minimizing a function with an array input
Question:
I want to use scipy.optimize.minimize on a function with an array type variable input. This is what I hope to do.
I have the following signal,
import numpy as np
time = np.linspace(0, 1, 501)
data = np.cos(2 * np.pi * 4 * time) + np.cos(2 * np.pi * 9 * time) + np.cos(2 * np.pi * 20 * time)
noise = np.sqrt(1 / 25) * np.random.randn(501)
signal = data + noise
and I am hoping to find a curve fit for this signal. Since I created the data myself, I know that a sum of cosine functions will work for this. So the function that I hope to optimize is the following:
def cos_sum(x, P):
assert isinstance(P, np.ndarray)
assert P.shape[0] == P.shape[1]
sums = []
for param in P:
a, b, c = param
sums.append(a * np.cos(b * (x - c)))
sums = np.array(sums)
return np.sum(sums, axis=0)
In order to use minimize to find the correct parameters, I create this residual function.
def resid(params, x):
assert isinstance(params, np.ndarray)
fit = cos_sum(x, params)
residual = np.sqrt(np.mean(np.abs(fit - signal)) ** 2)
return residual
I now need to create a guess. Since I already know how the signal was created, I made the following guess:
guess_A = np.random.normal(1, .2, size=3)
guess_B = 2 * np.pi * np.array([4, 9, 20], dtype=float)
guess_C = np.random.normal(0, .2, size=3)
guess = np.array([guess_A, guess_B, guess_C]).T
However, I am unable to run the following:
from scipy.optimize import minimize
optimization = minimize(resid, guess, args=(time))
and I receive the following error:
Traceback (most recent call last):
File "/Users/nickeisenberg/GitRepos/Python_Misc/Misc/minimize_curvefit_vector_variables.py", line 70, in <module>
optimization = minimize(resid, guess, args=(time))
File "/Library/Frameworks/Python.framework/Versions/3.10/lib/python3.10/site-packages/scipy/optimize/_minimize.py", line 676, in minimize
res = _minimize_bfgs(fun, x0, args, jac, callback, **options)
File "/Library/Frameworks/Python.framework/Versions/3.10/lib/python3.10/site-packages/scipy/optimize/_optimize.py", line 1296, in _minimize_bfgs
sf = _prepare_scalar_function(fun, x0, jac, args=args, epsilon=eps,
File "/Library/Frameworks/Python.framework/Versions/3.10/lib/python3.10/site-packages/scipy/optimize/_optimize.py", line 263, in _prepare_scalar_function
sf = ScalarFunction(fun, x0, args, grad, hess,
File "/Library/Frameworks/Python.framework/Versions/3.10/lib/python3.10/site-packages/scipy/optimize/_differentiable_functions.py", line 158, in __init__
self._update_fun()
File "/Library/Frameworks/Python.framework/Versions/3.10/lib/python3.10/site-packages/scipy/optimize/_differentiable_functions.py", line 251, in _update_fun
self._update_fun_impl()
File "/Library/Frameworks/Python.framework/Versions/3.10/lib/python3.10/site-packages/scipy/optimize/_differentiable_functions.py", line 155, in update_fun
self.f = fun_wrapped(self.x)
File "/Library/Frameworks/Python.framework/Versions/3.10/lib/python3.10/site-packages/scipy/optimize/_differentiable_functions.py", line 137, in fun_wrapped
fx = fun(np.copy(x), *args)
File "/Users/nickeisenberg/GitRepos/Python_Misc/Misc/minimize_curvefit_vector_variables.py", line 53, in resid
fit = cos_sum(x, params)
File "/Users/nickeisenberg/GitRepos/Python_Misc/Misc/minimize_curvefit_vector_variables.py", line 30, in cos_sum
assert P.shape[0] == P.shape[1]
IndexError: tuple index out of range
Is this possible to do?
Answers:
The problem is that minimize
treats parameters as 1D array. Adding print just before failing assert shows, that it reshaped guess
array to 1D array.
Changing cos_sum
so that it accepts 1D array of params fixes this problem. Here is the code.
def cos_sum(x, P):
assert isinstance(P, np.ndarray)
sums = []
for i in range(0, P.shape[0], 3):
a, b, c = P[i], P[i+1], P[i+2]
sums.append(a * np.cos(b * (x - c)))
sums = np.array(sums)
return np.sum(sums, axis=0)
Result:
optimization = minimize(resid, guess, args=(time))
print(optimization.x)
[ 0.96805816 25.1679919 0.25020317 1.00261543 56.44511497
0.77872223 1.00966167 125.71622787 0.55004217]
plt.figure(figsize=(8, 4))
plt.plot(data)
plt.plot([cos_sum(t, optimization.x) for t in time], 'C1--')
plt.show()
I want to use scipy.optimize.minimize on a function with an array type variable input. This is what I hope to do.
