├── src └── geostat │ ├── __init__.py │ ├── gaussian_sim.py │ ├── get_variogram.py │ ├── decomp.py │ └── gslib.py ├── README.md ├── pyproject.toml ├── .github └── workflows │ └── python-package.yml ├── .gitignore ├── tests └── test_geostat_decomp.py └── LICENSE /src/geostat/__init__.py: -------------------------------------------------------------------------------- 1 | """Geostatistical tools.""" 2 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # Geostatistics 2 | Code containing various geostatistical tools that are useful for PET. 3 | 4 | ## Installation 5 | Clone repository and install with pip: 6 | 7 | ```sh 8 | pip install -e . 9 | ``` 10 | ## Examples 11 | ```python 12 | from geostat.decomp import Cholesky 13 | import numpy as np 14 | 15 | stat = Cholesky() 16 | nx = 3 17 | mean = np.array([1., 2., 3.]) 18 | var = np.array([10., 20., 30.]) 19 | ne = 2 20 | cov = stat.gen_cov2d(x_size=nx, y_size=1, variance=var, 21 | var_range=1., aspect=1., angle=0., var_type='sph') 22 | sample = stat.gen_real(mean, cov, ne) 23 | ``` 24 | -------------------------------------------------------------------------------- /pyproject.toml: -------------------------------------------------------------------------------- 1 | [build-system] 2 | requires = ["setuptools>=61.0"] 3 | build-backend = "setuptools.build_meta" 4 | 5 | [project] 6 | name = "geostat" 7 | version = "0.0.1" 8 | authors = [ 9 | { name="Kristian Fossum", email="krfo@norceresearch.no" }, 10 | ] 11 | description = "A package containing some geostatistical tools that can be used by the Python Ensemble Toolbox." 12 | readme = "README.md" 13 | requires-python = ">=3.8" 14 | license = {file = "LICENSE"} 15 | dependencies = [ 16 | "numpy", 17 | "scipy" 18 | ] 19 | 20 | [project.urls] 21 | Homepage = "https://github.com/Python-Ensemble-Toolbox/Geostatistics" 22 | Issues = "https://github.com/Python-Ensemble-Toolbox/Geostatistics/ issues" -------------------------------------------------------------------------------- /.github/workflows/python-package.yml: -------------------------------------------------------------------------------- 1 | # This workflow will install Python dependencies and run tests with a variety of Python versions 2 | # For more information see: https://docs.github.com/en/actions/automating-builds-and-tests/building-and-testing-python 3 | 4 | name: CI tests 5 | 6 | on: 7 | push: 8 | branches: [ "main" ] 9 | pull_request: 10 | branches: [ "main" ] 11 | 12 | jobs: 13 | build: 14 | 15 | runs-on: ubuntu-latest 16 | strategy: 17 | fail-fast: false 18 | matrix: 19 | python-version: ["3.8", "3.9", "3.10", "3.11"] 20 | 21 | steps: 22 | - uses: actions/checkout@v4 23 | - name: Set up Python ${{ matrix.python-version }} 24 | uses: actions/setup-python@v3 25 | with: 26 | python-version: ${{ matrix.python-version }} 27 | - name: Install dependencies 28 | run: | 29 | python -m pip install --upgrade pip 30 | python -m pip install pytest 31 | python -m pip install . 32 | - name: Test with pytest 33 | run: | 34 | pytest 35 | -------------------------------------------------------------------------------- /.gitignore: -------------------------------------------------------------------------------- 1 | # Editors 2 | .vscode/ 3 | .idea/ 4 | 5 | # Vagrant 6 | .vagrant/ 7 | 8 | # Mac/OSX 9 | .DS_Store 10 | 11 | # Windows 12 | Thumbs.db 13 | 14 | # Source for the following rules: https://raw.githubusercontent.com/github/gitignore/master/Python.gitignore 15 | # Byte-compiled / optimized / DLL files 16 | __pycache__/ 17 | *.py[cod] 18 | *$py.class 19 | 20 | # C extensions 21 | *.so 22 | 23 | # Distribution / packaging 24 | .Python 25 | build/ 26 | develop-eggs/ 27 | dist/ 28 | downloads/ 29 | eggs/ 30 | .eggs/ 31 | lib/ 32 | lib64/ 33 | parts/ 34 | sdist/ 35 | var/ 36 | wheels/ 37 | *.egg-info/ 38 | .installed.cfg 39 | *.egg 40 | MANIFEST 41 | 42 | # PyInstaller 43 | # Usually these files are written by a python script from a template 44 | # before PyInstaller builds the exe, so as to inject date/other infos into it. 45 | *.manifest 46 | *.spec 47 | 48 | # Installer logs 49 | pip-log.txt 50 | pip-delete-this-directory.txt 51 | 52 | # Unit test / coverage reports 53 | htmlcov/ 54 | .tox/ 55 | .nox/ 56 | .coverage 57 | .coverage.* 58 | .cache 59 | nosetests.xml 60 | coverage.xml 61 | *.cover 62 | .hypothesis/ 63 | .pytest_cache/ 64 | 65 | # Translations 66 | *.mo 67 | *.pot 68 | 69 | # Django stuff: 70 | *.log 71 | local_settings.py 72 | db.sqlite3 73 | 74 | # Flask stuff: 75 | instance/ 76 | .webassets-cache 77 | 78 | # Scrapy stuff: 79 | .scrapy 80 | 81 | # Sphinx documentation 82 | docs/_build/ 83 | 84 | # PyBuilder 85 | target/ 86 | 87 | # Jupyter Notebook 88 | .ipynb_checkpoints 89 | 90 | # IPython 91 | profile_default/ 92 | ipython_config.py 93 | 94 | # pyenv 95 | .python-version 96 | 97 | # celery beat schedule file 98 | celerybeat-schedule 99 | 100 | # SageMath parsed files 101 | *.sage.py 102 | 103 | # Environments 104 | .env 105 | .venv 106 | env/ 107 | venv/ 108 | ENV/ 109 | env.bak/ 110 | venv.bak/ 111 | 112 | # Spyder project settings 113 | .spyderproject 114 | .spyproject 115 | 116 | # Rope project settings 117 | .ropeproject 118 | 119 | # mkdocs documentation 120 | /site 121 | 122 | # mypy 123 | .mypy_cache/ 124 | .dmypy.json 125 | dmypy.json 126 | -------------------------------------------------------------------------------- /tests/test_geostat_decomp.py: -------------------------------------------------------------------------------- 1 | import unittest 2 | import numpy as np 3 | 4 | from geostat.decomp import Cholesky 5 | 6 | 7 | class TestDecompChol(unittest.TestCase): 8 | """ 9 | Test for generating covariance and realizations with methods in Cholesky class 10 | """ 11 | 12 | def setUp(self): 13 | # Instantiate Cholesky class 14 | self.stat = Cholesky() 15 | 16 | def test_0d_grid(self): 17 | # Mean and var 18 | mean = np.array([1.0]) 19 | var = np.array([10.0]) 20 | ne = 2 21 | 22 | # Run gen_real directly 23 | np.random.seed(999) 24 | re = self.stat.gen_real(mean, var, ne) 25 | 26 | # Calculate by hand (re = mean + sqrt(var) * Z) 27 | np.random.seed(999) 28 | z = np.random.randn(ne) 29 | val = np.array([mean + np.sqrt(var) * z]) 30 | 31 | # Check 32 | self.assertEqual(re.shape, (1, ne)) 33 | self.assertTrue(np.all(np.isclose(re, val))) 34 | 35 | def test_1d_grid(self): 36 | # Mean and var 37 | nx = 3 38 | mean = np.array([1., 2., 3.]) 39 | var = np.array([10., 20., 30.]) 40 | ne = 2 41 | 42 | # Generate covariance 43 | cov = self.stat.gen_cov2d(x_size=nx, y_size=1, variance=var, 44 | var_range=1., aspect=1., angle=0., var_type='sph') 45 | 46 | # Check covariance. Should be equal to np.diag(var) 47 | self.assertTupleEqual(cov.shape, (nx, nx)) 48 | self.assertTrue(np.all(np.isclose(cov, np.diag(var)))) 49 | 50 | # Generate realizations 51 | np.random.seed(999) 52 | re = self.stat.gen_real(mean, cov, ne) 53 | 54 | # Calculate by hand (re = mean + sqrt(var) * Z) 55 | np.random.seed(999) 56 | z = np.random.randn(nx, ne) 57 | val = np.tile(mean[:, None], ne) + np.sqrt(np.tile(var[:, None], ne)) * z 58 | 59 | # Check realizations 60 | self.assertTupleEqual(re.shape, (nx, ne)) 61 | self.assertTrue(np.all(np.isclose(re, val))) 62 | 63 | def test_2d_grid(self): 64 | # Mean and var 65 | nx = 3 66 | ny = 2 67 | mean = np.array([1., 2., 3., 4., 5., 6.]) 68 | var = np.array([10., 20., 30., 40., 50., 60.]) 