From 89b05391d9246199b9f0b244a04ec8efddb1c5fa Mon Sep 17 00:00:00 2001 From: Daniel Marchand Date: Sat, 3 Apr 2021 10:57:45 +0200 Subject: [PATCH 1/2] added ability to read stress --- src/libnnp/Structure.cpp | 75 +++++++++++++++++++++++++++++++--------- src/libnnp/Structure.h | 7 ++++ src/libnnp/version.h | 6 ++-- 3 files changed, 69 insertions(+), 19 deletions(-) diff --git a/src/libnnp/Structure.cpp b/src/libnnp/Structure.cpp index 9609a92cb..ef2fc146d 100644 --- a/src/libnnp/Structure.cpp +++ b/src/libnnp/Structure.cpp @@ -30,6 +30,7 @@ using namespace nnp; Structure::Structure() : isPeriodic (false ), isTriclinic (false ), + hasStress (false ), hasNeighborList (false ), hasSymmetryFunctions (false ), hasSymmetryFunctionDerivatives(false ), @@ -54,6 +55,9 @@ Structure::Structure() : invbox[i][0] = 0.0; invbox[i][1] = 0.0; invbox[i][2] = 0.0; + stress[i][0] = 0.0; + stress[i][1] = 0.0; + stress[i][2] = 0.0; } } @@ -131,6 +135,7 @@ void Structure::readFromFile(ifstream& file) void Structure::readFromLines(vector const& lines) { size_t iBoxVector = 0; + size_t iStressVector = 0; vector splitLine; // read first line, should be keyword "begin". @@ -180,6 +185,18 @@ void Structure::readFromLines(vector const& lines) calculateVolume(); } } + else if (splitLine.at(0) == "stress") + { + hasStress = true; + if (iStressVector > 2) + { + throw runtime_error("ERROR: Too many stress vectors.\n"); + } + stress[iStressVector][0] = atof(splitLine.at(1).c_str()); + stress[iStressVector][1] = atof(splitLine.at(2).c_str()); + stress[iStressVector][2] = atof(splitLine.at(3).c_str()); + iStressVector++; + } else if (splitLine.at(0) == "atom") { atoms.push_back(Atom()); @@ -213,6 +230,11 @@ void Structure::readFromLines(vector const& lines) throw runtime_error("ERROR: Strange number of box vectors.\n"); } break; + if (!(iStressVector == 0 || iStressVector == 3)) + { + throw runtime_error("ERROR: Strange number of stress vectors.\n"); + } + break; } else { @@ -488,25 +510,41 @@ void Structure::toPhysicalUnits(double meanEnergy, double convEnergy, double convLength) { - if (isPeriodic) - { - box[0] /= convLength; - box[1] /= convLength; - box[2] /= convLength; - invbox[0] *= convLength; - invbox[1] *= convLength; - invbox[2] *= convLength; - } + if (isPeriodic) + { + box[0] /= convLength; + box[1] /= convLength; + box[2] /= convLength; + invbox[0] *= convLength; + invbox[0] *= convLength; + invbox[1] *= convLength; + invbox[2] *= convLength; + } + energyRef = energyRef / convEnergy + numAtoms * meanEnergy; + energy = energy / convEnergy + numAtoms * meanEnergy; + volume /= convLength * convLength * convLength; + + for (vector::iterator it = atoms.begin(); it != atoms.end(); ++it) + { + it->toPhysicalUnits(convEnergy, convLength); + } - energyRef = energyRef / convEnergy + numAtoms * meanEnergy; - energy = energy / convEnergy + numAtoms * meanEnergy; - volume /= convLength * convLength * convLength; +} - for (vector::iterator it = atoms.begin(); it != atoms.end(); ++it) - { - it->toPhysicalUnits(convEnergy, convLength); - } +void Structure::toNormalizedUnitsStress(double meanStress) +{ + stress[0] *= meanStress; + stress[1] *= meanStress; + stress[2] *= meanStress; + return; +} + +void Structure::toPhysicalUnitsStress(double meanStress) +{ + stress[0] /= meanStress; + stress[1] /= meanStress; + stress[2] /= meanStress; return; } @@ -526,6 +564,7 @@ void Structure::reset() { isPeriodic = false ; isTriclinic = false ; + hasStress = false ; hasNeighborList = false ; hasSymmetryFunctions = false ; hasSymmetryFunctionDerivatives = false ; @@ -842,6 +881,7 @@ vector Structure::info() const v.push_back(strpr("index : %d\n", index)); v.push_back(strpr("isPeriodic : %d\n", isPeriodic )); v.push_back(strpr("isTriclinic : %d\n", isTriclinic )); + v.push_back(strpr("hasStress : %d\n", hasStress )); v.push_back(strpr("hasNeighborList : %d\n", hasNeighborList )); v.push_back(strpr("hasSymmetryFunctions : %d\n", hasSymmetryFunctions)); v.push_back(strpr("hasSymmetryFunctionDerivatives : %d\n", hasSymmetryFunctionDerivatives)); @@ -862,6 +902,9 @@ vector Structure::info() const v.push_back(strpr("invbox[0] : %16.8E %16.8E %16.8E\n", invbox[0][0], invbox[0][1], invbox[0][2])); v.push_back(strpr("invbox[1] : %16.8E %16.8E %16.8E\n", invbox[1][0], invbox[1][1], invbox[1][2])); v.push_back(strpr("invbox[2] : %16.8E %16.8E %16.8E\n", invbox[2][0], invbox[2][1], invbox[2][2])); + v.push_back(strpr("stress[0] : %16.8E %16.8E %16.8E\n", stress[0][0], stress[0][1], stress[0][2])); + v.push_back(strpr("stress[1] : %16.8E %16.8E %16.8E\n", stress[1][0], stress[1][1], stress[1][2])); + v.push_back(strpr("stress[2] : %16.8E %16.8E %16.8E\n", stress[2][0], stress[2][1], stress[2][2])); v.push_back(strpr("--------------------------------\n")); v.push_back(strpr("numAtomsPerElement [*] : %d\n", numAtomsPerElement.size())); v.push_back(strpr("--------------------------------\n")); diff --git a/src/libnnp/Structure.h b/src/libnnp/Structure.h index 67f27b7df..14342bd9e 100644 --- a/src/libnnp/Structure.h +++ b/src/libnnp/Structure.h @@ -56,6 +56,8 @@ struct Structure bool isPeriodic; /// If the simulation box is triclinic. bool isTriclinic; + /// If the simulation box includes stresses. + bool hasStress; /// If the neighbor list has been calculated. bool hasNeighborList; /// If symmetry function values are saved for each atom. @@ -88,6 +90,8 @@ struct Structure std::string comment; /// Simulation box vectors. Vec3D box[3]; + /// Stress box vectors. + Vec3D stress[3]; /// Inverse simulation box vectors. Vec3D invbox[3]; /// Number of atoms of each element in this structure. @@ -220,6 +224,9 @@ struct Structure void toPhysicalUnits(double meanEnergy, double convEnergy, double convLength); + // Separate functions for stress since we will not always use these methods + void toNormalizedUnitsStress(double meanStress); + void toPhysicalUnitsStress(double meanStress); /** Find maximum number of neighbors. * * @return Maximum numbor of neighbors of all atoms in this structure. diff --git a/src/libnnp/version.h b/src/libnnp/version.h index 992d82785..b35e56585 100644 --- a/src/libnnp/version.h +++ b/src/libnnp/version.h @@ -18,8 +18,8 @@ #define VERSION_H #define N2P2_VERSION "v2.1.1" -#define N2P2_GIT_VERSION "" -#define N2P2_GIT_REV "" -#define N2P2_GIT_BRANCH "" +#define N2P2_GIT_VERSION "v2.1.1-20-g3f03449" +#define N2P2_GIT_REV "3f03449f24b1ef1704cb29d8c978f1459667e138" +#define N2P2_GIT_BRANCH "master" #endif From d7af3447c59b6bbb6643ad8c13297d976fac8f6f Mon Sep 17 00:00:00 2001 From: Daniel Marchand Date: Sat, 3 Apr 2021 10:59:33 +0200 Subject: [PATCH 2/2] add simple stress example --- examples/stresses/input.data | 3110 ++++++++++++++++++++++++++++++++++ examples/stresses/input.nn | 289 ++++ 2 files changed, 3399 insertions(+) create mode 100644 examples/stresses/input.data create mode 100755 examples/stresses/input.nn diff --git a/examples/stresses/input.data