Hello,
I have the following problem:
I have a set of n matrix equations in the form of :
[b1] = [A] * [b0]
[b2] = [A] * [b1]
etc.
vertical vectors [b0], [b1], ... are GIVEN. We try to estimate matrix A. As
there are many equations (more than cells in matrix A) the system has no
solutions.
A is transition matrix (stochastic matrix) or markov process, so the sum of
each row = 1 and each entry is probability (aij in <0;1>). I tried to
estimate A by using constrOptim the following way, but apparently it won't
work on matrices.
fr <- function(x) {
x%*%matrix(c(2,5,6), 3,1)-matrix(c(5,4,2), 3,1)
x%*%matrix(c(6,2,3), 3,1)-matrix(c(1,1,1), 3,1)
x%*%matrix(c(6,1,2), 3,1)-matrix(c(3,4,1), 3,1)
}
constrOptim(matrix(c(0.5,0.4,0.1,0.2,0.3,0.5,0.5,0.2,0.3),3,3), fr, NULL,
ui=matrix(c(1,0,0,0,1,0,0,0,1),3,3), ci=matrix(c(-.00001
,-.00001,-.00001,-.00001,-.00001,-.00001,-.00001,-.00001,-.00001),3,3))
It produces the following error:
"Error in ui %*% theta : non-conformable arguments"
Kind regards and thanks for help
Jacob
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