Data Base¶

In this preamble, we load the gstlearn package.

In [1]:
%%javascript
IPython.OutputArea.prototype._should_scroll = function(lines) {
    return false;
}
In [2]:
import gstlearn as gl
import gstlearn.plot as gp
import matplotlib.pyplot as plt
import numpy as np
import os
import urllib.request

flagInternetAvailable = True ## Set to false if no internet

Main classes¶

This is the (non-exhaustive) list of classes (of objects) in gstlearn:

  • Db, DbGrid: numerical data base
  • DirParam, VarioParam and Vario: experimental variograms
  • Model: variogram model
  • Neigh: neighborhood
  • Anam: gaussian anamorphosis
  • Polygon: 2-D polygonal shapes
  • Rule: lithotype rule for thresholds used for truncated plurigaussian models

Importing External File¶

Loading a CSV file¶

We start by downloading the ASCII file called Scotland_Temperatures.csv (organized as a CSV file) and we store it in a temporary directory and keep its path in the variable called temp_csv. The file is provided as a CSV format. We load it into a Pandas data frame (names datcsv) using the relevant Python command. Note that "MISS" keyword is used in this file to indicate a missing value. Such values will be replaced by NaN.

In [3]:
fileCSV='Scotland_Temperatures.csv'
if flagInternetAvailable:
    temp_csv, head = urllib.request.urlretrieve('https://soft.minesparis.psl.eu/gstlearn/data/Scotland/'+fileCSV,'./'+fileCSV)
else:
    temp_csv='./'+fileCSV
In [4]:
import pandas as pd
datcsv = pd.read_csv(temp_csv, na_values="MISS")
datcsv
Out[4]:
Longitude Latitude Elevation January_temp
0 372.1 658.9 255 1.7
1 303.5 665.9 125 2.0
2 218.4 597.9 8 4.6
3 245.0 955.0 90 NaN
4 326.8 691.2 32 3.1
... ... ... ... ...
231 273.2 564.6 47 2.8
232 333.9 730.1 30 2.6
233 185.0 655.0 115 NaN
234 259.8 587.9 119 2.1
235 260.8 668.6 107 2.6

236 rows × 4 columns

We can check the contents of the data frame (by simply typing its name) and see that it contains four columns (respectively called Longitude, Latitude, Elevation, January_temp) and 236 rows (header line excluded).

Creating Db object from a Pandas frame¶

The user can then create a database of the gstlearn package (Db class) directly from the previously imported Pandas frame. Note that the only numerical columns are copied.

In [5]:
dat = gl.Db_fromPanda(datcsv)
dat
Out[5]:
Data Base Characteristics
=========================

Data Base Summary
-----------------
File is organized as a set of isolated points
Space dimension              = 0
Number of Columns            = 4
Total number of samples      = 236

Variables
---------
Column = 0 - Name = Longitude - Locator = NA
Column = 1 - Name = Latitude - Locator = NA
Column = 2 - Name = Elevation - Locator = NA
Column = 3 - Name = January_temp - Locator = NA

Creating Db object directly from CSV file¶

These operations can be performed directly by reading the CSV file again and load it directly into a Db.

Note that we introduce a CSVformat description where we can specifiy the specificities of the file to be read, in particular we can tell how to spell the conventional value used for coding missing information.

In [6]:
csv = gl.CSVformat.create(flagHeader=True, naString = "MISS")
dat = gl.Db.createFromCSV(temp_csv, csv=csv)
dat
Out[6]:
Data Base Characteristics
=========================

Data Base Summary
-----------------
File is organized as a set of isolated points
Space dimension              = 0
Number of Columns            = 5
Total number of samples      = 236

Variables
---------
Column = 0 - Name = rank - Locator = NA
Column = 1 - Name = Longitude - Locator = NA
Column = 2 - Name = Latitude - Locator = NA
Column = 3 - Name = Elevation - Locator = NA
Column = 4 - Name = January_temp - Locator = NA

Note that a "rank" variable has been automatically added. The rank is always 1-based and must be distinguish from an index (0-based). The rank variable could be later useful for certain functions of the gstlearn package.

Importing Db File from a "Neutral File"¶

A last solution is to import it directly from the set of demonstration files (provided together with the package and called temp_nf) and stored in a specific format (Neutral file).

These NF (or neutral file) are currently used for serialization of the gstlearn objects. They will probably be replaced in the future by a facility backuping the whole workspace in one step.

