Description Usage Arguments Details Value Author(s) See Also Examples
We can formulate linear equation systems with tensors. This functions solves these systems or gives a least squares fit of minimal norm.
1 2 |
a |
The a of ax=b |
b |
The a of ax=b |
i |
The dimensions of the equation in a |
j |
The dimensions of the equation in b |
allowSingular |
A boolean, indicating the that a least squares fit should be generated with singular equations systems. |
... |
further arguments for generic use |
eps |
The limit for the smallest singular value in inversion |
by |
the operation is done in parallel for these dimensions |
A tensor can be seen as a linear mapping of a tensor to a tensor. Let denote R_i the space of real tensors with dimensions i_1...i_d.
solve.tensorSolves the equation for a_{i_1...i_dk_1...k_p}, b_{j_1...j_dl_1...l_q} and x_{k_1...k_pl_1...l_q} the equation
∑_{k_1,...,k_p} a_{i_1...i_dk_1...k_p}x_{k_1...k_pl_1...l_q}= b_{j_1...j_dl_1...l_q}
.
a tensor such that ax=b as good as possible for each combination of by values.
K. Gerald van den Boogaart
to.tensor
, svd.tensor
,
inv.tensor
, chol.tensor
,
power.tensor
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 | R1 <- matrix(rnorm(9),nrow=3)
R1i <- solve(R1)
R2 <- to.tensor(R1,c(a=3,b=3),what=1:2)
R2i <- to.tensor(R1i,c(b=3,a=3),what=1:2)
inv.tensor(R2,"a","b") - R2i
inv.tensor(R2,"a","b",allowSingular=TRUE) - R2i
inv.tensor(rep(R2,4,1,"K"),"a","b",by="K") - rep(R2i,4,1,"K")
inv.tensor(rep(R2,4,1,"K"),"a","b",by="K",allowSingular=TRUE) - rep(R2i,4,3,"K")
R3 <- to.tensor(rnorm(15),c(a=3,z=5))
mul.tensor(R2i,"b",mul.tensor(R2,"a",R3)) # R3
solve.tensor(R2i,R3[[z=1]],"a")
mul.tensor(R2,"a",R3[[z=1]])
solve.tensor(R2i,R3,"a")
mul.tensor(R2,"a",R3)
solve.tensor(R2i,R3[[z=1]],"a",allowSingular=TRUE)
mul.tensor(R2,"a",R3[[z=1]])
solve.tensor(R2i,R3,"a",allowSingular=TRUE)
mul.tensor(R2,"a",R3)
solve.tensor(rep(R2i,4,1,"K"),R3[[z=1]],"a",by="K")
rep(mul.tensor(R2,"a",R3[[z=1]]),4,1,"K")
solve.tensor(rep(R2i,4,1,"K"),rep(R3[[z=1]],4,1,"K"),"a",by="K")
rep(mul.tensor(R2,"a",R3[[z=1]]),4,1,"K")
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