Collapsing and Scaling Tensors
The tensor and sptensor classes support the notion of collapsing and scaling dimensions.
Contents
Examples of collapsing a tensor
X = tenrand([4 3 2]) %<-- Generate some data.
X is a tensor of size 4 x 3 x 2 X(:,:,1) = 0.5700 0.9278 0.8453 0.8867 0.6551 0.3683 0.9025 0.2050 0.1861 0.9622 0.2478 0.5658 X(:,:,2) = 0.6551 0.6102 0.2893 0.8380 0.8876 0.5269 0.0822 0.3187 0.7263 0.0506 0.5006 0.4659
Y = collapse(X,[2 3]) %<-- Sum of entries in each mode-1 slice.
Y is a tensor of size 4 Y(:) = 3.8977 4.1626 2.4208 2.7929
Y = collapse(X,-1) %<-- Same as above.
Y is a tensor of size 4 Y(:) = 3.8977 4.1626 2.4208 2.7929
Z = collapse(X,2) %<-- Sum of entries in each row fiber.
Z is a tensor of size 4 x 2 Z(:,:) = 2.3430 1.5546 1.9101 2.2525 1.2936 1.1272 1.7758 1.0171
collapse(X,1:3) %<-- Sum of all entries.
ans = 13.2740
Alternate accumulation functions for tensor
Y = collapse(X,[1 2],@max) %<-- Max entry in each mode-3 slice.
Y is a tensor of size 2 Y(:) = 0.9622 0.8876
Z = collapse(X,-3,@mean) %<-- Average entry in each mode-3 slice.
Z is a tensor of size 2 Z(:) = 0.6102 0.4960
Examples of collapsing a sptensor
X = sptenrand([4 3 2],6) %<-- Generate some data.
X is a sparse tensor of size 4 x 3 x 2 with 6 nonzeros (1,1,2) 0.9194 (1,3,1) 0.9742 (3,1,1) 0.9788 (4,2,1) 0.4579 (4,3,1) 0.1540 (4,3,2) 0.9585
Y = collapse(X,[2 3]) %<-- Sum of entries in each mode-1 slice.
Y =
1.8936
0
0.9788
1.5704
Y = collapse(X,-1) %<-- Same as above.
Y =
1.8936
0
0.9788
1.5704
Z = collapse(X,2) %<-- Sum of entries in each row fiber.
Z is a sparse tensor of size 4 x 2 with 5 nonzeros (1,1) 0.9742 (1,2) 0.9194 (3,1) 0.9788 (4,1) 0.6119 (4,2) 0.9585
collapse(X,1:3) %<-- Sum of all entries.
ans =
4.4428
Alternate accumulation functions for sptensor
Y = collapse(X,[1 2],@min) %<-- Min *nonzero* entry in each mode-3 slice.
Y =
0.1540
0.9194
Z = collapse(X,-3,@mean) %<-- Average *nonzero* entry in each mode-3 slice.
Z =
0.6412
0.9389
Scaling a tensor in different modes
X = tenones([3,4,5]); %<-- Generate data S = 10 * [1:5]'; Y = scale(X,S,3) %<-- Scale in mode-3
Y is a tensor of size 3 x 4 x 5 Y(:,:,1) = 10 10 10 10 10 10 10 10 10 10 10 10 Y(:,:,2) = 20 20 20 20 20 20 20 20 20 20 20 20 Y(:,:,3) = 30 30 30 30 30 30 30 30 30 30 30 30 Y(:,:,4) = 40 40 40 40 40 40 40 40 40 40 40 40 Y(:,:,5) = 50 50 50 50 50 50 50 50 50 50 50 50
S = tensor(10 * [1:5]',5); Y = scale(X,S,3) %<-- First argument is a tensor.
Y is a tensor of size 3 x 4 x 5 Y(:,:,1) = 10 10 10 10 10 10 10 10 10 10 10 10 Y(:,:,2) = 20 20 20 20 20 20 20 20 20 20 20 20 Y(:,:,3) = 30 30 30 30 30 30 30 30 30 30 30 30 Y(:,:,4) = 40 40 40 40 40 40 40 40 40 40 40 40 Y(:,:,5) = 50 50 50 50 50 50 50 50 50 50 50 50
S = tensor(1:12,[3 4]); Y = scale(X,S,[1 2]) %<-- Scale in two modes.
Y is a tensor of size 3 x 4 x 5 Y(:,:,1) = 1 4 7 10 2 5 8 11 3 6 9 12 Y(:,:,2) = 1 4 7 10 2 5 8 11 3 6 9 12 Y(:,:,3) = 1 4 7 10 2 5 8 11 3 6 9 12 Y(:,:,4) = 1 4 7 10 2 5 8 11 3 6 9 12 Y(:,:,5) = 1 4 7 10 2 5 8 11 3 6 9 12
S = tensor(1:12,[3 4]); Y = scale(X,S,-3) %<-- Same as above.
