*Memos:
- My post explains Matrix and Element-wise multiplication in PyTorch.
- My post explains the functions and operators for Dot and Matrix multiplication and Element-wise calculation in PyTorch.
<Dot multiplication(product)>
- Dot multiplication is the multiplication of 1D tensors(arrays).
- The rule which you must follow to do dot multiplication is the number of the rows of
AandBtensor(array) must be 1 and the number of the columns must be the same.
<A> <B>
[a, b, c] x [d, e, f] = ad+be+cf
1 row 1 row
3 columns 3 columns
[2, -7, 4] x [-5, 0, 8] = 22
2x(-5)-7x0+4x8
[2, -7, 4]
x x x
[-5, 0, 8]
||
[-10, 0, 32]
-10+0+32
||
22
In PyTorch with dot(), matmul() or @:
*Memos:
-
dot()can do dot multiplication with two of 1D tensors. -
matmul()or@can do dot, matrix-vector or matrix multiplication with two of 1D or more D tensors.
import torch
tensor1 = torch.tensor([2, -7, 4])
tensor2 = torch.tensor([-5, 0, 8])
torch.dot(input=tensor1, tensor=tensor2)
tensor1.dot(tensor=tensor2)
torch.matmul(input=tensor1, other=tensor2)
tensor1.matmul(other=tensor2)
tensor1 @ tensor2
# tensor(22)
In NumPy with dot(), matmul() or @:
*Memos:
-
dot()can do dot, matrix-vector or matrix multiplication with two of 0D or more D arrays. *dot()is basically used to multiply 1D arrays. -
matmul()or@can do dot, matrix-vector or matrix multiplication with two of 1D or more D arrays.
import numpy
array1 = numpy.array([2, -7, 4])
array2 = numpy.array([-5, 0, 8])
numpy.dot(array1, array2)
array1.dot(array2)
numpy.matmul(array1, array2)
array1 @ array2
# 22
<Matrix-vector multiplication(product)>
- Matrix-vector multiplication is the multiplication of a 2D or more D tensor(array) and 1D tensor(array). *The order must be a 2D or more D tensor and 1D tensor but not a 1D tensor and 2D or more D tensor(array).
- The rule which you must follow to do matrix-vector multiplication is the number of the columns of
AandBtensor(array) must be the same.
A 2D and 1D tensor(array):
<A> <B>
[[a, b, c], [d, e, f]] x [g, h, i] = [ag+bh+ci, dg+eh+fi]
2 rows 1 row
(3) columns (3) columns
[[2, -7, 4], [6, 3, -1]] x [-5, 0, 8] = [22, -38]
[2x(-5)-7x0+4x8, 6x(-5)+3x0-1x8]
[[2, -7, 4], [6, 3, -1]]
x x x x x x
[-5, 0, 8] [-5, 0, 8]
|| ||
[-10, 0, 32] [-30, 0, -8]
-10+0+32 -30+0-8
|| ||
[22, -38]
In PyTorch with matmul(), mv() or @. *mv() can do matrix-vector multiplication with a 2D tensor and 1D tensor:
import torch
tensor1 = torch.tensor([[2, -7, 4], [6, 3, -1]])
tensor2 = torch.tensor([-5, 0, 8])
torch.matmul(input=tensor1, other=tensor2)
tensor1.matmul(other=tensor2)
torch.mv(input=tensor1, vec=tensor2)
tensor1.mv(vec=tensor2)
tensor1 @ tensor2
# tensor([22, -38])
In NumPy with dot(), matmul() or @:
import numpy
array1 = numpy.array([[2, -7, 4], [6, 3, -1]])
array2 = numpy.array([-5, 0, 8])
numpy.dot(array1, array2)
array1.dot(array2)
numpy.matmul(array1, array2)
array1 @ array2
# array([22, -38])
A 3D and 1D tensor(array):
*The 3D tensor(array) of A has three of 2D tensors(arrays) which have 2 rows and 3 columns each.
<A> <B>
[[[a, b, c], [d, e, f]], x [s, t, u] = [[[as+bt+cu, ds+et+fu]],
[[g, h, i], [j, k, l]], [[gs+ht+iu, js+kt+lu]],
[[m, n, o], [p, q, r]]] [[ms+nt+ou, ps+qt+ru]]]
2 rows 1 row
(3) columns (3) columns
[[[2, -7, 4], [6, 3, -1]] x [-5, 0, 8] = [[22, -38],
[[-4, 9, 0], [5, 8, -2]], [20, -41],
[[-6, 7, 1], [0, -9, 5]]] [38, 40]])
[[2x(-5)-7x0+4x8, 6x(-5)+3x0-1x8],
[-4x(-5)+9x0+0x8, 5x(-5)+8x0-2x8],
[-6x(-5)+7x0+1x8, 0x(-5)-9x0+5x8]]
In PyTorch with matmul() or @:
import torch
tensor1 = torch.tensor([[[2, -7, 4], [6, 3, -1]],
[[-4, 9, 0], [5, 8, -2]],
[[-6, 7, 1], [0, -9, 5]]])
tensor2 = torch.tensor([-5, 0, 8])
torch.matmul(input=tensor1, other=tensor2)
tensor1.matmul(other=tensor2)
tensor1 @ tensor2
# tensor([[22, -38],
# [20, -41],
# [38, 40]])
In NumPy with dot(), matmul() or @:
import numpy
array1 = numpy.array([[[2, -7, 4], [6, 3, -1]],
[[-4, 9, 0], [5, 8, -2]],
[[-6, 7, 1], [0, -9, 5]]])
array2 = numpy.array([-5, 0, 8])
numpy.dot(array1, array2)
array1.dot(array2)
numpy.matmul(array1, array2)
array1 @ array2
# array([[22, -38],
# [20, -41],
# [38, 40]])
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