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ValueErrors and convergence failures in equilibrium #63

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bocklund opened this Issue Jan 7, 2017 · 2 comments

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bocklund commented Jan 7, 2017

In a database shared privately, equilibrium either fails with a ValueError: Invalid gradient_term or it fails to converge, depending on the passed conditions. One case of each is in the following comments. These use the latest pycalphad, ad385a0.

I have reproduced these results after removing magnetic parameters from the database. I also tried over a range of temperatures and compositions, all of which produced either a ValueError or convergence failure.

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bocklund commented Jan 7, 2017

from pycalphad import equilibrium, Database
import pycalphad.variables as v
phases = ['FCC', 'L12']
components = ["AL", "CO", "CR", "W", "VA"]
conditions = {"T": 1248, "P":101325, v.X("AL"):0.1, v.X("CR"): 0.1, v.X("W"):0.1}
equilibrium(dbf, components, phases, conditions, _diagnostic=True, verbose=True)

Results in:

Calculation Backend: Compiled (autowrap)
Components: AL CO CR VA W
Phases: FCC L12 [done]
('NEW_L_MULTIPLIERS', array([ -10039.86591697,   13736.35015675,  -29915.69836655,
         58324.13552384,  -59021.06171096,  119306.12513476,
        -15231.66211861,   32123.70215388,   67260.23631309,
        119673.31003308,   86796.00649573, -186619.0525651 ]))
('Chem pot progress', array([ 211969.66886443,  187514.23178945,  159919.72205784,
       -123464.60178055]))
('Energy progress', 64719.828339008818)
('Driving force', 6907.3899657838556)
('obj weight', 1.0)
('NEW_L_MULTIPLIERS', array([  1.00000000e+16,   1.00000000e+16,   1.00000000e+16,
         1.00000000e+16,  -1.00000000e+16,  -1.00000000e+16,
         1.00000000e+16,   1.00000000e+16,   1.00000000e+16,
         1.00000000e+16,   1.00000000e+16,  -1.00000000e+16]))
('Chem pot progress', array([  1.00000000e+16,   1.00000000e+16,   1.00000000e+16,
        -1.00000000e+16]))
('Energy progress', -447847.42265450658)
('Driving force', 30000000000468716.0)
('obj weight', 1.0)
('NEW_L_MULTIPLIERS', array([ -1.00000000e+16,  -1.00000000e+16,  -1.00000000e+16,
        -1.00000000e+16,  -1.00000000e+16,  -1.00000000e+16,
         1.00000000e+16,   1.00000000e+16,   1.00000000e+16,
        -1.00000000e+16,  -1.00000000e+16,   1.00000000e+16]))
('Chem pot progress', array([  0.00000000e+00,  -2.00000000e+16,  -2.00000000e+16,
         2.00000000e+16]))
('Energy progress', 342985.44283996138)
('Driving force', -9999999999874270.0)
('obj weight', 1.0)
('NEW_L_MULTIPLIERS', array([ -1.85347974e+04,   1.91389359e+05,  -5.37258913e+03,
        -2.31065562e+04,   4.13718864e+09,   3.06312941e+04,
