[Rd] solve.default(a, b) should not ignore names(dimnames(.))

[Mikael Jagan]

Hello,

Currently, solve.default() is defined such that

 > identical(dimnames(solve.default(a, b)),
             list(dimnames(a)[[2L]], dimnames(b)[[2L]]))

is always TRUE, i.e., ignoring names(dimnames(a)) and names(dimnames(b)).
Hence we see:

 > a <- b <- diag(2L)
 > dimnames(a) <- list(A1 = c("a11", "a12"), A2 = c("a21", "a22"))
 > dimnames(b) <- list(B1 = c("b11", "b12"), B2 = c("b21", "b22"))
 > a
      A2
A1    a21 a22
   a11   1   0
   a12   0   1
 > b
      B2
B1    b21 b22
   b11   1   0
   b12   0   1
 > solve.default(a, b)
     b21 b22
a21   1   0
a22   0   1

I claim that solve.default() should be changed to instead give:

 > identical(dimnames(solve.default(a, b)),
             c(dimnames(a)[2L], dimnames(b)[2L]))

This would make solve.default() consistent with `%*%`, which
_does_ respect names(dimnames(.)) :

 > a %*% b
      B2
A1    b21 b22
   a11   1   0
   a12   0   1

If others agree, then I would submit a minimal patch to the R-level
solve.default() in src/library/base/R/solve.R and to the C-level
La_solve() and La_solve_cmplx() in src/modules/lapack/Lapack.c ...

Mikael