block_bandsolve cannot invert matrix with zero-valued columns in bottom-right block

[goepp]

block_bandsolve(mat, vect, FALSE, lim) does not work when D[-(1:lim), -(1:lim)] has a column of zeros.

[goepp]

Minimal working example:

library(hazreg)
library(limSolve)
library(tidyverse)
set.seed(0)
A <- matrix(rnorm(36), 6, 6)
B <- matrix(rnorm(24), 6, 4)
D <- diag(rnorm(4)) + rbind(cbind(0, diag(rnorm(3))), 0)
D[4, ] <- 0
D[, 4] <- 0
mat <- rbind(cbind(A + t(A), B), cbind(t(B), D + t(D)))
vect <- rnorm(10)
vect[10] <- 0
lim <- 6
block_bandsolve(mat, vect, FALSE, lim)