Note that the contents of the Db is slightly different from the result obtained when reading from CSV. Essentially, some variables have a Locator field defined, some do not. This concept will be described later in this chapter and the difference can be ignored.

In [7]:
fileNF='Scotland_Temperatures.NF'
if flagInternetAvailable:
    temp_nf, head = urllib.request.urlretrieve('https://soft.minesparis.psl.eu/gstlearn/data/Scotland/'+fileNF,'./'+fileNF)
else:
    temp_nf='./'+fileNF

dat = gl.Db.createFromNF(temp_nf)
dat
Out[7]:
Data Base Characteristics
=========================

Data Base Summary
-----------------
File is organized as a set of isolated points
Space dimension              = 2
Number of Columns            = 5
Total number of samples      = 236

Variables
---------
Column = 0 - Name = rank - Locator = NA
Column = 1 - Name = Longitude - Locator = x1
Column = 2 - Name = Latitude - Locator = x2
Column = 3 - Name = Elevation - Locator = NA
Column = 4 - Name = January_temp - Locator = z1

Discovering Db¶

The Db class¶

Db objects (as all objects that inherits from AStringable) have a method display allowing to print a summary of the content of the data base. The same occurs when typing the name of the variable at the end of a cell (see above).

In [8]:
dat.display()

Data Base Characteristics
=========================

Data Base Summary
-----------------
File is organized as a set of isolated points
Space dimension              = 2
Number of Columns            = 5
Total number of samples      = 236

Variables
---------
Column = 0 - Name = rank - Locator = NA
Column = 1 - Name = Longitude - Locator = x1
Column = 2 - Name = Latitude - Locator = x2
Column = 3 - Name = Elevation - Locator = NA
Column = 4 - Name = January_temp - Locator = z1

There, we can check that the 4 initial fields have been considered, in addition to a first one, automatically called rank, for a total of 5 columns (the information regarding UID will not be addressed in this chapter).

We can check that each field is assigned to a numbered Column (0-based index). Finally the total number of samples is 236 as expected.

In addition, some interesting information tells you that this data base corresponds to a 2-D dimension one: this will be described later together with the use of the Locator information.

To get more information on the contents of the Db, it is possible to use the DbStringFormat option and to use use through the display method. There are several ways to specify the type of information that is searched for (see the documentation of this class for details): typically here we ask for statistics but restrict them to a list of variables

In [9]:
dbfmt = gl.DbStringFormat.createFromFlags(flag_stats=True, names=["Elevation", "January_temp"])
dat.display(dbfmt)

Data Base Characteristics
=========================

Data Base Summary
-----------------
File is organized as a set of isolated points
Space dimension              = 2
Number of Columns            = 5
Total number of samples      = 236

Data Base Statistics
--------------------
4 - Name Elevation - Locator NA
 Nb of data          =        236
 Nb of active values =        236
 Minimum value       =      2.000
 Maximum value       =    800.000
 Mean value          =    146.441
 Standard Deviation  =    165.138
 Variance            =  27270.713
5 - Name January_temp - Locator z1
 Nb of data          =        236
 Nb of active values =        151
 Minimum value       =      0.600
 Maximum value       =      5.200
 Mean value          =      2.815
 Standard Deviation  =      1.010
 Variance            =      1.020

Variables
---------
Column = 0 - Name = rank - Locator = NA
Column = 1 - Name = Longitude - Locator = x1
Column = 2 - Name = Latitude - Locator = x2
Column = 3 - Name = Elevation - Locator = NA
Column = 4 - Name = January_temp - Locator = z1

Monovariate statistics are better displayed using a single function called dbStatisticsMono. This function waits for a vector of enumerators of type EStatOption as statistic operators. Such vector is created using a static function called fromKeys which is available in all enumerators classes (i.e. inherits from AEnum).

In [10]:
gl.dbStatisticsMono(dat,
                     names=["Elevation", "January_temp"],
                     opers=gl.EStatOption.fromKeys(["MEAN","MINI","MAXI"]))
Out[10]:
                   Mean    Minimum    Maximum
   Elevation     87.974      3.000    387.000
January_temp      2.815      0.600      5.200

Assessors for Db class¶

We can also consider the data base as a 2D array and use the [ ] assessors. The following usage shows the whole content of the data base dumped as a 2D Numpy array.

