예제 #1
0
파일: ok3d.py 프로젝트: anirban-dgm/PyKrige
    def __init__(self,
                 x,
                 y,
                 z,
                 val,
                 variogram_model='linear',
                 variogram_parameters=None,
                 variogram_function=None,
                 nlags=6,
                 weight=False,
                 anisotropy_scaling_y=1.0,
                 anisotropy_scaling_z=1.0,
                 anisotropy_angle_x=0.0,
                 anisotropy_angle_y=0.0,
                 anisotropy_angle_z=0.0,
                 verbose=False,
                 enable_plotting=False):

        # Code assumes 1D input arrays. Ensures that any extraneous dimensions
        # don't get in the way. Copies are created to avoid any problems with
        # referencing the original passed arguments.
        self.X_ORIG = np.atleast_1d(np.squeeze(np.array(x, copy=True)))
        self.Y_ORIG = np.atleast_1d(np.squeeze(np.array(y, copy=True)))
        self.Z_ORIG = np.atleast_1d(np.squeeze(np.array(z, copy=True)))
        self.VALUES = np.atleast_1d(np.squeeze(np.array(val, copy=True)))

        self.verbose = verbose
        self.enable_plotting = enable_plotting
        if self.enable_plotting and self.verbose:
            print "Plotting Enabled\n"

        self.XCENTER = (np.amax(self.X_ORIG) + np.amin(self.X_ORIG)) / 2.0
        self.YCENTER = (np.amax(self.Y_ORIG) + np.amin(self.Y_ORIG)) / 2.0
        self.ZCENTER = (np.amax(self.Z_ORIG) + np.amin(self.Z_ORIG)) / 2.0
        self.anisotropy_scaling_y = anisotropy_scaling_y
        self.anisotropy_scaling_z = anisotropy_scaling_z
        self.anisotropy_angle_x = anisotropy_angle_x
        self.anisotropy_angle_y = anisotropy_angle_y
        self.anisotropy_angle_z = anisotropy_angle_z
        if self.verbose:
            print "Adjusting data for anisotropy..."
        self.X_ADJUSTED, self.Y_ADJUSTED, self.Z_ADJUSTED = \
            core.adjust_for_anisotropy_3d(np.copy(self.X_ORIG), np.copy(self.Y_ORIG), np.copy(self.Z_ORIG),
                                          self.XCENTER, self.YCENTER, self.ZCENTER, self.anisotropy_scaling_y,
                                          self.anisotropy_scaling_z, self.anisotropy_angle_x, self.anisotropy_angle_y,
                                          self.anisotropy_angle_z)

        self.variogram_model = variogram_model
        if self.variogram_model not in self.variogram_dict.keys(
        ) and self.variogram_model != 'custom':
            raise ValueError(
                "Specified variogram model '%s' is not supported." %
                variogram_model)
        elif self.variogram_model == 'custom':
            if variogram_function is None or not callable(variogram_function):
                raise ValueError(
                    "Must specify callable function for custom variogram model."
                )
            else:
                self.variogram_function = variogram_function
        else:
            self.variogram_function = self.variogram_dict[self.variogram_model]
        if self.verbose:
            print "Initializing variogram model..."
        self.lags, self.semivariance, self.variogram_model_parameters = \
            core.initialize_variogram_model_3d(self.X_ADJUSTED, self.Y_ADJUSTED, self.Z_ADJUSTED, self.VALUES,
                                               self.variogram_model, variogram_parameters, self.variogram_function,
                                               nlags, weight)
        if self.verbose:
            if self.variogram_model == 'linear':
                print "Using '%s' Variogram Model" % 'linear'
                print "Slope:", self.variogram_model_parameters[0]
                print "Nugget:", self.variogram_model_parameters[1], '\n'
            elif self.variogram_model == 'power':
                print "Using '%s' Variogram Model" % 'power'
                print "Scale:", self.variogram_model_parameters[0]
                print "Exponent:", self.variogram_model_parameters[1]
                print "Nugget:", self.variogram_model_parameters[2], '\n'
            elif self.variogram_model == 'custom':
                print "Using Custom Variogram Model"
            else:
                print "Using '%s' Variogram Model" % self.variogram_model
                print "Sill:", self.variogram_model_parameters[0]
                print "Range:", self.variogram_model_parameters[1]
                print "Nugget:", self.variogram_model_parameters[2], '\n'
        if self.enable_plotting:
            self.display_variogram_model()

        if self.verbose:
            print "Calculating statistics on variogram model fit..."
        self.delta, self.sigma, self.epsilon = core.find_statistics_3d(
            self.X_ADJUSTED, self.Y_ADJUSTED, self.Z_ADJUSTED, self.VALUES,
            self.variogram_function, self.variogram_model_parameters)
        self.Q1 = core.calcQ1(self.epsilon)
        self.Q2 = core.calcQ2(self.epsilon)
        self.cR = core.calc_cR(self.Q2, self.sigma)
        if self.verbose:
            print "Q1 =", self.Q1
            print "Q2 =", self.Q2
            print "cR =", self.cR, '\n'
예제 #2
0
파일: ok3d.py 프로젝트: anirban-dgm/PyKrige
    def update_variogram_model(self,
                               variogram_model,
                               variogram_parameters=None,
                               variogram_function=None,
                               nlags=6,
                               weight=False,
                               anisotropy_scaling_y=1.0,
                               anisotropy_scaling_z=1.0,
                               anisotropy_angle_x=0.0,
                               anisotropy_angle_y=0.0,
                               anisotropy_angle_z=0.0):
        """Allows user to update variogram type and/or variogram model parameters."""