         1.55647440e+15,  -1.24866372e+05]))
('Chem pot progress', array([ -9.99999586e+15,   1.00000000e+16,   1.15564744e+16,
        -1.00000000e+16]))
('Energy progress', 86560.305401504098)
('Driving force', 311294520446584.25)
('obj weight', 1.0)
('NEW_L_MULTIPLIERS', array([ -1.00000000e+16,  -1.00000000e+16,  -1.00000000e+16,
        -1.00000000e+16,   1.00000000e+16,   1.00000000e+16,
         1.00000000e+16,  -1.00000000e+16]))
('Chem pot progress', array([  9.99999586e+15,   1.00000000e+16,   8.44352560e+15,
        -1.00000000e+16]))
('Energy progress', -14885.39540228391)
('Driving force', 64054.646595575861)
('obj weight', 1.0)
('NEW_L_MULTIPLIERS', array([ -8.30119680e+15,   8.30119680e+15,   9.33884640e+15,
         1.00000000e+16,   8.30119680e+15,  -8.30119680e+15]))
('Chem pot progress', array([ -6.61153600e+14,   0.00000000e+00,  -1.69880320e+15,
         1.69880320e+15]))
('Energy progress', 32166.352239676773)
('Driving force', 793388464001608.62)
('obj weight', 1.0)
('NEW_L_MULTIPLIERS', array([  1.00000000e+16,   1.00000000e+16,   1.00000000e+16,
         1.00000000e+16,   1.00000000e+16,  -1.00000000e+16]))
('Chem pot progress', array([  6.61153600e+14,   0.00000000e+00,   1.69880320e+15,
        -1.69880320e+15]))
('Energy progress', -1953.6334963283134)
('Driving force', 868858800786577.12)
('obj weight', 1.0)
('NEW_L_MULTIPLIERS', array([  1.00000000e+16,   1.00000000e+16,   1.00000000e+16,
         1.00000000e+16,   1.00000000e+16,  -1.00000000e+16]))
('Chem pot progress', array([ 0.,  0.,  0.,  0.]))
('Energy progress', 408.03961188466747)
('Driving force', 749725549839085.0)
('obj weight', 1.0)
('NEW_L_MULTIPLIERS', array([  1.00000000e+16,   1.00000000e+16,  -1.00000000e+16,
        -1.00000000e+16,  -1.00000000e+16,   1.00000000e+16]))
('Chem pot progress', array([ -2.00000000e+16,  -2.00000000e+16,  -2.00000000e+16,
         2.00000000e+16]))
('Energy progress', 122.4553715516904)
('Driving force', -696997339821186.62)
('obj weight', 1.0)
...
...
...
('NEW_L_MULTIPLIERS', array([ -1.00000000e+16,  -1.00000000e+16,  -1.00000000e+16,
         1.00000000e+16,   1.00000000e+16,  -1.00000000e+16]))
('Chem pot progress', array([ -2.00000000e+10,   2.00000000e+10,   2.00000000e+10,
        -2.00000000e+10]))
('Energy progress', 0.0)
('Driving force', 184980324.67978525)
('obj weight', 1000000.0)
('NEW_L_MULTIPLIERS', array([  1.00000000e+16,   1.00000000e+16,   1.00000000e+16,
        -1.00000000e+16,  -1.00000000e+16,   1.00000000e+16]))
('Chem pot progress', array([  2.00000000e+10,  -2.00000000e+10,  -2.00000000e+10,
         2.00000000e+10]))
('Energy progress', 0.0)
('Driving force', -184953760.74483824)
('obj weight', 1000000.0)
('NEW_L_MULTIPLIERS', array([ -1.00000000e+16,  -1.00000000e+16,  -1.00000000e+16,
         1.00000000e+16,   1.00000000e+16,  -1.00000000e+16]))
