ineq module

This module contains functions to perform inequality simulations.

Warning

This module is obsolete and is not used in the main code.

ineq.Gibbs_estimate(data_org, covmodel, nit=50, krig_type='simple_kriging', mean=None, var=None, nmax=20)
ineq.krig_ineq(data_org, covmodel, nit=50, krig_type='simple_kriging', mean=None, var=None, nmax=20)
ineq.krige(x, v, xu, cov_model, method='simple_kriging', mean=None)

Performs kriging - interpolates at locations xu the values v measured at locations x. Covariance model given should be:

  • in same dimension as dimension of locations x, xu

  • in 1D, it is then used as an omni-directional covariance model

(see below).

Parameters:

  • x ((2-dimensional array of shape (n, d))) – coordinates of the data points (n: number of points, d: dimension) Note: for data in 1D, it can be a 1-dimensional array of shape (n,)

  • v ((1-dimensional array of shape (n,))) – values at data points

  • xu ((2-dimensional array of shape (nu, d))) – coordinates of the points where the interpolation has to be done (nu: number of points, d: dimension same as for x), called unknown points Note: for data in 1D, it can be a 1-dimensional array of shape (nu,)

  • cov_model ((CovModel1D or CovModel2D or CovModel3D or CovModel1D)) –

    covariance model:
    • in same dimension as dimension of points (d), i.e.:

      • CovModel1D class if data in 1D (d=1)

      • CovModel2D class if data in 2D (d=2)

      • CovModel3D class if data in 3D (d=3)

    • or CovModel1D whatever dimension of points (d):

      • used as an omni-directional covariance model

  • method ((string)) –

    indicates the method used:

    • ‘simple_kriging’: interpolation by simple kriging

    • ‘ordinary_kriging’: interpolation by ordinary kriging

  • mean ((None or float or ndarray)) –

    mean of the simulation (for simple kriging only):

    • None : mean of hard data values (stationary), i.e. mean of v

    • float : for stationary mean (set manually)

    • ndarray: of of shape (nu,) for non stationary mean,

      mean at point xu

    For ordinary kriging (method = ‘ordinary_kriging’), this parameter ignored (not used)

Returns:

  • vu ((1-dimensional array of shape (nu,))) – kriged values (estimates) at points xu

  • vu_std ((1-dimensional array of shape (nu,))) – kriged standard deviation at points xu

ineq.run_sim(data_org, xg, covmodel, var, nsim=10, nit=20)

Run a inequation simulation

Parameters:

  • data_org (array of size (nd,4)) – data_org[:,0] : position x of the data data_org[:,1] : equality value (nan if no equality) data_org[:,2] : lower bound (nan if no lower bound) data_org[:,3] : upper bound (nan if no upper bound)

  • xg (1d grid (np.arange(x0,x1+sx,sx), must be sorted)

  • nsim (int (default : 10)) – number of simulations

  • nit (int (default : 20)) – number of iterations in the gibbs sampler

  • covmodel (geone.CovModel1D) – geone covariance model

  • var (float) – variance of the simulation

Returns:

sim – list of all simulations in one 2D array

Return type:

array of size (nsim,nx)

ineq.run_sim_2d(data_org, xg, yg, covmodel, var=None, mean=None, krig_type='simple_kriging', nsim=1, nit=20, nmax=20, grf_method='fft', ncpu=-1, seed=123456789)

Run a 2D inequality simulation using the Gibbs sampler

Parameters:

  • data_org (2D array-like of size nd x 6) – [[x1, y1, z1, vineq_min1, vineq_max1], [x2, y2, z2, vineq_min2, vineq_max2], …, [xnd, ynd, znd, vineq_minnd, vineq_maxnd],]

  • xg (sequence of float) – x coordinate vector (np.arange(x0,x1+sx,sx)

  • yg (sequence of float) – y coordinate vector (np.arange(y0,y1+sy,sy)

  • covmodel (geone.CovModel) – covariance model to use. Must be 2D.

  • var (float or None, optional) – variance. If None, will be estimated from data.

  • mean (float or None, optional) – mean. If None, will be estimated from data.

  • krig_type (str, optional) – kriging type to use. Must be “simple_kriging” or “ordinary_kriging”.

  • nsim (int, optional) – number of simulations

  • nit (int, optional) – number of Gibbs iterations

  • nmax (int, optional) – maximum number of nearest neighbours to consider

  • grf_method (str, optional) – method to use for grf simulation. Must be “fft” or “lu”.

  • ncpu (int, optional) – number of cores to use. If -1, will use all available cores.

  • seed (int, optional) – seed for random number generator

Returns:

out – array of all simulations

Return type:

3D array of size (nsim,ny,nx)