def test_logic(types):
for option_set in [
types["scalar"],
types["vector"],
types["matrix"],
]:
for x in option_set:
for y in option_set:
### Comparisons
"""
Note: if warnings appear here, they're from `np.array(1) == cas.MX(1)` -
sensitive to order, as `cas.MX(1) == np.array(1)` is fine.
However, checking the outputs, these seem to be yielding correct results despite
the warning sooo...
"""
x == y # Warnings coming from here
x != y # Warnings coming from here
x > y
x >= y
x < y
x <= y
### Conditionals
np.where(x > 1, x**2, 0)
### Elementwise min/max
np.fmax(x, y)
np.fmin(x, y)
for x in types["all"]:
np.fabs(x)
np.floor(x)
np.ceil(x)
np.clip(x, 0, 1)
def airfoil_CL(alpha, Re, Ma):
alpha_rad = alpha * pi / 180
beta = (1 - Ma ** 2) ** 0.5
cl_0 = 0.5
cl_alpha = 5.8
cl_min = -0.3
cl_max = 1.2
cl = (alpha_rad * cl_alpha + cl_0) / beta
Cl = np.fmin(np.fmax(cl, cl_min), cl_max)
return Cl
def smoothmax(value1, value2, hardness):
"""
A smooth maximum between two functions. Also referred to as the logsumexp() function.
Useful because it's differentiable and preserves convexity!
Great writeup by John D Cook here:
https://www.johndcook.com/soft_maximum.pdf
:param value1: Value of function 1.
:param value2: Value of function 2.
:param hardness: Hardness parameter. Higher values make this closer to max(x1, x2).
:return: Soft maximum of the two supplied values.
"""
value1 = value1 * hardness
value2 = value2 * hardness
max = np.fmax(value1, value2)
min = np.fmin(value1, value2)
out = max + np.log(1 + np.exp(min - max))
out /= hardness
return out
def softmax(*args, hardness=1):
"""
An element-wise softmax between two or more arrays. Also referred to as the logsumexp() function.
Useful for optimization because it's differentiable and preserves convexity!
Great writeup by John D Cook here:
https://www.johndcook.com/soft_maximum.pdf
Args:
Provide any number of arguments as values to take the softmax of.
hardness: Hardness parameter. Higher values make this closer to max(x1, x2).
Returns:
Soft maximum of the supplied values.
"""
if hardness <= 0:
raise ValueError("The value of `hardness` must be positive.")
if len(args) <= 1:
raise ValueError("You must call softmax with the value of two or more arrays that you'd like to take the "
"element-wise softmax of.")
### Scale the args by hardness
args = [arg * hardness for arg in args]
### Find the element-wise max and min of the arrays:
min = args[0]
max = args[0]
for arg in args[1:]:
min = _np.fmin(min, arg)
max = _np.fmax(max, arg)
out = max + _np.log(sum(
[_np.exp(array - max) for array in args]
)
)
out = out / hardness
return out