower increment to avoid awful “bars” of points in the output.

Now doing the sunflower on a sphere

The changes that we need to make to dot the sphere with points merely involve switching out the polar coordinates for spherical coordinates. The radial coordinate of course doesn"t enter into this because we"re on a unit sphere. To keep things a little more consistent here, even though I was trained as a physicist I"ll use mathematicians" coordinates where 0 ≤ φ ≤ π is latitude coming down from the pole and 0 ≤ θ ≤ 2π is longitude. So the difference from above is that we are basically replacing the variable r with φ.

Our area element, which was r dr dθ, now becomes the not-much-more-complicated sin(φ) dφ dθ. So our joint density for uniform spacing is sin(φ)/4π. Integrating out θ, we find f(φ) = sin(φ)/2, thus F(φ) = (1 − cos(φ))/2. Inverting this we can see that a uniform random variable would look like acos(1 - 2 u), but we sample uniformly instead of randomly, so we instead use φk = acos(1 − 2 (k + 0.5)/N). And the rest of the algorithm is just projecting this onto the x, y, and z coordinates:

from numpy import pi, cos, sin, arccos, arange
import mpl_toolkits.mplot3d
import matplotlib.pyplot as pp

num_pts = 1000
indices = arange(0, num_pts, dtype=float) + 0.5

phi = arccos(1 - 2*indices/num_pts)
theta = pi * (1 + 5**0.5) * indices

x, y, z = cos(theta) * sin(phi), sin(theta) * sin(phi), cos(phi);

pp.figure().add_subplot(111, projection="3d").scatter(x, y, z);
pp.show()

Again for n=100 and n=1000 the results look like: enter image description here enter image description here

Further research

I wanted to give a shout out to Martin Roberts’s blog. Note that above I created an offset of my indices by adding 0.5 to each index. This was just visually appealing to me, but it turns out that the choice of offset matters a lot and is not constant over the interval and can mean getting as much as 8% better accuracy in packing if chosen correctly. There should also be a way to get his R2 sequence to cover a sphere and it would be interesting to see if this also produced a nice even covering, perhaps as-is but perhaps needing to be, say, taken from only a half of the unit square cut diagonally or so and stretched around to get a circle.

Notes

  1. Those “bars” are formed by rational approximations to a number, and the best rational approximations to a number come from its continued fraction expression, z + 1/(n_1 + 1/(n_2 + 1/(n_3 + ...))) where z is an integer and n_1, n_2, n_3, ... is either a finite or infinite sequence of positive integers:

    def continued_fraction(r):
        while r != 0:
            n = floor(r)
            yield n
            r = 1/(r - n)
    

    Since the fraction part 1/(...) is always between zero and one, a large integer in the continued fraction allows for a particularly good rational approximation: “one divided by something between 100 and 101” is better than “one divided by something between 1 and 2.” The most irrational number is therefore the one which is 1 + 1/(1 + 1/(1 + ...)) and has no particularly good rational approximations; one can solve φ = 1 + 1/φ by multiplying through by φ to get the formula for the golden ratio.

  2. For folks who are not so familiar with NumPy -- all of the functions are “vectorized,” so that sqrt(array) is the same as what other languages might write map(sqrt, array). So this is a component-by-component sqrt application. The same also holds for division by a scalar or addition with scalars -- those apply to all components in parallel.

  3. The proof is simple once you know that this is the result. If you ask what"s the probability that z < Z < z + dz, this is the same as asking what"s the probability that z < F-1(U) < z + dz, apply F to all three expressions noting that it is a monotonically increasing function, hence F(z) < U < F(z + dz), expand the right hand side out to find F(z) + f(z) dz, and since U is uniform this probability is just f(z) dz as promised.

Answer #2

Python has no built-in encryption schemes, no. You also should take encrypted data storage serious; trivial encryption schemes that one developer understands to be insecure and a toy scheme may well be mistaken for a secure scheme by a less experienced developer. If you encrypt, encrypt properly.

You don’t need to do much work to implement a proper encryption scheme however. First of all, don’t re-invent the cryptography wheel, use a trusted cryptography library to handle this for you. For Python 3, that trusted library is cryptography.

I also recommend that encryption and decryption applies to bytes; encode text messages to bytes first; stringvalue.encode() encodes to UTF8, easily reverted again using bytesvalue.decode().

Last but not least, when encrypting and decrypting, we talk about keys, not passwords. A key should not be human memorable, it is something you store in a secret location but machine readable, whereas a password often can be human-readable and memorised. You can derive a key from a password, with a little care.

But for a web application or process running in a cluster without human attention to keep running it, you want to use a key. Passwords are for when only an end-user needs access to the specific information. Even then, you usually secure the application with a password, then exchange encrypted information using a key, perhaps one attached to the user account.

Symmetric key encryption

Fernet – AES CBC + HMAC, strongly recommended

The cryptography library includes the Fernet recipe, a best-practices recipe for using cryptography. Fernet is an open standard, with ready implementations in a wide range of programming languages and it packages AES CBC encryption for you with version information, a timestamp and an HMAC signature to prevent message tampering.

Fernet makes it very easy to encrypt and decrypt messages and keep you secure. It is the ideal method for encrypting data with a secret.

I recommend you use Fernet.generate_key() to generate a secure key. You can use a password too (next section), but a full 32-byte secret key (16 bytes to encrypt with, plus another 16 for the signature) is going to be more secure than most passwords you could think of.

The key that Fernet generates is a bytes object with URL and file safe base64 characters, so printable:

from cryptography.fernet import Fernet

key = Fernet.generate_key()  # store in a secure location
print("Key:", key.decode())

To encrypt or decrypt messages, create a Fernet() instance with the given key, and call the Fernet.encrypt() or Fernet.decrypt(), both the plaintext message to encrypt and the encrypted token are bytes objects.

encrypt() and decrypt() functions would look like:

from cryptography.fernet import Fernet

def encrypt(message: bytes, key: bytes) -> bytes:
    return Fernet(key).encrypt(message)

def decrypt(token: bytes, key: bytes) -> bytes:
    return Fernet(key).decrypt(token)

Demo:

>>> key = Fernet.generate_key()
>>> print(key.decode())
GZWKEhHGNopxRdOHS4H4IyKhLQ8lwnyU7vRLrM3sebY=
>>> message = "John Doe"
>>> encrypt(message.encode(), key)
"gAAAAABciT3pFbbSihD_HZBZ8kqfAj94UhknamBuirZWKivWOukgKQ03qE2mcuvpuwCSuZ-X_Xkud0uWQLZ5e-aOwLC0Ccnepg=="
>>> token = _
>>> decrypt(token, key).decode()
"John Doe"

Fernet with password – key derived from password, weakens the security somewhat

You can use a password instead of a secret key, provided you use a strong key derivation method. You do then have to include the salt and the HMAC iteration count in the message, so the encrypted value is not Fernet-compatible anymore without first separating salt, count and Fernet token:

import secrets
from base64 import urlsafe_b64encode as b64e, urlsafe_b64decode as b64d

from cryptography.fernet import Fernet
from cryptography.hazmat.backends import default_backend
from cryptography.hazmat.primitives import hashes
from cryptography.hazmat.primitives.kdf.pbkdf2 import PBKDF2HMAC

backend = default_backend()
iterations = 100_000

def _derive_key(password: bytes, salt: bytes, iterations: int = iterations) -> bytes:
    """Derive a secret key from a given password and salt"""
    kdf = PBKDF2HMAC(
        algorithm=hashes.SHA256(), length=32, salt=salt,
        iterations=iterations, backend=backend)
    return b64e(kdf.derive(password))

def password_encrypt(message: bytes, password: str, iterations: int = iterations) -> bytes:
    salt = secrets.token_bytes(16)
    key = _derive_key(password.encode(), salt, iterations)
    return b64e(
        b"%b%b%b" % (
            salt,
            iterations.to_bytes(4, "big"),
            b64d(Fernet(key).encrypt(message)),
        )
    )

def password_decrypt(token: bytes, password: str) -> bytes:
    decoded = b64d(token)
    salt, iter, token = decoded[:16], decoded[16:20], b64e(decoded[20:])
    iterations = int.from_bytes(iter, "big")
    key = _derive_key(password.encode(), salt, iterations)
    return Fernet(key).decrypt(token)

