{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Solving models with rational and floating point." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Using [cobrapy](http://opencobra.github.io/cobrapy/) (version 0.4.0b1 or later), we have interfaces to serveral floating point solvers ([gurobi](http://www.gurobi.com), [MOSEK](http://www.mosek.com/), [CPLEX](http://www-01.ibm.com/software/commerce/optimization/cplex-optimizer/), [Clp](https://projects.coin-or.org/Clp), and two different versions of [GLPK](https://www.gnu.org/software/glpk/)). Additionally, we can use the rational solving capabilities of GLPK and esolver (also known as [QSopt_ex](http://www.dii.uchile.cl/~daespino/ESolver_doc/main.html)). We will use all of these solvers on all the models in the collection." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [], "source": [ "import os\n", "\n", "from numpy import array\n", "import pandas\n", "import sympy\n", "\n", "import cobra\n", "\n", "pandas.set_option(\"display.max_rows\", 100)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We will verify all of our solutions by writing out the Stoichiometrix matrix $\\mathbf S$ using the [sympy](http://sympy.org/) symbolic math library. The total error will be equivalent to \n", "$$ \\sum \\left|\\mathbf S \\cdot v \\right| $$" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def convert_to_rational(value):\n", " return sympy.Rational(\"%.15g\" % value)\n", "\n", "def construct_exact_S(model):\n", " # intialize to 0\n", " S = sympy.SparseMatrix(len(model.metabolites), len(model.reactions), 0)\n", " # populate with stoichiometry\n", " for i, r in enumerate(model.reactions):\n", " for met, value in r._metabolites.iteritems():\n", " S[model.metabolites.index(met), i] = convert_to_rational(value)\n", " return S\n", "\n", "def total_error(S, v):\n", " return sum(abs(i) for i in S * v)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Some of these models were exported from [BiGG](http://bigg.ucsd.edu/bigg/export.pl) as SBML, and others were downloaded from their respective publications. All of the models are available in a [git repository](https://github.com/opencobra/m_model_collection). They were parsed into a single mat file by an [included script](load_models.ipynb)." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [], "source": [ "models = []\n", "for filename in sorted(os.listdir(\"sbml3\")):\n", " if not filename.endswith(\".xml\"):\n", " continue\n", " models.append(cobra.io.read_sbml_model(os.path.join(\"sbml3\", filename)))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "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](http://dx.doi.org/doi:10.1038/nprot.2011.308), as shown [here](http://nbviewer.ipython.org/github/opencobra/m_model_collection/blob/master/MATLAB.ipynb)." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [], "source": [ "results = {}\n", "exact_results = {}\n", "errors = {}\n", "for m in models:\n", " S = construct_exact_S(m)\n", " S_float = m.to_array_based_model().S\n", " rational_solution = m.optimize(solver=\"esolver\", rational_solution=True)\n", " rational_v = sympy.Matrix(rational_solution.x)\n", " exact_results[m.id] = {\"Rational\": rational_solution.f,\n", " \"Decimal\": float(rational_solution.f),\n", " \"Error\": total_error(S, rational_v),\n", " # Ensure the upper and lwoer bounds are satisfied.\n", " \"Bounds\": all([r.upper_bound >= value >= r.lower_bound\n", " for r, value in zip(m.reactions, rational_v)])}\n", " # solve this model with all the solvers\n", " solutions = {solver: m.optimize(solver=solver)\n", " for solver in cobra.solvers.solver_dict}\n", " solutions[\"cglpk_exact\"] = m.optimize(solver=\"cglpk\", exact=True)\n", " # store the objective value and errors\n", " results[m.id] = {k: v.f for k, v in solutions.iteritems()}\n", " errors[m.id] = {k: sum(abs(S_float * array(v.x))) for k, v in solutions.iteritems()}\n", "# format the results as pandas dataframes\n", "exact_results = pandas.DataFrame.from_dict(exact_results).T\n", "results = pandas.DataFrame.from_dict(results)\n", "errors = pandas.DataFrame.from_dict(errors)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For all of these models, we can demonstrate they satisfy the model constraints using exact operations." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\\sum\\left|\\mathbf S \\cdot v\\right| = 0$$" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "0" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "abs(exact_results.Error).max()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$ub \\ge v \\ge lb$$" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "exact_results.Bounds.all()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here are objective values of the rational results provided by esolver:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "
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DecimalRational
AbyMBEL891119.233386664062500000/3242927908653
AraGEM1010
GSMN_TB0.1312623576559343750000/4392422515431629
PpaMBEL125478.700594725000000000/60037666259
PpuMBEL1071132.3654644062500000/4865793703
STM_v1_00.4778337178576000/373720009
S_coilicolor_fixed860.0888408741530000000000/475231759036371
SpoMBEL169363.785661237500000000/19400913101
T_Maritima0.359469180000000/500738623
VvuMBEL94396.4023214000000000/145224717
iAC5604.04261235000000/8657769
iAF12600.7367009146888000/199386199
iAF6920.02725005107424000/3942157643
iAI54984.17419114000000000/1354334333
iAN840m0.340136150/147
iAO358255.1805586000000000/2296413281
iAbaylyiV412.3065534263125839313509122373268880000000/2784138406...