        if anisotropy_scaling_y != self.anisotropy_scaling_y or anisotropy_scaling_z != self.anisotropy_scaling_z or \
           anisotropy_angle_x != self.anisotropy_angle_x or anisotropy_angle_y != self.anisotropy_angle_y or \
           anisotropy_angle_z != self.anisotropy_angle_z:
            if self.verbose:
                print "Adjusting data for anisotropy..."
            self.anisotropy_scaling_y = anisotropy_scaling_y
            self.anisotropy_scaling_z = anisotropy_scaling_z
            self.anisotropy_angle_x = anisotropy_angle_x
            self.anisotropy_angle_y = anisotropy_angle_y
            self.anisotropy_angle_z = anisotropy_angle_z
            self.X_ADJUSTED, self.Y_ADJUSTED, self.Z_ADJUSTED = \
                core.adjust_for_anisotropy_3d(np.copy(self.X_ORIG), np.copy(self.Y_ORIG), np.copy(self.Z_ORIG),
                                              self.XCENTER, self.YCENTER, self.ZCENTER, self.anisotropy_scaling_y,
                                              self.anisotropy_scaling_z, self.anisotropy_angle_x,
                                              self.anisotropy_angle_y, self.anisotropy_angle_z)

        self.variogram_model = variogram_model
        if self.variogram_model not in self.variogram_dict.keys(
        ) and self.variogram_model != 'custom':
            raise ValueError(
                "Specified variogram model '%s' is not supported." %
                variogram_model)
        elif self.variogram_model == 'custom':
            if variogram_function is None or not callable(variogram_function):
                raise ValueError(
                    "Must specify callable function for custom variogram model."
                )
            else:
                self.variogram_function = variogram_function
        else:
            self.variogram_function = self.variogram_dict[self.variogram_model]
        if self.verbose:
            print "Updating variogram mode..."
        self.lags, self.semivariance, self.variogram_model_parameters = \
            core.initialize_variogram_model_3d(self.X_ADJUSTED, self.Y_ADJUSTED, self.Z_ADJUSTED, self.VALUES,
                                               self.variogram_model, variogram_parameters, self.variogram_function,
                                               nlags, weight)
        if self.verbose:
            if self.variogram_model == 'linear':
                print "Using '%s' Variogram Model" % 'linear'
                print "Slope:", self.variogram_model_parameters[0]
                print "Nugget:", self.variogram_model_parameters[1], '\n'
            elif self.variogram_model == 'power':
                print "Using '%s' Variogram Model" % 'power'
                print "Scale:", self.variogram_model_parameters[0]
                print "Exponent:", self.variogram_model_parameters[1]
                print "Nugget:", self.variogram_model_parameters[2], '\n'
            elif self.variogram_model == 'custom':
                print "Using Custom Variogram Model"
            else:
                print "Using '%s' Variogram Model" % self.variogram_model
                print "Sill:", self.variogram_model_parameters[0]
                print "Range:", self.variogram_model_parameters[1]
                print "Nugget:", self.variogram_model_parameters[2], '\n'
        if self.enable_plotting:
            self.display_variogram_model()

        if self.verbose:
            print "Calculating statistics on variogram model fit..."
        self.delta, self.sigma, self.epsilon = core.find_statistics_3d(
            self.X_ADJUSTED, self.Y_ADJUSTED, self.Z_ADJUSTED, self.VALUES,
            self.variogram_function, self.variogram_model_parameters)
        self.Q1 = core.calcQ1(self.epsilon)
        self.Q2 = core.calcQ2(self.epsilon)
        self.cR = core.calc_cR(self.Q2, self.sigma)
        if self.verbose:
            print "Q1 =", self.Q1
            print "Q2 =", self.Q2
            print "cR =", self.cR, '\n'
예제 #3
0
파일: ok.py 프로젝트: yejingxin/PyKrige
    def __init__(self, x, y, z, variogram_model='linear', variogram_parameters=None,
                 variogram_function=None, nlags=6, weight=False, anisotropy_scaling=1.0,
                 anisotropy_angle=0.0, verbose=False, enable_plotting=False,
                 enable_statistics=False):

        # Code assumes 1D input arrays. Ensures that any extraneous dimensions
        # don't get in the way. Copies are created to avoid any problems with
        # referencing the original passed arguments.
        self.X_ORIG = np.atleast_1d(np.squeeze(np.array(x, copy=True)))
        self.Y_ORIG = np.atleast_1d(np.squeeze(np.array(y, copy=True)))
        self.Z = np.atleast_1d(np.squeeze(np.array(z, copy=True)))

        self.verbose = verbose
        self.enable_plotting = enable_plotting
        if self.enable_plotting and self.verbose:
            print "Plotting Enabled\n"

        self.XCENTER = (np.amax(self.X_ORIG) + np.amin(self.X_ORIG))/2.0
        self.YCENTER = (np.amax(self.Y_ORIG) + np.amin(self.Y_ORIG))/2.0
        self.anisotropy_scaling = anisotropy_scaling
        self.anisotropy_angle = anisotropy_angle
        if self.verbose:
            print "Adjusting data for anisotropy..."
        self.X_ADJUSTED, self.Y_ADJUSTED = \
            core.adjust_for_anisotropy(np.copy(self.X_ORIG), np.copy(self.Y_ORIG),
                                       self.XCENTER, self.YCENTER,
                                       self.anisotropy_scaling, self.anisotropy_angle)

        self.variogram_model = variogram_model
        if self.variogram_model not in self.variogram_dict.keys() and self.variogram_model != 'custom':
            raise ValueError("Specified variogram model '%s' is not supported." % variogram_model)
        elif self.variogram_model == 'custom':
            if variogram_function is None or not callable(variogram_function):
                raise ValueError("Must specify callable function for custom variogram model.")
            else:
                self.variogram_function = variogram_function
        else:
            self.variogram_function = self.variogram_dict[self.variogram_model]
        if self.verbose:
            print "Initializing variogram model..."
        self.lags, self.semivariance, self.variogram_model_parameters = \
            core.initialize_variogram_model(self.X_ADJUSTED, self.Y_ADJUSTED, self.Z,
                                            self.variogram_model, variogram_parameters,
                                            self.variogram_function, nlags, weight)
        if self.verbose:
            if self.variogram_model == 'linear':
                print "Using '%s' Variogram Model" % 'linear'
                print "Slope:", self.variogram_model_parameters[0]
                print "Nugget:", self.variogram_model_parameters[1], '\n'
            elif self.variogram_model == 'power':
                print "Using '%s' Variogram Model" % 'power'
                print "Scale:", self.variogram_model_parameters[0]
                print "Exponent:", self.variogram_model_parameters[1]
                print "Nugget:", self.variogram_model_parameters[2], '\n'
            elif self.variogram_model == 'custom':
                print "Using Custom Variogram Model"
            else:
                print "Using '%s' Variogram Model" % self.variogram_model
                print "Sill:", self.variogram_model_parameters[0]
                print "Range:", self.variogram_model_parameters[1]
                print "Nugget:", self.variogram_model_parameters[2], '\n'
        if self.enable_plotting:
            self.display_variogram_model()

