He hana koʻikoʻi ka hoʻonui matrix ma ka algebra linear.
Hoʻohana maʻamau mākou i nā noi he nui e like me ka hoʻoili kiʻi, ke aʻo ʻana i ka mīkini, a me nā mea hou aku. ʻO NumPy kahi pūʻolo Python kaulana no ka helu ʻepekema.
Eia nō naʻe, i kēia pou, e nānā mākou i nā ʻano hana like ʻole no ka hoʻonui ʻana i ka matrix ma Python me ka hoʻohana ʻole ʻana iā NumPy.
E hoʻohana mākou pūnana piko, ka hana palapala 'āina (), a me ka hoʻomaopopo papa inoa.
Eia kekahi, e nānā mākou i nā pono a me nā hemahema o kēlā me kēia hoʻolālā, a me ka manawa e hoʻohana ai i kēlā me kēia. Inā he mea hou ʻoe i ka algebra linear a makemake ʻoe e aʻo hou e pili ana i ka hoʻonui matrix; e hoomau i ka heluhelu.
Ma hea mākou e hoʻohana ai i ka hoʻonui matrix?
Hoʻohana ʻia ka hoʻonui matrix ma polokalamu kamepiula e hoʻololi i nā kiʻi 2D a me 3D. No ka laʻana, hiki iā ʻoe ke hoʻololi, hoʻonui, a unuhi i nā mea ma ka pale. Hoʻohana ʻia nā matrixes i ka hoʻoili kiʻi e hōʻike i nā kiʻi ma ke ʻano he pūʻulu o nā pika. Ma waho aʻe, hiki ke hoʻohana ʻia nā matrix e hana i nā hana e like me ke kānana kiʻi.
Hoʻohana pū mākou i nā matrixes ma aʻo aʻo. Hiki iā lākou ke kōkua iā mākou e hōʻike i ka ʻikepili a me nā ʻāpana hoʻohālike. Hiki iā mākou ke hana i nā hana he nui, e like me nā huahana dot a me nā huahana matrix-vector.
ʻOiaʻiʻo, ʻoi aku ka maikaʻi o kēia hana i nā hana ʻepekema. Hiki iā mākou ke hoʻohana iā ia ma ka physics a me ka ʻenekinia e wehewehe i ka nui kino. No laila, hiki iā mākou ke hana me nā vectors a me nā tensor.
No ke aha e koho ʻole ai mākou e hoʻohana i ka NumPy?
ʻOiai ʻo NumPy he Hale waihona puke Python, ʻaʻole ia he koho kūpono no ka hoʻonui ʻana i ka matrix. ʻAʻole paha mākou e koho e hoʻohana i ka NumPy no nā kumu e like me ka nui a me ka hilinaʻi, ke aʻo ʻana, a me nā ʻōnaehana hoʻoilina.
ʻOi aku ka maikaʻi o ka hoʻohana ʻana i nā hana i kūkulu ʻia a Python a i ʻole ka hoʻomohala ʻana i nā code maʻamau i kekahi mau manawa. He mea koʻikoʻi ia e hoʻomaopopo, akā naʻe, he hale waihona puke ikaika ʻo NumPy. Ma waho aʻe, hiki iā ʻoe ke hoʻohana iā ia no ka hoʻonui matrix.
I kēia manawa, e nānā kākou pehea e hiki ai iā mākou ke hoʻokō i ka hoʻonui matrix me ka ʻole o NumPy.
ʻO ke ʻano puka lou nested
Hoʻohana ka ʻenehana nested loops i nā puka nested e hoʻokō i ka hoʻonui matrix ma Python. Hoʻololi ka hana ma luna o kēlā me kēia matrix element. A, hoʻomāhuahua ia iā lākou me ka hoʻohana ʻana i nā pūnana puka. Hoʻihoʻi ka hana i ka hopena, i mālama ʻia i loko o kahi matrix hou.
He maʻalahi kēia ala e ʻike ai. Akā naʻe, ʻaʻole ʻoi aku ka maikaʻi e like me nā ala ʻē aʻe, ʻoi aku no nā matrices nui aʻe. Akā naʻe, he koho maikaʻi loa ia iā ʻoe inā he mea hou ʻoe i ka algebra linear.
def matrix_multiplication(A, B):
# Determine the matrices' dimensions.
rows_A = len(A)
cols_A = len(A[0])
rows_B = len(B)
cols_B = len(B[0])
# E hoʻonoho i ka matrix hopena i nā zeroes.
result = [[0 for row in range(cols_B)] for col in
range(rows_A)]
# Iterate through rows of A
for s in range(rows_A):
# Iterate through columns of B
for j in range(cols_B):
# Iterate through rows of B
for k in range(cols_A):
result[s][j] += A[s][k] * B[k][j]
return result
E loaʻa iā mākou kahi laʻana o ka hana ʻana i kēia. Hiki iā ʻoe ke hoʻohui i kēia mau laina code ma lalo nei e hoʻāʻo i kēia hiʻohiʻona.
# Sample matrices
A = [[1, 4, 3], [4, 9, 6]]
B = [[7, 8], [9, 10], [11, 12]]
# Perform matrix multiplication
result = matrix_multiplication(A, B)
# Print the result
print(result)
# Output: [[76, 84], [175, 194]]
maika:
- Maʻalahi e hoʻomaopopo.
