Exact Hessians with SymEngine lambda backend #249

richardotis · 2019-10-28T15:15:52Z

Fixes gh-235.

… for performance reasons

…bstract LLVM versus Lambda backends

…garbage collection

…prevent garbage collection" This reverts commit 0d3c9c0.

…conditions, for now

bocklund · 2019-10-28T19:30:13Z

I have found some odd behavior when different sets of parameters are provided:

tdb = """$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$ Date: 2018-12-18 11:03
$ Components: CU, MG, VA
$ Phases: CUMG2, FCC_A1, HCP_A3, LAVES_C15, LIQUID
$ Generated by brandon (pycalphad 0.7.1.post2)
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$

ELEMENT CU BLANK 0 0 0 !
ELEMENT MG BLANK 0 0 0 !
ELEMENT VA BLANK 0 0 0 !


FUNCTION GFCCCU 1.0 GHSERCU#; 10000.0 N !
FUNCTION GFCCMG 0.01 -2.18283562784578E-6*T**3 - 6.21802726222479E-5*T**2 +
   3.2404446864*T*LN(EXP(95.82831*T**(-1)) - 1.0) +
   21.6535319868*T*LN(EXP(247.8675*T**(-1)) - 1.0) + 0.246565697987779*T -
   8158.16393259455; 298.15 Y -1.393669E-6*T**3 + 0.0004858*T**2 -
   26.1849782*T*LN(T) + 142.775547*T - 5767.34 + 78950*T**(-1);
   922.205302616508 Y -34.3088*T*LN(T) + 203.816215*T - 11530.1836392866 +
   1.038192E+28*T**(-9); 3000.0 N !
FUNCTION GHCPCU 0.01 -3.38438862938597E-7*T**3 - 0.00121182291077191*T**2 +
   8.7685671186*T*LN(EXP(155.1404*T**(-1)) - 1.0) +
   16.1968683846*T*LN(EXP(290.9421*T**(-1)) - 1.0) - 0.321147237334052*T -
   10441.4393392344; 298.15 Y 1.29223E-7*T**3 - 0.00265684*T**2 -
   24.112392*T*LN(T) + 130.685235*T - 7170.458 + 52478*T**(-1); 1357.77 Y
   -31.38*T*LN(T) + 184.003828*T - 12942.0252504739 + 3.64167E+29*T**(-9);
   3200.0 N !
FUNCTION GHCPMG 1.0 GHSERMG#; 10000.0 N !
FUNCTION GHSERCU 0.01 -0.0010514335*T**2 +
   8.7685671186*T*LN(EXP(155.1404*T**(-1)) - 1.0) +
   16.1968683846*T*LN(EXP(290.9421*T**(-1)) - 1.0) - 11038.0904080745;
   103.57591 Y -2.15621953171362E-6*T**3 + 0.000288560900942072*T**2 -
   0.13879113947248*T*LN(T) + 8.7685671186*T*LN(EXP(155.1404*T**(-1)) - 1.0)
   + 16.1968683846*T*LN(EXP(290.9421*T**(-1)) - 1.0) + 0.574637617323048*T -
   11042.8822142647; 210.33309 Y -0.002432585*T**2 + 0.4335558862135*T*LN(T)
   + 8.7685671186*T*LN(EXP(155.1404*T**(-1)) - 1.0) +
   16.1968683846*T*LN(EXP(290.9421*T**(-1)) - 1.0) - 2.20049706600083*T -
   11002.7543747764; 1357.77 Y -31.38*T*LN(T) + 183.555483717662*T -
   12730.2995781851 + 7.42232714807953E+28*T**(-9); 3200.0 N !
FUNCTION GHSERMG 0.01 0.0047195465*T**2 +
   3.2404446864*T*LN(EXP(95.82831*T**(-1)) - 1.0) +
   21.6535319868*T*LN(EXP(247.8675*T**(-1)) - 1.0) - 10652.1012810789;
   36.71926 Y -1.53643054262276E-5*T**3 + 0.00810454205399037*T**2 -
   0.124294531845816*T*LN(T) + 3.2404446864*T*LN(EXP(95.82831*T**(-1)) - 1.0)
   + 21.6535319868*T*LN(EXP(247.8675*T**(-1)) - 1.0) + 0.385723396310737*T -
   10653.6226154894; 143.18844 Y -0.0050954035*T**2 + 1.765785080115*T*LN(T)
   + 3.2404446864*T*LN(EXP(95.82831*T**(-1)) - 1.0) +
   21.6535319868*T*LN(EXP(247.8675*T**(-1)) - 1.0) - 8.0518972866125*T -
   10563.4100984519; 922.205302616508 Y -34.3088*T*LN(T) + 204.341485347575*T
   - 13775.4156328263 + 9.4687256586798E+27*T**(-9); 10000.0 N !
FUNCTION GHSERVA 1 0; 10000 N !
FUNCTION GLIQCU 0.01 -3.40056501515466E-7*T**3 - 0.00121066539331185*T**2 +
   8.7685671186*T*LN(EXP(155.1404*T**(-1)) - 1.0) +
   16.1968683846*T*LN(EXP(290.9421*T**(-1)) - 1.0) - 10.033338832193*T +
   2379.36422209194; 298.15 Y -5.8489E-21*T**7 + 1.29223E-7*T**3 -
   0.00265684*T**2 - 24.112392*T*LN(T) + 120.973331*T + 5650.32106235287 +
   52478*T**(-1); 1357.77 Y -31.38*T*LN(T) + 173.881484*T + 409.498458129716;
   3200.0 N !
FUNCTION GLIQMG 0.01 -2.2050100179942E-6*T**3 - 4.63131660076452E-5*T**2 +
   3.2404446864*T*LN(EXP(95.82831*T**(-1)) - 1.0) +
   21.6535319868*T*LN(EXP(247.8675*T**(-1)) - 1.0) - 7.6943066168765*T -
   2555.58510336379; 298.15 Y -8.0176E-20*T**7 - 1.393669E-6*T**3 +
   0.0004858*T**2 - 26.1849782*T*LN(T) + 134.838617*T - 165.096999676889 +
   78950*T**(-1); 922.205302616508 Y -34.3088*T*LN(T) + 195.324057*T -
   5439.86911093575; 10000.0 N !
FUNCTION VV0000 1 -32539.5; 10000 N !
FUNCTION VV0001 1 8236.3; 10000 N !
FUNCTION VV0002 1 -14675.0; 10000 N !
FUNCTION VV0003 1 -24441.2; 10000 N !
FUNCTION VV0004 1 20149.6; 10000 N !
FUNCTION VV0005 1 46500.0; 10000 N !
FUNCTION VV0006 1 -39591.3; 10000 N !
FUNCTION VV0007 1 104160.0; 10000 N !
FUNCTION VV0008 1 21000.0; 10000 N !
FUNCTION VV0009 1 17772.0; 10000 N !
FUNCTION VV0010 1 21240.0; 10000 N !
FUNCTION VV0011 1 14321.1; 10000 N !
FUNCTION VV0012 1 -4923.18; 10000 N !
FUNCTION VV0013 1 -1962.8; 10000 N !
FUNCTION VV0014 1 -31626.6; 10000 N !

