Using cobrapy (version 0.4.0b1 or later), we have interfaces to serveral floating point solvers (gurobi, MOSEK, CPLEX, Clp, and two different versions of GLPK). Additionally, we can use the rational solving capabilities of GLPK and esolver (also known as QSopt_ex). We will use all of these solvers on all the models in the collection.
import os
from numpy import array
import pandas
import sympy
import cobra
pandas.set_option("display.max_rows", 100)
We will verify all of our solutions by writing out the Stoichiometrix matrix $\mathbf S$ using the sympy symbolic math library. The total error will be equivalent to $$ \sum \left|\mathbf S \cdot v \right| $$
def convert_to_rational(value):
return sympy.Rational("%.15g" % value)
def construct_exact_S(model):
# intialize to 0
S = sympy.SparseMatrix(len(model.metabolites), len(model.reactions), 0)
# populate with stoichiometry
for i, r in enumerate(model.reactions):
for met, value in r._metabolites.iteritems():
S[model.metabolites.index(met), i] = convert_to_rational(value)
return S
def total_error(S, v):
return sum(abs(i) for i in S * v)
Some of these models were exported from BiGG as SBML, and others were downloaded from their respective publications. All of the models are available in a git repository. They were parsed into a single mat file by an included script.
models = []
for filename in sorted(os.listdir("sbml3")):
if not filename.endswith(".xml"):
continue
models.append(cobra.io.read_sbml_model(os.path.join("sbml3", filename)))
These models all compute rationally with esolver and also with the other floating point solvers, as shown below. They also compute with floating point solvers in the COBRA toolbox, as shown here.
results = {}
exact_results = {}
errors = {}
for m in models:
S = construct_exact_S(m)
S_float = m.to_array_based_model().S
rational_solution = m.optimize(solver="esolver", rational_solution=True)
rational_v = sympy.Matrix(rational_solution.x)
exact_results[m.id] = {"Rational": rational_solution.f,
"Decimal": float(rational_solution.f),
"Error": total_error(S, rational_v),
# Ensure the upper and lwoer bounds are satisfied.
"Bounds": all([r.upper_bound >= value >= r.lower_bound
for r, value in zip(m.reactions, rational_v)])}
# solve this model with all the solvers
solutions = {solver: m.optimize(solver=solver)
for solver in cobra.solvers.solver_dict}
solutions["cglpk_exact"] = m.optimize(solver="cglpk", exact=True)
# store the objective value and errors
results[m.id] = {k: v.f for k, v in solutions.iteritems()}
errors[m.id] = {k: sum(abs(S_float * array(v.x))) for k, v in solutions.iteritems()}
# format the results as pandas dataframes
exact_results = pandas.DataFrame.from_dict(exact_results).T
results = pandas.DataFrame.from_dict(results)
errors = pandas.DataFrame.from_dict(errors)
For all of these models, we can demonstrate they satisfy the model constraints using exact operations.
abs(exact_results.Error).max()
0
exact_results.Bounds.all()
True
Here are objective values of the rational results provided by esolver:
exact_results[["Decimal", "Rational"]]
Decimal | Rational | |
---|---|---|
AbyMBEL891 | 119.233 | 386664062500000/3242927908653 |
AraGEM | 10 | 10 |
GSMN_TB | 0.1312623 | 576559343750000/4392422515431629 |
PpaMBEL1254 | 78.70059 | 4725000000000/60037666259 |
PpuMBEL1071 | 132.3654 | 644062500000/4865793703 |
STM_v1_0 | 0.4778337 | 178576000/373720009 |
S_coilicolor_fixed | 860.0888 | 408741530000000000/475231759036371 |
SpoMBEL1693 | 63.78566 | 1237500000000/19400913101 |
T_Maritima | 0.359469 | 180000000/500738623 |
VvuMBEL943 | 96.40232 | 14000000000/145224717 |
iAC560 | 4.042612 | 35000000/8657769 |
iAF1260 | 0.7367009 | 146888000/199386199 |
iAF692 | 0.02725005 | 107424000/3942157643 |
iAI549 | 84.17419 | 114000000000/1354334333 |
iAN840m | 0.3401361 | 50/147 |
iAO358 | 255.1805 | 586000000000/2296413281 |
iAbaylyiV4 | 12.30655 | 34263125839313509122373268880000000/2784138406... |
iBT721_fixed | 0.5 | 1/2 |
iBsu1103 | 1229.657 | 1687500000000000/1372333638281 |
iCA1273 | 0.7402418 | 293776000/396864911 |
iCB925 | 0.1194276 | 1614000000/13514458561 |
iCR744 | 41.47674 | 179687500000/4332247261 |
iCS291 | 0.1405489 | 38125/271258 |
iCS400 | 0.215639 | 63750/295633 |
iCac802 | 0.209597 | 99830000000/476294907501 |
iFF708 | 14.91711 | 113942000000/7638344959 |
iGB555_fixed | 127.7891 | 142500000000000/1115118722693 |
iHD666_fixed | 0.2556721 | 163316006250/638771297231 |
iIB711 | 84.68841 | 100000000000/1180799053 |
iIT341 | 0.6928127 | 814668000000/1175884921963 |
iJL432 | 0.3287407 | 3750000000/11407166737 |
iJN678 | 0.06314984 | 869550000000/13769631712373 |
iJN746 | 3.679412 | 40000000/10871301 |
iJO1366 | 0.9823718 | 189480000/192880127 |
iJP815 | 0.861512 | 179500000/208354621 |
iJR904 | 0.9219481 | 6380800/6920997 |
iJS747 | 34.17266 | 15000000000000/438947370703 |
iKF1028 | 0.517807 | 1900000/3669321 |
iLC915 | 79.02123 | 786562500000000/9953812160053 |
iLL672 | 3.475283 | 62750000000/18056084533 |
iMA871 | 27.79298 | 100000000000/3598031369 |
iMA945 | 79.58958 | 5000000000/62822291 |
iMB745 | 0.03094245 | 161000000/5203208413 |
iMH551 | 0.7750811 | 27300000000/35222122883 |
iMM1415 | 1.363428 | 110000/80679 |
iMM904 | 0.2878657 | 145400000/505096641 |
iMO1056 | 1.047929 | 100000000/95426353 |
iMP429_fixed | 0.8044324 | 7063000000/8780103713 |
iND750 | 0.09732338 | 21000000/215775499 |
iNJ661 | 0.05219947 | 894000/17126611 |
iNJ661m | 0.0521992 | 107280000/2055203801 |
iNV213 | 11.53886 | 12500000000000000/1083295987243349 |
iOG654 | 0.3554469 | 12500/35167 |
iOR363 | 250 | 250 |
iPP668 | 3.891474 | 95000000/24412341 |
iPS189_fixed | 2.238961 | 90000000/40197209 |
iRC1080 | 6.156851 | 1000000000000000000000/162420679450988000257 |
iRM588 | 1000 | 1000 |
iRR1083 | 77.94736 | 1250000000/16036463 |
iRS1563 | 0.07996249 | 16170000000000000000/202219826710707573821 |
iRS1597 | 8.969346 | 37500000/4180907 |
iRS605_fixed | 2.11678 | 2051250000/969042437 |
iRsp1095 | 9.686899 | 1514600000000000000000000/15635550882015213602... |
iSB619 | 0.1580503 | 10000/63271 |
iSH335 | 1.159211 | 87700000000/75654904569 |
iSO783 | 17.92031 | 100000000000/5580261343 |
iSR432 | 11.48257 | 72500000000000000/6313917669853967 |
iSS724 | 22.42152 | 5000/223 |
iSS884 | 70.35929 | 7513000000000/106780503717 |
iSyn669 | 0.1790899 | 6802000000/37980929237 |
iTH366 | 27890.89 | 10741489258500000/385125386207 |
iTL885 | 7.098836 | 697400000000/98241455449 |
iTY425_fixed | 0.8868335 | 5000000/5638037 |
iVM679 | 2.82657 | 26520000000/9382396471 |
iVS941_fixed | 0.5233846 | 10000000/19106407 |
iWV1314 | 25.6824 | 10504392200845731410/409011287584573141 |
iWZ663 | 34.07588 | 350000000000/10271194511 |
iYL1228 | 1.042637 | 1590492000/1525450603 |
iYO844 | 1.582798 | 256250000000/161896806353 |
iZM363 | 2.532606 | 181250000/71566597 |
iZmobMBEL601 | 0.3500804 | 61718750/176298791 |
mus_musculus | 129.1006 | 10000000/77459 |
textbook | 0.8739215 | 686440/785471 |
Here is the $\sum\left|\mathbf S \cdot v\right|$ error computed using floating point operations for every solver. When computed rationally with esolver above, this value was exactly 0. Howver, when rounding the fractional values to floating point, there is a very small amount of resulting error, so even esolver does not give 0 error for this computation.