b/examples/stresses/input.data new file mode 100644 index 000000000..8ab84ac07 --- /dev/null +++ b/examples/stresses/input.data @@ -0,0 +1,3110 @@ +begin +comment uuid: 5fc9fca1-96ee-49aa-b8e1-e1c6ac877be0 +lattice 6.9553390259 0.0000000000 0.0000000000 +lattice 0.0000000000 6.9553390259 0.0000000000 +lattice 0.0000000000 0.0000000000 6.9553390259 +stress 0.00078027494659142175 0.00004084499720422495 -0.00001816999875629251 +stress 0.00004084499720422495 0.00080676994477788151 0.00002134499853896882 +stress -0.00001816999875629251 0.00002134499853896882 0.00074339994911545675 +atom 0.000000 0.000000 0.000000 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-0.0000007300 -0.0000007450 +atom 16.093559 0.000006 7.663605 Al 0.0 0.0 0.0000002950 -0.0000003550 -0.0000003450 +atom 8.046789 11.477411 11.515640 Al 0.0 0.0 -0.0000006100 -0.0005257750 0.0006701700 +atom 12.051286 7.663593 3.811555 Al 0.0 0.0 0.0001418300 0.0000006900 0.0001739400 +atom 12.070183 11.495397 15.327197 Al 0.0 0.0 -0.0000003800 0.0000008100 0.0000004950 +atom 0.000003 11.513396 3.811554 Al 0.0 0.0 -0.0000005150 0.0005255800 -0.0006691500 +atom 4.042280 7.663605 3.811571 Al 0.0 0.0 -0.0001419700 -0.0000004700 0.0001724250 +atom 4.023394 11.495404 0.000005 Al 0.0 0.0 -0.0000000100 -0.0000005300 -0.0000007500 +atom 16.093551 7.663604 15.327203 Al 0.0 0.0 0.0000008600 -0.0000001900 -0.0000001900 +atom 8.046787 3.849786 3.811568 Al 0.0 0.0 -0.0000005200 0.0005256950 -0.0006695800 +atom 12.089059 0.000006 3.811571 Al 0.0 0.0 -0.0001418250 -0.0000006050 0.0001724150 +atom 12.070181 3.831804 0.000006 Al 0.0 0.0 -0.0000001450 -0.0000007050 -0.0000008550 +atom 8.046772 0.000005 0.000000 Al 0.0 0.0 0.0000007200 -0.0000002850 -0.0000000700 +atom 16.093554 3.813812 3.811565 Al 0.0 0.0 0.0000004900 -0.0005255850 -0.0006697200 +atom 4.004499 15.327197 3.811554 Al 0.0 0.0 0.0001419450 0.0000005850 0.0001737600 +atom 4.023399 3.831798 15.327197 Al 0.0 0.0 -0.0000003200 0.0000005500 0.0000004300 +atom 12.051282 7.663610 11.515649 Al 0.0 0.0 0.0001418300 -0.0000007400 -0.0001737300 +atom 8.046800 7.663599 0.000028 Si 0.0 0.0 -0.0000002650 0.0000000950 -0.0000004200 +atom 0.000029 0.000005 0.000014 Si 0.0 0.0 -0.0000004150 0.0000000150 -0.0000003700 +energy -603.905357190000018 +charge 0.000000000000000 +end +begin +comment uuid: ca8c1063-7cc3-48a3-9d1a-919a541789a0 +lattice 15.3332370572 0.0000000000 0.0000000000 +lattice 0.0000000000 15.3332370572 0.0000000000 +lattice 0.0000000000 0.0000000000 15.3332370572 +stress -0.00001660999886307201 -0.00000346999976248404 0.00000710499951367409 +stress -0.00000346999976248404 -0.00001776499878401411 0.00000038499997364736 +stress 0.00000710499951367409 0.00000038499997364736 -0.00000945499935282034 +atom 0.284589 15.219279 0.023426 Al 0.0 0.0 -0.0016368300 0.0025977900 0.0007492600 +atom 11.601381 11.561515 8.017509 Al 0.0 0.0 0.0005769700 -0.0035433750 -0.0036062450 +atom 0.246549 11.527592 11.469264 Al 0.0 0.0 -0.0027378350 -0.0012800500 0.0025492650 +atom 0.379714 7.709495 7.847230 Al 0.0 0.0 -0.0097738900 -0.0030250200 -0.0055030650 +atom 11.565071 15.324685 11.689206 Al 0.0 0.0 -0.0000881900 0.0017056500 -0.0035961000 +atom 7.620899 14.916435 7.717327 Al 0.0 0.0 0.0039153050 0.0064751450 0.0000654850 +atom 0.170181 3.741853 11.488972 Al 0.0 0.0 -0.0048958300 -0.0001197650 -0.0024772050 +atom 3.880721 15.207041 11.237821 Al 0.0 0.0 -0.0007367350 0.0061549850 0.0056194850 +atom 15.278779 15.328727 7.554831 