Solving models with rational and floating point.

Using cobrapy (version 0.3.0b4 or later), we have interfaces to serveral floating point solvers (gurobi, MOSEK, CPLEX, soplex compiled with long double (80 bit) precision, 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 bigg, as well as some other models.

In [1]:
from os import listdir
from os.path import join
import warnings
import re

import pandas
import sympy
import scipy.io

import cobra

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 $$ \sum \left|\mathbf S \cdot v \right| $$

In [2]:
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.

In [3]:
models = []
model_file = scipy.io.loadmat("m_model_collection/all_models.mat")
for possible_name in model_file.keys():
    if possible_name.startswith("_"):
        continue
    with warnings.catch_warnings():
        warnings.simplefilter("ignore")
        model = cobra.io.mat.from_mat_struct(model_file[possible_name], model_id=possible_name)
    models.append(model)

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 demonstrated in this test script.

In [4]:
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 Value": rational_solution.f,
                           "Decimal Value": float(rational_solution.f),
                           "Total Error": total_error(S, rational_v),
                           # Ensure the upper and lwoer bounds are satisfied.
                           "bounds_sat": 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)

Here is are objective values and error of the rational results provided by esolver.

In [5]:
exact_results.rename(columns={"bounds_sat": r"$ub \ge v \ge lb$",
                              "Total Error": r"$\sum\left|\mathbf S \cdot v\right|$"})
Out[5]:
Decimal Value Rational Value $\sum\left|\mathbf S \cdot v\right|$ $ub \ge v \ge lb$
AORYZAE_COBRA 25.6824 10504392200845731410/409011287584573141 0 True
AbyMBEL891 119.233 386664062500000/3242927908653 0 True
AraGEM 10 10 0 True
PpaMBEL1254 78.70059 4725000000000/60037666259 0 True
PpuMBEL1071 132.3654 644062500000/4865793703 0 True
STM_v1.0 0.4778337 178576000/373720009 0 True
S_coilicolor_fixed 860.0888 408741530000000000/475231759036371 0 True
SpoMBEL1693 63.78566 1237500000000/19400913101 0 True
T_Maritima 0.359469 180000000/500738623 0 True
VvuMBEL943 96.40232 14000000000/145224717 0 True
iAC560 4.042612 35000000/8657769 0 True
iAF1260 0.7367009 146888000/199386199 0 True
iAF692 0.02725005 107424000/3942157643 0 True
iAI549 84.17419 114000000000/1354334333 0 True
iAN840m 0.3401361 50/147 0 True
iBsu1103 1229.657 1687500000000000/1372333638281 0 True
iCA1273 0.7402418 293776000/396864911 0 True
iCB925 0.1194276 1614000000/13514458561 0 True
iCac802 0.209597 99830000000/476294907501 0 True
iFF708 14.91711 113942000000/7638344959 0 True
iIB711 84.68841 100000000000/1180799053 0 True
iIT341 0.6928127 814668000000/1175884921963 0 True
iJN678 0.06314984 869550000000/13769631712373 0 True
iJN746 1.397457 139745688763/100000000000 0 True
iJO1366 0.9823718 189480000/192880127 0 True
iJP815 0.861512 179500000/208354621 0 True
iJR904 0.9219481 6380800/6920997 0 True
iKF1028 0.517807 1900000/3669321 0 True
iLC915 79.02123 786562500000000/9953812160053 0 True
iMA871 27.79298 100000000000/3598031369 0 True
iMB745 0.03094245 161000000/5203208413 0 True
iMM1415 1.363428 110000/80679 0 True
iMM904 0.2878657 145400000/505096641 0 True
iMO1056 1.047929 100000000/95426353 0 True
iND750 0.09732338 21000000/215775499 0 True
iNJ661 0.05219947 894000/17126611 0 True
iNJ661m 0.0521992 107280000/2055203801 0 True
iPS189_fixed 2.238961 90000000/40197209 0 True
iRC1080 6.156851 1000000000000000000000/162420679450988000257 0 True
iRS1563 0.07996249 16170000000000000000/202219826710707573821 0 True
iRS1597 8.969346 37500000/4180907 0 True
iRsp1095 9.686899 1514600000000000000000000/15635550882015213602... 0 True
iSB619 0.1580503 10000/63271 0 True
iSR432 11.48257 72500000000000000/6313917669853967 0 True
iSS884 70.35929 7513000000000/106780503717 0 True
iSyn669 0.1790899 6802000000/37980929237 0 True
iTH366 27890.89 10741489258500000/385125386207 0 True
iVS941_fixed 0.5233846 10000000/19106407 0 True
iYL1228 1.042637 1590492000/1525450603 0 True
mus_musculus 129.1006 10000000/77459 0 True
textbook 0.8739215 686440/785471 0 True