        if self.verbose:
            print "Calculating statistics on variogram model fit..."
        if enable_statistics:
            self.delta, self.sigma, self.epsilon = core.find_statistics(self.X_ADJUSTED, self.Y_ADJUSTED,
                                                                        self.Z, self.variogram_function,
                                                                        self.variogram_model_parameters)
            self.Q1 = core.calcQ1(self.epsilon)
            self.Q2 = core.calcQ2(self.epsilon)
            self.cR = core.calc_cR(self.Q2, self.sigma)
            if self.verbose:
                print "Q1 =", self.Q1
                print "Q2 =", self.Q2
                print "cR =", self.cR, '\n'
        else:
            self.delta, self.sigma, self.epsilon, self.Q1, self.Q2, self.cR = [None]*6
예제 #4
0
파일: ok.py 프로젝트: yejingxin/PyKrige
    def update_variogram_model(self, variogram_model, variogram_parameters=None,
                               variogram_function=None, nlags=6, weight=False,
                               anisotropy_scaling=1.0, anisotropy_angle=0.0):
        """Allows user to update variogram type and/or variogram model parameters."""

        if anisotropy_scaling != self.anisotropy_scaling or \
           anisotropy_angle != self.anisotropy_angle:
            if self.verbose:
                print "Adjusting data for anisotropy..."
            self.anisotropy_scaling = anisotropy_scaling
            self.anisotropy_angle = anisotropy_angle
            self.X_ADJUSTED, self.Y_ADJUSTED = \
                core.adjust_for_anisotropy(np.copy(self.X_ORIG),
                                           np.copy(self.Y_ORIG),
                                           self.XCENTER, self.YCENTER,
                                           self.anisotropy_scaling,
                                           self.anisotropy_angle)

        self.variogram_model = variogram_model
        if self.variogram_model not in self.variogram_dict.keys() and self.variogram_model != 'custom':
            raise ValueError("Specified variogram model '%s' is not supported." % variogram_model)
        elif self.variogram_model == 'custom':
            if variogram_function is None or not callable(variogram_function):
                raise ValueError("Must specify callable function for custom variogram model.")
            else:
                self.variogram_function = variogram_function
        else:
            self.variogram_function = self.variogram_dict[self.variogram_model]
        if self.verbose:
            print "Updating variogram mode..."
        self.lags, self.semivariance, self.variogram_model_parameters = \
            core.initialize_variogram_model(self.X_ADJUSTED, self.Y_ADJUSTED, self.Z,
                                            self.variogram_model, variogram_parameters,
                                            self.variogram_function, nlags, weight)
        if self.verbose:
            if self.variogram_model == 'linear':
                print "Using '%s' Variogram Model" % 'linear'
                print "Slope:", self.variogram_model_parameters[0]
                print "Nugget:", self.variogram_model_parameters[1], '\n'
            elif self.variogram_model == 'power':
                print "Using '%s' Variogram Model" % 'power'
                print "Scale:", self.variogram_model_parameters[0]
                print "Exponent:", self.variogram_model_parameters[1]
                print "Nugget:", self.variogram_model_parameters[2], '\n'
            elif self.variogram_model == 'custom':
                print "Using Custom Variogram Model"
            else:
                print "Using '%s' Variogram Model" % self.variogram_model
                print "Sill:", self.variogram_model_parameters[0]
                print "Range:", self.variogram_model_parameters[1]
                print "Nugget:", self.variogram_model_parameters[2], '\n'
        if self.enable_plotting:
            self.display_variogram_model()

        if self.verbose:
            print "Calculating statistics on variogram model fit..."
        self.delta, self.sigma, self.epsilon = core.find_statistics(self.X_ADJUSTED, self.Y_ADJUSTED,
                                                                    self.Z, self.variogram_function,
                                                                    self.variogram_model_parameters)
        self.Q1 = core.calcQ1(self.epsilon)
        self.Q2 = core.calcQ2(self.epsilon)
        self.cR = core.calc_cR(self.Q2, self.sigma)
        if self.verbose:
            print "Q1 =", self.Q1
            print "Q2 =", self.Q2
            print "cR =", self.cR, '\n'
예제 #5
0
파일: ok.py 프로젝트: scollis/PyKrige
    def update_variogram_model(self, variogram_model,
                               variogram_parameters=None,
                               nlags=6, anisotropy_scaling=1.0,
                               anisotropy_angle=0.0):
        """Allows user to update variogram type and/or variogram model parameters."""

        if anisotropy_scaling != self.anisotropy_scaling or \
           anisotropy_angle != self.anisotropy_angle:
            if self.verbose:
                print "Adjusting data for anisotropy..."
            self.anisotropy_scaling = anisotropy_scaling
            self.anisotropy_angle = anisotropy_angle
            self.X_ADJUSTED, self.Y_ADJUSTED = \
                core.adjust_for_anisotropy(np.copy(self.X_ORIG),
                                           np.copy(self.Y_ORIG),
                                           self.XCENTER, self.YCENTER,
                                           self.anisotropy_scaling,
                                           self.anisotropy_angle)

        self.variogram_model = variogram_model
        if self.variogram_model == 'linear':
            self.variogram_function = variogram_models.linear_variogram_model
        if self.variogram_model == 'power':
            self.variogram_function = variogram_models.power_variogram_model
        if self.variogram_model == 'gaussian':
            self.variogram_function = variogram_models.gaussian_variogram_model
        if self.variogram_model == 'spherical':
            self.variogram_function = variogram_models.spherical_variogram_model
        if self.variogram_model == 'exponential':
            self.variogram_function = variogram_models.exponential_variogram_model
        if self.verbose:
            print "Updating variogram mode..."
        self.lags, self.semivariance, self.variogram_model_parameters = \
            core.initialize_variogram_model(self.X_ADJUSTED, self.Y_ADJUSTED, self.Z,
                                            self.variogram_model, variogram_parameters,
                                            self.variogram_function, nlags)
        if self.verbose:
            if self.variogram_model == 'linear':
                print "Using '%s' Variogram Model" % 'linear'
                print "Slope:", self.variogram_model_parameters[0]
                print "Nugget:", self.variogram_model_parameters[1], '\n'
            elif self.variogram_model == 'power':
                print "Using '%s' Variogram Model" % 'power'
                print "Scale:", self.variogram_model_parameters[0]
                print "Exponent:", self.variogram_model_parameters[1]
                print "Nugget:", self.variogram_model_parameters[2], '\n'
            else:
                print "Using '%s' Variogram Model" % self.variogram_model
                print "Sill:", self.variogram_model_parameters[0]
                print "Range:", self.variogram_model_parameters[1]
                print "Nugget:", self.variogram_model_parameters[2], '\n'
        if self.enable_plotting:
            self.display_variogram_model()

