### Example Usage of StaticStep

Source: https://slippy.readthedocs.io/en/latest/_modules/slippy/contact/static_step.html

Demonstrates the setup and solving of a static contact model involving a round surface and a flat surface with different materials. This example shows how to define surfaces, materials, a contact model, and a static step, then solve the model.

```python
import slippy.surface as s
import slippy.contact as c
# make surface geometry
flat_surface = s.FlatSurface(shift=(0,0))
round_surface = s.RoundSurface((1,1,1), extent = (0.006, 0.006),
                               shape = (255, 255), generate = True)
# make and set materials
steel = c.Elastic('Steel', {'E': 200e9, 'v':0.3})
aluminum = c.Elastic('Aluminum', {'E': 70e9, 'v':0.33})
flat_surface.material = aluminum
round_surface.material = steel
# make contact model
my_model = c.ContactModel('model-1', round_surface, flat_surface)
# make and add step
total_load = 100
my_step = c.StaticStep('contact', normal_load=total_load, rtol_interference=1e-2)
my_model.add_step(my_step)
# solve the model
result = my_model.solve()
```

--------------------------------

### Install Jupyter

Source: https://slippy.readthedocs.io/en/latest/_sources/examples.rst.txt

Install Jupyter using pip. This is a prerequisite for running the example notebooks locally.

```shell
python -m pip install jupyter
```

--------------------------------

### Full Lubrication Contact Model Setup

Source: https://slippy.readthedocs.io/en/latest/_modules/slippy/contact/lubrication_steps.html

This comprehensive example demonstrates the setup of a contact model involving a ball and a flat surface with a non-Newtonian lubricant. It includes Hertzian contact calculations, surface generation, material assignment, lubricant property definition, and the creation of a Reynolds solver and a contact step.

```python
import slippy
slippy.CUDA = False  # Note: we are using a reynolds solver which does not currently support the CUDA back end
import slippy.surface as s
import slippy.contact as c

radius = 0.01905       # The radius of the ball
load = 800             # The load on the ball in N
rolling_speed = 4      # The rolling speed in m/s (The mean speed of the surfaces)
youngs_modulus = 200e9 # The youngs modulus of the surfaces
p_ratio = 0.3          # The poission's ratio of the surfaces
grid_size = 65         # The number of points in the descretisation grid
eta_0 = 0.096          # Coefficient in the roelands pressure-viscosity equation
roelands_p_0 = 1/5.1e-9# Coefficient in the roelands pressure-viscosity equation
roelands_z = 0.68      # Coefficient in the roelands pressure-viscosity equation

# Solving the hertzian contact to get the domain size and the initial guess
hertz_result = c.hertz_full([radius, radius], [float('inf'), float('inf')],
                            [youngs_modulus, youngs_modulus],
                            [p_ratio, p_ratio], load)
hertz_pressure = hertz_result['max_pressure']
hertz_a = hertz_result['contact_radii'][0]
hertz_deflection = hertz_result['total_deflection']
hertz_pressure_function = hertz_result['pressure_f']

# make the surfaces
ball = s.RoundSurface((radius,)*3, shape = (grid_size, grid_size),
                      extent=(hertz_a*4,hertz_a*4), generate = True)
flat = s.FlatSurface()

# assigning materials
steel = c.Elastic('steel', {'E' : youngs_modulus, 'v' : p_ratio})
ball.material = steel
flat.material = steel

# make the non newtonian fluid
oil = c.Lubricant('oil') # Making a lubricant object to contain our sub models
oil.add_sub_model('nd_viscosity', c.lubricant_models.nd_roelands(eta_0, roelands_p_0,
                                                                 hertz_pressure, roelands_z))
oil.add_sub_model('nd_density', c.lubricant_models.nd_dowson_higginson(hertz_pressure))

# make the contact model
my_model = c.ContactModel('lubrication_test', ball, flat, oil)

# make a reynolds solver
reynolds = c.UnifiedReynoldsSolver(time_step = 0,
                                   grid_spacing = ball.grid_spacing,
                                   hertzian_pressure = hertz_pressure,
                                   radius_in_rolling_direction=radius,
                                   hertzian_half_width=hertz_a,
                                   dimentional_viscosity=eta_0,
                                   dimentional_density=872)

# Find the hertzian pressure distribution as an initial guess
X, Y = ball.get_points_from_extent()
X, Y = X + ball._total_shift[0], Y + ball._total_shift[1]
hertzian_pressure_dist = hertz_pressure_function(X, Y)

# Making the step
step = c.IterSemiSystem('main', reynolds, rolling_speed, 1, no_time=True, normal_load=load,
                        initial_guess=[hertz_deflection, hertzian_pressure_dist],
                        relaxation_factor=0.05, max_it_interference=3000)

# Adding the step to the contact model
my_model.add_step(step)

# solve the model:
state = my_model.solve()
```

--------------------------------

### Example: Recreating Hertz Solution with StaticStep

Source: https://slippy.readthedocs.io/en/latest/generated/slippy.contact.StaticStep.html

This example demonstrates how to set up and solve a static contact problem, recreating the Hertz solution. It involves defining surfaces, materials, a contact model, and a StaticStep with a specified normal load.

```python
>>> import slippy.surface as s
>>> import slippy.contact as c
>>> # make surface geometry
>>> flat_surface = s.FlatSurface(shift=(0,0))
>>> round_surface = s.RoundSurface((1,1,1), extent = (0.006, 0.006),
>>>                                shape = (255, 255), generate = True)
>>> # make and set materials
>>> steel = c.Elastic('Steel', {'E': 200e9, 'v':0.3})
>>> aluminum = c.Elastic('Aluminum', {'E': 70e9, 'v':0.33})
>>> flat_surface.material = aluminum
>>> round_surface.material = steel
>>> # make contact model
>>> my_model = c.ContactModel('model-1', round_surface, flat_surface)
>>> # make and add step
>>> total_load = 100
>>> my_step = c.StaticStep('contact', normal_load=total_load, rtol_interference=1e-2)
>>> my_model.add_step(my_step)
>>> # solve the model
>>> result = my_model.solve()
```

