implement [] in mxAlgebra/mxConstraint

It's handy, but not available in algebra or the algebra of a constraint:


# ======================================
# = 1. Try bracket access in mxAlgebra =
# ======================================
nOrd = 3
nVar = 5
fit1 = mxModel("fit1",
mxMatrix(name="a" , "Full", nrow=nVar, ncol=nVar, free=T, values=1:25),
mxMatrix(name="unit", "Unit", nrow=nOrd, ncol=1),
mxAlgebra(diag2vec(a)[1:3], name = "ordElements"),
mxConstraint(name = "con1", ordElements == unit),
mxFitFunctionAlgebra("ordElements")
)
fit1 = mxRun(fit1)
# Error: In algebra 'fit1.ordElements' could not find function with name [ and 2 arguments.

# =========================================
# = 1. Try bracket access in mxConstraint =
# =========================================
fit1 = mxModel("fit1",
mxMatrix(name="a" , "Full", nrow=nVar, ncol=nVar, free=T, values=1:25),
mxMatrix(name="unit", "Unit", nrow=nOrd, ncol=1),
mxAlgebra(diag2vec(a), name = "diagElements"),
mxConstraint(name = "con1", diagElements[1:3] == unit),
mxFitFunctionAlgebra("ordElements")
)
fit1 = mxRun(fit1)
# Error: In algebra 'fit1.untitled52' could not find function with name [ and 2 arguments.


One kind of work-around is that Bracket access of a single cell "works" because it is interpreted as a bracket-style matrix address, so this is OK:


# Goal = constrain third cell on diagonal of "a" == 1
fit1 = mxModel("fit1",
mxMatrix(name="a", "Full", nrow=5, ncol=5, free=T, values=1:25),
# next line fails with error
mxConstraint(a[1,1] == 1, name = "out1"),
mxConstraint(a[2,2] == 1, name = "out2"),
mxConstraint(a[3,3] == 1, name = "out3"),
mxFitFunctionAlgebra("a")
)
fit1 = mxRun(fit1); mxEval(a, fit1)

# Running fit1
# Warning message:
# In model 'fit1' Optimizer returned a non-zero status code 1. The final iterate satisfies the optimality
# conditions to the accuracy requested, but the sequence of iterates has not yet converged. Optimizer was
# terminated because no further improvement could be made in the merit function (Mx status GREEN).
[,1] [,2] [,3] [,4] [,5]
[1,] 1 6 11 16 21
[2,] 2 1 12 17 22
[3,] 3 8 1 18 23
[4,] 4 9 14 19 24
[5,] 5 10 15 20 25


There's a work-around of using matrix transforms to do the accessing, but easier to avoid if possible? ...


# ====================================
# = Use matrix transform work around =
# ====================================

nOrd = 3
nVar = 5
fit1 = mxModel("fit1",
mxMatrix(name="a", "Full", nrow=nVar, ncol=nVar, free=T, values=1:25),
mxMatrix(name="b", "Full", nrow=nVar, ncol=nOrd, free=T, values=
c(1, 0, 0,
0, 1, 0,
0, 0, 1,
0, 0, 0,
0, 0, 0
)
),
mxMatrix(name="unit", "Full", nrow=1, ncol=nOrd, free=F, values=1),
mxAlgebra(t(diag2vec(a)) %*% b, name="z"),
mxConstraint(name = "f", z == unit),
mxFitFunctionAlgebra("z", numObs= NA, numStats=NA)
)
fit1 = mxRun(fit1)
# Running fit1
# Warning message:
# In model 'fit1' Optimizer returned a non-zero status code 1. The final iterate satisfies the optimality conditions to the accuracy requested, but the sequence of iterates has not yet converged. Optimizer was terminated because no further improvement could be made in the merit function (Mx status GREEN).
mxEval(list(z), fit1)
[[1]]
[,1] [,2] [,3]
[1,] 0.9999998 0.9999998 1