        if self.verbose:
            print "Calculating statistics on variogram model fit..."
        self.delta, self.sigma, self.epsilon = core.find_statistics(self.X_ADJUSTED,
                                                                    self.Y_ADJUSTED,
                                                                    self.Z,
                                                                    self.variogram_function,
                                                                    self.variogram_model_parameters)
        self.Q1 = core.calcQ1(self.epsilon)
        self.Q2 = core.calcQ2(self.epsilon)
        self.cR = core.calc_cR(self.Q2, self.sigma)
        if self.verbose:
            print "Q1 =", self.Q1
            print "Q2 =", self.Q2
            print "cR =", self.cR, '\n'
예제 #6
0
파일: uk3d.py 프로젝트: glinsky007/PyKrige
    def __init__(self, x, y, z, val, variogram_model='linear', variogram_parameters=None,
                 variogram_function=None, nlags=6, weight=False, anisotropy_scaling_y=1.0,
                 anisotropy_scaling_z=1.0, anisotropy_angle_x=0.0, anisotropy_angle_y=0.0,
                 anisotropy_angle_z=0.0, drift_terms=None, specified_drift=None,
                 functional_drift=None, verbose=False, enable_plotting=False):

        # Deal with mutable default argument
        if drift_terms is None:
            drift_terms = []
        if specified_drift is None:
            specified_drift = []
        if functional_drift is None:
            functional_drift = []

        # Code assumes 1D input arrays. Ensures that any extraneous dimensions
        # don't get in the way. Copies are created to avoid any problems with
        # referencing the original passed arguments.
        self.X_ORIG = np.atleast_1d(np.squeeze(np.array(x, copy=True)))
        self.Y_ORIG = np.atleast_1d(np.squeeze(np.array(y, copy=True)))
        self.Z_ORIG = np.atleast_1d(np.squeeze(np.array(z, copy=True)))
        self.VALUES = np.atleast_1d(np.squeeze(np.array(val, copy=True)))

        self.verbose = verbose
        self.enable_plotting = enable_plotting
        if self.enable_plotting and self.verbose:
            print "Plotting Enabled\n"

        self.XCENTER = (np.amax(self.X_ORIG) + np.amin(self.X_ORIG))/2.0
        self.YCENTER = (np.amax(self.Y_ORIG) + np.amin(self.Y_ORIG))/2.0
        self.ZCENTER = (np.amax(self.Z_ORIG) + np.amin(self.Z_ORIG))/2.0
        self.anisotropy_scaling_y = anisotropy_scaling_y
        self.anisotropy_scaling_z = anisotropy_scaling_z
        self.anisotropy_angle_x = anisotropy_angle_x
        self.anisotropy_angle_y = anisotropy_angle_y
        self.anisotropy_angle_z = anisotropy_angle_z
        if self.verbose:
            print "Adjusting data for anisotropy..."
        self.X_ADJUSTED, self.Y_ADJUSTED, self.Z_ADJUSTED = \
            core.adjust_for_anisotropy_3d(np.copy(self.X_ORIG), np.copy(self.Y_ORIG), np.copy(self.Z_ORIG),
                                          self.XCENTER, self.YCENTER, self.ZCENTER, self.anisotropy_scaling_y,
                                          self.anisotropy_scaling_z, self.anisotropy_angle_x, self.anisotropy_angle_y,
                                          self.anisotropy_angle_z)

        self.variogram_model = variogram_model
        if self.variogram_model not in self.variogram_dict.keys() and self.variogram_model != 'custom':
            raise ValueError("Specified variogram model '%s' is not supported." % variogram_model)
        elif self.variogram_model == 'custom':
            if variogram_function is None or not callable(variogram_function):
                raise ValueError("Must specify callable function for custom variogram model.")
            else:
                self.variogram_function = variogram_function
        else:
            self.variogram_function = self.variogram_dict[self.variogram_model]
        if self.verbose:
            print "Initializing variogram model..."
        self.lags, self.semivariance, self.variogram_model_parameters = \
            core.initialize_variogram_model_3d(self.X_ADJUSTED, self.Y_ADJUSTED, self.Z_ADJUSTED, self.VALUES,
                                               self.variogram_model, variogram_parameters, self.variogram_function,
                                               nlags, weight)
        if self.verbose:
            if self.variogram_model == 'linear':
                print "Using '%s' Variogram Model" % 'linear'
                print "Slope:", self.variogram_model_parameters[0]
                print "Nugget:", self.variogram_model_parameters[1], '\n'
            elif self.variogram_model == 'power':
                print "Using '%s' Variogram Model" % 'power'
                print "Scale:", self.variogram_model_parameters[0]
                print "Exponent:", self.variogram_model_parameters[1]
                print "Nugget:", self.variogram_model_parameters[2], '\n'
            elif self.variogram_model == 'custom':
                print "Using Custom Variogram Model"
            else:
                print "Using '%s' Variogram Model" % self.variogram_model
                print "Sill:", self.variogram_model_parameters[0]
                print "Range:", self.variogram_model_parameters[1]
                print "Nugget:", self.variogram_model_parameters[2], '\n'
        if self.enable_plotting:
            self.display_variogram_model()

        if self.verbose:
            print "Calculating statistics on variogram model fit..."
        self.delta, self.sigma, self.epsilon = core.find_statistics_3d(self.X_ADJUSTED, self.Y_ADJUSTED,
                                                                       self.Z_ADJUSTED, self.VALUES,
                                                                       self.variogram_function,
                                                                       self.variogram_model_parameters)
        self.Q1 = core.calcQ1(self.epsilon)
        self.Q2 = core.calcQ2(self.epsilon)
        self.cR = core.calc_cR(self.Q2, self.sigma)
        if self.verbose:
            print "Q1 =", self.Q1
            print "Q2 =", self.Q2
            print "cR =", self.cR, '\n'

        if self.verbose:
            print "Initializing drift terms..."