Al 0.0 0.0 0.0014336200 0.0030783550 0.0015600150 +atom 11.480712 7.634236 11.597594 Al 0.0 0.0 -0.0016925450 -0.0019322550 -0.0035284400 +atom 11.513551 11.542752 15.250578 Al 0.0 0.0 0.0011190800 -0.0020602400 0.0034680700 +atom 7.656781 7.458319 0.167726 Al 0.0 0.0 0.0014429150 0.0042227850 -0.0047051000 +atom 7.620502 11.408891 11.775210 Al 0.0 0.0 -0.0010306250 -0.0011295250 -0.0025205850 +atom 7.525120 0.197167 15.192789 Al 0.0 0.0 0.0012187800 -0.0025164200 0.0024249400 +atom 3.973901 11.345786 0.222790 Al 0.0 0.0 -0.0008089700 0.0025350950 -0.0031045000 +atom 15.300868 7.752011 15.141105 Al 0.0 0.0 0.0023517500 -0.0008506550 0.0050026150 +atom 3.804388 4.034352 15.207749 Al 0.0 0.0 -0.0001407900 -0.0031522400 -0.0012337500 +atom 11.374877 15.084335 3.691147 Al 0.0 0.0 0.0012462000 0.0043176950 0.0031825450 +atom 11.536744 3.725377 15.326634 Al 0.0 0.0 0.0005480700 0.0017271850 0.0028483250 +atom 0.186697 11.528170 3.939866 Al 0.0 0.0 -0.0026418650 -0.0009079750 -0.0023444950 +atom 3.961533 0.214238 3.977937 Al 0.0 0.0 -0.0024829600 -0.0058592650 -0.0039333650 +atom 0.187642 3.931373 3.687498 Al 0.0 0.0 -0.0050666600 -0.0003764150 0.0028934850 +atom 11.508902 7.840744 4.014270 Mg 0.0 0.0 0.0017344650 -0.0007122200 -0.0056343550 +atom 7.139310 7.953055 7.481787 Mg 0.0 0.0 0.0192069500 -0.0101413500 0.0089642550 +atom 11.336750 3.758785 7.617819 Mg 0.0 0.0 -0.0009510850 -0.0010588200 0.0008840600 +atom 3.873410 7.629624 11.338718 Si 0.0 0.0 0.0001725850 0.0008945000 0.0155748950 +atom 3.788973 7.714296 3.884366 Si 0.0 0.0 -0.0099332550 -0.0019951100 -0.0137835550 +atom 7.439863 3.770175 11.367195 Si 0.0 0.0 0.0026757100 0.0003362200 0.0005524700 +atom 7.332073 3.857001 3.748165 Si 0.0 0.0 0.0094065900 0.0003333750 0.0027686100 +atom 3.764308 3.912735 7.549837 Si 0.0 0.0 0.0000410850 -0.0080035350 0.0033635850 +atom 3.768650 11.563298 7.594382 Si 0.0 0.0 -0.0070760550 0.0111068300 0.0006407100 +atom 7.548836 11.593611 3.853512 Si 0.0 0.0 0.0046040450 0.0031786150 -0.0071413100 +energy -524.790935450000006 +charge 0.000000000000000 +end diff --git a/examples/stresses/input.nn b/examples/stresses/input.nn new file mode 100755 index 000000000..9bd943ffe --- /dev/null +++ b/examples/stresses/input.nn @@ -0,0 +1,289 @@ +############################################################################### +# GENERAL NNP SETTINGS +############################################################################### +number_of_elements 3 # Number of elements. +elements Al Mg Si # Specification of elements. +atom_energy Al -19.6283516 #-2.4092354 +atom_energy Mg -16.7493351 #-62.6068620 +atom_energy Si -5.5274864 #-5.5597835 +#atom_energy S 0.0 # Free atom reference energy (S). +#atom_energy Cu 0.0 # Free atom reference energy (Cu). +cutoff_type 2 # Cutoff type (optional argument: shift parameter alpha). +scale_symmetry_functions # Scale all symmetry functions with min/max values. +#scale_symmetry_functions_sigma # Scale all symmetry functions with sigma. +scale_min_short 0.0 # Minimum value for scaling. +scale_max_short 1.0 # Maximum value for scaling. +center_symmetry_functions # Center all symmetry functions, i.e. subtract mean value. +global_hidden_layers_short 2 # Number of hidden layers. +global_nodes_short 24 24 # Number of nodes in each hidden layer. +global_activation_short p p l +#normalize_nodes # Normalize input of nodes. + +############################################################################### +# ADDITIONAL