Demo:

>>> message = "John Doe"
>>> password = "mypass"
>>> password_encrypt(message.encode(), password)
b"9Ljs-w8IRM3XT1NDBbSBuQABhqCAAAAAAFyJdhiCPXms2vQHO7o81xZJn5r8_PAtro8Qpw48kdKrq4vt-551BCUbcErb_GyYRz8SVsu8hxTXvvKOn9QdewRGDfwx"
>>> token = _
>>> password_decrypt(token, password).decode()
"John Doe"

Including the salt in the output makes it possible to use a random salt value, which in turn ensures the encrypted output is guaranteed to be fully random regardless of password reuse or message repetition. Including the iteration count ensures that you can adjust for CPU performance increases over time without losing the ability to decrypt older messages.

A password alone can be as safe as a Fernet 32-byte random key, provided you generate a properly random password from a similar size pool. 32 bytes gives you 256 ^ 32 number of keys, so if you use an alphabet of 74 characters (26 upper, 26 lower, 10 digits and 12 possible symbols), then your password should be at least math.ceil(math.log(256 ** 32, 74)) == 42 characters long. However, a well-selected larger number of HMAC iterations can mitigate the lack of entropy somewhat as this makes it much more expensive for an attacker to brute force their way in.

Just know that choosing a shorter but still reasonably secure password won’t cripple this scheme, it just reduces the number of possible values a brute-force attacker would have to search through; make sure to pick a strong enough password for your security requirements.

Alternatives

Obscuring

An alternative is not to encrypt. Don"t be tempted to just use a low-security cipher, or a home-spun implementation of, say Vignere. There is no security in these approaches, but may give an inexperienced developer that is given the task to maintain your code in future the illusion of security, which is worse than no security at all.

If all you need is obscurity, just base64 the data; for URL-safe requirements, the base64.urlsafe_b64encode() function is fine. Don"t use a password here, just encode and you are done. At most, add some compression (like zlib):

import zlib
from base64 import urlsafe_b64encode as b64e, urlsafe_b64decode as b64d

def obscure(data: bytes) -> bytes:
    return b64e(zlib.compress(data, 9))

def unobscure(obscured: bytes) -> bytes:
    return zlib.decompress(b64d(obscured))

This turns b"Hello world!" into b"eNrzSM3JyVcozy_KSVEEAB0JBF4=".

Integrity only

If all you need is a way to make sure that the data can be trusted to be unaltered after having been sent to an untrusted client and received back, then you want to sign the data, you can use the hmac library for this with SHA1 (still considered secure for HMAC signing) or better:

import hmac
import hashlib

def sign(data: bytes, key: bytes, algorithm=hashlib.sha256) -> bytes:
    assert len(key) >= algorithm().digest_size, (
        "Key must be at least as long as the digest size of the "
        "hashing algorithm"
    )
    return hmac.new(key, data, algorithm).digest()

def verify(signature: bytes, data: bytes, key: bytes, algorithm=hashlib.sha256) -> bytes:
    expected = sign(data, key, algorithm)
    return hmac.compare_digest(expected, signature)

Use this to sign data, then attach the signature with the data and send that to the client. When you receive the data back, split data and signature and verify. I"ve set the default algorithm to SHA256, so you"ll need a 32-byte key:

key = secrets.token_bytes(32)

You may want to look at the itsdangerous library, which packages this all up with serialisation and de-serialisation in various formats.

Using AES-GCM encryption to provide encryption and integrity

Fernet builds on AEC-CBC with a HMAC signature to ensure integrity of the encrypted data; a malicious attacker can"t feed your system nonsense data to keep your service busy running in circles with bad input, because the ciphertext is signed.

The Galois / Counter mode block cipher produces ciphertext and a tag to serve the same purpose, so can be used to serve the same purposes. The downside is that unlike Fernet there is no easy-to-use one-size-fits-all recipe to reuse on other platforms. AES-GCM also doesn"t use padding, so this encryption ciphertext matches the length of the input message (whereas Fernet / AES-CBC encrypts messages to blocks of fixed length, obscuring the message length somewhat).

AES256-GCM takes the usual 32 byte secret as a key:

key = secrets.token_bytes(32)

then use

import binascii, time
from base64 import urlsafe_b64encode as b64e, urlsafe_b64decode as b64d

from cryptography.hazmat.primitives.ciphers import Cipher, algorithms, modes
from cryptography.hazmat.backends import default_backend
from cryptography.exceptions import InvalidTag

backend = default_backend()

def aes_gcm_encrypt(message: bytes, key: bytes) -> bytes:
    current_time = int(time.time()).to_bytes(8, "big")
    algorithm = algorithms.AES(key)
    iv = secrets.token_bytes(algorithm.block_size // 8)
    cipher = Cipher(algorithm, modes.GCM(iv), backend=backend)
    encryptor = cipher.encryptor()
    encryptor.authenticate_additional_data(current_time)
    ciphertext = encryptor.update(message) + encryptor.finalize()        
    return b64e(current_time + iv + ciphertext + encryptor.tag)

def aes_gcm_decrypt(token: bytes, key: bytes, ttl=None) -> bytes:
    algorithm = algorithms.AES(key)
    try:
        data = b64d(token)
    except (TypeError, binascii.Error):
        raise InvalidToken
    timestamp, iv, tag = data[:8], data[8:algorithm.block_size // 8 + 8], data[-16:]
    if ttl is not None:
        current_time = int(time.time())
        time_encrypted, = int.from_bytes(data[:8], "big")
        if time_encrypted + ttl < current_time or current_time + 60 < time_encrypted:
            # too old or created well before our current time + 1 h to account for clock skew
            raise InvalidToken
    cipher = Cipher(algorithm, modes.GCM(iv, tag), backend=backend)
    decryptor = cipher.decryptor()
    decryptor.authenticate_additional_data(timestamp)
    ciphertext = data[8 + len(iv):-16]
    return decryptor.update(ciphertext) + decryptor.finalize()

I"ve included a timestamp to support the same time-to-live use-cases that Fernet supports.

Other approaches on this page, in Python 3

AES CFB - like CBC but without the need to pad

This is the approach that All –Ü—ï V–∞–∏—ñ—Çy follows, albeit incorrectly. This is the cryptography version, but note that I include the IV in the ciphertext, it should not be stored as a global (reusing an IV weakens the security of the key, and storing it as a module global means it"ll be re-generated the next Python invocation, rendering all ciphertext undecryptable):

import secrets
from base64 import urlsafe_b64encode as b64e, urlsafe_b64decode as b64d

from cryptography.hazmat.primitives.ciphers import Cipher, algorithms, modes
from cryptography.hazmat.backends import default_backend

backend = default_backend()

def aes_cfb_encrypt(message, key):
    algorithm = algorithms.AES(key)
    iv = secrets.token_bytes(algorithm.block_size // 8)
    cipher = Cipher(algorithm, modes.CFB(iv), backend=backend)
    encryptor = cipher.encryptor()
    ciphertext = encryptor.update(message) + encryptor.finalize()
    return b64e(iv + ciphertext)

def aes_cfb_decrypt(ciphertext, key):
    iv_ciphertext = b64d(ciphertext)
    algorithm = algorithms.AES(key)
    size = algorithm.block_size // 8
    iv, encrypted = iv_ciphertext[:size], iv_ciphertext[size:]
    cipher = Cipher(algorithm, modes.CFB(iv), backend=backend)
    decryptor = cipher.decryptor()
    return decryptor.update(encrypted) + decryptor.finalize()

This lacks the added armoring of an HMAC signature and there is no timestamp; you’d have to add those yourself.