('Chem pot progress', array([ -2.00000000e+10,   2.00000000e+10,   2.00000000e+10,
        -2.00000000e+10]))
('Energy progress', 0.0)
('Driving force', 184980324.67978525)
('obj weight', 1000000.0)
('NEW_L_MULTIPLIERS', array([  1.00000000e+16,   1.00000000e+16,   1.00000000e+16,
        -1.00000000e+16,  -1.00000000e+16,   1.00000000e+16]))
('Chem pot progress', array([  2.00000000e+10,  -2.00000000e+10,  -2.00000000e+10,
         2.00000000e+10]))
('Energy progress', 0.0)
('Driving force', -184953760.74483824)
('obj weight', 1000000.0)
('NEW_L_MULTIPLIERS', array([ -1.00000000e+16,  -1.00000000e+16,  -1.00000000e+16,
         1.00000000e+16,   1.00000000e+16,  -1.00000000e+16]))
('Chem pot progress', array([ -2.00000000e+10,   2.00000000e+10,   2.00000000e+10,
        -2.00000000e+10]))
('Energy progress', 0.0)
('Driving force', 184980324.67978525)
('obj weight', 1000000.0)
('NEW_L_MULTIPLIERS', array([  1.00000000e+16,   1.00000000e+16,   1.00000000e+16,
        -1.00000000e+16,  -1.00000000e+16,   1.00000000e+16]))
('Chem pot progress', array([  2.00000000e+10,  -2.00000000e+10,  -2.00000000e+10,
         2.00000000e+10]))
('Energy progress', 0.0)
('Driving force', -184953760.74483824)
('obj weight', 1000000.0)
('NEW_L_MULTIPLIERS', array([ -1.00000000e+16,  -1.00000000e+16,  -1.00000000e+16,
         1.00000000e+16,   1.00000000e+16,  -1.00000000e+16]))
('Chem pot progress', array([ -2.00000000e+10,   2.00000000e+10,   2.00000000e+10,
        -2.00000000e+10]))
('Energy progress', 0.0)
('Driving force', 184980324.67978525)
('obj weight', 1000000.0)
Failed to converge: OrderedDict([('P', array(101325.0)), ('T', array(1248.0)), ('X_AL', array(0.1)), ('X_CR', array(0.1)), ('X_W', array(0.1))])
Out[3]:
<xarray.Dataset>
Dimensions:       (P: 1, T: 1, X_AL: 1, X_CR: 1, X_W: 1, component: 4, internal_dof: 9, vertex: 4)
Coordinates:
  * X_CR          (X_CR) float64 0.1
  * P             (P) float64 1.013e+05
  * X_AL          (X_AL) float64 0.1
  * vertex        (vertex) int64 0 1 2 3
  * X_W           (X_W) float64 0.1
  * component     (component) <U2 'AL' 'CO' 'CR' 'W'
  * T             (T) float64 1.248e+03
  * internal_dof  (internal_dof) int64 0 1 2 3 4 5 6 7 8
Data variables:
    X             (P, T, X_AL, X_CR, X_W, vertex, component) float64 nan nan ...
    Y             (P, T, X_AL, X_CR, X_W, vertex, internal_dof) float64 nan ...
    GM            (P, T, X_AL, X_CR, X_W) float64 nan
    NP            (P, T, X_AL, X_CR, X_W, vertex) float64 nan nan nan nan
    MU            (P, T, X_AL, X_CR, X_W, component) float64 nan nan nan nan
    Phase         (P, T, X_AL, X_CR, X_W, vertex) <U6 '' '' '' ''
Attributes:
    engine: pycalphad 0.4.2+93.gad385a0.dirty
    hull_iterations: 1
    solve_iterations: 300
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bocklund commented Jan 7, 2017

