Calculate gradients of quantities over links.
calc_grad_at_active_link(\*args, \*\*kwargs) |
Calculate gradients of node values over active links. |
calc_grad_at_link(grid, vals, \*args, \*\*kwds) |
Calculate gradients of node values at links. |
calculate_gradients_at_faces(\*args, \*\*kwargs) |
Calculate gradients of node values over faces. |
calculate_diff_at_links(\*args, \*\*kwargs) |
Calculate differences of node values over links. |
calculate_diff_at_active_links(\*args, \*\*kwargs) |
Calculate differences of node values over active links. |
calc_aspect_at_node(grid, slope_component_tuple=None, elevs='topographic__elevation', unit='degrees', ignore_closed_nodes=True)[source]¶Get array of aspect of a surface.
Calculates at returns the aspect of a surface. Aspect is returned as radians clockwise of north, unless input parameter units is set to ‘degrees’.
If slope_component_tuple is provided, i.e., (slope_x, slope_y), the aspect will be calculated from these data.
If it is not, it will be derived from elevation data at the nodes, which can either be a string referring to a grid field (default: ‘topographic__elevation’), or an nnodes-long numpy array of the values themselves.
If ignore_closed_nodes is False, all proximal elevation values will be used in the calculation. If True, only unclosed nodes are used.
| Parameters: | grid : ModelGrid
slope_component_tuple : (slope_x_array, slope_y_array) (optional)
elevs : str or array (optional)
unit : {‘degrees’, ‘radians’}
ignore_closed_nodes : bool
|
|---|
Examples
>>> from landlab import RasterModelGrid
>>> mg = RasterModelGrid((4, 4))
>>> z = mg.node_x ** 2 + mg.node_y ** 2
>>> mg.calc_aspect_at_node(elevs=z)
array([ 225. , 240.16585039, 255.2796318 , 258.69006753,
209.83414961, 225. , 243.54632481, 248.77808974,
194.7203682 , 206.45367519, 225. , 231.94498651,
191.30993247, 201.22191026, 218.05501349, 225. ])
>>> z = z.max() - z
>>> mg.calc_aspect_at_node(elevs=z)
array([ 45. , 60.16585039, 75.2796318 , 78.69006753,
29.83414961, 45. , 63.54632481, 68.77808974,
14.7203682 , 26.45367519, 45. , 51.94498651,
11.30993247, 21.22191026, 38.05501349, 45. ])
>>> mg = RasterModelGrid((4, 4), (2., 3.))
>>> z = mg.node_x ** 2 + mg.node_y ** 2
>>> mg.calc_aspect_at_node(elevs=z)
array([ 236.30993247, 247.52001262, 259.97326008, 262.40535663,
220.75264634, 234.41577266, 251.13402374, 255.29210302,
201.54258265, 215.47930877, 235.73541937, 242.24162456,
196.69924423, 209.43534223, 229.19345757, 236.30993247])
Note that a small amount of asymmetry arises at the grid edges due to the “missing” nodes beyond the edge of the grid.
LLCATS: NINF SURF
calc_diff_at_link(grid, vals, *args, **kwds)[source]¶Calculate differences of node values over links.
Calculates the difference in quantity node_values at each link in the grid.
Construction:
calc_diff_at_link(grid, node_values, out=None)
| Parameters: | grid : ModelGrid
node_values : ndarray or field name
out : ndarray, optional
|
|---|---|
| Returns: | ndarray
|
Examples
>>> import numpy as np
>>> from landlab import RasterModelGrid
>>> rmg = RasterModelGrid((3, 3))
>>> z = np.zeros(9)
>>> z[4] = 1.
>>> rmg.calc_diff_at_link(z)
array([ 0., 0., 0., 1., 0., 1., -1., 0., -1., 0., 0., 0.])
LLCATS: LINF GRAD
calc_grad_at_active_link(*args, **kwargs)[source]¶Calculate gradients of node values over active links.
Calculates the gradient in quantity node values at each active link in the grid.
Construction:
calc_grad_at_active_link(grid, node_values, out=None)
| Parameters: | grid : ModelGrid
node_values : ndarray or field name
out : ndarray, optional
|
|---|---|
| Returns: | ndarray
LLCATS: DEPR LINF GRAD |
calc_grad_at_link(grid, vals, *args, **kwds)[source]¶Calculate gradients of node values at links.
Calculates the gradient in node_values at each link in the grid, returning an array of length number_of_links.