TYPE_DEFINITION % SEQ * !
DEFINE_SYSTEM_DEFAULT ELEMENT 2 !
DEFAULT_COMMAND DEFINE_SYSTEM_ELEMENT VA !

PHASE CUMG2 %  2 1 2 !
CONSTITUENT CUMG2 :CU:MG: !

PHASE FCC_A1 %  1 1 !
CONSTITUENT FCC_A1 :CU,MG: !

PHASE HCP_A3 %  1 1 !
CONSTITUENT HCP_A3 :CU,MG: !

PHASE LAVES_C15 %  2 2 1 !
CONSTITUENT LAVES_C15 :CU,MG:CU,MG: !

PHASE LIQUID %  1 1 !
CONSTITUENT LIQUID :CU,MG: !



$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$                                     CU                                     $
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$

PARAMETER G(FCC_A1,CU;0) 1 GFCCCU#; 10000 N !
PARAMETER G(HCP_A3,CU;0) 1 GHCPCU#; 10000 N !
PARAMETER G(LAVES_C15,CU:CU;0) 1 3*GHSERCU# + VV0005#; 10000 N !
PARAMETER G(LIQUID,CU;0) 1 GLIQCU#; 10000 N !


$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$                                     MG                                     $
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$

PARAMETER G(FCC_A1,MG;0) 1 GFCCMG#; 10000 N !
PARAMETER G(HCP_A3,MG;0) 1 GHCPMG#; 10000 N !
PARAMETER G(LAVES_C15,MG:MG;0) 1 3*GHSERMG# + VV0008#; 10000 N !
PARAMETER G(LIQUID,MG;0) 1 GLIQMG#; 10000 N !


$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$                                   CU-MG                                    $
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$

PARAMETER G(CUMG2,CU:MG;0) 1 GHSERCU# + 2*GHSERMG# + VV0000#; 10000 N !
PARAMETER L(FCC_A1,CU,MG;0) 1 VV0002#; 10000 N !
PARAMETER L(FCC_A1,CU,MG;1) 1 VV0001#; 10000 N !
PARAMETER L(HCP_A3,CU,MG;0) 1 VV0004#; 10000 N !
PARAMETER L(HCP_A3,CU,MG;1) 1 VV0003#; 10000 N !
PARAMETER G(LAVES_C15,CU:MG;0) 1 2*GHSERCU# + GHSERMG# + VV0006#; 10000 N !
PARAMETER G(LAVES_C15,MG:CU;0) 1 GHSERCU# + 2*GHSERMG# + VV0007#; 10000 N !
PARAMETER L(LAVES_C15,CU:CU,MG;0) 1 VV0009#; 10000 N !
PARAMETER L(LAVES_C15,CU,MG:MG;0) 1 VV0010#; 10000 N !
PARAMETER L(LIQUID,CU,MG;0) 1 VV0014#; 10000 N !
PARAMETER L(LIQUID,CU,MG;1) 1 VV0013#; 10000 N !
PARAMETER L(LIQUID,CU,MG;2) 1 VV0012#; 10000 N !
PARAMETER L(LIQUID,CU,MG;3) 1 VV0011#; 10000 N !
"""

