如何在MATLAB中从3D矩阵的每一行中选择矢量元素？

Question

I have a 3D matrix for example a 1000-by-4-by-20 matrix A and I want to select one of the 1-by-20 vectors from each row of A according to a 1000-by-1 index vector B. This index vector includes numbers form 1 to 4. Also, I do not want to use a for loop. How should I do that (with and/or without "sub2ind")?

Thank you.

Answer 1

I'm not sure this is the most elegant way, but it gets the job done:

[r,c,~]=size(A);
Q=reshape(A,r*c,[]);
P=sub2ind([r,c],[1:r]',B);
result=Q(P,:);

This will put each of the 1x1x20 vectors into the appropriate row in a 1000x20 result matrix. You can combine the last two lines if you want.

Here are the first 20 rows of a sample run with the vector B appended to the front to show which column we were supposed to take. The construction of A should be pretty obvious (first digit is the column number, next 3 are the row number - 1. All elements of the 1x1x20 vector are the same.)

  B       result
  2       2000   2000   2000   2000   2000   2000   2000   2000   2000   2000   2000   2000   2000   2000   2000   2000   2000   2000   2000   2000
  1       1001   1001   1001   1001   1001   1001   1001   1001   1001   1001   1001   1001   1001   1001   1001   1001   1001   1001   1001   1001
  4       4002   4002   4002   4002   4002   4002   4002   4002   4002   4002   4002   4002   4002   4002   4002   4002   4002   4002   4002   4002
  4       4003   4003   4003   4003   4003   4003   4003   4003   4003   4003   4003   4003   4003   4003   4003   4003   4003   4003   4003   4003
  3       3004   3004   3004   3004   3004   3004   3004   3004   3004   3004   3004   3004   3004   3004   3004   3004   3004   3004   3004   3004
  4       4005   4005   4005   4005   4005   4005   4005   4005   4005   4005   4005   4005   4005   4005   4005   4005   4005   4005   4005   4005
  3       3006   3006   3006   3006   3006   3006   3006   3006   3006   3006   3006   3006   3006   3006   3006   3006   3006   3006   3006   3006
  1       1007   1007   1007   1007   1007   1007   1007   1007   1007   1007   1007   1007   1007   1007   1007   1007   1007   1007   1007   1007
  3       3008   3008   3008   3008   3008   3008   3008   3008   3008   3008   3008   3008   3008   3008   3008   3008   3008   3008   3008   3008
  4       4009   4009   4009   4009   4009   4009   4009   4009   4009   4009   4009   4009   4009   4009   4009   4009   4009   4009   4009   4009
  2       2010   2010   2010   2010   2010   2010   2010   2010   2010   2010   2010   2010   2010   2010   2010   2010   2010   2010   2010   2010
  4       4011   4011   4011   4011   4011   4011   4011   4011   4011   4011   4011   4011   4011   4011   4011   4011   4011   4011   4011   4011
  3       3012   3012   3012   3012   3012   3012   3012   3012   3012   3012   3012   3012   3012   3012   3012   3012   3012   3012   3012   3012
  2       2013   2013   2013   2013   2013   2013   2013   2013   2013   2013   2013   2013   2013   2013   2013   2013   2013   2013   2013   2013
  4       4014   4014   4014   4014   4014   4014   4014   4014   4014   4014   4014   4014   4014   4014   4014   4014   4014   4014   4014   4014
  4       4015   4015   4015   4015   4015   4015   4015   4015   4015   4015   4015   4015   4015   4015   4015   4015   4015   4015   4015   4015
  1       1016   1016   1016   1016   1016   1016   1016   1016   1016   1016   1016   1016   1016   1016   1016   1016   1016   1016   1016   1016
  2       2017   2017   2017   2017   2017   2017   2017   2017   2017   2017   2017   2017   2017   2017   2017   2017   2017   2017   2017   2017
  4       4018   4018   4018   4018   4018   4018   4018   4018   4018   4018   4018   4018   4018   4018   4018   4018   4018   4018   4018   4018
  3       3019   3019   3019   3019   3019   3019   3019   3019   3019   3019   3019   3019   3019   3019   3019   3019   3019   3019   3019   3019

Answer 2

Here's a another way using bsxfun :

[r, c, t] = size(A);
result = A(bsxfun(@plus, (1:r).'+r*(B-1), (0:t-1)*r*c));

Answer 3

Say the vector is called A . You can index it like so:

A(1:1000,B,:)

Where index1 can range from 1 to 1000, and index2 can range from 1 to 4. The colon selects everything at that index level.