Construction:
calc_grad_at_link(grid, node_values, out=None)
| Parameters: | grid : ModelGrid
node_values : ndarray or field name (x number of nodes)
out : ndarray, optional (x number of links)
|
|---|---|
| Returns: | ndarray
|
Examples
>>> from landlab import RasterModelGrid
>>> rg = RasterModelGrid(3, 4, 10.0)
>>> z = rg.add_zeros('node', 'topographic__elevation')
>>> z[5] = 50.0
>>> z[6] = 36.0
>>> calc_grad_at_link(rg, z) # there are 17 links
array([ 0. , 0. , 0. , 0. , 5. , 3.6, 0. , 5. , -1.4, -3.6, 0. ,
-5. , -3.6, 0. , 0. , 0. , 0. ])
>>> from landlab import HexModelGrid
>>> hg = HexModelGrid(3, 3, 10.0)
>>> z = hg.add_zeros('node', 'topographic__elevation', noclobber=False)
>>> z[4] = 50.0
>>> z[5] = 36.0
>>> calc_grad_at_link(hg, z) # there are 11 faces
array([ 0. , 0. , 0. , 5. , 5. , 3.6, 3.6, 0. , 5. , -1.4, -3.6,
0. , -5. , -5. , -3.6, -3.6, 0. , 0. , 0. ])
LLCATS: LINF GRAD
calc_grad_at_patch(grid, elevs='topographic__elevation', ignore_closed_nodes=True, unit_normal=None, slope_magnitude=None)[source]¶Calculate the components of the gradient at each patch.
If ignore_closed_nodes is True, closed nodes do not affect gradient calculations. If a closed node is present in a patch, the patch gradient is set to zero in both x and y directions.
| Parameters: | grid : ModelGrid
elevs : str or ndarray, optional
ignore_closed_nodes : bool
unit_normal : array with shape (num_patches, 3) (optional)
slope_magnitude : array with size num_patches (optional)
|
|---|---|
| Returns: | gradient_tuple : (x_component_at_patch, y_component_at_patch)
|
Examples
>>> import numpy as np
>>> from landlab import RasterModelGrid
>>> mg = RasterModelGrid((4, 5))
>>> z = mg.node_y
>>> (x_grad, y_grad) = mg.calc_grad_at_patch(elevs=z)
>>> np.allclose(y_grad, np.pi / 4.)
True
>>> np.allclose(x_grad, 0.)
True
LLCATS: PINF GRAD
calc_grad_of_active_link(*args, **kwargs)[source]¶Calculate gradients at active links.
Examples
>>> import numpy as np
>>> from landlab import RasterModelGrid
>>> grid = RasterModelGrid((3, 4))
>>> z = np.array([0., 0., 0., 0.,
... 1., 1., 1., 1.,
... 3., 3., 3., 3.])
>>> grid.calc_grad_of_active_link(z)
array([ 1., 1., 0., 0., 0., 2., 2.])
This method is deprecated. Instead, use calc_grad_at_link.
>>> vals = grid.calc_grad_at_link(z)
>>> vals[grid.active_links]
array([ 1., 1., 0., 0., 0., 2., 2.])
LLCATS: DEPR
calc_slope_at_node(grid, elevs='topographic__elevation', method='patch_mean', ignore_closed_nodes=True, return_components=False, **kwds)[source]¶Array of slopes at nodes, averaged over neighboring patches.
Produces a value for node slope (i.e., mean gradient magnitude) at each node in a manner analogous to a GIS-style slope map. It averages the gradient on each of the patches surrounding the node, creating a value for node slope that better incorporates nonlocal elevation information. Directional information can still be returned through use of the return_components keyword.
Note that under these definitions, it is not always true that:
mag, cmp = mg.calc_slope_at_node(z)
mag ** 2 == cmp[0] ** 2 + cmp[1] ** 2 # not always true
If ignore_closed_nodes is False, all proximal elevation values will be used in the calculation. If True, only unclosed nodes are used.
| Parameters: | grid : ModelGrid
elevs : str or ndarray, optional
method : {‘patch_mean’, ‘Horn’}
ignore_closed_nodes : bool
return_components : bool
|
|---|---|
| Returns: | float array or length-2 tuple of float arrays
|
Examples
>>> import numpy as np
>>> from landlab import RadialModelGrid, RasterModelGrid
>>> mg = RasterModelGrid((4, 5), 1.)
>>> z = mg.node_x
>>> slopes = mg.calc_slope_at_node(elevs=z)
>>> np.allclose(slopes, 45. / 180. * np.pi)
True
>>> mg = RasterModelGrid((4, 5), 1.)
>>> z = - mg.node_y
>>> slope_mag, cmp = mg.calc_slope_at_node(elevs=z,
... return_components=True)
>>> np.allclose(slope_mag, np.pi / 4.)
True
>>> np.allclose(cmp[0], 0.)
True
>>> np.allclose(cmp[1], - np.pi / 4.)