In [11]:
dat[:]
Out[11]:
array([[  1. , 372.1, 658.9, 255. ,   1.7],
       [  2. , 303.5, 665.9, 125. ,   2. ],
       [  3. , 218.4, 597.9,   8. ,   4.6],
       ...,
       [234. , 185. , 655. , 115. ,   nan],
       [235. , 259.8, 587.9, 119. ,   2.1],
       [236. , 260.8, 668.6, 107. ,   2.6]])

We can access to one or several variables. Note that the contents of the Column corresponding to the target variable (i.e. January_temp) is produced as a 1D numpy array.

Also note the presence of samples with nan corresponding to those where the target variable is not informed ('MISS' in the original dataset file).

In [12]:
dat["January_temp"]
Out[12]:
array([1.7, 2. , 4.6, nan, 3.1, 3.5, 3.4, 3. , 4.9, 2.9, nan, 1.3, nan,
       4. , 1.7, nan, 1.9, 3.3, 2.3, nan, 2.3, 2.6, nan, 2.7, 2.9, nan,
       1. , 1.2, nan, 3.1, nan, 3.7, 2.1, 2.5, 2.9, nan, nan, nan, 3.1,
       2.1, nan, 2.7, 3. , nan, nan, 1.8, nan, nan, 2.2, 2.9, 3.3, nan,
       5. , 1.6, nan, 2.1, 3.2, 4.2, 1.1, nan, 2.7, 0.6, 3.2, nan, 2.5,
       2. , 2.8, nan, 3.2, 3.2, 4.5, 3.3, 4.1, 2.2, 1.7, 4.3, 5.2, nan,
       1.6, 3.9, 3.1, nan, 3.5, 4.7, 3.6, nan, 1.8, 1.7, nan, nan, nan,
       nan, nan, nan, nan, 1.7, nan, 3. , 4.6, 3.9, 3.2, 1.3, nan, nan,
       nan, 4.7, nan, 2.6, 2. , 4.7, 1.2, 2.9, 0.9, 3. , nan, 3.6, 0.7,
       3.3, nan, nan, nan, 2.7, nan, 2.7, 2.4, nan, nan, 2. , 2.6, nan,
       4.3, nan, nan, nan, nan, 3.1, 3.4, 3.1, 2. , 1.3, 1.9, nan, 3.3,
       2.7, 4.4, nan, 3. , 0.9, 0.7, nan, 3.6, nan, 3.5, nan, 2.4, 1. ,
       nan, 3.6, nan, nan, nan, nan, 3. , nan, 3.5, 4. , 3. , 3.6, nan,
       3.2, 1.7, 2.7, 1.9, nan, nan, 4.4, 1.9, 3.3, nan, nan, 3.5, 1.7,
       3. , nan, 2.7, nan, 1. , 3.3, nan, nan, 3.2, 3.9, nan, nan, 3. ,
       nan, 3.8, nan, 2.8, nan, 2.9, 1.4, 2.6, 3. , nan, 2.8, 2.9, 3.6,
       nan, 2. , 4.6, 3.7, nan, nan, 4.5, 2.7, nan, 4.7, 1.7, 1.9, 3.5,
       nan, nan, nan, 2.1, 2.3, 3.1, nan, nan, 2. , 2.6, 2.8, 2.6, nan,
       2.1, 2.6])

But it can be more restrictive as in the following paragraph, where we only consider the samples 10 to 15, and only consider the variables rank, Latitude, Elevation. Remind that indices start from 0 to N-1. Indices slice '10:15' in Python means indices {10,11,12,13,14} (different from R) which means ranks {11,12,13,14,15}.

In [13]:
dat[10:15, ["rank", "Latitude", "Elevation"]]
Out[13]:
array([[ 11. , 865. ,  37. ],
       [ 12. , 602.6, 242. ],
       [ 13. , 835. , 295. ],
       [ 14. , 933.2,  15. ],
       [ 15. , 648.8, 183. ]])

We can also replace the variable Name by their Column index. Although this is not recommanded as the Column index may vary over time.

In [14]:
dat[10:15, 2:4]
Out[14]:
array([[865. ,  37. ],
       [602.6, 242. ],
       [835. , 295. ],
       [933.2,  15. ],
       [648.8, 183. ]])

A particular function is available to convert all the data base in an appropriate object of the Target Langage (here Python). A gstlearn Db is converted into a Pandas frame using toTL.