iBT721_fixed0.51/2
iBsu11031229.6571687500000000000/1372333638281
iCA12730.7402418293776000/396864911
iCB9250.11942761614000000/13514458561
iCR74441.47674179687500000/4332247261
iCS2910.140548938125/271258
iCS4000.21563963750/295633
iCac8020.20959799830000000/476294907501
iFF70814.91711113942000000/7638344959
iGB555_fixed127.7891142500000000000/1115118722693
iHD666_fixed0.2556721163316006250/638771297231
iIB71184.68841100000000000/1180799053
iIT3410.6928127814668000000/1175884921963
iJL4320.32874073750000000/11407166737
iJN6780.06314984869550000000/13769631712373
iJN7463.67941240000000/10871301
iJO13660.9823718189480000/192880127
iJP8150.861512179500000/208354621
iJR9040.92194816380800/6920997
iJS74734.1726615000000000000/438947370703
iKF10280.5178071900000/3669321
iLC91579.02123786562500000000/9953812160053
iLL6723.47528362750000000/18056084533
iMA87127.79298100000000000/3598031369
iMA94579.589585000000000/62822291
iMB7450.03094245161000000/5203208413
iMH5510.775081127300000000/35222122883
iMM14151.363428110000/80679
iMM9040.2878657145400000/505096641
iMO10561.047929100000000/95426353
iMP429_fixed0.80443247063000000/8780103713
iND7500.0973233821000000/215775499
iNJ6610.05219947894000/17126611
iNJ661m0.0521992107280000/2055203801
iNV21311.5388612500000000000000/1083295987243349
iOG6540.355446912500/35167
iOR363250250
iPP6683.89147495000000/24412341
iPS189_fixed2.23896190000000/40197209
iRC10806.1568511000000000000000000000/162420679450988000257
iRM58810001000
iRR108377.947361250000000/16036463
iRS15630.0799624916170000000000000000/202219826710707573821
iRS15978.96934637500000/4180907
iRS605_fixed2.116782051250000/969042437
iRsp10959.6868991514600000000000000000000/15635550882015213602...
iSB6190.158050310000/63271
iSH3351.15921187700000000/75654904569
iSO78317.92031100000000000/5580261343
iSR43211.4825772500000000000000/6313917669853967
iSS72422.421525000/223
iSS88470.359297513000000000/106780503717
iSyn6690.17908996802000000/37980929237
iTH36627890.8910741489258500000/385125386207
iTL8857.098836697400000000/98241455449
iTY425_fixed0.88683355000000/5638037
iVM6792.8265726520000000/9382396471
iVS941_fixed0.523384610000000/19106407
iWV131425.682410504392200845731410/409011287584573141
iWZ66334.07588350000000000/10271194511
iYL12281.0426371590492000/1525450603
iYO8441.582798256250000000/161896806353
iZM3632.532606181250000/71566597
iZmobMBEL6010.350080461718750/176298791
mus_musculus129.100610000000/77459
textbook0.8739215686440/785471
\n", "
" ], "text/plain": [ " Decimal \\\n", "AbyMBEL891 119.233 \n", "AraGEM 10 \n", "GSMN_TB 0.1312623 \n", "PpaMBEL1254 78.70059 \n", "PpuMBEL1071 132.3654 \n", "STM_v1_0 0.4778337 \n", "S_coilicolor_fixed 860.0888 \n", "SpoMBEL1693 63.78566 \n", "T_Maritima 0.359469 \n", "VvuMBEL943 96.40232 \n", "iAC560 4.042612 \n", "iAF1260 0.7367009 \n", "iAF692 0.02725005 \n", "iAI549 84.17419 \n", "iAN840m 0.3401361 \n", "iAO358 255.1805 \n", "iAbaylyiV4 12.30655 \n", "iBT721_fixed 0.5 \n", "iBsu1103 1229.657 \n", "iCA1273 0.7402418 \n", "iCB925 0.1194276 \n", "iCR744 41.47674 \n", "iCS291 0.1405489 \n", "iCS400 0.215639 \n", "iCac802 0.209597 \n", "iFF708 14.91711 \n", "iGB555_fixed 127.7891 \n", "iHD666_fixed 0.2556721 \n", "iIB711 84.68841 \n", "iIT341 0.6928127 \n", "iJL432 0.3287407 \n", "iJN678 0.06314984 \n", "iJN746 3.679412 \n", "iJO1366 0.9823718 \n", "iJP815 0.861512 \n", "iJR904 0.9219481 \n", "iJS747 34.17266 \n", "iKF1028 0.517807 \n", "iLC915 79.02123 \n", "iLL672 3.475283 \n", "iMA871 27.79298 \n", "iMA945 79.58958 \n", "iMB745 0.03094245 \n", "iMH551 0.7750811 \n", "iMM1415 1.363428 \n", "iMM904 0.2878657 \n", "iMO1056 1.047929 \n", "iMP429_fixed 0.8044324 \n", "iND750 0.09732338 \n", "iNJ661 0.05219947 \n", "iNJ661m 0.0521992 \n", "iNV213 11.53886 \n", "iOG654 0.3554469 \n", "iOR363 250 \n", "iPP668 3.891474 \n", "iPS189_fixed 2.238961 \n", "iRC1080 6.156851 \n", "iRM588 1000 \n", "iRR1083 77.94736 \n", "iRS1563 0.07996249 \n", "iRS1597 8.969346 \n", "iRS605_fixed 2.11678 \n", "iRsp1095 9.686899 \n", "iSB619 0.1580503 \n", "iSH335 1.159211 \n", "iSO783 17.92031 \n", "iSR432 11.48257 \n", "iSS724 22.42152 \n", "iSS884 70.35929 \n", "iSyn669 0.1790899 \n", "iTH366 27890.89 \n", "iTL885 7.098836 \n", "iTY425_fixed 0.8868335 \n", "iVM679 2.82657 \n", "iVS941_fixed 0.5233846 \n", "iWV1314 25.6824 \n", "iWZ663 34.07588 \n", "iYL1228 1.042637 \n", "iYO844 1.582798 \n", "iZM363 2.532606 \n", "iZmobMBEL601 0.3500804 \n", "mus_musculus 129.1006 \n", "textbook 0.8739215 \n", "\n", " Rational \n", "AbyMBEL891 