Arrays and plots

Misinterpreting array axes or time intervals can give a physically incorrect meaning even when the calculation runs.

Starting conditions

$A=\begin{bmatrix}1&2&3\\4&5&6\end{bmatrix}$, $B=\begin{bmatrix}2&0\\1&3\\0&1\end{bmatrix}$.

Procedure

1. Before execution, write down A's sums and means by axis and the shapes of A*A and A@B.
2. Calculate using NumPy and check the (0,1) element of A@B by hand.
3. Record the result array and shape for each axis and operation in a table.

Results to retain

• A table with at least 6 rows, including axis aggregation and the two kinds of multiplication.

Starting conditions

Use $t=\begin{bmatrix}0&0.1&0.2&0.3&0.4\end{bmatrix}$ s and $V=\begin{bmatrix}0&0.8&1.3&1.6&1.8\end{bmatrix}$ V.

Procedure

1. Check the number of elements in the voltage and time arrays, and draw a line plot.
2. Use np.diff(V)/np.diff(t) to calculate interval slopes and plot them at interval midpoints.
3. Calculate the first interval's slope by hand and compare with the code.

Results to retain

• Voltage and slope plots, and a 4-row table.

Starting conditions

With seed=7, create 101 points over $0\le t\le 2$ s and add noise with a standard deviation of .2 to $\sin(2\pi t)$.

Procedure

1. Apply np.convolve(...,mode="same") to the same noisy signal using uniform kernels of lengths 3 and 9.
2. Plot the original signal, noisy signal, and two filter outputs on the same time axis. Calculate both RMSE values from the difference between the original signal and filter output over the common interval [4:-4], excluding the four samples at each end.
3. Record kernel length, comparison sample count, and RMSE in two rows. Use the plots and RMSE to distinguish apparent smoothness from closeness to the original signal.

Results to retain

• Plots of the original signal, noisy signal, and two filter outputs, and an RMSE table for 2 conditions.