aerosandbox.numpy.calculus#

Module Contents#

Functions#

diff(a[, n, axis, period])

Calculate the n-th discrete difference along the given axis.

gradient(f, *varargs[, axis, edge_order, n, period])

Return the gradient of an N-dimensional array.

trapz(x[, modify_endpoints])

Computes each piece of the approximate integral of x via the trapezoidal method with unit spacing.
aerosandbox.numpy.calculus.diff(a, n=1, axis=-1, period=None)[source]#

Calculate the n-th discrete difference along the given axis.

See syntax here: https://numpy.org/doc/stable/reference/generated/numpy.diff.html

Adds one new argument, period, which is the period of the data. If provided, the difference is taken assuming the data “wraps around” at the period (i.e., modulo the period). For example: >>> diff([345, 355, 5, 15], period=360) >>> [10, 10, 10, 10]

aerosandbox.numpy.calculus.gradient(f, *varargs, axis=None, edge_order=1, n=1, period=None)[source]#

Return the gradient of an N-dimensional array.

The gradient is computed using second order accurate central differences in the interior points and either first or second order accurate one-sides (forward or backwards) differences at the boundaries. The returned gradient hence has the same shape as the input array.

See syntax here: https://numpy.org/doc/stable/reference/generated/numpy.gradient.html

Parameters:

  • f – The array-like object to take the gradient of.

  • *varargs – The spacing between the points of f. If a scalar, the spacing is assumed to be uniform in all dimensions. If an array, the array must have the same shape as f.

  • axis – The axis along which the difference is taken. If None, the gradient is taken for all axes.

  • edge_order – The order of the error at the boundaries. 1 means first order, 2 means second order.

  • n – This is a new argument (not in NumPy) that specifies the order of the derivative to take. 1 is the first derivative (default), 2 is the second derivative. Doing np.gradient(f, n=2) results in less discretization error than doing np.gradient(np.gradient(f)).

  • period – The period of the data. If provided, the gradient is taken assuming the data “wraps around” at the period (i.e., modulo the period). See aerosandbox.numpy.diff() for more information.

Returns: The gradient of f.

aerosandbox.numpy.calculus.trapz(x, modify_endpoints=False)[source]#

Computes each piece of the approximate integral of x via the trapezoidal method with unit spacing. Can be viewed as the opposite of diff().

Parameters:

x – The vector-like object (1D np.ndarray, cas.MX) to be integrated.

Returns: A vector of length N-1 with each piece corresponding to the mean value of the function on the interval

starting at index i.