--------------------------------

### DiscFreqSurface Initialization Example

Source: https://slippy.readthedocs.io/en/latest/_modules/slippy/surface/FFTBased.html

Instantiates a DiscFreqSurface with specified frequencies and amplitudes, sets the extent, and then discretizes the surface.

```python
mySurf=DiscFreqSurface(10, 0.1)
mySurf.extent=[0.5,0.5]
mySurf.discretise(0.001)
```

--------------------------------

### Run Jupyter Notebook

Source: https://slippy.readthedocs.io/en/latest/_sources/examples.rst.txt

Start the Jupyter Notebook server. This will open a notebook interface in your browser, allowing you to access and run example files.

```shell
jupyter notebook
```

--------------------------------

### Set Up Local Development Environment

Source: https://slippy.readthedocs.io/en/latest/contributing.html

Install SlipPY into a virtual environment for local development using python setup.py develop.

```bash
$ mkvirtualenv slippy
$ cd slippy/
$ python setup.py develop

```

--------------------------------

### FlatSurface Example

Source: https://slippy.readthedocs.io/en/latest/_modules/slippy/surface/Geometric.html

Demonstrates creating and using a FlatSurface with a specified slope. This is useful for simulating planar terrains.

```python
>>> import numpy as np
>>> my_surface=FlatSurface(slope=(1,1))
>>> x, y = np.arange(10), np.arange(10)
>>> X, Y = np.meshgrid(x,y)
>>> Z=my_surface.height(X, Y)
```

--------------------------------

### Install SlipPY using Pip

Source: https://slippy.readthedocs.io/en/latest/installation.html

Once the virtual environment is activated, use this command to install SlipPY and its dependencies within that environment.

```bash
python -m pip install slippy

```

--------------------------------

### Install Slippy using Pip

Source: https://slippy.readthedocs.io/en/latest/_sources/installation.rst.txt

Once the virtual environment is activated, use this command to install Slippy and its dependencies within that environment.

```bash
python -m pip install slippy
```

--------------------------------

### RoundSurface Initialization Examples

Source: https://slippy.readthedocs.io/en/latest/_modules/slippy/surface/Geometric.html

Shows how to initialize RoundSurface for different scenarios, including spherical and cylindrical surfaces, with options for extent, grid spacing, and rotation.

```python
>>> import slippy.surface as s
>>> my_surface = s.RoundSurface((1,1,1), extent=(0.5,0.5))
```

```python
>>> my_surface = s.RoundSurface((1,float('inf'),1), extent=(0.5,0.5), grid_spacing=0.001, generate = True)
```

```python
>>> my_surface = s.RoundSurface((1,float('inf'),1), extent=(0.5, 0.5), shape=(512, 512), generate = True,
>>>                             rotation=3.14/4)
```

--------------------------------

### Quasi-Static Contact Modeling Example

Source: https://slippy.readthedocs.io/en/latest/generated/slippy.contact.QuasiStaticStep.html

This example demonstrates how to model the contact between a rough cylinder and a flat plane using slippy.contact.QuasiStaticStep. It covers defining surfaces, materials, creating a contact model, setting up the quasi-static step with specified parameters, adding output requests, and solving the model. This code can be used to generate load-displacement curves.

```python
import slippy.surface as s
import slippy.contact as c
# define contact geometry
cylinder = s.RoundSurface((1 ,np.inf, 1), shape=(256, 256), grid_spacing=0.001)
roughness = s.HurstFractalSurface(1, 0.2, 1000, shape=(256, 256), grid_spacing=0.001,
                                   generate = True)
combined = cylinder + roughness * 0.00001
flat = s.FlatSurface(shape=(256, 256), grid_spacing=0.001, generate = True)
# define material behaviour and assign to surfaces
material = c.Elastic('steel', properties = {'E':200e9, 'v':0.3})
combined.material = material
flat.material = material
# make a contact model
my_model = c.ContactModel('qss_test', combined, flat)
# make a modelling step to describe the problem
max_int = 0.002
n_time_steps = 20
my_step = c.QuasiStaticStep('loading', n_time_steps, no_time=True,
                            interference = [max_int*0.001, max_int],
                            periodic_geometry=True, periodic_axes = (False, True))
# add the steps to the model
my_model.add_step(my_step)
# add output requests
output_request = c.OutputRequest('Output-1',
                                 ['interference', 'total_normal_load',
                                  'loads_z', 'total_displacement',
                                  'converged'])
my_step.add_output(output_request)
# solve the model
final_result = my_model.solve()
```

--------------------------------

### Create and Discretize a Hurst Fractal Surface

Source: https://slippy.readthedocs.io/en/latest/_modules/slippy/surface/FFTBased.html

Example of creating a HurstFractalSurface object with specified fractal parameters and then discretizing it to generate a surface profile. The show() method is called to visualize the generated surface.

```python
my_surface=HurstFractalSurface(1,0.2,1000, shape=(128, 128), grid_spacing=0.01)
my_surface.discretise()
my_surface.show()
```

--------------------------------

### Elastic Material Model Example

Source: https://slippy.readthedocs.io/en/latest/_modules/slippy/core/elastic_material.html

