pflm.utils.trapz

trapz(y: ndarray, x: ndarray) → ndarray | float

Compute the integrated area using the trapezoidal rule.

For a single curve y of length n and x of the same length:

\[T(y, x) = \sum_{i=0}^{n-2} (x_{i+1}-x_i) \, \frac{y_i + y_{i+1}}{2}.\]

For a matrix Y of shape (m, n) with len(x) = n (integrate along axis 1):

\[[T(Y, x)]_k = \sum_{i=0}^{n-2} (x_{i+1}-x_i) \, \frac{Y_{k,i} + Y_{k,i+1}}{2}, \quad k=0,\dots,m-1.\]

If instead len(x) = m (integrate along axis 0):

\[[T(Y, x)]_k = \sum_{i=0}^{m-2} (x_{i+1}-x_i) \, \frac{Y_{i,k} + Y_{i+1,k}}{2}, \quad k=0,\dots,n-1.\]

Parameters:

yarray_like

1D or 2D array of function values with respect to x.

Accepted shapes:

• (n,) for a single curve.

• (m, n) for multiple curves.

If y is 1D, it is treated as a single row (1, n).

xarray_like of shape (n,)

1D array of x-coordinates corresponding to the function values.

Returns:

np.ndarray or float

If y was 1D, returns a scalar float. If y was 2D, returns a 1D array of shape (m,) with the integral per row of y.

Raises:

ValueError

If the number of points in x does not match either the number of rows or the number of columns of y.

See also

numpy.trapz

Reference implementation for simple cases.

Notes

• The implementation dispatches to a float32/float64 optimized backend.

• x is coerced to the dtype of y to avoid unintended up/down-casts.