The above also illustrates how easy it is to combine basic cryptography building blocks incorrectly; All Іѕ Vаиітy‘s incorrect handling of the IV value can lead to a data breach or all encrypted messages being unreadable because the IV is lost. Using Fernet instead protects you from such mistakes.

AES ECB – not secure

If you previously implemented AES ECB encryption and need to still support this in Python 3, you can do so still with cryptography too. The same caveats apply, ECB is not secure enough for real-life applications. Re-implementing that answer for Python 3, adding automatic handling of padding:

from base64 import urlsafe_b64encode as b64e, urlsafe_b64decode as b64d

from cryptography.hazmat.primitives.ciphers import Cipher, algorithms, modes
from cryptography.hazmat.primitives import padding
from cryptography.hazmat.backends import default_backend

backend = default_backend()

def aes_ecb_encrypt(message, key):
    cipher = Cipher(algorithms.AES(key), modes.ECB(), backend=backend)
    encryptor = cipher.encryptor()
    padder = padding.PKCS7(cipher.algorithm.block_size).padder()
    padded = padder.update(msg_text.encode()) + padder.finalize()
    return b64e(encryptor.update(padded) + encryptor.finalize())

def aes_ecb_decrypt(ciphertext, key):
    cipher = Cipher(algorithms.AES(key), modes.ECB(), backend=backend)
    decryptor = cipher.decryptor()
    unpadder = padding.PKCS7(cipher.algorithm.block_size).unpadder()
    padded = decryptor.update(b64d(ciphertext)) + decryptor.finalize()
    return unpadder.update(padded) + unpadder.finalize()

Again, this lacks the HMAC signature, and you shouldn’t use ECB anyway. The above is there merely to illustrate that cryptography can handle the common cryptographic building blocks, even the ones you shouldn’t actually use.

Answer #3

import matplotlib.pyplot as plt

circle1 = plt.Circle((0, 0), 0.2, color="r")
plt.gca().add_patch(circle1)

A quick condensed version of the accepted answer, to quickly plug a circle into an existing plot. Refer to the accepted answer and other answers to understand the details.

By the way:

  • gca() means Get Current Axis

Answer #4

There is a picture show all markers" name and description, i hope it will help you.

import matplotlib.pylab as plt

markers = [".",",","o","v","^","<",">","1","2","3","4","8","s","p","P","*","h","H","+","x","X","D","d","|","_"]
descriptions = ["point", "pixel", "circle", "triangle_down", "triangle_up","triangle_left",
                "triangle_right", "tri_down", "tri_up", "tri_left", "tri_right", "octagon",
                "square", "pentagon", "plus (filled)","star", "hexagon1", "hexagon2", "plus",
                "x", "x (filled)","diamond", "thin_diamond", "vline", "hline"]
x=[]
y=[]

for i in range(5):
    for j in range(5):
        x.append(i)
        y.append(j)
        
plt.figure(figsize=(8, 8))

for i,j,m,l in zip(x,y,markers,descriptions):
    plt.scatter(i,j,marker=m)
    plt.text(i-0.15,j+0.15,s=m+" : "+l)
    
plt.axis([-0.1,4.8,-0.1,4.5])

plt.axis("off")
plt.tight_layout()
plt.show() 

enter image description here

Answer #5

By definition, isdecimal() ⊆ isdigit() ⊆ isnumeric(). That is, if a string is decimal, then it"ll also be digit and numeric.

Therefore, given a string s and test it with those three methods, there"ll only be 4 types of results.

+-------------+-----------+-------------+----------------------------------+
| isdecimal() | isdigit() | isnumeric() |          Example                 |
+-------------+-----------+-------------+----------------------------------+
|    True     |    True   |    True     | "038", "੦੩੮", "038"           |
|  False      |    True   |    True     | "⁰³⁸", "🄀⒊⒏", "⓪③⑧"          |
|  False      |  False    |    True     | "↉⅛⅘", "ⅠⅢⅧ", "⑩⑬㊿", "壹貳參"  |
|  False      |  False    |  False      | "abc", "38.0", "-38"             |
+-------------+-----------+-------------+----------------------------------+

1. Some examples of characters isdecimal()==True

(thus isdigit()==True and isnumeric()==True)

"0123456789"  DIGIT ZERO~NINE
"٠١٢٣٤٥٦٧٨٩"  ARABIC-INDIC DIGIT ZERO~NINE
"०१२३४५६७८९"  DEVANAGARI DIGIT ZERO~NINE
"০১২৩৪৫৬৭৮৯"  BENGALI DIGIT ZERO~NINE
"੦੧੨੩੪੫੬੭੮੯"  GURMUKHI DIGIT ZERO~NINE
"૦૧૨૩૪૫૬૭૮૯"  GUJARATI DIGIT ZERO~NINE
"୦୧୨୩୪୫୬୭୮୯"  ORIYA DIGIT ZERO~NINE
"௦௧௨௩௪௫௬௭௮௯"  TAMIL DIGIT ZERO~NINE
"౦౧౨౩౪౫౬౭౮౯"  TELUGU DIGIT ZERO~NINE
"೦೧೨೩೪೫೬೭೮೯"  KANNADA DIGIT ZERO~NINE
"൦൧൨൩൪൫൬൭൮൯"  MALAYALAM DIGIT ZERO~NINE
"๐๑๒๓๔๕๖๗๘๙"  THAI DIGIT ZERO~NINE
"໐໑໒໓໔໕໖໗໘໙"  LAO DIGIT ZERO~NINE
"༠༡༢༣༤༥༦༧༨༩"  TIBETAN DIGIT ZERO~NINE
"·ÅÄ·ÅÅ·ÅÇ·ÅÉ·ÅÑ·ÅÖ·ÅÜ·Åá·Åà·Åâ"  MYANMAR DIGIT ZERO~NINE
"០១២៣៤៥៦៧៨៩"  KHMER DIGIT ZERO~NINE
"0123456789"  FULLWIDTH DIGIT ZERO~NINE
"ùüéùüèùüêùüëùüíùüìùüîùüïùüñùüó"  MATHEMATICAL BOLD DIGIT ZERO~NINE
"𝟘𝟙𝟚𝟛𝟜𝟝𝟞𝟟𝟠𝟡"  MATHEMATICAL DOUBLE-STRUCK DIGIT ZERO~NINE
"𝟢𝟣𝟤𝟥𝟦𝟧𝟨𝟩𝟪𝟫"  MATHEMATICAL SANS-SERIF DIGIT ZERO~NINE
"𝟬𝟭𝟮𝟯𝟰𝟱𝟲𝟳𝟴𝟵"  MATHEMATICAL SANS-SERIF BOLD DIGIT ZERO~NINE
"𝟶𝟷𝟸𝟹𝟺𝟻𝟼𝟽𝟾𝟿"  MATHEMATICAL MONOSPACE DIGIT ZERO~NINE

2. Some examples of characters isdecimal()==False but isdigit()==True

(thus isnumeric()==True)

