numbacs.utils

Module Contents

numbacs.utils.unravel_index(index, shape)

Numba currently does not implement np.unravel_index so we create an implementation here for the specific case where order=’C’ (row-major).

Parameters:

• index (int) – raveled index.

• shape (np.ndarray, shape = (ndims,)) – shape of array used for unraveling index.

Returns:

array containing the unraveled index.

Return type:

np.ndarray

numbacs.utils.ravel_index(inds, shape)

Finds raveled index corresponding to grid index given by inds from array with shape=shape where shape must be a np.ndarray.

Parameters:

• inds (np.ndarray, shape = (ndims,)) – array containing indices to be raveled.

• shape (np.ndarray, shape = (ndims,)) – shape of array used for raveling index.

Returns:

r_ind – raveled index.

Return type:

int

numbacs.utils.finite_diff_2D(f, i, j, h, axis, direction='c')

Compute 2nd order partial finite difference in the array f @ [i,j] along axis=axis and using a directional difference scheme defined by direction.

Parameters:

• f (np.ndarray, shape = (nx,ny)) – array on which finite differencing is performed.

• i (int) – index for axis=0 at which finite differencing is performed.

• j (int) – index for axis=1 at which finite differencing is performed.

• h (float) – spacing in axis direction.

• axis (int) – axis over which finite differencing is performed.

• direction (str, optional) – finite differencing direction, optional values are ‘b’ for backward, ‘c’ for centered, and ‘f’ for forward. The default is ‘c’.

Returns:

df – finite difference value.

Return type:

float

numbacs.utils.finite_diff_ND(f, ind, h, axis, shape, direction=0)

Compute 2nd order partial finite difference in the array f @ [ind] where f is an (n_1*n_2*…*n_ndims) array. Axis=axis determines the axis the finite differencing will be performed along shape is [n1,n2,…,n_ndims]. shape must be a np.array and ‘ij’ indexing is assumed.

Parameters:

• f (np.ndarray, shape = (nx_1*nx_2*...*nx_ndims,)) – flattened array of which finite differencing is performed.

• ind (int) – raveled index at which finite differencing is performed.

• h (float) – spacing in axis direction.

• axis (int) – axis over which finite differencing is performed.

• shape (np.ndarray, shape = (ndims,)) – shape of original array before raveled.

• direction (str, optional) – finite differencing direction, optional values are -1 for backward, 0 for centered, and 1 for forward. The default is 0.

Returns:

df – finite difference value.

Return type:

float

numbacs.utils.finite_diff_2D_2nd(f, i, j, h, axis, direction='c')

Compute 2nd order partial finite difference in the array f @ [i,j] along axis=axis and using a directional difference scheme defined by direction for the second derivative. axis=2 is for the mixed partial finite difference.

numbacs.utils.curl_vel(u, v, dx, dy)

Compute curl of vector field defined by u and v.

Parameters:

• u (np.ndarray, shape = (nx,ny)) – array containing x component of vector field.

• v (np.ndarray, shape = (nx,ny)) – array containing y component of vector field.

• dx (float) – spacing in grid in x-direction.

• dy (float) – spacing in grid in y-direction.

Returns:

curl – array containing values of curl of vector field defined by u and v.

Return type:

np.ndarray, shape = (nx,ny)

numbacs.utils.curl_vel_tspan(u, v, dx, dy)

Compute curl of vector field defined by u and v over some timespan.

Parameters:

• u (np.ndarray, shape = (nt,nx,ny)) – array containing x component of vector field.

• v (np.ndarray, shape = (nt,nx,ny)) – array containing y component of vector field.

• dx (float) – spacing in grid in x-direction.

• dy (float) – spacing in grid in y-direction.

Returns:

curl – array containing values of curl of vector field defined by u and v.

Return type:

np.ndarray, shape = (nt,nx,ny)

numbacs.utils.curl_func(fnc, x, y, h=0.001)

Compute curl over x,y of vector field defined by fnc.

Parameters:

• fnc (jit-callable) – callable containing returing x and y components of vector field.

• x (np.ndarray, shape = (nx,)) – array containing x-values.

• y (np.ndarray, shape = (ny,)) – array containing y-values.

• h (float, optional) – spacing used in finite differencing. The default is 1e-3.

Returns:

curlf – array containing values of curl of f.

Return type:

np.ndarray, shape = (nx,ny)

numbacs.utils.curl_func_tspan(fnc, t, x, y, h=0.001)

Compute curl over x,y of vector field defined by func over times t.