386664062500000/3242927908653 \n", "AraGEM 10 \n", "GSMN_TB 576559343750000/4392422515431629 \n", "PpaMBEL1254 4725000000000/60037666259 \n", "PpuMBEL1071 644062500000/4865793703 \n", "STM_v1_0 178576000/373720009 \n", "S_coilicolor_fixed 408741530000000000/475231759036371 \n", "SpoMBEL1693 1237500000000/19400913101 \n", "T_Maritima 180000000/500738623 \n", "VvuMBEL943 14000000000/145224717 \n", "iAC560 35000000/8657769 \n", "iAF1260 146888000/199386199 \n", "iAF692 107424000/3942157643 \n", "iAI549 114000000000/1354334333 \n", "iAN840m 50/147 \n", "iAO358 586000000000/2296413281 \n", "iAbaylyiV4 34263125839313509122373268880000000/2784138406... \n", "iBT721_fixed 1/2 \n", "iBsu1103 1687500000000000/1372333638281 \n", "iCA1273 293776000/396864911 \n", "iCB925 1614000000/13514458561 \n", "iCR744 179687500000/4332247261 \n", "iCS291 38125/271258 \n", "iCS400 63750/295633 \n", "iCac802 99830000000/476294907501 \n", "iFF708 113942000000/7638344959 \n", "iGB555_fixed 142500000000000/1115118722693 \n", "iHD666_fixed 163316006250/638771297231 \n", "iIB711 100000000000/1180799053 \n", "iIT341 814668000000/1175884921963 \n", "iJL432 3750000000/11407166737 \n", "iJN678 869550000000/13769631712373 \n", "iJN746 40000000/10871301 \n", "iJO1366 189480000/192880127 \n", "iJP815 179500000/208354621 \n", "iJR904 6380800/6920997 \n", "iJS747 15000000000000/438947370703 \n", "iKF1028 1900000/3669321 \n", "iLC915 786562500000000/9953812160053 \n", "iLL672 62750000000/18056084533 \n", "iMA871 100000000000/3598031369 \n", "iMA945 5000000000/62822291 \n", "iMB745 161000000/5203208413 \n", "iMH551 27300000000/35222122883 \n", "iMM1415 110000/80679 \n", "iMM904 145400000/505096641 \n", "iMO1056 100000000/95426353 \n", "iMP429_fixed 7063000000/8780103713 \n", "iND750 21000000/215775499 \n", "iNJ661 894000/17126611 \n", "iNJ661m 107280000/2055203801 \n", "iNV213 12500000000000000/1083295987243349 \n", "iOG654 12500/35167 \n", "iOR363 250 \n", "iPP668 95000000/24412341 \n", "iPS189_fixed 90000000/40197209 \n", "iRC1080 1000000000000000000000/162420679450988000257 \n", "iRM588 1000 \n", "iRR1083 1250000000/16036463 \n", "iRS1563 16170000000000000000/202219826710707573821 \n", "iRS1597 37500000/4180907 \n", "iRS605_fixed 2051250000/969042437 \n", "iRsp1095 1514600000000000000000000/15635550882015213602... \n", "iSB619 10000/63271 \n", "iSH335 87700000000/75654904569 \n", "iSO783 100000000000/5580261343 \n", "iSR432 72500000000000000/6313917669853967 \n", "iSS724 5000/223 \n", "iSS884 7513000000000/106780503717 \n", "iSyn669 6802000000/37980929237 \n", "iTH366 10741489258500000/385125386207 \n", "iTL885 697400000000/98241455449 \n", "iTY425_fixed 5000000/5638037 \n", "iVM679 26520000000/9382396471 \n", "iVS941_fixed 10000000/19106407 \n", "iWV1314 10504392200845731410/409011287584573141 \n", "iWZ663 350000000000/10271194511 \n", "iYL1228 1590492000/1525450603 \n", "iYO844 256250000000/161896806353 \n", "iZM363 181250000/71566597 \n", "iZmobMBEL601 61718750/176298791 \n", "mus_musculus 10000000/77459 \n", "textbook 686440/785471 " ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "exact_results[[\"Decimal\", \"Rational\"]]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "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." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "
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cglpkcglpk_exactcoincplexesolverglpkgurobimosek
AbyMBEL8911.030879e-116.538390e-123.057219e-111.652062e-116.093565e-121.168024e-112.098006e-111.866628e-11
AraGEM4.518242e-123.761263e-124.350840e-111.031621e-113.953687e-125.721206e-121.492412e-111.607253e-11
GSMN_TB3.265029e-101.438631e-104.422610e-101.794655e-091.318417e-101.580843e-072.451718e-091.055735e-09
PpaMBEL12545.524246e-125.503863e-121.686022e-111.653475e-111.599098e-125.808043e-126.458234e-121.327733e-11
PpuMBEL10719.213515e-121.006636e-072.682011e-116.212253e-125.611067e-126.928756e-121.996325e-111.154134e-11
STM_v1_02.442772e-127.615986e-091.558550e-096.747805e-134.133462e-134.027310e-122.884140e-111.424397e-11
S_coilicolor_fixed6.094508e-113.403941e-111.417303e-105.070666e-113.497688e-114.686266e-115.399156e-112.215057e-10
SpoMBEL16939.424184e-126.328653e-122.409888e-117.634511e-125.512237e-128.155074e-129.632115e-122.056227e-11
T_Maritima1.149696e-121.017970e-092.680799e-121.312999e-121.125577e-121.578348e-124.792797e-121.448889e-11
VvuMBEL9431.291556e-111.200139e-111.619902e-115.522043e-121.396693e-118.099037e-127.938761e-122.371747e-11