SETTINGS FOR TRAINING +############################################################################### +epochs 500 # Number of training epochs. +updater_type 1 # Weight update method (0 = Gradient Descent, 1 = Kalman filter). +parallel_mode 4 # Training parallelization used (0 = Serial, 1-4 = MSEKF implementations (2 or 4 are fastest)). +update_strategy 0 # Update strategy (0 = Combined, 1 = Per-element). +selection_mode 0 # Update candidate selection mode (0 = Random, 1 = Sort, 2 = Threshold). +memorize_symfunc_results # Keep symmetry function results in memory. +random_seed 22190 +test_fraction 0.1 +use_short_forces # Use forces for training. +force_weight 8.0 # Weight of force updates relative to energy updates. +short_energy_fraction 1.000 # Fraction of energy updates per epoch. +short_force_fraction 0.02115 # Fraction of force updates per epoch. +short_energy_error_threshold 0.00 # RMSE threshold for energy update candidates. +short_force_error_threshold 1.00 # RMSE threshold for force update candidates. +rmse_threshold_trials 3 # Maximum number of RMSE threshold trials. +#repeated_energy_update # After force update perform energy update for corresponding structure. +#use_old_weights_short # Restart fitting with old weight parameters. +weights_min -1.0 # Minimum value for initial random weights. +weights_max 1.0 # Maximum value for initial random weights. +#precondition_weights # Precondition weights with initial energies. +#nguyen_widrow_weights_short # Initialize neural network weights according to Nguyen-Widrow scheme. +write_trainpoints 10 # Write energy comparison every this many epochs. +write_trainforces 50 # Write force comparison every this many epochs. +write_weights_epoch 1 # Write weights every this many epochs. +#write_neuronstats 1 # Write neuron statistics every this many epochs. +write_trainlog # Write training log file. +#################### +# GRADIENT DESCENT # +#################### +#gradient_type 0 # Gradient descent type (0 = Fixed step size). +#gradient_eta 1.0E-4 # Gradient descent parameter eta (fixed step size). +############################ +# KALMAN FILTER (STANDARD) # +############################ +#kalman_type 0 # Kalman filter type (0 = Standard, 1 = Fading memory). +#kalman_epsilon 1.0E-2 # General Kalman filter parameter epsilon (sigmoidal: 0.01, linear: 0.001). +#kalman_q0 0.01 # General Kalman filter parameter q0 ("large"). +#kalman_qtau 2.302 # General Kalman filter parameter qtau (2.302 => 1 order of magnitude per epoch). +#kalman_qmin 1.0E-6 # General Kalman filter parameter qmin (typ. 1.0E-6). +#kalman_eta 0.01 # Standard Kalman filter parameter eta (0.001-1.0). +#kalman_etatau 2.302 # Standard Kalman filter parameter etatau (2.302 => 1 order of magnitude per epoch). +#kalman_etamax 1.0 # Standard Kalman filter parameter etamax (1.0+). +################################# +# KALMAN FILTER (FADING MEMORY) # +################################# +kalman_type 1 # Kalman filter type (0 = Standard, 1 = Fading memory). +kalman_epsilon 0.07 # General Kalman filter parameter epsilon (sigmoidal: 0.01, linear: 0.001). +kalman_q0 0.00 # General Kalman filter parameter q0 ("large"). +kalman_qtau 2.302 # General Kalman filter parameter qtau (2.302 => 1 order of magnitude per epoch). +kalman_qmin 1.0E-6 # General Kalman filter parameter qmin (typ. 1.0E-6). +kalman_lambda_short 0.98500 # Fading memory Kalman filter parameter lambda (forgetting factor 0.95-0.99). +kalman_nue_short 