from pycalphad import Database, equilibrium, variables as v, __version__ as pycalphad_version
print(f'pycalphad version: {pycalphad_version}')
dbf= Database(tdb)
comps = ['CU', 'MG']

parameters={'VV0000': -33134.699474175846, 'VV0001': 7734.114029426941, 'VV0002': -13498.542175596054, 'VV0003': -26555.048975092268, 'VV0004': 20777.637577083482, 'VV0005': 41915.70425630003, 'VV0006': -34525.21964215504, 'VV0007': 95457.14639216446, 'VV0008': 21139.578967453144, 'VV0009': 19047.833726419598, 'VV0010': 20468.91829601273, 'VV0011': 19601.617855958328, 'VV0012': -4546.9325861738, 'VV0013': -1640.6354331231278, 'VV0014': -35682.950005357634}
print('1 run: all parameters')
# I am getting "Status: -2 b"Restoration phase failed, algorithm doesn't know how to proceed.""
eq = equilibrium(dbf, comps, ['HCP_A3'], {v.X('CU'): 0.0001052, v.P: 101325.0, v.T: 743.15, v.N: 1}, parameters=parameters, verbose=True)
print('\n\n2 run: some parameters')
# I am getting "Status: -1 b'Maximum number of iterations exceeded (can be specified by an option).'"
eq = equilibrium(dbf, comps, ['HCP_A3'], {v.X('CU'): 0.0001052, v.P: 101325.0, v.T: 743.15, v.N: 1}, parameters={'VV0003': -26555.048975092268, 'VV0004': 20777.637577083482}, verbose=True)
print('\n\n3 run: parameters pre-subbed')
dbf.symbols.update(parameters)
# I am getting "Status: 0 b'Algorithm terminated successfully at a locally optimal point, satisfying the convergence tolerances (can be specified by options).'"
eq = equilibrium(dbf, comps, ['HCP_A3'], {v.X('CU'): 0.0001052, v.P: 101325.0, v.T: 743.15, v.N: 1}, verbose=True)

I get the output:

pycalphad version: 0.8+27.g19bf29a6
1 run: all parameters
<snip>
Status: -2 b"Restoration phase failed, algorithm doesn't know how to proceed."


2 run: some parameters
<snip>
Status: -1 b'Maximum number of iterations exceeded (can be specified by an option).'


3 run: parameters pre-subbed
<snip>
Status: 0 b'Algorithm terminated successfully at a locally optimal point, satisfying the convergence tolerances (can be specified by options).'

This is interesting because the HCP_A3 only has VV0003 and VV0004 parameters in it. VV0003 and VV0004 are the same across all versions, but something about having other parameters (or no parameters) passed is messing with the solution.

bocklund · 2019-10-28T19:51:32Z

Also, looks like the test failures on Travis's PR build are caused by NumPy Python 3 syntax for matrix multiplication (A @ B).

Based on our release cadence, I expect that this will be the last release where our upstream dependencies are officially supporting Python 2.

bocklund · 2019-10-28T21:06:23Z

I compared all the outputs of phase_record for a dof array corresponding to the starting point of the equilibrium calculations above. Prx1 and Prx2 have identical entries for VV0003 and VV0004, but different entries for other parameters. Since, VV0003 and VV0004 are the only parameters that show up in the Gibbs energy of HCP_A3, the phase records outputs should all be equal. This script confirms that they are, so something else must be causing the discrepancy in the different equilibrium calls (above). I'm thinking it could be either

My phase records are not built consistently with how equilibrium is building them (I believe they are, but my logic could use a second look)
Something happening in how Problem is putting together the outputs from the phase records with the two composition set starting point is off

Self contained MWE:

tdb = """$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$ Date: 2018-12-18 11:03
$ Components: CU, MG, VA
$ Phases: CUMG2, FCC_A1, HCP_A3, LAVES_C15, LIQUID
$ Generated by brandon (pycalphad 0.7.1.post2)
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$

ELEMENT CU BLANK 0 0 0 !
ELEMENT MG BLANK 0 0 0 !
ELEMENT VA BLANK 0 0 0 !