iAC5608.194865e-129.868076e-122.435742e-118.923992e-126.451882e-127.145092e-121.873765e-111.947821e-11
iAF12601.781254e-091.946048e-095.678922e-091.214388e-098.198651e-107.152690e-099.012081e-091.764879e-08
iAF6923.386389e-092.220311e-098.946148e-091.759396e-081.963760e-091.222407e-098.575538e-091.040327e-08
iAI5491.612223e-119.931913e-124.028457e-112.568619e-111.368209e-111.323319e-111.541363e-112.428250e-11
iAN840m3.298200e-101.804508e-101.107875e-102.751869e-102.302759e-102.859458e-108.054293e-101.172849e-09
iAO3581.124310e-111.091583e-113.182512e-111.906676e-111.175427e-111.348169e-111.847833e-112.943036e-11
iAbaylyiV42.977077e-123.012134e-128.290163e-125.293440e-126.227974e-124.977532e-121.004922e-111.594689e-11
iBT721_fixed6.197820e-123.083755e-124.031970e-111.364242e-122.629008e-124.273915e-123.751666e-121.984154e-11
iBsu11032.972863e-106.526051e-067.303685e-103.339946e-102.010636e-103.242728e-105.418732e-108.971953e-10
iCA12732.755569e-122.649891e-129.081865e-112.677644e-121.519041e-123.057492e-128.550924e-121.762628e-11
iCB9251.736274e-149.613512e-152.816809e-141.165951e-141.306301e-142.114921e-145.169930e-121.014086e-11
iCR7441.018664e-116.352933e-123.419470e-111.823183e-116.848318e-126.607602e-121.363850e-111.417687e-11
iCS2914.977130e-133.683998e-131.375014e-128.569881e-133.690381e-133.893899e-134.744788e-126.790318e-12
iCS4001.469269e-121.157699e-122.533241e-111.845843e-124.832384e-131.527389e-125.889844e-129.199558e-12
iCac8028.493680e-143.153588e-141.363077e-131.898222e-137.927829e-147.058789e-141.260632e-111.055401e-11
iFF7089.631808e-125.780962e-121.847612e-116.812400e-125.430347e-121.020766e-118.761480e-122.012872e-11
iGB555_fixed1.618755e-114.991450e-103.935196e-118.029397e-125.976067e-121.892854e-118.302095e-123.028083e-11
iHD666_fixed6.101243e-122.778296e-111.746997e-113.751388e-123.346992e-127.398641e-126.864509e-121.167770e-11
iIB7118.816919e-129.826012e-122.293666e-112.186360e-111.150156e-111.309052e-111.211514e-112.583597e-11
iIT3411.014080e-091.807772e-095.907021e-098.119830e-102.710340e-101.470638e-095.405914e-097.601729e-09
iJL4321.174412e-123.901074e-131.789826e-123.963390e-133.900797e-137.603562e-134.689371e-123.737990e-12
iJN6782.398464e-142.797895e-101.930007e-141.396985e-142.238604e-142.488953e-147.036177e-125.716085e-12
iJN7465.745402e-091.309358e-089.719125e-093.280881e-092.846633e-094.145871e-098.716805e-091.037925e-08
iJO13663.229136e-122.352308e-091.235567e-115.307026e-128.026430e-134.692354e-129.259564e-121.267621e-11
iJP8151.020123e-097.944625e-103.420634e-091.550045e-087.528140e-101.367096e-091.359488e-085.964099e-09
iJR9041.099850e-093.218263e-094.340962e-096.192079e-101.427380e-101.365733e-096.213569e-091.420731e-08
iJS7477.176808e-123.632675e-079.697313e-129.643009e-123.800987e-124.923902e-125.578066e-128.495003e-12
iKF10284.410775e-092.512140e-093.931006e-094.556265e-091.713361e-094.626908e-091.043391e-081.115077e-08
iLC9158.942108e-125.859216e-122.288417e-119.887922e-126.807457e-121.100345e-111.760760e-111.649339e-11
iLL6727.130910e-127.483421e-093.135656e-117.181390e-125.127530e-121.080215e-115.221250e-121.864336e-11
iMA8718.159995e-124.129003e-123.886357e-119.557480e-124.393495e-127.955587e-121.248793e-112.376854e-11
iMA9451.398577e-111.241593e-116.318794e-101.253969e-117.349408e-129.134488e-122.082624e-111.493498e-11
iMB7455.070478e-124.316394e-123.264610e-116.657764e-123.221213e-125.698374e-121.078196e-111.047325e-10
iMH5512.251095e-121.368655e-121.658942e-111.702092e-121.852061e-122.130895e-127.064203e-121.524475e-11
iMM14151.248012e-096.982713e-103.418482e-098.552331e-106.642941e-101.483438e-092.067248e-095.278308e-09
iMM9043.595750e-093.644007e-098.308698e-092.982506e-091.531252e-094.619449e-097.938743e-091.828506e-08
iMO10564.451167e-124.065560e-095.216133e-122.091337e-122.158161e-124.592567e-127.587645e-121.088813e-11
iMP429_fixed1.037411e-126.876871e-132.242258e-125.857062e-131.149136e-121.776228e-126.084059e-129.247175e-12
iND7502.859207e-092.514810e-095.778406e-098.041428e-092.058405e-093.681656e-097.571422e-091.155155e-08
iNJ6614.577143e-094.961898e-096.366734e-093.712113e-093.654260e-094.502374e-091.052895e-081.091361e-08
iNJ661m4.915935e-121.054765e-111.969559e-111.044025e-072.524202e-125.219989e-074.698032e-071.416549e-11
iNV2134.984638e-122.831209e-071.319748e-114.020673e-121.957150e-123.845659e-126.196237e-128.082979e-12
iOG6549.605928e-126.018975e-122.579665e-116.017891e-129.601608e-121.360856e-111.486815e-112.803368e-11
iOR3632.717474e-120.000000e+003.817827e-112.046363e-120.000000e+004.687704e-123.893774e-124.926430e-12
