Solving equation with two unknowns

Hi this is my code for solving quadratic equation. This is working fine but problem is when I try to add one more unknown.

x = torch.nn.Parameter(torch.zeros(1), requires_grad=True)

def model(x):
    b=3
    a=2
    c=1
    global y
    y = a*x ** 2 + b*x + c
    return y

optimizer = torch.optim.Adam([x], lr=0.1)

for i in range(150):
    a = model(x)

    loss = (0 - a) ** 2

    optimizer.zero_grad()
    loss.backward()
    optimizer.step()
    print(loss)

I am computing loss from x. and my optimizer is optimizing x after every loop. When I change my equation to System of linear equations and I have one more unknown how could I calculate loss and update both unknowns ?
For example equation like this
image

Hi Samuel!

Let’s say you have nUnknowns unknowns in your system and
also nUnknowns equations. Make the variable you optimize a
1d tensor of length nUnknowns:

x = torch.nn.Parameter (torch.zeros (nUnknowns))

Then have your model return the left-hand sides of your nUnknowns
equations as a tensor of shape [nUnknowns] and supply the
right-hand sides of your equations as a target vector, also of shape
[nUnknowns]. You could calculate the loss “by hand” as you do in
your example, or you could use MSELoss:

loss = torch.nn.MSELoss() (model (x), target)

(You could also have your model return a vector of differences
between the left-hand and right-hand sides of your equations,
and use its sum of squares as your loss.)

Two side comments:

torch.nn.Parameter has requires_grad = True) by default,
so you don’t need to specify this explicitly. (But it doesn’t hurt to
do so.)

As a pure python comment, not specific to pytorch. in the context
of just the code you posted, global y doesn’t do anything. But, in
general, you should try to avoid global; there are usually cleaner,
“safer” ways of accomplishing whatever it is you might be trying to
do with global.

Best.

K. Frank

1 Like

To this sentence I want to ask you one more thing. “return a vector of differences” Please please, can you give me example how can I write this in python ? I understand what you mean but how to write vector like this in python. Thank you.

Hi Samuel!

Consider the following:

>>> import torch
>>> torch.__version__
'1.9.0'
>>>
>>> # your scalar x = z[0] and y = z[1]
>>> z = torch.nn.Parameter (torch.tensor ([3.0, 7.0]))   # just to make it more interesting than 0.0
>>> equationCoefficients = torch.tensor ([[1.0, 1.0], [1.0, -1.0]])
>>> rhs = torch.tensor ([5.0, 1.0])
>>> lhs = equationCoefficients @ z
>>> lhs
tensor([10., -4.], grad_fn=<MvBackward>)
>>> vectorOfDifferences = lhs - rhs
>>> vectorOfDifferences
tensor([ 5., -5.], grad_fn=<SubBackward0>)
>>> loss = (vectorOfDifferences**2).sum()
>>> loss
tensor(50., grad_fn=<SumBackward0>)

Best.

K. Frank

1 Like