In [15]:
dat.toTL()
Out[15]:
rank Longitude Latitude Elevation January_temp
0 1.0 372.1 658.9 255.0 1.7
1 2.0 303.5 665.9 125.0 2.0
2 3.0 218.4 597.9 8.0 4.6
3 4.0 245.0 955.0 90.0 NaN
4 5.0 326.8 691.2 32.0 3.1
... ... ... ... ... ...
231 232.0 273.2 564.6 47.0 2.8
232 233.0 333.9 730.1 30.0 2.6
233 234.0 185.0 655.0 115.0 NaN
234 235.0 259.8 587.9 119.0 2.1
235 236.0 260.8 668.6 107.0 2.6

236 rows × 5 columns

Please also note the feature that a variable whose name does not exist (newvar) in the data base, is created on the fly. Also note that variables may be specified with names referred to using traditional regexp expressions (i.e. the symbol '*' replaces any list of characters):

In [16]:
dat["newvar"] = 12.3 * dat["Elevation"] - 2.1 * dat["*temp"]
dat
Out[16]:
Data Base Characteristics
=========================

Data Base Summary
-----------------
File is organized as a set of isolated points
Space dimension              = 2
Number of Columns            = 6
Total number of samples      = 236

Variables
---------
Column = 0 - Name = rank - Locator = NA
Column = 1 - Name = Longitude - Locator = x1
Column = 2 - Name = Latitude - Locator = x2
Column = 3 - Name = Elevation - Locator = NA
Column = 4 - Name = January_temp - Locator = z1
Column = 5 - Name = newvar - Locator = NA

The user also can remove a variable from the data base by doing the following:

In [17]:
dat.deleteColumn("newvar")
dat.display()

Data Base Characteristics
=========================

Data Base Summary
-----------------
File is organized as a set of isolated points
Space dimension              = 2
Number of Columns            = 5
Total number of samples      = 236

Variables
---------
Column = 0 - Name = rank - Locator = NA
Column = 1 - Name = Longitude - Locator = x1
Column = 2 - Name = Latitude - Locator = x2
Column = 3 - Name = Elevation - Locator = NA
Column = 4 - Name = January_temp - Locator = z1

Locators¶

The locators are used to specify the role assigned to a Column for the rest of the study (unless changed further). The locator is characterized by its name (Z for a variable and X for a coordinate) within the Enumerator ELoc.

In [18]:
dat.setLocators(["Longitude","Latitude"], gl.ELoc.X)
dat.setLocator("January_temp", gl.ELoc.Z)
dat
Out[18]:
Data Base Characteristics
=========================

Data Base Summary
-----------------
File is organized as a set of isolated points
Space dimension              = 2
Number of Columns            = 5
Total number of samples      = 236

Variables
---------
Column = 0 - Name = rank - Locator = NA
Column = 1 - Name = Longitude - Locator = x1
Column = 2 - Name = Latitude - Locator = x2
Column = 3 - Name = Elevation - Locator = NA
Column = 4 - Name = January_temp - Locator = z1

As can be seen in the printout, variables Latitude and Longitude have been designated as coordinates (pay attention to the order) and January_temp is the (unique) variable of interest. Therefore any subsequent step will be performed as a monovariate 2-D process.

The locator is translated into a letter,number pair for better legibility: e.g. x1 for the first coordinate.

Here are all the roles known by gstlearn:

In [19]:
gl.ELoc.printAll()

  -1 -     UNKNOWN : Unknown locator
    0 -           X : Coordinate
    1 -           Z : Variable
    2 -           V : Variance of measurement error
    3 -           F : External Drift
    4 -           G : Gradient component
    5 -           L : Lower bound of an inequality
    6 -           U : Upper bound of an inequality
    7 -           P : Proportion
    8 -           W : Weight
    9 -           C : Code
   10 -         SEL : Selection
   11 -         DOM : Domain
   12 -        BLEX : Block Extension
   13 -        ADIR : Dip direction Angle
   14 -        ADIP : Dip Angle
   15 -        SIZE : Object height
   16 -          BU : Fault UP termination
   17 -          BD : Fault DOWN termination
   18 -        TIME : Time variable
   19 -       LAYER : Layer rank
   20 -      NOSTAT : Non-stationary parameter
   21 -        TGTE : Tangent
   22 -        SIMU : Conditional or non-conditional simulations
   23 -      FACIES : Facies simulated
   24 -     GAUSFAC : Gaussian value for Facies
   25 -        DATE : Date
   26 -       RKLOW : Rank for lower bound (when discretized)
   27 -        RKUP : Rank for upper bound (when discretized)
   28 -         SUM : Constraints on the Sum

More with Db¶

Plotting a Db¶

Plot the contents of a Db using functions of the gstlearn.plot sub-package (which relies on matplotlib). The color option (nameColor) is used to represent the january_temp variable.