Y is a tensor of size 3 x 4 x 5 Y(:,:,1) = 1 4 7 10 2 5 8 11 3 6 9 12 Y(:,:,2) = 1 4 7 10 2 5 8 11 3 6 9 12 Y(:,:,3) = 1 4 7 10 2 5 8 11 3 6 9 12 Y(:,:,4) = 1 4 7 10 2 5 8 11 3 6 9 12 Y(:,:,5) = 1 4 7 10 2 5 8 11 3 6 9 12
S = tensor(1:60,[3 4 5]); Y = scale(X,S,1:3) %<-- Scale in every mode.
Y is a tensor of size 3 x 4 x 5 Y(:,:,1) = 1 4 7 10 2 5 8 11 3 6 9 12 Y(:,:,2) = 13 16 19 22 14 17 20 23 15 18 21 24 Y(:,:,3) = 25 28 31 34 26 29 32 35 27 30 33 36 Y(:,:,4) = 37 40 43 46 38 41 44 47 39 42 45 48 Y(:,:,5) = 49 52 55 58 50 53 56 59 51 54 57 60
Y = S .* X %<-- Same as above.
Y is a tensor of size 3 x 4 x 5 Y(:,:,1) = 1 4 7 10 2 5 8 11 3 6 9 12 Y(:,:,2) = 13 16 19 22 14 17 20 23 15 18 21 24 Y(:,:,3) = 25 28 31 34 26 29 32 35 27 30 33 36 Y(:,:,4) = 37 40 43 46 38 41 44 47 39 42 45 48 Y(:,:,5) = 49 52 55 58 50 53 56 59 51 54 57 60
Scaling a sptensor in different modes
X = ones(sptenrand([3 4 5], 10)) %<-- Generate data.
X is a sparse tensor of size 3 x 4 x 5 with 10 nonzeros (1,3,1) 1 (1,3,5) 1 (2,1,2) 1 (2,2,1) 1 (2,3,3) 1 (3,2,1) 1 (3,2,4) 1 (3,3,4) 1 (3,4,3) 1 (3,4,5) 1
S = 10 * [1:5]'; Y = scale(X,S,3) %<-- Scale in one mode.
Y is a sparse tensor of size 3 x 4 x 5 with 10 nonzeros (1,3,1) 10 (1,3,5) 50 (2,1,2) 20 (2,2,1) 10 (2,3,3) 30 (3,2,1) 10 (3,2,4) 40 (3,3,4) 40 (3,4,3) 30 (3,4,5) 50
S = tensor(10 * [1:5]',5); Y = scale(X,S,3) %<-- Same as above.
Y is a sparse tensor of size 3 x 4 x 5 with 10 nonzeros (1,3,1) 10 (1,3,5) 50 (2,1,2) 20 (2,2,1) 10 (2,3,3) 30 (3,2,1) 10 (3,2,4) 40 (3,3,4) 40 (3,4,3) 30 (3,4,5) 50
S = tensor(1:12,[3 4]); Y = scale(X,S,[1 2]) %<-- Scale in two modes.
Y is a sparse tensor of size 3 x 4 x 5 with 10 nonzeros (1,3,1) 7 (1,3,5) 7 (2,1,2) 2 (2,2,1) 5 (2,3,3) 8 (3,2,1) 6 (3,2,4) 6 (3,3,4) 9 (3,4,3) 12 (3,4,5) 12
S = tensor(1:12,[3 4]); Y = scale(X,S,-3) %<-- Same as above.
Y is a sparse tensor of size 3 x 4 x 5 with 10 nonzeros (1,3,1) 7 (1,3,5) 7 (2,1,2) 2 (2,2,1) 5 (2,3,3) 8 (3,2,1) 6 (3,2,4) 6 (3,3,4) 9 (3,4,3) 12 (3,4,5) 12
Z = scale(X,Y,1:3) %<-- Scale by a sparse tensor.
Z is a sparse tensor of size 3 x 4 x 5 with 10 nonzeros (1,3,1) 7 (1,3,5) 7 (2,1,2) 2 (2,2,1) 5 (2,3,3) 8 (3,2,1) 6 (3,2,4) 6 (3,3,4) 9 (3,4,3) 12 (3,4,5) 12
X .* Y %<-- Same as above.
ans is a sparse tensor of size 3 x 4 x 5 with 10 nonzeros (1,3,1) 7 (1,3,5) 7 (2,1,2) 2 (2,2,1) 5 (2,3,3) 8 (3,2,1) 6 (3,2,4) 6 (3,3,4) 9 (3,4,3) 12 (3,4,5) 12