CONTRACCIÓN SIMPLE Y CONTRACCIÓN DOBLE DE TENSORES

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Ronald Mijail 2023-8-29

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https://ww2.mathworks.cn/matlabcentral/answers/2014666-contraccion-simple-y-contraccion-doble-de-tensores

回答： Vedant 2023-9-12

Hola, tengo estos datos:

D=[0,1,2]

A=[1 0 2;2 1 2;1 1 0]

A(:,:,2)=[2 1 1;0 1 2;0 1 1]

A(:,:,3)=[3 1 2;0 1 1;0 0 2]

B=[1 1 1]

C=[1 2 1; 1 2 0;0 1 0]

La Operación es D⋅(A⊗B)⋅C

Hice el producto tensorial de A,B, del cual tengo un tensor de 5 dimensiones.

K=tensorprod(A,B)

y Ahora quiero hacer la contracción simple de D.K, para obtener un tensor de 4D,(L)

Al resultado anterior, quiero hacer la Contracción simple L*C, Y obtener un tensor de 3D (F)

Intente con todas las variantes de tensorprod(a,b...) y no logro hacerlo.

De paso si sería molestia, si me podrían indicarme como hago la contracción doble de tensores de difenrte orden. Gracias!

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NAVNEET NAYAN 2023-9-12

Can you please put your question in English? I am not getting anything.

Dyuman Joshi 2023-9-12

Google translation of the problem description -

Hello, I have this data:

D=[0,1,2]

A=[1 0 2;2 1 2;1 1 0]

A(:,:,2)=[2 1 1;0 1 2;0 1 1]

A(:,:,3)=[3 1 2;0 1 1;0 0 2]

B=[1 1 1]

C=[1 2 1; 1 2 0;0 1 0]

The Operation is D⋅(A⊗B)⋅C

I made the tensor product of A,B, of which I have a 5-dimensional tensor.

K=tensorprod(A,B)

and Now I want to do the simple contraction of D.K, to obtain a 4D tensor,(L)

To the previous result, I want to do the Simple Contraction L*C, and obtain a 3D tensor (F)

I tried all the variants of tensorprod(a,b...) and I can't do it.

By the way, if it would be a bother, if you could tell me how I do the double contraction of tensioners of different orders. Thank you!

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Answer 1

Vedant 2023-9-12

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2014666-contraccion-simple-y-contraccion-doble-de-tensores#answer_1308256

Hi Ronald,

Este mensaje se envía en inglés con el fin de proporcionarle una respuesta de manera más rápida. Si prefiere mantener su correspondencia en español, por favor háganoslo saber y le enviaremos una traducción del mensaje.

To perform the operations you described using tensor contractions in MATLAB, you can use the `tensorprod` function from the Tensor Toolbox. Here's how you can calculate the tensors L and F based on the given data:

% Given data

D = [0, 1, 2];

A = cat(3, [1 0 2; 2 1 2; 1 1 0], [2 1 1; 0 1 2; 0 1 1], [3 1 2; 0 1 1; 0 0 2]);

B = [1 1 1];

C = [1 2 1; 1 2 0; 0 1 0];

% Perform tensor product of A and B

K = tensorprod(A, B);

% Perform contraction of D and K

L = tensorprod(D, K, [1]);

% Perform contraction of L and C

F = tensorprod(L, C, [2]);

% Display the resulting tensor F

disp(F);

In this code, the `cat` function is used to concatenate the three matrices in A along the third dimension, creating a 3D tensor. Then, the `tensorprod` function is used to calculate the tensor product of A and B, resulting in the 5D tensor K.

Next, the `tensorprod` function is used again to perform the contraction of D and K along the first dimension, resulting in the 4D tensor L.

Finally, another `tensorprod` operation is performed to contract L and C along the second dimension, resulting in the 3D tensor F.

To perform a double contraction of tensors of different orders, you can use the `tensorprod` function multiple times, specifying the appropriate dimensions to contract. For example, to perform a double contraction of tensors A and B along dimensions 2 and 3 respectively, you can use:

result = tensorprod(A, B, [2], [3]);

Make sure to adjust the dimensions according to the specific contraction you want to perform.

Note: The Tensor Toolbox is a third-party library for MATLAB that provides various functions for tensor operations. You may need to install and add the Tensor Toolbox to your MATLAB environment before using the `tensorprod` function.