errors.T
cglpk | cglpk_exact | coin | cplex | esolver | glpk | gurobi | mosek | |
---|---|---|---|---|---|---|---|---|
AbyMBEL891 | 1.030879e-11 | 6.538390e-12 | 3.057219e-11 | 1.652062e-11 | 6.093565e-12 | 1.168024e-11 | 2.098006e-11 | 1.866628e-11 |
AraGEM | 4.518242e-12 | 3.761263e-12 | 4.350840e-11 | 1.031621e-11 | 3.953687e-12 | 5.721206e-12 | 1.492412e-11 | 1.607253e-11 |
GSMN_TB | 3.265029e-10 | 1.438631e-10 | 4.422610e-10 | 1.794655e-09 | 1.318417e-10 | 1.580843e-07 | 2.451718e-09 | 1.055735e-09 |
PpaMBEL1254 | 5.524246e-12 | 5.503863e-12 | 1.686022e-11 | 1.653475e-11 | 1.599098e-12 | 5.808043e-12 | 6.458234e-12 | 1.327733e-11 |
PpuMBEL1071 | 9.213515e-12 | 1.006636e-07 | 2.682011e-11 | 6.212253e-12 | 5.611067e-12 | 6.928756e-12 | 1.996325e-11 | 1.154134e-11 |
STM_v1_0 | 2.442772e-12 | 7.615986e-09 | 1.558550e-09 | 6.747805e-13 | 4.133462e-13 | 4.027310e-12 | 2.884140e-11 | 1.424397e-11 |
S_coilicolor_fixed | 6.094508e-11 | 3.403941e-11 | 1.417303e-10 | 5.070666e-11 | 3.497688e-11 | 4.686266e-11 | 5.399156e-11 | 2.215057e-10 |
SpoMBEL1693 | 9.424184e-12 | 6.328653e-12 | 2.409888e-11 | 7.634511e-12 | 5.512237e-12 | 8.155074e-12 | 9.632115e-12 | 2.056227e-11 |
T_Maritima | 1.149696e-12 | 1.017970e-09 | 2.680799e-12 | 1.312999e-12 | 1.125577e-12 | 1.578348e-12 | 4.792797e-12 | 1.448889e-11 |
VvuMBEL943 | 1.291556e-11 | 1.200139e-11 | 1.619902e-11 | 5.522043e-12 | 1.396693e-11 | 8.099037e-12 | 7.938761e-12 | 2.371747e-11 |
iAC560 | 8.194865e-12 | 9.868076e-12 | 2.435742e-11 | 8.923992e-12 | 6.451882e-12 | 7.145092e-12 | 1.873765e-11 | 1.947821e-11 |
iAF1260 | 1.781254e-09 | 1.946048e-09 | 5.678922e-09 | 1.214388e-09 | 8.198651e-10 | 7.152690e-09 | 9.012081e-09 | 1.764879e-08 |
iAF692 | 3.386389e-09 | 2.220311e-09 | 8.946148e-09 | 1.759396e-08 | 1.963760e-09 | 1.222407e-09 | 8.575538e-09 | 1.040327e-08 |
iAI549 | 1.612223e-11 | 9.931913e-12 | 4.028457e-11 | 2.568619e-11 | 1.368209e-11 | 1.323319e-11 | 1.541363e-11 | 2.428250e-11 |
iAN840m | 3.298200e-10 | 1.804508e-10 | 1.107875e-10 | 2.751869e-10 | 2.302759e-10 | 2.859458e-10 | 8.054293e-10 | 1.172849e-09 |
iAO358 | 1.124310e-11 | 1.091583e-11 | 3.182512e-11 | 1.906676e-11 | 1.175427e-11 | 1.348169e-11 | 1.847833e-11 | 2.943036e-11 |
iAbaylyiV4 | 2.977077e-12 | 3.012134e-12 | 8.290163e-12 | 5.293440e-12 | 6.227974e-12 | 4.977532e-12 | 1.004922e-11 | 1.594689e-11 |
iBT721_fixed | 6.197820e-12 | 3.083755e-12 | 4.031970e-11 | 1.364242e-12 | 2.629008e-12 | 4.273915e-12 | 3.751666e-12 | 1.984154e-11 |
iBsu1103 | 2.972863e-10 | 6.526051e-06 | 7.303685e-10 | 3.339946e-10 | 2.010636e-10 | 3.242728e-10 | 5.418732e-10 | 8.971953e-10 |
iCA1273 | 2.755569e-12 | 2.649891e-12 | 9.081865e-11 | 2.677644e-12 | 1.519041e-12 | 3.057492e-12 | 8.550924e-12 | 1.762628e-11 |
iCB925 | 1.736274e-14 | 9.613512e-15 | 2.816809e-14 | 1.165951e-14 | 1.306301e-14 | 2.114921e-14 | 5.169930e-12 | 1.014086e-11 |
iCR744 | 1.018664e-11 | 6.352933e-12 | 3.419470e-11 | 1.823183e-11 | 6.848318e-12 | 6.607602e-12 | 1.363850e-11 | 1.417687e-11 |
iCS291 | 4.977130e-13 | 3.683998e-13 | 1.375014e-12 | 8.569881e-13 | 3.690381e-13 | 3.893899e-13 | 4.744788e-12 | 6.790318e-12 |
iCS400 | 1.469269e-12 | 1.157699e-12 | 2.533241e-11 | 1.845843e-12 | 4.832384e-13 | 1.527389e-12 | 5.889844e-12 | 9.199558e-12 |
iCac802 | 8.493680e-14 | 3.153588e-14 | 1.363077e-13 | 1.898222e-13 | 7.927829e-14 | 7.058789e-14 | 1.260632e-11 | 1.055401e-11 |
iFF708 | 9.631808e-12 | 5.780962e-12 | 1.847612e-11 | 6.812400e-12 | 5.430347e-12 | 1.020766e-11 | 8.761480e-12 | 2.012872e-11 |
iGB555_fixed | 1.618755e-11 | 4.991450e-10 | 3.935196e-11 | 8.029397e-12 | 5.976067e-12 | 1.892854e-11 | 8.302095e-12 | 3.028083e-11 |