FUNCTION GFCCCU 1.0 GHSERCU#; 10000.0 N !
FUNCTION GFCCMG 0.01 -2.18283562784578E-6*T**3 - 6.21802726222479E-5*T**2 +
   3.2404446864*T*LN(EXP(95.82831*T**(-1)) - 1.0) +
   21.6535319868*T*LN(EXP(247.8675*T**(-1)) - 1.0) + 0.246565697987779*T -
   8158.16393259455; 298.15 Y -1.393669E-6*T**3 + 0.0004858*T**2 -
   26.1849782*T*LN(T) + 142.775547*T - 5767.34 + 78950*T**(-1);
   922.205302616508 Y -34.3088*T*LN(T) + 203.816215*T - 11530.1836392866 +
   1.038192E+28*T**(-9); 3000.0 N !
FUNCTION GHCPCU 0.01 -3.38438862938597E-7*T**3 - 0.00121182291077191*T**2 +
   8.7685671186*T*LN(EXP(155.1404*T**(-1)) - 1.0) +
   16.1968683846*T*LN(EXP(290.9421*T**(-1)) - 1.0) - 0.321147237334052*T -
   10441.4393392344; 298.15 Y 1.29223E-7*T**3 - 0.00265684*T**2 -
   24.112392*T*LN(T) + 130.685235*T - 7170.458 + 52478*T**(-1); 1357.77 Y
   -31.38*T*LN(T) + 184.003828*T - 12942.0252504739 + 3.64167E+29*T**(-9);
   3200.0 N !
FUNCTION GHCPMG 1.0 GHSERMG#; 10000.0 N !
FUNCTION GHSERCU 0.01 -0.0010514335*T**2 +
   8.7685671186*T*LN(EXP(155.1404*T**(-1)) - 1.0) +
   16.1968683846*T*LN(EXP(290.9421*T**(-1)) - 1.0) - 11038.0904080745;
   103.57591 Y -2.15621953171362E-6*T**3 + 0.000288560900942072*T**2 -
   0.13879113947248*T*LN(T) + 8.7685671186*T*LN(EXP(155.1404*T**(-1)) - 1.0)
   + 16.1968683846*T*LN(EXP(290.9421*T**(-1)) - 1.0) + 0.574637617323048*T -
   11042.8822142647; 210.33309 Y -0.002432585*T**2 + 0.4335558862135*T*LN(T)
   + 8.7685671186*T*LN(EXP(155.1404*T**(-1)) - 1.0) +
   16.1968683846*T*LN(EXP(290.9421*T**(-1)) - 1.0) - 2.20049706600083*T -
   11002.7543747764; 1357.77 Y -31.38*T*LN(T) + 183.555483717662*T -
   12730.2995781851 + 7.42232714807953E+28*T**(-9); 3200.0 N !
FUNCTION GHSERMG 0.01 0.0047195465*T**2 +
   3.2404446864*T*LN(EXP(95.82831*T**(-1)) - 1.0) +
   21.6535319868*T*LN(EXP(247.8675*T**(-1)) - 1.0) - 10652.1012810789;
   36.71926 Y -1.53643054262276E-5*T**3 + 0.00810454205399037*T**2 -
   0.124294531845816*T*LN(T) + 3.2404446864*T*LN(EXP(95.82831*T**(-1)) - 1.0)
   + 21.6535319868*T*LN(EXP(247.8675*T**(-1)) - 1.0) + 0.385723396310737*T -
   10653.6226154894; 143.18844 Y -0.0050954035*T**2 + 1.765785080115*T*LN(T)
   + 3.2404446864*T*LN(EXP(95.82831*T**(-1)) - 1.0) +
   21.6535319868*T*LN(EXP(247.8675*T**(-1)) - 1.0) - 8.0518972866125*T -
   10563.4100984519; 922.205302616508 Y -34.3088*T*LN(T) + 204.341485347575*T
   - 13775.4156328263 + 9.4687256586798E+27*T**(-9); 10000.0 N !
FUNCTION GHSERVA 1 0; 10000 N !
FUNCTION GLIQCU 0.01 -3.40056501515466E-7*T**3 - 0.00121066539331185*T**2 +
   8.7685671186*T*LN(EXP(155.1404*T**(-1)) - 1.0) +
   16.1968683846*T*LN(EXP(290.9421*T**(-1)) - 1.0) - 10.033338832193*T +
   2379.36422209194; 298.15 Y -5.8489E-21*T**7 + 1.29223E-7*T**3 -
   0.00265684*T**2 - 24.112392*T*LN(T) + 120.973331*T + 5650.32106235287 +
   52478*T**(-1); 1357.77 Y -31.38*T*LN(T) + 173.881484*T + 409.498458129716;
   3200.0 N !
FUNCTION GLIQMG 0.01 -2.2050100179942E-6*T**3 - 4.63131660076452E-5*T**2 +
   3.2404446864*T*LN(EXP(95.82831*T**(-1)) - 1.0) +
   21.6535319868*T*LN(EXP(247.8675*T**(-1)) - 1.0) - 7.6943066168765*T -
   2555.58510336379; 298.15 Y -8.0176E-20*T**7 - 1.393669E-6*T**3 +
   0.0004858*T**2 - 26.1849782*T*LN(T) + 134.838617*T - 165.096999676889 +
   78950*T**(-1); 922.205302616508 Y -34.3088*T*LN(T) + 195.324057*T -
   5439.86911093575; 10000.0 N !
FUNCTION VV0000 1 -32539.5; 10000 N !
FUNCTION VV0001 1 8236.3; 10000 N !
FUNCTION VV0002 1 -14675.0; 10000 N !
FUNCTION VV0003 1 -24441.2; 10000 N !
FUNCTION VV0004 1 20149.6; 10000 N !
FUNCTION VV0005 1 46500.0; 10000 N !
FUNCTION VV0006 1 -39591.3; 10000 N !
FUNCTION VV0007 1 104160.0; 10000 N !
FUNCTION VV0008 1 21000.0; 10000 N !
FUNCTION VV0009 1 17772.0; 10000 N !
FUNCTION VV0010 1 21240.0; 10000 N !
FUNCTION VV0011 1 14321.1; 10000 N !
FUNCTION VV0012 1 -4923.18; 10000 N !
FUNCTION VV0013 1 -1962.8; 10000 N !
FUNCTION VV0014 1 -31626.6; 10000 N !