        # Note that the regional linear drift values will be based on the adjusted coordinate system.
        # Really, it doesn't actually matter which coordinate system is used here.
        if 'regional_linear' in drift_terms:
            self.regional_linear_drift = True
            if self.verbose:
                print "Implementing regional linear drift."
        else:
            self.regional_linear_drift = False

        if 'specified' in drift_terms:
            if type(specified_drift) is not list:
                raise TypeError("Arrays for specified drift terms must be encapsulated in a list.")
            if len(specified_drift) == 0:
                raise ValueError("Must provide at least one drift-value array when using the "
                                 "'specified' drift capability.")
            self.specified_drift = True
            self.specified_drift_data_arrays = []
            for term in specified_drift:
                specified = np.squeeze(np.array(term, copy=True))
                if specified.size != self.X_ORIG.size:
                    raise ValueError("Must specify the drift values for each data point when using the "
                                     "'specified' drift capability.")
                self.specified_drift_data_arrays.append(specified)
        else:
            self.specified_drift = False

        # The provided callable functions will be evaluated using the adjusted coordinates.
        if 'functional' in drift_terms:
            if type(functional_drift) is not list:
                raise TypeError("Callables for functional drift terms must be encapsulated in a list.")
            if len(functional_drift) == 0:
                raise ValueError("Must provide at least one callable object when using the "
                                 "'functional' drift capability.")
            self.functional_drift = True
            self.functional_drift_terms = functional_drift
        else:
            self.functional_drift = False
예제 #7
0
파일: ok.py 프로젝트: scollis/PyKrige
    def __init__(self, x, y, z, variogram_model='linear',
                 variogram_parameters=None, nlags=6,
                 anisotropy_scaling=1.0, anisotropy_angle=0.0,
                 verbose=False, enable_plotting=False):

        # Code assumes 1D input arrays. Ensures that this is the case.
        self.X_ORIG = np.array(x).flatten()
        self.Y_ORIG = np.array(y).flatten()
        self.Z = np.array(z).flatten()

        self.verbose = verbose
        self.enable_plotting = enable_plotting
        if self.enable_plotting and self.verbose:
            print "Plotting Enabled\n"

        self.XCENTER = (np.amax(self.X_ORIG) + np.amin(self.X_ORIG))/2.0
        self.YCENTER = (np.amax(self.Y_ORIG) + np.amin(self.Y_ORIG))/2.0
        self.anisotropy_scaling = anisotropy_scaling
        self.anisotropy_angle = anisotropy_angle
        if self.verbose:
            print "Adjusting data for anisotropy..."
        self.X_ADJUSTED, self.Y_ADJUSTED = \
            core.adjust_for_anisotropy(np.copy(self.X_ORIG), np.copy(self.Y_ORIG),
                                       self.XCENTER, self.YCENTER,
                                       self.anisotropy_scaling, self.anisotropy_angle)

        self.variogram_model = variogram_model
        if self.variogram_model == 'linear':
            self.variogram_function = variogram_models.linear_variogram_model
        if self.variogram_model == 'power':
            self.variogram_function = variogram_models.power_variogram_model
        if self.variogram_model == 'gaussian':
            self.variogram_function = variogram_models.gaussian_variogram_model
        if self.variogram_model == 'spherical':
            self.variogram_function = variogram_models.spherical_variogram_model
        if self.variogram_model == 'exponential':
            self.variogram_function = variogram_models.exponential_variogram_model
        if self.verbose:
            print "Initializing variogram model..."
        self.lags, self.semivariance, self.variogram_model_parameters = \
            core.initialize_variogram_model(self.X_ADJUSTED, self.Y_ADJUSTED, self.Z,
                                            self.variogram_model, variogram_parameters,
                                            self.variogram_function, nlags)
        if self.verbose:
            if self.variogram_model == 'linear':
                print "Using '%s' Variogram Model" % 'linear'
                print "Slope:", self.variogram_model_parameters[0]
                print "Nugget:", self.variogram_model_parameters[1], '\n'
            elif self.variogram_model == 'power':
                print "Using '%s' Variogram Model" % 'power'
                print "Scale:", self.variogram_model_parameters[0]
                print "Exponent:", self.variogram_model_parameters[1]
                print "Nugget:", self.variogram_model_parameters[2], '\n'
            else:
                print "Using '%s' Variogram Model" % self.variogram_model
                print "Sill:", self.variogram_model_parameters[0]
                print "Range:", self.variogram_model_parameters[1]
                print "Nugget:", self.variogram_model_parameters[2], '\n'
        if self.enable_plotting:
            self.display_variogram_model()

        if self.verbose:
            print "Calculating statistics on variogram model fit..."
        self.delta, self.sigma, self.epsilon = core.find_statistics(self.X_ADJUSTED,
                                                                    self.Y_ADJUSTED,
                                                                    self.Z,
                                                                    self.variogram_function,
                                                                    self.variogram_model_parameters)
        self.Q1 = core.calcQ1(self.epsilon)
        self.Q2 = core.calcQ2(self.epsilon)
        self.cR = core.calc_cR(self.Q2, self.sigma)
        if self.verbose:
            print "Q1 =", self.Q1
            print "Q2 =", self.Q2
            print "cR =", self.cR, '\n'
예제 #8
0
파일: uk.py 프로젝트: scollis/PyKrige
    def __init__(self, x, y, z, variogram_model='linear',
                 variogram_parameters=None, nlags=6,
                 anisotropy_scaling=1.0, anisotropy_angle=0.0,
                 drift_terms=[None], point_drift=None, external_drift=None,
                 external_drift_x=None, external_drift_y=None,
                 external_drift_xspacing=None, external_drift_yspacing=None,
                 verbose=False, enable_plotting=False):

        # Code assumes 1D input arrays. Ensures that this is the case.
        self.X_ORIG = np.array(x).flatten()
        self.Y_ORIG = np.array(y).flatten()
        self.Z = np.array(z).flatten()

        self.verbose = verbose
        self.enable_plotting = enable_plotting
        if self.enable_plotting and self.verbose:
            print "Plotting Enabled\n"

        self.XCENTER = (np.amax(self.X_ORIG) + np.amin(self.X_ORIG))/2.0
        self.YCENTER = (np.amax(self.Y_ORIG) + np.amin(self.Y_ORIG))/2.0
        self.anisotropy_scaling = anisotropy_scaling
        self.anisotropy_angle = anisotropy_angle
        if self.verbose:
            print "Adjusting data for anisotropy..."
        self.X_ADJUSTED, self.Y_ADJUSTED = \
            core.adjust_for_anisotropy(np.copy(self.X_ORIG), np.copy(self.Y_ORIG),
                                       self.XCENTER, self.YCENTER,
                                       self.anisotropy_scaling, self.anisotropy_angle)

