Tools¶
Burnman has a number of high-level tools to help achieve common goals.
- burnman.tools.copy_documentation(copy_from)[source]¶
Decorator @copy_documentation(another_function) will copy the documentation found in a different function (for example from a base class). The docstring applied to some function a() will be
(copied from BaseClass.some_function): <documentation from BaseClass.some_function> <optionally the documentation found in a()>
- burnman.tools.unit_normalize(a, order=2, axis=- 1)[source]¶
Calculates the L2 normalized array of numpy array a of a given order and along a given axis.
- burnman.tools.pretty_print_values(popt, pcov, params)[source]¶
Takes a numpy array of parameters, the corresponding covariance matrix and a set of parameter names and prints the parameters and principal 1-s.d.uncertainties (np.sqrt(pcov[i][i])) in a nice text based format.
- burnman.tools.pretty_print_table(table, use_tabs=False)[source]¶
Takes a 2d table and prints it in a nice text based format. If use_tabs=True then only is used as a separator. This is useful for importing the data into other apps (Excel, …). The default is to pad the columns with spaces to make them look neat. The first column is left aligned, while the remainder is right aligned.
- burnman.tools.pretty_plot()[source]¶
Makes pretty plots. Overwrites the matplotlib default settings to allow for better fonts. Slows down plotting
- burnman.tools.linear_interpol(x, x1, x2, y1, y2)[source]¶
Linearly interpolate to point x, between the points (x1,y1), (x2,y2)
- burnman.tools.array_from_file(filename)[source]¶
Generic function to read a file containing floats and commented lines into a 2D numpy array.
Commented lines are prefixed by the characters # or %.
- burnman.tools.molar_volume_from_unit_cell_volume(unit_cell_v, z)[source]¶
Converts a unit cell volume from Angstroms^3 per unitcell, to m^3/mol.
- Parameters
- unit_cell_vfloat
Unit cell volumes [A^3/unit cell]
- zfloat
Number of formula units per unit cell
- Returns
- Vfloat
Volume [m^3/mol]
- burnman.tools.equilibrium_pressure(minerals, stoichiometry, temperature, pressure_initial_guess=100000.0)[source]¶
Given a list of minerals, their reaction stoichiometries and a temperature of interest, compute the equilibrium pressure of the reaction.
- Parameters
- mineralslist of minerals
List of minerals involved in the reaction.
- stoichiometrylist of floats
Reaction stoichiometry for the minerals provided. Reactants and products should have the opposite signs [mol]
- temperaturefloat
Temperature of interest [K]
- pressure_initial_guessoptional float
Initial pressure guess [Pa]
- Returns
- pressurefloat
The equilibrium pressure of the reaction [Pa]
- burnman.tools.equilibrium_temperature(minerals, stoichiometry, pressure, temperature_initial_guess=1000.0)[source]¶
Given a list of minerals, their reaction stoichiometries and a pressure of interest, compute the equilibrium temperature of the reaction.
- Parameters
- mineralslist of minerals
List of minerals involved in the reaction.
- stoichiometrylist of floats
Reaction stoichiometry for the minerals provided. Reactants and products should have the opposite signs [mol]
- pressurefloat
Pressure of interest [Pa]
- temperature_initial_guessoptional float
Initial temperature guess [K]
- Returns
- temperaturefloat
The equilibrium temperature of the reaction [K]
- burnman.tools.invariant_point(minerals_r1, stoichiometry_r1, minerals_r2, stoichiometry_r2, pressure_temperature_initial_guess=[1000000000.0, 1000.0])[source]¶
Given a list of minerals, their reaction stoichiometries and a pressure of interest, compute the equilibrium temperature of the reaction.
- Parameters
- mineralslist of minerals
List of minerals involved in the reaction.
- stoichiometrylist of floats
Reaction stoichiometry for the minerals provided. Reactants and products should have the opposite signs [mol]
- pressurefloat
Pressure of interest [Pa]
- temperature_initial_guessoptional float
Initial temperature guess [K]
- Returns
- temperaturefloat
The equilibrium temperature of the reaction [K]
- burnman.tools.hugoniot(mineral, P_ref, T_ref, pressures, reference_mineral=None)[source]¶
Calculates the temperatures (and volumes) along a Hugoniot as a function of pressure according to the Hugoniot equation U2-U1 = 0.5*(p2 - p1)(V1 - V2) where U and V are the internal energies and volumes (mass or molar) and U = F + TS
- Parameters
- mineralmineral
Mineral for which the Hugoniot is to be calculated.