Demonstrates how to create an Elastic material model for steel and retrieve its properties like p-wave modulus and speed of sound. Requires the 'numpy' library.

```python
import numpy as np
from slippy.core.elastic_material import Elastic

# Make a material model for elastic steel
steel = Elastic('steel', {'E': 200e9, 'v': 0.3})
# Find it's p-wave modulus:
pwm = steel.M
# Find the speeds of sound:
sos = steel.speed_of_sound(7890)
```

--------------------------------

### _ArrayReader Initialization and Usage Example

Source: https://slippy.readthedocs.io/en/latest/_modules/slippy/core/outputs.html

Demonstrates how to create and use an _ArrayReader object for lazily accessing array data stored within a zip file. It shows how to initialize the reader with file details and then access array properties like maximum value and individual elements.

```python
>>> with OutputSaver('test') as output_files:
>>>     output_files.write({'my_array':np.array([1,2,3,4])})
>>> lazy_array = _ArrayReader('test.sar', '**array**#0#(4,)#int32')
>>> #                                                ^ file name in zip repo
>>> #                                                   ^ shape of array
>>> #                                                       ^ dtype of array
>>> np.max(lazy_array)
4
>>> lazy_array[0]
1
```

--------------------------------

### Example Usage of alicona_read

Source: https://slippy.readthedocs.io/en/latest/_modules/slippy/surface/alicona.html

Demonstrates how to use the alicona_read function to load data from an .al3d file and display the depth data using matplotlib.

```python
if __name__ == '__main__':
    file_name_t = "D:\\Downloads\\Alicona_data\\Surface Profile Data\\dem.al3d"
    from matplotlib.pyplot import imshow

    data_t = alicona_read(file_name_t)

    imshow(data_t['DepthData'])
```

--------------------------------

### Rigid Material Initialization

Source: https://slippy.readthedocs.io/en/latest/_modules/slippy/core/materials.html

Instantiates a Rigid material object with a given name. This is a basic setup for defining a rigid material within the system.

```python
rigid = Rigid('rigid')
```

--------------------------------

### QuasiStaticStep Initialization

Source: https://slippy.readthedocs.io/en/latest/_modules/slippy/contact/quasi_static_step.html

Demonstrates the initialization of the QuasiStaticStep class with various parameters controlling the simulation behavior, such as time stepping, loading conditions, and numerical methods.

```python
def __init__(self, step_name: str, number_of_steps: int, no_time: bool = False,
             time_period: float = 1.0,
             off_set_x: typing.Union[float, typing.Sequence[float]] = 0.0,
             off_set_y: typing.Union[float, typing.Sequence[float]] = 0.0,
             interference: typing.Union[float, typing.Sequence[float]] = None,
             normal_load: typing.Union[float, typing.Sequence[float]] = None,
             mean_gap: typing.Union[float, typing.Sequence[float]] = None,
             relative_loading: bool = False,
             adhesion: bool = True,
             unloading: bool = False,
             fast_ld: bool = False,
             impact_properties: dict = None,
             movement_interpolation_mode: str = 'linear',
             profile_interpolation_mode: str = 'nearest',
             periodic_geometry: bool = False, periodic_axes: tuple = (False, False),
             method: str = 'auto',
             max_it: int = 1000, tolerance=1e-8,
             max_it_outer: int = 100, tolerance_outer=1e-4,
             no_update_warning: bool = True,
             upper: float = 4.0):

    # movement interpolation mode sort out movement interpolation mode make array of values
    if impact_properties is not None:
        raise NotImplementedError("Impacts are not yet implemented")
    # work out the time step if needed:
    self._no_time = no_time
    self.total_time = time_period
    if not no_time and fast_ld:
        raise ValueError("Cannot have time dependence and fast_ld, either set no_time True or set fast_ld False")
    self._fast_ld = fast_ld
    self._relative_loading = relative_loading
    self.profile_interpolation_mode = profile_interpolation_mode
    self._periodic_profile = periodic_geometry
    self._periodic_axes = periodic_axes
    self._max_it_outer = max_it_outer
    self._r_tol_outer = tolerance_outer
    self._max_it = max_it
    self._r_tol = tolerance
    self.number_of_steps = int(round(number_of_steps))

    if method not in {'auto', 'pk', 'double', 'rey'}:
        raise ValueError(f"Unrecognised method for step {step_name}: {method}")
    sum_param = (normal_load is not None) + (interference is not None) + (mean_gap is not None)
    if sum_param > 1 or sum_param == 0:
        raise ValueError(f"Exactly one of normal_load, interference and mean_gap must be set, {sum_param} were set")
    if mean_gap is not None:
        if method not in {'auto', 'rey'}:
            raise ValueError("pk and double methods don't support mean gap")
        else:
            method = 'rey'
    if interference is not None and method == 'rey':
        raise ValueError("Rey method doesn't support interference")

    self._method = method
    self._height_optimisation_func = None
    self._adhesion = adhesion
    self._unloading = unloading
    self._upper_factor = upper

    self.time_step = time_period / number_of_steps

    # check that something is actually changing
    self.update = set()
```

--------------------------------

### Smooth Surface EHL with Non-Newtonian Fluid Example

Source: https://slippy.readthedocs.io/en/latest/generated/slippy.contact.IterSemiSystem.html

