safe.gis.numerics module¶

Numerical tools

safe.gis.numerics.axes_to_points(x, y)[source]¶

Generate all combinations of grid point coordinates from x and y axes

Parameters:

Parameters:	x (numpy.ndarray) – x coordinates (array) y (numpy.ndarray) – y coordinates (array)
Returns:	P: Nx2 array consisting of coordinates for all grid points defined by x and y axes. The x coordinate will vary the fastest to match the way 2D numpy arrays are laid out by default (‘C’ order). That way, the x and y coordinates will match a corresponding 2D array A when flattened (A.flat[:] or A.reshape(-1))

x (numpy.ndarray) – x coordinates (array)
y (numpy.ndarray) – y coordinates (array)

Returns:

P: Nx2 array consisting of coordinates for all

grid points defined by x and y axes. The x coordinate will vary the fastest to match the way 2D numpy arrays are laid out by default (‘C’ order). That way, the x and y coordinates will match a corresponding 2D array A when flattened (A.flat[:] or A.reshape(-1))

Note:

Example

x = [1, 2, 3] y = [10, 20]

P = [[1, 10],: [2, 10], [3, 10], [1, 20], [2, 20], [3, 20]]

safe.gis.numerics.ensure_numeric(A, typecode=None)[source]¶

Ensure that sequence is a numeric array.

Parameters:	A – Is one of the following: Sequence. If A is already a numeric array it will be returned unaltered If not, an attempt is made to convert it to a numeric array Scalar. Return 0-dimensional array containing that value. Note that a 0-dim array DOES NOT HAVE A LENGTH UNDER numpy. String. Array of ASCII values (numpy can’t handle this) typecode – numeric type. If specified, use this in the conversion. If not, let numeric package decide. typecode will always be one of num.float, num.int, etc.
Raises:	Exception
Returns:	An array of A if it is found to be of a numeric type
Return type:	numpy.ndarray

Note

that numpy.array(A, dtype) will sometimes copy. Use ‘copy=False’ to copy only when required.

This function is necessary as array(A) can cause memory overflow.

safe.gis.numerics.erf(z)[source]¶

Approximation to ERF

Parameters:	z (numpy.ndarray, float) – input array or scalar to perform erf on
Returns:	the approximate error
Return type:	numpy.ndarray, float

Note:

from: http://www.cs.princeton.edu/introcs/21function/ErrorFunction.java.html Implements the Gauss error function. erf(z) = 2 / sqrt(pi) * integral(exp(-t*t), t = 0..z)

Fractional error in math formula less than 1.2 * 10 ^ -7. although subject to catastrophic cancellation when z in very close to 0 from Chebyshev fitting formula for erf(z) from Numerical Recipes, 6.2

Source: http://stackoverflow.com/questions/457408/ is-there-an-easily-available-implementation-of-erf-for-python

safe.gis.numerics.geotransform_to_axes(G, nx, ny)[source]¶

Convert geotransform to coordinate axes

Parameters:

Parameters:	G (tuple) – GDAL geotransform (6-tuple). (top left x, w-e pixel resolution, rotation, top left y, rotation, n-s pixel resolution). nx (int) – Number of cells in the w-e direction ny – Number of cells in the n-s direction
Returns:	Two vectors (longitudes and latitudes) representing the grid defined by the geotransform. The values are offset by half a pixel size to correspond to pixel registration. I.e. If the grid origin (top left corner) is (105, 10) and the resolution is 1 degrees in each direction, then the vectors will take the form longitudes = [100.5, 101.5, ..., 109.5] latitudes = [0.5, 1.5, ..., 9.5]

G (tuple) – GDAL geotransform (6-tuple). (top left x, w-e pixel resolution, rotation, top left y, rotation, n-s pixel resolution).
nx (int) – Number of cells in the w-e direction
ny – Number of cells in the n-s direction

Returns:

Two vectors (longitudes and latitudes) representing the grid defined by the geotransform.

The values are offset by half a pixel size to correspond to pixel registration.

I.e. If the grid origin (top left corner) is (105, 10) and the resolution is 1 degrees in each direction, then the vectors will take the form

longitudes = [100.5, 101.5, ..., 109.5] latitudes = [0.5, 1.5, ..., 9.5]

safe.gis.numerics.grid_to_points(A, x, y)[source]¶

Convert grid data to point data

Parameters:	A (numpy.ndarray) – Array of pixel values x (numpy.ndarray) – Longitudes corresponding to columns in A (west->east) y (numpy.ndarray) – Latitudes corresponding to rows in A (south->north)

Returns:

P: Nx2 array of point coordinates
V: N array of point values

safe.gis.numerics.log_normal_cdf(x, median=1, sigma=1)[source]¶

Cumulative Log Normal Distribution Function

Parameters:	x (numpy.ndarray, float) – scalar or array of real numbers median (float) – Median (exp(mean of log(x)). Default 1 sigma (float) – Log normal standard deviation. Default 1
Returns:	An approximation of the cdf of the normal
Return type:	numpy.ndarray

Note

CDF of the normal distribution is defined as frac12 [1 + erf(frac{x - mu}{sigma sqrt{2}})], x in R

Source: http://en.wikipedia.org/wiki/Normal_distribution

safe.gis.numerics.nan_allclose(x, y, rtol=1e-05, atol=1e-08)[source]¶

Does element comparison within a tolerance, excludes overlapped NaN.

Parameters:	x (numpy.ndarray, float) – scalar or numpy array y (numpy.ndarray, float) – scalar or numpy array rtol (float) – The relative tolerance parameter atol (float) – The absolute tolerance parameter
Raises:
Returns:	The result of the allclose on non NaN elements
Return type:	bool

Note:: Returns True if all non-nan elements pass.

safe.gis.numerics.normal_cdf(x, mu=0, sigma=1)[source]¶

Cumulative Normal Distribution Function

Parameters:	x (numpy.ndarray, float) – scalar or array of real numbers mu (float, numpy.ndarray) – Mean value. Default 0 sigma (float) – Standard deviation. Default 1
Returns:	An approximation of the cdf of the normal
Return type:	numpy.ndarray

Note:

CDF of the normal distribution is defined as frac12 [1 + erf(frac{x - mu}{sigma sqrt{2}})], x in R

Source: http://en.wikipedia.org/wiki/Normal_distribution