- Maikaʻi no ka poʻe hou a i ʻole ka poʻe e ʻimi nei i ka ʻike hohonu o ka hoʻonui ʻana i ka matrix.
keakea:
- ʻAʻole maikaʻi e like me nā ʻenehana ʻē aʻe, ʻoi aku no nā matrices nui aʻe.
- ʻAʻole hiki ke heluhelu ʻia e like me nā ala ʻē aʻe.
palapala () hana hana
Hāʻawi ke ʻano hana palapala () i kahi ala ʻē aʻe no ka hoʻonui ʻana i ka matrix ma Python. Ma kēia ala, hoʻohana mākou i ka hana palapala i kūkulu ʻia (). No laila, hoʻohana mākou i kahi hāmeʻa hoʻolālā hana e pili ana i kahi hana i hāʻawi ʻia i kēlā me kēia mea iterable (papa inoa, tuple, etc.). Eia kekahi, ʻae ka hana palapala () i ʻelua mau palena, kahi hana a me kahi iterable. A, hoʻihoʻi ia i kahi iterator e pili ana i ka hana i kēlā me kēia mea iterable.
Ma kēia ala, hele mākou i kēlā me kēia lālā o ka matrix a hana i ka hoʻonui ʻana me ka hana nested map().
Hoʻohana ʻia ka hana zip () e hoʻololi i kēlā me kēia mea o nā matrices i ka like.
ʻO ka hope, hoʻohana ʻia ka hana sum() e hoʻohui i nā hopena.
def matrix_multiplication(A, B):
# To get the dimensions of the matrices
rows_A = len(A)
cols_A = len(A[0])
rows_B = len(B)
cols_B = len(B[0])
# We use map() function for multiplication.
result = [[sum(a * b for a, b in zip(row_a, col_b)) for
col_b in zip(*B)] for row_a in A]
return result
I kēia manawa, hiki iā mākou ke hoʻāʻo i kā mākou code me kahi laʻana.
# Example matrices
A = [[3, 2, 3], [4, 5, 6]]
B = [[7, 8], [9, 10], [11, 12]]
# Use map() function to perform matrix multiplication
result = list(map(lambda x: list(map(lambda y: sum(i*j
for i,j in zip(x,y)), zip(*B))), A))
# Print the result
print(result)
# Output: [[72, 80], [139, 154]]
pono
- ʻOi aku ka maikaʻi ma mua o ka hoʻokokoke ʻana i nā puka lou
- Hoʻohana ia i ka hoʻolālā hana e maʻalahi ai ke code.
keakea
- ʻO kekahi poʻe i kamaʻāina ʻole i ka hoʻolālā hana hiki ke ʻike i ka liʻiliʻi o ka heluhelu ʻana.
- ʻAʻole hiki ke hoʻomaopopo ʻia ma mua o ka ʻenehana nested loops.
Papa inoa o ka hoomaopopo ana
Hiki i ka ʻike papa inoa iā ʻoe ke hana i kahi papa inoa hou ma kahi laina code. No laila, e pili ana kēia i kahi ʻōlelo i kēlā me kēia lālā o kahi papa inoa e kū nei.
Ma kēia ala, hana ʻia ka hoʻonui ʻana ma ka hoʻonui pinepine ʻana i kēlā me kēia lālā matrix. Ke hoʻohana nei mākou i ka ʻike papa inoa papa.
# Sample matrices
A = [[1, 12, 3], [14, 5, 6]]
B = [[7, 8], [9, 10], [12, 12]]
# Matrix multiplication using list comprehension
result = [[sum(A[i][k] * B[k][j] for k in range(len(A[0])))
for j in range(len(B[0]))] for i in range(len(A))]
# Print the result
print(result)
[[151, 164], [215, 234]]
maika
- Hoʻohālikelike ʻia me ka palapala ʻāina () ʻano hana, ʻoi aku ka pōkole a hiki ke heluhelu ʻia.
keakea
- ʻAʻole ʻoi aku ka maikaʻi ma mua o ka hoʻohana ʻana i ka hana palapala () no nā matrices nui.
- ʻOi aku ka paʻakikī ma mua o ka nested loops approach.
Panina
Ma kēia pou, ua nānā mākou i nā mea ʻē aʻe i ka hoʻohana ʻana iā NumPy i ka hoʻonui ʻana i nā matrices ma Python. Hana mākou i ka hoʻonui matrix ma nā puka puka pūnana, ka hana palapala () i kūkulu ʻia, a me ka ʻike papa inoa.
ʻO ka hoʻolālā maikaʻi loa e hilinaʻi i nā pono kūikawā o kāu papahana.
Loaʻa i kēlā me kēia hoʻolālā nā pono a me nā pōʻino. No ka hōʻoia i ka holo pono ʻana o ka hana, pono e hoʻohui i kekahi mau hihia hoʻāʻo me nā ana matrix like ʻole a me nā waiwai.
Pono ʻoe e hoʻokomo i kekahi mau hoʻokolohua hana e hoʻohālikelike ai i ka maikaʻi o kēia mau ʻano hana.
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