        self.variogram_model = variogram_model
        if self.variogram_model == 'linear':
            self.variogram_function = variogram_models.linear_variogram_model
        if self.variogram_model == 'power':
            self.variogram_function = variogram_models.power_variogram_model
        if self.variogram_model == 'gaussian':
            self.variogram_function = variogram_models.gaussian_variogram_model
        if self.variogram_model == 'spherical':
            self.variogram_function = variogram_models.spherical_variogram_model
        if self.variogram_model == 'exponential':
            self.variogram_function = variogram_models.exponential_variogram_model
        if self.verbose:
            print "Initializing variogram model..."
        self.lags, self.semivariance, self.variogram_model_parameters = \
            core.initialize_variogram_model(self.X_ADJUSTED, self.Y_ADJUSTED, self.Z,
                                            self.variogram_model, variogram_parameters,
                                            self.variogram_function, nlags)
        if self.verbose:
            if self.variogram_model == 'linear':
                print "Using '%s' Variogram Model" % 'linear'
                print "Slope:", self.variogram_model_parameters[0]
                print "Nugget:", self.variogram_model_parameters[1], '\n'
            elif self.variogram_model == 'power':
                print "Using '%s' Variogram Model" % 'power'
                print "Scale:", self.variogram_model_parameters[0]
                print "Exponent:", self.variogram_model_parameters[1]
                print "Nugget:", self.variogram_model_parameters[2], '\n'
            else:
                print "Using '%s' Variogram Model" % self.variogram_model
                print "Sill:", self.variogram_model_parameters[0]
                print "Range:", self.variogram_model_parameters[1]
                print "Nugget:", self.variogram_model_parameters[2]
        if self.enable_plotting:
            self.display_variogram_model()

        if self.verbose:
            print "Calculating statistics on variogram model fit..."
        self.delta, self.sigma, self.epsilon = core.find_statistics(self.X_ADJUSTED,
                                                                    self.Y_ADJUSTED,
                                                                    self.Z,
                                                                    self.variogram_function,
                                                                    self.variogram_model_parameters)
        self.Q1 = core.calcQ1(self.epsilon)
        self.Q2 = core.calcQ2(self.epsilon)
        self.cR = core.calc_cR(self.Q2, self.sigma)
        if self.verbose:
            print "Q1 =", self.Q1
            print "Q2 =", self.Q2
            print "cR =", self.cR, '\n'

        if self.verbose:
            print "Initializing drift terms..."

        if 'regional_linear' in drift_terms:
            self.regional_linear_drift = True
            if self.verbose:
                print "Implementing regional linear drift."
        else:
            self.regional_linear_drift = False

        if 'external_Z' in drift_terms:
            if external_drift is None:
                raise ValueError("Must specify external Z drift terms.")
            if external_drift_x is None or external_drift_y is None:
                raise ValueError("Must specify coordinates of external Z drift terms.")
            self.external_Z_drift = True
            self.external_Z_array = np.array(external_drift)
            self.external_Z_array_x = np.array(external_drift_x).flatten()
            self.external_Z_array_y = np.array(external_drift_y).flatten()
            if np.unique(self.external_Z_array_x[1:] - self.external_Z_array_x[:-1]).size != 1:
                if external_drift_xspacing is None:
                    raise ValueError("X-coordinate spacing is not constant. "
                                     "Must provide X-coordinate grid size.")
                else:
                    self.external_Z_array_x_spacing = np.array(external_drift_xspacing).flatten()
            else:
                self.external_Z_array_x_spacing = np.zeros(self.external_Z_array_x.shape)
                self.external_Z_array_x_spacing.fill(
                    np.unique(self.external_Z_array_x[1:] - self.external_Z_array_x[:-1])[0])
            if np.unique(self.external_Z_array_y[1:] - self.external_Z_array_y[:-1]).size != 1:
                if external_drift_yspacing is None:
                    raise ValueError("Y-coordinate spacing is not constant. "
                                     "Must provide Y-coordinate grid size.")
                else:
                    self.external_Z_array_y_spacing = np.array(external_drift_yspacing).flatten()
            else:
                self.external_Z_array_y_spacing = np.zeros(self.external_Z_array_y.shape)
                self.external_Z_array_y_spacing.fill(
                    np.unique(self.external_Z_array_y[1:] - self.external_Z_array_y[:-1])[0])
            self.z_scalars = self._calculate_data_point_zscalars(self.X_ORIG,
                                                                 self.Y_ORIG)
            if self.verbose:
                print "Implementing external Z drift."
        else:
            self.external_Z_drift = False

        if 'point_log' in drift_terms:
            if point_drift is None:
                raise ValueError("Must specify location(s) and strength(s) of point drift terms.")
            self.point_log_drift = True
            self.point_log_array = np.atleast_2d(np.array(point_drift))
            if self.verbose:
                print "Implementing external point-logarithmic drift; " \
                      "number of points =", self.point_log_array.shape[0], '\n'
        else:
            self.point_log_drift = False
예제 #9
0
파일: uk3d.py 프로젝트: anirban-dgm/PyKrige
    def __init__(self,
                 x,
                 y,
                 z,
                 val,
                 variogram_model='linear',
                 variogram_parameters=None,
                 variogram_function=None,
                 nlags=6,
                 weight=False,
                 anisotropy_scaling_y=1.0,
                 anisotropy_scaling_z=1.0,
                 anisotropy_angle_x=0.0,
                 anisotropy_angle_y=0.0,
                 anisotropy_angle_z=0.0,
                 drift_terms=None,
                 specified_drift=None,
                 functional_drift=None,
                 verbose=False,
                 enable_plotting=False):

        # Deal with mutable default argument
        if drift_terms is None:
            drift_terms = []
        if specified_drift is None:
            specified_drift = []
        if functional_drift is None:
            functional_drift = []