iHD666_fixed | 6.101243e-12 | 2.778296e-11 | 1.746997e-11 | 3.751388e-12 | 3.346992e-12 | 7.398641e-12 | 6.864509e-12 | 1.167770e-11 |
iIB711 | 8.816919e-12 | 9.826012e-12 | 2.293666e-11 | 2.186360e-11 | 1.150156e-11 | 1.309052e-11 | 1.211514e-11 | 2.583597e-11 |
iIT341 | 1.014080e-09 | 1.807772e-09 | 5.907021e-09 | 8.119830e-10 | 2.710340e-10 | 1.470638e-09 | 5.405914e-09 | 7.601729e-09 |
iJL432 | 1.174412e-12 | 3.901074e-13 | 1.789826e-12 | 3.963390e-13 | 3.900797e-13 | 7.603562e-13 | 4.689371e-12 | 3.737990e-12 |
iJN678 | 2.398464e-14 | 2.797895e-10 | 1.930007e-14 | 1.396985e-14 | 2.238604e-14 | 2.488953e-14 | 7.036177e-12 | 5.716085e-12 |
iJN746 | 5.745402e-09 | 1.309358e-08 | 9.719125e-09 | 3.280881e-09 | 2.846633e-09 | 4.145871e-09 | 8.716805e-09 | 1.037925e-08 |
iJO1366 | 3.229136e-12 | 2.352308e-09 | 1.235567e-11 | 5.307026e-12 | 8.026430e-13 | 4.692354e-12 | 9.259564e-12 | 1.267621e-11 |
iJP815 | 1.020123e-09 | 7.944625e-10 | 3.420634e-09 | 1.550045e-08 | 7.528140e-10 | 1.367096e-09 | 1.359488e-08 | 5.964099e-09 |
iJR904 | 1.099850e-09 | 3.218263e-09 | 4.340962e-09 | 6.192079e-10 | 1.427380e-10 | 1.365733e-09 | 6.213569e-09 | 1.420731e-08 |
iJS747 | 7.176808e-12 | 3.632675e-07 | 9.697313e-12 | 9.643009e-12 | 3.800987e-12 | 4.923902e-12 | 5.578066e-12 | 8.495003e-12 |
iKF1028 | 4.410775e-09 | 2.512140e-09 | 3.931006e-09 | 4.556265e-09 | 1.713361e-09 | 4.626908e-09 | 1.043391e-08 | 1.115077e-08 |
iLC915 | 8.942108e-12 | 5.859216e-12 | 2.288417e-11 | 9.887922e-12 | 6.807457e-12 | 1.100345e-11 | 1.760760e-11 | 1.649339e-11 |
iLL672 | 7.130910e-12 | 7.483421e-09 | 3.135656e-11 | 7.181390e-12 | 5.127530e-12 | 1.080215e-11 | 5.221250e-12 | 1.864336e-11 |
iMA871 | 8.159995e-12 | 4.129003e-12 | 3.886357e-11 | 9.557480e-12 | 4.393495e-12 | 7.955587e-12 | 1.248793e-11 | 2.376854e-11 |
iMA945 | 1.398577e-11 | 1.241593e-11 | 6.318794e-10 | 1.253969e-11 | 7.349408e-12 | 9.134488e-12 | 2.082624e-11 | 1.493498e-11 |
iMB745 | 5.070478e-12 | 4.316394e-12 | 3.264610e-11 | 6.657764e-12 | 3.221213e-12 | 5.698374e-12 | 1.078196e-11 | 1.047325e-10 |
iMH551 | 2.251095e-12 | 1.368655e-12 | 1.658942e-11 | 1.702092e-12 | 1.852061e-12 | 2.130895e-12 | 7.064203e-12 | 1.524475e-11 |
iMM1415 | 1.248012e-09 | 6.982713e-10 | 3.418482e-09 | 8.552331e-10 | 6.642941e-10 | 1.483438e-09 | 2.067248e-09 | 5.278308e-09 |
iMM904 | 3.595750e-09 | 3.644007e-09 | 8.308698e-09 | 2.982506e-09 | 1.531252e-09 | 4.619449e-09 | 7.938743e-09 | 1.828506e-08 |
iMO1056 | 4.451167e-12 | 4.065560e-09 | 5.216133e-12 | 2.091337e-12 | 2.158161e-12 | 4.592567e-12 | 7.587645e-12 | 1.088813e-11 |
iMP429_fixed | 1.037411e-12 | 6.876871e-13 | 2.242258e-12 | 5.857062e-13 | 1.149136e-12 | 1.776228e-12 | 6.084059e-12 | 9.247175e-12 |
iND750 | 2.859207e-09 | 2.514810e-09 | 5.778406e-09 | 8.041428e-09 | 2.058405e-09 | 3.681656e-09 | 7.571422e-09 | 1.155155e-08 |
iNJ661 | 4.577143e-09 | 4.961898e-09 | 6.366734e-09 | 3.712113e-09 | 3.654260e-09 | 4.502374e-09 | 1.052895e-08 | 1.091361e-08 |
iNJ661m | 4.915935e-12 | 1.054765e-11 | 1.969559e-11 | 1.044025e-07 | 2.524202e-12 | 5.219989e-07 | 4.698032e-07 | 1.416549e-11 |
iNV213 | 4.984638e-12 | 2.831209e-07 | 1.319748e-11 | 4.020673e-12 | 1.957150e-12 | 3.845659e-12 | 6.196237e-12 | 8.082979e-12 |
iOG654 | 9.605928e-12 | 6.018975e-12 | 2.579665e-11 | 6.017891e-12 | 9.601608e-12 | 1.360856e-11 | 1.486815e-11 | 2.803368e-11 |
iOR363 | 2.717474e-12 | 0.000000e+00 | 3.817827e-11 | 2.046363e-12 | 0.000000e+00 | 4.687704e-12 | 3.893774e-12 | 4.926430e-12 |
iPP668 | 5.361779e-12 | 2.598573e-12 | 1.432983e-11 | 1.154974e-12 | 1.613025e-12 | 4.027082e-12 | 3.367375e-12 | 1.306011e-11 |