TYPE_DEFINITION % SEQ * !
DEFINE_SYSTEM_DEFAULT ELEMENT 2 !
DEFAULT_COMMAND DEFINE_SYSTEM_ELEMENT VA !

PHASE CUMG2 %  2 1 2 !
CONSTITUENT CUMG2 :CU:MG: !

PHASE FCC_A1 %  1 1 !
CONSTITUENT FCC_A1 :CU,MG: !

PHASE HCP_A3 %  1 1 !
CONSTITUENT HCP_A3 :CU,MG: !

PHASE LAVES_C15 %  2 2 1 !
CONSTITUENT LAVES_C15 :CU,MG:CU,MG: !

PHASE LIQUID %  1 1 !
CONSTITUENT LIQUID :CU,MG: !



$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$                                     CU                                     $
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$

PARAMETER G(FCC_A1,CU;0) 1 GFCCCU#; 10000 N !
PARAMETER G(HCP_A3,CU;0) 1 GHCPCU#; 10000 N !
PARAMETER G(LAVES_C15,CU:CU;0) 1 3*GHSERCU# + VV0005#; 10000 N !
PARAMETER G(LIQUID,CU;0) 1 GLIQCU#; 10000 N !


$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$                                     MG                                     $
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$

PARAMETER G(FCC_A1,MG;0) 1 GFCCMG#; 10000 N !
PARAMETER G(HCP_A3,MG;0) 1 GHCPMG#; 10000 N !
PARAMETER G(LAVES_C15,MG:MG;0) 1 3*GHSERMG# + VV0008#; 10000 N !
PARAMETER G(LIQUID,MG;0) 1 GLIQMG#; 10000 N !


$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$                                   CU-MG                                    $
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$

PARAMETER G(CUMG2,CU:MG;0) 1 GHSERCU# + 2*GHSERMG# + VV0000#; 10000 N !
PARAMETER L(FCC_A1,CU,MG;0) 1 VV0002#; 10000 N !
PARAMETER L(FCC_A1,CU,MG;1) 1 VV0001#; 10000 N !
PARAMETER L(HCP_A3,CU,MG;0) 1 VV0004#; 10000 N !
PARAMETER L(HCP_A3,CU,MG;1) 1 VV0003#; 10000 N !
PARAMETER G(LAVES_C15,CU:MG;0) 1 2*GHSERCU# + GHSERMG# + VV0006#; 10000 N !
PARAMETER G(LAVES_C15,MG:CU;0) 1 GHSERCU# + 2*GHSERMG# + VV0007#; 10000 N !
PARAMETER L(LAVES_C15,CU:CU,MG;0) 1 VV0009#; 10000 N !
PARAMETER L(LAVES_C15,CU,MG:MG;0) 1 VV0010#; 10000 N !
PARAMETER L(LIQUID,CU,MG;0) 1 VV0014#; 10000 N !
PARAMETER L(LIQUID,CU,MG;1) 1 VV0013#; 10000 N !
PARAMETER L(LIQUID,CU,MG;2) 1 VV0012#; 10000 N !
PARAMETER L(LIQUID,CU,MG;3) 1 VV0011#; 10000 N !
"""


def calc_output(phase_rec, verbose=False):
    dof = np.array([1.0, 101325.0, 743.15, 0.79759519, 0.20240481])
    nspecies = len(phase_rec.components)
    wrt_size = len(phase_rec.state_variables) + phase_rec.phase_dof
    int_cons_size = phase_rec.num_internal_cons
    mp_cons_size = phase_rec.num_multiphase_cons