I have the following signal,
import numpy as np
time = np.linspace(0, 1, 501)
data = np.cos(2 * np.pi * 4 * time) + np.cos(2 * np.pi * 9 * time) + np.cos(2 * np.pi * 20 * time)
noise = np.sqrt(1 / 25) * np.random.randn(501)
signal = data + noise
and I am hoping to find a curve fit for this signal. Since I created the data myself, I know that a sum of cosine functions will work for this. So the function that I hope to optimize is the following:
def cos_sum(x, P):
assert isinstance(P, np.ndarray)
assert P.shape[0] == P.shape[1]
sums = []
for param in P:
a, b, c = param
sums.append(a * np.cos(b * (x - c)))
sums = np.array(sums)
return np.sum(sums, axis=0)
In order to use minimize to find the correct parameters, I create this residual function.
def resid(params, x):
assert isinstance(params, np.ndarray)
fit = cos_sum(x, params)
residual = np.sqrt(np.mean(np.abs(fit - signal)) ** 2)
return residual
I now need to create a guess. Since I already know how the signal was created, I made the following guess:
guess_A = np.random.normal(1, .2, size=3)
guess_B = 2 * np.pi * np.array([4, 9, 20], dtype=float)
guess_C = np.random.normal(0, .2, size=3)
guess = np.array([guess_A, guess_B, guess_C]).T
However, I am unable to run the following:
from scipy.optimize import minimize
optimization = minimize(resid, guess, args=(time))
and I receive the following error:
Traceback (most recent call last):
File "/Users/nickeisenberg/GitRepos/Python_Misc/Misc/minimize_curvefit_vector_variables.py", line 70, in <module>
optimization = minimize(resid, guess, args=(time))
File "/Library/Frameworks/Python.framework/Versions/3.10/lib/python3.10/site-packages/scipy/optimize/_minimize.py", line 676, in minimize
res = _minimize_bfgs(fun, x0, args, jac, callback, **options)
File "/Library/Frameworks/Python.framework/Versions/3.10/lib/python3.10/site-packages/scipy/optimize/_optimize.py", line 1296, in _minimize_bfgs
sf = _prepare_scalar_function(fun, x0, jac, args=args, epsilon=eps,
File "/Library/Frameworks/Python.framework/Versions/3.10/lib/python3.10/site-packages/scipy/optimize/_optimize.py", line 263, in _prepare_scalar_function
sf = ScalarFunction(fun, x0, args, grad, hess,
File "/Library/Frameworks/Python.framework/Versions/3.10/lib/python3.10/site-packages/scipy/optimize/_differentiable_functions.py", line 158, in __init__
self._update_fun()
File "/Library/Frameworks/Python.framework/Versions/3.10/lib/python3.10/site-packages/scipy/optimize/_differentiable_functions.py", line 251, in _update_fun
self._update_fun_impl()
File "/Library/Frameworks/Python.framework/Versions/3.10/lib/python3.10/site-packages/scipy/optimize/_differentiable_functions.py", line 155, in update_fun
self.f = fun_wrapped(self.x)
File "/Library/Frameworks/Python.framework/Versions/3.10/lib/python3.10/site-packages/scipy/optimize/_differentiable_functions.py", line 137, in fun_wrapped
fx = fun(np.copy(x), *args)
File "/Users/nickeisenberg/GitRepos/Python_Misc/Misc/minimize_curvefit_vector_variables.py", line 53, in resid
fit = cos_sum(x, params)
File "/Users/nickeisenberg/GitRepos/Python_Misc/Misc/minimize_curvefit_vector_variables.py", line 30, in cos_sum
assert P.shape[0] == P.shape[1]
IndexError: tuple index out of range
Is this possible to do?
The problem is that minimize
treats parameters as 1D array. Adding print just before failing assert shows, that it reshaped guess
array to 1D array.
Changing cos_sum
so that it accepts 1D array of params fixes this problem. Here is the code.
def cos_sum(x, P):
assert isinstance(P, np.ndarray)
sums = []
for i in range(0, P.shape[0], 3):
a, b, c = P[i], P[i+1], P[i+2]
sums.append(a * np.cos(b * (x - c)))
sums = np.array(sums)
return np.sum(sums, axis=0)
Result:
optimization = minimize(resid, guess, args=(time))
print(optimization.x)
[ 0.96805816 25.1679919 0.25020317 1.00261543 56.44511497
0.77872223 1.00966167 125.71622787 0.55004217]
plt.figure(figsize=(8, 4))
plt.plot(data)
plt.plot([cos_sum(t, optimization.x) for t in time], 'C1--')
plt.show()