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.

In [6]:
errors.T
Out[6]:
cglpk cglpk_exact cplex esolver glpk gurobi mosek soplex
AORYZAE_COBRA 8.397096e-12 7.876394e-12 9.102191e-12 7.278331e-12 9.208338e-12 1.312897e-11 1.755370e-11 5.941914e-12
AbyMBEL891 1.030879e-11 1.003474e-11 1.609881e-11 6.093565e-12 1.168024e-11 2.244530e-11 2.173014e-11 7.435998e-12
AraGEM 4.518242e-12 5.055873e-12 1.031621e-11 3.953687e-12 5.721206e-12 1.075971e-11 1.607253e-11 4.703434e-12
PpaMBEL1254 5.524246e-12 6.130557e-12 1.653475e-11 1.599098e-12 5.808043e-12 7.211558e-12 1.327733e-11 3.710988e-12
PpuMBEL1071 9.213515e-12 1.006637e-07 6.212253e-12 5.611067e-12 6.928756e-12 3.708822e-11 1.154134e-11 6.461942e-12
STM_v1.0 2.442772e-12 7.616228e-09 9.155728e-13 4.133462e-13 4.027310e-12 2.906957e-11 1.424397e-11 2.233929e-12
S_coilicolor_fixed 6.094508e-11 5.231821e-11 5.070666e-11 3.497688e-11 4.686266e-11 8.191589e-11 2.215057e-10 2.802614e-11
SpoMBEL1693 9.424184e-12 8.661221e-12 8.002987e-12 5.512237e-12 8.155074e-12 1.530839e-11 2.056227e-11 5.011248e-12
T_Maritima 1.149696e-12 1.018268e-09 1.312999e-12 1.125577e-12 1.578348e-12 4.416971e-12 1.510734e-11 1.516991e-12
VvuMBEL943 1.291556e-11 1.499405e-11 1.001312e-11 1.396693e-11 8.099037e-12 1.663013e-11 2.356213e-11 1.508854e-11
iAC560 8.194865e-12 1.086580e-11 8.923992e-12 6.451882e-12 7.145092e-12 2.157194e-11 1.947821e-11 1.092283e-11
iAF1260 1.781254e-09 2.317057e-09 1.214389e-09 8.198651e-10 7.152690e-09 9.152921e-09 1.764879e-08 2.210171e-09
iAF692 3.386389e-09 1.658786e-09 1.631230e-08 1.963760e-09 1.222407e-09 9.790088e-09 9.934678e-09 3.282749e-07
iAI549 1.612223e-11 1.635750e-11 2.568619e-11 1.368209e-11 1.323319e-11 1.431488e-11 2.102636e-11 9.576010e-12
iAN840m 3.298200e-10 1.590948e-10 2.751869e-10 2.302759e-10 2.859458e-10 9.040576e-10 1.172849e-09 2.037961e-10
iBsu1103 2.972863e-10 6.526070e-06 2.472710e-10 2.010636e-10 3.242728e-10 6.813292e-10 8.936830e-10 2.348458e-10
iCA1273 2.755569e-12 2.510899e-12 2.677644e-12 1.519041e-12 3.057492e-12 2.003935e-11 1.762628e-11 1.413854e-12
iCB925 1.736274e-14 8.833104e-15 1.165951e-14 1.306301e-14 2.114921e-14 5.571875e-12 6.289154e-12 1.105572e-14
iCac802 8.493680e-14 3.819428e-14 1.898222e-13 7.927829e-14 7.058789e-14 1.341451e-11 1.029223e-11 3.950239e-14
iFF708 9.631808e-12 7.577920e-12 7.416481e-12 5.430347e-12 1.020766e-11 8.490127e-12 2.012872e-11 5.210327e-12
iIB711 8.816919e-12 1.383682e-11 2.195908e-11 1.150156e-11 1.309052e-11 1.538718e-11 2.583597e-11 7.610506e-12
iIT341 1.014080e-09 1.238232e-09 8.119830e-10 2.710340e-10 1.470638e-09 5.846785e-09 7.601729e-09 1.514078e-09
iJN678 2.398464e-14 2.797801e-10 1.396985e-14 2.238604e-14 2.488953e-14 8.051307e-12 5.716085e-12 2.776961e-13
iJN746 4.619685e-09 6.488544e-09 6.687020e-09 4.391777e-09 5.307806e-09 9.431021e-09 1.182201e-08 2.626600e-09
iJO1366 3.229136e-12 2.352584e-09 5.214601e-12 8.026430e-13 4.692354e-12 9.346213e-12 1.267621e-11 2.973008e-12