0.99870 # Fading memory Kalman filter parameter nu (0.99-0.9995). + +############################################################################### +# SYMMETRY FUNCTIONS +############################################################################### + +# Radial symmetry function (type 2): +#symfunction_short 2 + +# Narrow Angular symmetry function (type 3): +#symfunction_short 3 < + +# Wide Angular symmetry function (type 9): +#symfunction_short 9 < + +# Generating radial symmetry function set: +# mode = shift +# r_0 = 1.500E+00 +# r_c = 6.000E+00 +# r_N = 5.500E+00 +# N = 9 +# grid = 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 +symfunction_short Mg 2 Mg 0.003 0.000 20.000 +symfunction_short Mg 2 Si 0.003 0.000 20.000 +symfunction_short Mg 2 Al 0.003 0.000 20.000 +symfunction_short Mg 2 Mg 0.016 0.000 8.000 +symfunction_short Mg 2 Si 0.016 0.000 8.000 +symfunction_short Mg 2 Mg 0.117 7.071 20.000 +symfunction_short Mg 2 Si 0.029 14.142 20.000 +symfunction_short Mg 2 Al 0.016 0.000 8.000 +symfunction_short Mg 2 Si 0.045 11.314 16.000 +symfunction_short Mg 2 Mg 0.071 16.259 20.000 +symfunction_short Mg 2 Mg 0.058 10.000 20.000 +symfunction_short Mg 3 Si Si 0.007 1.000 1.000 12.000 +symfunction_short Mg 2 Mg 0.108 13.218 20.000 +symfunction_short Mg 3 Mg Si 0.007 1.000 1.000 12.000 +symfunction_short Mg 2 Si 0.112 13.007 16.000 +symfunction_short Mg 3 Mg Mg 0.007 1.000 1.000 12.000 +symfunction_short Mg 2 Al 0.108 13.218 20.000 +symfunction_short Mg 2 Al 0.058 10.000 20.000 +symfunction_short Mg 2 Si 0.117 7.071 20.000 +symfunction_short Mg 3 Mg Al 0.007 1.000 1.000 12.000 +symfunction_short Mg 3 Al Si 0.007 1.000 1.000 12.000 +symfunction_short Mg 2 Al 0.091 8.000 16.000 +symfunction_short Mg 2 Mg 0.112 13.007 16.000 +symfunction_short Mg 2 Al 0.071 16.259 20.000 +symfunction_short Mg 3 Si Si 0.007 -1.000 1.000 12.000 +symfunction_short Mg 2 Si 0.108 13.218 20.000 +symfunction_short Mg 2 Mg 0.062 0.000 8.000 +symfunction_short Mg 3 Al Al 0.007 1.000 1.000 12.000 +symfunction_short Mg 2 Al 0.112 13.007 16.000 +symfunction_short Mg 3 Mg Si 0.007 -1.000 1.000 12.000 +symfunction_short Mg 2 Si 0.082 0.000 8.000 +symfunction_short Mg 3 Al Si 0.007 -1.000 1.000 12.000 +symfunction_short Mg 3 Mg Si 0.020 1.000 1.000 12.000 +symfunction_short Mg 3 Mg Mg 0.007 -1.000 1.000 12.000 +symfunction_short Mg 3 Si Si 0.016 1.000 1.000 8.000 +symfunction_short Mg 2 Al 0.082 0.000 8.000 +symfunction_short Mg 3 Mg Al 0.007 -1.000 1.000 12.000 +symfunction_short Mg 3 Mg Mg 0.020 1.000 1.000 12.000 +symfunction_short Mg 3 Si Si 0.007 1.000 4.000 12.000 +symfunction_short Mg 3 Mg Si 0.007 1.000 4.000 12.000 +symfunction_short Mg 3 Al Si 0.020 1.000 1.000 12.000 +symfunction_short Mg 2 Si 0.071 16.259 20.000 +symfunction_short Mg 3 Mg Al 0.020 1.000 1.000 12.000 +symfunction_short Mg 2 Mg 0.016 0.000 16.000 +symfunction_short Mg 3 Mg Mg 0.007 1.000 4.000 12.000 +symfunction_short Mg 3 Si Si 0.020 1.000 4.000 12.000 +symfunction_short Mg 3 Al Si 0.007 1.000 4.000 12.000 +symfunction_short Mg 2 Si 0.016 0.000 16.000 +symfunction_short Mg 3 Al Al 0.007 -1.000 1.000 12.000 +symfunction_short Mg 2 Mg 0.124 0.000 8.000 +symfunction_short Mg 2 Mg 0.091 8.000 16.000 +symfunction_short Mg 3 Mg Al 0.007 1.000 4.000 12.000 +symfunction_short Mg 2 Si 0.036 0.000 8.000 +symfunction_short Mg 3 Mg Si 0.016 1.000 1.000 8.000 +symfunction_short Mg 3 Si Si 0.007 -1.000 4.000 12.000 +symfunction_short Mg 3 Al Al 0.016 1.000 