69 | ne = 2 70 | 71 | # Generate covariance 72 | cov = self.stat.gen_cov2d(x_size=nx, y_size=ny, variance=var, var_range=1., aspect=1., angle=0., 73 | var_type='sph') 74 | 75 | # Check covariance. Should be equal to np.diag(var) 76 | self.assertTupleEqual(cov.shape, (nx * ny, nx * ny)) 77 | self.assertTrue(np.all(np.isclose(cov, np.diag(var)))) 78 | 79 | # Generate realizations 80 | np.random.seed(999) 81 | re = self.stat.gen_real(mean, cov, ne) 82 | 83 | # Calculate by hand (re = mean + sqrt(var) * Z) 84 | np.random.seed(999) 85 | z = np.random.randn(nx * ny, ne) 86 | val = np.tile(mean[:, None], ne) + np.sqrt(np.tile(var[:, None], ne)) * z 87 | 88 | # Check realizations 89 | self.assertTupleEqual(re.shape, (nx * ny, ne)) 90 | self.assertTrue(np.all(np.isclose(re, val))) 91 | 92 | def test_3d_grid(self): 93 | # Mean and var 94 | nx = 2 95 | ny = 3 96 | nz = 4 97 | mean = np.arange(1, nx * ny * nz + 1) 98 | var = 10 * np.arange(1, nx * ny * nz + 1) 99 | ne = 2 100 | 101 | # Generate covariance 102 | cov = self.stat.gen_cov3d(nx=nx, ny=ny, nz=nz, sill=var, var_range=1., aniso1=1., aniso2=1., ang1=0., ang2=0., 103 | ang3=0., var_type='sph') 104 | 105 | # Check covariance. Should be equal to np.diag(var) 106 | self.assertTupleEqual(cov.shape, (nx * ny * nz, nx * ny * nz)) 107 | self.assertTrue(np.all(np.isclose(cov, np.diag(var)))) 108 | 109 | # Generate realizations 110 | np.random.seed(999) 111 | re = self.stat.gen_real(mean, cov, ne) 112 | 113 | # Calculate by hand (re = mean + sqrt(var) * Z) 114 | np.random.seed(999) 115 | z = np.random.randn(nx * ny * nz, ne) 116 | val = np.tile(mean[:, None], ne) + np.sqrt(np.tile(var[:, None], ne)) * z 117 | 118 | # Check realizations 119 | self.assertTupleEqual(re.shape, (nx * ny * nz, ne)) 120 | self.assertTrue(np.all(np.isclose(re, val))) 121 | -------------------------------------------------------------------------------- /src/geostat/gaussian_sim.py: -------------------------------------------------------------------------------- 1 | """Fast Gaussian field generation.""" 2 | import sys 3 | import numpy as np 4 | from scipy.linalg import toeplitz 5 | 6 | 7 | def fast_gaussian(dimension, sdev, corr, num_samples=1): 8 | """ 9 | 10 | Generates random vector from distribution satisfying Gaussian variogram in dimension up to 3-d. 11 | 12 | Parameters 13 | ---------- 14 | dimension : int 15 | Dimension of the grid. 16 | 17 | sdev : float 18 | Standard deviation. 19 | 20 | corr : float or array-like 21 | Correlation length, in units of block length. 22 | If a single float is provided, it represents the correlation length in all directions. 23 | If an array-like object with length 3 is provided, it represents the correlation length in the x-, y-, and z-directions. 24 | 25 | num_samples : int, optional 26 | Number of samples to generate. Default is 1. 27 | If greater than 1, the function will return an array of shape (dimension, num_samples). 28 | 29 | Returns 30 | ------- 31 | x : array-like 32 | The generated random vectors of shape (dimension, num_samples). 33 | 34 | Notes 35 | ----- 36 | The parametrization of the grid is assumed to have size dimension, if dimension is a vector, 37 | or [dimension,1] if dimension is scalar. The coefficients of the grid is assumed to be reordered 38 | columnwise into the parameter vector. The grid is assumed to have a local basis. 39 | 40 | Example of use: 41 | 42 | Want to generate a field on a 3-d grid with dimension m x n x p, with correlation length a along first coordinate 43 | axis, b along second coordinate axis, c alone third coordinate axis, and standard deviation sigma: 44 | 45 | x=fast_gaussian(np.array([m, n, p]),np.array([sigma]),np.array([a b c])) 46 | 47 | If the dimension is n x 1 one can write 48 | 49 | x=fast_gaussian(np.array([n]),np.array([sigma]),np.array([a])) 50 | 51 | If the correlation length is the same in all directions: 52 | 53 | x=fast_gaussian(np.array([m n p]),np.array([sigma]),np.array([a])) 54 | 55 | The properties on the Kronecker product behind this algorithm can be found in 56 | Horn & Johnson: Topics in Matrix Analysis, Cambridge UP, 1991. 57 | 58 | Note that we add a small number on the diagonal of the covariance matrix to avoid numerical problems with Cholesky 59 | decomposition (a nugget effect). 60 | 61 | Also note that reshape with order='F' is used to keep the code identical to the Matlab code. 62 | 63 | The method was invented and implemented in Matlab by Geir Nævdal in 2011. 64 | Memory-efficient implementation for batch generation of samples was added in 2025. 65 | """ 66 | 67 | if len(dimension) == 0: 68 | sys.exit("fast_gaussian: Wrong input, dimension should have length at least 1") 69 | m = dimension[0] 70 | n = 1 71 | p = None 72 | if len(dimension) > 1: 73 | n = dimension[1] 74 | dim = m * n 75 | if len(dimension) > 2: 76 | p = dimension[2] 77 | dim = dim * p 78 | if len(dimension) > 3: 79 | sys.exit("fast_gaussian: Wrong input, dimension should have length at most 3") 80 | 81 | if len(sdev) > 1: 82 | std = 1 83 | else: 84 | std = sdev 85 | 86 | if len(corr) == 0: 87 | sys.exit("fast_gaussian: Wrong input, corr should have length at least 1") 88 | if len(corr) == 1: 89 | corr = np.append(corr, corr[0]) 90 | if len(corr) == 2 and p is not None: 91 | corr = np.append(corr, corr[1]) 92 | corr = np.maximum(corr, 1) 93 | 94 | dist1 = np.arange(m) / corr[0] 95 | t1 = toeplitz(dist1) 96 | t1 = std * np.exp(-t1 ** 2) + 1e-10 * np.eye(m) 97 | cholt1 = np.linalg.cholesky(t1) 98 | 99 | if corr[0] == corr[1] and n == m: 100 | cholt2 = cholt1 101 | else: 102 | dist2 = np.arange(n) / corr[1] 103 | t2 = toeplitz(dist2) 104 | t2 = std * np.exp(-t2 ** 2) + 1e-10 * np.eye(n) 105 | cholt2 = np.linalg.cholesky(t2) 106 | 107 | cholt3 = None 108 | if p is not None: 109 | dist3 = np.arange(p) / corr[2] 110 | t3 = toeplitz(dist3) 111 | t3 = np.exp(-t3 ** 2) + 1e-10 * np.eye(p) 112 | cholt3 = np.linalg.cholesky(t3) 113 | 114 | x = np.random.randn(dim, num_samples) 115 | 116 | # Memory-efficient multiplication without explicit large Kronecker product 117 | if p is None: 118 | x = x.reshape(m, n, num_samples, order='F') 119 | x = np.tensordot(cholt1, x, axes=([1], [0])) 120 | x = np.tensordot(cholt2, x, axes=([1], [1])) 121 | else: 122 | x = x.reshape(m, n, p, num_samples, order='F') 123 | x = np.tensordot(cholt1, x, axes=([1], [0])) 124 | x = np.tensordot(cholt2, x, axes=([1], [1])) 125 | x = np.tensordot(cholt3, x, axes=([1], [2])) 126 | 127 | # Reshape back to (dim, num_samples) (order='C' is used here to match the original function's output) 128 | x = x.reshape((dim, num_samples), order='C') 129 | 130 | if len(sdev) > 1: 131 | if len(sdev) == dim: 132 | x = sdev[:, None] * x 133 | else: 134 | sys.exit('fast_gaussian: Inconsistent dimension of sdev') 135 | 136 | return x 137 | 138 | -------------------------------------------------------------------------------- /src/geostat/get_variogram.py: -------------------------------------------------------------------------------- 1 | """Variogram generation.""" 2 | import numpy as np 3 | from scipy.interpolate import interp2d 4 | import sys 5 | # For testing: 6 | # ------------ 7 | # from geostat.gaussian_sim import fast_gaussian 8 | # import time 9 | # import matplotlib.pyplot as plt 10 | 11 | 12 | def semivariogram(field, angle=0.0, actnum=None, num_h=None): 13 | 14 | # semivariogram(field, angle = 0, actnum = None, num_h = None) 15 | # 16 | # Get semivariogram in a given direction (assuming stationary field 17 | # and equidistant grid). 