       Re: Re: how to build pattern for a square matrix of reals?

• To: mathgroup at smc.vnet.net
• Subject: [mg98539] Re: [mg98492] Re: how to build pattern for a square matrix of reals?
• From: DrMajorBob <btreat1 at austin.rr.com>
• Date: Sun, 12 Apr 2009 03:46:43 -0400 (EDT)
• References: <grhp95\$mj7\$1@smc.vnet.net> <grkgmm\$6kq\$1@smc.vnet.net>

```You called l a "lower diagonal vector" and u an "upper diagonal vector" --
neither of which makes any sense. Only matrices, not vectors, can be upper
or lower diagonal.

I also noticed that you want 0 (an integer) to be treated as if it were
Real.

So here's a rendition of your "TridiagonalSolve":

tridiagonal[___] := False
tridiagonal[lower : {0 | 0., __Real}, d : {__Real},
upper : {__Real, 1 | 1.}, b : {__Real}] /;
Equal @@ Length /@ {lower, d, upper, b} := True

Notice I'd never, EVER use "l" as a variable name, as it's
indistinguishable from "1" for many of us. I used the "lower" and "upper"
names because you're thinking of them that way, even though vectors can't
physically BE lower or upper.

And here's a replacement for the second line of code, where I would NOT
redefine the built-in Solve:

realQ = True;
realQ[x_] := MatchQ[x, _Real]
realQ[_] = False;
commensurable[a_ /; MatrixQ[a, realQ], b : {__Real}] /;
Union@Dimensions@a == {Length@b} := True
commensurable[__] = False;

Bobby

On Sat, 11 Apr 2009 02:52:47 -0500, <sagrailo at gmail.com> wrote:

> Once again: big thanks to all who replied!  I think I'm able now to
> fully get what I wanted.
>
> I guess it would be better if I explained initially what is all about:
> I have some simple Fortran routines for solving tri-diagonal, and then
> regular, system of linear equations, that I'm wrapping, through
> Mathlink, for use from Mathematica. I want Mathematica to do arguments
> checking for me, and this could be achieved through specifying
> corresponding patterns for functions signature in the MathLink
> template file.
>
> So, my functions are:
>   TridiagonalSolve[l, d, u, b] - for tridiagonal solver
>   Solve[A, b] - for regular solver
> If the dimension of system is n in both cases, then here:
>   l - lower diagonal vector, of size n, with first element set to 0
>   d - diagonal vector, of size n
>   u - upper diagonal vector, of size n, with last element set to 0
>   b - right-side vector, of size n
>   A - matrix of the system, of size nxn
>
> So, I want to check that dimensions of all vectors match, for
> tridiagonal solver function, and also that vector l has 0 as first,
> and vector u has 0 as last element.  Also, for regular solver
> function, I want to check that dimensions of system matrix, and the
> length of the right-side vector match.  Of course, I also want to
> check that A is matrix of reals, and that l, d,u and b are vectors of
> reals.  So here are final patterns I came up with (these seem to work
> fine, but I'd appreciate any further suggestions on improvement):
>
> TridiagonalSolve[l_/;(VectorQ[l,MatchQ[#,_Real]&]&&l[]
> ==0),d_/;VectorQ[d,MatchQ[#,_Real]&],u_/;(VectorQ[u,MatchQ[#,_Real]&]
> &&u[[-1]]==0),b_/;VectorQ[b,MatchQ[#,_Real]&]]/;Length[l]==Length[d]
> ==Length[u]==Length[b]:="OK"
>
> Solve[A_/;(MatrixQ[A,MatchQ[#,_Real]&]&&Equal@@Dimensions
> [A]),b_/;VectorQ[b,MatchQ[#,_Real]&]]/;Dimensions[A][]==Length
> [b]:="OK"
>
> Regards.
>

--
DrMajorBob at bigfoot.com

```

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