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# Module: safe.common.numerics

Numerical tools

`safe.common.numerics.``axes2points`(x, y)

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

  Args:
    - x: x coordinates (array)
    - y: 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.common.numerics.``ensure_numeric`(A, typecode=None)

  Ensure that sequence is a numeric array.

  Args:
    - A: 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

    - A: Scalar. Return 0-dimensional array containing that value. Note

        that a 0-dim array DOES NOT HAVE A LENGTH UNDER numpy.

    - A: 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.

  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.common.numerics.``erf`(z)

  Approximation to ERF

  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.common.numerics.``geotransform2axes`(G, nx, ny)

  Convert geotransform to coordinate axes

  Args:
    - G: GDAL geotransform (6-tuple).
        (top left x, w-e pixel resolution, rotation,

          top left y, rotation, n-s pixel resolution).

    - nx: Number of cells in the w-e direction

    - ny: Number of cells in the n-s direction

  Returns:

    - Return 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.common.numerics.``grid2points`(A, x, y)

  Convert grid data to point data

  Args:
    - A: Array of pixel values
    - x: Longitudes corresponding to columns in A (west->east)
    - y: Latitudes corresponding to rows in A (south->north)
  Returns:
    - P: Nx2 array of point coordinates
    - V: N array of point values

`safe.common.numerics.``lognormal_cdf`(x, median=1, sigma=1)

  Cumulative Log Normal Distribution Function

  > Args:
  >   - x: scalar or array of real numbers
  >   - mu: Median (exp(mean of log(x)). Default 1
  >   - sigma: Log normal standard deviation. Default 1
  > Returns:
  >   - An approximation of the cdf of the normal
  > Note:
  >   CDF of the normal distribution is defined as

  rac12 [1 + erf( rac{x - mu}{sigma sqrt{2}})], x in R

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

`safe.common.numerics.``nanallclose`(x, y, rtol=1e-05, atol=1e-08)

  Numpy allclose function which allows NaN

  Args:
    - x, y: Either scalars or numpy arrays
  Returns:
    - True or False
  Note:
    Returns True if all non-nan elements pass.

`safe.common.numerics.``normal_cdf`(x, mu=0, sigma=1)

  Cumulative Normal Distribution Function

  > Args:
  >   - x: scalar or array of real numbers
  >   - mu: Mean value. Default 0
  >   - sigma: Standard deviation. Default 1
  > Returns:
  >   - An approximation of the cdf of the normal
  > Note:
  >   CDF of the normal distribution is defined as

  rac12 [1 + erf( rac{x - mu}{sigma sqrt{2}})], x in R

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

This module forms part of the InaSAFE tool.

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