    # Placeholder arrays
    obj1 = np.zeros(1)
    grad1 = np.zeros(wrt_size)
    hess1 = np.zeros((wrt_size, wrt_size))
    mass_obj1 = np.zeros(1)
    mass_grad1 = np.zeros(wrt_size)
    mass_hess1 = np.zeros((wrt_size, wrt_size))
    internal_obj1 = np.zeros(int_cons_size)
    internal_grad1 = np.zeros((wrt_size, int_cons_size))
    internal_hess1 = np.zeros((wrt_size, wrt_size, int_cons_size))
    multiphase_obj1 = np.zeros(mp_cons_size)
    multiphase_grad1 = np.zeros((wrt_size + 1, mp_cons_size)) # + 1 because NP variable
    # Calculate
    ## Objectives
    if verbose:
      print("Objectives...", end=' ')
    phase_rec.obj(obj1, np.atleast_2d(dof))
    phase_rec.grad(grad1, dof)
    phase_rec.hess(hess1, dof)
    ## Mass
    if verbose:
      print("Mass...", end=' ')
    mass_obj1 =  np.array([(phase_rec.mass_obj(mass_obj1, np.atleast_2d(dof), i), copy.deepcopy(mass_obj1))[1] for i in range(nspecies)])
    mass_grad1 = np.array([(phase_rec.mass_grad(mass_grad1, dof, i), copy.copy(mass_grad1))[1] for i in range(nspecies)])
    mass_hess1 = np.array([(phase_rec.mass_hess(mass_hess1, dof, i), copy.copy(mass_hess1))[1] for i in range(nspecies)])
    ## Internal constraints
    if verbose:
      print("Internal constraints...", end=' ')
    phase_rec.internal_constraints(internal_obj1, dof)
    phase_rec.internal_jacobian(internal_grad1, dof)
    phase_rec.internal_cons_hessian(internal_hess1, dof)
    ## Multiphase constraints
    mpdof = np.concatenate([dof, [1.0]], axis=0)
    if verbose:
      print("Multiphase constraints...")
      print(mpdof)
    phase_rec.multiphase_constraints(multiphase_obj1, mpdof)
    phase_rec.multiphase_jacobian(multiphase_grad1, mpdof)
    # Results
    if verbose:
      print(f"objective {obj1}")
      print(f"gradient {grad1}")
      print(f"hessian {hess1}")
      print(f"mass objective {mass_obj1}")
      print(f"mass gradient {mass_grad1}")
      print(f"mass hessian {mass_hess1}")
      print(f"internal objective {internal_obj1}")
      print(f"internal gradient {internal_grad1}")
      print(f"internal hessian {internal_hess1}")
      print(f"multiphase objective {multiphase_obj1}")
      print(f"multiphase gradient {multiphase_grad1}")
    return obj1, grad1, hess1, mass_obj1, mass_grad1, mass_hess1, internal_obj1, internal_grad1, internal_hess1, multiphase_obj1, multiphase_grad1

from pycalphad import Database, equilibrium, variables as v, __version__ as pycalphad_version
from pycalphad.core.utils import instantiate_models
from pycalphad.codegen.callables import build_phase_records, unpack_components
from pycalphad import Model
import numpy as np
import copy

print(f'pycalphad version: {pycalphad_version}')
dbf= Database(tdb)
comps = ['CU', 'MG']
phases = ['HCP_A3']
species = unpack_components(dbf, comps)

# Lots of parameters
parameters = {'VV0000': -33134.699474175846, 'VV0001': 7734.114029426941, 'VV0002': -13498.542175596054, 'VV0003': -26555.048975092268, 'VV0004': 20777.637577083482, 'VV0005': 41915.70425630003, 'VV0006': -34525.21964215504, 'VV0007': 95457.14639216446, 'VV0008': 21139.578967453144, 'VV0009': 19047.833726419598, 'VV0010': 20468.91829601273, 'VV0011': 19601.617855958328, 'VV0012': -4546.9325861738, 'VV0013': -1640.6354331231278, 'VV0014': -35682.950005357634}
models = instantiate_models(dbf, comps, phases, parameters=parameters)
prxs = build_phase_records(dbf, species, ['HCP_A3'], {v.X('CU'): 0.0001052, v.P: 101325.0, v.T: 743.15, v.N: 1}, models, parameters=parameters, build_gradients=True, build_hessians=True)
prx1 = prxs['HCP_A3']
outp1 = calc_output(prx1)