Note: Non availalble values (NaN) are converted into 0 for display purpose. This behavior will be modified and tunable in future versions.

In [20]:
fig, ax = gp.initGeographic()
ax.symbol(dat, nameColor="January_temp", flagLegendColor=True, legendNameColor="Temperature")
ax.decoration(title="January Temperature", xlabel="Easting", ylabel="Northing")
plt.show()

A more elaborated graphic representation displays the samples with a symbol proportional to the Elevation (nameSize) and a color representing the Temperature (nameColor).

In [21]:
fig, ax = gp.initGeographic()
ax.symbol(dat, nameSize="Elevation", nameColor="*temp", flagLegendSize=True, legendNameSize="Elevation")
ax.decoration(title="January Temperature", xlabel="Easting", ylabel="Northing")
plt.show()

Of course, you can use your own graphical routines (for example, a direct call to matplotlib) by simply accessing to the gstlearn data base values (using '[ ]' accessor):

In [22]:
plt.figure(figsize=(20,8))
plt.scatter(dat["x1"], dat["x2"], s=20, c=dat["*temp"]) # Locator or variable name is OK
plt.title("January Temperatures")
plt.xlabel("Easting")
plt.ylabel("Northing")
plt.colorbar(label="Temperature (°C)")
plt.gca().set_aspect('equal') # Respect aspect ratio
plt.show()

Grid Data Base¶

On the same area, a terrain model is available (as a demonstration file available in the package distribution). We first download it and create the corresponding data base defined on a grid support (DbGrid).

In [23]:
fileNF='Scotland_Elevations.NF'
if flagInternetAvailable:
    elev_nf, head = urllib.request.urlretrieve('https://soft.minesparis.psl.eu/gstlearn/data/Scotland/'+fileNF,'./'+fileNF)
else:
    elev_nf='./'+fileNF

grid = gl.DbGrid.createFromNF(elev_nf)
grid
Out[23]:
Data Base Grid Characteristics
==============================

Data Base Summary
-----------------
File is organized as a regular grid
Space dimension              = 2
Number of Columns            = 4
Total number of samples      = 11097
Number of active samples     = 3092

Grid characteristics:
---------------------
Origin :     65.000   535.000
Mesh   :      4.938     4.963
Number :         81       137

Variables
---------
Column = 0 - Name = Longitude - Locator = x1
Column = 1 - Name = Latitude - Locator = x2
Column = 2 - Name = Elevation - Locator = f1
Column = 3 - Name = inshore - Locator = sel

We can check that the grid is constituted of 81 columns and 137 rows, or 11097 grid cells. We can also notice that some locators are already defined (these information are stored in the Neutral File).

Selection¶

We can check the presence of a variable (called inshore) which is assigned to the sel locator: this corresponds to a Selection which acts as a binary filter: some grid cells are active and others are masked off. The count of active samples is given in the previous printout (3092). This selection remains active until the locator 'sel' is replaced or deleted (there may not be more than one selection defined at a time per data base). This is what can be seen in the following display where the Elevation is automatically represented only within the inshore selection.

Note that any variable (having values equal to 0/1 or True/False) can be considered as a Selection: it must simply be assigned to the sel locator using the setLocator method described earlier.

In [24]:
fig, ax = gp.initGeographic()
ax.raster(grid, name="Elevation", flagLegend=True)
ax.decoration(title="Elevation", xlabel="Easting", ylabel="Northing")
plt.show()

Final plot¶

On this final plot, we combine grid and point representations.

In [25]:
fig, ax = gp.initGeographic()
ax.raster(grid, name="Elevation", flagLegend=True)
ax.symbol(dat, nameSize="*temp", flagLegendSize=True, legendNameSize="Temperature", sizmin=10, sizmax=30, c="yellow")
ax.decoration(title="Elevation and Temperatures", xlabel="Easting", ylabel="Northing")
plt.show()