fatiandofatiando.gridder)¶Create and operate on grids and profiles.
Grid generation
Grid operations
Interpolation
Padding
Input/Output
load_surfer: Read a Surfer grid file and return
three 1d numpy arrays and the grid shapeMisc
Point scatter generation
fatiando.gridder.circular_scatter(area, n, z=None, random=False, seed=None)[source]¶Generate a set of n points positioned in a circular array.
The diameter of the circle is equal to the smallest dimension of the area
Parameters:
Area inside of which the points are contained
Number of points
Optional. z coordinate of the points. If given, will return an array with the value z.
If True, positions of the points on the circle will be chosen at random
Seed used to generate the pseudo-random numbers if random==True. If None, will use a different seed every time. Use the same seed to generate the same random sequence.
Returns:
[x, y]Numpy arrays with the x and y coordinates of the points
[x, y, z]If z given. Arrays with the x, y, and z coordinates of the points
fatiando.gridder.cut(x, y, scalars, area)[source]¶Return a subsection of a grid.
The returned subsection is not a copy! In technical terms, returns a slice of the numpy arrays. So changes made to the subsection reflect on the original grid. Use numpy.copy to make copies of the subsections and avoid this.
Parameters:
Arrays with the x and y coordinates of the data points.
List of arrays with the scalar values assigned to the grid points.
(x1, x2, y1, y2): Borders of the subsection
Returns:
[subx, suby, subscalars]Arrays with x and y coordinates and scalar values of the subsection.
fatiando.gridder.extrapolate_nans(x, y, v)[source]¶Extrapolate the NaNs or masked values in a grid INPLACE using nearest value.
Warning
Replaces the NaN or masked values of the original array!
Parameters:
Arrays with the x and y coordinates of the data points.
Array with the scalar value assigned to the data points.
Returns:
The array with NaNs or masked values extrapolated.
fatiando.gridder.interp(x, y, v, shape, area=None, algorithm='cubic', extrapolate=False)[source]¶Interpolate data onto a regular grid.
Parameters:
Arrays with the x and y coordinates of the data points.
Array with the scalar value assigned to the data points.
Shape of the interpolated regular grid, ie (nx, ny).
The are where the data will be interpolated. If None, then will get the area from x and y.
Interpolation algorithm. Either 'cubic', 'nearest',
'linear' (see scipy.interpolate.griddata).
If True, will extrapolate values outside of the convex hull of the data points.
Returns:
[x, y, v]Three 1D arrays with the interpolated x, y, and v
fatiando.gridder.interp_at(x, y, v, xp, yp, algorithm='cubic', extrapolate=False)[source]¶Interpolate data onto the specified points.
Parameters:
Arrays with the x and y coordinates of the data points.
Array with the scalar value assigned to the data points.
Points where the data values will be interpolated
Interpolation algorithm. Either 'cubic', 'nearest',
'linear' (see scipy.interpolate.griddata)
If True, will extrapolate values outside of the convex hull of the data points.
Returns:
1D array with the interpolated v values.
fatiando.gridder.load_surfer(fname, fmt='ascii')[source]¶Read a Surfer grid file and return three 1d numpy arrays and the grid shape
Surfer is a contouring, gridding and surface mapping software from GoldenSoftware. The names and logos for Surfer and Golden Software are registered trademarks of Golden Software, Inc.
http://www.goldensoftware.com/products/surfer
Parameters:
Name of the Surfer grid file
File type, can be ‘ascii’ or ‘binary’
Returns:
Value of the North-South coordinate of each grid point.
Value of the East-West coordinate of each grid point.
Values of the field in each grid point. Field can be for example topography, gravity anomaly etc
The number of points in the x and y grid dimensions, respectively
fatiando.gridder.pad_array(a, npd=None, padtype='OddReflectionTaper')[source]¶Return a padded array of arbitrary dimension.
The function takes an array of arbitrary dimension and pads it either to the dimensions given by the tuple npd, or to the next power of 2 if npd is not given.
An odd reflection with a cosine taper is the author’s preferred method of padding for Fourier operations. The odd reflection optimally preserves the frequency content while adding minimal sharp inflections. The cosine taper is a smooth function which also adds few sharp inflection points.