import pycalphad.variables as v
phases = ['FCC', 'L12']
components = ["AL", "CO", "CR", "W", "VA"]
conditions = {"T": 1248, "P":101325, v.X("AL"):0.081, v.X("CR"): 0.020, v.X("W"):0.094}
equilibrium(dbf, components, phases, conditions, _diagnostic=True, verbose=True)

Results in:

Is the Reset p_z due to singular matrix contributing to this?

Calculation Backend: Compiled (autowrap)
Components: AL CO CR VA W
Phases: FCC L12 [done]
('NEW_L_MULTIPLIERS', array([ -16320.58819977,   19764.95377284,  -55684.13516122,
         74110.49657867,  -56631.11062394,  110420.00848496,
        -13980.66179765,     299.7036293 ,   45644.54023309,
         85166.89982361,  154977.18724234,  114624.76184827,
       -211728.01003363]))
('Chem pot progress', array([ 239343.70356815,  219793.72535814,  214169.41158258,
       -144460.33720764]))
('Energy progress', 59077.910976714731)
('Driving force', 7369.0024694008243)
('obj weight', 1.0)
('NEW_L_MULTIPLIERS', array([ -1.00000000e+16,  -1.00000000e+16,  -1.00000000e+16,
        -1.00000000e+16,  -1.00000000e+16,  -1.00000000e+16,
        -1.00000000e+16,  -1.00000000e+16,  -1.00000000e+16,
         1.00000000e+16,   1.00000000e+16,  -1.00000000e+16,
        -1.00000000e+16]))
('Chem pot progress', array([  1.00000000e+16,   1.00000000e+16,  -1.00000000e+16,
        -1.00000000e+16]))
('Energy progress', -679120.01108766976)
('Driving force', -19999999999286976.0)
('obj weight', 1.0)
('NEW_L_MULTIPLIERS', array([ -1.00000000e+16,  -1.00000000e+16,   1.00000000e+16,
         1.00000000e+16,   1.00000000e+16,   1.00000000e+16,
         1.00000000e+16,   1.00000000e+16,   1.00000000e+16,
         1.00000000e+16,   1.00000000e+16,   1.00000000e+16,
        -1.00000000e+16]))
('Chem pot progress', array([  0.00000000e+00,   0.00000000e+00,   2.00000000e+16,
         0.00000000e+00]))
('Energy progress', 519852.68938627455)
('Driving force', 2500000000210669.0)
('obj weight', 1.0)
('NEW_L_MULTIPLIERS', array([  1.44791462e+00,   5.73336116e+00,  -3.10438890e+04,
        -4.48029889e+04,   1.67536485e+04,   9.56529953e+02,
         1.14587542e+05,   1.06735191e+05,  -1.14206199e+04,
        -2.92918619e+04,  -5.56281084e+04]))
('Chem pot progress', array([ -1.00000000e+16,  -1.00000000e+16,  -1.00000000e+16,
         1.00000000e+16]))
('Energy progress', 124895.4447652001)
('Driving force', -3928.5696828584769)
('obj weight', 1.0)
('NEW_L_MULTIPLIERS', array([ -1.00000000e+16,  -1.00000000e+16,   1.00000000e+16,
         1.00000000e+16,  -1.00000000e+16,  -1.00000000e+16,
        -1.00000000e+16,   1.00000000e+16,   1.00000000e+16,
        -1.00000000e+16,   1.00000000e+16]))
('Chem pot progress', array([  1.00000000e+16,   1.00000000e+16,  -1.00000000e+16,
         1.00000000e+16]))
('Energy progress', -27407.435436476284)
('Driving force', 16332896032455566.0)
('obj weight', 1.0)
('NEW_L_MULTIPLIERS', array([ -1.00000000e+16,  -1.00000000e+16,  -1.00000000e+16,
        -1.00000000e+16,   1.00000000e+16,   1.00000000e+16,
         1.00000000e+16,  -1.00000000e+16,  -1.00000000e+16,
        -1.00000000e+16,   1.00000000e+16]))
('Chem pot progress', array([ -2.00000000e+16,  -2.00000000e+16,   0.00000000e+00,
         0.00000000e+00]))
('Energy progress', 31626.443327239635)
('Driving force', 24052.646595575854)
('obj weight', 1.0)
('NEW_L_MULTIPLIERS', array([  1.00000000e+16,   1.00000000e+16,  -1.00000000e+16,
        -1.00000000e+16,   1.00000000e+16,   1.00000000e+16,
         1.00000000e+16,   1.00000000e+16,   1.00000000e+16,
        -1.00000000e+16,   1.00000000e+16]))
('Chem pot progress', array([  2.00000000e+16,   2.00000000e+16,   0.00000000e+00,
         0.00000000e+00]))
('Energy progress', -17948.212347695029)
('Driving force', 20000000000062004.0)
('obj weight', 1.0)
