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<div class="section" id="module-pymatgen.analysis.elasticity.elastic">
<span id="pymatgen-analysis-elasticity-elastic-module"></span><h1>pymatgen.analysis.elasticity.elastic module<a class="headerlink" href="#module-pymatgen.analysis.elasticity.elastic" title="Permalink to this headline">¶</a></h1>
<dl class="class">
<dt id="pymatgen.analysis.elasticity.elastic.ComplianceTensor">
<em class="property">class </em><code class="descname">ComplianceTensor</code><a class="reference internal" href="_modules/pymatgen/analysis/elasticity/elastic.html#ComplianceTensor"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.ComplianceTensor" title="Permalink to this definition">¶</a></dt>
<dd><p>Bases: <a class="reference internal" href="pymatgen.core.tensors.html#pymatgen.core.tensors.Tensor" title="pymatgen.core.tensors.Tensor"><code class="xref py py-class docutils literal notranslate"><span class="pre">pymatgen.core.tensors.Tensor</span></code></a></p>
<p>This class represents the compliance tensor, and exists
primarily to keep the voigt-conversion scheme consistent
since the compliance tensor has a unique vscale</p>
</dd></dl>
<dl class="class">
<dt id="pymatgen.analysis.elasticity.elastic.ElasticTensor">
<em class="property">class </em><code class="descname">ElasticTensor</code><a class="reference internal" href="_modules/pymatgen/analysis/elasticity/elastic.html#ElasticTensor"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.ElasticTensor" title="Permalink to this definition">¶</a></dt>
<dd><p>Bases: <a class="reference internal" href="#pymatgen.analysis.elasticity.elastic.NthOrderElasticTensor" title="pymatgen.analysis.elasticity.elastic.NthOrderElasticTensor"><code class="xref py py-class docutils literal notranslate"><span class="pre">pymatgen.analysis.elasticity.elastic.NthOrderElasticTensor</span></code></a></p>
<p>This class extends Tensor to describe the 3x3x3x3
second-order elastic tensor, C_{ijkl}, with various
methods for estimating other properties derived from
the second order elastic tensor</p>
<p>Create an ElasticTensor object. The constructor throws an error if
the shape of the input_matrix argument is not 3x3x3x3, i. e. in true
tensor notation. Issues a warning if the input_matrix argument does
not satisfy standard symmetries. Note that the constructor uses
__new__ rather than __init__ according to the standard method of
subclassing numpy ndarrays.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>input_array</strong> (<em>3x3x3x3 array-like</em>) – the 3x3x3x3 array-like
representing the elastic tensor</p></li>
<li><p><strong>tol</strong> (<em>float</em>) – tolerance for initial symmetry test of tensor</p></li>
</ul>
</dd>
</dl>
<dl class="method">
<dt id="pymatgen.analysis.elasticity.elastic.ElasticTensor.cahill_thermalcond">
<code class="descname">cahill_thermalcond</code><span class="sig-paren">(</span><em>*args</em>, <em>**kwargs</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pymatgen/analysis/elasticity/elastic.html#ElasticTensor.cahill_thermalcond"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.ElasticTensor.cahill_thermalcond" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="method">
<dt id="pymatgen.analysis.elasticity.elastic.ElasticTensor.clarke_thermalcond">
<code class="descname">clarke_thermalcond</code><span class="sig-paren">(</span><em>*args</em>, <em>**kwargs</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pymatgen/analysis/elasticity/elastic.html#ElasticTensor.clarke_thermalcond"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.ElasticTensor.clarke_thermalcond" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="attribute">
<dt id="pymatgen.analysis.elasticity.elastic.ElasticTensor.compliance_tensor">
<code class="descname">compliance_tensor</code><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.ElasticTensor.compliance_tensor" title="Permalink to this definition">¶</a></dt>
<dd><p>returns the Voigt-notation compliance tensor,
which is the matrix inverse of the
Voigt-notation elastic tensor</p>
</dd></dl>
<dl class="method">
<dt id="pymatgen.analysis.elasticity.elastic.ElasticTensor.debye_temperature">
<code class="descname">debye_temperature</code><span class="sig-paren">(</span><em>*args</em>, <em>**kwargs</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pymatgen/analysis/elasticity/elastic.html#ElasticTensor.debye_temperature"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.ElasticTensor.debye_temperature" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="method">
<dt id="pymatgen.analysis.elasticity.elastic.ElasticTensor.debye_temperature_from_sound_velocities">
<code class="descname">debye_temperature_from_sound_velocities</code><span class="sig-paren">(</span><em>**kwargs</em><span class="sig-paren">)</span><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.ElasticTensor.debye_temperature_from_sound_velocities" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="method">
<dt id="pymatgen.analysis.elasticity.elastic.ElasticTensor.directional_elastic_mod">
<code class="descname">directional_elastic_mod</code><span class="sig-paren">(</span><em>n</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pymatgen/analysis/elasticity/elastic.html#ElasticTensor.directional_elastic_mod"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.ElasticTensor.directional_elastic_mod" title="Permalink to this definition">¶</a></dt>