# Only parameters in this phase
parameters={'VV0003': -26555.048975092268, 'VV0004': 20777.637577083482}
models = instantiate_models(dbf, comps, phases, parameters=parameters)
prxs = build_phase_records(dbf, species, ['HCP_A3'], {v.X('CU'): 0.0001052, v.P: 101325.0, v.T: 743.15, v.N: 1}, models, parameters=parameters, build_gradients=True, build_hessians=True)
prx2 = prxs['HCP_A3']
outp2 = calc_output(prx2)

qty_names = ['Obj', 'Jac', 'Hess', 'Mass Obj', 'Mass Jac', 'Mass Hess', 'Internal Cons Obj', 'Internal Cons Jac', 'Internal Cons Hess', 'Multiphase Cons Obj', 'Multiphase Cons Jac']
print("Comparing prx1 and prx2 (expected to match)")
num_matches = 0
for qty, o1, o2 in zip(qty_names,  outp1, outp2):
    if not np.all(o1 == o2):
        num_matches += 1
        print(f"{qty} not matched ", o1, o2)
else:
    if num_matches == 0:
      print("All outputs match")

print()
# Sanity check, compare prx2 and prx3 where 3 has different parameters that should affect the values
parameters={'VV0003': 1e5, 'VV0004': 1e5}
prxs = build_phase_records(dbf, species, ['HCP_A3'], {v.X('CU'): 0.0001052, v.P: 101325.0, v.T: 743.15, v.N: 1}, {'HCP_A3': Model(dbf, comps, 'HCP_A3', parameters=sorted(parameters.keys()))}, parameters=parameters, build_gradients=True, build_hessians=True)
prx3 = prxs['HCP_A3']
outp3 = calc_output(prx3)

print("Comparing prx2 and prx3 (expected to not match)")
num_matches = 0
for qty, o1, o2 in zip(qty_names,  outp2, outp3):
    if not np.all(o1 == o2):
        num_matches += 1
        print(f"{qty} not matched ", o1, o2)
else:
    if num_matches == 0:
      print("All outputs match")

with output:

pycalphad version: 0.8+27.g19bf29a6
Comparing prx1 and prx2 (expected to match)
All outputs match

Comparing prx2 and prx3 (expected to not match)
Obj not matched  [-32270.97962691] [-7321.40648521]
Jac not matched  [   0.            0.          -61.03871068 3915.09258244 6459.41400703] [ 0.00000000e+00  0.00000000e+00 -6.10387107e+01  3.06771974e+04
  8.43448730e+04]
Hess not matched  [[ 0.00000000e+00  0.00000000e+00  0.00000000e+00  0.00000000e+00
   0.00000000e+00]
 [ 0.00000000e+00  0.00000000e+00  0.00000000e+00  0.00000000e+00
   0.00000000e+00]
 [ 0.00000000e+00  0.00000000e+00 -3.77598461e-02  1.08113490e+01
  -1.52456842e+00]
 [ 0.00000000e+00  0.00000000e+00  1.08113490e+01 -1.08329862e+04
  -2.12074884e+04]
 [ 0.00000000e+00  0.00000000e+00 -1.52456842e+00 -2.12074884e+04
   5.99690694e+04]] [[ 0.00000000e+00  0.00000000e+00  0.00000000e+00  0.00000000e+00
   0.00000000e+00]
 [ 0.00000000e+00  0.00000000e+00  0.00000000e+00  0.00000000e+00
   0.00000000e+00]
 [ 0.00000000e+00  0.00000000e+00 -3.77598461e-02  1.08113490e+01
  -1.52456842e+00]
 [ 0.00000000e+00  0.00000000e+00  1.08113490e+01 -1.31264946e+04
   1.04016006e+05]
 [ 0.00000000e+00  0.00000000e+00 -1.52456842e+00  1.04016006e+05
  -2.97681245e+05]]

…rs. This change corrects a case where dof and parameter arrays could be misaligned during concatenation, when the caller specified an oversized dof array. See gh-249 for details.

richardotis · 2019-10-29T16:48:34Z

The bug discussed above should be fixed now. To understand the issue, a little background:
The PhaseRecord object is designed to insulate callers (notably Problem) from having to know about model parameters (VV0001, VV0002, etc.). The caller specifies the degrees of freedom (dof) array with state variables and site fractions, which then get passed to the underlying callables for the objective, gradient, Hessian, constraints, etc.

Now, it's important to note that the underlying callables require the input array (dof+parameters) to be contiguous in memory. The PhaseRecord object has two helper functions, alloc_dof_with_parameters and alloc_dof_with_parameters_vectorized, which its primary functions call to guarantee that the input array is contiguous in memory. Since the dof array is already contiguous by construction, these helpers only allocate new memory if the parameters array is nonzero in size, which is why this bug only shows up in that case.

The other important fact to know is that, in some parts of the Problem class, oversized dof arrays are allocated and reused, for performance reasons. At this point you're probably seeing the issue: PhaseRecord is concatenating an oversized dof array with the parameters array, causing the input array to be contiguous, but misaligned, with padding zeros crowding out the parameters. The solution is simple: slice the dof array to be the known correct size prior to concatenation.

