Maxima Function
lsquares_residuals (D, x, e, a)
Returns the residuals for the equation e with specified parameters a and data D.
D is a matrix, x is a list of variables,
e is an equation or general expression;
if not an equation, e is treated as if it were e = 0
.
a is a list of equations which specify values for any free parameters in e aside from x.
The residuals are defined as:
lhs(e ) - rhs(e ) i i
where e[i]
is the equation e
evaluated with the variables in x assigned values from the i
-th datum, D[i]
,
and assigning any remaining free variables from a.
load(lsquares)
loads this function.
Example:
(%i1) load (lsquares)$ (%i2) M : matrix ([1, 1, 1], [3/2, 1, 2], [9/4, 2, 1], [3, 2, 2], [2, 2, 1]); [ 1 1 1 ] [ ] [ 3 ] [ - 1 2 ] [ 2 ] [ ] (%o2) [ 9 ] [ - 2 1 ] [ 4 ] [ ] [ 3 2 2 ] [ ] [ 2 2 1 ] (%i3) a : lsquares_estimates (M, [z, x, y], (z + D)^2 = A*x + B*y + C, [A, B, C, D]); 59 27 10921 107 (%o3) [[A = - --, B = - --, C = -----, D = - ---]] 16 16 1024 32 (%i4) lsquares_residuals (M, [z, x, y], (z + D)^2 = A*x + B*y + C, first (a)); 13 13 13 13 13 (%o4) [--, - --, - --, --, --] 64 64 32 64 64