This example demonstrates setting up and solving an Elasto-Hydrodynamic Lubrication (EHL) contact with a non-Newtonian fluid using slippy.contact.IterSemiSystem. It includes defining surfaces, materials, lubricants with specific rheological models, and the iterative solver setup.

```python
>>> import slippy
>>> slippy.CUDA = False  # Note: we are using a reynolds solver which does not currently support the CUDA back end
>>> import slippy.surface as s
>>> import slippy.contact as c
>>> 
>>> radius = 0.01905       # The radius of the ball
>>> load = 800             # The load on the ball in N
>>> rolling_speed = 4      # The rolling speed in m/s (The mean speed of the surfaces)
>>> youngs_modulus = 200e9 # The youngs modulus of the surfaces
>>> p_ratio = 0.3          # The poission's ratio of the surfaces
>>> grid_size = 65         # The number of points in the descretisation grid
>>> eta_0 = 0.096          # Coefficient in the roelands pressure-viscosity equation
>>> roelands_p_0 = 1/5.1e-9# Coefficient in the roelands pressure-viscosity equation
>>> roelands_z = 0.68      # Coefficient in the roelands pressure-viscosity equation
>>> 
>>> # Solving the hertzian contact to get the domain size and the initial guess
>>> hertz_result = c.hertz_full([radius, radius], [float('inf'), float('inf')],
>>>                             [youngs_modulus, youngs_modulus],
>>>                             [p_ratio, p_ratio], load)
>>> hertz_pressure = hertz_result['max_pressure']
>>> hertz_a = hertz_result['contact_radii'][0]
>>> hertz_deflection = hertz_result['total_deflection']
>>> hertz_pressure_function = hertz_result['pressure_f']
>>> 
>>> # make the surfaces
>>> ball = s.RoundSurface((radius,)*3, shape = (grid_size, grid_size),
>>>                       extent=(hertz_a*4,hertz_a*4), generate = True)
>>> flat = s.FlatSurface()
>>> 
>>> # assigning materials
>>> steel = c.Elastic('steel', {'E' : youngs_modulus, 'v' : p_ratio})
>>> ball.material = steel
>>> flat.material = steel
>>> 
>>> # make the non newtonian fluid
>>> oil = c.Lubricant('oil') # Making a lubricant object to contain our sub models
>>> oil.add_sub_model('nd_viscosity', c.lubricant_models.nd_roelands(eta_0, roelands_p_0,
>>>                                                                  hertz_pressure, roelands_z))
>>> oil.add_sub_model('nd_density', c.lubricant_models.nd_dowson_higginson(hertz_pressure))
>>> 
>>> # make the contact model
>>> my_model = c.ContactModel('lubrication_test', ball, flat, oil)
>>> 
>>> # make a reynolds solver
>>> reynolds = c.UnifiedReynoldsSolver(time_step = 0,
>>>                                    grid_spacing = ball.grid_spacing,
>>>                                    hertzian_pressure = hertz_pressure,
>>>                                    radius_in_rolling_direction=radius,
>>>                                    hertzian_half_width=hertz_a,
>>>                                    dimentional_viscosity=eta_0,
>>>                                    dimentional_density=872)
>>> 
>>> # Find the hertzian pressure distribution as an initial guess
>>> X, Y = ball.get_points_from_extent()
>>> X, Y = X + ball._total_shift[0], Y + ball._total_shift[1]
>>> hertzian_pressure_dist = hertz_pressure_function(X, Y)
>>> 
>>> # Making the step
>>> step = c.IterSemiSystem('main', reynolds, rolling_speed, 1, no_time=True, normal_load=load,
>>>                         initial_guess=[hertz_deflection, hertzian_pressure_dist],
>>>                         relaxation_factor=0.05, max_it_interference=3000)
>>> 
>>> # Adding the step to the contact model
>>> my_model.add_step(step)
>>> 
>>> # solve the model: 
>>> state = my_model.solve()
```

--------------------------------

### Initialize Quasi-Static Step Parameters

Source: https://slippy.readthedocs.io/en/latest/_modules/slippy/contact/quasi_static_step.html

Sets up initial conditions for quasi-static steps, including offsets, loads, and interference. Handles cases where parameters are functions of time or constant values. Raises errors for conflicting or insufficient input parameters.

```python
if not isinstance(off_set_x, Number) or not isinstance(off_set_y, Number):
            if no_time:
                raise ValueError("Can not have no time dependence and sliding contact")
            off_set_x = [off_set_x] * 2 if isinstance(off_set_x, Number) else off_set_x
            off_set_y = [off_set_y] * 2 if isinstance(off_set_y, Number) else off_set_y
            off_set_x_func = make_interpolation_func(off_set_x, movement_interpolation_mode, 'relative_off_set_x')
            off_set_y_func = make_interpolation_func(off_set_y, movement_interpolation_mode, 'relative_off_set_y')
            self._off_set_upd = lambda time: np.array([off_set_y_func(time), off_set_x_func(time)])
            self.update.add('off_set')
            self.off_set = None
        else:
            self.off_set = np.array([off_set_y, off_set_x])

        if normal_load is not None and interference is not None:
            raise ValueError("Both normal_load and interference are set, only one of these can be set")
        if normal_load is None and interference is None:
            if relative_loading:
                interference = 0
            else:
                raise ValueError("Cannot have no set load or interference and not relative loading, set either the"
                                 "normal load, normal interference or change relative_loading to True")

        self.load_controlled = False

        if normal_load is not None:
            if isinstance(normal_load, Number):
                self.normal_load = normal_load
            else:
                self.normal_load = None
                self._normal_load_upd = make_interpolation_func(normal_load, movement_interpolation_mode,
                                                                'normal_load')
                self.update.add('normal_load')
            self.load_controlled = True
        else:
            self.normal_load = None

        if mean_gap is not None:
            if isinstance(mean_gap, Number):
                self.mean_gap = mean_gap
            else:
                self.mean_gap = None
                self._mean_gap_upd = make_interpolation_func(mean_gap, movement_interpolation_mode,
                                                             'mean_gap')
                self.update.add('mean_gap')
        else:
            self.mean_gap = None

        if interference is not None:
            if isinstance(interference, Number):
                self.interference = interference
            else:
                self.interference = None
                self._interference_upd = make_interpolation_func(interference, movement_interpolation_mode,
                                                                 'interference')
                self.update.add('interference')
        else:
            self.interference = None

        if not self.update and no_update_warning:
            warnings.warn("Nothing set to update")

        provides = {'off_set', 'loads_z', 'surface_1_displacement_z', 'surface_2_displacement_z',
                    'total_displacement_z', 'interference', 'just_touching_gap', 'surface_1_points', 'contact_nodes',
                    'surface_2_points', 'time', 'time_step', 'new_step', 'converged', 'gap', 'total_normal_load'}
        super().__init__(step_name, time_period, provides)
```