<dd><p>Calculates directional elastic modulus for a specific vector</p>
</dd></dl>
<dl class="method">
<dt id="pymatgen.analysis.elasticity.elastic.ElasticTensor.directional_poisson_ratio">
<code class="descname">directional_poisson_ratio</code><span class="sig-paren">(</span><em>n</em>, <em>m</em>, <em>tol=1e-08</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pymatgen/analysis/elasticity/elastic.html#ElasticTensor.directional_poisson_ratio"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.ElasticTensor.directional_poisson_ratio" title="Permalink to this definition">¶</a></dt>
<dd><p>Calculates the poisson ratio for a specific direction
relative to a second, orthogonal direction</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>n</strong> (<em>3-d vector</em>) – principal direction</p></li>
<li><p><strong>m</strong> (<em>3-d vector</em>) – secondary direction orthogonal to n</p></li>
<li><p><strong>tol</strong> (<em>float</em>) – tolerance for testing of orthogonality</p></li>
</ul>
</dd>
</dl>
</dd></dl>
<dl class="classmethod">
<dt id="pymatgen.analysis.elasticity.elastic.ElasticTensor.from_independent_strains">
<em class="property">classmethod </em><code class="descname">from_independent_strains</code><span class="sig-paren">(</span><em>strains</em>, <em>stresses</em>, <em>eq_stress=None</em>, <em>vasp=False</em>, <em>tol=1e-10</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pymatgen/analysis/elasticity/elastic.html#ElasticTensor.from_independent_strains"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.ElasticTensor.from_independent_strains" title="Permalink to this definition">¶</a></dt>
<dd><p>Constructs the elastic tensor least-squares fit of independent strains
:param strains: list of strain objects to fit
:type strains: list of Strains
:param stresses: list of stress objects to use in fit</p>
<blockquote>
<div><p>corresponding to the list of strains</p>
</div></blockquote>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>eq_stress</strong> (<a class="reference internal" href="pymatgen.analysis.elasticity.stress.html#pymatgen.analysis.elasticity.stress.Stress" title="pymatgen.analysis.elasticity.stress.Stress"><em>Stress</em></a>) – equilibrium stress to use in fitting</p></li>
<li><p><strong>vasp</strong> (<em>boolean</em>) – flag for whether the stress tensor should be
converted based on vasp units/convention for stress</p></li>
<li><p><strong>tol</strong> (<em>float</em>) – tolerance for removing near-zero elements of the
resulting tensor</p></li>
</ul>
</dd>
</dl>
</dd></dl>
<dl class="classmethod">
<dt id="pymatgen.analysis.elasticity.elastic.ElasticTensor.from_pseudoinverse">
<em class="property">classmethod </em><code class="descname">from_pseudoinverse</code><span class="sig-paren">(</span><em>strains</em>, <em>stresses</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pymatgen/analysis/elasticity/elastic.html#ElasticTensor.from_pseudoinverse"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.ElasticTensor.from_pseudoinverse" title="Permalink to this definition">¶</a></dt>
<dd><p>Class method to fit an elastic tensor from stress/strain
data. Method uses Moore-Penrose pseudoinverse to invert
the s = C*e equation with elastic tensor, stress, and
strain in voigt notation</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>stresses</strong> (<em>Nx3x3 array-like</em>) – list or array of stresses</p></li>
<li><p><strong>strains</strong> (<em>Nx3x3 array-like</em>) – list or array of strains</p></li>
</ul>
</dd>
</dl>
</dd></dl>
<dl class="attribute">
<dt id="pymatgen.analysis.elasticity.elastic.ElasticTensor.g_reuss">
<code class="descname">g_reuss</code><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.ElasticTensor.g_reuss" title="Permalink to this definition">¶</a></dt>
<dd><p>returns the G_r shear modulus</p>
</dd></dl>
<dl class="attribute">
<dt id="pymatgen.analysis.elasticity.elastic.ElasticTensor.g_voigt">
<code class="descname">g_voigt</code><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.ElasticTensor.g_voigt" title="Permalink to this definition">¶</a></dt>
<dd><p>returns the G_v shear modulus</p>
</dd></dl>
<dl class="attribute">
<dt id="pymatgen.analysis.elasticity.elastic.ElasticTensor.g_vrh">
<code class="descname">g_vrh</code><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.ElasticTensor.g_vrh" title="Permalink to this definition">¶</a></dt>
<dd><p>returns the G_vrh (Voigt-Reuss-Hill) average shear modulus</p>
</dd></dl>
<dl class="method">
<dt id="pymatgen.analysis.elasticity.elastic.ElasticTensor.get_structure_property_dict">
<code class="descname">get_structure_property_dict</code><span class="sig-paren">(</span><em>structure</em>, <em>include_base_props=True</em>, <em>ignore_errors=False</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pymatgen/analysis/elasticity/elastic.html#ElasticTensor.get_structure_property_dict"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.ElasticTensor.get_structure_property_dict" title="Permalink to this definition">¶</a></dt>
<dd><p>returns a dictionary of properties derived from the elastic tensor
and an associated structure</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>structure</strong> (<a class="reference internal" href="pymatgen.core.structure.html#pymatgen.core.structure.Structure" title="pymatgen.core.structure.Structure"><em>Structure</em></a>) – structure object for which to calculate
associated properties</p></li>
<li><p><strong>include_base_props</strong> (<em>bool</em>) – whether to include base properties,