1.000 8.000 +symfunction_short Mg 3 Si Si 0.020 -1.000 1.000 12.000 +symfunction_short Mg 2 Al 0.016 0.000 16.000 +symfunction_short Mg 3 Mg Si 0.020 -1.000 1.000 12.000 +symfunction_short Mg 2 Al 0.036 0.000 8.000 +symfunction_short Mg 3 Mg Si 0.007 -1.000 4.000 12.000 +symfunction_short Mg 3 Mg Mg 0.007 -1.000 4.000 12.000 +symfunction_short Mg 2 Mg 0.045 11.314 16.000 +symfunction_short Mg 3 Al Al 0.007 1.000 4.000 12.000 +symfunction_short Si 2 Si 0.003 0.000 20.000 +symfunction_short Si 2 Mg 0.003 0.000 20.000 +symfunction_short Si 2 Al 0.003 0.000 20.000 +symfunction_short Si 2 Si 0.016 0.000 8.000 +symfunction_short Si 2 Mg 0.016 0.000 8.000 +symfunction_short Si 2 Si 0.108 13.218 20.000 +symfunction_short Si 2 Mg 0.108 13.218 20.000 +symfunction_short Si 2 Si 0.058 10.000 20.000 +symfunction_short Si 2 Mg 0.058 10.000 20.000 +symfunction_short Si 2 Si 0.091 8.000 16.000 +symfunction_short Si 2 Al 0.016 0.000 8.000 +symfunction_short Si 3 Mg Si 0.007 1.000 1.000 12.000 +symfunction_short Si 2 Si 0.071 16.259 20.000 +symfunction_short Si 3 Si Si 0.007 1.000 1.000 12.000 +symfunction_short Si 2 Mg 0.071 16.259 20.000 +symfunction_short Si 3 Al Si 0.007 1.000 1.000 12.000 +symfunction_short Si 2 Mg 0.091 8.000 16.000 +symfunction_short Si 3 Mg Mg 0.007 1.000 1.000 12.000 +symfunction_short Si 2 Al 0.016 0.000 16.000 +symfunction_short Si 3 Mg Al 0.007 1.000 1.000 12.000 +symfunction_short Si 2 Si 0.082 0.000 8.000 +symfunction_short Si 2 Al 0.091 8.000 16.000 +symfunction_short Si 2 Al 0.108 13.218 20.000 +symfunction_short Si 3 Mg Si 0.007 -1.000 1.000 12.000 +symfunction_short Si 2 Mg 0.112 13.007 16.000 +symfunction_short Si 2 Si 0.112 13.007 16.000 +symfunction_short Si 3 Al Al 0.007 1.000 1.000 12.000 +symfunction_short Si 2 Al 0.112 13.007 16.000 +symfunction_short Si 3 Si Si 0.007 -1.000 2.000 12.000 +symfunction_short Si 2 Al 0.071 16.259 20.000 +symfunction_short Si 2 Mg 0.082 0.000 8.000 +symfunction_short Si 2 Si 0.124 0.000 8.000 +symfunction_short Si 3 Mg Mg 0.007 -1.000 1.000 12.000 +symfunction_short Si 2 Al 0.082 0.000 8.000 +symfunction_short Si 3 Mg Si 0.016 1.000 1.000 8.000 +symfunction_short Si 3 Si Si 0.007 1.000 4.000 12.000 +symfunction_short Si 3 Mg Al 0.007 -1.000 1.000 12.000 +symfunction_short Si 3 Al Si 0.007 -1.000 1.000 12.000 +symfunction_short Si 3 Si Si 0.020 1.000 1.000 12.000 +symfunction_short Si 3 Mg Si 0.007 -1.000 4.000 12.000 +symfunction_short Si 3 Si Si 0.016 1.000 1.000 8.000 +symfunction_short Si 3 Al Si 0.020 1.000 4.000 12.000 +symfunction_short Si 3 Mg Mg 0.020 1.000 1.000 12.000 +symfunction_short Si 3 Mg Mg 0.007 -1.000 4.000 12.000 +symfunction_short Si 2 Si 0.021 0.000 16.000 +symfunction_short Si 3 Si Si 0.007 -1.000 4.000 12.000 +symfunction_short Si 3 Mg Si 0.020 1.000 1.000 12.000 +symfunction_short Si 3 Al Si 0.007 1.000 4.000 12.000 +symfunction_short Si 2 Si 0.117 7.071 20.000 +symfunction_short Si 3 Mg Al 0.007 -1.000 4.000 12.000 +symfunction_short Si 3 Si Si 0.020 -1.000 1.000 12.000 +symfunction_short Si 3 Mg Si 0.007 1.000 4.000 12.000 +symfunction_short Si 3 Mg Al 0.020 1.000 1.000 12.000 +symfunction_short Si 2 Mg 0.016 0.000 16.000 +symfunction_short Si 3 Al Al 0.007 -1.000 1.000 12.000 +symfunction_short Si 2 Mg 0.117 7.071 20.000 +symfunction_short Si 3 Mg Si 0.020 -1.000 1.000 12.000 +symfunction_short Si 3 Al Si 0.016 1.000 1.000 8.000 +symfunction_short Si 2 Si 0.036 0.000 8.000 +symfunction_short Si 3 Al Al 0.016 1.000 1.000 