--------------------------------

### Show Surface Profile as Image

Source: https://slippy.readthedocs.io/en/latest/_modules/slippy/surface/Surface_class.html

Demonstrates how to display the surface profile as an image using the show method. Requires importing slippy.surface and numpy.

```python
import slippy.surface as s
import numpy as np
my_surface=s.assurface(np.random.rand(10,10))
my_surface.show('profile', 'image')
```

--------------------------------

### RandomFilterSurface.get_points_from_extent

Source: https://slippy.readthedocs.io/en/latest/_sources/generated/slippy.surface.RandomFilterSurface.rst.txt

Gets points from the surface extent.

```APIDOC
## RandomFilterSurface.get_points_from_extent

### Description
Gets points from the surface extent.

### Method
get_points_from_extent

### Parameters
This method does not explicitly list parameters in the source documentation.
```

--------------------------------

### RandomFilterSurface.get_height_of_mat_vr

Source: https://slippy.readthedocs.io/en/latest/_sources/generated/slippy.surface.RandomFilterSurface.rst.txt

Gets the height of the material volume (VR).

```APIDOC
## RandomFilterSurface.get_height_of_mat_vr

### Description
Gets the height of the material volume (VR).

### Method
get_height_of_mat_vr

### Parameters
This method does not explicitly list parameters in the source documentation.
```

--------------------------------

### get_summit_curvature

Source: https://slippy.readthedocs.io/en/latest/_modules/slippy/surface/Surface_class.html

Gets summit curvatures. This method is an alias for the `slippy.surface.get_summit_curvature` function.

```APIDOC
## get_summit_curvature

### Description
Gets summit curvatures. This method is an alias for the `slippy.surface.get_summit_curvature` function.

### Method
`get_summit_curvature(self, summits=None, mask=None, filter_cut_off=None, four_nearest=False)`

### Parameters
#### Path Parameters
None

#### Query Parameters
* **summits** (array, optional) - The summits to calculate curvature for. If None, all summits are considered.
* **mask** (array, optional) - The mask to apply to the surface.
* **filter_cut_off** (float, optional) - The cut-off frequency for filtering.
* **four_nearest** (bool, optional) - Whether to use the four nearest neighbors for calculations.

### Request Example
None

### Response
#### Success Response (200)
Returns the summit curvatures.

#### Response Example
None
```

--------------------------------

### ProbFreqSurface Initialization and Height Calculation

Source: https://slippy.readthedocs.io/en/latest/_modules/slippy/surface/FFTBased.html

Initializes a probabilistic frequency surface with parameters H, qr, and qs. The _height method generates a surface profile using FFT, calculating frequencies and variances based on input parameters and random normal distribution.

```python
def __init__(self, h=2, qr=0.05, qs=10,
                 generate: bool = False, grid_spacing: float = None,
                 extent: tuple = None, shape: tuple = None):
        self.h = h
        self.qs = qs
        self.qr = qr
        super().__init__(grid_spacing=grid_spacing, extent=extent, shape=shape, generate=generate)


    def rotate(self, radians: Number):
        raise NotImplementedError("Probabilistic frequency surface cannot be rotated")

    def shift(self, shift: tuple = None):
        if shift is None:
            return
        raise NotImplementedError("Probabilistic frequency surface cannot be shifted")

    def _height(self, x_mesh, y_mesh):
        grid_spacing, extent, shape = check_coords_are_simple(x_mesh, y_mesh)

        qny = np.pi / grid_spacing

        u = np.linspace(0, qny, shape[0])
        u_mesh, v_mesh = np.meshgrid(u, u)
        freqs = np.abs(u_mesh + v_mesh)
        varience = np.zeros(freqs.shape)
        varience[np.logical_and((1 / freqs) > (1 / self.qr), (2 * np.pi / freqs) <= (extent[0]))] = 1
        varience[np.logical_and((1 / freqs) >= (1 / self.qs), (1 / freqs) < (1 / self.qr))] = \
            (freqs[np.logical_and(1 / freqs >= 1 / self.qs, 1 / freqs < 1 / self.qr)] / self.qr) ** (-2 * (1 + self.h))

        fou_trans = np.reshape(np.array([np.random.normal() * var ** 0.5 for var in varience.flatten()]), freqs.shape)
        return np.real(np.fft.ifft2(fou_trans))

    def __repr__(self):
        string = self._repr_helper()
        return f'ProbFreqSurface(h={self.h}, qr={self.qr}, qs={self.qs}{string})'
```

--------------------------------

### Surface Shape Property

Source: https://slippy.readthedocs.io/en/latest/_modules/slippy/surface/Surface_class.html