iPP6685.361779e-122.598573e-121.432983e-111.154974e-121.613025e-124.027082e-123.367375e-121.306011e-11
iPS189_fixed4.986594e-132.228602e-096.076497e-136.313791e-132.516057e-138.629994e-131.503601e-113.438656e-12
iRC10801.212713e-115.622330e-082.998578e-111.227949e-115.134023e-121.027390e-113.109267e-113.641264e-11
iRM5884.377281e-106.098593e-069.950361e-103.434693e-102.256777e-107.210925e-108.615869e-107.823844e-10
iRR10838.190296e-121.242195e-062.693539e-111.105927e-115.338382e-129.888460e-121.179566e-111.757284e-11
iRS15632.844885e-122.288953e-121.005008e-114.673761e-121.709565e-123.843955e-121.646831e-111.570177e-11
iRS15972.635014e-123.367490e-121.371104e-113.210002e-121.169068e-121.140946e-121.451179e-115.307929e-12
iRS605_fixed5.301002e-125.221034e-121.443769e-118.543278e-124.211766e-124.851140e-121.006191e-111.255027e-11
iRsp10954.771094e-121.286166e-071.499878e-115.990567e-125.702781e-125.757338e-121.136189e-113.360485e-11
iSB6196.677286e-102.461952e-106.072867e-102.292188e-112.877589e-111.436060e-106.720453e-091.817552e-08
iSH3358.608735e-137.918396e-131.719772e-112.412978e-131.354082e-127.116117e-134.743332e-125.824515e-12
iSO7839.201850e-122.860468e-103.880035e-112.266519e-115.511215e-121.131129e-111.612790e-111.880562e-11
iSR4325.763678e-122.818245e-071.616559e-115.417731e-125.851002e-124.656121e-121.018306e-111.522397e-11
iSS7241.263471e-111.255100e-115.174531e-111.577047e-119.879180e-121.510881e-112.661788e-114.044156e-10
iSS8841.354254e-119.174448e-122.825013e-116.639951e-128.284437e-129.998729e-123.226585e-112.586860e-11
iSyn6698.127297e-111.040794e-101.415821e-106.030044e-112.003912e-113.519071e-111.160358e-101.517444e-10
iTH3664.467643e-096.915386e-091.450880e-084.967946e-094.431032e-098.734066e-091.281431e-082.244135e-08
iTL8857.174270e-127.233351e-121.081575e-117.574101e-122.522095e-123.749231e-129.384046e-122.773719e-11
iTY425_fixed1.357132e-126.821528e-133.765527e-121.813959e-129.112030e-131.091689e-125.685786e-121.324586e-11
iVM6795.441300e-123.543573e-091.112015e-111.859461e-112.503111e-122.679210e-121.226340e-118.445926e-12
iVS941_fixed5.781317e-123.985063e-122.889106e-114.555880e-124.109086e-123.148214e-128.170712e-125.949118e-12
iWV13148.397096e-129.542499e-124.617399e-111.552834e-117.278331e-129.208338e-121.366008e-111.755370e-11
iWZ6637.253877e-123.519589e-084.027807e-118.397005e-125.308528e-124.786052e-121.215181e-111.217298e-11
iYL12283.579303e-125.812428e-106.740615e-121.638551e-126.258599e-131.245614e-129.171871e-121.130580e-11
iYO8446.749347e-121.459393e-085.658764e-121.799575e-121.478164e-121.119653e-126.888139e-122.063596e-11
iZM3635.369345e-125.353776e-121.529245e-117.623997e-124.478320e-125.519462e-128.284732e-121.405405e-11
iZmobMBEL6011.672617e-121.524215e-124.595579e-122.783999e-124.085307e-131.355290e-126.795329e-126.571501e-12
mus_musculus9.798615e-124.947154e-122.169150e-116.331269e-124.835687e-128.265638e-121.813938e-111.927275e-11
textbook7.371881e-142.203700e-092.109380e-135.417888e-144.862777e-148.348877e-141.268388e-092.745516e-09
\n", "
" ], "text/plain": [ " cglpk cglpk_exact coin cplex \\\n", "AbyMBEL891 1.030879e-11 6.538390e-12 3.057219e-11 1.652062e-11 \n", "AraGEM 4.518242e-12 3.761263e-12 4.350840e-11 1.031621e-11 \n", "GSMN_TB 3.265029e-10 1.438631e-10 4.422610e-10 1.794655e-09 \n", "PpaMBEL1254 5.524246e-12 5.503863e-12 1.686022e-11 1.653475e-11 \n", "PpuMBEL1071 9.213515e-12 1.006636e-07 2.682011e-11 6.212253e-12 \n", "STM_v1_0 2.442772e-12 7.615986e-09 1.558550e-09 6.747805e-13 \n", "S_coilicolor_fixed 6.094508e-11 3.403941e-11 1.417303e-10 5.070666e-11 \n", "SpoMBEL1693 9.424184e-12 6.328653e-12 2.409888e-11 7.634511e-12 \n", "T_Maritima 1.149696e-12 1.017970e-09 2.680799e-12 1.312999e-12 \n", "VvuMBEL943 1.291556e-11 1.200139e-11 1.619902e-11 5.522043e-12 \n", "iAC560 8.194865e-12 9.868076e-12 2.435742e-11 8.923992e-12 \n", "iAF1260 1.781254e-09 1.946048e-09 5.678922e-09 1.214388e-09 \n", "iAF692 3.386389e-09 2.220311e-09 8.946148e-09 1.759396e-08 \n", "iAI549 1.612223e-11 9.931913e-12 4.028457e-11 2.568619e-11 \n", "iAN840m 3.298200e-10 1.804508e-10 1.107875e-10 2.751869e-10 \n", "iAO358 1.124310e-11 1.091583e-11 3.182512e-11 1.906676e-11 \n", "iAbaylyiV4 2.977077e-12 3.012134e-12 8.290163e-12 5.293440e-12 \n", "iBT721_fixed 6.197820e-12 3.083755e-12 4.031970e-11 1.364242e-12 \n", "iBsu1103 2.972863e-10 6.526051e-06 7.303685e-10 3.339946e-10 \n", "iCA1273 2.755569e-12 2.649891e-12 9.081865e-11 2.677644e-12 \n", "iCB925 1.736274e-14 9.613512e-15 