Parameters:

• fnc (jit-callable) – callable containing returing x and y components of vector field.

• x (np.ndarray, shape = (nx,)) – array containing x-values.

• y (np.ndarray, shape = (ny,)) – array containing y-values.

• h (float, optional) – spacing used in finite differencing. The default is 1e-3.

Returns:

curlf – array containing values of curl of f.

Return type:

np.ndarray, shape = (nx,ny)

numbacs.utils.composite_simpsons(f, h)

Composite Simpson’s 1/3 rule to compute integral of f between endpoitns of pts with regular spacing given by h.

Parameters:

• f (np.ndarray, shape = (n+1,)) – values of f at regularly spaced points.

• h (float) – value of spacing between points at which f was evaluated.

Returns:

val – value of integral.

Return type:

float

numbacs.utils.composite_simpsons_38_irregular(f, h)

Composite Simpson’s 3/8 rule to compute integral of f between endpoitns of pts with irregular spacing given by h which is an np.ndarray.

Parameters:

• f (np.ndarray, shape = (n+1,)) – values of f at irregularly spaced points.

• h (np.ndarray, shape = (n,)) – values of spacing between points at which f was evaluated.

Returns:

val – value of integral.

Return type:

float

numbacs.utils.dist_2d(p1, p2)

Compute 2D Euclidean distance between p1 and p2.

Parameters:

• p1 (np,ndarry, shape = (2,)) – point 1.

• p2 (np,ndarry, shape = (2,)) – point 2.

Returns:

distance between p1 and p2.

Return type:

float

numbacs.utils.dist_tol(point, arr, tol)

Check if pt is within tolerance of any point in arr.

Parameters:

• point (np.ndarray, shape = (2,)) – point.

• arr (np.ndarray, shape = (n,2)) – array containing points.

• tol (float) – tolerance used for checking distance.

Returns:

near – truth value determining if point is within tol of any point in arr.

Return type:

boolean

numbacs.utils.shoelace(polygon)

Compute area of simple polygon using shoelace algorithm.

Parameters:

polygon (np.ndarray, shape = (n,2)) – array containing vertices of polygon, first and last vertex should be the same.

Returns:

area – area of polygon.

Return type:

float

numbacs.utils.max_in_radius(arr, r, dx, dy, n=-1, min_val=0.0)

Finds n local maxima values in arr such that each max is a local maximum within radius r where spacing in arr is given by dx,dy. If all local maxima are desired, set n = -1. Should pass a copy of arr to the function to avoid orginial arr being overwritten (i.e. pass in arr.copy()).

Parameters:

• arr (np.ndarray, shape = (nx,ny)) – array in which local maxima are to be found.

• r (float) – radius in which points will be discared after a maximum is found at the center.

• dx (float) – gird spacing in x-direction.

• dy (float) – grid spacing in y-direction.

• n (int, optional) – number of maxima to return, -1 returns all. The default is -1.

• min_val (float, optional) – miniumum value allowed for local maxima. The default is 0.0.

Returns:

• max_vals (np.ndarray, shape = (k,) where k number of maxima found) – maxima values in radius.

• max_inds (np.ndarray, shape = (k,) where k number of maxima found) – indices corresponding to max_vals.

numbacs.utils.gen_circ(r, c, n, xlims=None, ylims=None)

Generate n points on a circle with radius r and center c.

Parameters:

• r (float) – radius of circle.

• c (np.ndarray, shape = (2,)) – center of circle.

• n (int) – number of points on circle.

• xlims (tuple, optional) – boundary in x-direction, points outside of this boundary will not be returned. The default is None.

• ylims (tuple, optional) – boundary in y-direction, points outside of this boundary will not be returned. The default is None.

Returns:

pts – points on the circle.

Return type:

np.ndarray, shape = (n,2)

numbacs.utils.gen_filled_circ(r, n, alpha=3.0, c=np.array([0.0, 0.0]), xlims=None, ylims=None)

Generate points filling a circle with radius r and center c. Uses the sunflower seed arangement.

Parameters:

• r (float) – radius of circle.

• n (int) – number of points to fill the circle.

• alpha (float, optional) – parameter determining how smooth the boundary is. The default is 3.0.

• c (np.ndarray, shape = (2,), optional) – center of the circle. The default is np.array([0.0,0.0]).

• xlims (tuple, optional) – boundary in x-direction, points outside of this boundary will not be returned. The default is None.