Sets or gets the shape of the surface profile array. Cannot be set if a profile is already present.

```python
    @property
    def shape(self):
        """The shape of the surface profile array, the number of points in each direction
        """
        return self._shape
```

```python
    @shape.setter
    def shape(self, value: typing.Sequence[int]):
        if not isinstance(value, Sequence):
            raise ValueError(f"Shape should be a Sequence type, got: {type(value)}")

        if self._profile is not None:
            raise ValueError("Cannot set shape when profile is present")

        self._shape = tuple([int(x) for x in value])
        self._size = np.product(self._shape)
        if self.grid_spacing is not None:
            self._extent = tuple([v * self.grid_spacing for v in value])
        elif self.extent is not None:
            self._grid_spacing = self._extent[0] / self._shape[0]
            self._extent = tuple([sz * self.grid_spacing for sz in self.shape])
```

```python
    @shape.deleter
    def shape(self):
        if self.profile is None:
            self._shape = None
            self._size = None
            self._extent = None
            self._grid_spacing = None
        else:
            msg = "Cannot delete shape with a surface profile set"
            raise ValueError(msg)
```

--------------------------------

### Create and Discretize HurstFractalSurface

Source: https://slippy.readthedocs.io/en/latest/generated/slippy.surface.HurstFractalSurface.html

Instantiates a HurstFractalSurface object with specified fractal parameters and then discretizes it over a defined grid. The 'show()' method is then called to visualize the generated surface.

```python
>>> #create the surface object with the specified fractal parameters
>>> my_surface=HurstFractalSurface(1,0.2,1000, shape=(128, 128), grid_spacing=0.01)
>>> #descrtise the surface over a grid 1 unit by 1 unit with a grid_spacing of 0.01
>>> my_surface.discretise()
>>> my_surface.show()
```

--------------------------------

### grid_spacing property

Source: https://slippy.readthedocs.io/en/latest/_modules/slippy/surface/Surface_class.html

Gets or sets the grid spacing of the surface. Handles type conversion and validation, and updates the surface extent accordingly.

```APIDOC
## `grid_spacing` property

### Description
Manages the distance between grid points. When set, it validates the input, converts it to a float, and recalculates the surface extent based on the profile shape or vice versa.

### Getter
Returns the current grid spacing.

### Setter
```python
@grid_spacing.setter
def grid_spacing(self, grid_spacing: float):
    # ... setter logic ...
```

#### Parameters
*   **grid_spacing** (float): The new grid spacing value.

### Deleter
```python
@grid_spacing.deleter
def grid_spacing(self):
    # ... deleter logic ...
```

#### Description
Resets the grid spacing and extent to `None`.
```

--------------------------------

### Surface Extent Property

Source: https://slippy.readthedocs.io/en/latest/_modules/slippy/surface/Surface_class.html

Sets or gets the overall dimensions of the surface. Ensures aspect ratio consistency with the profile if the profile exists.

```python
    @property
    def extent(self):
        """ The overall dimensions of the surface in the same units as grid spacing
        """
        return self._extent
```

```python
    @extent.setter
    def extent(self, value: typing.Sequence[float]):
        if not isinstance(value, Sequence):
            msg = "Extent must be a Sequence, got {}".format(type(value))
            raise TypeError(msg)
        if len(value) > 2:
            raise ValueError("Too many elements in extent, must be a maximum of two dimensions")

        if self.profile is not None:
            p_aspect = (self.shape[0]) / (self.shape[1])
            e_aspect = value[0] / value[1]
            if abs(e_aspect - p_aspect) > 0.0001:
                msg = "Extent aspect ratio doesn't match profile aspect ratio"
                raise ValueError(msg)
            else:
                self._extent = tuple(value)
                self._grid_spacing = value[0] / (self.shape[0])
        else:
            self._extent = tuple(value)
            self.dimensions = len(value)
            if self.grid_spacing is not None:
                self._shape = tuple([int(v / self.grid_spacing) for v in value])
                self._size = np.product(self._shape)
            if self._shape is not None:
                self._grid_spacing = self._extent[0] / self._shape[0]
                self._extent = tuple([sz * self._grid_spacing for sz in self._shape])
        return
```

```python
    @extent.deleter
    def extent(self):
        self._extent = None
        self._grid_spacing = None
        if self.profile is None:
            self._shape = None
            self._size = None
```

--------------------------------

### OutputRequest.__init__

Source: https://slippy.readthedocs.io/en/latest/_sources/generated/slippy.contact.OutputRequest.rst.txt

Initializes a new instance of the OutputRequest class.

```APIDOC
## OutputRequest.__init__

### Description
Initializes a new instance of the OutputRequest class.

### Method
__init__

### Parameters
(No parameters explicitly documented)

### Request Example
(No request example provided)

### Response
(No response details provided)
```

--------------------------------

### Create and Configure Contact Model Step

Source: https://slippy.readthedocs.io/en/latest/_modules/slippy/contact/quasi_static_step.html

Initializes a QuasiStaticStep for a contact model, specifying simulation parameters like maximum interference, number of time steps, and periodicity.

```python
# make a contact model
my_model = c.ContactModel('qss_test', combined, flat)

# make a modelling step to describe the problem
max_int = 0.002
n_time_steps = 20
my_step = c.QuasiStaticStep('loading', n_time_steps, no_time=True,
                            interference = [max_int*0.001, max_int],
                            periodic_geometry=True, periodic_axes = (False, True))
```

--------------------------------

### Get Summit Curvatures

Source: https://slippy.readthedocs.io/en/latest/_modules/slippy/surface/roughness_funcs.html