2.816809e-14 1.165951e-14 \n", "iCR744 1.018664e-11 6.352933e-12 3.419470e-11 1.823183e-11 \n", "iCS291 4.977130e-13 3.683998e-13 1.375014e-12 8.569881e-13 \n", "iCS400 1.469269e-12 1.157699e-12 2.533241e-11 1.845843e-12 \n", "iCac802 8.493680e-14 3.153588e-14 1.363077e-13 1.898222e-13 \n", "iFF708 9.631808e-12 5.780962e-12 1.847612e-11 6.812400e-12 \n", "iGB555_fixed 1.618755e-11 4.991450e-10 3.935196e-11 8.029397e-12 \n", "iHD666_fixed 6.101243e-12 2.778296e-11 1.746997e-11 3.751388e-12 \n", "iIB711 8.816919e-12 9.826012e-12 2.293666e-11 2.186360e-11 \n", "iIT341 1.014080e-09 1.807772e-09 5.907021e-09 8.119830e-10 \n", "iJL432 1.174412e-12 3.901074e-13 1.789826e-12 3.963390e-13 \n", "iJN678 2.398464e-14 2.797895e-10 1.930007e-14 1.396985e-14 \n", "iJN746 5.745402e-09 1.309358e-08 9.719125e-09 3.280881e-09 \n", "iJO1366 3.229136e-12 2.352308e-09 1.235567e-11 5.307026e-12 \n", "iJP815 1.020123e-09 7.944625e-10 3.420634e-09 1.550045e-08 \n", "iJR904 1.099850e-09 3.218263e-09 4.340962e-09 6.192079e-10 \n", "iJS747 7.176808e-12 3.632675e-07 9.697313e-12 9.643009e-12 \n", "iKF1028 4.410775e-09 2.512140e-09 3.931006e-09 4.556265e-09 \n", "iLC915 8.942108e-12 5.859216e-12 2.288417e-11 9.887922e-12 \n", "iLL672 7.130910e-12 7.483421e-09 3.135656e-11 7.181390e-12 \n", "iMA871 8.159995e-12 4.129003e-12 3.886357e-11 9.557480e-12 \n", "iMA945 1.398577e-11 1.241593e-11 6.318794e-10 1.253969e-11 \n", "iMB745 5.070478e-12 4.316394e-12 3.264610e-11 6.657764e-12 \n", "iMH551 2.251095e-12 1.368655e-12 1.658942e-11 1.702092e-12 \n", "iMM1415 1.248012e-09 6.982713e-10 3.418482e-09 8.552331e-10 \n", "iMM904 3.595750e-09 3.644007e-09 8.308698e-09 2.982506e-09 \n", "iMO1056 4.451167e-12 4.065560e-09 5.216133e-12 2.091337e-12 \n", "iMP429_fixed 1.037411e-12 6.876871e-13 2.242258e-12 5.857062e-13 \n", "iND750 2.859207e-09 2.514810e-09 5.778406e-09 8.041428e-09 \n", "iNJ661 4.577143e-09 4.961898e-09 6.366734e-09 3.712113e-09 \n", "iNJ661m 4.915935e-12 1.054765e-11 1.969559e-11 1.044025e-07 \n", "iNV213 4.984638e-12 2.831209e-07 1.319748e-11 4.020673e-12 \n", "iOG654 9.605928e-12 6.018975e-12 2.579665e-11 6.017891e-12 \n", "iOR363 2.717474e-12 0.000000e+00 3.817827e-11 2.046363e-12 \n", "iPP668 5.361779e-12 2.598573e-12 1.432983e-11 1.154974e-12 \n", "iPS189_fixed 4.986594e-13 2.228602e-09 6.076497e-13 6.313791e-13 \n", "iRC1080 1.212713e-11 5.622330e-08 2.998578e-11 1.227949e-11 \n", "iRM588 4.377281e-10 6.098593e-06 9.950361e-10 3.434693e-10 \n", "iRR1083 8.190296e-12 1.242195e-06 2.693539e-11 1.105927e-11 \n", "iRS1563 2.844885e-12 2.288953e-12 1.005008e-11 4.673761e-12 \n", "iRS1597 2.635014e-12 3.367490e-12 1.371104e-11 3.210002e-12 \n", "iRS605_fixed 5.301002e-12 5.221034e-12 1.443769e-11 8.543278e-12 \n", "iRsp1095 4.771094e-12 1.286166e-07 1.499878e-11 5.990567e-12 \n", "iSB619 6.677286e-10 2.461952e-10 6.072867e-10 2.292188e-11 \n", "iSH335 8.608735e-13 7.918396e-13 1.719772e-11 2.412978e-13 \n", "iSO783 9.201850e-12 2.860468e-10 3.880035e-11 2.266519e-11 \n", "iSR432 5.763678e-12 2.818245e-07 1.616559e-11 5.417731e-12 \n", "iSS724 1.263471e-11 1.255100e-11 5.174531e-11 1.577047e-11 \n", "iSS884 1.354254e-11 9.174448e-12 2.825013e-11 6.639951e-12 \n", "iSyn669 8.127297e-11 1.040794e-10 1.415821e-10 6.030044e-11 \n", "iTH366 4.467643e-09 6.915386e-09 1.450880e-08 4.967946e-09 \n", "iTL885 7.174270e-12 7.233351e-12 1.081575e-11 7.574101e-12 \n", "iTY425_fixed 1.357132e-12 6.821528e-13 3.765527e-12 1.813959e-12 \n", "iVM679 5.441300e-12 3.543573e-09 1.112015e-11 1.859461e-11 \n", "iVS941_fixed 5.781317e-12 3.985063e-12 2.889106e-11 4.555880e-12 \n", "iWV1314 8.397096e-12 9.542499e-12 4.617399e-11 1.552834e-11 \n", "iWZ663 7.253877e-12 3.519589e-08 4.027807e-11 8.397005e-12 \n", "iYL1228 3.579303e-12 5.812428e-10 6.740615e-12 1.638551e-12 \n", "iYO844 6.749347e-12 1.459393e-08 5.658764e-12 1.799575e-12 \n", "iZM363 5.369345e-12 5.353776e-12 1.529245e-11 7.623997e-12 \n", "iZmobMBEL601 1.672617e-12 1.524215e-12 4.595579e-12 2.783999e-12 \n", "mus_musculus 9.798615e-12 4.947154e-12 2.169150e-11 6.331269e-12 \n", "textbook 7.371881e-14 2.203700e-09 2.109380e-13 5.417888e-14 \n", "\n", " esolver glpk gurobi mosek \n", "AbyMBEL891 6.093565e-12 1.168024e-11 2.098006e-11 1.866628e-11 \n", "AraGEM 3.953687e-12 5.721206e-12 1.492412e-11 1.607253e-11 \n", "GSMN_TB 1.318417e-10 1.580843e-07 2.451718e-09 1.055735e-09 \n", "PpaMBEL1254 1.599098e-12 5.808043e-12 6.458234e-12 1.327733e-11 \n", "PpuMBEL1071 5.611067e-12 6.928756e-12 1.996325e-11 1.154134e-11 \n", "STM_v1_0 