iPS189_fixed | 4.986594e-13 | 2.228602e-09 | 6.076497e-13 | 6.313791e-13 | 2.516057e-13 | 8.629994e-13 | 1.503601e-11 | 3.438656e-12 |
iRC1080 | 1.212713e-11 | 5.622330e-08 | 2.998578e-11 | 1.227949e-11 | 5.134023e-12 | 1.027390e-11 | 3.109267e-11 | 3.641264e-11 |
iRM588 | 4.377281e-10 | 6.098593e-06 | 9.950361e-10 | 3.434693e-10 | 2.256777e-10 | 7.210925e-10 | 8.615869e-10 | 7.823844e-10 |
iRR1083 | 8.190296e-12 | 1.242195e-06 | 2.693539e-11 | 1.105927e-11 | 5.338382e-12 | 9.888460e-12 | 1.179566e-11 | 1.757284e-11 |
iRS1563 | 2.844885e-12 | 2.288953e-12 | 1.005008e-11 | 4.673761e-12 | 1.709565e-12 | 3.843955e-12 | 1.646831e-11 | 1.570177e-11 |
iRS1597 | 2.635014e-12 | 3.367490e-12 | 1.371104e-11 | 3.210002e-12 | 1.169068e-12 | 1.140946e-12 | 1.451179e-11 | 5.307929e-12 |
iRS605_fixed | 5.301002e-12 | 5.221034e-12 | 1.443769e-11 | 8.543278e-12 | 4.211766e-12 | 4.851140e-12 | 1.006191e-11 | 1.255027e-11 |
iRsp1095 | 4.771094e-12 | 1.286166e-07 | 1.499878e-11 | 5.990567e-12 | 5.702781e-12 | 5.757338e-12 | 1.136189e-11 | 3.360485e-11 |
iSB619 | 6.677286e-10 | 2.461952e-10 | 6.072867e-10 | 2.292188e-11 | 2.877589e-11 | 1.436060e-10 | 6.720453e-09 | 1.817552e-08 |
iSH335 | 8.608735e-13 | 7.918396e-13 | 1.719772e-11 | 2.412978e-13 | 1.354082e-12 | 7.116117e-13 | 4.743332e-12 | 5.824515e-12 |
iSO783 | 9.201850e-12 | 2.860468e-10 | 3.880035e-11 | 2.266519e-11 | 5.511215e-12 | 1.131129e-11 | 1.612790e-11 | 1.880562e-11 |
iSR432 | 5.763678e-12 | 2.818245e-07 | 1.616559e-11 | 5.417731e-12 | 5.851002e-12 | 4.656121e-12 | 1.018306e-11 | 1.522397e-11 |
iSS724 | 1.263471e-11 | 1.255100e-11 | 5.174531e-11 | 1.577047e-11 | 9.879180e-12 | 1.510881e-11 | 2.661788e-11 | 4.044156e-10 |
iSS884 | 1.354254e-11 | 9.174448e-12 | 2.825013e-11 | 6.639951e-12 | 8.284437e-12 | 9.998729e-12 | 3.226585e-11 | 2.586860e-11 |
iSyn669 | 8.127297e-11 | 1.040794e-10 | 1.415821e-10 | 6.030044e-11 | 2.003912e-11 | 3.519071e-11 | 1.160358e-10 | 1.517444e-10 |
iTH366 | 4.467643e-09 | 6.915386e-09 | 1.450880e-08 | 4.967946e-09 | 4.431032e-09 | 8.734066e-09 | 1.281431e-08 | 2.244135e-08 |
iTL885 | 7.174270e-12 | 7.233351e-12 | 1.081575e-11 | 7.574101e-12 | 2.522095e-12 | 3.749231e-12 | 9.384046e-12 | 2.773719e-11 |
iTY425_fixed | 1.357132e-12 | 6.821528e-13 | 3.765527e-12 | 1.813959e-12 | 9.112030e-13 | 1.091689e-12 | 5.685786e-12 | 1.324586e-11 |
iVM679 | 5.441300e-12 | 3.543573e-09 | 1.112015e-11 | 1.859461e-11 | 2.503111e-12 | 2.679210e-12 | 1.226340e-11 | 8.445926e-12 |
iVS941_fixed | 5.781317e-12 | 3.985063e-12 | 2.889106e-11 | 4.555880e-12 | 4.109086e-12 | 3.148214e-12 | 8.170712e-12 | 5.949118e-12 |
iWV1314 | 8.397096e-12 | 9.542499e-12 | 4.617399e-11 | 1.552834e-11 | 7.278331e-12 | 9.208338e-12 | 1.366008e-11 | 1.755370e-11 |
iWZ663 | 7.253877e-12 | 3.519589e-08 | 4.027807e-11 | 8.397005e-12 | 5.308528e-12 | 4.786052e-12 | 1.215181e-11 | 1.217298e-11 |
iYL1228 | 3.579303e-12 | 5.812428e-10 | 6.740615e-12 | 1.638551e-12 | 6.258599e-13 | 1.245614e-12 | 9.171871e-12 | 1.130580e-11 |
iYO844 | 6.749347e-12 | 1.459393e-08 | 5.658764e-12 | 1.799575e-12 | 1.478164e-12 | 1.119653e-12 | 6.888139e-12 | 2.063596e-11 |
iZM363 | 5.369345e-12 | 5.353776e-12 | 1.529245e-11 | 7.623997e-12 | 4.478320e-12 | 5.519462e-12 | 8.284732e-12 | 1.405405e-11 |
iZmobMBEL601 | 1.672617e-12 | 1.524215e-12 | 4.595579e-12 | 2.783999e-12 | 4.085307e-13 | 1.355290e-12 | 6.795329e-12 | 6.571501e-12 |
mus_musculus | 9.798615e-12 | 4.947154e-12 | 2.169150e-11 | 6.331269e-12 | 4.835687e-12 | 8.265638e-12 | 1.813938e-11 | 1.927275e-11 |
textbook | 7.371881e-14 | 2.203700e-09 | 2.109380e-13 | 5.417888e-14 | 4.862777e-14 | 8.348877e-14 | 1.268388e-09 | 2.745516e-09 |
Here are all the computed biomass flux rates for each solver and model.
