I'm having trouble to get the positive area (above y=0). Mathematically the area should be 1.125.
x=np.arange(1,5,1)
y=np.array([-1.5,-0.5,0.5,1.5])
But none of the function below gives me the answer. The first one is 0. The second one gives me 1.25 which doesn't interpolate to calculate the area. I need to get the answer 1.125. Can anyone help? Thanks!
np.trapz(y,x)
np.trapz(y.clip(min=0),x)
To do this, you have to find where the linear interpolation of your data crosses the x axis. This function is a variation of a function that I included in another answer (Digitizing an analog signal):
def find_zero_crossings(t, y):
"""
Given the input signal `y` with samples at times `t`,
find the times where the linearly interpolated graph
crosses 0.
`t` and `y` must be 1-D numpy arrays.
"""
transition_indices = np.where((np.sign(y[:-1]) * np.sign(y[1:])) == -1)[0]
# Linearly interpolate the time values where the transition occurs.
t0 = t[transition_indices]
t1 = t[transition_indices + 1]
y0 = y[transition_indices]
y1 = y[transition_indices + 1]
slope = (y1 - y0) / (t1 - t0)
transition_times = t0 - y0 / slope
return transition_times
You can use this for your example in a script such as this:
xx = np.arange(1, 5, 1)
yy = np.array([-1.5, -0.5, 0.5, 1.5])
xz = find_zero_crossings(xx, yy)
print("xz:", xz)
# Insert the x intercepts into the data.
xx2 = np.append(xx, xz)
yy2 = np.append(yy, np.zeros_like(xz))
# Restore the order of xx2, and order yy2 in the same way.
k = xx2.argsort()
xx2 = xx2[k]
yy2 = yy2[k]
print("xx2:", xx2)
print("yy2:", yy2)
# pos_yy2 is the clipped version of yy2.
pos_yy2 = np.maximum(yy2, 0.0)
print("pos_yy2:", pos_yy2)
# Compute the area with `trapz`.
pos_area = np.trapz(pos_yy2, xx2)
print("pos_area:", pos_area)
Output:
xz: [2.5]
xx2: [1. 2. 2.5 3. 4. ]
yy2: [-1.5 -0.5 0. 0.5 1.5]
pos_yy2: [0. 0. 0. 0.5 1.5]
pos_area: 1.125
A function to do all that is:
def pos_trapz(y, x=None, dx=1.0):
if x is None:
x = np.arange(len(y))*dx
xz = find_zero_crossings(x, y)
# Insert the x intercepts into the data.
x2 = np.append(x, xz)
y2 = np.append(y, np.zeros_like(xz))
# Restore the order of x2, and order y2 in the same way.
# (The function assumes that the input `x` is in ascending order.)
k = x2.argsort()
x2 = x2[k]
y2 = y2[k]
# pos_y2 is the clipped version of y2.
pos_y2 = np.maximum(y2, 0.0)
# Compute the area with `trapz`.
return np.trapz(pos_y2, x2)
In an ipython session:
In [107]: xx = np.arange(1, 5, 1)
In [108]: yy = np.array([-1.5, -0.5, 0.5, 1.5])
In [109]: pos_trapz(yy, xx)
Out[109]: 1.125