like k_vrh, etc.</p></li>
<li><p><strong>ignore_errors</strong> (<em>bool</em>) – if set to true, will set problem properties
that depend on a physical tensor to None, defaults to False</p></li>
</ul>
</dd>
</dl>
</dd></dl>
<dl class="method">
<dt id="pymatgen.analysis.elasticity.elastic.ElasticTensor.green_kristoffel">
<code class="descname">green_kristoffel</code><span class="sig-paren">(</span><em>u</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pymatgen/analysis/elasticity/elastic.html#ElasticTensor.green_kristoffel"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.ElasticTensor.green_kristoffel" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns the Green-Kristoffel tensor for a second-order tensor</p>
</dd></dl>
<dl class="attribute">
<dt id="pymatgen.analysis.elasticity.elastic.ElasticTensor.homogeneous_poisson">
<code class="descname">homogeneous_poisson</code><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.ElasticTensor.homogeneous_poisson" title="Permalink to this definition">¶</a></dt>
<dd><p>returns the homogeneous poisson ratio</p>
</dd></dl>
<dl class="attribute">
<dt id="pymatgen.analysis.elasticity.elastic.ElasticTensor.k_reuss">
<code class="descname">k_reuss</code><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.ElasticTensor.k_reuss" title="Permalink to this definition">¶</a></dt>
<dd><p>returns the K_r bulk modulus</p>
</dd></dl>
<dl class="attribute">
<dt id="pymatgen.analysis.elasticity.elastic.ElasticTensor.k_voigt">
<code class="descname">k_voigt</code><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.ElasticTensor.k_voigt" title="Permalink to this definition">¶</a></dt>
<dd><p>returns the K_v bulk modulus</p>
</dd></dl>
<dl class="attribute">
<dt id="pymatgen.analysis.elasticity.elastic.ElasticTensor.k_vrh">
<code class="descname">k_vrh</code><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.ElasticTensor.k_vrh" title="Permalink to this definition">¶</a></dt>
<dd><p>returns the K_vrh (Voigt-Reuss-Hill) average bulk modulus</p>
</dd></dl>
<dl class="method">
<dt id="pymatgen.analysis.elasticity.elastic.ElasticTensor.long_v">
<code class="descname">long_v</code><span class="sig-paren">(</span><em>*args</em>, <em>**kwargs</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pymatgen/analysis/elasticity/elastic.html#ElasticTensor.long_v"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.ElasticTensor.long_v" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="attribute">
<dt id="pymatgen.analysis.elasticity.elastic.ElasticTensor.property_dict">
<code class="descname">property_dict</code><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.ElasticTensor.property_dict" title="Permalink to this definition">¶</a></dt>
<dd><p>returns a dictionary of properties derived from the elastic tensor</p>
</dd></dl>
<dl class="method">
<dt id="pymatgen.analysis.elasticity.elastic.ElasticTensor.snyder_ac">
<code class="descname">snyder_ac</code><span class="sig-paren">(</span><em>*args</em>, <em>**kwargs</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pymatgen/analysis/elasticity/elastic.html#ElasticTensor.snyder_ac"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.ElasticTensor.snyder_ac" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="method">
<dt id="pymatgen.analysis.elasticity.elastic.ElasticTensor.snyder_opt">
<code class="descname">snyder_opt</code><span class="sig-paren">(</span><em>*args</em>, <em>**kwargs</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pymatgen/analysis/elasticity/elastic.html#ElasticTensor.snyder_opt"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.ElasticTensor.snyder_opt" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="method">
<dt id="pymatgen.analysis.elasticity.elastic.ElasticTensor.snyder_total">
<code class="descname">snyder_total</code><span class="sig-paren">(</span><em>*args</em>, <em>**kwargs</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pymatgen/analysis/elasticity/elastic.html#ElasticTensor.snyder_total"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.ElasticTensor.snyder_total" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="method">
<dt id="pymatgen.analysis.elasticity.elastic.ElasticTensor.trans_v">
<code class="descname">trans_v</code><span class="sig-paren">(</span><em>*args</em>, <em>**kwargs</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pymatgen/analysis/elasticity/elastic.html#ElasticTensor.trans_v"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.ElasticTensor.trans_v" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="attribute">
<dt id="pymatgen.analysis.elasticity.elastic.ElasticTensor.universal_anisotropy">
<code class="descname">universal_anisotropy</code><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.ElasticTensor.universal_anisotropy" title="Permalink to this definition">¶</a></dt>
<dd><p>returns the universal anisotropy value</p>
</dd></dl>
<dl class="attribute">
<dt id="pymatgen.analysis.elasticity.elastic.ElasticTensor.y_mod">
<code class="descname">y_mod</code><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.ElasticTensor.y_mod" title="Permalink to this definition">¶</a></dt>
<dd><p>Calculates Young’s modulus (in SI units) using the
Voigt-Reuss-Hill averages of bulk and shear moduli</p>
</dd></dl>
</dd></dl>
<dl class="class">
<dt id="pymatgen.analysis.elasticity.elastic.ElasticTensorExpansion">