results.T
cglpk | cglpk_exact | coin | cplex | esolver | glpk | gurobi | mosek | |
---|---|---|---|---|---|---|---|---|
AbyMBEL891 | 119.233012 | 119.233012 | 119.233012 | 119.233012 | 119.233012 | 119.233012 | 119.233012 | 119.233012 |
AraGEM | 10.000000 | 10.000000 | 10.000000 | 10.000000 | 10.000000 | 10.000000 | 10.000000 | 10.000000 |
GSMN_TB | 0.131262 | 0.131262 | 0.131262 | 0.131262 | 0.131262 | 0.131262 | 0.131262 | 0.131262 |
PpaMBEL1254 | 78.700594 | 78.700594 | 78.700594 | 78.700594 | 78.700594 | 78.700594 | 78.700594 | 78.700594 |
PpuMBEL1071 | 132.365353 | 132.365353 | 132.365353 | 132.365353 | 132.365353 | 132.365353 | 132.365353 | 132.365353 |
STM_v1_0 | 0.477834 | 0.477834 | 0.477834 | 0.477834 | 0.477834 | 0.477834 | 0.477834 | 0.477834 |
S_coilicolor_fixed | 860.088835 | 860.088835 | 860.088835 | 860.088835 | 860.088835 | 860.088835 | 860.088835 | 860.088835 |
SpoMBEL1693 | 63.785658 | 63.785658 | 63.785658 | 63.785658 | 63.785658 | 63.785658 | 63.785658 | 63.785658 |
T_Maritima | 0.359469 | 0.359469 | 0.359469 | 0.359469 | 0.359469 | 0.359469 | 0.359469 | 0.359469 |
VvuMBEL943 | 96.402322 | 96.402322 | 96.402322 | 96.402322 | 96.402322 | 96.402322 | 96.402322 | 96.402322 |
iAC560 | 4.042612 | 4.042612 | 4.042612 | 4.042612 | 4.042612 | 4.042612 | 4.042612 | 4.042612 |
iAF1260 | 0.736701 | 0.736701 | 0.736701 | 0.736701 | 0.736701 | 0.736701 | 0.736701 | 0.736701 |
iAF692 | 0.027250 | 0.027250 | 0.027250 | 0.027250 | 0.027250 | 0.027250 | 0.027250 | 0.027250 |
iAI549 | 84.174193 | 84.174193 | 84.174193 | 84.174193 | 84.174193 | 84.174193 | 84.174193 | 84.174193 |
iAN840m | 0.340136 | 0.340136 | 0.340136 | 0.340136 | 0.340136 | 0.340136 | 0.340136 | 0.340136 |
iAO358 | 255.180548 | 255.180548 | 255.180548 | 255.180548 | 255.180548 | 255.180548 | 255.180548 | 255.180548 |
iAbaylyiV4 | 12.306545 | 12.306545 | 12.306545 | 12.306545 | 12.306545 | 12.306545 | 12.306545 | 12.306545 |
iBT721_fixed | 0.500000 | 0.500000 | 0.500000 | 0.500000 | 0.500000 | 0.500000 | 0.500000 | 0.500000 |
iBsu1103 | 1229.657244 | 1229.657244 | 1229.657244 | 1229.657244 | 1229.657244 | 1229.657244 | 1229.657244 | 1229.657244 |
iCA1273 | 0.740242 | 0.740242 | 0.740242 | 0.740242 | 0.740242 | 0.740242 | 0.740242 | 0.740242 |
iCB925 | 0.119428 | 0.119428 | 0.119428 | 0.119428 | 0.119428 | 0.119428 | 0.119428 | 0.119428 |
iCR744 | 41.476742 | 41.476742 | 41.476742 | 41.476742 | 41.476742 | 41.476742 | 41.476742 | 41.476742 |
iCS291 | 0.140549 | 0.140549 | 0.140549 | 0.140549 | 0.140549 | 0.140549 | 0.140549 | 0.140549 |
iCS400 | 0.215639 | 0.215639 | 0.215639 | 0.215639 | 0.215639 | 0.215639 | 0.215639 | 0.215639 |
iCac802 | 0.209597 | 0.209597 | 0.209597 | 0.209597 | 0.209597 | 0.209597 | 0.209597 | 0.209597 |
iFF708 | 14.917106 | 14.917106 | 14.917106 | 14.917106 | 14.917106 | 14.917106 | 14.917106 | 14.917106 |
iGB555_fixed | 127.789084 | 127.789084 | 127.789084 | 127.789084 | 127.789084 | 127.789084 | 127.789084 | 127.789084 |
iHD666_fixed | 0.255672 | 0.255672 | 0.255672 | 0.255672 | 0.255672 | 0.255672 | 0.255672 | 0.255672 |
iIB711 | 84.688415 | 84.688415 | 84.688415 | 84.688415 | 84.688415 | 84.688415 | 84.688415 | 84.688415 |
iIT341 | 0.692813 | 0.692813 | 0.692813 | 0.692813 | 0.692813 | 0.692813 | 0.692813 | 0.692813 |
iJL432 | 0.328741 | 0.328741 | 0.328741 | 0.328741 | 0.328741 | 0.328741 | 0.328741 | 0.328741 |
iJN678 | 0.063150 | 0.063150 | 0.063150 | 0.063150 | 0.063150 | 0.063150 | 0.063150 | 0.063150 |
iJN746 | 3.679412 | 3.679412 | 3.679412 | 3.679412 | 3.679412 | 3.679412 | 3.679412 | 3.679412 |
iJO1366 | 0.982372 | 0.982372 | 0.982372 | 0.982372 | 0.982372 | 0.982372 | 0.982372 | 0.982372 |
iJP815 | 0.861512 | 0.861512 | 0.861512 | 0.861512 | 0.861512 | 0.861512 | 0.861512 | 0.861512 |
iJR904 | 0.921948 | 0.921948 | 0.921948 | 0.921948 | 0.921948 | 0.921948 | 0.921948 | 0.921948 |
iJS747 | 34.172662 | 34.172662 | 34.172662 | 34.172662 | 34.172662 | 34.172662 | 34.172662 | 34.172662 |
iKF1028 | 0.517807 | 0.517807 | 0.517807 | 0.517807 | 0.517807 | 0.517807 | 0.517807 | 0.517807 |
iLC915 | 79.021232 | 79.021232 | 79.021232 | 79.021232 | 79.021232 | 79.021232 | 79.021232 | 79.021232 |
iLL672 | 3.475283 | 3.475283 | 3.475283 | 3.475283 | 3.475283 | 3.475283 | 3.475283 | 3.475283 |
iMA871 | 27.792976 | 27.792976 | 27.792976 | 27.792976 | 27.792976 | 27.792976 | 27.792976 | 27.792976 |