('NEW_L_MULTIPLIERS', array([  1.00000000e+16,   1.00000000e+16,  -1.00000000e+16,
        -1.00000000e+16,   1.00000000e+16,   1.00000000e+16,
         1.00000000e+16,   1.00000000e+16,  -1.00000000e+16,
        -1.00000000e+16,   1.00000000e+16]))
('Chem pot progress', array([  0.00000000e+00,  -2.00000000e+16,   0.00000000e+00,
         0.00000000e+00]))
('Energy progress', -78741.218290388395)
('Driving force', 10000000000130744.0)
('obj weight', 1.0)
('NEW_L_MULTIPLIERS', array([  1.00000000e+16,   1.00000000e+16,   1.00000000e+16,
         1.00000000e+16,   1.00000000e+16,   1.00000000e+16,
         1.00000000e+16,   1.00000000e+16,  -1.00000000e+16,
        -1.00000000e+16,  -1.00000000e+16]))
('Chem pot progress', array([  0.00000000e+00,   0.00000000e+00,   0.00000000e+00,
        -2.00000000e+16]))
('Energy progress', 25515.999069631012)
('Driving force', -29999999999874772.0)
('obj weight', 1.0)
Reset p_z due to singular matrix
('NEW_L_MULTIPLIERS', array([  1.00000000e+16,   1.00000000e+16,   1.00000000e+16,
         1.00000000e+16,   1.00000000e+16,   1.00000000e+16,
         1.00000000e+16,   1.00000000e+16,   1.00000000e+16,
         1.00000000e+16,  -1.00000000e+16]))
('Chem pot progress', array([  0.00000000e+00,   2.00000000e+16,   2.00000000e+16,
         0.00000000e+00]))
('Energy progress', -4980.3116286194709)
('Driving force', 6442666425443647.0)
('obj weight', 1.0)
('NEW_L_MULTIPLIERS', array([ -1.00000000e+16,  -1.00000000e+16,   1.00000000e+16,
         1.00000000e+16,  -1.00000000e+16,  -1.00000000e+16,
        -1.00000000e+16,  -1.00000000e+16,   1.00000000e+16,
         1.00000000e+16,  -1.00000000e+16]))
('Chem pot progress', array([ -2.00000000e+16,   0.00000000e+00,   0.00000000e+00,
         0.00000000e+00]))
('Energy progress', -277265.63463890209)
('Driving force', 397474.02443154983)
('obj weight', 1.0)
('NEW_L_MULTIPLIERS', array([  1.00000000e+16,   1.00000000e+16,  -1.00000000e+16,
        -1.00000000e+16,   1.00000000e+16,   1.00000000e+16,
         1.00000000e+16,  -1.00000000e+16,  -1.00000000e+16,
        -1.00000000e+16,   1.00000000e+16]))
('Chem pot progress', array([  0.00000000e+00,  -2.00000000e+16,  -2.00000000e+16,
         2.00000000e+16]))
('Energy progress', -48407.523686925764)
('Driving force', -27499999999566616.0)
('obj weight', 1.0)
('NEW_L_MULTIPLIERS', array([  1.00000000e+16,   1.00000000e+16,  -1.00000000e+16,
        -1.00000000e+16,  -1.00000000e+16,  -1.00000000e+16,
        -1.00000000e+16,  -1.00000000e+16,   1.00000000e+16,
        -1.00000000e+16,   1.00000000e+16]))
('Chem pot progress', array([  0.00000000e+00,   2.00000000e+16,   0.00000000e+00,
         0.00000000e+00]))
('Energy progress', 247493.39953132375)
('Driving force', 10000000000188388.0)
('obj weight', 1.0)
('NEW_L_MULTIPLIERS', array([ -6.41523452e+15,   7.48444027e+15,  -1.16095993e+04,
         1.18019747e+04,   9.05771196e+04,   6.41523452e+15,
         6.41523452e+15,   1.00000000e+16,  -7.48444027e+15]))
('Chem pot progress', array([  1.64152345e+16,  -3.58476548e+15,   2.00000000e+16,
        -1.74844403e+16]))
('Energy progress', 81447.782545792186)
('Driving force', 3921186629956887.5)
('obj weight', 1.0)
Reset p_z due to singular matrix
('NEW_L_MULTIPLIERS', array([  1.00000000e+16,   1.00000000e+16,  -1.00000000e+16,
        -1.00000000e+16,  -1.00000000e+16,  -1.00000000e+16,
         1.00000000e+16,  -1.00000000e+16,   1.00000000e+16]))
('Chem pot progress', array([ -1.64152345e+16,   3.58476548e+15,  -2.00000000e+16,
         1.74844403e+16]))
('Energy progress', 40612.797036933669)
('Driving force', 11977016237456360.0)
('obj weight', 1.0)
('NEW_L_MULTIPLIERS', array([  1.00000000e+16,   1.00000000e+16,   1.00000000e+16,
         1.00000000e+16,   1.00000000e+16,  -1.00000000e+16,