18 | # 19 | # Input 20 | # ----- 21 | # field : The realization 22 | # angle : The direction (between -pi/2 and pi/2 radians) 23 | # actnum : Specify active /nonactive gridcells 24 | # num_h : Number of h-values to evaluate 25 | # 26 | # Output 27 | # ------ 28 | # variogram : Variogram in direction given by angle 29 | 30 | # dimension 31 | dim = field.shape 32 | if len(dim) != 2: 33 | sys.exit('Only 2-D implemented') 34 | 35 | # initialzize 36 | variogram = np.empty((0, 2), float) 37 | if actnum is None: 38 | actnum = np.ones(dim) 39 | actnum = actnum.astype(bool) 40 | field[~actnum] = np.nan 41 | angle_crit = np.arctan(dim[1]/dim[0]) 42 | if angle < -np.pi/2 or angle > np.pi/2: 43 | sys.exit('Angle must be between -pi/2 and pi/2 radians') 44 | if np.abs(angle) < angle_crit: 45 | if num_h is None: 46 | num_h = dim[1] 47 | max_h = dim[1] / np.cos(np.abs(angle)) 48 | delta_h = max_h / num_h 49 | else: 50 | if num_h is None: 51 | num_h = dim[0] 52 | max_h = dim[0] / np.sin(np.abs(angle)) 53 | delta_h = max_h / num_h 54 | 55 | # loop through all h-values 56 | for h in np.arange(delta_h, max_h, delta_h): 57 | 58 | # loop through grid 59 | v = np.array([]) 60 | num = 0 61 | for i in range(dim[0]): 62 | for j in range(dim[1]): 63 | if actnum[i, j]: 64 | s = np.round(np.array([i + np.sin(angle) * h, j + np.cos(angle) * h])) 65 | if dim[0] > int(s[0]) >= 0 and dim[1] > int(s[1]) >= 0: 66 | f1 = field[i, j] 67 | f2 = field[int(s[0]), int(s[1])] 68 | if ~np.isnan(f1) and ~np.isnan(f2): 69 | v = np.append(v, (f1 - f2) ** 2) 70 | num += 1 71 | 72 | if v.size != 0: 73 | variogram_value = (1/(2*num))*np.sum(v) 74 | variogram = np.append(variogram, np.array([[h, variogram_value]]), axis=0) 75 | 76 | return variogram 77 | 78 | 79 | def variogram_map(fields, point=np.array([0, 0]), actnum=None): 80 | 81 | # variogram_map(fields, point=np.array([0, 0]), actnum=None) 82 | # 83 | # Get variogram map based on a given point in the grid. 84 | # The input must be an ensemble of realizations. 85 | # Aassuming stationary field and equidistant grid. 86 | # 87 | # Input 88 | # ----- 89 | # fields : Ensemble of realizations 90 | # point : The reference point in the grid 91 | # actnum : Specify active /nonactive gridcells 92 | # 93 | # Output 94 | # ------ 95 | # variogram_map : Variogram map 96 | 97 | # dimension 98 | dim = fields.shape 99 | if len(dim) != 3: 100 | sys.exit('Input must be an ensemble of 2-D fields') 101 | 102 | # initialzize 103 | vario_map = np.nan * np.ones((dim[0], dim[1]), float) 104 | ne = dim[2] 105 | if actnum is None: 106 | actnum = np.ones(dim[0:2]) 107 | actnum = actnum.astype(bool) 108 | if ~actnum[point[0], point[1]]: 109 | sys.exit('Selected point is not active') 110 | 111 | # loop through grid 112 | f = fields[point[0], point[1]] 113 | for i in range(dim[0]): 114 | for j in range(dim[1]): 115 | if actnum[i, j]: 116 | f1 = fields[i, j] 117 | v = np.sum((f - f1)**2) 118 | vario_map[i, j] = v / (2*ne) 119 | 120 | return vario_map 121 | 122 | 123 | def semivariogram_interp(field, angle=0.0, actnum=None, sx=None, sy=None): 124 | 125 | # semivariogram_interp(field, angle = 0, actnum = None, sx = None, sy = None) 126 | # 127 | # Get semivariogram in a given direction (assuming stationary field). 128 | # The field and coordinates are assumed arranged in the following order 129 | # 130 | # (i,j) --- (i,j+1) 131 | # | | 132 | # | | 133 | # | | 134 | # (i+1,j) --- (i+1,j+1) 135 | # 136 | # Input 137 | # ----- 138 | # field : The realization 139 | # angle : The direction (between -pi/2 and pi/2 radians) 140 | # actnum : Specify active /nonactive gridcells 141 | # sx : Coordinates in x-direction (assume unit grid if None) 142 | # sy : Coordinates in y-direction (assume unit grid if None) 143 | # 144 | # Output 145 | # ------ 146 | # variogram : Variogram in direction given by angle 147 | 148 | # dimension 149 | dim = field.shape 150 | if len(dim) != 2: 151 | sys.exit('Only 2-D implemented') 152 | 153 | # initialzize 154 | variogram = np.empty((0, 2), float) 155 | if actnum is None: 156 | actnum = np.ones(dim) 157 | actnum = actnum.astype(bool) 158 | field[~actnum] = np.nan 159 | if sx is None or sy is None: 160 | sx = np.linspace(1, dim[1], dim[1]) 161 | sy = np.linspace(dim[0], 1, dim[0]) 162 | sx, sy = np.meshgrid(sx, sy) 163 | lx = np.amax(sx) - np.amin(sx) 164 | ly = np.amax(sy) - np.amin(sy) 165 | angle_crit = np.arctan(ly/lx) 166 | if angle < -np.pi/2 or angle > np.pi/2: 167 | sys.exit('Angle must be between -pi/2 and pi/2 radians') 168 | if np.abs(angle) < angle_crit: 169 | max_h = lx / np.cos(np.abs(angle)) 170 | delta_h = max_h / dim[1] 171 | else: 172 | max_h = ly / np.sin(np.abs(angle)) 173 | delta_h = max_h / dim[0] 174 | 175 | # interpolate 176 | f = interp2d(sx[0, :], sy[:, 0], field, kind='linear', fill_value=np.nan) 177 | 178 | # loop through all h-values 179 | for h in np.arange(delta_h, max_h, delta_h): 180 | 181 | # loop through grid 182 | v = np.array([]) 183 | num = 0 184 | for i in range(dim[0]): 185 | for j in range(dim[1]): 186 | s1 = np.array([sx[i, j], sy[i, j]]) 187 | s2 = np.array([s1[0]+np.cos(angle)*h, s1[1]+np.sin(angle)*h]) 188 | f1 = f(s1[0], s1[1]) 189 | f2 = f(s2[0], s2[1]) 190 | if ~np.isnan(f1) and ~np.isnan(f2): 191 | v = np.append(v, (f1-f2)**2) 192 | num += 1 193 | 194 | if v.size != 0: 195 | variogram_value = (1/(2*num))*np.sum(v) 196 | variogram = np.append(variogram, np.array([[h, variogram_value]]), axis=0) 197 | 198 | return variogram 199 | 200 | 201 | # Test code: 202 | # ---------- 203 | # grid_dim = np.array([100, 200]) 204 | # corr = np.array([3, 5]) 205 | # test_field = fast_gaussian(grid_dim, np.array([2]), corr) 206 | # test_field = np.reshape(test_field, grid_dim, order='F') 207 | # actnum = np.ones(grid_dim) 208 | # actnum[:, 2] = 0 209 | # actnum[33, :] = 0 210 | # actnum = actnum.astype(bool) 211 | # starttime = time.time() 212 | # x = np.linspace(0, grid_dim[1], grid_dim[1]) 213 | # y = np.linspace(0, grid_dim[0], grid_dim[0]) 214 | # sx, sy = np.meshgrid(x, y) 215 | # test_vario = semivariogram_interp(test_field, np.pi/6, actnum, sx, sy) 216 | # endtime = time.time() 217 | # elapsed_time = endtime - starttime 218 | # print('Exe time: ' + str(elapsed_time)) 219 | # plt.figure() 220 | # plt.plot(test_vario[:,0],test_vario[:,1]) 221 | # plt.show() 222 | -------------------------------------------------------------------------------- /src/geostat/decomp.py: -------------------------------------------------------------------------------- 1 | """Covariance matrix tools""" 2 | __author__ = 'svenn' 3 | 4 | # External imports 5 | import numpy as np 6 | # Linear algebra tools (from scipy rather than numpy; see scipy website) 7 | from scipy import linalg 8 | import sys 9 | 10 | 11 | class Cholesky: 12 | """ 13 | Class with various geo-statistical algorithms, s.a., generation of covariance, unconditional random variable, etc. 14 | 15 | .. danger:: In danger of being deprecated due to lack of class structure. May become an assemblage of methods instead. 16 | """ 17 | 18 | def __init__(self): 19 | pass 20 | 21 | def gen_real(self, mean, var, number, limits=None, return_chol=False): 22 | """ 23 | Function for generating unconditional random realizations of a variable using Cholesky decomposition. 24 | 25 | Parameters 26 | ---------- 27 | mean : numpy.ndarray or float 28 | Mean vector or scalar. 29 | 30 | var : numpy.ndarray or float 31 | (Co)variance. 32 | 33 | number : int 34 | Number of realizations. 35 | 36 | limits : tuple, optional 37 | Truncation limits. 38 | 39 | return_chol : bool, optional 40 | Boolean indicating if the square root of the covariance should be returned. 41 | 42 | Changelog 43 | --------- 44 | - ST 18/6-15: Wholesale copy of code written by Kristian Fossum. Some modification has been done 45 | - KF 15/6-16: Added option to return sqrt of matrix. 