<em class="property">class </em><code class="descname">ElasticTensorExpansion</code><span class="sig-paren">(</span><em>c_list</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pymatgen/analysis/elasticity/elastic.html#ElasticTensorExpansion"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.ElasticTensorExpansion" title="Permalink to this definition">¶</a></dt>
<dd><p>Bases: <a class="reference internal" href="pymatgen.core.tensors.html#pymatgen.core.tensors.TensorCollection" title="pymatgen.core.tensors.TensorCollection"><code class="xref py py-class docutils literal notranslate"><span class="pre">pymatgen.core.tensors.TensorCollection</span></code></a></p>
<p>This class is a sequence of elastic tensors corresponding
to an elastic tensor expansion, which can be used to
calculate stress and energy density and inherits all
of the list-based properties of TensorCollection
(e. g. symmetrization, voigt conversion, etc.)</p>
<p>Initialization method for ElasticTensorExpansion</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>c_list</strong> (<em>list</em><em> or </em><em>tuple</em>) – sequence of Tensor inputs
or tensors from which the elastic tensor
expansion is constructed.</p>
</dd>
</dl>
<dl class="method">
<dt id="pymatgen.analysis.elasticity.elastic.ElasticTensorExpansion.calculate_stress">
<code class="descname">calculate_stress</code><span class="sig-paren">(</span><em>strain</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pymatgen/analysis/elasticity/elastic.html#ElasticTensorExpansion.calculate_stress"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.ElasticTensorExpansion.calculate_stress" title="Permalink to this definition">¶</a></dt>
<dd><p>Calculate’s a given elastic tensor’s contribution to the
stress using Einstein summation</p>
</dd></dl>
<dl class="method">
<dt id="pymatgen.analysis.elasticity.elastic.ElasticTensorExpansion.energy_density">
<code class="descname">energy_density</code><span class="sig-paren">(</span><em>strain</em>, <em>convert_GPa_to_eV=True</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pymatgen/analysis/elasticity/elastic.html#ElasticTensorExpansion.energy_density"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.ElasticTensorExpansion.energy_density" title="Permalink to this definition">¶</a></dt>
<dd><p>Calculates the elastic energy density due to a strain</p>
</dd></dl>
<dl class="classmethod">
<dt id="pymatgen.analysis.elasticity.elastic.ElasticTensorExpansion.from_diff_fit">
<em class="property">classmethod </em><code class="descname">from_diff_fit</code><span class="sig-paren">(</span><em>strains</em>, <em>stresses</em>, <em>eq_stress=None</em>, <em>tol=1e-10</em>, <em>order=3</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pymatgen/analysis/elasticity/elastic.html#ElasticTensorExpansion.from_diff_fit"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.ElasticTensorExpansion.from_diff_fit" title="Permalink to this definition">¶</a></dt>
<dd><p>Generates an elastic tensor expansion via the fitting function
defined below in diff_fit</p>
</dd></dl>
<dl class="method">
<dt id="pymatgen.analysis.elasticity.elastic.ElasticTensorExpansion.get_compliance_expansion">
<code class="descname">get_compliance_expansion</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/pymatgen/analysis/elasticity/elastic.html#ElasticTensorExpansion.get_compliance_expansion"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.ElasticTensorExpansion.get_compliance_expansion" title="Permalink to this definition">¶</a></dt>
<dd><p>Gets a compliance tensor expansion from the elastic
tensor expansion.</p>
</dd></dl>
<dl class="method">
<dt id="pymatgen.analysis.elasticity.elastic.ElasticTensorExpansion.get_effective_ecs">
<code class="descname">get_effective_ecs</code><span class="sig-paren">(</span><em>strain</em>, <em>order=2</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pymatgen/analysis/elasticity/elastic.html#ElasticTensorExpansion.get_effective_ecs"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.ElasticTensorExpansion.get_effective_ecs" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns the effective elastic constants
from the elastic tensor expansion.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>strain</strong> (<a class="reference internal" href="pymatgen.analysis.elasticity.strain.html#pymatgen.analysis.elasticity.strain.Strain" title="pymatgen.analysis.elasticity.strain.Strain"><em>Strain</em></a><em> or </em><em>3x3 array-like</em>) – strain condition
under which to calculate the effective constants</p></li>
<li><p><strong>order</strong> (<em>int</em>) – order of the ecs to be returned</p></li>
</ul>
</dd>
</dl>
</dd></dl>
<dl class="method">
<dt id="pymatgen.analysis.elasticity.elastic.ElasticTensorExpansion.get_ggt">
<code class="descname">get_ggt</code><span class="sig-paren">(</span><em>n</em>, <em>u</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pymatgen/analysis/elasticity/elastic.html#ElasticTensorExpansion.get_ggt"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.ElasticTensorExpansion.get_ggt" title="Permalink to this definition">¶</a></dt>
<dd><p>Gets the Generalized Gruneisen tensor for a given
third-order elastic tensor expansion.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>n</strong> (<em>3x1 array-like</em>) – normal mode direction</p></li>
<li><p><strong>u</strong> (<em>3x1 array-like</em>) – polarization direction</p></li>
</ul>
</dd>
</dl>
</dd></dl>
<dl class="method">