iMA945 | 79.589584 | 79.589584 | 79.589584 | 79.589584 | 79.589584 | 79.589584 | 79.589584 | 79.589584 |
iMB745 | 0.030942 | 0.030942 | 0.030942 | 0.030942 | 0.030942 | 0.030942 | 0.030942 | 0.030942 |
iMH551 | 0.775081 | 0.775081 | 0.775081 | 0.775081 | 0.775081 | 0.775081 | 0.775081 | 0.775081 |
iMM1415 | 1.363428 | 1.363428 | 1.363428 | 1.363428 | 1.363428 | 1.363428 | 1.363428 | 1.363428 |
iMM904 | 0.287866 | 0.287866 | 0.287866 | 0.287866 | 0.287866 | 0.287866 | 0.287866 | 0.287866 |
iMO1056 | 1.047929 | 1.047929 | 1.047929 | 1.047929 | 1.047929 | 1.047929 | 1.047929 | 1.047929 |
iMP429_fixed | 0.804432 | 0.804432 | 0.804432 | 0.804432 | 0.804432 | 0.804432 | 0.804432 | 0.804432 |
iND750 | 0.097323 | 0.097323 | 0.097323 | 0.097323 | 0.097323 | 0.097323 | 0.097323 | 0.097323 |
iNJ661 | 0.052199 | 0.052199 | 0.052199 | 0.052199 | 0.052199 | 0.052199 | 0.052199 | 0.052199 |
iNJ661m | 0.052199 | 0.052199 | 0.052199 | 0.052199 | 0.052199 | 0.052199 | 0.052199 | 0.052199 |
iNV213 | 11.538859 | 11.538859 | 11.538859 | 11.538859 | 11.538859 | 11.538859 | 11.538859 | 11.538859 |
iOG654 | 0.355447 | 0.355447 | 0.355447 | 0.355447 | 0.355447 | 0.355447 | 0.355447 | 0.355447 |
iOR363 | 250.000000 | 250.000000 | 250.000000 | 250.000000 | 250.000000 | 250.000000 | 250.000000 | 250.000000 |
iPP668 | 3.891474 | 3.891474 | 3.891474 | 3.891474 | 3.891474 | 3.891474 | 3.891474 | 3.891474 |
iPS189_fixed | 2.238961 | 2.238961 | 2.238961 | 2.238961 | 2.238961 | 2.238961 | 2.238961 | 2.238961 |
iRC1080 | 6.156851 | 6.156851 | 6.156851 | 6.156851 | 6.156851 | 6.156851 | 6.156851 | 6.156851 |
iRM588 | 1000.000000 | 1000.000000 | 1000.000000 | 1000.000000 | 1000.000000 | 1000.000000 | 1000.000000 | 1000.000000 |
iRR1083 | 77.947363 | 77.947363 | 77.947363 | 77.947363 | 77.947363 | 77.947363 | 77.947363 | 77.947363 |
iRS1563 | 0.079962 | 0.079962 | 0.079962 | 0.079962 | 0.079962 | 0.079962 | 0.079962 | 0.079962 |
iRS1597 | 8.969346 | 8.969346 | 8.969346 | 8.969346 | 8.969346 | 8.969346 | 8.969346 | 8.969346 |
iRS605_fixed | 2.116780 | 2.116780 | 2.116780 | 2.116780 | 2.116780 | 2.116780 | 2.116780 | 2.116780 |
iRsp1095 | 9.686899 | 9.686899 | 9.686899 | 9.686899 | 9.686899 | 9.686899 | 9.686899 | 9.686899 |
iSB619 | 0.158050 | 0.158050 | 0.158050 | 0.158050 | 0.158050 | 0.158050 | 0.158050 | 0.158050 |
iSH335 | 1.159211 | 1.159211 | 1.159211 | 1.159211 | 1.159211 | 1.159211 | 1.159211 | 1.159211 |
iSO783 | 17.920308 | 17.920308 | 17.920308 | 17.920308 | 17.920308 | 17.920308 | 17.920308 | 17.920308 |
iSR432 | 11.482570 | 11.482570 | 11.482570 | 11.482570 | 11.482570 | 11.482570 | 11.482570 | 11.482570 |
iSS724 | 22.421525 | 22.421525 | 22.421525 | 22.421525 | 22.421525 | 22.421525 | 22.421525 | 22.421525 |
iSS884 | 70.359286 | 70.359286 | 70.359286 | 70.359286 | 70.359286 | 70.359286 | 70.359286 | 70.359286 |
iSyn669 | 0.179090 | 0.179090 | 0.179090 | 0.179090 | 0.179090 | 0.179090 | 0.179090 | 0.179090 |
iTH366 | 27890.888638 | 27890.888638 | 27890.888638 | 27890.888638 | 27890.888638 | 27890.888638 | 27890.888638 | 27890.888638 |
iTL885 | 7.098836 | 7.098836 | 7.098836 | 7.098836 | 7.098836 | 7.098836 | 7.098836 | 7.098836 |
iTY425_fixed | 0.886833 | 0.886833 | 0.886833 | 0.886833 | 0.886833 | 0.886833 | 0.886833 | 0.886833 |
iVM679 | 2.826570 | 2.826570 | 2.826570 | 2.826570 | 2.826570 | 2.826570 | 2.826570 | 2.826570 |
iVS941_fixed | 0.523385 | 0.523385 | 0.523385 | 0.523385 | 0.523385 | 0.523385 | 0.523385 | 0.523385 |
iWV1314 | 25.682402 | 25.682402 | 25.682402 | 25.682402 | 25.682402 | 25.682402 | 25.682402 | 25.682402 |
iWZ663 | 34.075881 | 34.075881 | 34.075881 | 34.075881 | 34.075881 | 34.075881 | 34.075881 | 34.075881 |
iYL1228 | 1.042637 | 1.042637 | 1.042638 | 1.042637 | 1.042637 | 1.042637 | 1.042637 | 1.042637 |
iYO844 | 1.582798 | 1.582798 | 1.582798 | 1.582798 | 1.582798 | 1.582798 | 1.582798 | 1.582798 |
iZM363 | 2.532606 | 2.532606 | 2.532606 | 2.532606 | 2.532606 | 2.532606 | 2.532606 | 2.532606 |
iZmobMBEL601 | 0.350080 | 0.350080 | 0.350080 | 0.350080 | 0.350080 | 0.350080 | 0.350080 | 0.350080 |
mus_musculus | 129.100556 | 129.100556 | 129.100556 | 129.100556 | 129.100556 | 129.100556 | 129.100556 | 129.100556 |
textbook | 0.873922 | 0.873922 | 0.873922 | 0.873922 | 0.873922 | 0.873922 | 0.873922 | 0.873922 |
The objectives computed for these solvers are effectively the same as those computed by esolver.