46 | - ST 24/1-18: Code clean-up. 47 | - KF 21/3-19: Option to store only diagonal of CD matrix 48 | """ 49 | parsize = len(mean) 50 | if parsize == 1 or len(var.shape) == 1: 51 | l = np.sqrt(var) 52 | # real = mean + L*np.random.randn(1, number) 53 | else: 54 | # Check if the covariance matrix is diagonal (only entries in the main diagonal). If so, we can use 55 | # numpy.sqrt for efficiency 56 | if np.count_nonzero(var - np.diagonal(var)) == 0: 57 | l = np.sqrt(var) # only variance (diagonal) term 58 | else: 59 | # Cholesky decomposition 60 | l = linalg.cholesky(var) # cov. matrix has off-diag. terms 61 | 62 | # Gen. realizations 63 | if len(var.shape) == 1: 64 | real = np.dot(np.expand_dims(mean, axis=1), np.ones((1, number))) + np.expand_dims(l, axis=1)*np.random.randn( 65 | np.size(mean), number) 66 | else: 67 | real = np.tile(np.reshape(mean, (len(mean), 1)), (1, number)) + np.dot(l.T, np.random.randn(np.size(mean), 68 | number)) 69 | 70 | # Truncate values that are outside limits 71 | # TODO: Make better truncation rules, or switch truncation on/off 72 | if limits is not None: 73 | # Truncate 74 | real[real > limits['upper']] = limits['upper'] 75 | real[real < limits['lower']] = limits['lower'] 76 | 77 | if return_chol: 78 | return real, l 79 | else: 80 | return real 81 | 82 | def gen_cov2d(self, x_size, y_size, variance, var_range, aspect, angle, var_type): 83 | """ 84 | Function for generating a stationary covariance matrix based on variogram models. 85 | 86 | Parameters 87 | ---------- 88 | x_size : int 89 | Number of grid cells in the x-direction. 90 | 91 | y_size : int 92 | Number of grid cells in the y-direction. 93 | 94 | variance : float 95 | Sill. 96 | 97 | var_range : float 98 | Variogram range. 99 | 100 | aspect : float 101 | Ratio between the x-axis (major axis) and y-axis. 102 | 103 | angle : float 104 | Rotation of the x-axis. Measured in degrees clockwise. 105 | 106 | var_type : str 107 | Variogram model. 108 | 109 | Returns 110 | ------- 111 | cov : numpy.ndarray 112 | Covariance matrix (size: x_size x y_size). 113 | 114 | Changelog 115 | --------- 116 | - ST 18/6-15: Wholesale copy of code written by Kristian Fossum. Some modifications have been made... 117 | - KF 04/11-15: Added two new variogram models: exponentioal and cubic. Also updated the 118 | coefficients in the spherical model. 119 | """ 120 | # If var_range is 0, the covariance matrix is diagonal with variance. If var_range != 0, we proceed to make a 121 | # correlated covariance matrix 122 | if var_range == 0: 123 | cov = np.diag(variance * np.ones((x_size * y_size))) 124 | 125 | else: 126 | # TODO: General input coordinates 127 | [xx, yy] = np.mgrid[1:x_size+1, 1:y_size+1] 128 | pos = np.zeros((xx.size, 2)) 129 | pos[:, 0] = np.reshape(xx, xx.size) 130 | pos[:, 1] = np.reshape(yy, yy.size) 131 | 132 | d = np.zeros((xx.size, yy.size)) 133 | 134 | for i in range(0, xx.size): 135 | jj = np.arange(0, yy.size) 136 | 137 | p1 = np.tile(pos[i, :], (yy.size, 1)) 138 | p2 = pos[jj, :] 139 | 140 | d[i, :] = self._edist2d(p1, p2, aspect, angle) 141 | 142 | cov = self.variogram_model(d, var_range, variance, var_type) 143 | 144 | return cov 145 | 146 | def variogram_model(self, d, var_range, variance, var_type): 147 | """ 148 | Various 1D analytical variogram models. 149 | 150 | Parameters 151 | ---------- 152 | d : float 153 | Distance. 154 | 155 | var_range : float 156 | Range. 157 | 158 | variance : float 159 | Variance (value at d=0). 160 | 161 | var_type : str 162 | Variogram model. 163 | 'sph' : Spherical. 164 | 'exp' : Exponential. 165 | 'cub' : Cubic. 166 | 167 | Returns 168 | ------- 169 | gamma : float 170 | Covariance value. 171 | 172 | Changelog 173 | --------- 174 | - ST 24/1-18: Moved from gen_cov2d. 175 | """ 176 | # Variogram models are for 1-d fields given by equations on pg. 641 in "Geostatistics Modeling spatial 177 | # uncertainty, J.P. Chiles and P. Delfiner, 2. ed, 2012 178 | if var_type == 'sph': 179 | s1 = np.nonzero(d < var_range) 180 | s2 = np.nonzero(d >= var_range) 181 | gamma = d * 0 182 | gamma[s1] = variance - variance * ((3 / 2) * np.fabs(d[s1]) / var_range - (1 / 2) * 183 | (d[s1] / var_range) ** 3) 184 | gamma[s2] = 0 185 | 186 | elif var_type == 'exp': 187 | smoothing = 1.9 # if extra smoothing is requires 188 | gamma = variance * (np.exp(-3*(np.fabs(d) / var_range)**smoothing)) 189 | 190 | elif var_type == 'cub': 191 | s1 = np.nonzero(d < var_range) 192 | s2 = np.nonzero(d >= var_range) 193 | gamma = d * 0 194 | gamma[s1] = variance * (1 - 7 * (np.fabs(d[s1]) / var_range) ** 2 + (35 / 4) * 195 | (np.fabs(d[s1]) / var_range) ** 3 - (7 / 2) * (np.fabs(d[s1]) / var_range) ** 5 + 196 | (3 / 4) * (np.fabs(d[s1]) / var_range) ** 7) 197 | gamma[s2] = 0 198 | 199 | else: 200 | print('\033[1;31mERROR: Variogram model "{0)" has not been implemented!\033[1;m'.format( 201 | var_type)) 202 | sys.exit(1) 203 | 204 | return gamma 205 | 206 | def _edist2d(self, v1, v2, aspect, rotate): 207 | """ 208 | Function for calculating the Euclidean distance of, possibly, anisotropic (rotated and scaled) vectors 209 | 210 | Parameters 211 | ---------- 212 | v1 : array_like 213 | First vector to calculate distance between. 214 | 215 | v2 : array_like 216 | Second vector to calculate distance between. 217 | 218 | r : float 219 | Range of the variogram. 220 | 221 | aspect : float 222 | Ratio between the x-axis (major axis) and y-axis. 223 | 224 | rotate : float 225 | Rotation of the x-axis, measured in degrees clockwise. 226 | 227 | Returns 228 | ------- 229 | dist : float 230 | Euclidean distance between v1 and v2. 231 | 232 | ST 18/6-15: Wholesale copy of code written by Kristian Fossum. Some modifications have been made... 233 | """ 234 | # Rotation matrix 235 | rot_mat = np.array([[np.cos((rotate / 180) * np.pi), -np.sin((rotate / 180) * np.pi)], 236 | [np.sin((rotate / 180) * np.pi), np.cos((rotate / 180) * np.pi)]]) 237 | 238 | # Compressing matrix (since aspect>=1) 239 | rescale_mat = np.array([[1, 0], [0, aspect]]) 240 | 241 | # Coordinates 242 | dp = v1 - v2 243 | 244 | # Do rotation and scaling 245 | dp = np.dot(rescale_mat * rot_mat, dp.T) 246 | 247 | # Taken from org. GeoStat code: 248 | # Move compressing of y-axis to stretching of x-axis 249 | dp = dp/aspect 250 | 251 | # Calc. distance 252 | dist = np.array(np.sqrt(np.sum(np.multiply(dp, dp), 0))) 253 | 254 | return dist 255 | 256 | def gen_cov3d(self, nx, ny, nz, sill, var_range, aniso1, aniso2, ang1, ang2, ang3, var_type): 257 | """ 258 | Function for generating a stationary covariance matrix based on variogram models. 259 | 260 | Parameters 261 | ---------- 262 | nx : int 263 | Number of grid cells in the x-direction. 264 | 265 | ny : int 266 | Number of grid cells in the y-direction. 267 | 268 | nz : int 269 | Number of grid cells in the z-direction. 270 | 271 | Sill : float 272 | Covariance at distance 0. 273 | 274 | var_range : float 275 | Variogram range. 276 | 277 | aspect : float 278 | Ratio between the x-axis (major axis) and y-axis. 279 | 280 | angle : float 281 | Rotation of the x-axis, measured in degrees clockwise. 282 | 283 | var_type : str 284 | Variogram model. 285 | 286 | Returns 287 | ------- 288 | cov : ndarray 289 | Covariance matrix (size: nx * ny * nz x nx * ny * nz). 290 | 291 | Changelog 292 | --------- 293 | - ST 24/1-18: Expanded 2D cov. model (gen_cov2d) to 3D. This method may be merged with gen_cov2d in the future. 294 | Also, simplified the code a bit. 295 | """ 296 | # If var_range is 0, the covariance matrix is diagonal with variance. If var_range != 0, we proceed to make a 297 | # correlated covariance matrix 298 | if var_range == 0: 299 | # Diagonal matrix with variance as entries 300 | cov = np.diag(sill * np.ones((nx * ny * nz))) 301 | 302 | else: 303 | # TODO: General input coordinates 304 | # Generate coordinate matrix (equidistant from 1 to n^+1, ^=x,y,z) 305 | [xx, yy, zz] = np.mgrid[1:nx + 1, 1:ny + 1, 1:nz + 1] 306 | pos = np.vstack((xx.flatten('F'), yy.flatten('F'), zz.flatten('F'))).T 307 | 308 | # Calculate distance between coordinates, taking into account possible anisotropy 309 | d = self._edist3d(pos, ang1, ang2, ang3, aniso1, aniso2) 310 | 311 | # Calculate covariance matrix by inserting the (isotropic) distance into an analytical covariance model, 312 | # together with variance (sill) and correlation range 313 | cov = self.variogram_model(d, var_range, sill, var_type) 314 | 315 | return cov 316 | 317 | def _edist3d(self, pos, ang1, ang2, ang3, ani1, ani2): 318 | """ 319 | Calculate isotropic distance between coordinates that are in physical space. It is assumed that 320 | anisotropy in physical space is elliptic, hence transformation to isotropic space can be done with rotation 321 | and stretching of the coordinate system. 