<dt id="pymatgen.analysis.elasticity.elastic.ElasticTensorExpansion.get_gruneisen_parameter">
<code class="descname">get_gruneisen_parameter</code><span class="sig-paren">(</span><em>temperature=None</em>, <em>structure=None</em>, <em>quad=None</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pymatgen/analysis/elasticity/elastic.html#ElasticTensorExpansion.get_gruneisen_parameter"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.ElasticTensorExpansion.get_gruneisen_parameter" title="Permalink to this definition">¶</a></dt>
<dd><p>Gets the single average gruneisen parameter from the TGT.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>temperature</strong> (<em>float</em>) – Temperature in kelvin, if not specified
will return non-cv-normalized value</p></li>
<li><p><strong>structure</strong> (<em>float</em>) – Structure to be used in directional heat
capacity determination, only necessary if temperature
is specified</p></li>
<li><p><strong>quad</strong> (<em>dict</em>) – quadrature for integration, should be
dictionary with “points” and “weights” keys defaults
to quadpy.sphere.Lebedev(19) as read from file</p></li>
</ul>
</dd>
</dl>
</dd></dl>
<dl class="method">
<dt id="pymatgen.analysis.elasticity.elastic.ElasticTensorExpansion.get_heat_capacity">
<code class="descname">get_heat_capacity</code><span class="sig-paren">(</span><em>temperature</em>, <em>structure</em>, <em>n</em>, <em>u</em>, <em>cutoff=100.0</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pymatgen/analysis/elasticity/elastic.html#ElasticTensorExpansion.get_heat_capacity"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.ElasticTensorExpansion.get_heat_capacity" title="Permalink to this definition">¶</a></dt>
<dd><p>Gets the directional heat capacity for a higher order tensor
expansion as a function of direction and polarization.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>temperature</strong> (<em>float</em>) – Temperature in kelvin</p></li>
<li><p><strong>structure</strong> (<em>float</em>) – Structure to be used in directional heat
capacity determination</p></li>
<li><p><strong>n</strong> (<em>3x1 array-like</em>) – direction for Cv determination</p></li>
<li><p><strong>u</strong> (<em>3x1 array-like</em>) – polarization direction, note that
no attempt for verification of eigenvectors is made</p></li>
<li><p><strong>cutoff</strong> (<em>float</em>) – cutoff for scale of kt / (hbar * omega)
if lower than this value, returns 0</p></li>
</ul>
</dd>
</dl>
</dd></dl>
<dl class="method">
<dt id="pymatgen.analysis.elasticity.elastic.ElasticTensorExpansion.get_stability_criteria">
<code class="descname">get_stability_criteria</code><span class="sig-paren">(</span><em>s</em>, <em>n</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pymatgen/analysis/elasticity/elastic.html#ElasticTensorExpansion.get_stability_criteria"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.ElasticTensorExpansion.get_stability_criteria" title="Permalink to this definition">¶</a></dt>
<dd><p>Gets the stability criteria from the symmetric
Wallace tensor from an input vector and stress
value.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>s</strong> (<em>float</em>) – Stress value at which to evaluate
the stability criteria</p></li>
<li><p><strong>n</strong> (<em>3x1 array-like</em>) – direction of the applied
stress</p></li>
</ul>
</dd>
</dl>
</dd></dl>
<dl class="method">
<dt id="pymatgen.analysis.elasticity.elastic.ElasticTensorExpansion.get_strain_from_stress">
<code class="descname">get_strain_from_stress</code><span class="sig-paren">(</span><em>stress</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pymatgen/analysis/elasticity/elastic.html#ElasticTensorExpansion.get_strain_from_stress"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.ElasticTensorExpansion.get_strain_from_stress" title="Permalink to this definition">¶</a></dt>
<dd><p>Gets the strain from a stress state according
to the compliance expansion corresponding to the
tensor expansion.</p>
</dd></dl>
<dl class="method">
<dt id="pymatgen.analysis.elasticity.elastic.ElasticTensorExpansion.get_symmetric_wallace_tensor">
<code class="descname">get_symmetric_wallace_tensor</code><span class="sig-paren">(</span><em>tau</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pymatgen/analysis/elasticity/elastic.html#ElasticTensorExpansion.get_symmetric_wallace_tensor"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.ElasticTensorExpansion.get_symmetric_wallace_tensor" title="Permalink to this definition">¶</a></dt>
<dd><p>Gets the symmetrized wallace tensor for determining
yield strength criteria.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>tau</strong> (<em>3x3 array-like</em>) – stress at which to evaluate
the wallace tensor.</p>
</dd>
</dl>
</dd></dl>
<dl class="method">
<dt id="pymatgen.analysis.elasticity.elastic.ElasticTensorExpansion.get_tgt">
<code class="descname">get_tgt</code><span class="sig-paren">(</span><em>temperature=None</em>, <em>structure=None</em>, <em>quad=None</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pymatgen/analysis/elasticity/elastic.html#ElasticTensorExpansion.get_tgt"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.ElasticTensorExpansion.get_tgt" title="Permalink to this definition">¶</a></dt>
<dd><p>Gets the thermodynamic Gruneisen tensor (TGT) by via an
integration of the GGT weighted by the directional heat
capacity.</p>
<dl class="simple">
<dt>See refs:</dt><dd><p>R. N. Thurston and K. Brugger, Phys. Rev. 113, A1604 (1964).
