Band Matrices
Author Message
Band Matrices

NB. I would like to see the posting of more
NB. well-defined problems (such as the diag-
NB. onal and band matrices posted by Faust),
NB. together with executable treatments of
NB. them in any or all dialects of APL. Here
NB. is a treatment of band matrices in J:

sh=. |. !. 0  NB. Shift in zeroes

NB. Try:
diag 2 3 5 7
2 0 0 0
0 3 0 0
0 0 5 0
0 0 0 7
0 band 2 3 5 7
2 0 0 0
0 3 0 0
0 0 5 0
0 0 0 7
1 band 3 5 7
0 3 0 0
0 0 5 0
0 0 0 7
0 0 0 0
_1 band 3 5 7
0 0 0 0
3 0 0 0
0 5 0 0
0 0 7 0
_1 0 1 band&> y=. 1 2 3;4 5 6 7;8 9 10
0 0 0  0
1 0 0  0
0 2 0  0
0 0 3  0

4 0 0  0
0 5 0  0
0 0 6  0
0 0 0  7

0 8 0  0
0 0 9  0
0 0 0 10
0 0 0  0

_1 0 1 B y  NB. Tri-diagonal matrix
4 8 0  0
1 5 9  0
0 2 6 10
0 0 3  7

Tue, 11 Mar 1997 03:31:48 GMT
Band Matrices
Ken Iverson writes :

Quote:
>   NB. I would like to see the posting of more
>   NB. well-defined problems (such as the diag-
>   NB. onal and band matrices posted by Faust),
>   NB. together with executable treatments of
>   NB. them in any or all dialects of APL. Here
>   NB. is a treatment of band matrices in J:

One such well defined problem comes about in the
derivation of the psuedo inverse based upon the
SVD. You have a rectangular matrix, n by m, which
is all zeros except along the diagonal. The diagonal
entries are real (actually, complex in the general case).
The (i,i)th entries of the matrix to be formed are the
reciprocals of the (i,i)th entries of the old matrix
except in the case of being either zeros or machine zeros
whose tolerance value is specified. For example, both

3 0     0
0 4     0
0 0 1e_40
0 0     0

and

3 0 0
0 4 0
0 0 0
0 0 0

with tolerance 1e_30 become :

0.333333    0 0 0
0 0.25 0 0
0    0 1 0

-e

Wed, 12 Mar 1997 15:51:24 GMT
Band Matrices
hello,

posted a set of J verbs to to manipulate diag and band matrices.
MY version of J (J7, compiled under linux) doesn't like the entry

I won't have access to J7 or J8 under windows for a few more  days.
Could someone tell me if is this J8 exclusive code or does it run

thanks,

ira ekhaus

Wed, 12 Mar 1997 23:07:21 GMT
Band Matrices
Ira B Ekhaus:

. a set of J verbs to to manipulate diag and band matrices.  MY
. version of J (J7, compiled under linux) doesn't like the entry
.

_1: isn't defined in J7.  Use _1"_ instead.

Raul D. Miller           n =: p*q             NB. 9<##:##:n [.large prime p, q

NB.  public e, n, y
x -: n&|&(*&y)^:d 1  NB. 1=(d*e)+.p*&<:q

Thu, 13 Mar 1997 06:14:44 GMT

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