differences = (results - results.ix["esolver"]).T
differences.pop("esolver")
differences
cglpk | cglpk_exact | coin | cplex | glpk | gurobi | mosek | |
---|---|---|---|---|---|---|---|
AbyMBEL891 | 1.136868e-13 | 0.000000e+00 | 3.844036e-11 | -5.684342e-14 | 1.136868e-13 | -2.415845e-13 | 9.947598e-14 |
AraGEM | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 |
GSMN_TB | -4.656553e-13 | 0.000000e+00 | 5.085987e-12 | -2.345454e-11 | 1.011393e-08 | -1.665335e-15 | -1.402767e-12 |
PpaMBEL1254 | 0.000000e+00 | 0.000000e+00 | 5.805134e-11 | -1.847411e-13 | 0.000000e+00 | 0.000000e+00 | -7.105427e-14 |
PpuMBEL1071 | 8.526513e-14 | 5.117897e-10 | 4.602612e-10 | 5.684342e-14 | 8.526513e-14 | 5.684342e-14 | -1.136868e-13 |
STM_v1_0 | 3.863576e-14 | 4.957084e-10 | 3.605212e-07 | -1.498801e-15 | 1.086908e-13 | -4.996004e-16 | 4.814482e-13 |
S_coilicolor_fixed | 1.136868e-13 | 0.000000e+00 | 1.364242e-12 | 0.000000e+00 | 1.136868e-13 | 0.000000e+00 | -1.250555e-12 |
SpoMBEL1693 | -1.421085e-14 | 0.000000e+00 | 2.098943e-11 | -1.421085e-14 | 7.105427e-14 | -2.842171e-14 | -6.039613e-13 |
T_Maritima | -3.214096e-14 | 9.456913e-11 | 2.230516e-09 | 3.330669e-16 | -2.114975e-14 | -3.330669e-16 | 8.437695e-14 |
VvuMBEL943 | 1.421085e-14 | 0.000000e+00 | 1.922729e-11 | 4.263256e-14 | 4.263256e-14 | 0.000000e+00 | 1.563194e-13 |
iAC560 | 2.664535e-15 | 0.000000e+00 | 8.553158e-13 | 8.881784e-16 | 0.000000e+00 | 1.776357e-15 | 1.421085e-14 |
iAF1260 | 2.087197e-11 | 0.000000e+00 | 8.428154e-08 | -2.066280e-11 | 1.858336e-11 | -1.196998e-11 | 1.749767e-11 |
iAF692 | -3.651770e-11 | -2.846202e-11 | 1.981591e-09 | 6.965345e-09 | -4.769716e-12 | 2.617935e-09 | -1.106832e-09 |
iAI549 | -7.673862e-13 | 0.000000e+00 | 5.840661e-11 | -5.826450e-13 | 1.705303e-13 | -1.236344e-12 | 6.963319e-13 |
iAN840m | 0.000000e+00 | 0.000000e+00 | 1.872813e-08 | -5.551115e-17 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 |
iAO358 | -8.526513e-14 | 0.000000e+00 | 1.497824e-11 | -1.989520e-13 | 2.842171e-14 | -5.115908e-13 | -5.684342e-14 |
iAbaylyiV4 | 4.796163e-14 | -1.776357e-15 | 8.941647e-11 | -1.776357e-15 | 1.953993e-14 | 1.065814e-14 | -4.494183e-13 |
iBT721_fixed | 0.000000e+00 | 0.000000e+00 | -6.938894e-15 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 1.110223e-16 |
iBsu1103 | -2.273737e-13 | -2.653928e-08 | 5.934453e-11 | -1.136868e-12 | 2.273737e-13 | 0.000000e+00 | 2.046363e-12 |
iCA1273 | -3.275158e-14 | 0.000000e+00 | 1.637933e-08 | 4.685141e-14 | 5.406786e-14 | -4.696243e-14 | 2.265965e-13 |
iCB925 | 7.494005e-16 | 0.000000e+00 | 2.920300e-11 | -3.191891e-16 | -1.942890e-16 | 2.636780e-16 | -2.703671e-13 |
iCR744 | 3.552714e-14 | 0.000000e+00 | 2.358817e-09 | -5.826450e-13 | -1.350031e-13 | 1.705303e-13 | 5.186962e-13 |
iCS291 | 1.193490e-15 | 0.000000e+00 | 2.731065e-12 | -6.938894e-16 | -1.110223e-15 | -1.276756e-15 | -3.608225e-16 |
iCS400 | -1.026956e-15 | 0.000000e+00 | 4.090339e-13 | -1.110223e-16 | 2.470246e-15 | 0.000000e+00 | 1.956768e-14 |
iCac802 | 4.440892e-16 | 0.000000e+00 | 9.617439e-09 | -1.665335e-16 | -1.249001e-15 | 3.885781e-16 | -3.314016e-14 |
iFF708 | 1.776357e-15 | 0.000000e+00 | 2.838618e-12 | -5.329071e-14 | 1.421085e-14 | 5.329071e-15 | -4.263256e-14 |
iGB555_fixed | -1.037392e-12 | 5.440199e-10 | 4.702940e-10 | 1.705303e-13 | -2.060574e-12 | 2.700062e-13 | 1.577405e-12 |
iHD666_fixed | 3.774758e-14 | 9.730550e-13 | 1.013567e-08 | 4.718448e-15 | -7.366330e-14 | 3.164136e-15 | -2.220446e-16 |
iIB711 | -1.421085e-14 | 0.000000e+00 | 2.015099e-11 | 4.263256e-14 | -2.842171e-14 | -2.842171e-14 | -1.421085e-14 |
iIT341 | -1.129519e-11 | 2.245907e-10 | 6.851687e-08 | -4.440892e-15 | -1.403899e-11 | -2.111644e-13 | -6.530149e-10 |
iJL432 | -1.554312e-14 | 0.000000e+00 | 4.104939e-12 | -1.193490e-14 | 2.103873e-14 | 2.708944e-14 | 1.809664e-13 |
iJN678 | -4.718448e-16 | 2.856902e-11 | 2.463432e-08 | -1.082467e-15 | -2.220446e-16 | -2.775558e-17 | 1.214445e-13 |
iJN746 | 1.231681e-10 | 1.059390e-09 | 2.485335e-08 | 1.167688e-10 | 7.149392e-11 | -6.661338e-15 | 1.743801e-10 |
iJO1366 | 4.973799e-14 | 1.739909e-10 | 1.544051e-07 | 8.881784e-16 | 5.107026e-14 | -2.664535e-15 | 5.774270e-13 |
iJP815 | 1.783040e-11 | 0.000000e+00 | 3.016005e-09 | 2.160384e-10 | 2.299161e-12 | 3.759559e-11 | 1.973555e-11 |
iJR904 | -3.364420e-12 | 2.154040e-10 | 1.404389e-07 | 1.258993e-13 | -3.852363e-11 | 2.146194e-11 | 3.302114e-11 |
iJS747 | -1.421085e-13 | -9.758267e-09 | 1.937650e-11 | -5.186962e-13 | 7.105427e-15 | 0.000000e+00 | -2.842171e-14 |
iKF1028 | -1.799028e-11 | 0.000000e+00 | 4.904080e-09 | 5.995204e-15 | -6.050105e-11 | 6.877166e-11 | -3.783374e-11 |
iLC915 | 2.103206e-12 | 0.000000e+00 | 1.007605e-08 | -3.609557e-12 | 3.211653e-12 | 1.278977e-13 | 2.231104e-11 |
iLL672 | 5.151435e-14 | -3.967990e-10 | 2.029425e-09 | 3.019807e-14 | 4.529710e-14 | 4.440892e-16 | -8.260059e-14 |
iMA871 | 0.000000e+00 | 0.000000e+00 | 2.038192e-11 | -3.552714e-15 | 0.000000e+00 | 0.000000e+00 | -1.065814e-14 |