K. Brugger Phys. Rev. 137, A1826 (1965).</p>
</dd>
</dl>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>temperature</strong> (<em>float</em>) – Temperature in kelvin, if not specified
will return non-cv-normalized value</p></li>
<li><p><strong>structure</strong> (<em>float</em>) – Structure to be used in directional heat
capacity determination, only necessary if temperature
is specified</p></li>
<li><p><strong>quad</strong> (<em>dict</em>) – quadrature for integration, should be
dictionary with “points” and “weights” keys defaults
to quadpy.sphere.Lebedev(19) as read from file</p></li>
</ul>
</dd>
</dl>
</dd></dl>
<dl class="method">
<dt id="pymatgen.analysis.elasticity.elastic.ElasticTensorExpansion.get_wallace_tensor">
<code class="descname">get_wallace_tensor</code><span class="sig-paren">(</span><em>tau</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pymatgen/analysis/elasticity/elastic.html#ElasticTensorExpansion.get_wallace_tensor"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.ElasticTensorExpansion.get_wallace_tensor" title="Permalink to this definition">¶</a></dt>
<dd><p>Gets the Wallace Tensor for determining yield strength
criteria.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>tau</strong> (<em>3x3 array-like</em>) – stress at which to evaluate
the wallace tensor</p>
</dd>
</dl>
</dd></dl>
<dl class="method">
<dt id="pymatgen.analysis.elasticity.elastic.ElasticTensorExpansion.get_yield_stress">
<code class="descname">get_yield_stress</code><span class="sig-paren">(</span><em>n</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pymatgen/analysis/elasticity/elastic.html#ElasticTensorExpansion.get_yield_stress"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.ElasticTensorExpansion.get_yield_stress" title="Permalink to this definition">¶</a></dt>
<dd><p>Gets the yield stress for a given direction</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>n</strong> (<em>3x1 array-like</em>) – direction for which to find the
yield stress</p>
</dd>
</dl>
</dd></dl>
<dl class="method">
<dt id="pymatgen.analysis.elasticity.elastic.ElasticTensorExpansion.omega">
<code class="descname">omega</code><span class="sig-paren">(</span><em>structure</em>, <em>n</em>, <em>u</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pymatgen/analysis/elasticity/elastic.html#ElasticTensorExpansion.omega"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.ElasticTensorExpansion.omega" title="Permalink to this definition">¶</a></dt>
<dd><p>Finds directional frequency contribution to the heat
capacity from direction and polarization</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>structure</strong> (<a class="reference internal" href="pymatgen.core.structure.html#pymatgen.core.structure.Structure" title="pymatgen.core.structure.Structure"><em>Structure</em></a>) – Structure to be used in directional heat
capacity determination</p></li>
<li><p><strong>n</strong> (<em>3x1 array-like</em>) – direction for Cv determination</p></li>
<li><p><strong>u</strong> (<em>3x1 array-like</em>) – polarization direction, note that
no attempt for verification of eigenvectors is made</p></li>
</ul>
</dd>
</dl>
</dd></dl>
<dl class="attribute">
<dt id="pymatgen.analysis.elasticity.elastic.ElasticTensorExpansion.order">
<code class="descname">order</code><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.ElasticTensorExpansion.order" title="Permalink to this definition">¶</a></dt>
<dd><p>Order of the elastic tensor expansion, i. e. the order of the
highest included set of elastic constants</p>
</dd></dl>
<dl class="method">
<dt id="pymatgen.analysis.elasticity.elastic.ElasticTensorExpansion.thermal_expansion_coeff">
<code class="descname">thermal_expansion_coeff</code><span class="sig-paren">(</span><em>structure</em>, <em>temperature</em>, <em>mode='debye'</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pymatgen/analysis/elasticity/elastic.html#ElasticTensorExpansion.thermal_expansion_coeff"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.ElasticTensorExpansion.thermal_expansion_coeff" title="Permalink to this definition">¶</a></dt>
<dd><p>Gets thermal expansion coefficient from third-order constants.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>temperature</strong> (<em>float</em>) – Temperature in kelvin, if not specified
will return non-cv-normalized value</p></li>
<li><p><strong>structure</strong> (<a class="reference internal" href="pymatgen.core.structure.html#pymatgen.core.structure.Structure" title="pymatgen.core.structure.Structure"><em>Structure</em></a>) – Structure to be used in directional heat
capacity determination, only necessary if temperature
is specified</p></li>
<li><p><strong>mode</strong> (<em>string</em>) – mode for finding average heat-capacity,
current supported modes are ‘debye’ and ‘dulong-petit’</p></li>
</ul>
</dd>
</dl>
</dd></dl>
</dd></dl>
<dl class="class">
<dt id="pymatgen.analysis.elasticity.elastic.NthOrderElasticTensor">
<em class="property">class </em><code class="descname">NthOrderElasticTensor</code><a class="reference internal" href="_modules/pymatgen/analysis/elasticity/elastic.html#NthOrderElasticTensor"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.NthOrderElasticTensor" title="Permalink to this definition">¶</a></dt>
<dd><p>Bases: <a class="reference internal" href="pymatgen.core.tensors.html#pymatgen.core.tensors.Tensor" title="pymatgen.core.tensors.Tensor"><code class="xref py py-class docutils literal notranslate"><span class="pre">pymatgen.core.tensors.Tensor</span></code></a></p>
<p>An object representing an nth-order tensor expansion
of the stress-strain constitutive equations</p>
<dl class="attribute">
<dt id="pymatgen.analysis.elasticity.elastic.NthOrderElasticTensor.GPa_to_eV_A3">
<code class="descname">GPa_to_eV_A3</code><em class="property"> = 0.006241509125883258</em><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.NthOrderElasticTensor.GPa_to_eV_A3" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="method">