4.133462e-13 4.027310e-12 2.884140e-11 1.424397e-11 \n", "S_coilicolor_fixed 3.497688e-11 4.686266e-11 5.399156e-11 2.215057e-10 \n", "SpoMBEL1693 5.512237e-12 8.155074e-12 9.632115e-12 2.056227e-11 \n", "T_Maritima 1.125577e-12 1.578348e-12 4.792797e-12 1.448889e-11 \n", "VvuMBEL943 1.396693e-11 8.099037e-12 7.938761e-12 2.371747e-11 \n", "iAC560 6.451882e-12 7.145092e-12 1.873765e-11 1.947821e-11 \n", "iAF1260 8.198651e-10 7.152690e-09 9.012081e-09 1.764879e-08 \n", "iAF692 1.963760e-09 1.222407e-09 8.575538e-09 1.040327e-08 \n", "iAI549 1.368209e-11 1.323319e-11 1.541363e-11 2.428250e-11 \n", "iAN840m 2.302759e-10 2.859458e-10 8.054293e-10 1.172849e-09 \n", "iAO358 1.175427e-11 1.348169e-11 1.847833e-11 2.943036e-11 \n", "iAbaylyiV4 6.227974e-12 4.977532e-12 1.004922e-11 1.594689e-11 \n", "iBT721_fixed 2.629008e-12 4.273915e-12 3.751666e-12 1.984154e-11 \n", "iBsu1103 2.010636e-10 3.242728e-10 5.418732e-10 8.971953e-10 \n", "iCA1273 1.519041e-12 3.057492e-12 8.550924e-12 1.762628e-11 \n", "iCB925 1.306301e-14 2.114921e-14 5.169930e-12 1.014086e-11 \n", "iCR744 6.848318e-12 6.607602e-12 1.363850e-11 1.417687e-11 \n", "iCS291 3.690381e-13 3.893899e-13 4.744788e-12 6.790318e-12 \n", "iCS400 4.832384e-13 1.527389e-12 5.889844e-12 9.199558e-12 \n", "iCac802 7.927829e-14 7.058789e-14 1.260632e-11 1.055401e-11 \n", "iFF708 5.430347e-12 1.020766e-11 8.761480e-12 2.012872e-11 \n", "iGB555_fixed 5.976067e-12 1.892854e-11 8.302095e-12 3.028083e-11 \n", "iHD666_fixed 3.346992e-12 7.398641e-12 6.864509e-12 1.167770e-11 \n", "iIB711 1.150156e-11 1.309052e-11 1.211514e-11 2.583597e-11 \n", "iIT341 2.710340e-10 1.470638e-09 5.405914e-09 7.601729e-09 \n", "iJL432 3.900797e-13 7.603562e-13 4.689371e-12 3.737990e-12 \n", "iJN678 2.238604e-14 2.488953e-14 7.036177e-12 5.716085e-12 \n", "iJN746 2.846633e-09 4.145871e-09 8.716805e-09 1.037925e-08 \n", "iJO1366 8.026430e-13 4.692354e-12 9.259564e-12 1.267621e-11 \n", "iJP815 7.528140e-10 1.367096e-09 1.359488e-08 5.964099e-09 \n", "iJR904 1.427380e-10 1.365733e-09 6.213569e-09 1.420731e-08 \n", "iJS747 3.800987e-12 4.923902e-12 5.578066e-12 8.495003e-12 \n", "iKF1028 1.713361e-09 4.626908e-09 1.043391e-08 1.115077e-08 \n", "iLC915 6.807457e-12 1.100345e-11 1.760760e-11 1.649339e-11 \n", "iLL672 5.127530e-12 1.080215e-11 5.221250e-12 1.864336e-11 \n", "iMA871 4.393495e-12 7.955587e-12 1.248793e-11 2.376854e-11 \n", "iMA945 7.349408e-12 9.134488e-12 2.082624e-11 1.493498e-11 \n", "iMB745 3.221213e-12 5.698374e-12 1.078196e-11 1.047325e-10 \n", "iMH551 1.852061e-12 2.130895e-12 7.064203e-12 1.524475e-11 \n", "iMM1415 6.642941e-10 1.483438e-09 2.067248e-09 5.278308e-09 \n", "iMM904 1.531252e-09 4.619449e-09 7.938743e-09 1.828506e-08 \n", "iMO1056 2.158161e-12 4.592567e-12 7.587645e-12 1.088813e-11 \n", "iMP429_fixed 1.149136e-12 1.776228e-12 6.084059e-12 9.247175e-12 \n", "iND750 2.058405e-09 3.681656e-09 7.571422e-09 1.155155e-08 \n", "iNJ661 3.654260e-09 4.502374e-09 1.052895e-08 1.091361e-08 \n", "iNJ661m 2.524202e-12 5.219989e-07 4.698032e-07 1.416549e-11 \n", "iNV213 1.957150e-12 3.845659e-12 6.196237e-12 8.082979e-12 \n", "iOG654 9.601608e-12 1.360856e-11 1.486815e-11 2.803368e-11 \n", "iOR363 0.000000e+00 4.687704e-12 3.893774e-12 4.926430e-12 \n", "iPP668 1.613025e-12 4.027082e-12 3.367375e-12 1.306011e-11 \n", "iPS189_fixed 2.516057e-13 8.629994e-13 1.503601e-11 3.438656e-12 \n", "iRC1080 5.134023e-12 1.027390e-11 3.109267e-11 3.641264e-11 \n", "iRM588 2.256777e-10 7.210925e-10 8.615869e-10 7.823844e-10 \n", "iRR1083 5.338382e-12 9.888460e-12 1.179566e-11 1.757284e-11 \n", "iRS1563 1.709565e-12 3.843955e-12 1.646831e-11 1.570177e-11 \n", "iRS1597 1.169068e-12 1.140946e-12 1.451179e-11 5.307929e-12 \n", "iRS605_fixed 4.211766e-12 4.851140e-12 1.006191e-11 1.255027e-11 \n", "iRsp1095 5.702781e-12 5.757338e-12 1.136189e-11 3.360485e-11 \n", "iSB619 2.877589e-11 1.436060e-10 6.720453e-09 1.817552e-08 \n", "iSH335 1.354082e-12 7.116117e-13 4.743332e-12 5.824515e-12 \n", "iSO783 5.511215e-12 1.131129e-11 1.612790e-11 1.880562e-11 \n", "iSR432 5.851002e-12 4.656121e-12 1.018306e-11 1.522397e-11 \n", "iSS724 9.879180e-12 1.510881e-11 2.661788e-11 4.044156e-10 \n", "iSS884 8.284437e-12 9.998729e-12 3.226585e-11 2.586860e-11 \n", "iSyn669 2.003912e-11 3.519071e-11 1.160358e-10 1.517444e-10 \n", "iTH366 4.431032e-09 8.734066e-09 1.281431e-08 2.244135e-08 \n", "iTL885 2.522095e-12 3.749231e-12 9.384046e-12 2.773719e-11 \n", "iTY425_fixed 9.112030e-13 1.091689e-12 5.685786e-12 1.324586e-11 \n", "iVM679 