"⁰¹²³⁴⁵⁶⁷⁸⁹"  SUPERSCRIPT ZERO~NINE
"‚ÇÄ‚ÇÅ‚ÇÇ‚ÇÉ‚ÇÑ‚ÇÖ‚ÇÜ‚Çá‚Çà‚Çâ"  SUBSCRIPT ZERO~NINE
"🄀⒈⒉⒊⒋⒌⒍⒎⒏⒐"  DIGIT ZERO~NINE FULL STOP
"🄁🄂🄃🄄🄅🄆🄇🄈🄉🄊"  DIGIT ZERO~NINE COMMA
"⓪①②③④⑤⑥⑦⑧⑨"  CIRCLED DIGIT ZERO~NINE
"⓿❶❷❸❹❺❻❼❽❾"  NEGATIVE CIRCLED DIGIT ZERO~NINE
"⑴⑵⑶⑷⑸⑹⑺⑻⑼"  PARENTHESIZED DIGIT ONE~NINE
"‚ûÄ‚ûÅ‚ûÇ‚ûÉ‚ûÑ‚ûÖ‚ûÜ‚ûá‚ûà"  DINGBAT CIRCLED SANS-SERIF DIGIT ONE~NINE
"⓵⓶⓷⓸⓹⓺⓻⓼⓽"  DOUBLE CIRCLED DIGIT ONE~NINE
"‚ûä‚ûã‚ûå‚ûç‚ûé‚ûè‚ûê‚ûë‚ûí"  DINGBAT NEGATIVE CIRCLED SANS-SERIF DIGIT ONE~NINE
"፩፪፫፬፭፮፯፰፱"  ETHIOPIC DIGIT ONE~NINE

3. Some examples of characters isdecimal()==False and isdigit()==False but isnumeric()==True

"½⅓¼⅕⅙⅐⅛⅑⅒⅔¾⅖⅗⅘⅚⅜⅝⅞⅟↉"  VULGAR FRACTION
"৴৵৶৷৸৹"  BENGALI CURRENCY NUMERATOR
"௰௱௲"  TAMIL NUMBER TEN, ONE HUNDRED, ONE THOUSAND
"౸౹౺౻౼౽౾"  TELUGU FRACTION DIGIT
"൰൱൲൳൴൵"  MALAYALAM NUMBER, MALAYALAM FRACTION
"༳༪༫༬༭༮༯༰༱༲"  TIBETAN DIGIT HALF ZERO~NINE
"፲፳፴፵፶፷፸፹፺፻፼"  ETHIOPIC NUMBER TEN~NINETY, HUNDRED, TEN THOUSAND
"៰៱៲៳៴៵៶៷៸៹"  KHMER SYMBOL LEK ATTAK
"ⅠⅡⅢⅣⅤⅥⅦⅧⅨⅩⅪⅫⅬⅭⅮⅯ"  ROMAN NUMERAL
"ⅰⅱⅲⅳⅴⅵⅶⅷⅸⅹⅺⅻⅼⅽⅾⅿ"  SMALL ROMAN NUMERAL
"‚ÜÄ‚ÜÅ‚ÜÇ‚ÜÖ‚ÜÜ"  ROMAN NUMERAL
"⑩⑪⑫⑬⑭⑮⑯⑰⑱⑲⑳㉑㉒㉓㉔㉕㉖㉗㉘㉙㉚㉛㉜㉝㉞㉟㊱㊲㊳㊴㊵㊶㊷㊸㊹㊺㊻㊼㊽㊾㊿"  CIRCLED NUMBER TEN~FIFTY
"„âà„ââ„âä„âã„âå„âç„âé„âè"  CIRCLED NUMBER TEN~EIGHTY ON BLACK SQUARE
"⑽⑾⑿⒀⒁⒂⒃⒄⒅⒆⒇"  PARENTHESIZED NUMBER TEN~TWENTY
"‚íë‚íí‚íì‚íî‚íï‚íñ‚íó‚íò‚íô‚íö‚íõ"  NUMBER TEN~TWENTY FULL STOP
"⓫⓬⓭⓮⓯⓰⓱⓲⓳⓴"  NEGATIVE CIRCLED NUMBER ELEVEN
"‚ìæ‚ûâ‚ùø‚ûì"  various styles of CIRCLED NUMBER TEN
"🄌"  DINGBAT NEGATIVE CIRCLED SANS-SERIF DIGIT ZERO
"„Äá"  IDEOGRAPHIC NUMBER ZERO
"〡〢〣〤〥〦〧〨〩〸〹〺"  HANGZHOU NUMERAL ONE~TEN, TWENTY, THIRTY
"„Üí„Üì„Üî„Üï"  IDEOGRAPHIC ANNOTATION ONE~FOUR MARK
"㈠㈡㈢㈣㈤㈥㈦㈧㈨㈩"  PARENTHESIZED IDEOGRAPH ONE~TEN
"㊀㊁㊂㊃㊄㊅㊆㊇㊈㊉"  CIRCLED IDEOGRAPH ONE~TEN
"一二三四五六七八九十壹貳參肆伍陸柒捌玖拾零百千萬億兆弐貮贰㒃㭍漆什㐅陌阡佰仟万亿幺兩㠪亖卄卅卌廾廿"  CJK UNIFIED IDEOGRAPH
"參拾兩零六陸什"  CJK COMPATIBILITY IDEOGRAPH
"𐄇𐄈𐄉𐄊𐄋𐄌𐄍𐄎𐄏𐄐𐄑𐄒𐄓𐄔𐄕𐄖𐄗𐄘"  AEGEAN NUMBER ONE~NINE, TEN~NINETY
"𐄙𐄚𐄛𐄜𐄝𐄞𐄟𐄠𐄡𐄢𐄣𐄤𐄥𐄦𐄧𐄨𐄩𐄪"  AEGEAN NUMBER ONE~NINE HUNDRED, ONE~NINE THOUSAND
"𐄬𐄭𐄮𐄯𐄰𐄱𐄲𐄳"  AEGEAN NUMBER TEN~NINETY THOUSAND
"𐅀𐅁𐅂𐅃𐅆𐅇𐅈𐅉𐅊𐅋𐅌𐅍𐅎𐅏𐅐𐅑𐅒𐅓𐅔𐅕𐅖𐅗𐅘𐅙𐅚𐅛𐅜𐅝𐅞𐅟𐅠𐅡𐅢𐅣𐅤𐅥𐅦𐅧𐅨𐅩𐅪𐅫𐅬𐅭𐅮𐅯𐅰𐅱𐅲𐅳𐅴"  GREEK ACROPHONIC ATTIC
"𝍠𝍡𝍢𝍣𝍤𝍥𝍦𝍧𝍨"  COUNTING ROD UNIT DIGIT ONE~NINE
"𝍩𝍪𝍫𝍬𝍭𝍮𝍯𝍰𝍱"  COUNTING ROD TENS DIGIT ONE~NINE

Answer #6

@Jan Kuiken"s answer is certainly well-thought and thorough, but there are some caveats:

  • it does not work in all cases
  • it requires a fair amount of extra code
  • it may vary considerably from one plot to the next

A much simpler approach is to annotate the last point of each plot. The point can also be circled, for emphasis. This can be accomplished with one extra line:

from matplotlib import pyplot as plt

for i, (x, y) in enumerate(samples):
    plt.plot(x, y)
    plt.text(x[-1], y[-1], "sample {i}".format(i=i))

A variant would be to use ax.annotate.

Answer #7

If you are not into long explanations, see Paolo Bergantino’s answer.