<dt id="pymatgen.analysis.elasticity.elastic.NthOrderElasticTensor.calculate_stress">
<code class="descname">calculate_stress</code><span class="sig-paren">(</span><em>strain</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pymatgen/analysis/elasticity/elastic.html#NthOrderElasticTensor.calculate_stress"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.NthOrderElasticTensor.calculate_stress" title="Permalink to this definition">¶</a></dt>
<dd><p>Calculate’s a given elastic tensor’s contribution to the
stress using Einstein summation</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>strain</strong> (<em>3x3 array-like</em>) – matrix corresponding to strain</p>
</dd>
</dl>
</dd></dl>
<dl class="method">
<dt id="pymatgen.analysis.elasticity.elastic.NthOrderElasticTensor.energy_density">
<code class="descname">energy_density</code><span class="sig-paren">(</span><em>strain</em>, <em>convert_GPa_to_eV=True</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pymatgen/analysis/elasticity/elastic.html#NthOrderElasticTensor.energy_density"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.NthOrderElasticTensor.energy_density" title="Permalink to this definition">¶</a></dt>
<dd><p>Calculates the elastic energy density due to a strain</p>
</dd></dl>
<dl class="classmethod">
<dt id="pymatgen.analysis.elasticity.elastic.NthOrderElasticTensor.from_diff_fit">
<em class="property">classmethod </em><code class="descname">from_diff_fit</code><span class="sig-paren">(</span><em>strains</em>, <em>stresses</em>, <em>eq_stress=None</em>, <em>order=2</em>, <em>tol=1e-10</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pymatgen/analysis/elasticity/elastic.html#NthOrderElasticTensor.from_diff_fit"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.NthOrderElasticTensor.from_diff_fit" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="attribute">
<dt id="pymatgen.analysis.elasticity.elastic.NthOrderElasticTensor.order">
<code class="descname">order</code><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.NthOrderElasticTensor.order" title="Permalink to this definition">¶</a></dt>
<dd><p>Order of the elastic tensor</p>
</dd></dl>
<dl class="attribute">
<dt id="pymatgen.analysis.elasticity.elastic.NthOrderElasticTensor.symbol">
<code class="descname">symbol</code><em class="property"> = 'C'</em><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.NthOrderElasticTensor.symbol" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
</dd></dl>
<dl class="function">
<dt id="pymatgen.analysis.elasticity.elastic.diff_fit">
<code class="descname">diff_fit</code><span class="sig-paren">(</span><em>strains</em>, <em>stresses</em>, <em>eq_stress=None</em>, <em>order=2</em>, <em>tol=1e-10</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pymatgen/analysis/elasticity/elastic.html#diff_fit"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.diff_fit" title="Permalink to this definition">¶</a></dt>
<dd><p>nth order elastic constant fitting function based on
central-difference derivatives with respect to distinct
strain states. The algorithm is summarized as follows:</p>
<ol class="arabic simple">
<li><p>Identify distinct strain states as sets of indices
for which nonzero strain values exist, typically
[(0), (1), (2), (3), (4), (5), (0, 1) etc.]</p></li>
<li><p>For each strain state, find and sort strains and
stresses by strain value.</p></li>
<li><p>Find first, second .. nth derivatives of each stress
with respect to scalar variable corresponding to
the smallest perturbation in the strain.</p></li>
<li><p>Use the pseudoinverse of a matrix-vector expression
corresponding to the parameterized stress-strain
relationship and multiply that matrix by the respective
calculated first or second derivatives from the
previous step.</p></li>
<li><p>Place the calculated nth-order elastic
constants appropriately.</p></li>
</ol>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>order</strong> (<em>int</em>) – order of the elastic tensor set to return</p></li>
<li><p><strong>strains</strong> (<em>nx3x3 array-like</em>) – Array of 3x3 strains
to use in fitting of ECs</p></li>
<li><p><strong>stresses</strong> (<em>nx3x3 array-like</em>) – Array of 3x3 stresses
to use in fitting ECs. These should be PK2 stresses.</p></li>
<li><p><strong>eq_stress</strong> (<em>3x3 array-like</em>) – stress corresponding to
equilibrium strain (i. e. “0” strain state).
If not specified, function will try to find
the state in the list of provided stresses
and strains. If not found, defaults to 0.</p></li>
<li><p><strong>tol</strong> (<em>float</em>) – value for which strains below
are ignored in identifying strain states.</p></li>
</ul>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p>Set of tensors corresponding to nth order expansion of
the stress/strain relation</p>
</dd>
</dl>
</dd></dl>
<dl class="function">
<dt id="pymatgen.analysis.elasticity.elastic.find_eq_stress">
<code class="descname">find_eq_stress</code><span class="sig-paren">(</span><em>strains</em>, <em>stresses</em>, <em>tol=1e-10</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pymatgen/analysis/elasticity/elastic.html#find_eq_stress"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.find_eq_stress" title="Permalink to this definition">¶</a></dt>
<dd><p>Finds stress corresponding to zero strain state in stress-strain list</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>strains</strong> (<em>Nx3x3 array-like</em>) – array corresponding to strains</p></li>
<li><p><strong>stresses</strong> (<em>Nx3x3 array-like</em>) – array corresponding to stresses</p></li>
<li><p><strong>tol</strong> (<em>float</em>) – tolerance to find zero strain state</p></li>
</ul>
</dd>
</dl>
</dd></dl>
<dl class="function">
<dt id="pymatgen.analysis.elasticity.elastic.generate_pseudo">
<code class="descname">generate_pseudo</code><span class="sig-paren">(</span><em>strain_states</em>, <em>order=3</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pymatgen/analysis/elasticity/elastic.html#generate_pseudo"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.generate_pseudo" title="Permalink to this definition">¶</a></dt>
