Differences in Home vs CAS

[ftneek]

Hello, I'm fairly new to the HP Prime and PPL. I started out by trying to recreate a program I wrote in python as a CAS program, but was running into some problems. After a few days of debugging and writing it as a non-CAS program, it works as I'm expecting in the home view, but when I run it in the CAS view it generates warnings that "A/B with B a square matrix is misleading notation interpreted as inv(B)*A", and error "Ifte: Unable to check test Error: Bad Argument Value". Can someone help me understand why that is? Are matrix calculations treated differently in Home vs CAS mode? Ideally I would like my program to works in both modes, with decimals returned in home view and fractions in CAS. I have also tried using the syntax for a cas program but then it errors in either mode. I would appreciate any insights or suggestions.

For reference it is the iterative conjugate gradient method to solve Ax=b, where in this case A is the nxn Hilbert matrix and b is an nx1 matrix which is the rowsum of A, so the exact solution for x is an nx1 matrix composed of 1's, but the computed solution should be "close" to 1's.

Code:

EXPORT conjugate_gradient(A, b)
BEGIN

LOCAL x, t, r, I, n;

n := DIM(A);
x := MAKEMAT(0, n(1), 1);
x(1, 1) := 1;
I := 1;
r := A*x - b;

WHILE I < 75 DO
t := (TRN(r)*r) / (TRN(r)*A*r);
x := x - r*t;
r := A*x - b;
IF ROWNORM(r) < .001 THEN
BREAK;
END;
I := I + 1;
END;

RETURN {I, x};
END;

Here is also a method for generating the rowsum, since I couldn't find an easy way to that with any of the built in methods. It works in both CAS and home view.

Code:

#cas
rowsum(A):=
BEGIN

LOCAL n;
LOCAL b;
LOCAL I;

n := dim(A);
b := makemat(0, n(1), 1);

FOR I FROM 1 TO n(1) DO
b(I,1) += ΣLIST(row(A, I));
END;

RETURN b;

END;
#end

update: So after some more digging, I think it those warnings came from a leftover file from when I was writing it as a CAS program. I reset my virtual calculator and retransferred the files. It works in Home mode but when I call

Code:

conjugate_gradient(hilbert(20), rowsum(hilbert(20)))

in CAS mode I no longer get the previous warnings, instead I get this error: "Error: Bad argument type". Why is that? I would like the conjugate_gradient method to work in CAS mode if possible. My question still stands if there are differences between how matrix calculations are performed in CAS mode. Thank you