        -1.00000000e+16,   1.00000000e+16,  -1.00000000e+16]))
('Chem pot progress', array([  0.00000000e+00,  -2.00000000e+16,   2.00000000e+16,
        -2.00000000e+16]))
('Energy progress', -62214.383062406472)
('Driving force', -24881147840035432.0)
('obj weight', 1.0)
Reset p_z due to singular matrix
('NEW_L_MULTIPLIERS', array([  1.00000000e+16,   1.00000000e+16,   1.00000000e+16,
         1.00000000e+16,   1.00000000e+16,  -1.00000000e+16,
         1.00000000e+16,   1.00000000e+16,   1.00000000e+16]))
('Chem pot progress', array([  0.00000000e+00,   2.00000000e+16,   0.00000000e+00,
         2.00000000e+16]))
('Energy progress', 106137.98778894162)
('Driving force', 7264888408267814.0)
('obj weight', 1.0)
('NEW_L_MULTIPLIERS', array([ -1.00000000e+16,  -1.00000000e+16,   1.00000000e+16,
         1.00000000e+16,   1.00000000e+16,   1.00000000e+16,
        -1.00000000e+16,   1.00000000e+16,  -1.00000000e+16]))
('Chem pot progress', array([  2.00000000e+16,  -2.00000000e+16,   0.00000000e+00,
        -2.00000000e+16]))
('Energy progress', -30114.169740083773)
('Driving force', -2100352652459538.5)
('obj weight', 1.0)
('NEW_L_MULTIPLIERS', array([ -1.00000000e+16,  -1.00000000e+16,   1.00000000e+16,
         1.00000000e+16,   1.00000000e+16,   1.00000000e+16,
        -1.00000000e+16,  -1.00000000e+16,   1.00000000e+16]))
('Chem pot progress', array([  0.00000000e+00,   0.00000000e+00,  -2.00000000e+16,
         2.00000000e+16]))
('Energy progress', -78225.943215684674)
('Driving force', 10000000000130744.0)
('obj weight', 1.0)
Reset p_z due to singular matrix
('NEW_L_MULTIPLIERS', array([ -1.00000000e+16,  -1.00000000e+16,  -1.00000000e+16,
        -1.00000000e+16,  -1.00000000e+16,  -1.00000000e+16,
         1.00000000e+16,  -1.00000000e+16,   1.00000000e+16]))
('Chem pot progress', array([ -2.00000000e+16,   2.00000000e+16,   0.00000000e+00,
         0.00000000e+00]))
('Energy progress', 88865.868812334505)
('Driving force', 2566611604332015.0)
('obj weight', 1.0)
Reset p_z due to singular matrix
('NEW_L_MULTIPLIERS', array([ -1.00000000e+16,  -1.00000000e+16,  -1.00000000e+16,
        -1.00000000e+16,  -1.00000000e+16,   1.00000000e+16,
        -1.00000000e+16,   1.00000000e+16,  -1.00000000e+16]))
('Chem pot progress', array([  2.00000000e+16,  -2.00000000e+16,   2.00000000e+16,
        -2.00000000e+16]))
('Energy progress', -32952.230058132409)
('Driving force', -9412083178367970.0)
('obj weight', 1.0)
Increasing objective weight
('NEW_L_MULTIPLIERS', array([  1.00000000e+16,   1.00000000e+16,  -1.00000000e+16,
        -1.00000000e+16,  -1.00000000e+16,   1.00000000e+16,
        -1.00000000e+16,  -1.00000000e+16,   1.00000000e+16]))
('Chem pot progress', array([ -9.00000000e+15,   9.00000000e+15,  -1.10000000e+16,
         1.10000000e+16]))
('Energy progress', 40567.367631031128)
('Driving force', 182753047585158.19)
('obj weight', 10.0)
('NEW_L_MULTIPLIERS', array([  1.00000000e+16,   1.00000000e+16,   1.00000000e+16,
         1.00000000e+16,   1.00000000e+16,   1.00000000e+16,
         1.00000000e+16,   1.00000000e+16,  -1.00000000e+16]))
('Chem pot progress', array([  0.00000000e+00,   2.00000000e+15,   2.00000000e+15,
        -2.00000000e+15]))
('Energy progress', 44263.070848426054)
('Driving force', 0.0)
('obj weight', 10.0)
Invalid l_hessian
/Users/brandon/anaconda3/envs/espei/lib/python3.5/site-packages/dask/async.py:249: RuntimeWarning: invalid value encountered in less
  return func(*args2)
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
<ipython-input-4-2b5629a28dd6> in <module>()
      1 conditions = {"T": 1248, "P":101325, v.X("AL"):0.081, v.X("CR"): 0.020, v.X("W"):0.094}
----> 2 equilibrium(dbf, components, phases, conditions, _diagnostic=True, verbose=True)

