Greetings:
If it is an error it is treated very consistently in the text!
For example, the following (from the text):
===================
VOLS D.1 lwh
1 0 0
3 4 0
6 8 12
This table merits attention. The last row is the gradient of the product over
the entire
argument, and therefore agrees with gradient of vol shown earlier. The second
row is the
gradient of the product over the first two elements (the base); its value does
not depend at
all on the height, and the derivative with respect to the height is therefore
zero (as shown
by the last element).
=====================
Okay, I suppose I could just go on reading the text and replacing "row" with
"column"
wherever it occurs. However, later in Chapter 7, section H is the following:
==================================
Linear Functions and Operators
..." the derivative of a linear function gives the matrix that represents it."
[which makes perfect sense]
[As an example, the text defines:]
]L=:(3 3$i.9)&(mp=:+/ . *)
┌─────┬─┬──┐
│0 1 2│&│mp│
│3 4 5│ │ │
│6 7 8│ │ │
└─────┴─┴──┘
VD=:("1) D. 1
L VD 1 1 1
0 1 2
3 4 5
6 7 8
=================================
So this example makes sense. The derivative of a linear operator is indeed the
matrix that
represents it. But here is what J6.02 gives:
=================================
L VD 1 1 1
0 3 6
1 4 7
2 5 8
================================
The transpose!
Something is very wrong. Methematically, the derivative of a linear function
SHOULD give the matrix, NOT the transpose!
Andrew Seary
se...@sfu.ca
PS. I had already checked the J help page for D. and found the definition you
pointed me to.
I also checked the history of J changes, but found no references to any changes
in the
definition of D.
D. McCormick writes:
>It looks like the book is incorrect. Here's more up-to-date
>information on how " D. " works:
>http://www.jsoftware.com/help/dictionary/ddcapdot.htm .
On Fri, Jun 22, 2012 at 4:42 PM, Andrew Seary <se...@sfu.ca> wrote:
> Hi there:
>
> I hought it was time to give J another try, so I downloaded J602 and
> started following the examples in Iverson's Calculus -- I always enjoy his
> expositions.
>
> The following has stopped me in my tracks.
> From the examples in Chapter 3 (copy/paste from a J session):
> ===From J session====
> ? lwh=:4 3 2
> ? vol=:*/
> ? vol lwh
> 24
> ? vol D.1 lwh
> 6 8 12
> ? VOLS=:vol\
> ? VOLS lwh
> 4 12 24
> ? VOLS D.1 lwh
> 1 3 ?6
> 0 4 ?8
> 0 0 12
> =======================
>
> That last result is the TRANPOSE of the what is shown in the text:
>
> ====From Calculus Ch. 3=
>
> ? VOLS D.1 lwh
> 1 0 0
> 3 4 0
> 6 8 12
> ========================
>
> Showstoppper! What the heck is going on?
>
> Andrew Seary
> se...@sfu.ca
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