iJP815 1.020123e-09 1.263897e-09 1.550045e-08 7.528140e-10 1.367096e-09 1.480841e-08 6.830615e-09 1.754968e-13
iJR904 1.099850e-09 2.948835e-09 4.445673e-10 1.427380e-10 1.365733e-09 8.422848e-09 1.420731e-08 5.069783e-10
iKF1028 4.410775e-09 3.251033e-09 4.556265e-09 1.713361e-09 4.626908e-09 6.951025e-09 9.571061e-09 1.402554e-09
iLC915 8.942108e-12 7.341506e-12 6.786460e-12 6.807457e-12 1.100345e-11 2.001077e-11 2.595469e-09 6.767324e-12
iMA871 8.159995e-12 7.914335e-12 9.557480e-12 4.393495e-12 7.955587e-12 1.058580e-11 1.738133e-11 5.867922e-12
iMB745 5.070478e-12 4.596056e-12 6.657764e-12 3.221213e-12 5.698374e-12 1.030674e-11 7.238292e-11 2.735226e-12
iMM1415 1.570216e-09 1.239422e-09 8.968702e-10 8.350148e-10 1.399133e-09 1.985386e-09 1.625218e-08 1.051536e-09
iMM904 3.595750e-09 4.833053e-09 2.982506e-09 1.531252e-09 4.619449e-09 8.978975e-09 1.828506e-08 1.866155e-09
iMO1056 4.451167e-12 4.065253e-09 2.091337e-12 2.158161e-12 4.592567e-12 7.228196e-12 1.088813e-11 6.606378e-13
iND750 2.859207e-09 3.247899e-09 8.041428e-09 2.058405e-09 3.681656e-09 8.144421e-09 1.155155e-08 2.719886e-09
iNJ661 4.577143e-09 4.692796e-09 3.712113e-09 3.654260e-09 4.502374e-09 1.148863e-08 1.308405e-08 3.472951e-09
iNJ661m 4.915935e-12 1.078748e-11 1.044025e-07 2.524202e-12 5.219989e-07 3.654090e-07 1.416549e-11 7.307954e-07
iPS189_fixed 4.986594e-13 2.228617e-09 6.313791e-13 2.516057e-13 8.629994e-13 1.490655e-11 3.172817e-12 4.561349e-13
iRC1080 1.212713e-11 5.622372e-08 1.456314e-11 5.134023e-12 1.027390e-11 2.536731e-11 3.641264e-11 9.311547e-12
iRS1563 2.844885e-12 2.415537e-12 4.673761e-12 1.709565e-12 3.843955e-12 1.515478e-11 1.570177e-11 2.564564e-12
iRS1597 2.635014e-12 3.304423e-12 3.210002e-12 1.169068e-12 1.140946e-12 1.117675e-11 5.307929e-12 1.102493e-12
iRsp1095 4.771094e-12 1.286166e-07 3.834673e-12 5.702781e-12 5.757338e-12 1.368581e-11 3.346712e-11 4.093764e-12
iSB619 6.677286e-10 2.563839e-10 2.292188e-11 2.877589e-11 1.436060e-10 5.811579e-09 1.817552e-08 4.394801e-10
iSR432 5.763678e-12 2.818231e-07 5.417731e-12 5.851002e-12 4.656121e-12 8.798916e-12 1.248002e-11 3.473549e-12
iSS884 1.012953e-11 9.508621e-12 9.887681e-12 9.827828e-12 9.738816e-12 1.818995e-11 2.586860e-11 9.911760e-12
iSyn669 8.127297e-11 1.060315e-10 6.030044e-11 2.003912e-11 3.519071e-11 1.452439e-10 1.517444e-10 6.519089e-11
iTH366 4.467643e-09 6.151925e-09 4.967946e-09 4.431032e-09 8.734066e-09 1.164260e-08 2.244135e-08 6.293012e-09
iVS941_fixed 5.781317e-12 4.646162e-12 4.555880e-12 4.109086e-12 3.148214e-12 8.335240e-12 8.427532e-12 2.488732e-12
iYL1228 3.579303e-12 5.818149e-10 1.638551e-12 6.258599e-13 1.245614e-12 8.727630e-12 1.130580e-11 1.130485e-12
mus_musculus 9.798615e-12 6.567552e-12 9.245493e-12 4.835687e-12 8.265638e-12 9.112100e-12 1.927275e-11 7.827294e-12
textbook 7.371881e-14 2.203658e-09 5.417888e-14 4.862777e-14 8.348877e-14 1.268388e-09 2.745516e-09 3.197442e-14