Decorator Basics

Python’s functions are objects

To understand decorators, you must first understand that functions are objects in Python. This has important consequences. Let’s see why with a simple example :

def shout(word="yes"):
    return word.capitalize()+"!"

print(shout())
# outputs : "Yes!"

# As an object, you can assign the function to a variable like any other object 
scream = shout

# Notice we don"t use parentheses: we are not calling the function,
# we are putting the function "shout" into the variable "scream".
# It means you can then call "shout" from "scream":

print(scream())
# outputs : "Yes!"

# More than that, it means you can remove the old name "shout",
# and the function will still be accessible from "scream"

del shout
try:
    print(shout())
except NameError as e:
    print(e)
    #outputs: "name "shout" is not defined"

print(scream())
# outputs: "Yes!"

Keep this in mind. We’ll circle back to it shortly.

Another interesting property of Python functions is they can be defined inside another function!

def talk():

    # You can define a function on the fly in "talk" ...
    def whisper(word="yes"):
        return word.lower()+"..."

    # ... and use it right away!
    print(whisper())

# You call "talk", that defines "whisper" EVERY TIME you call it, then
# "whisper" is called in "talk". 
talk()
# outputs: 
# "yes..."

# But "whisper" DOES NOT EXIST outside "talk":

try:
    print(whisper())
except NameError as e:
    print(e)
    #outputs : "name "whisper" is not defined"*
    #Python"s functions are objects

Functions references

Okay, still here? Now the fun part...

You’ve seen that functions are objects. Therefore, functions:

  • can be assigned to a variable
  • can be defined in another function

That means that a function can return another function.

def getTalk(kind="shout"):

    # We define functions on the fly
    def shout(word="yes"):
        return word.capitalize()+"!"

    def whisper(word="yes") :
        return word.lower()+"..."

    # Then we return one of them
    if kind == "shout":
        # We don"t use "()", we are not calling the function,
        # we are returning the function object
        return shout  
    else:
        return whisper

# How do you use this strange beast?

# Get the function and assign it to a variable
talk = getTalk()      

# You can see that "talk" is here a function object:
print(talk)
#outputs : <function shout at 0xb7ea817c>

# The object is the one returned by the function:
print(talk())
#outputs : Yes!

# And you can even use it directly if you feel wild:
print(getTalk("whisper")())
#outputs : yes...

There’s more!

If you can return a function, you can pass one as a parameter:

def doSomethingBefore(func): 
    print("I do something before then I call the function you gave me")
    print(func())

doSomethingBefore(scream)
#outputs: 
#I do something before then I call the function you gave me
#Yes!

Well, you just have everything needed to understand decorators. You see, decorators are “wrappers”, which means that they let you execute code before and after the function they decorate without modifying the function itself.

Handcrafted decorators

How you’d do it manually:

# A decorator is a function that expects ANOTHER function as parameter
def my_shiny_new_decorator(a_function_to_decorate):

    # Inside, the decorator defines a function on the fly: the wrapper.
    # This function is going to be wrapped around the original function
    # so it can execute code before and after it.
    def the_wrapper_around_the_original_function():

        # Put here the code you want to be executed BEFORE the original function is called
        print("Before the function runs")

        # Call the function here (using parentheses)
        a_function_to_decorate()

        # Put here the code you want to be executed AFTER the original function is called
        print("After the function runs")

    # At this point, "a_function_to_decorate" HAS NEVER BEEN EXECUTED.
    # We return the wrapper function we have just created.
    # The wrapper contains the function and the code to execute before and after. It’s ready to use!
    return the_wrapper_around_the_original_function

# Now imagine you create a function you don"t want to ever touch again.
def a_stand_alone_function():
    print("I am a stand alone function, don"t you dare modify me")

a_stand_alone_function() 
#outputs: I am a stand alone function, don"t you dare modify me

# Well, you can decorate it to extend its behavior.
# Just pass it to the decorator, it will wrap it dynamically in 
# any code you want and return you a new function ready to be used:

a_stand_alone_function_decorated = my_shiny_new_decorator(a_stand_alone_function)
a_stand_alone_function_decorated()
#outputs:
#Before the function runs
#I am a stand alone function, don"t you dare modify me
#After the function runs

Now, you probably want that every time you call a_stand_alone_function, a_stand_alone_function_decorated is called instead. That’s easy, just overwrite a_stand_alone_function with the function returned by my_shiny_new_decorator:

a_stand_alone_function = my_shiny_new_decorator(a_stand_alone_function)
a_stand_alone_function()
#outputs:
#Before the function runs
#I am a stand alone function, don"t you dare modify me
#After the function runs

# That’s EXACTLY what decorators do!

Decorators demystified

The previous example, using the decorator syntax:

@my_shiny_new_decorator
def another_stand_alone_function():
    print("Leave me alone")

another_stand_alone_function()  
#outputs:  
#Before the function runs
#Leave me alone
#After the function runs

Yes, that’s all, it’s that simple. @decorator is just a shortcut to:

another_stand_alone_function = my_shiny_new_decorator(another_stand_alone_function)

Decorators are just a pythonic variant of the decorator design pattern. There are several classic design patterns embedded in Python to ease development (like iterators).

Of course, you can accumulate decorators:

def bread(func):
    def wrapper():
        print("</"""""">")
        func()
        print("<\______/>")
    return wrapper

def ingredients(func):
    def wrapper():
        print("#tomatoes#")
        func()
        print("~salad~")
    return wrapper

def sandwich(food="--ham--"):
    print(food)

sandwich()
#outputs: --ham--
sandwich = bread(ingredients(sandwich))
sandwich()
#outputs:
#</"""""">
# #tomatoes#
# --ham--
# ~salad~
#<\______/>

Using the Python decorator syntax:

@bread
@ingredients
def sandwich(food="--ham--"):
    print(food)

sandwich()
#outputs:
#</"""""">
# #tomatoes#
# --ham--
# ~salad~
#<\______/>

The order you set the decorators MATTERS:

@ingredients
@bread
def strange_sandwich(food="--ham--"):
    print(food)

strange_sandwich()
#outputs:
##tomatoes#
#</"""""">
# --ham--
#<\______/>
# ~salad~

Now: to answer the question...

As a conclusion, you can easily see how to answer the question:

# The decorator to make it bold
def makebold(fn):
    # The new function the decorator returns
    def wrapper():
        # Insertion of some code before and after
        return "<b>" + fn() + "</b>"
    return wrapper

# The decorator to make it italic
def makeitalic(fn):
    # The new function the decorator returns
    def wrapper():
        # Insertion of some code before and after
        return "<i>" + fn() + "</i>"
    return wrapper

@makebold
@makeitalic
def say():
    return "hello"

print(say())
#outputs: <b><i>hello</i></b>

# This is the exact equivalent to 
def say():
    return "hello"
say = makebold(makeitalic(say))

print(say())
#outputs: <b><i>hello</i></b>

You can now just leave happy, or burn your brain a little bit more and see advanced uses of decorators.


Taking decorators to the next level

Passing arguments to the decorated function

# It’s not black magic, you just have to let the wrapper 
# pass the argument:

def a_decorator_passing_arguments(function_to_decorate):
    def a_wrapper_accepting_arguments(arg1, arg2):
        print("I got args! Look: {0}, {1}".format(arg1, arg2))
        function_to_decorate(arg1, arg2)
    return a_wrapper_accepting_arguments

# Since when you are calling the function returned by the decorator, you are
# calling the wrapper, passing arguments to the wrapper will let it pass them to 
# the decorated function

@a_decorator_passing_arguments
def print_full_name(first_name, last_name):
    print("My name is {0} {1}".format(first_name, last_name))
    
print_full_name("Peter", "Venkman")
# outputs:
#I got args! Look: Peter Venkman
#My name is Peter Venkman

Decorating methods

One nifty thing about Python is that methods and functions are really the same. The only difference is that methods expect that their first argument is a reference to the current object (self).