- P_reffloat
Reference pressure [Pa]
- T_reffloat
Reference temperature [K]
- pressuresnumpy array of floats
Set of pressures [Pa] for which the Hugoniot temperature and volume should be calculated
- reference_mineralmineral
Mineral which is stable at the reference conditions Provides an alternative U_0 and V_0 when the reference mineral transforms to the mineral of interest at some (unspecified) pressure.
- Returns
- temperaturesnumpy array of floats
The Hugoniot temperatures at pressure
- volumesnumpy array of floats
The Hugoniot volumes at pressure
- burnman.tools.convert_fractions(composite, phase_fractions, input_type, output_type)[source]¶
Takes a composite with a set of user defined molar, volume or mass fractions (which do not have to be the fractions currently associated with the composite) and converts the fractions to molar, mass or volume.
Conversions to and from mass require a molar mass to be defined for all phases. Conversions to and from volume require set_state to have been called for the composite.
- Parameters
- compositeComposite
Composite for which fractions are to be defined.
- phase_fractionslist of floats
List of input phase fractions (of type input_type)
- input_typestring
Input fraction type: ‘molar’, ‘mass’ or ‘volume’
- output_typestring
Output fraction type: ‘molar’, ‘mass’ or ‘volume’
- Returns
- output_fractionslist of floats
List of output phase fractions (of type output_type)
- burnman.tools.bracket(fn, x0, dx, args=(), ratio=1.618, maxiter=100)[source]¶
Given a function and a starting guess, find two inputs for the function that bracket a root.
- Parameters
- fnfunction
The function to bracket
- x0float
The starting guess
- dxfloat
Small step for starting the search
- argsparameter list
Additional arguments to give to fn
- ratio :
The step size increases by this ratio every step in the search. Defaults to the golden ratio.
- maxiterint
The maximum number of steps before giving up.
- Returns
- xa, xb, fa, fb: floats
xa and xb are the inputs which bracket a root of fn. fa and fb are the values of the function at those points. If the bracket function takes more than maxiter steps, it raises a ValueError.
- burnman.tools.check_eos_consistency(m, P=1000000000.0, T=300.0, tol=0.0001, verbose=False, including_shear_properties=True)[source]¶
Compute numerical derivatives of the gibbs free energy of a mineral under given conditions, and check these values against those provided analytically by the equation of state
- Parameters
- mmineral
The mineral for which the equation of state is to be checked for consistency
- Pfloat
The pressure at which to check consistency
- Tfloat
The temperature at which to check consistency
- tolfloat
The fractional tolerance for each of the checks
- verboseboolean
Decide whether to print information about each check
- including_shear_propertiesboolean
Decide whether to check shear information, which is pointless for liquids and equations of state without shear modulus parameterizations
- Returns
- consistency: boolean
If all checks pass, returns True
- burnman.tools.smooth_array(array, grid_spacing, gaussian_rms_widths, truncate=4.0, mode='inverse_mirror')[source]¶
Creates a smoothed array by convolving it with a gaussian filter. Grid resolutions and gaussian RMS widths are required for each of the axes of the numpy array. The smoothing is truncated at a user-defined number of standard deviations. The edges of the array can be padded in a number of different ways given by the ‘mode’ parameter.
- Parameters
- arraynumpy ndarray
The array to smooth
- grid_spacingnumpy array of floats
The spacing of points along each axis
- gaussian_rms_widthsnumpy array of floats
The Gaussian RMS widths/standard deviations for the Gaussian convolution.
- truncatefloat (default=4.)
The number of standard deviations at which to truncate the smoothing.
- mode{‘reflect’, ‘constant’, ‘nearest’, ‘mirror’, ‘wrap’, ‘inverse_mirror’}
The mode parameter determines how the array borders are handled either by scipy.ndimage.filters.gaussian_filter. Default is ‘inverse_mirror’, which uses burnman.tools._pad_ndarray_inverse_mirror().