• ylims (tuple, optional) – boundary in y-direction, points outside of this boundary will not be returned. The default is None.

Returns:

pts – array containing points which fill the circle.

Return type:

np.ndarray, shape = (n,2)

numbacs.utils.gen_filled_circ_radius(r, n, alpha=3.0, c=np.array([0.0, 0.0]), xlims=None, ylims=None)

Generate points filling a circle with radius r and center c. Uses the sunflower seed arangement. Also returns radius of each point from center c.

Parameters:

• r (float) – radius of circle.

• n (int) – number of points to fill the circle.

• alpha (float, optional) – parameter determining how smooth the boundary is. The default is 3.0.

• c (np.ndarray, shape = (2,), optional) – center of the circle. The default is np.array([0.0,0.0]).

• xlims (tuple, optional) – boundary in x-direction, points outside of this boundary will not be returned. The default is None.

• ylims (tuple, optional) – boundary in y-direction, points outside of this boundary will not be returned. The default is None.

Returns:

• pts (np.ndarray, shape = (n,2)) – array containing points which fill the circle.

• radius (np.ndarray, shape = (n,), optional) – array containing radius of each point from center c.

numbacs.utils.arclength(pts)

Compute total arclength of curve defined by pts.

Parameters:

pts (np.ndarray, shape=(npts,)) – points representing curve for which arclength is to be computed.

Returns:

arclength_ – arclength of curve defined by points.

Return type:

float

numbacs.utils.arclength_along_arc(pts)

Compute cummulative arclength at each point defining a curve.

Parameters:

pts (np.ndarray, shape=(npts,)) – points representing curve for which arclength is to be computed.

Returns:

arclength_ – array containing cummulative arclength of curve defined by pts.

Return type:

np.ndarray, shape = (npts,)

numbacs.utils.interp_curve(curve, n, s=0, k=3, per=0)

Return n interpolated values of curve.

Parameters:

• curve (np.ndarray, shape = (npts,2)) – array containing x,y-coordinates of curve being interpolated.

• n (int) – number of equally spaced interpolated points to return.

• s (float, optional) – smoothing parameter for spline, 0 will fit all data points exactly. The default is 0.

• k (int, optional) – degree of spline, using even numbers is not recommended, must be 1 <= k <= 5. The default is 3.

• per (int, optional) – if nonzero, data points are considered periodic. The default is 0.

Returns:

curvei – array containing interpolated values of curve.

Return type:

np.ndarray, shape = (n,2)

numbacs.utils.wn_pt_in_poly(polygon, point)

Winding number algorithm to determine if point is inside polygon. Based off of java implementation - https://observablehq.com/@jrus/winding-number - by Jacob Rus.

Parameters:

• polygon (np.ndarray, shape = (n,2)) – array containing vertices of polygon, first and last points should match.

• point (np.ndarray, shape = (2,)) – array containing the coordinates of point to be checked.

Returns:

wn – winding number, returns 1 if point is inside polygon and 0 if not.

Return type:

int

numbacs.utils.pts_in_poly(polygon, pts)

Checks if any point from pts is inside polygon. If a point is, the index of the first point found inside polygon is returned. Else, -1 is returned.

Parameters:

• polygon (np.ndarray, shape = (n,2)) – array containing vertices of polygon, first and last points should match.

• pts (np.ndarray, shape = (npts,2)) – array containing the coordinates of the points to be checked.

Returns:

if point from pts is found inside polygon, its index is returned, if not, -1 is returned.

Return type:

int

numbacs.utils.pts_in_poly_mask(polygon, pts)

Checks which points from pts are inside polygon. Returns a boolean mask corresponding to points inside polygon.

Parameters:

• polygon (np.ndarray, shape = (n,2)) – array containing vertices of polygon, first and last points should match.

• pts (np.ndarray, shape = (npts,2)) – array containing the coordinates of the points to be checked.

Returns:

mask – bool mask with indices matching those of pts, True if in polygon, False if not.

Return type:

np.ndarray, shape = (npts,)

numbacs.utils.cart_prod(vecs)

Computes the Cartesian product using vectors from vecs, works for any number of vectors.

Parameters:

vecs (tuple) – tuple containing vectors representing the sets which will be used to compute Cartestian product, all vectors must be 1D np.ndarrays of the same type.

Returns:

prod – array containing the Cartesian product.

Return type:

np.ndarray, shape = (npts,nvecs)