Calculates the curvatures of identified summits on a surface profile. Optionally finds summits if not provided and applies filtering.

```python
def get_summit_curvatures(profile: np.ndarray, summits: typing.Optional[np.ndarray] = None, grid_spacing: float = None,
                          mask: typing.Optional[typing.Union[np.ndarray, float]] = None,
                          filter_cut_off: typing.Optional[float] = None, four_nearest: bool = False):
    """ find the curvatures of the summits

    Parameters
    ----------
    profile: N by M array-like or Surface object
        The surface profile for analysis
    summits: N by M array (optional)
        A bool array True at the location of the summits, if not supplied the
        summits are found using find_summits first, see notes
    grid_spacing: float optional (False)
        The distance between points on the grid of the surface profile. Required
        only if the filter_cut_off is set and profile is not a surface object
    mask: array-like (bool)N by M or float optional (None)
        If an array, the array is used as a mask for the profile, must be the
        same shape as the profile, if a float is given, values which match are
        excluded from the calculation
    filter_cut_off: float, optional (None)
        The cutoff frequency of the low pass filter that is applied before finding summits
    four_nearest: bool, optional (False)
        If true a summit is found if it is higher than it's four nearest neighbours, else it must be higher than it's
        eight nearest neighbours
    Returns
    -------
    curves : array
        Array of summit curvatures of size sum(summits.flatten())

    Other parameters
    ----------------
    four_nearest : bool optional (False)
        If true any point that is higher than it's 4 nearest neighbours will be
        counted as a summit, otherwise a point must be higher than it's 8
        nearest neighbours to be a summit. Only used is summits are not given.
    filter_cut_off : float optional (None)
        If given the surface will be low pass filtered before finding summits.
        Only used if summits are not given

    See also
    --------
    find_summits
    roughness

    Notes
    -----
    If the summits parameter is not set, any key word arguments that can be
    passed to find_summits can be passed through this function.

    Examples
    --------

    """
    profile, grid_spacing = _check_surface(profile, grid_spacing)

    gs2 = grid_spacing ** 2

    if summits is None:
        summits = find_summits(profile, filter_cut_off=filter_cut_off,
                               grid_spacing=grid_spacing,
                               four_nearest=four_nearest, mask=mask)
    verts = np.transpose(np.nonzero(summits))
    curves = [-0.5 * (profile[vert[0] - 1, vert[1]] + profile[vert[0] + 1, vert[1]] + 
                      profile[vert[0], vert[1] - 1] + profile[vert[0], vert[1] + 1]
                      - 4 * profile[vert[0], vert[1]]) / gs2 for vert in verts]
    return curves
```

--------------------------------

### Create and Analyze Elastic Material Properties

Source: https://slippy.readthedocs.io/en/latest/generated/slippy.contact.Elastic.html

Demonstrates how to instantiate an Elastic material with its properties and retrieve derived values like the p-wave modulus and speed of sound. Requires density for speed of sound calculation.

```python
>>> # Make a material model for elastic steel
>>> steel = Elastic('steel', {'E': 200e9, 'v': 0.3})
>>> # Find it's p-wave modulus:
>>> pwm = steel.M
>>> # Find the speeds of sound:
>>> sos = steel.speed_of_sound(7890)
```

--------------------------------

### Quasi-Static Step Load Control Logic

Source: https://slippy.readthedocs.io/en/latest/_modules/slippy/contact/quasi_static_step.html

Handles different solver methods ('pk', 'rey', or default) for load-controlled steps. Sets up bounds and calls the appropriate optimization function.

```python
if self._method == 'pk':
            opt_func.contact_nodes = None
            opt_func.p_and_k(self.normal_load)
        elif self._method == 'rey':
            opt_func.contact_nodes = None
            opt_func.rey(target_load=self.normal_load)
        else:
            opt_func.change_load(self.normal_load, contact_nodes)
            # need to set bounds and pick a sensible starting point
            upper = self.upper
            print(f'upper bound set at: {upper}')
            if self._no_time:
                brackets = opt_func.get_bounds_from_cache(0, upper)
            else:
                brackets = (0, upper)
            print(f'Bounds adjusted using cache to: {brackets}')
            print(f'Interference tolerance set to {self._r_tol_outer} Relative')
            opt_func.brent(0, upper)

        # noinspection PyProtectedMember

        results = opt_func.results
        load_conv = (np.abs(results['total_normal_load'] - self.normal_load) / self.normal_load) < 0.05
        results['converged'] = bool(load_conv) and not opt_func.last_call_failed
        return results
```

--------------------------------

### Activate a Conda Virtual Environment

Source: https://slippy.readthedocs.io/en/latest/_sources/installation.rst.txt

Activate the previously created virtual environment to isolate package installations. The prompt will change to indicate the active environment.

```bash
conda activate name_of_env
```

--------------------------------

### QuasiStaticStep Constructor

Source: https://slippy.readthedocs.io/en/latest/generated/slippy.contact.QuasiStaticStep.html