/Users/brandon/Projects/pycalphad/pycalphad/core/equilibrium.py in equilibrium(dbf, comps, phases, conditions, output, model, verbose, broadcast, calc_opts, scheduler, parameters, **kwargs)
    356     delayed(properties.attrs.__setitem__, pure=False)('created', datetime.utcnow())
    357     if scheduler is not None:
--> 358         properties = dask.compute(properties, get=scheduler)[0]
    359     return properties

/Users/brandon/anaconda3/envs/espei/lib/python3.5/site-packages/dask/base.py in compute(*args, **kwargs)
    176         dsk = merge(var.dask for var in variables)
    177     keys = [var._keys() for var in variables]
--> 178     results = get(dsk, keys, **kwargs)
    179 
    180     results_iter = iter(results)

/Users/brandon/anaconda3/envs/espei/lib/python3.5/site-packages/dask/async.py in get_sync(dsk, keys, **kwargs)
    548     kwargs.pop('num_workers', None)    # if num_workers present, remove it
    549     return get_async(apply_sync, 1, dsk, keys,
--> 550                      raise_on_exception=True, **kwargs)
    551 
    552 

/Users/brandon/anaconda3/envs/espei/lib/python3.5/site-packages/dask/async.py in get_async(apply_async, num_workers, dsk, result, cache, get_id, raise_on_exception, rerun_exceptions_locally, callbacks, dumps, loads, **kwargs)
    507 
    508             while state['ready'] and len(state['running']) < num_workers:
--> 509                 fire_task()
    510 
    511     except KeyboardInterrupt:

/Users/brandon/anaconda3/envs/espei/lib/python3.5/site-packages/dask/async.py in fire_task()
    474                         args=(key, dumps((dsk[key], data)),
    475                               dumps, loads, get_id, raise_on_exception),
--> 476                         callback=queue.put)
    477 
    478         # Seed initial tasks into the thread pool

/Users/brandon/anaconda3/envs/espei/lib/python3.5/site-packages/dask/async.py in apply_sync(func, args, kwds, callback)
    536 def apply_sync(func, args=(), kwds={}, callback=None):
    537     """ A naive synchronous version of apply_async """
--> 538     res = func(*args, **kwds)
    539     if callback is not None:
    540         callback(res)

/Users/brandon/anaconda3/envs/espei/lib/python3.5/site-packages/dask/async.py in execute_task(key, task_info, dumps, loads, get_id, raise_on_exception)
    266     try:
    267         task, data = loads(task_info)
--> 268         result = _execute_task(task, data)
    269         id = get_id()
    270         result = dumps((result, None, id))

/Users/brandon/anaconda3/envs/espei/lib/python3.5/site-packages/dask/async.py in _execute_task(arg, cache, dsk)
    247         func, args = arg[0], arg[1:]
    248         args2 = [_execute_task(a, cache) for a in args]
--> 249         return func(*args2)
    250     elif not ishashable(arg):
    251         return arg

/Users/brandon/Projects/pycalphad/pycalphad/core/eqsolver.pyx in pycalphad.core.eqsolver._solve_eq_at_conditions (pycalphad/core/eqsolver.c:14195)()

ValueError: Invalid gradient_term
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