        # Code assumes 1D input arrays. Ensures that any extraneous dimensions
        # don't get in the way. Copies are created to avoid any problems with
        # referencing the original passed arguments.
        self.X_ORIG = np.atleast_1d(np.squeeze(np.array(x, copy=True)))
        self.Y_ORIG = np.atleast_1d(np.squeeze(np.array(y, copy=True)))
        self.Z_ORIG = np.atleast_1d(np.squeeze(np.array(z, copy=True)))
        self.VALUES = np.atleast_1d(np.squeeze(np.array(val, copy=True)))

        self.verbose = verbose
        self.enable_plotting = enable_plotting
        if self.enable_plotting and self.verbose:
            print "Plotting Enabled\n"

        self.XCENTER = (np.amax(self.X_ORIG) + np.amin(self.X_ORIG)) / 2.0
        self.YCENTER = (np.amax(self.Y_ORIG) + np.amin(self.Y_ORIG)) / 2.0
        self.ZCENTER = (np.amax(self.Z_ORIG) + np.amin(self.Z_ORIG)) / 2.0
        self.anisotropy_scaling_y = anisotropy_scaling_y
        self.anisotropy_scaling_z = anisotropy_scaling_z
        self.anisotropy_angle_x = anisotropy_angle_x
        self.anisotropy_angle_y = anisotropy_angle_y
        self.anisotropy_angle_z = anisotropy_angle_z
        if self.verbose:
            print "Adjusting data for anisotropy..."
        self.X_ADJUSTED, self.Y_ADJUSTED, self.Z_ADJUSTED = \
            core.adjust_for_anisotropy_3d(np.copy(self.X_ORIG), np.copy(self.Y_ORIG), np.copy(self.Z_ORIG),
                                          self.XCENTER, self.YCENTER, self.ZCENTER, self.anisotropy_scaling_y,
                                          self.anisotropy_scaling_z, self.anisotropy_angle_x, self.anisotropy_angle_y,
                                          self.anisotropy_angle_z)

        self.variogram_model = variogram_model
        if self.variogram_model not in self.variogram_dict.keys(
        ) and self.variogram_model != 'custom':
            raise ValueError(
                "Specified variogram model '%s' is not supported." %
                variogram_model)
        elif self.variogram_model == 'custom':
            if variogram_function is None or not callable(variogram_function):
                raise ValueError(
                    "Must specify callable function for custom variogram model."
                )
            else:
                self.variogram_function = variogram_function
        else:
            self.variogram_function = self.variogram_dict[self.variogram_model]
        if self.verbose:
            print "Initializing variogram model..."
        self.lags, self.semivariance, self.variogram_model_parameters = \
            core.initialize_variogram_model_3d(self.X_ADJUSTED, self.Y_ADJUSTED, self.Z_ADJUSTED, self.VALUES,
                                               self.variogram_model, variogram_parameters, self.variogram_function,
                                               nlags, weight)
        if self.verbose:
            if self.variogram_model == 'linear':
                print "Using '%s' Variogram Model" % 'linear'
                print "Slope:", self.variogram_model_parameters[0]
                print "Nugget:", self.variogram_model_parameters[1], '\n'
            elif self.variogram_model == 'power':
                print "Using '%s' Variogram Model" % 'power'
                print "Scale:", self.variogram_model_parameters[0]
                print "Exponent:", self.variogram_model_parameters[1]
                print "Nugget:", self.variogram_model_parameters[2], '\n'
            elif self.variogram_model == 'custom':
                print "Using Custom Variogram Model"
            else:
                print "Using '%s' Variogram Model" % self.variogram_model
                print "Sill:", self.variogram_model_parameters[0]
                print "Range:", self.variogram_model_parameters[1]
                print "Nugget:", self.variogram_model_parameters[2], '\n'
        if self.enable_plotting:
            self.display_variogram_model()

        if self.verbose:
            print "Calculating statistics on variogram model fit..."
        self.delta, self.sigma, self.epsilon = core.find_statistics_3d(
            self.X_ADJUSTED, self.Y_ADJUSTED, self.Z_ADJUSTED, self.VALUES,
            self.variogram_function, self.variogram_model_parameters)
        self.Q1 = core.calcQ1(self.epsilon)
        self.Q2 = core.calcQ2(self.epsilon)
        self.cR = core.calc_cR(self.Q2, self.sigma)
        if self.verbose:
            print "Q1 =", self.Q1
            print "Q2 =", self.Q2
            print "cR =", self.cR, '\n'

        if self.verbose:
            print "Initializing drift terms..."

        # Note that the regional linear drift values will be based on the adjusted coordinate system.
        # Really, it doesn't actually matter which coordinate system is used here.
        if 'regional_linear' in drift_terms:
            self.regional_linear_drift = True
            if self.verbose:
                print "Implementing regional linear drift."
        else:
            self.regional_linear_drift = False

        if 'specified' in drift_terms:
            if type(specified_drift) is not list:
                raise TypeError(
                    "Arrays for specified drift terms must be encapsulated in a list."
                )
            if len(specified_drift) == 0:
                raise ValueError(
                    "Must provide at least one drift-value array when using the "
                    "'specified' drift capability.")
            self.specified_drift = True
            self.specified_drift_data_arrays = []
            for term in specified_drift:
                specified = np.squeeze(np.array(term, copy=True))
                if specified.size != self.X_ORIG.size:
                    raise ValueError(
                        "Must specify the drift values for each data point when using the "
                        "'specified' drift capability.")
                self.specified_drift_data_arrays.append(specified)
        else:
            self.specified_drift = False

        # The provided callable functions will be evaluated using the adjusted coordinates.
        if 'functional' in drift_terms:
            if type(functional_drift) is not list:
                raise TypeError(
                    "Callables for functional drift terms must be encapsulated in a list."
                )
            if len(functional_drift) == 0:
                raise ValueError(
                    "Must provide at least one callable object when using the "
                    "'functional' drift capability.")
            self.functional_drift = True
            self.functional_drift_terms = functional_drift
        else:
            self.functional_drift = False
예제 #10
0
    def update_variogram_model(self,
                               variogram_model,
                               variogram_parameters=None,
                               nlags=6,
                               weight=False,
                               anisotropy_scaling=1.0,
                               anisotropy_angle=0.0):
        """Allows user to update variogram type and/or variogram model parameters."""