iMA945 | 1.421085e-14 | 0.000000e+00 | 4.755066e-09 | 0.000000e+00 | 0.000000e+00 | 1.421085e-14 | 9.947598e-14 |
iMB745 | 2.247508e-14 | 0.000000e+00 | 5.139368e-10 | 4.757412e-10 | -2.697495e-14 | -2.733924e-15 | -3.323893e-12 |
iMH551 | -4.263256e-14 | 0.000000e+00 | 2.145972e-11 | 6.772360e-15 | -2.420286e-14 | 4.440892e-16 | -2.721157e-13 |
iMM1415 | -2.347234e-12 | 0.000000e+00 | 1.605315e-08 | 5.881740e-12 | -1.929346e-11 | -6.439294e-15 | 1.410982e-11 |
iMM904 | 1.060230e-11 | 0.000000e+00 | 2.990649e-09 | -9.992007e-15 | -9.139328e-11 | 1.054712e-15 | -5.305936e-10 |
iMO1056 | -7.860379e-14 | -6.367740e-10 | 1.085125e-08 | -1.287859e-14 | 5.107026e-15 | -2.664535e-15 | -3.352874e-14 |
iMP429_fixed | 2.293721e-13 | 0.000000e+00 | 1.916863e-10 | -2.886580e-15 | 1.887379e-15 | -1.443290e-15 | -3.357314e-13 |
iND750 | -2.235294e-10 | 3.722161e-13 | 4.941149e-08 | -1.627079e-10 | 3.478570e-11 | 2.220446e-16 | -2.592769e-10 |
iNJ661 | -5.478381e-11 | -1.366268e-14 | 6.874230e-10 | 1.412759e-14 | -1.110825e-11 | -2.481532e-10 | -3.497474e-10 |
iNJ661m | 7.542578e-15 | -1.365574e-14 | 1.140270e-08 | 7.253811e-08 | 1.649386e-07 | 1.528997e-07 | -2.329942e-13 |
iNV213 | 8.881784e-15 | -8.495142e-10 | 1.006306e-11 | 0.000000e+00 | -8.881784e-15 | 3.552714e-15 | -2.486900e-14 |
iOG654 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 |
iOR363 | 2.842171e-14 | 0.000000e+00 | 6.735945e-12 | -5.684342e-14 | -5.684342e-14 | -2.842171e-14 | 2.842171e-14 |
iPP668 | -3.552714e-15 | 0.000000e+00 | 1.800928e-10 | 4.440892e-16 | 3.597123e-14 | -7.549517e-15 | -7.238654e-14 |
iPS189_fixed | 2.353673e-14 | -1.108655e-10 | 9.894308e-12 | 7.549517e-15 | 9.015011e-14 | 3.108624e-15 | 1.656453e-13 |
iRC1080 | -1.341149e-13 | 9.275872e-09 | 7.015366e-11 | 5.062617e-13 | 4.121148e-13 | 6.838974e-14 | -1.287859e-13 |
iRM588 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 |
iRR1083 | 0.000000e+00 | 1.977781e-08 | 1.978151e-10 | 0.000000e+00 | -2.842171e-14 | 0.000000e+00 | -2.842171e-14 |
iRS1563 | 6.800116e-16 | 0.000000e+00 | 9.173981e-12 | -4.163336e-16 | 5.967449e-16 | -9.478529e-15 | -8.118506e-15 |
iRS1597 | 3.552714e-15 | 0.000000e+00 | 9.791457e-11 | -8.881784e-15 | 5.329071e-15 | -2.842171e-14 | -2.842171e-14 |
iRS605_fixed | 1.199041e-14 | 0.000000e+00 | 4.111211e-09 | -2.975398e-14 | -3.996803e-15 | 3.552714e-15 | -1.865175e-14 |
iRsp1095 | -1.065814e-14 | 1.172156e-09 | 2.692957e-11 | -5.151435e-14 | 1.421085e-14 | -2.131628e-14 | -8.526513e-14 |
iSB619 | -3.088640e-13 | 0.000000e+00 | 9.349807e-11 | 4.496403e-15 | -1.181277e-13 | 1.437739e-14 | 9.064693e-13 |
iSH335 | 3.552714e-15 | 0.000000e+00 | 9.279755e-11 | 4.662937e-15 | -1.620926e-14 | -2.664535e-15 | 4.016787e-13 |
iSO783 | 0.000000e+00 | -3.318235e-12 | 7.798739e-10 | -5.684342e-14 | 1.776357e-14 | 0.000000e+00 | 3.552714e-15 |
iSR432 | -3.019807e-14 | -1.671046e-09 | 4.089173e-12 | -2.167155e-13 | 5.151435e-14 | -2.593481e-13 | -3.552714e-13 |
iSS724 | 0.000000e+00 | 0.000000e+00 | 4.753531e-12 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 |
iSS884 | 1.421085e-13 | 0.000000e+00 | 6.156000e-10 | -1.563194e-13 | 7.105427e-14 | -5.684342e-14 | -1.847411e-13 |
iSyn669 | -6.186440e-13 | -1.463274e-12 | 6.855544e-12 | -5.084516e-12 | 6.528666e-13 | 5.661027e-13 | -1.837835e-12 |
iTH366 | 3.274181e-11 | 0.000000e+00 | 2.655725e-10 | 1.091394e-11 | 1.455192e-11 | 2.182787e-11 | 1.818989e-11 |
iTL885 | 3.552714e-14 | 6.856737e-13 | 1.468498e-08 | 8.881784e-14 | -4.973799e-14 | -1.572076e-13 | 5.204726e-13 |
iTY425_fixed | -2.775558e-15 | 0.000000e+00 | 2.184031e-12 | 2.775558e-15 | -5.551115e-16 | 6.661338e-16 | 2.079448e-13 |
iVM679 | -2.398082e-14 | 1.689826e-10 | 1.038440e-10 | 4.352074e-14 | 7.549517e-15 | -2.131628e-14 | -3.819167e-14 |
iVS941_fixed | 2.153833e-14 | 0.000000e+00 | 1.439289e-08 | 3.785861e-14 | -3.352874e-14 | -1.498801e-14 | -3.141931e-14 |
iWV1314 | 5.329071e-14 | 3.552714e-15 | 4.255085e-11 | -3.552714e-15 | -3.552714e-15 | 0.000000e+00 | -9.947598e-14 |
iWZ663 | 3.552714e-14 | 2.741011e-09 | 3.468870e-11 | 8.526513e-14 | -5.684342e-14 | 4.263256e-14 | -2.842171e-14 |
iYL1228 | -7.904788e-14 | 0.000000e+00 | 2.068377e-09 | -1.332268e-15 | -1.265654e-14 | 6.217249e-15 | -2.731149e-13 |
iYO844 | -6.439294e-15 | -3.056155e-11 | 4.923346e-10 | -1.554312e-15 | 1.110223e-15 | 6.661338e-16 | -3.130829e-14 |
iZM363 | 2.664535e-15 | 0.000000e+00 | 6.776801e-12 | -8.348877e-14 | 7.549517e-15 | -2.220446e-15 | 8.881784e-15 |
iZmobMBEL601 | -1.004752e-14 | 0.000000e+00 | 2.098571e-11 | -3.115286e-13 | -3.136380e-14 | -4.996004e-15 | 3.836931e-13 |
mus_musculus | -2.842171e-14 | 0.000000e+00 | 1.811600e-10 | -2.842171e-14 | 0.000000e+00 | -2.842171e-14 | 0.000000e+00 |
textbook | 1.110223e-16 | 9.818923e-12 | 4.750644e-13 | 0.000000e+00 | -1.110223e-16 | -1.110223e-16 | 4.566791e-12 |
abs(differences).max().max()
3.6052116270113288e-07