Here are all the computed growth rates for each solver and model.

In [7]:
results.T
Out[7]:
cglpk cglpk_exact cplex esolver glpk gurobi mosek soplex
AORYZAE_COBRA 25.682402 25.682402 25.682402 25.682402 25.682402 25.682402 25.682402 25.682402
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
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
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
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
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
iJN678 0.063150 0.063150 0.063150 0.063150 0.063150 0.063150 0.063150 0.063150
iJN746 1.397457 1.397457 1.397457 1.397457 1.397457 1.397457 1.397457 1.397457
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
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
iMA871 27.792976 27.792976 27.792976 27.792976 27.792976 27.792976 27.792976 27.792976
iMB745 0.030942 0.030942 0.030942 0.030942 0.030942 0.030942 0.030942 0.030942
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
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
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
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
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
iSR432 11.482570 11.482570 11.482570 11.482570 11.482570 11.482570 11.482570 11.482570
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
iVS941_fixed 0.523385 0.523385 0.523385 0.523385 0.523385 0.523385 0.523385 0.523385
iYL1228 1.042637 1.042637 1.042637 1.042637 1.042637 1.042637 1.042637 1.042637
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.

In [8]:
differences = (results - results.ix["esolver"])
differences.T
Out[8]:
cglpk cglpk_exact cplex esolver glpk gurobi mosek soplex
AORYZAE_COBRA 5.329071e-14 0.000000e+00 -1.065814e-14 0 -3.552714e-15 7.105427e-15 -9.947598e-14 0.000000e+00
AbyMBEL891 1.136868e-13 -1.421085e-14 -8.526513e-14 0 1.136868e-13 -3.552714e-13 -7.105427e-14 0.000000e+00
AraGEM 0.000000e+00 0.000000e+00 0.000000e+00 0 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
PpaMBEL1254 0.000000e+00 -1.421085e-14 -1.847411e-13 0 0.000000e+00 -1.421085e-14 -7.105427e-14 0.000000e+00
PpuMBEL1071 8.526513e-14 5.117897e-10 5.684342e-14 0 8.526513e-14 3.410605e-13 -1.136868e-13 0.000000e+00
STM_v1.0 3.863576e-14 4.957084e-10 -1.110223e-15 0 1.086908e-13 7.771561e-16 4.814482e-13 5.551115e-17
