Sample the Test Function
The first thing we might want to do with a new function is define an input range of interest and sample the domain of interest using a uniform grid.
This sample will provide the basis for generating a plot later.
In this case, we will define a domain of interest around the optima of x=0.0 from x=-5.0 to x=5.0 and sample a grid of values in this range with 0.1 increments, such as -5.0, -4.9, -4.8, etc.
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define range for input
r_min, r_max = -5.0, 5.0
sample input range uniformly at 0.1 increments
inputs = arange(r_min, r_max, 0.1)
summarize some of the input domain
print(inputs[:5])
We can then evaluate each of the x values in our sample.
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compute targets
results = objective(inputs)
summarize some of the results
print(results[:5])
Finally, we can check some of the input and their corresponding outputs.
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create a mapping of some inputs to some results
for i in range(5):
print(‘f(%.3f) = %.3f’ % (inputs[i], results[i]))
Tying this together, the complete example of sampling the input space and evaluating all points in the sample is listed below.
sample 1d objective function
from numpy import arange
objective function
def objective(x):
return x**2.0
define range for input
r_min, r_max = -5.0, 5.0
sample input range uniformly at 0.1 increments
inputs = arange(r_min, r_max, 0.1)
summarize some of the input domain
print(inputs[:5])
compute targets
results = objective(inputs)
summarize some of the results
print(results[:5])
create a mapping of some inputs to some results
for i in range(5):
print(‘f(%.3f) = %.3f’ % (inputs[i], results[i]))
Running the example first generates a uniform sample of input points as we expected.
The input points are then evaluated using the objective function and finally, we can see a simple mapping of inputs to outputs of the objective function.
[-5. -4.9 -4.8 -4.7 -4.6]
[25. 24.01 23.04 22.09 21.16]
f(-5.000) = 25.000
f(-4.900) = 24.010
f(-4.800) = 23.040
f(-4.700) = 22.090
f(-4.600) = 21.160