True
>>> mg = RadialModelGrid(num_shells=9)
>>> z = mg.radius_at_node
>>> slopes = mg.calc_slope_at_node(elevs=z)
>>> mean_ring_slope = []
>>> for i in range(10):
... mean_ring_slope.append(
... slopes[np.isclose(mg.radius_at_node, i)].mean())
Notice the small amounts of numerical error here:
>>> target_mean_ring_slope = [0.85707194785013108, 0.79363155567711452,
... 0.77922185867135429, 0.78359813570962411,
... 0.78433070957439543, 0.78452745144699965,
... 0.78477643475446901, 0.78506472422668094,
... 0.78505793680521629, 0.78661256633611021]
>>> np.allclose(mean_ring_slope, target_mean_ring_slope)
True
LLCATS: NINF GRAD SURF
calc_slope_at_patch(grid, elevs='topographic__elevation', ignore_closed_nodes=True, unit_normal=None)[source]¶Calculate the slope (positive magnitude of gradient) at patches.
If ignore_closed_nodes is True, closed nodes do not affect slope calculations. If a closed node is present in a patch, the patch slope is set to zero.
| Parameters: | grid : ModelGrid
elevs : str or ndarray, optional
ignore_closed_nodes : bool
unit_normal : array with shape (num_patches, 3) (optional)
|
|---|---|
| Returns: | slopes_at_patch : n_patches-long array
|
Examples
>>> import numpy as np
>>> from landlab import RasterModelGrid
>>> mg = RasterModelGrid((4, 5))
>>> z = mg.node_x
>>> S = mg.calc_slope_at_patch(elevs=z)
>>> S.size == mg.number_of_patches
True
>>> np.allclose(S, np.pi / 4.)
True
LLCATS: PINF GRAD
calc_unit_normal_at_patch(grid, elevs='topographic__elevation')[source]¶Calculate and return the unit normal vector <a, b, c> to a patch.
| Parameters: | grid : ModelGrid
elevs : str or ndarray, optional
|
|---|---|
| Returns: | nhat : num-patches x length-3 array
|
Examples
>>> from landlab import HexModelGrid
>>> mg = HexModelGrid(3, 3)
>>> z = mg.node_x * 3. / 4.
>>> mg.calc_unit_normal_at_patch(z)
array([[-0.6, 0. , 0.8],
[-0.6, 0. , 0.8],
[-0.6, 0. , 0.8],
[-0.6, 0. , 0.8],
[-0.6, 0. , 0.8],
[-0.6, 0. , 0.8],
[-0.6, 0. , 0.8],
[-0.6, 0. , 0.8],
[-0.6, 0. , 0.8],
[-0.6, 0. , 0.8]])
LLCATS: PINF GRAD
calculate_diff_at_active_links(*args, **kwargs)[source]¶Calculate differences of node values over active links.
Calculates the difference in quantity node_values at each active link in the grid.
Construction:
calculate_diff_at_active_links(grid, node_values, out=None)
| Parameters: | grid : ModelGrid
node_values : ndarray or field name
out : ndarray, optional
|
|---|---|
| Returns: | ndarray
LLCATS: DEPR LINF GRAD |
calculate_diff_at_links(*args, **kwargs)[source]¶Calculate differences of node values over links.
Examples
>>> import numpy as np
>>> from landlab import RasterModelGrid
>>> grid = RasterModelGrid((3, 3))
>>> z = np.zeros(9)
>>> z[4] = 1.
>>> grid.calculate_diff_at_links(z)
array([ 0., 0., 0., 1., 0., 1., -1., 0., -1., 0., 0., 0.])
>>> grid.calc_diff_at_link(z)
array([ 0., 0., 0., 1., 0., 1., -1., 0., -1., 0., 0., 0.])
LLCATS: DEPR LINF GRAD
calculate_gradients_at_faces(*args, **kwargs)[source]¶Calculate gradients of node values over faces.
Calculate and return gradient in node_values at each face in the grid. Gradients are calculated from the nodes at either end of the link that crosses each face.
Construction:
calculate_gradients_at_faces(grid, node_values, out=None)
| Parameters: | grid : ModelGrid
node_values : ndarray or field name
out : ndarray, optional
|
|---|---|
| Returns: | ndarray (x number of faces)
|
Examples
>>> from landlab import RasterModelGrid
>>> rg = RasterModelGrid(3, 4, 10.0)
>>> z = rg.add_zeros('node', 'topographic__elevation')
>>> z[5] = 50.0
>>> z[6] = 36.0
>>> calculate_gradients_at_faces(rg, z) # there are 7 faces
array([ 5. , 3.6, 5. , -1.4, -3.6, -5. , -3.6])
>>> from landlab import HexModelGrid
>>> hg = HexModelGrid(3, 3, 10.0)
>>> z = hg.add_zeros('node', 'topographic__elevation', noclobber=False)
>>> z[4] = 50.0
>>> z[5] = 36.0
>>> calculate_gradients_at_faces(hg, z) # there are 11 faces
array([ 5. , 5. , 3.6, 3.6, 5. , -1.4, -3.6, -5. , -5. , -3.6, -3.6])
LLCATS: DEPR GRAD