<dd><p>Generates the pseudoinverse for a given set of strains.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>strain_states</strong> (<em>6xN array like</em>) – a list of voigt-notation
“strain-states”, i. e. perturbed indices of the strain
as a function of the smallest strain e. g. (0, 1, 0, 0, 1, 0)</p></li>
<li><p><strong>order</strong> (<em>int</em>) – order of pseudoinverse to calculate</p></li>
</ul>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p><dl class="simple">
<dt>pseudo inverses for each order tensor, these can</dt><dd><p>be multiplied by the central difference derivative
of the stress with respect to the strain state</p>
</dd>
<dt>absent_syms: symbols of the tensor absent from the PI</dt><dd><p>expression</p>
</dd>
</dl>
</p>
</dd>
<dt class="field-odd">Return type</dt>
<dd class="field-odd"><p>mis</p>
</dd>
</dl>
</dd></dl>
<dl class="function">
<dt id="pymatgen.analysis.elasticity.elastic.get_diff_coeff">
<code class="descname">get_diff_coeff</code><span class="sig-paren">(</span><em>hvec</em>, <em>n=1</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pymatgen/analysis/elasticity/elastic.html#get_diff_coeff"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.get_diff_coeff" title="Permalink to this definition">¶</a></dt>
<dd><p>Helper function to find difference coefficients of an
derivative on an arbitrary mesh.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>hvec</strong> (<em>1D array-like</em>) – sampling stencil</p></li>
<li><p><strong>n</strong> (<em>int</em>) – degree of derivative to find</p></li>
</ul>
</dd>
</dl>
</dd></dl>
<dl class="function">
<dt id="pymatgen.analysis.elasticity.elastic.get_strain_state_dict">
<code class="descname">get_strain_state_dict</code><span class="sig-paren">(</span><em>strains</em>, <em>stresses</em>, <em>eq_stress=None</em>, <em>tol=1e-10</em>, <em>add_eq=True</em>, <em>sort=True</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pymatgen/analysis/elasticity/elastic.html#get_strain_state_dict"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.get_strain_state_dict" title="Permalink to this definition">¶</a></dt>
<dd><p>Creates a dictionary of voigt-notation stress-strain sets
keyed by “strain state”, i. e. a tuple corresponding to
the non-zero entries in ratios to the lowest nonzero value,
e.g. [0, 0.1, 0, 0.2, 0, 0] -> (0,1,0,2,0,0)
This allows strains to be collected in stencils as to
evaluate parameterized finite difference derivatives</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>strains</strong> (<em>Nx3x3 array-like</em>) – strain matrices</p></li>
<li><p><strong>stresses</strong> (<em>Nx3x3 array-like</em>) – stress matrices</p></li>
<li><p><strong>eq_stress</strong> (<em>Nx3x3 array-like</em>) – equilibrium stress</p></li>
<li><p><strong>tol</strong> (<em>float</em>) – tolerance for sorting strain states</p></li>
<li><p><strong>add_eq</strong> (<em>bool</em>) – flag for whether to add eq_strain
to stress-strain sets for each strain state</p></li>
<li><p><strong>sort</strong> (<em>bool</em>) – flag for whether to sort strain states</p></li>
</ul>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p>OrderedDict with strain state keys and dictionaries
with stress-strain data corresponding to strain state</p>
</dd>
</dl>
</dd></dl>
<dl class="function">
<dt id="pymatgen.analysis.elasticity.elastic.get_symbol_list">
<code class="descname">get_symbol_list</code><span class="sig-paren">(</span><em>rank</em>, <em>dim=6</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pymatgen/analysis/elasticity/elastic.html#get_symbol_list"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.get_symbol_list" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns a symbolic representation of the voigt-notation
tensor that places identical symbols for entries related
by index transposition, i. e. C_1121 = C_1211 etc.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>dim</strong> (<em>int</em>) – dimension of matrix/tensor, e. g. 6 for
voigt notation and 3 for standard</p></li>
<li><p><strong>rank</strong> (<em>int</em>) – rank of tensor, e. g. 3 for third-order ECs</p></li>
</ul>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p><p>array representing distinct indices
c_arr (array): array representing tensor with equivalent</p>
<blockquote>
<div><p>indices assigned as above</p>
</div></blockquote>
</p>
</dd>
<dt class="field-odd">Return type</dt>
<dd class="field-odd"><p>c_vec (array)</p>
</dd>
</dl>
</dd></dl>
<dl class="function">
<dt id="pymatgen.analysis.elasticity.elastic.raise_error_if_unphysical">
<code class="descname">raise_error_if_unphysical</code><span class="sig-paren">(</span><em>f</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pymatgen/analysis/elasticity/elastic.html#raise_error_if_unphysical"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.raise_error_if_unphysical" title="Permalink to this definition">¶</a></dt>
<dd><p>Wrapper for functions or properties that should raise an error
if tensor is unphysical.</p>
</dd></dl>
<dl class="function">
<dt id="pymatgen.analysis.elasticity.elastic.subs">
<code class="descname">subs</code><span class="sig-paren">(</span><em>entry</em>, <em>cmap</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pymatgen/analysis/elasticity/elastic.html#subs"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.subs" title="Permalink to this definition">¶</a></dt>
<dd><p>Sympy substitution function, primarily for the purposes
of numpy vectorization</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>entry</strong> (<em>symbol</em><em> or </em><em>exp</em>) – sympy expr to undergo subs</p></li>
<li><p><strong>cmap</strong> (<em>dict</em>) – map for symbols to values to use in subs</p></li>
</ul>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p>Evaluated expression with substitution</p>
</dd>
</dl>
</dd></dl>
</div>
</div>
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