Note
Requires gridded data of the same dimension as desired (i.e. no flattened arrays; use reshape).
Note
This function returns a deep copy of the original array.
Warning
This function returns the coordinate vectors as a list of arrays. This means that even for a 1D input array, the returned vector will be in a list of one element.
Parameters:
Array (N-D) to be padded
Desired shape of new padded array. If not provided, the nearest power of 2 will be used.
String describing with what to pad the new values. Options:
[ oddreflectiontaper | oddreflection | reflection | value | lintaper | edge | mean ]
oddreflectiontaper - Generates odd reflection then tapers to the mean using a cosine function (Default)
oddreflection - Pads with the odd reflection, with no taper
reflection - Pads with simple reflection
lintaper - Linearly tapers to the mean
value - Numeric value. Input a float or integer directly.
edge - Uses the edge value as a constant pad
mean - Uses the mean of the vector along each axis
Returns:
Padded array. The array core is a deep copy of the original array
List of tuples containing the number of elements padded onto each dimension.
Examples:
>>> z = numpy.array([3, 4, 4, 5, 6])
>>> zpad, nps = pad_array(z)
>>> zpad
array([ 4.4, 3.2, 3. , 4. , 4. , 5. , 6. , 4.4])
>>> print(nps)
[(2, 1)]
>>> shape = (5, 6)
>>> z = numpy.ones(shape, dtype='int')
>>> zpad, nps = pad_array(z, padtype='5')
>>> zpad
array([[5, 5, 5, 5, 5, 5, 5, 5],
[5, 5, 5, 5, 5, 5, 5, 5],
[5, 1, 1, 1, 1, 1, 1, 5],
[5, 1, 1, 1, 1, 1, 1, 5],
[5, 1, 1, 1, 1, 1, 1, 5],
[5, 1, 1, 1, 1, 1, 1, 5],
[5, 1, 1, 1, 1, 1, 1, 5],
[5, 5, 5, 5, 5, 5, 5, 5]])
>>> print(nps)
[(2, 1), (1, 1)]
fatiando.gridder.pad_coords(xy, shape, nps)[source]¶Pads coordinate vectors.
Designed to be used in concert with pad_array,
this function takes a list of coordinate vectors and pads them using the
same discretization.
Note
This function returns a list of arrays in the same format
as, for example, regular. It is a list of
flattened meshgrids for each vector in the same order as was input.
Parameters:
List of arrays of coordinates
Size of original array
dimension (uses output from pad_array).
Returns:
List of padded coordinate arrays
Examples:
>>> shape = (5, 6)
>>> x, y, z = regular((-10,10,-20,0), shape, z=-25)
>>> gz = numpy.zeros(shape)
>>> gzpad, nps = pad_array(gz)
>>> x.reshape(shape)[:,0]
array([-10., -5., 0., 5., 10.])
>>> y.reshape(shape)[0,:]
array([-20., -16., -12., -8., -4., 0.])
>>> xy = [x, y]
>>> N = pad_coords(xy, shape, nps)
>>> N[0].reshape(gzpad.shape)[:,0]
array([-20., -15., -10., -5., 0., 5., 10., 15.])
>>> N[1].reshape(gzpad.shape)[0,:]
array([-24., -20., -16., -12., -8., -4., 0., 4.])
fatiando.gridder.profile(x, y, v, point1, point2, size, extrapolate=False)[source]¶Extract a data profile between 2 points.
Uses interpolation to calculate the data values at the profile points.
Parameters:
Arrays with the x and y coordinates of the data points.
Array with the scalar value assigned to the data points.
Lists the x, y coordinates of the 2 points between which the profile will be extracted.
Number of points along the profile.
If True, will extrapolate values outside of the convex hull of the data points.
Returns:
xp and yp are the x, y coordinates of the points along the
profile.
distances are the distances of the profile points to point1
vp are the data points along the profile.
fatiando.gridder.regular(area, shape, z=None)[source]¶Create a regular grid.
The x directions is North-South and y East-West. Imagine the grid as a matrix with x varying in the lines and y in columns.
Returned arrays will be flattened to 1D with numpy.ravel.
