kron .\. ./.
Kronecker left and right divisions
Syntax
X = A .\. B // while B = A .*. X X = B ./. A // while B = X .*. A
Arguments
- X
- Array of decimal or complex numbers, of size (x1,x2,..).
- A
- Array of decimal or complex numbers, of size (a1,a2,..), with any number of dimensions.
- B
- Array of decimal or complex numbers, of size (a1*x1, a2*x2,..), with any number of dimensions.
Description
B ./. A computes and provides the array
X such that B = X .*. A.
A .\. B computes and provides the array
X such that B = A .*. X.
In both cases, each X coefficient is constrained by length(A)
proportional equations. The divisions are so performed in a least-square way
minimizing norm(A.*.X - B, 2) or norm(X.*.A - B, 2).
Examples
Simple example with low and crossed dimensions:
A = 0:3 B = [1 10 100]' P = A .*. B
--> A = 0:3 A = 0. 1. 2. 3. --> B = [1 10 100]' B = 1. 10. 100. --> P = A .*. B P = 0. 1. 2. 3. 0. 10. 20. 30. 0. 100. 200. 300. --> P ./. B ans = 0. 1. 2. 3. --> A .\. P ans = 1. 10. 100.
Still with some low dimensions, and with noisy data:
A = 1:3 B = 0:4 P = A .*. B P ./. B A .\. P // Let's add some additive noise, and process noisy data: P = P + grand(P, "unf", -0.3, 0.3) P ./. B A .\. P
--> A = 1:3
A =
1. 2. 3.
--> B = 0:4
B =
0. 1. 2. 3. 4.
--> P = A .*. B
P =
0. 1. 2. 3. 4. 0. 2. 4. 6. 8. 0. 3. 6. 9. 12.
--> P ./. B
ans =
1. 2. 3.
--> A .\. P
ans =
0. 1. 2. 3. 4.
--> // Let's add some additive noise, and process noisy data:
--> P = P + grand(P, "unf", -0.3, 0.3)
P =
column 1 to 8
-0.2793324 1.0981633 1.9632466 2.775538 3.9289351 -0.1738746 2.1593101 3.7307299
column 9 to 15
6.1771199 7.7218648 -0.1878764 2.9452387 5.9938586 8.9747935 11.967352
--> P ./. B
ans =
0.9689004 1.9679863 2.9908914
--> A .\. P
ans =
-0.0850508 1.0180357 1.9575916 3.0038685 3.9481943
With hypermatrices:
M = [-9.4 -7. 8.6 -2.3 0.1 -3. -0.4 -0.7 -6.9 -5.3 3.6 -6.6 ]; H = cat(3,-2,3) P = M .*. H P ./. H M .\. P
M = -9.4 -7. 8.6 -2.3 0.1 -3. -0.4 -0.7 -6.9 -5.3 3.6 -6.6 --> H = cat(3,-2,3) H = (:,:,1) -2. (:,:,2) 3. --> P = M .*. H P = (:,:,1) 18.8 14. -17.2 4.6 -0.2 6. 0.8 1.4 13.8 10.6 -7.2 13.2 (:,:,2) -28.2 -21. 25.8 -6.9 0.3 -9. -1.2 -2.1 -20.7 -15.9 10.8 -19.8 --> P ./. H ans = -9.4 -7. 8.6 -2.3 0.1 -3. -0.4 -0.7 -6.9 -5.3 3.6 -6.6 --> M .\. P ans = (:,:,1) -2. (:,:,2) 3.
See Also
History
| バージョン | 記述 |
| 6.1.0 | .\. and ./. actually implemented, for decimal and complex numbers. |
| Report an issue | ||
| << kron .*. | matrixoperations | max >> |