That means you can build a decorator for methods the same way! Just remember to take self into consideration:

def method_friendly_decorator(method_to_decorate):
    def wrapper(self, lie):
        lie = lie - 3 # very friendly, decrease age even more :-)
        return method_to_decorate(self, lie)
    return wrapper
    
    
class Lucy(object):
    
    def __init__(self):
        self.age = 32
    
    @method_friendly_decorator
    def sayYourAge(self, lie):
        print("I am {0}, what did you think?".format(self.age + lie))
        
l = Lucy()
l.sayYourAge(-3)
#outputs: I am 26, what did you think?

If you’re making general-purpose decorator--one you’ll apply to any function or method, no matter its arguments--then just use *args, **kwargs:

def a_decorator_passing_arbitrary_arguments(function_to_decorate):
    # The wrapper accepts any arguments
    def a_wrapper_accepting_arbitrary_arguments(*args, **kwargs):
        print("Do I have args?:")
        print(args)
        print(kwargs)
        # Then you unpack the arguments, here *args, **kwargs
        # If you are not familiar with unpacking, check:
        # http://www.saltycrane.com/blog/2008/01/how-to-use-args-and-kwargs-in-python/
        function_to_decorate(*args, **kwargs)
    return a_wrapper_accepting_arbitrary_arguments

@a_decorator_passing_arbitrary_arguments
def function_with_no_argument():
    print("Python is cool, no argument here.")

function_with_no_argument()
#outputs
#Do I have args?:
#()
#{}
#Python is cool, no argument here.

@a_decorator_passing_arbitrary_arguments
def function_with_arguments(a, b, c):
    print(a, b, c)
    
function_with_arguments(1,2,3)
#outputs
#Do I have args?:
#(1, 2, 3)
#{}
#1 2 3 
 
@a_decorator_passing_arbitrary_arguments
def function_with_named_arguments(a, b, c, platypus="Why not ?"):
    print("Do {0}, {1} and {2} like platypus? {3}".format(a, b, c, platypus))

function_with_named_arguments("Bill", "Linus", "Steve", platypus="Indeed!")
#outputs
#Do I have args ? :
#("Bill", "Linus", "Steve")
#{"platypus": "Indeed!"}
#Do Bill, Linus and Steve like platypus? Indeed!

class Mary(object):
    
    def __init__(self):
        self.age = 31
    
    @a_decorator_passing_arbitrary_arguments
    def sayYourAge(self, lie=-3): # You can now add a default value
        print("I am {0}, what did you think?".format(self.age + lie))

m = Mary()
m.sayYourAge()
#outputs
# Do I have args?:
#(<__main__.Mary object at 0xb7d303ac>,)
#{}
#I am 28, what did you think?

Passing arguments to the decorator

Great, now what would you say about passing arguments to the decorator itself?

This can get somewhat twisted, since a decorator must accept a function as an argument. Therefore, you cannot pass the decorated function’s arguments directly to the decorator.

Before rushing to the solution, let’s write a little reminder:

# Decorators are ORDINARY functions
def my_decorator(func):
    print("I am an ordinary function")
    def wrapper():
        print("I am function returned by the decorator")
        func()
    return wrapper

# Therefore, you can call it without any "@"

def lazy_function():
    print("zzzzzzzz")

decorated_function = my_decorator(lazy_function)
#outputs: I am an ordinary function
            
# It outputs "I am an ordinary function", because that’s just what you do:
# calling a function. Nothing magic.

@my_decorator
def lazy_function():
    print("zzzzzzzz")
    
#outputs: I am an ordinary function

It’s exactly the same. "my_decorator" is called. So when you @my_decorator, you are telling Python to call the function "labelled by the variable "my_decorator"".

This is important! The label you give can point directly to the decorator—or not.

Let’s get evil. ☺

def decorator_maker():
    
    print("I make decorators! I am executed only once: "
          "when you make me create a decorator.")
            
    def my_decorator(func):
        
        print("I am a decorator! I am executed only when you decorate a function.")
               
        def wrapped():
            print("I am the wrapper around the decorated function. "
                  "I am called when you call the decorated function. "
                  "As the wrapper, I return the RESULT of the decorated function.")
            return func()
        
        print("As the decorator, I return the wrapped function.")
        
        return wrapped
    
    print("As a decorator maker, I return a decorator")
    return my_decorator
            
# Let’s create a decorator. It’s just a new function after all.
new_decorator = decorator_maker()       
#outputs:
#I make decorators! I am executed only once: when you make me create a decorator.
#As a decorator maker, I return a decorator

# Then we decorate the function
            
def decorated_function():
    print("I am the decorated function.")
   
decorated_function = new_decorator(decorated_function)
#outputs:
#I am a decorator! I am executed only when you decorate a function.
#As the decorator, I return the wrapped function
     
# Let’s call the function:
decorated_function()
#outputs:
#I am the wrapper around the decorated function. I am called when you call the decorated function.
#As the wrapper, I return the RESULT of the decorated function.
#I am the decorated function.

No surprise here.

Let’s do EXACTLY the same thing, but skip all the pesky intermediate variables:

def decorated_function():
    print("I am the decorated function.")
decorated_function = decorator_maker()(decorated_function)
#outputs:
#I make decorators! I am executed only once: when you make me create a decorator.
#As a decorator maker, I return a decorator
#I am a decorator! I am executed only when you decorate a function.
#As the decorator, I return the wrapped function.

# Finally:
decorated_function()    
#outputs:
#I am the wrapper around the decorated function. I am called when you call the decorated function.
#As the wrapper, I return the RESULT of the decorated function.
#I am the decorated function.

Let’s make it even shorter:

@decorator_maker()
def decorated_function():
    print("I am the decorated function.")
#outputs:
#I make decorators! I am executed only once: when you make me create a decorator.
#As a decorator maker, I return a decorator
#I am a decorator! I am executed only when you decorate a function.
#As the decorator, I return the wrapped function.

#Eventually: 
decorated_function()    
#outputs:
#I am the wrapper around the decorated function. I am called when you call the decorated function.
#As the wrapper, I return the RESULT of the decorated function.
#I am the decorated function.

Hey, did you see that? We used a function call with the "@" syntax! :-)

So, back to decorators with arguments. If we can use functions to generate the decorator on the fly, we can pass arguments to that function, right?

def decorator_maker_with_arguments(decorator_arg1, decorator_arg2):
    
    print("I make decorators! And I accept arguments: {0}, {1}".format(decorator_arg1, decorator_arg2))
            
    def my_decorator(func):
        # The ability to pass arguments here is a gift from closures.
        # If you are not comfortable with closures, you can assume it’s ok,
        # or read: https://stackoverflow.com/questions/13857/can-you-explain-closures-as-they-relate-to-python
        print("I am the decorator. Somehow you passed me arguments: {0}, {1}".format(decorator_arg1, decorator_arg2))
               
