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Post-Processing

Once the system is solved, Temporal Variables contain numerical data. vip-ivp provides several utilities to access and export this data for analysis and visualization.

Accessing the Values of Variables​

After solving, a TemporalVar instance has two key properties:

  • .values: a NumPy array containing the evolution of the variable's value over time
  • .t: a NumPy array of the corresponding time values
import matplotlib.pyplot as plt
import vip_ivp as vip

# Exponential decay: dN/dt = -λ * N
d_n = vip.loop_node()
n = vip.integrate(d_n, 1)
d_n.loop_into(-0.5 * n)
vip.solve(10, time_step=0.001)

# Manual plotting
plt.plot(n.t, n.values)
plt.xlabel("Time (s)")
plt.ylabel("Evolution (-)")
plt.show()

Export to DataFrame​

To convert one or more TemporalVar instances into a pandas DataFrame, use:

vip.export_to_df(*variables)

Example:

# Create the system
acceleration = vip.temporal(-9.81)
velocity = vip.integrate(acceleration, x0=0)
height = vip.integrate(velocity, x0=10)

vip.solve(10, time_step=1)

# Convert to a pandas DataFrame
dataframe = vip.export_to_df(velocity, height)
print(dataframe)

Console output:

    Time (s)  velocity   height
0        0.0      0.00   10.000
1        1.0     -9.81    5.095
2        2.0    -19.62   -9.620
...
10      10.0    -98.10 -480.500

Export to a File​

You can export the results to a CSV or JSON file using:

vip.export_file(filename, variable_list, file_format)
  • filename: path to the output file
  • variable_list: a tuple of TemporalVar instances
  • file_format: either "csv" or "json"

Export to CSV​

vip.export_file("result.csv", (velocity, height), "csv")

Content of result.csv:

result.csv
Time (s),velocity,height
0.0,0.0,10.0
1.0,-9.81,5.09
2.0,-19.62,-9.62
...
10.0,-98.10,-480.50

Export to JSON​

vip.export_file("result.json", (velocity, height), "json")

Content of result.json:

result.json
[
  {
    "Time (s)": 0.0,
    "velocity": 0.0,
    "height": 10.0
  },
  {
    "Time (s)": 1.0,
    "velocity": -9.81,
    "height": 5.095
  },
  {
    "Time (s)": 2.0,
    "velocity": -19.62,
    "height": -9.62
  },
...
  {
    "Time (s)": 10.0,
    "velocity": -98.1,
    "height": -480.5
  }
]