S_coilicolor_fixed 1.136868e-13 -1.136868e-13 0.000000e+00 0 1.136868e-13 0.000000e+00 -1.250555e-12 0.000000e+00
SpoMBEL1693 -1.421085e-14 -7.105427e-15 7.815970e-14 0 7.105427e-14 -1.421085e-14 -6.039613e-13 -7.105427e-15
T_Maritima -3.214096e-14 9.456907e-11 3.330669e-16 0 -2.114975e-14 9.436896e-16 -3.308465e-14 -3.330669e-16
VvuMBEL943 1.421085e-14 0.000000e+00 0.000000e+00 0 4.263256e-14 4.263256e-14 4.263256e-14 0.000000e+00
iAC560 2.664535e-15 0.000000e+00 8.881784e-16 0 0.000000e+00 1.776357e-15 1.421085e-14 0.000000e+00
iAF1260 2.087197e-11 0.000000e+00 -2.066314e-11 0 1.858336e-11 -1.203304e-11 1.749767e-11 2.220446e-16
iAF692 -3.651770e-11 -2.846203e-11 4.426832e-09 0 -4.769716e-12 5.128266e-09 3.623219e-11 2.902875e-07
iAI549 -7.673862e-13 -1.421085e-14 -5.826450e-13 0 1.705303e-13 2.131628e-13 -1.421085e-13 0.000000e+00
iAN840m 0.000000e+00 0.000000e+00 -5.551115e-17 0 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
iBsu1103 -2.273737e-13 -2.653928e-08 -4.547474e-13 0 2.273737e-13 4.547474e-13 4.547474e-13 2.273737e-13
iCA1273 -3.275158e-14 0.000000e+00 4.685141e-14 0 5.406786e-14 5.551115e-16 2.265965e-13 1.110223e-16
iCB925 7.494005e-16 -1.387779e-17 -3.191891e-16 0 -1.942890e-16 2.498002e-16 2.530753e-13 -1.387779e-17
iCac802 4.440892e-16 0.000000e+00 -1.665335e-16 0 -1.249001e-15 2.775558e-17 5.651035e-14 0.000000e+00
iFF708 1.776357e-15 0.000000e+00 9.592327e-14 0 1.421085e-14 2.131628e-14 -4.263256e-14 0.000000e+00
iIB711 -1.421085e-14 0.000000e+00 4.263256e-14 0 -2.842171e-14 -9.947598e-14 -1.421085e-14 0.000000e+00
iIT341 -1.129519e-11 2.245906e-10 -4.440892e-15 0 -1.403899e-11 -1.850742e-13 -6.530149e-10 2.220446e-16
iJN678 -4.718448e-16 2.856901e-11 -1.082467e-15 0 -2.220446e-16 -3.469447e-16 1.214445e-13 -4.163336e-17
iJN746 0.000000e+00 4.757172e-11 0.000000e+00 0 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
iJO1366 4.973799e-14 1.739908e-10 5.773160e-15 0 5.107026e-14 -2.220446e-15 5.774270e-13 4.440892e-16
iJP815 1.783040e-11 0.000000e+00 2.160384e-10 0 2.299161e-12 3.759559e-11 -1.644941e-10 0.000000e+00
iJR904 -3.364420e-12 2.154040e-10 -7.549517e-15 0 -3.852363e-11 1.960387e-11 3.302114e-11 1.110223e-16
iKF1028 -1.799028e-11 -1.110223e-16 5.995204e-15 0 -6.050105e-11 -4.764367e-11 8.776668e-11 0.000000e+00
iLC915 2.103206e-12 0.000000e+00 -7.105427e-14 0 3.211653e-12 7.105427e-14 1.196554e-11 0.000000e+00