In terms of impact, by luck it turns out we were using correctly-sized dof arrays in the objective, gradient, as well as all the chemical potential calculation code, so, if the system converged, the answers were correct. (The Hessian and certain constraint code use oversized dof arrays.)

bocklund

Exciting performance and accuracy improvements here. Great work!

pycalphad/codegen/sympydiff_utils.py

pycalphad/core/constraints.py

pycalphad/core/phase_rec.pyx

pycalphad/core/solver.py

pycalphad/model.py

setup.py

…d Hessians now

… methods

bocklund · 2019-11-04T16:53:58Z

I think the macOS failures are due to symengine 0.4 being installed on the latest commits (for some reason?). We probably just should update the deps to 'symengine>=0.5' and 'python-symengine>=0.5' everywhere

bocklund

Approved pending passing tests

richardotis and others added 23 commits June 11, 2019 10:00

ENH: solver: Reduce number of times solution refinement gets invoked,…

dba47b5

… for performance reasons

FIX: solver: Enforce minimum length scale for numerical stability

2e9c422

FIX: variables: Latex printing with sympy

b2b6704

ENH/WIP: Exact Hessian support

f680569

FIX/WIP: Corrected Hessian return value

3b1c7f3

FIX: Avoid building gradients and Hessians inside calculate()

49e8e85

WIP: Try using lambda backend for symengine

16fb2fa

Merge branch 'develop' into use-lambda-backend

5eb1c97

FIX: map_binary: Enable build_hessians for PhaseRecords

dfcb810

ENH: PhaseRecord: Switch to symengine upstream unsafe_real_ptr API; a…

5bbf53d

…bstract LLVM versus Lambda backends

BLD: setup.py: Remove link to libsymengine

34dc2c5

WIP: build_functions: Add backend toggle based on count_ops()

c9ccc93

ENH: PhaseRecord: Use symengine's as_ctypes() API for FastFunctions

a7c48a8

FIX/BLD: Remove symengine as a build-time dependency

496a46a

FIX: FastFunction: Preserve references to addr1 and addr2 to prevent …

0d3c9c0

…garbage collection

Revert "FIX: FastFunction: Preserve references to addr1 and addr2 to …

3834d3d

…prevent garbage collection" This reverts commit 0d3c9c0.

MAINT: setup.py: obsolete comment

e7a3c19

ENH: FastFunction: pickle support

ca69f5d

WIP/ENH: Model: IHJ magnetic model piecewise flattening for performance

2bad926

WIP: Chemical potential gradient fixes

8ec7333

FIX: mass_cons_hessian: Indexing fix

0ea0f0e

FIX: chemical_potential_gradient: Einstein summation error

9938441

WIP: Problem/solver: Use approximate Hessians for chemical potential …

19bf29a

…conditions, for now

richardotis added the enhancement label Oct 28, 2019

richardotis added this to the 0.8.1 milestone Oct 28, 2019

richardotis requested a review from bocklund October 28, 2019 15:28

Merge branch 'develop' into lambda-without-usp

fdef1e0

richardotis added 4 commits October 29, 2019 08:14

FIX: Problem: _pinv_derivative py2 matmul compatibility

3b2aa75

TST: Equilibrium calculation with parameters test case (gh-249)

b7dd85f

FIX: PhaseRecord: Do not trust the size of dof input array from calle…

e164903

…rs. This change corrects a case where dof and parameter arrays could be misaligned during concatenation, when the caller specified an oversized dof array. See gh-249 for details.

Merge branch 'develop' into lambda-without-usp

a7b883b

bocklund requested changes Nov 1, 2019

View reviewed changes

richardotis added 6 commits November 2, 2019 16:04

MAINT: constraints: Remove obsolete need_hess variable. We always nee…

fdc730f

…d Hessians now

MAINT: constraints: Remove include_hess kwarg

0a6b69d

MAINT: solver: Remove debugging code

cfc8fe0

MAINT: Model: Clean up old comments

a099445

MAINT: Model: Magnetic model optimization explanatory comment

ab21cef

MAINT: core/codegen: Callable function naming consistency

6d3a653

richardotis requested a review from bocklund November 3, 2019 22:55

ENH: PhaseRecord: Create separate 1d and 2d APIs for obj and mass_obj…

e301227

… methods

bocklund approved these changes Nov 4, 2019

View reviewed changes

BLD: setup.py/meta.yaml: Bump symengine version to 0.5.1

f66a216

richardotis merged commit 05ff0cf into develop Nov 4, 2019

bocklund mentioned this pull request Dec 3, 2019

New Algorithm for Calculating ZPF Error PhasesResearchLab/ESPEI#110

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bocklund mentioned this pull request Nov 20, 2020

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Exact Hessians with SymEngine lambda backend #249

Exact Hessians with SymEngine lambda backend #249

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Exact Hessians with SymEngine lambda backend #249

Exact Hessians with SymEngine lambda backend #249

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