322 | 323 | Input: 324 | 325 | - pos: Coordinate array (ncoord x 3 array) 326 | - ang*: Rotation angles (see below) 327 | - ani*: Ratio between axes (see below) 328 | 329 | Output: 330 | 331 | - dist: Euclidean distance(s) between coordinates in pos (size: ncoord x ncoord). 332 | 333 | 334 | Notes, ST 24/1-18: 335 | ------------------ 336 | 337 | ROTATION: 338 | The rotation of the coordinate system follows the logic: 339 | 340 | ang1: Rotation of the x-y axis with z-axis fixed. Positive ang1 => counter-clockwise rotation. 341 | New coord. sys. = x'-y'-z 342 | 343 | [[cos(ang1), -sin(ang1), 0], 344 | R = [sin(ang1), cos(ang1), 0], 345 | [ 0 , 0 , 1]] 346 | 347 | ang2: Rotation of y'-z axis with x'-axis fixed. Positive ang2 => clockwise rotation 348 | New coord. sys. = x'-y"-z' 349 | [[1, 0 , 0 ], 350 | R = [0, cos(ang2), sin(ang2)], 351 | [0, -sin(ang2), cos(ang2)]] 352 | 353 | ang3: Rotation of x'-z' axis with y"-axis fixed. Positive ang3 => counter-clockwise rotation 354 | 355 | [[cos(ang3), 0, -sin(ang3)], 356 | R = [ 0 , 1, 0 ], 357 | [sin(ang3), 0, cos(ang3)]] 358 | 359 | STRETCHING: 360 | The anisotropy factors, ani1 and ani2, factors to stretch the x- and z-axis, s.t. the elliptic anisotropy 361 | becomes isotropic. 362 | """ 363 | # No. of coordinates 364 | n = pos.shape[0] 365 | 366 | # Generate the rotation and stretching matrices required to transform coordinates from physical space to 367 | # isotropic space 368 | # 369 | # Rotation matrix 370 | # 371 | # Transform from degree to radian 372 | a = np.radians(ang1) 373 | b = np.radians(ang2) 374 | c = np.radians(ang3) 375 | 376 | # Formula taken from report ("Angle rotation in GSLIB") by C. Neufeld & C. V. Deutsch on how rotation matrices 377 | # are implemented in GSLIB. 378 | rot_mat = [[np.cos(a) * np.cos(c) + np.sin(a) * np.sin(b) * np.sin(c), -np.sin(a) * np.cos(c) + np.cos(a) * 379 | np.sin(b) * np.sin(c), -np.cos(b) * np.sin(c)], 380 | [np.sin(a) * np.cos(b), np.cos(a) * np.cos(b), np.sin(b)], 381 | [np.cos(a) * np.sin(c) - np.sin(a) * np.sin(b) * np.cos(c), -np.sin(a) * np.sin(c) - np.cos(a) * 382 | np.sin(b) * np.cos(c), np.cos(b) * np.cos(c)]] 383 | 384 | # 385 | # Stretching matrix 386 | # 387 | # Convert aniostropy factors to stretching factors 388 | s1 = 1 / ani1 389 | s2 = 1 / ani2 390 | 391 | # Set up the (diagonal) stretching matrix 392 | stretch_mat = np.diag([s1, 1, s2]) 393 | 394 | # Init. distance matrix 395 | dist = np.zeros((n, n)) 396 | 397 | # 398 | # Calculate distance 399 | # 400 | # Loop over coord. in pos 401 | for i in range(pos.shape[0]): 402 | # Copy current coord. to ncoord x 3 array for easy subtraction with pos 403 | coord = np.tile(pos[i, :], (n, 1)) 404 | 405 | # Subtract coord and pos 406 | dcoord = coord - pos 407 | 408 | # Calc. rotation 409 | rotation = np.dot(rot_mat, dcoord.T) 410 | 411 | # Calc. stretching 412 | d = np.dot(stretch_mat, rotation) 413 | 414 | # Calc. distance (norm of d) 415 | dist[i, :] = np.linalg.norm(d, axis=0) 416 | 417 | # Return 418 | return dist 419 | 420 | 421 | if __name__ == '__main__': 422 | import decomp 423 | import matplotlib.pyplot as plt 424 | 425 | # Covariance calc. 426 | nx = 100 427 | ny = 75 428 | nz = 1 429 | chol = decomp.Cholesky() 430 | cov = chol.gen_cov3d(nx, ny, nz, 5, 5, 0.01, 1, 0, 0, 0, 'sph') # nz = 1 431 | # cov = chol.gen_cov3d(nx, ny, nz, 5, 5, 1, 0.01, 0, 0, 0, 'sph') # nx = 1 432 | # cov = chol.gen_cov3d(nx, ny, nz, 5, 5, 1, 0.01, 0, 0, 0, 'sph') # ny = 1 433 | # c = chol.gen_cov2d(nx, ny, 5, 5, 0.25, 45, 'sph') 434 | 435 | # Realization calc. 436 | m = np.random.randn(nx * ny * nz) 437 | r = chol.gen_real(m, cov, 1) 438 | # rr = chol.gen_real(m, c, 100) 439 | 440 | # Plot 441 | plt.figure() 442 | plt.imshow(r[:, 0].reshape(nx, ny, order='F'), interpolation=None) # nz = 1 443 | # plt.imshow(r[:, 0].reshape(ny, nz, order='F'), interpolation=None) # nx = 1 444 | # plt.imshow(r[:, 0].reshape(nx, nz, order='F'), interpolation=None) # ny = 1 445 | plt.title('3D') 446 | # plt.figure() 447 | # plt.imshow(rr[:, 0].reshape(nx, ny, order='F'), interpolation=None) 448 | # plt.title('2D') 449 | plt.show() 450 | -------------------------------------------------------------------------------- /src/geostat/gslib.py: -------------------------------------------------------------------------------- 1 | """Descriptive description.""" 2 | 3 | import glob 4 | import os 5 | import sys 6 | from datetime import datetime 7 | from subprocess import call, DEVNULL 8 | 9 | import numpy as np 10 | 11 | 12 | class Sgsim: 13 | 14 | def __init__(self, x_size, y_size, z_size, data='foo.dat', var=1, mean=None, var_type='sph', outfile='sgsim.out', 15 | corr_range=1, corr_aniso=[1, 1], corr_angl=[0, 0, 0], limits=[-1.0e21, 1.0e21], number=1): 16 | """ 17 | This script writes the input file for gslib's sequential Gaussian simulation package. 18 | Parameters 19 | ---------- 20 | x_size : float 21 | Size of the field in the x-direction. 22 | 23 | y_size : float 24 | Size of the field in the y-direction. 25 | 26 | data : str, optional 27 | Directory giving hard data constraints in Geo-EAS format. Default value does not exist. 28 | 29 | var : float, optional 30 | Variance value (sill). Default value gives variance = 1. 31 | 32 | mean : float, optional 33 | Stationary mean. Default value gives 0. 34 | 35 | var_type : int, optional 36 | Which variogram type should be selected. 1: Spherical, 2: Exponential, 3: Gaussian. 37 | Default value gives a spherical variogram model. 38 | 39 | outfile : str, optional 40 | Directory of the output file where the field is written. Default value is 'foo.out'. 41 | 42 | corr_range : float, optional 43 | Correlation range. Default value is 1. 44 | 45 | corr_aniso : float, optional 46 | Correlation anisotropy coefficient [0, 1]. Default value is 1 (isotropic). 47 | 48 | corr_angl : float, optional 49 | Correlation angle (from the y-axis). Default value is 0 (correlation along the y-axis). 50 | 51 | limits : tuple, optional 52 | Min and max truncation limits. Default values: min = -1.0e21, max = 1.0e21. 53 | 54 | number : int, optional 55 | Number of ensemble members. Default value is 1. 56 | 57 | 58 | Changelog 59 | --------- 60 | - KF 06/11-2015 61 | 62 | Notes 63 | ----- 64 | The sgsim is capable of simulating 3-d fields, however, we have only 65 | given paramters for simulation of a 2-D field. Upgrading this 66 | """ 67 | 68 | # Allocate for use when generating the realizations 69 | self.mean = mean 70 | self.outfile = outfile 71 | self.number = number 72 | 73 | self.sgsim_input = os.getcwd() + os.sep + 'sgsim.par' 74 | # write the sgsim input file following the outline given in the GSLIB book 75 | with open(self.sgsim_input, 'w') as file: 76 | file.write('\t\t\t Parameters for SGSIM \n') 77 | file.write('\t\t\t ******************** \n\n') 78 | file.write('START OF PARAMETERS:\n') 79 | file.write('{} \n'.format(data)) # file with data 80 | # Column number for x, y, and the variable in data file, 81 | file.write('1 2 0 3 0 0 \n') 82 | # decluster weight, secondary variable (external drift) 83 | # tmin, and tmax. Values below or above are ignored 84 | file.write('{} {} \n'.format(limits[0], limits[1])) 85 | # 0: assume standard normal (no transfomation). 