Warning
As of version 0.4, the shape argument was corrected to be
shape = (nx, ny) instead of shape = (ny, nx).
Parameters:
(x1, x2, y1, y2): Borders of the grid
Shape of the regular grid, ie (nx, ny).
Optional. z coordinate of the grid points. If given, will return an array with the value z.
Returns:
[x, y]Numpy arrays with the x and y coordinates of the grid points
[x, y, z]If z given. Numpy arrays with the x, y, and z coordinates of the grid points
Examples:
>>> x, y = regular((0, 10, 0, 5), (5, 3))
>>> x
array([ 0. , 0. , 0. , 2.5, 2.5, 2.5, 5. , 5. , 5. ,
7.5, 7.5, 7.5, 10. , 10. , 10. ])
>>> x.reshape((5, 3))
array([[ 0. , 0. , 0. ],
[ 2.5, 2.5, 2.5],
[ 5. , 5. , 5. ],
[ 7.5, 7.5, 7.5],
[ 10. , 10. , 10. ]])
>>> y.reshape((5, 3))
array([[ 0. , 2.5, 5. ],
[ 0. , 2.5, 5. ],
[ 0. , 2.5, 5. ],
[ 0. , 2.5, 5. ],
[ 0. , 2.5, 5. ]])
>>> x, y = regular((0, 0, 0, 5), (1, 3))
>>> x.reshape((1, 3))
array([[ 0., 0., 0.]])
>>> y.reshape((1, 3))
array([[ 0. , 2.5, 5. ]])
>>> x, y, z = regular((0, 10, 0, 5), (5, 3), z=-10)
>>> z.reshape((5, 3))
array([[-10., -10., -10.],
[-10., -10., -10.],
[-10., -10., -10.],
[-10., -10., -10.],
[-10., -10., -10.]])
fatiando.gridder.scatter(area, n, z=None, seed=None)[source]¶Create an irregular grid with a random scattering of points.
Parameters:
(x1, x2, y1, y2): Borders of the grid
Number of points
Optional. z coordinate of the points. If given, will return an array with the value z.
Seed used to generate the pseudo-random numbers. If None, will use a different seed every time. Use the same seed to generate the same random points.
Returns:
[x, y]Numpy arrays with the x and y coordinates of the points
[x, y, z]If z given. Arrays with the x, y, and z coordinates of the points
Examples:
>>> x, y = scatter((0, 10, 0, 2), 4, seed=0)
>>> x
array([ 5.48813504, 7.15189366, 6.02763376, 5.44883183])
>>> y
array([ 0.8473096 , 1.29178823, 0.87517442, 1.783546 ])
fatiando.gridder.spacing(area, shape)[source]¶Returns the spacing between grid nodes
Parameters:
(x1, x2, y1, y2): Borders of the grid
Shape of the regular grid, ie (nx, ny).
Returns:
[dx, dy]Spacing the y and x directions
Examples:
>>> spacing((0, 10, 0, 20), (11, 11))
[1.0, 2.0]
>>> spacing((0, 10, 0, 20), (11, 21))
[1.0, 1.0]
>>> spacing((0, 10, 0, 20), (5, 21))
[2.5, 1.0]
>>> spacing((0, 10, 0, 20), (21, 21))
[0.5, 1.0]
fatiando.gridder.unpad_array(a, nps)[source]¶Unpads an array using the outputs from pad_array.
This function takes a padded array and removes the padding from both. Effectively, this is a complement to gridder.cut for when you already know the number of elements to remove.
Note
Unlike pad_array, this returns a slice
of the input array. Therefore, any changes to the padded array will be
reflected in the unpadded array.
Parameters:
Array to be un-padded. Can be of arbitrary dimension.
List of tuples giving the min and max indices for the cutoff. Identical to nps returned by pad_array
Returns:
Array of same dimension as a, with padding removed
Examples:
>>> z = numpy.array([3, 4, 4, 5, 6])
>>> zpad, nps = pad_array(z)
>>> zpad
array([ 4.4, 3.2, 3. , 4. , 4. , 5. , 6. , 4.4])
>>> zunpad = unpad_array(zpad, nps)
>>> zunpad
array([ 3., 4., 4., 5., 6.])