        # Don"t confuse decorator arguments and function arguments!
        def wrapped(function_arg1, function_arg2) :
            print("I am the wrapper around the decorated function.
"
                  "I can access all the variables
"
                  "	- from the decorator: {0} {1}
"
                  "	- from the function call: {2} {3}
"
                  "Then I can pass them to the decorated function"
                  .format(decorator_arg1, decorator_arg2,
                          function_arg1, function_arg2))
            return func(function_arg1, function_arg2)
        
        return wrapped
    
    return my_decorator

@decorator_maker_with_arguments("Leonard", "Sheldon")
def decorated_function_with_arguments(function_arg1, function_arg2):
    print("I am the decorated function and only knows about my arguments: {0}"
           " {1}".format(function_arg1, function_arg2))
          
decorated_function_with_arguments("Rajesh", "Howard")
#outputs:
#I make decorators! And I accept arguments: Leonard Sheldon
#I am the decorator. Somehow you passed me arguments: Leonard Sheldon
#I am the wrapper around the decorated function. 
#I can access all the variables 
#   - from the decorator: Leonard Sheldon 
#   - from the function call: Rajesh Howard 
#Then I can pass them to the decorated function
#I am the decorated function and only knows about my arguments: Rajesh Howard

Here it is: a decorator with arguments. Arguments can be set as variable:

c1 = "Penny"
c2 = "Leslie"

@decorator_maker_with_arguments("Leonard", c1)
def decorated_function_with_arguments(function_arg1, function_arg2):
    print("I am the decorated function and only knows about my arguments:"
           " {0} {1}".format(function_arg1, function_arg2))

decorated_function_with_arguments(c2, "Howard")
#outputs:
#I make decorators! And I accept arguments: Leonard Penny
#I am the decorator. Somehow you passed me arguments: Leonard Penny
#I am the wrapper around the decorated function. 
#I can access all the variables 
#   - from the decorator: Leonard Penny 
#   - from the function call: Leslie Howard 
#Then I can pass them to the decorated function
#I am the decorated function and only know about my arguments: Leslie Howard

As you can see, you can pass arguments to the decorator like any function using this trick. You can even use *args, **kwargs if you wish. But remember decorators are called only once. Just when Python imports the script. You can"t dynamically set the arguments afterwards. When you do "import x", the function is already decorated, so you can"t change anything.


Let’s practice: decorating a decorator

Okay, as a bonus, I"ll give you a snippet to make any decorator accept generically any argument. After all, in order to accept arguments, we created our decorator using another function.

We wrapped the decorator.

Anything else we saw recently that wrapped function?

Oh yes, decorators!

Let’s have some fun and write a decorator for the decorators:

def decorator_with_args(decorator_to_enhance):
    """ 
    This function is supposed to be used as a decorator.
    It must decorate an other function, that is intended to be used as a decorator.
    Take a cup of coffee.
    It will allow any decorator to accept an arbitrary number of arguments,
    saving you the headache to remember how to do that every time.
    """
    
    # We use the same trick we did to pass arguments
    def decorator_maker(*args, **kwargs):
       
        # We create on the fly a decorator that accepts only a function
        # but keeps the passed arguments from the maker.
        def decorator_wrapper(func):
       
            # We return the result of the original decorator, which, after all, 
            # IS JUST AN ORDINARY FUNCTION (which returns a function).
            # Only pitfall: the decorator must have this specific signature or it won"t work:
            return decorator_to_enhance(func, *args, **kwargs)
        
        return decorator_wrapper
    
    return decorator_maker
       

It can be used as follows:

# You create the function you will use as a decorator. And stick a decorator on it :-)
# Don"t forget, the signature is "decorator(func, *args, **kwargs)"
@decorator_with_args 
def decorated_decorator(func, *args, **kwargs): 
    def wrapper(function_arg1, function_arg2):
        print("Decorated with {0} {1}".format(args, kwargs))
        return func(function_arg1, function_arg2)
    return wrapper
    
# Then you decorate the functions you wish with your brand new decorated decorator.

@decorated_decorator(42, 404, 1024)
def decorated_function(function_arg1, function_arg2):
    print("Hello {0} {1}".format(function_arg1, function_arg2))

decorated_function("Universe and", "everything")
#outputs:
#Decorated with (42, 404, 1024) {}
#Hello Universe and everything

# Whoooot!

I know, the last time you had this feeling, it was after listening a guy saying: "before understanding recursion, you must first understand recursion". But now, don"t you feel good about mastering this?


Best practices: decorators

  • Decorators were introduced in Python 2.4, so be sure your code will be run on >= 2.4.
  • Decorators slow down the function call. Keep that in mind.
  • You cannot un-decorate a function. (There are hacks to create decorators that can be removed, but nobody uses them.) So once a function is decorated, it‚Äôs decorated for all the code.
  • Decorators wrap functions, which can make them hard to debug. (This gets better from Python >= 2.5; see below.)

The functools module was introduced in Python 2.5. It includes the function functools.wraps(), which copies the name, module, and docstring of the decorated function to its wrapper.

(Fun fact: functools.wraps() is a decorator! ‚ò∫)

# For debugging, the stacktrace prints you the function __name__
def foo():
    print("foo")
    
print(foo.__name__)
#outputs: foo
    
# With a decorator, it gets messy    
def bar(func):
    def wrapper():
        print("bar")
        return func()
    return wrapper

@bar
def foo():
    print("foo")

print(foo.__name__)
#outputs: wrapper

# "functools" can help for that

import functools

def bar(func):
    # We say that "wrapper", is wrapping "func"
    # and the magic begins
    @functools.wraps(func)
    def wrapper():
        print("bar")
        return func()
    return wrapper

@bar
def foo():
    print("foo")

print(foo.__name__)
#outputs: foo

How can the decorators be useful?

Now the big question: What can I use decorators for?

Seem cool and powerful, but a practical example would be great. Well, there are 1000 possibilities. Classic uses are extending a function behavior from an external lib (you can"t modify it), or for debugging (you don"t want to modify it because it’s temporary).

You can use them to extend several functions in a DRY’s way, like so:

def benchmark(func):
    """
    A decorator that prints the time a function takes
    to execute.
    """
    import time
    def wrapper(*args, **kwargs):
        t = time.clock()
        res = func(*args, **kwargs)
        print("{0} {1}".format(func.__name__, time.clock()-t))
        return res
    return wrapper


def logging(func):
    """
    A decorator that logs the activity of the script.
    (it actually just prints it, but it could be logging!)
    """
    def wrapper(*args, **kwargs):
        res = func(*args, **kwargs)
        print("{0} {1} {2}".format(func.__name__, args, kwargs))
        return res
    return wrapper


def counter(func):
    """
    A decorator that counts and prints the number of times a function has been executed
    """
    def wrapper(*args, **kwargs):
        wrapper.count = wrapper.count + 1
        res = func(*args, **kwargs)
        print("{0} has been used: {1}x".format(func.__name__, wrapper.count))
        return res
    wrapper.count = 0
    return wrapper

@counter
@benchmark
@logging
def reverse_string(string):
    return str(reversed(string))

print(reverse_string("Able was I ere I saw Elba"))
print(reverse_string("A man, a plan, a canoe, pasta, heros, rajahs, a coloratura, maps, snipe, percale, macaroni, a gag, a banana bag, a tan, a tag, a banana bag again (or a camel), a crepe, pins, Spam, a rut, a Rolo, cash, a jar, sore hats, a peon, a canal: Panama!"))

