An warware: wanda ya samo asali na pytorch mai aiki da yawa

Nazarin da nazarin ayyukan lissafi wani muhimmin al'amari ne na fannoni daban-daban, gami da aikin injiniya, kimiyyar lissafi, da kimiyyar kwamfuta. Musamman, abubuwan da suka samo asali na ayyuka masu yawa suna da aikace-aikace da yawa kuma suna taka muhimmiyar rawa wajen fahimtar halaye da kaddarorin waɗannan ayyuka. Wannan labarin yana nufin samar da zurfin bincike game da samuwar ayyuka masu yawa a cikin mahallin shirye-shiryen Python. Za mu yi nazarin misali-hannun-on misali, yin bayanin kowane mataki na tsari da mahimman abubuwan da ke tattare da samun aiki mai iya canzawa.

Matsala: Samar da Aiki Mai Daban-daban

A fagen lissafi, aiki mai iya canzawa shine wanda ya dogara da mabambanta fiye da ɗaya. Don fara aiki tare da irin wannan aikin, da farko muna buƙatar fahimtar manufar abubuwan ban sha'awa. Ƙarƙashin ɓangarori shine abin da ya samo asali na aiki mai iya canzawa dangane da mai canzawa ɗaya, yana kula da duk sauran masu canji a matsayin masu canzawa. Ana kiran tsarin gano ɓangarori daban-daban masu alaƙa da kowane maɗaukaki da ke da hannu a cikin aiki mai yawa samuwar aikin multivariable.

Bari mu yi la'akari da misali don mafi kyawun kwatanta manufar. Muna da aiki:

““
f(x, y) = 3x^2*y + x*y^2
““

Manufarmu ita ce nemo abin da aka samo asali game da x (∂f/∂x) da kuma abin da ya shafi y (∂f/∂y).

Maganin Python don Samar da Aiki Mai Sauri

Don ƙididdige abubuwan da suka samo asali a cikin Python, za mu yi amfani da ɗakin karatu mai ƙarfi SymPy, wanda ke ba da ƙaƙƙarfan yanayi don lissafi na alama.

Da farko, muna buƙatar shigar da ɗakin karatu ta amfani da pip:

““
pip shigar sympy
““

Yanzu, zamu iya rubuta shirin Python don ƙididdige abubuwan da suka samo asali:

import sympy as sp

x, y = sp.symbols('x y')
f = 3*x**2*y + x*y**2

partial_derivative_x = sp.diff(f, x)
partial_derivative_y = sp.diff(f, y)

print("∂f/∂x:", partial_derivative_x)
print("∂f/∂y:", partial_derivative_y)

Bayan aiwatar da lambar, za mu sami abubuwan ban sha'awa:

““
∂f/∂x: 6*x*y + y**2
∂f/∂y: 3*x**2 + 2*x*y
““

Bayanin mataki-mataki na Code

1. Da farko, muna shigo da ɗakin karatu na SymPy:

"'shigo da tausayi kamar sp"'

2. Na gaba, muna ayyana masu canji x da y a matsayin alamomi:

"'x, y = sp.alamomi('x y')"'

3. Sa'an nan, mun ayyana aikin multivariable f(x, y):

“`f = 3*x**2*y + x*y*2“`

4. Bayan ayyana aikin, za mu ci gaba da ƙididdige abubuwan ban sha'awa game da x da y:

““
partial_derivative_x = sp.diff(f, x)
partial_derivative_y = sp.diff(f, y)
““

5. A ƙarshe, muna buga sakamakon:

““
buga ("∂f/∂x:", partial_derivative_x)
buga ("∂f/∂y:", partial_derivative_y)
““

Laburaren SymPy: Kayan aiki mai ƙarfi don Lissafin Alama

The SymPy library kayan aiki ne mai mahimmanci ga duk wanda ke aiki da lissafi na alama a Python. Yana ba da damar sarrafa maganganun lissafi mara kyau, sauƙaƙawa, warware daidaito, da ƙari mai yawa. A cikin misalinmu, mun yi amfani da SymPy don ƙididdige abubuwan ban sha'awa, amma ƙarfinsa ya wuce hakan.

• Maganin Magana: Gyara maganganun lissafi ta hanyar alama, ba da damar ayyuka daban-daban kamar musanyawa, haɓakawa, da ƙima.
• Sauƙaƙe: Sauƙaƙe rikitattun maganganu zuwa mafi ƙarancin tsari ko canza su zuwa takamaiman tsari.
• Magance Equation: Warware ma'auni na algebra a alamance, gami da layin layi, da yawa, da tsarin daidaitawa.
• Ƙwararren Lissafi: Yi ayyuka masu alaƙa da haɗin kai, ka'idar jadawali, da ka'idar lamba.

A ƙarshe, fahimtar ma'anar abubuwan da aka samo asali a cikin ayyuka masu yawa, tare da amfani da Python da ɗakin karatu na SymPy, yana da nau'o'in aikace-aikace masu yawa a fannoni kamar aikin injiniya, kimiyyar lissafi, da kimiyyar kwamfuta. Sanin kanku da waɗannan kayan aikin na iya haɓaka ikon ku na tinkarar ƙalubalen ilmin lissafi da haɓaka ƙwarewar ku wajen warware matsala.