1: transform 86 | file.write('0 \n') 87 | file.write('sgsim_rans.out \n') # Output file for transformation table 88 | # 0:data histogram used for transformation, 1: transformed according to 89 | file.write('0 \n') 90 | # file (given in next key) 91 | file.write('sgsim_smth.in \n') # File with transformation values 92 | # Columns for variable and weight in foosmth 93 | file.write('1 2 \n') 94 | file.write('0.0 15.0 \n') # min and max allowable data values 95 | file.write('1 0.0 \n') # Interpolation in lower tail... 96 | file.write('1 15.0 \n') # Interpolation in upper tail... 97 | # Debugging level [0-3], 0 least debug info 98 | file.write('0 \n') 99 | file.write('sgsim_debug.dbg \n') # File with debug info 100 | file.write('{} \n'.format(outfile)) # file containing output-info 101 | file.write('{} \n'.format(number)) # number of simulations 102 | file.write('{} 0.5 1.0 \n'.format(x_size)) # define grid system along x axis 103 | file.write('{} 0.5 1.0 \n'.format(y_size)) # define grid system along y axis 104 | # define grid system along z axis (Not implemented) 105 | file.write('{} 0.5 1.0 \n'.format(z_size)) 106 | seed_set = datetime.now().microsecond # set seed given the time 107 | if seed_set % 2 == 0: # Check if even, sgsim need odd integer 108 | seed_set += 1 109 | file.write('{} \n'.format(seed_set)) # Random number seed 110 | # min and max numb. data points used for each node 111 | file.write('0 8 \n') 112 | # maximum number of previously simulated nodes to use 113 | file.write('20 \n') 114 | # 0: data and simulated nodes searched separately, 1: they are combined 115 | file.write('1 \n') 116 | # 0: standard spiral, search. 1 num: multiple grid. How many grids 117 | file.write('0 0\n') 118 | # number of data pr. octant. If 0, not used 119 | file.write('0 \n') 120 | file.write('{:1.1f} {:1.1f} {:1.1f} \n'.format(corr_range, corr_range*corr_aniso[0], 121 | corr_range*corr_aniso[1])) # search radius in max, min, vert 122 | # horizontal direction, and vertical (set to 1) 123 | file.write('{:1.1f} {:1.1f} {:1.1f} \n'.format( 124 | corr_angl[0], corr_angl[1], corr_angl[2])) # orientation 125 | # of search ellipse, rotation around y-axis (principal). 126 | # 3-D rotation is not utilized yet. 127 | file.write('51 51 11 \n') # Size of covariance lookup table 128 | # Kriging type. 0:SK, 1:OK, 2:SK with locally varying mean, 3:K with 129 | file.write('0 0 0 \n') 130 | # external drift, 4: Collocated cokriging with secondary variable. 131 | # 4 can be usefull if one simulated correlated fields 132 | # Corr coeff and var reduction for collocated cokriging 133 | # File for locally varying mean, external drift variable, or 134 | file.write('bar.in \n') 135 | # secondary variable for cokriging. 136 | file.write('1 \n') # Column for secondary variable 137 | # Number of varigram structures (set to 1) and nugget constant 138 | file.write('1 0 \n') 139 | if var_type == 'sph': 140 | var_ind = 1 141 | elif var_type == 'exp': 142 | var_ind = 2 143 | elif var_type == 'Gauss': 144 | var_ind = 3 145 | else: 146 | sys.exit('Please define a valid variogram structure') 147 | file.write('{} {} {:1.1f} {:1.1f} {:1.1f} \n'.format(var_ind, var, corr_angl[0], corr_angl[1], 148 | corr_angl[2])) 149 | file.write(' {:1.1f} {:1.1f} {:1.1f} \n'.format(corr_range, corr_range*corr_aniso[0], 150 | corr_range*corr_aniso[1])) 151 | 152 | def gen_real(self, simpath=os.getcwd() + os.sep): 153 | """ 154 | Function for running the GSLIB package sGsim. It is assumed that we already have run init_sgsim such that the 155 | input file is generated. It is further assumed that GSLIB is installed an in the system path. For more 156 | information regarding GSLIB, source code and executables see: http://www.gslib.com/ 157 | """ 158 | 159 | # Run sGsim 160 | call([simpath + 'sgsim', self.sgsim_input], stdout=DEVNULL) 161 | 162 | with open(self.outfile, 'r') as file: 163 | lines = file.readlines() 164 | 165 | top_head = lines[0] 166 | info = lines[1].strip().split() 167 | head = lines[2].strip() 168 | 169 | assert head == 'value' # Head should be value or something might be wrong 170 | 171 | tmp = np.array([float(elem.strip()) for elem in lines[3:]]).reshape((self.number, int(info[1]) * int(info[2]) 172 | * int(info[3]))).T 173 | # Must be transposed to match the general structure of the parameters 174 | if self.mean is not None: 175 | tmp += np.tile(self.mean.reshape(len(self.mean), 1), (1, self.number)) 176 | 177 | # Remove all tmp files that sgsim creates 178 | for fl in glob.glob('sgsim*'): 179 | os.remove(fl) 180 | 181 | self.real = tmp 182 | return self.real 183 | 184 | 185 | class Sisim: 186 | 187 | def __init__(self, x_size, y_size, cat, thresh, var_type, var, cdf, data='foo.dat', cat_type=0, M_B=0, 188 | limits=[0, 1], outfile='sisim.out', number=1, corr_range=[1], corr_aniso=[1], corr_angl=[0], 189 | mean=None, facies_var=None): 190 | """ 191 | This script writes the input file for gslib's sequential indicator simulation program. 192 | 193 | Parameters 194 | ---------- 195 | x_size : float 196 | Size of the field in the x-direction. 197 | 198 | y_size : float 199 | Size of the field in the y-direction. 200 | 201 | cat : int 202 | Number of categories. 203 | 204 | thresh : iterable 205 | Threshold values for the categories. 206 | 207 | cdf : iterable 208 | Global CDF or PDF values for the categories. 209 | 210 | var_type : list 211 | List of variogram types, as long as the number of categories. 212 | 213 | var : iterable 214 | Variance values for the different categories, as long as the number of categories. 215 | 216 | Data : str, optional 217 | File with data. If it does not exist, the simulation is unconditional. 218 | 219 | cat_type : int, optional 220 | Variable type. 1 for continuous, 0 for categorical. 221 | 222 | M_B : int, optional 223 | Markov-Bayes type simulation. 0 for no, 1 for yes. 224 | 225 | limits : iterable, optional 226 | Trimming limits. 227 | 228 | outfile : str, optional 229 | Name of the file where the data are stored. 230 | 231 | number : int, optional 232 | Number of simulations. 233 | 234 | corr_range : float, optional 235 | Correlation range in the maximum horizontal direction. 236 | 237 | corr_aniso : float, optional 238 | Anisotropy factor for correlation. 239 | 240 | corr_angl : float, optional 241 | Angle of primary correlation. Defined clockwise around the y-axis. 242 | 243 | """ 244 | self.outfile = outfile 245 | self.sisim_input = os.getcwd() + os.sep + 'sisim.par' 246 | self.number = number 247 | self.mean = mean 248 | self.facies_var = facies_var 249 | 250 | with open(self.sisim_input, 'w') as file: 251 | file.write('\t\t\t Parameters for SISIM \n') 252 | file.write('\t\t\t ******************** \n\n') 253 | file.write('START OF PARAMETERS:\n') 254 | file.write('{}\n'.format(cat_type)) # 1=continous, 0=categorical 255 | file.write('{}\n'.format(cat)) # Numb theresholds/categories 256 | for val in thresh: 257 | file.write('{} '.format(val)) # Write the threshold values 258 | file.write('\n') 259 | for val in cdf: 260 | file.write('{} '.format(val)) # Write the cdf values 261 | file.write('\n') 262 | file.write('{}\n'.format(data)) # File with data 263 | file.write('1 2 0 3\n') # Columns for x,y,z and data 264 | # File with soft input (not used by us) 265 | file.write('sisim_soft.in\n') 266 | file.write('1 2 0 3 4 5 6 7\n') # Clumns for x,y,z and indicators 267 | file.write('{}\n'.format(M_B)) # Markov-Bayes simulation (0 = no, 1=yes) 268 | file.write('0.61 0.54 0.56 0.53\n') # calibration B(z) values, (if M_B = 1) 269 | file.write('{} {} \n'.format(limits[0], limits[1])) # trimming limits 270 | file.write('{} {} \n'.format(limits[0], limits[1])) # max and min data values 271 | file.write('1 0.0\n') # extrapolation in the lower tail 272 | file.write('1 0.0\n') # Extrapolation in the middle tail 273 | file.write('1 0.0\n') # Extraoilation in the upper tail 274 | # Values if # 3 is selected in the extrapolation 275 | file.write('NA.dat\n') 276 | file.write('3 0\n') # Column values in file above 277 | file.write('0\n') # debug level, 0 is lowest detail 278 | file.write('sisim.dbg\n') # Debug