- Returns
- smoothed_array: numpy ndarray
The smoothed array
- burnman.tools.interp_smoothed_array_and_derivatives(array, x_values, y_values, x_stdev=0.0, y_stdev=0.0, truncate=4.0, mode='inverse_mirror', indexing='xy')[source]¶
Creates a smoothed array on a regular 2D grid. Smoothing is achieved using burnman.tools.smooth_array(). Outputs scipy.interpolate.interp2d() interpolators which can be used to query the array, or its derivatives in the x- and y- directions.
- Parameters
- array2D numpy array
The array to smooth. Each element array[i][j] corresponds to the position x_values[i], y_values[j]
- x_values1D numpy array
The gridded x values over which to create the smoothed grid
- y_values1D numpy array
The gridded y_values over which to create the smoothed grid
- x_stdevfloat
The standard deviation for the Gaussian filter along the x axis
- y_stdevfloat
The standard deviation for the Gaussian filter along the x axis
- truncatefloat (optional)
The number of standard deviations at which to truncate the smoothing (default = 4.).
- mode{‘reflect’, ‘constant’, ‘nearest’, ‘mirror’, ‘wrap’, ‘inverse_mirror’}
The mode parameter determines how the array borders are handled either by scipy.ndimage.filters.gaussian_filter. Default is ‘inverse_mirror’, which uses burnman.tools._pad_ndarray_inverse_mirror().
- indexing{‘xy’, ‘ij’}, optional
Cartesian (‘xy’, default) or matrix (‘ij’) indexing of output. See numpy.meshgrid for more details.
- Returns
- interps: tuple of three interp2d functors
interpolation functions for the smoothed property and the first derivatives with respect to x and y.
- burnman.tools.attribute_function(m, attributes, powers=[])[source]¶
Function which returns a function which can be used to evaluate material properties at a point. This function allows the user to define the property returned as a string. The function can itself be passed to another function (such as nonlinear_fitting.confidence_prediction_bands()).
Properties can either be simple attributes (e.g. K_T) or a product of attributes, each raised to some power.
- Parameters
- mMaterial
The material instance evaluated by the output function.
- attributeslist of strings
The list of material attributes / properties to be evaluated in the product
- powerslist of floats
The powers to which each attribute should be raised during evaluation
- Returns
- ——-
- ffunction(x)
Function which returns the value of product(a_i**p_i) as a function of condition (x = [P, T, V])
- burnman.tools.compare_l2(depth, calc, obs)[source]¶
Computes the L2 norm for N profiles at a time (assumed to be linear between points).
- Parameters
depths (array of float) – depths. \([m]\)
calc (list of arrays of float) – N arrays calculated values, e.g. [mat_vs,mat_vphi]
obs (list of arrays of float) – N arrays of values (observed or calculated) to compare to , e.g. [seis_vs, seis_vphi]
- Returns
array of L2 norms of length N
- Return type
array of floats
- burnman.tools.compare_chifactor(calc, obs)[source]¶
Computes the chi factor for N profiles at a time. Assumes a 1% a priori uncertainty on the seismic model.
- Parameters
calc (list of arrays of float) – N arrays calculated values, e.g. [mat_vs,mat_vphi]
obs (list of arrays of float) – N arrays of values (observed or calculated) to compare to , e.g. [seis_vs, seis_vphi]
- Returns
error array of length N
- Return type
array of floats
- burnman.tools.l2(x, funca, funcb)[source]¶
Computes the L2 norm for one profile(assumed to be linear between points).
- Parameters
x (array of float) – depths \([m]\).
funca (list of arrays of float) – array calculated values
funcb (list of arrays of float) – array of values (observed or calculated) to compare to
- Returns
L2 norm
- Return type
array of floats
- burnman.tools.nrmse(x, funca, funcb)[source]¶
Normalized root mean square error for one profile :type x: array of float :param x: depths in m. :type funca: list of arrays of float :param funca: array calculated values :type funcb: list of arrays of float :param funcb: array of values (observed or calculated) to compare to
- Returns
RMS error
- Return type
array of floats
- burnman.tools.chi_factor(calc, obs)[source]¶
\(\chi\) factor for one profile assuming 1% uncertainty on the reference model (obs) :type calc: list of arrays of float :param calc: array calculated values :type obs: list of arrays of float :param obs: array of reference values to compare to
- Returns
\(\chi\) factor
- Return type
array of floats