On 10/29/10 5:59 PM, Oscar Gerardo Lazo Arjona wrote:
I want to propose the following changes to the output format of find_fit
and solve:
for find_fit the current output format is a list of equations:
sage: data = [(i, 1.2 * sin(0.5*i-0.2) + 0.1 * normalvariate(0, 1)) for
i in xsrange(0, 4*pi, 0.2)]
sage: var('a, b, c, x')
sage: model(x) = a * sin(b * x - c)
sage: find_fit(data, model)
[a == 1.2204167610363676, b == 0.50171964598627838, c
==0.22401763827376933]
or a dictionary:
sage: find_fit(data,model,solution_dict=True)
{c: 0.22401763827376933, b: 0.50171964598627838, a: 1.2204167610363676}
I'd like to get an expression where the values found for the parameters
are put in the model given to find_fit:
sage: find_fit(data, model)
1.2204167610363676*sin(0.50171964598627838 *x -0.22401763827376933 )
Why not make solution_dict=True the default, since then you could say:
fit=find_fit(data,model)
model.subs(fit)
to get the model with those parameters?
In fact, it would be great if this worked too:
fit=find_fit(data,model)
model(**fit)
but (even if solution_dict=True is the default) that complains that the
keys in the dictionary are not strings.
However, we could make this work:
fit=find_fit(data,model)
model(fit)
but it require changes to the __call__ method to allow a dictionary
input that would do the same as .subs() would do if handed a dictionary.
For solve the current output format depends on the input:
sage: var('x y')
sage: eq1=x+4==0
sage: eq2=x^2+4*x+2==0
sage: sys1=x+y==1
sage: sys2=x-2*y==-2
sage: solve(eq1,x)
[x == -4]
A list containing solutions (even when there is only one solution).
sage: solve(eq2,x)
[x == -sqrt(2) - 2, x == sqrt(2) - 2]
A list containing solutions when there is more than one solution
solve([sys1,sys2],x,y)
[[x == 0, y == 1]]
A list containing a list containing solutions (this is the worst)
The format I would like to see is:
sage: solve(eq1,x)
x == -4
A single equation
sage: solve(eq2,x)
[x == -sqrt(2) - 2, x == sqrt(2) - 2]
This one is fine
solve([sys1,sys2],x,y)
[x == 0, y == 1]
Just a list of solutions. It is harder to work with the solutions if
they are inside another list.
What if there are two different solutions, like (x=0, y=0) and (x=0,y=1)?
Personally, I think returning an equation is okay for situations where I
am just checking something, and don't plan on using the solution again.
Returning a list of equations is horrible for actually doing anything
with the results, which is my intent in the vast majority of situations.
Having to always append the not-very-obvious "solution_dict=True" to
use solve in the common case is not very user-friendly. If we're
changing the output of solve, I'd propose returning either a single
dictionary (a single solution) or a list of dictionaries (multiple
solutions). Solve seems like it would be much more useful that way.
Thanks,
Jason
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