[Rd] Problem with hessian in deriv3 (PR#2577)

j.c.rougier@durham.ac.uk j.c.rougier@durham.ac.uk
Mon Feb 24 18:06:02 2003

```Hi Everyone,

I noticed the following in deriv3:

> deriv3(expression(x * y - b * z), c("x", "y", "z"))
expression({
.value <- x * y - b * z
.grad <- array(0, c(length(.value), 3), list(NULL, c("x",
"y", "z")))
.hessian <- array(0, c(length(.value), 3, 3), list(NULL,
c("x", "y", "z"), c("x", "y", "z")))
.grad[, "x"] <- y
.grad[, "y"] <- x
.grad[, "z"] <- -b
.hessian[, "z", "z"] <- 0
attr(.value, "hessian") <- .hessian
.value
})

where the hessian is incorrectly computed as being 0 everywhere -- it
should be 1 at (x, y) and (y, x).  Interestingly, if I precede x * y
by unary minus the hessian is correct:

> deriv3(expression(- x * y - b * z), c("x", "y", "z"))
expression({
.expr1 <- -x
.value <- .expr1 * y - b * z
.grad <- array(0, c(length(.value), 3), list(NULL, c("x",
"y", "z")))
.hessian <- array(0, c(length(.value), 3, 3), list(NULL,
c("x", "y", "z"), c("x", "y", "z")))
.grad[, "x"] <- -y
.hessian[, "x", "x"] <- 0
.hessian[, "x", "y"] <- .hessian[, "y", "x"] <- -1
.hessian[, "x", "z"] <- .hessian[, "z", "x"] <- 0
.grad[, "y"] <- .expr1
.hessian[, "y", "y"] <- 0
.hessian[, "y", "z"] <- .hessian[, "z", "y"] <- 0
.grad[, "z"] <- -b
.hessian[, "z", "z"] <- 0
attr(.value, "hessian") <- .hessian
.value
})

Cheers, Jonathan.

--please do not edit the information below--

Version:
platform = i686-pc-linux-gnu
arch = i686
os = linux-gnu
system = i686, linux-gnu
status =
major = 1
minor = 6.1
year = 2002
month = 11
day = 01
language = R

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