Initializes a QuasiStaticStep object for quasi-static analysis. This constructor allows for detailed configuration of the simulation, including time stepping, interference, material properties, and geometric periodicity.

```APIDOC
## QuasiStaticStep Constructor

### Description
Initializes a QuasiStaticStep object for quasi-static analysis. This constructor allows for detailed configuration of the simulation, including time stepping, interference, material properties, and geometric periodicity.

### Method
__init__

### Parameters
- **_step_name** (str) - Required - The name of the step.
- **_number_of_steps** (int) - Required - The total number of time steps for the simulation.
- **_no_time** (bool) - Optional (default: False) - If True, time is not considered in the simulation.
- **_time_period** (float) - Optional (default: 1.0) - The total time period for the simulation.
- **_off_set_x** (Union[float, Sequence[float]]) - Optional (default: 0.0) - Offset in the x-direction.
- **_off_set_y** (Union[float, Sequence[float]]) - Optional (default: 0.0) - Offset in the y-direction.
- **_interference** (Optional[Union[float, Sequence[float]]]) - Optional (default: None) - The initial interference between bodies.
- **_normal_load** (Optional[Union[float, Sequence[float]]]) - Optional (default: None) - The normal load applied to the bodies.
- **_mean_gap** (Optional[Union[float, Sequence[float]]]) - Optional (default: None) - The mean gap between the bodies.
- **_relative_loading** (bool) - Optional (default: False) - If True, loading is relative.
- **_adhesion** (bool) - Optional (default: True) - If True, adhesion is considered.
- **_unloading** (bool) - Optional (default: False) - If True, unloading is simulated.
- **_fast_ld** (bool) - Optional (default: False) - If True, uses a faster loading/unloading method.
- **_impact_properties** (Optional[dict]) - Optional (default: None) - Properties for impact simulation.
- **_movement_interpolation_mode** (str) - Optional (default: 'linear') - Mode for interpolating movement.
- **_profile_interpolation_mode** (str) - Optional (default: 'nearest') - Mode for interpolating profiles.
- **_periodic_geometry** (bool) - Optional (default: False) - If True, the geometry is periodic.
- **_periodic_axes** (tuple) - Optional (default: (False, False)) - Specifies the axes for periodicity.
- **_method** (str) - Optional (default: 'auto') - The solution method to use.
- **_max_it** (int) - Optional (default: 1000) - Maximum number of iterations for the solver.
- **_tolerance** (float) - Optional (default: 1e-08) - Tolerance for the solver.
- **_max_it_outer** (int) - Optional (default: 100) - Maximum number of outer iterations.
- **_tolerance_outer** (float) - Optional (default: 0.0001) - Tolerance for outer iterations.
- **_no_update_warning** (bool) - Optional (default: True) - Suppress warning if no movement or loading changes are specified.
- **_upper** (float) - Optional (default: 4.0) - Upper bound factor for interference in load-controlled contact.
```

--------------------------------

### Subtract profile ignoring NaN values

Source: https://slippy.readthedocs.io/en/latest/generated/slippy.surface.subtract_polynomial.html

This example demonstrates subtracting a polynomial from a profile while ignoring NaN height values by using a float mask.

```python
flat_profile, coefs = subtract_polynomial(profile_2, 1, mask=float('nan'))
```

--------------------------------

### RoundSurface Height Calculation Example

Source: https://slippy.readthedocs.io/en/latest/_modules/slippy/surface/Geometric.html

Demonstrates calculating the height of a RoundSurface at specified points using its analytical height function. This is an alternative to discretizing the surface.

```python
>>> import numpy as np
>>> my_surface=RoundSurface(radius=(1,1,1))
>>> x, y = np.arange(10), np.arange(10)
>>> x_mesh, y_mesh = np.meshgrid(x,y)
>>> Z=my_surface.height(x_mesh, y_mesh)
```

--------------------------------

### Initialize Surface Profile and Wear Volumes

Source: https://slippy.readthedocs.io/en/latest/_modules/slippy/surface/Surface_class.html

Initializes the unworn and current surface profiles from a given value. It also sets up a defaultdict for tracking wear volumes, keyed by wear source names.

```python
try:
            self.unworn_profile = np.asarray(value, dtype=float).copy()
            # this has to be before _profile is set (rewritten for rolling surface)
            self.wear_volumes = defaultdict(lambda: np.zeros_like(self.unworn_profile))
            self._profile = np.asarray(value, dtype=float).copy()
        except ValueError:
            msg = "Could not convert profile to array of floats, profile contains invalid values"
            raise ValueError(msg)
```

--------------------------------

### Analytical Surface Initialization

Source: https://slippy.readthedocs.io/en/latest/_modules/slippy/surface/Surface_class.html

Initializes an analytical surface, optionally applying rotation and shift, and can generate the surface profile upon initialization.

```python
def __init__(self, generate: bool = False, rotation: Number = None,
                 shift: typing.Union[str, tuple] = None,
                 grid_spacing: float = None, extent: tuple = None, shape: tuple = None):
        super().__init__(grid_spacing=grid_spacing, extent=extent, shape=shape)
        if rotation is not None:
            self.rotate(rotation)

        self.shift(shift)

        if generate:
            self.discretise()
```

--------------------------------

### Instantiate and Discretize DiscFreqSurface

Source: https://slippy.readthedocs.io/en/latest/generated/slippy.surface.DiscFreqSurface.html

Instantiates a DiscFreqSurface with specified frequencies and amplitude, sets the extent, and then discretizes the surface with a given grid spacing.

```python
>>> mySurf=DiscFreqSurface(10, 0.1)
>>> mySurf.extent=[0.5,0.5]
>>> mySurf.discretise(0.001)
```

--------------------------------

### Perform Data Check on Model

Source: https://slippy.readthedocs.io/en/latest/_modules/slippy/contact/models.html

Initiates a data check for the entire model, printing the start time and model name, then sequentially checks each step.

```python
    def data_check(self):
        print("Data check started at:")
        print(datetime.now().strftime('%H:%M:%S %d-%m-%Y'))
        print(f"Checking model {self.name}:")
        self._model_check()

        current_state = None

        for this_step in self.steps:
            current_state = self.steps[this_step]._data_check(current_state)
```