#outputs:
#reverse_string ("Able was I ere I saw Elba",) {}
#wrapper 0.0
#wrapper has been used: 1x 
#ablE was I ere I saw elbA
#reverse_string ("A man, a plan, a canoe, pasta, heros, rajahs, a coloratura, maps, snipe, percale, macaroni, a gag, a banana bag, a tan, a tag, a banana bag again (or a camel), a crepe, pins, Spam, a rut, a Rolo, cash, a jar, sore hats, a peon, a canal: Panama!",) {}
#wrapper 0.0
#wrapper has been used: 2x
#!amanaP :lanac a ,noep a ,stah eros ,raj a ,hsac ,oloR a ,tur a ,mapS ,snip ,eperc a ,)lemac a ro( niaga gab ananab a ,gat a ,nat a ,gab ananab a ,gag a ,inoracam ,elacrep ,epins ,spam ,arutaroloc a ,shajar ,soreh ,atsap ,eonac a ,nalp a ,nam A

Of course the good thing with decorators is that you can use them right away on almost anything without rewriting. DRY, I said:

@counter
@benchmark
@logging
def get_random_futurama_quote():
    from urllib import urlopen
    result = urlopen("http://subfusion.net/cgi-bin/quote.pl?quote=futurama").read()
    try:
        value = result.split("<br><b><hr><br>")[1].split("<br><br><hr>")[0]
        return value.strip()
    except:
        return "No, I"m ... doesn"t!"

    
print(get_random_futurama_quote())
print(get_random_futurama_quote())

#outputs:
#get_random_futurama_quote () {}
#wrapper 0.02
#wrapper has been used: 1x
#The laws of science be a harsh mistress.
#get_random_futurama_quote () {}
#wrapper 0.01
#wrapper has been used: 2x
#Curse you, merciful Poseidon!

Python itself provides several decorators: property, staticmethod, etc.

  • Django uses decorators to manage caching and view permissions.
  • Twisted to fake inlining asynchronous functions calls.

This really is a large playground.

Answer #8

Specify the keyword args linestyle and/or marker in your call to plot.

For example, using a dashed line and blue circle markers:

plt.plot(range(10), linestyle="--", marker="o", color="b")

A shortcut call for the same thing:

plt.plot(range(10), "--bo")

example1

Here is a list of the possible line and marker styles:

================    ===============================
character           description
================    ===============================
   -                solid line style
   --               dashed line style
   -.               dash-dot line style
   :                dotted line style
   .                point marker
   ,                pixel marker
   o                circle marker
   v                triangle_down marker
   ^                triangle_up marker
   <                triangle_left marker
   >                triangle_right marker
   1                tri_down marker
   2                tri_up marker
   3                tri_left marker
   4                tri_right marker
   s                square marker
   p                pentagon marker
   *                star marker
   h                hexagon1 marker
   H                hexagon2 marker
   +                plus marker
   x                x marker
   D                diamond marker
   d                thin_diamond marker
   |                vline marker
   _                hline marker
================    ===============================

edit: with an example of marking an arbitrary subset of points, as requested in the comments:

import numpy as np
import matplotlib.pyplot as plt

xs = np.linspace(-np.pi, np.pi, 30)
ys = np.sin(xs)
markers_on = [12, 17, 18, 19]
plt.plot(xs, ys, "-gD", markevery=markers_on)
plt.show()

example2

This last example using the markevery kwarg is possible in since 1.4+, due to the merge of this feature branch. If you are stuck on an older version of matplotlib, you can still achieve the result by overlaying a scatterplot on the line plot. See the edit history for more details.

Answer #9

First find the difference between the start point and the end point (here, this is more of a directed line segment, not a "line", since lines extend infinitely and don"t start at a particular point).

deltaY = P2_y - P1_y
deltaX = P2_x - P1_x

Then calculate the angle (which runs from the positive X axis at P1 to the positive Y axis at P1).

angleInDegrees = arctan(deltaY / deltaX) * 180 / PI

But arctan may not be ideal, because dividing the differences this way will erase the distinction needed to distinguish which quadrant the angle is in (see below). Use the following instead if your language includes an atan2 function:

angleInDegrees = atan2(deltaY, deltaX) * 180 / PI

EDIT (Feb. 22, 2017): In general, however, calling atan2(deltaY,deltaX) just to get the proper angle for cos and sin may be inelegant. In those cases, you can often do the following instead:

  1. Treat (deltaX, deltaY) as a vector.
  2. Normalize that vector to a unit vector. To do so, divide deltaX and deltaY by the vector"s length (sqrt(deltaX*deltaX+deltaY*deltaY)), unless the length is 0.
  3. After that, deltaX will now be the cosine of the angle between the vector and the horizontal axis (in the direction from the positive X to the positive Y axis at P1).
  4. And deltaY will now be the sine of that angle.
  5. If the vector"s length is 0, it won"t have an angle between it and the horizontal axis (so it won"t have a meaningful sine and cosine).

EDIT (Feb. 28, 2017): Even without normalizing (deltaX, deltaY):

  • The sign of deltaX will tell you whether the cosine described in step 3 is positive or negative.
  • The sign of deltaY will tell you whether the sine described in step 4 is positive or negative.
  • The signs of deltaX and deltaY will tell you which quadrant the angle is in, in relation to the positive X axis at P1:
    • +deltaX, +deltaY: 0 to 90 degrees.
    • -deltaX, +deltaY: 90 to 180 degrees.
    • -deltaX, -deltaY: 180 to 270 degrees (-180 to -90 degrees).
    • +deltaX, -deltaY: 270 to 360 degrees (-90 to 0 degrees).

An implementation in Python using radians (provided on July 19, 2015 by Eric Leschinski, who edited my answer):

from math import *
def angle_trunc(a):
    while a < 0.0:
        a += pi * 2
    return a

def getAngleBetweenPoints(x_orig, y_orig, x_landmark, y_landmark):
    deltaY = y_landmark - y_orig
    deltaX = x_landmark - x_orig
    return angle_trunc(atan2(deltaY, deltaX))

angle = getAngleBetweenPoints(5, 2, 1,4)
assert angle >= 0, "angle must be >= 0"
angle = getAngleBetweenPoints(1, 1, 2, 1)
assert angle == 0, "expecting angle to be 0"
angle = getAngleBetweenPoints(2, 1, 1, 1)
assert abs(pi - angle) <= 0.01, "expecting angle to be pi, it is: " + str(angle)
angle = getAngleBetweenPoints(2, 1, 2, 3)
assert abs(angle - pi/2) <= 0.01, "expecting angle to be pi/2, it is: " + str(angle)
angle = getAngleBetweenPoints(2, 1, 2, 0)
assert abs(angle - (pi+pi/2)) <= 0.01, "expecting angle to be pi+pi/2, it is: " + str(angle)
angle = getAngleBetweenPoints(1, 1, 2, 2)
assert abs(angle - (pi/4)) <= 0.01, "expecting angle to be pi/4, it is: " + str(angle)
angle = getAngleBetweenPoints(-1, -1, -2, -2)
assert abs(angle - (pi+pi/4)) <= 0.01, "expecting angle to be pi+pi/4, it is: " + str(angle)
angle = getAngleBetweenPoints(-1, -1, -1, 2)
assert abs(angle - (pi/2)) <= 0.01, "expecting angle to be pi/2, it is: " + str(angle)

All tests pass. See https://en.wikipedia.org/wiki/Unit_circle

Answer #10

Here"s a Python version:

from math import radians, cos, sin, asin, sqrt

def haversine(lon1, lat1, lon2, lat2):
    """
    Calculate the great circle distance in kilometers between two points 
    on the earth (specified in decimal degrees)
    """
    # convert decimal degrees to radians 
    lon1, lat1, lon2, lat2 = map(radians, [lon1, lat1, lon2, lat2])

    # haversine formula 
    dlon = lon2 - lon1 
    dlat = lat2 - lat1 
    a = sin(dlat/2)**2 + cos(lat1) * cos(lat2) * sin(dlon/2)**2
    c = 2 * asin(sqrt(a)) 
    r = 6371 # Radius of earth in kilometers. Use 3956 for miles. Determines return value units.
    return c * r

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