8.000 +symfunction_short Si 3 Si Si 0.016 1.000 8.000 8.000 +symfunction_short Si 3 Mg Mg 0.020 -1.000 1.000 12.000 +symfunction_short Si 3 Si Si 0.016 -1.000 2.000 8.000 +symfunction_short Si 3 Mg Mg 0.007 1.000 4.000 12.000 +symfunction_short Al 2 Al 0.003 0.000 20.000 +symfunction_short Al 2 Si 0.003 0.000 20.000 +symfunction_short Al 2 Mg 0.003 0.000 20.000 +symfunction_short Al 2 Si 0.016 0.000 8.000 +symfunction_short Al 2 Mg 0.016 0.000 8.000 +symfunction_short Al 2 Mg 0.108 13.218 20.000 +symfunction_short Al 2 Si 0.108 13.218 20.000 +symfunction_short Al 2 Al 0.016 0.000 8.000 +symfunction_short Al 2 Si 0.058 10.000 20.000 +symfunction_short Al 2 Mg 0.058 10.000 20.000 +symfunction_short Al 2 Mg 0.071 16.259 20.000 +symfunction_short Al 2 Si 0.071 16.259 20.000 +symfunction_short Al 2 Al 0.108 13.218 20.000 +symfunction_short Al 3 Si Si 0.007 1.000 1.000 12.000 +symfunction_short Al 3 Mg Si 0.007 1.000 1.000 12.000 +symfunction_short Al 2 Al 0.091 8.000 16.000 +symfunction_short Al 2 Al 0.058 10.000 20.000 +symfunction_short Al 2 Si 0.091 8.000 16.000 +symfunction_short Al 3 Mg Mg 0.007 1.000 1.000 12.000 +symfunction_short Al 2 Mg 0.091 8.000 16.000 +symfunction_short Al 3 Al Si 0.007 1.000 1.000 12.000 +symfunction_short Al 2 Al 0.071 16.259 20.000 +symfunction_short Al 3 Mg Al 0.007 1.000 1.000 12.000 +symfunction_short Al 2 Al 0.112 13.007 16.000 +symfunction_short Al 2 Al 0.124 0.000 8.000 +symfunction_short Al 3 Al Al 0.007 1.000 1.000 12.000 +symfunction_short Al 2 Si 0.112 13.007 16.000 +symfunction_short Al 3 Si Si 0.007 -1.000 1.000 12.000 +symfunction_short Al 2 Mg 0.112 13.007 16.000 +symfunction_short Al 3 Mg Mg 0.007 -1.000 1.000 12.000 +symfunction_short Al 3 Mg Si 0.007 -1.000 1.000 12.000 +symfunction_short Al 2 Si 0.082 0.000 8.000 +symfunction_short Al 2 Mg 0.082 0.000 8.000 +symfunction_short Al 3 Mg Al 0.007 -1.000 1.000 12.000 +symfunction_short Al 3 Al Si 0.007 -1.000 1.000 12.000 +symfunction_short Al 3 Si Si 0.016 1.000 1.000 8.000 +symfunction_short Al 3 Mg Si 0.020 1.000 1.000 12.000 +symfunction_short Al 3 Si Si 0.007 1.000 4.000 12.000 +symfunction_short Al 3 Al Al 0.007 -1.000 1.000 12.000 +symfunction_short Al 2 Al 0.062 0.000 8.000 +symfunction_short Al 3 Mg Si 0.007 1.000 4.000 12.000 +symfunction_short Al 3 Al Si 0.016 1.000 1.000 8.000 +symfunction_short Al 3 Al Al 0.016 1.000 1.000 8.000 +symfunction_short Al 3 Mg Mg 0.020 1.000 1.000 12.000 +symfunction_short Al 2 Mg 0.016 0.000 16.000 +symfunction_short Al 3 Mg Al 0.016 1.000 1.000 8.000 +symfunction_short Al 3 Mg Mg 0.007 -1.000 4.000 12.000 +symfunction_short Al 2 Si 0.016 0.000 16.000 +symfunction_short Al 3 Al Si 0.007 1.000 4.000 12.000 +symfunction_short Al 3 Mg Al 0.007 1.000 4.000 12.000 +symfunction_short Al 3 Si Si 0.020 1.000 2.000 12.000 +symfunction_short Al 3 Si Si 0.020 -1.000 1.000 12.000 +symfunction_short Al 2 Si 0.117 7.071 20.000 +symfunction_short Al 2 Al 0.016 0.000 16.000 +symfunction_short Al 3 Al Al 0.007 1.000 4.000 12.000 +symfunction_short Al 2 Mg 0.036 0.000 8.000 +symfunction_short Al 3 Mg Si 0.007 -1.000 4.000 12.000 +symfunction_short Al 3 Al Si 0.020 1.000 1.000 12.000 +symfunction_short Al 3 Si Si 0.007 -1.000 4.000 12.000 +symfunction_short Al 2 Mg 0.117 7.071 20.000 +symfunction_short Al 3 Al Al 0.016 -1.000 1.000 8.000 +symfunction_short Al 3 Mg Al 0.020 1.000 2.000 12.000 +symfunction_short Al 2 Al 0.045 11.314 16.000 +symfunction_short Al 3 Mg Mg 0.007 1.000 4.000 12.000