        if anisotropy_scaling != self.anisotropy_scaling or \
           anisotropy_angle != self.anisotropy_angle:
            if self.verbose:
                print "Adjusting data for anisotropy..."
            self.anisotropy_scaling = anisotropy_scaling
            self.anisotropy_angle = anisotropy_angle
            self.X_ADJUSTED, self.Y_ADJUSTED = \
                core.adjust_for_anisotropy(np.copy(self.X_ORIG),
                                           np.copy(self.Y_ORIG),
                                           self.XCENTER, self.YCENTER,
                                           self.anisotropy_scaling,
                                           self.anisotropy_angle)

        self.variogram_model = variogram_model
        if self.variogram_model == 'linear':
            self.variogram_function = variogram_models.linear_variogram_model
        elif self.variogram_model == 'power':
            self.variogram_function = variogram_models.power_variogram_model
        elif self.variogram_model == 'gaussian':
            self.variogram_function = variogram_models.gaussian_variogram_model
        elif self.variogram_model == 'spherical':
            self.variogram_function = variogram_models.spherical_variogram_model
        elif self.variogram_model == 'exponential':
            self.variogram_function = variogram_models.exponential_variogram_model
        else:
            raise ValueError(
                "Specified variogram model '%s' is not supported." %
                variogram_model)
        if self.verbose:
            print "Updating variogram mode..."
        self.lags, self.semivariance, self.variogram_model_parameters = \
            core.initialize_variogram_model(self.X_ADJUSTED, self.Y_ADJUSTED, self.Z,
                                            self.variogram_model, variogram_parameters,
                                            self.variogram_function, nlags, weight)
        if self.verbose:
            if self.variogram_model == 'linear':
                print "Using '%s' Variogram Model" % 'linear'
                print "Slope:", self.variogram_model_parameters[0]
                print "Nugget:", self.variogram_model_parameters[1], '\n'
            elif self.variogram_model == 'power':
                print "Using '%s' Variogram Model" % 'power'
                print "Scale:", self.variogram_model_parameters[0]
                print "Exponent:", self.variogram_model_parameters[1]
                print "Nugget:", self.variogram_model_parameters[2], '\n'
            else:
                print "Using '%s' Variogram Model" % self.variogram_model
                print "Sill:", self.variogram_model_parameters[0]
                print "Range:", self.variogram_model_parameters[1]
                print "Nugget:", self.variogram_model_parameters[2], '\n'
        if self.enable_plotting:
            self.display_variogram_model()

        if self.verbose:
            print "Calculating statistics on variogram model fit..."
        self.delta, self.sigma, self.epsilon = core.find_statistics(
            self.X_ADJUSTED, self.Y_ADJUSTED, self.Z, self.variogram_function,
            self.variogram_model_parameters)
        self.Q1 = core.calcQ1(self.epsilon)
        self.Q2 = core.calcQ2(self.epsilon)
        self.cR = core.calc_cR(self.Q2, self.sigma)
        if self.verbose:
            print "Q1 =", self.Q1
            print "Q2 =", self.Q2
            print "cR =", self.cR, '\n'
예제 #11
0
    def __init__(self,
                 x,
                 y,
                 z,
                 variogram_model='linear',
                 variogram_parameters=None,
                 nlags=6,
                 weight=False,
                 anisotropy_scaling=1.0,
                 anisotropy_angle=0.0,
                 verbose=False,
                 enable_plotting=False):

        # Code assumes 1D input arrays. Ensures that this is the case.
        # Copies are created to avoid any problems with referencing
        # the original passed arguments.
        self.X_ORIG = np.array(x, copy=True).flatten()
        self.Y_ORIG = np.array(y, copy=True).flatten()
        self.Z = np.array(z, copy=True).flatten()

        self.verbose = verbose
        self.enable_plotting = enable_plotting
        if self.enable_plotting and self.verbose:
            print "Plotting Enabled\n"

        self.XCENTER = (np.amax(self.X_ORIG) + np.amin(self.X_ORIG)) / 2.0
        self.YCENTER = (np.amax(self.Y_ORIG) + np.amin(self.Y_ORIG)) / 2.0
        self.anisotropy_scaling = anisotropy_scaling
        self.anisotropy_angle = anisotropy_angle
        if self.verbose:
            print "Adjusting data for anisotropy..."
        self.X_ADJUSTED, self.Y_ADJUSTED = \
            core.adjust_for_anisotropy(np.copy(self.X_ORIG), np.copy(self.Y_ORIG),
                                       self.XCENTER, self.YCENTER,
                                       self.anisotropy_scaling, self.anisotropy_angle)

        self.variogram_model = variogram_model
        if self.variogram_model == 'linear':
            self.variogram_function = variogram_models.linear_variogram_model
        elif self.variogram_model == 'power':
            self.variogram_function = variogram_models.power_variogram_model
        elif self.variogram_model == 'gaussian':
            self.variogram_function = variogram_models.gaussian_variogram_model
        elif self.variogram_model == 'spherical':
            self.variogram_function = variogram_models.spherical_variogram_model
        elif self.variogram_model == 'exponential':
            self.variogram_function = variogram_models.exponential_variogram_model
        else:
            raise ValueError(
                "Specified variogram model '%s' is not supported." %
                variogram_model)
        if self.verbose:
            print "Initializing variogram model..."
        self.lags, self.semivariance, self.variogram_model_parameters = \
            core.initialize_variogram_model(self.X_ADJUSTED, self.Y_ADJUSTED, self.Z,
                                            self.variogram_model, variogram_parameters,
                                            self.variogram_function, nlags, weight)
        if self.verbose:
            if self.variogram_model == 'linear':
                print "Using '%s' Variogram Model" % 'linear'
                print "Slope:", self.variogram_model_parameters[0]
                print "Nugget:", self.variogram_model_parameters[1], '\n'
            elif self.variogram_model == 'power':
                print "Using '%s' Variogram Model" % 'power'
                print "Scale:", self.variogram_model_parameters[0]
                print "Exponent:", self.variogram_model_parameters[1]
                print "Nugget:", self.variogram_model_parameters[2], '\n'
            else:
                print "Using '%s' Variogram Model" % self.variogram_model
                print "Sill:", self.variogram_model_parameters[0]
                print "Range:", self.variogram_model_parameters[1]
                print "Nugget:", self.variogram_model_parameters[2], '\n'
        if self.enable_plotting:
            self.display_variogram_model()

        if self.verbose:
            print "Calculating statistics on variogram model fit..."
        self.delta, self.sigma, self.epsilon = core.find_statistics(
            self.X_ADJUSTED, self.Y_ADJUSTED, self.Z, self.variogram_function,
            self.variogram_model_parameters)
        self.Q1 = core.calcQ1(self.epsilon)
        self.Q2 = core.calcQ2(self.epsilon)
        self.cR = core.calc_cR(self.Q2, self.sigma)
        if self.verbose:
            print "Q1 =", self.Q1
            print "Q2 =", self.Q2
            print "cR =", self.cR, '\n'