file 279 | file.write('{}\n'.format(outfile)) # file containing output 280 | file.write('{} \n'.format(number)) # number of simulations 281 | file.write('{} 0.5 1.0 \n'.format(x_size)) # define grid system along x axis 282 | file.write('{} 0.5 1.0 \n'.format(y_size)) # define grid system along y axis 283 | # define grid system along z axis (Not implemented) 284 | file.write('1 0.5 1.0 \n') 285 | seed_set = datetime.now().microsecond # set seed given the time 286 | if seed_set % 2 == 0: # Check if even, sgsim need odd integer 287 | seed_set += 1 288 | file.write('{} \n'.format(seed_set)) # Random number seed 289 | # max number of grid points used in simulation 290 | file.write('20\n') 291 | file.write('20\n') # Max numb of previous nodes to use 292 | file.write('20\n') # Max numb of soft dataa as node locations 293 | file.write('1\n') # data are merged with grid nodes 294 | file.write('1\n') # If set to 1, a multiple grid simulator is used 295 | file.write('5\n') # Target numb of multgrid refinements 296 | file.write('0\n') # Number of original data per octant 297 | file.write('{:1.1f} {:1.1f} 1.0 \n'.format(max(corr_range), max( 298 | corr_range)*max(corr_aniso))) # search radius in maximum minimum 299 | # horizontal direction, and vertical (set to 1) 300 | # orientation of search ellipse, rotation around y-axis. 301 | file.write('{:1.1f} 0.0 0.0 \n'.format(min(corr_angl))) 302 | # 3-D rotation is not utilized yet. 303 | file.write('51 51 11 \n') # Size of covariance lookup table 304 | file.write('0 1\n') # Full indicator kriging 305 | file.write('0\n') # Simple kriging 306 | for i in range(cat): 307 | # Number of varigram structures (set to 1) and nugget constant 308 | file.write('1 0 \n') 309 | if var_type[i] == 'sph': 310 | var_ind = 1 311 | elif var_type[i] == 'exp': 312 | var_ind = 2 313 | elif var_type[i] == 'Gauss': 314 | var_ind = 3 315 | else: 316 | sys.exit('Plase define a valud varigram structure') 317 | file.write('{} {} {} 0.0 0.0 \n {:1.1f} {:1.1f} 1.0 \n'.format(var_ind, var[i], corr_angl[i], 318 | corr_range[i], corr_range[i]*corr_aniso[i])) # struct number, variogram, variance(sill), 319 | 320 | def gen_real(self): 321 | """ 322 | Function for running the GSLIB package sIsim. It is assumed that we already have run init_sisim such that 323 | the input file is generated. It is further assumed that GSLIB is installed an in the system path. For more 324 | information regarding GSLIB, source code and executables see: http://www.gslib.com/ 325 | """ 326 | # Run sIsim 327 | call(['sisim', self.sisim_input], stdout=DEVNULL) 328 | 329 | with open(self.outfile, 'r') as file: 330 | lines = file.readlines() 331 | 332 | top_head = lines[0] 333 | info = lines[1].strip().split() 334 | head = lines[2].strip() 335 | 336 | assert head == 'Simulated Value' # Head should be value or something might be wrong 337 | 338 | tmp = np.array([float(elem.strip()) for elem in lines[3:]]).reshape((self.number, 339 | float(info[1])*float(info[2]))).T 340 | # Must be transposed to match the general structure of the parameters 341 | if self.mean is not None: 342 | # For the categorical values we multiply the mean and to the realizations 343 | for i in range(self.number): 344 | tmp[:, i] = self.mean*tmp[:, i] 345 | if self.facies_var is not None: 346 | for i in range(self.number): 347 | tmp[:, i] += self.facies_var[:, i] 348 | 349 | # Remove all tmp files that sgsim creates 350 | for fl in glob.glob('sisim*'): 351 | os.remove(fl) 352 | 353 | self.real = tmp 354 | return self.real 355 | -------------------------------------------------------------------------------- /LICENSE: -------------------------------------------------------------------------------- 1 | GNU GENERAL PUBLIC LICENSE 2 | Version 3, 29 June 2007 3 | 4 | Copyright (C) 2007 Free Software Foundation, Inc. 5 | Everyone is permitted to copy and distribute verbatim copies 6 | of this license document, but changing it is not allowed. 7 | 8 | Preamble 9 | 10 | The GNU General Public License is a free, copyleft license for 11 | software and other kinds of works. 12 | 13 | The licenses for most software and other practical works are designed 14 | to take away your freedom to share and change the works. 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Patents. 472 | 473 | A "contributor" is a copyright holder who authorizes use under this 474 | License of the Program or a work on which the Program is based. The 475 | work thus licensed is called the contributor's "contributor version". 476 | 477 | A contributor's "essential patent claims" are all patent claims 478 | owned or controlled by the contributor, whether already acquired or 479 | hereafter acquired, that would be infringed by some manner, permitted 480 | by this License, of making, using, or selling its contributor version, 481 | but do not include claims that would be infringed only as a 482 | consequence of further modification of the contributor version. For 483 | purposes of this definition, "control" includes the right to grant 484 | patent sublicenses in a manner consistent with the requirements of 485 | this License. 486 | 487 | Each contributor grants you a non-exclusive, worldwide, royalty-free 488 | patent license under the contributor's essential patent claims, to 489 | make, use, sell, offer for sale, import and otherwise run, modify and 490 | propagate the contents of its contributor version. 491 | 492 | In the following three paragraphs, a "patent license" is any express 493 | agreement or commitment, however denominated, not to enforce a patent 494 | (such as an express permission to practice a patent or covenant not to 495 | sue for patent infringement). To "grant" such a patent license to a 496 | party means to make such an agreement or commitment not to enforce a 497 | patent against the party. 498 | 499 | If you convey a covered work, knowingly relying on a patent license, 500 | and the Corresponding Source of the work is not available for anyone 501 | to copy, free of charge and under the terms of this License, through a 502 | publicly available network server or other readily accessible means, 503 | then you must either (1) cause the Corresponding Source to be so 504 | available, or (2) arrange to deprive yourself of the benefit of the 505 | patent license for this particular work, or (3) arrange, in a manner 506 | consistent with the requirements of this License, to extend the patent 507 | license to downstream recipients. "Knowingly relying" means you have 508 | actual knowledge that, but for the patent license, your conveying the 509 | covered work in a country, or your recipient's use of the covered work 510 | in a country, would infringe one or more identifiable patents in that 511 | country that you have reason to believe are valid. 512 | 513 | If, pursuant to or in connection with a single transaction or 514 | arrangement, you convey, or propagate by procuring conveyance of, a 515 | covered work, and grant a patent license to some of the parties 516 | receiving the covered work authorizing them to use, propagate, modify 517 | or convey a specific copy of the covered work, then the patent license 518 | you grant is automatically extended to all recipients of the covered 519 | work and works based on it. 520 | 521 | A patent license is "discriminatory" if it does not include within 522 | the scope of its coverage, prohibits the exercise of, or is 523 | conditioned on the non-exercise of one or more of the rights that are 524 | specifically granted under this License. You may not convey a covered 525 | work if you are a party to an arrangement with a third party that is 526 | in the business of distributing software, under which you make payment 527 | to the third party based on the extent of your activity of conveying 528 | the work, and under which the third party grants, to any of the 529 | parties who would receive the covered work from you, a discriminatory 530 | patent license (a) in connection with copies of the covered work 531 | conveyed by you (or copies made from those copies), or (b) primarily 532 | for and in connection with specific products or compilations that 533 | contain the covered work, unless you entered into that arrangement, 534 | or that patent license was granted, prior to 28 March 2007. 