iMA871 0.000000e+00 -3.552714e-15 -3.552714e-15 0 0.000000e+00 -3.552714e-15 -1.065814e-14 0.000000e+00
iMB745 2.247508e-14 0.000000e+00 4.757412e-10 0 -2.697495e-14 -2.657596e-15 -3.501529e-12 0.000000e+00
iMM1415 3.918843e-11 -2.220446e-16 -1.776357e-15 0 4.864575e-11 1.776357e-15 3.898259e-11 4.884981e-15
iMM904 1.060230e-11 -5.551115e-17 -9.992007e-15 0 -9.139328e-11 -8.881784e-16 -5.305936e-10 -5.551115e-17
iMO1056 -7.860379e-14 -6.367742e-10 -1.287859e-14 0 5.107026e-15 -1.776357e-15 -3.352874e-14 2.220446e-16
iND750 -2.235294e-10 3.722023e-13 -1.627079e-10 0 3.478570e-11 4.103134e-12 -2.592769e-10 -1.387779e-17
iNJ661 -5.478381e-11 -1.366268e-14 1.412759e-14 0 -1.110825e-11 1.833117e-13 -4.726380e-11 -9.173218e-14
iNJ661m 7.542578e-15 -1.365574e-14 7.253811e-08 0 1.649386e-07 1.464993e-07 -2.329942e-13 2.609968e-07
iPS189_fixed 2.353673e-14 -1.108660e-10 7.549517e-15 0 9.015011e-14 -1.776357e-15 -4.667378e-13 4.440892e-16
iRC1080 -1.341149e-13 9.275872e-09 7.638334e-14 0 4.121148e-13 7.362999e-13 -1.287859e-13 7.105427e-15
iRS1563 6.800116e-16 0.000000e+00 -4.163336e-16 0 5.967449e-16 -9.478529e-15 -8.118506e-15 0.000000e+00
iRS1597 3.552714e-15 0.000000e+00 -8.881784e-15 0 5.329071e-15 -1.776357e-15 -2.842171e-14 0.000000e+00
iRsp1095 -1.065814e-14 1.172156e-09 8.881784e-15 0 1.421085e-14 1.509903e-13 -8.526513e-14 1.776357e-15
iSB619 -3.088640e-13 0.000000e+00 4.496403e-15 0 -1.181277e-13 -6.578071e-15 9.064693e-13 2.775558e-17
iSR432 -3.019807e-14 -1.671046e-09 -2.167155e-13 0 5.151435e-14 -3.552714e-14 -1.847411e-13 -1.776357e-15
iSS884 1.136868e-13 0.000000e+00 -1.278977e-13 0 1.563194e-13 -1.705303e-13 -1.847411e-13 0.000000e+00
iSyn669 -6.186440e-13 -1.463302e-12 -5.084516e-12 0 6.528666e-13 -2.153278e-13 -1.837835e-12 -2.775558e-17
iTH366 3.274181e-11 0.000000e+00 1.091394e-11 0 1.455192e-11 2.910383e-11 1.818989e-11 1.091394e-11
iVS941_fixed 2.153833e-14 -1.110223e-16 3.785861e-14 0 -3.352874e-14 0.000000e+00 9.936496e-14 0.000000e+00
iYL1228 -7.904788e-14 0.000000e+00 -1.332268e-15 0 -1.265654e-14 -2.664535e-15 -2.731149e-13 1.332268e-15
mus_musculus -2.842171e-14 -2.842171e-14 0.000000e+00 0 0.000000e+00 2.842171e-14 0.000000e+00 0.000000e+00
textbook 1.110223e-16 9.818812e-12 0.000000e+00 0 -1.110223e-16 -1.110223e-16 4.566791e-12 0.000000e+00