535 | 536 | Nothing in this License shall be construed as excluding or limiting 537 | any implied license or other defenses to infringement that may 538 | otherwise be available to you under applicable patent law. 539 | 540 | 12. No Surrender of Others' Freedom. 541 | 542 | If conditions are imposed on you (whether by court order, agreement or 543 | otherwise) that contradict the conditions of this License, they do not 544 | excuse you from the conditions of this License. If you cannot convey a 545 | covered work so as to satisfy simultaneously your obligations under this 546 | License and any other pertinent obligations, then as a consequence you may 547 | not convey it at all. For example, if you agree to terms that obligate you 548 | to collect a royalty for further conveying from those to whom you convey 549 | the Program, the only way you could satisfy both those terms and this 550 | License would be to refrain entirely from conveying the Program. 551 | 552 | 13. Use with the GNU Affero General Public License. 553 | 554 | Notwithstanding any other provision of this License, you have 555 | permission to link or combine any covered work with a work licensed 556 | under version 3 of the GNU Affero General Public License into a single 557 | combined work, and to convey the resulting work. The terms of this 558 | License will continue to apply to the part which is the covered work, 559 | but the special requirements of the GNU Affero General Public License, 560 | section 13, concerning interaction through a network will apply to the 561 | combination as such. 562 | 563 | 14. Revised Versions of this License. 564 | 565 | The Free Software Foundation may publish revised and/or new versions of 566 | the GNU General Public License from time to time. Such new versions will 567 | be similar in spirit to the present version, but may differ in detail to 568 | address new problems or concerns. 569 | 570 | Each version is given a distinguishing version number. If the 571 | Program specifies that a certain numbered version of the GNU General 572 | Public License "or any later version" applies to it, you have the 573 | option of following the terms and conditions either of that numbered 574 | version or of any later version published by the Free Software 575 | Foundation. If the Program does not specify a version number of the 576 | GNU General Public License, you may choose any version ever published 577 | by the Free Software Foundation. 578 | 579 | If the Program specifies that a proxy can decide which future 580 | versions of the GNU General Public License can be used, that proxy's 581 | public statement of acceptance of a version permanently authorizes you 582 | to choose that version for the Program. 583 | 584 | Later license versions may give you additional or different 585 | permissions. However, no additional obligations are imposed on any 586 | author or copyright holder as a result of your choosing to follow a 587 | later version. 588 | 589 | 15. Disclaimer of Warranty. 590 | 591 | THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY 592 | APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT 593 | HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY 594 | OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, 595 | THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR 596 | PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM 597 | IS WITH YOU. SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF 598 | ALL NECESSARY SERVICING, REPAIR OR CORRECTION. 599 | 600 | 16. Limitation of Liability. 601 | 602 | IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING 603 | WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS 604 | THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY 605 | GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE 606 | USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF 607 | DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD 608 | PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS), 609 | EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF 610 | SUCH DAMAGES. 611 | 612 | 17. Interpretation of Sections 15 and 16. 613 | 614 | If the disclaimer of warranty and limitation of liability provided 615 | above cannot be given local legal effect according to their terms, 616 | reviewing courts shall apply local law that most closely approximates 617 | an absolute waiver of all civil liability in connection with the 618 | Program, unless a warranty or assumption of liability accompanies a 619 | copy of the Program in return for a fee. 620 | 621 | END OF TERMS AND CONDITIONS 622 | 623 | How to Apply These Terms to Your New Programs 624 | 625 | If you develop a new program, and you want it to be of the greatest 626 | possible use to the public, the best way to achieve this is to make it 627 | free software which everyone can redistribute and change under these terms. 628 | 629 | To do so, attach the following notices to the program. It is safest 630 | to attach them to the start of each source file to most effectively 631 | state the exclusion of warranty; and each file should have at least 632 | the "copyright" line and a pointer to where the full notice is found. 633 | 634 | 635 | Copyright (C) 636 | 637 | This program is free software: you can redistribute it and/or modify 638 | it under the terms of the GNU General Public License as published by 639 | the Free Software Foundation, either version 3 of the License, or 640 | (at your option) any later version. 641 | 642 | This program is distributed in the hope that it will be useful, 643 | but WITHOUT ANY WARRANTY; without even the implied warranty of 644 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 645 | GNU General Public License for more details. 646 | 647 | You should have received a copy of the GNU General Public License 648 | along with this program. If not, see . 649 | 650 | Also add information on how to contact you by electronic and paper mail. 651 | 652 | If the program does terminal interaction, make it output a short 653 | notice like this when it starts in an interactive mode: 654 | 655 | Copyright (C) 656 | This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'. 657 | This is free software, and you are welcome to redistribute it 658 | under certain conditions; type `show c' for details. 659 | 660 | The hypothetical commands `show w' and `show c' should show the appropriate 661 | parts of the General Public License. Of course, your program's commands 662 | might be different; for a GUI interface, you would use an "about box". 663 | 664 | You should also get your employer (if you work as a programmer) or school, 665 | if any, to sign a "copyright disclaimer" for the program, if necessary. 666 | For more information on this, and how to apply and follow the GNU GPL, see 667 | . 668 | 669 | The GNU General Public License does not permit incorporating your program 670 | into proprietary programs. If your program is a subroutine library, you 671 | may consider it more useful to permit linking proprietary applications with 672 | the library. If this is what you want to do, use the GNU Lesser General 673 | Public License instead of this License. But first, please read 674 | . 675 | --------------------------------------------------------------------------------