2.503111e-12 2.679210e-12 1.226340e-11 8.445926e-12 \n", "iVS941_fixed 4.109086e-12 3.148214e-12 8.170712e-12 5.949118e-12 \n", "iWV1314 7.278331e-12 9.208338e-12 1.366008e-11 1.755370e-11 \n", "iWZ663 5.308528e-12 4.786052e-12 1.215181e-11 1.217298e-11 \n", "iYL1228 6.258599e-13 1.245614e-12 9.171871e-12 1.130580e-11 \n", "iYO844 1.478164e-12 1.119653e-12 6.888139e-12 2.063596e-11 \n", "iZM363 4.478320e-12 5.519462e-12 8.284732e-12 1.405405e-11 \n", "iZmobMBEL601 4.085307e-13 1.355290e-12 6.795329e-12 6.571501e-12 \n", "mus_musculus 4.835687e-12 8.265638e-12 1.813938e-11 1.927275e-11 \n", "textbook 4.862777e-14 8.348877e-14 1.268388e-09 2.745516e-09 " ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "errors.T" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here are all the computed biomass flux rates for each solver and model." ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "
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cglpkcglpk_exactcoincplexesolverglpkgurobimosek
AbyMBEL891119.233012119.233012119.233012119.233012119.233012119.233012119.233012119.233012
AraGEM10.00000010.00000010.00000010.00000010.00000010.00000010.00000010.000000
GSMN_TB0.1312620.1312620.1312620.1312620.1312620.1312620.1312620.131262
PpaMBEL125478.70059478.70059478.70059478.70059478.70059478.70059478.70059478.700594
PpuMBEL1071132.365353132.365353132.365353132.365353132.365353132.365353132.365353132.365353
STM_v1_00.4778340.4778340.4778340.4778340.4778340.4778340.4778340.477834
S_coilicolor_fixed860.088835860.088835860.088835860.088835860.088835860.088835860.088835860.088835
SpoMBEL169363.78565863.78565863.78565863.78565863.78565863.78565863.78565863.785658
T_Maritima0.3594690.3594690.3594690.3594690.3594690.3594690.3594690.359469
VvuMBEL94396.40232296.40232296.40232296.40232296.40232296.40232296.40232296.402322
iAC5604.0426124.0426124.0426124.0426124.0426124.0426124.0426124.042612
iAF12600.7367010.7367010.7367010.7367010.7367010.7367010.7367010.736701
iAF6920.0272500.0272500.0272500.0272500.0272500.0272500.0272500.027250
iAI54984.17419384.17419384.17419384.17419384.17419384.17419384.17419384.174193
iAN840m0.3401360.3401360.3401360.3401360.3401360.3401360.3401360.340136
iAO358255.180548255.180548255.180548255.180548255.180548255.180548255.180548255.180548
iAbaylyiV412.30654512.30654512.30654512.30654512.30654512.30654512.30654512.306545
iBT721_fixed0.5000000.5000000.5000000.5000000.5000000.5000000.5000000.500000
iBsu11031229.6572441229.6572441229.6572441229.6572441229.6572441229.6572441229.6572441229.657244
iCA12730.7402420.7402420.7402420.7402420.7402420.7402420.7402420.740242
iCB9250.1194280.1194280.1194280.1194280.1194280.1194280.1194280.119428
iCR74441.47674241.47674241.47674241.47674241.47674241.47674241.47674241.476742
iCS2910.1405490.1405490.1405490.1405490.1405490.1405490.1405490.140549
iCS4000.2156390.2156390.2156390.2156390.2156390.2156390.2156390.215639
iCac8020.2095970.2095970.2095970.2095970.2095970.2095970.2095970.209597
iFF70814.91710614.91710614.91710614.91710614.91710614.91710614.91710614.917106
iGB555_fixed127.789084127.789084127.789084127.789084127.789084127.789084127.789084127.789084
iHD666_fixed0.2556720.2556720.2556720.2556720.2556720.2556720.2556720.255672
iIB71184.68841584.68841584.68841584.68841584.68841584.68841584.68841584.688415
iIT3410.6928130.6928130.6928130.6928130.6928130.6928130.6928130.692813
iJL4320.3287410.3287410.3287410.3287410.3287410.3287410.3287410.328741
iJN6780.0631500.0631500.0631500.0631500.0631500.0631500.0631500.063150
iJN7463.6794123.6794123.6794123.6794123.6794123.6794123.6794123.679412
iJO13660.9823720.9823720.9823720.9823720.9823720.9823720.9823720.982372
iJP8150.8615120.8615120.8615120.8615120.8615120.8615120.8615120.861512
iJR9040.9219480.9219480.9219480.9219480.9219480.9219480.9219480.921948
iJS74734.17266234.17266234.17266234.17266234.17266234.17266234.17266234.172662
iKF10280.5178070.5178070.5178070.5178070.5178070.5178070.5178070.517807
iLC91579.02123279.02123279.02123279.02123279.02123279.02123279.02123279.021232
iLL6723.4752833.4752833.4752833.4752833.4752833.4752833.4752833.475283
iMA87127.79297627.79297627.79297627.79297627.79297627.79297627.79297627.792976
iMA94579.58958479.58958479.58958479.58958479.58958479.58958479.58958479.589584
iMB7450.0309420.0309420.0309420.0309420.0309420.0309420.0309420.030942
iMH5510.7750810.7750810.7750810.7750810.7750810.7750810.7750810.775081
iMM14151.3634281.3634281.3634281.3634281.3634281.3634281.3634281.363428
iMM9040.2878660.2878660.2878660.2878660.2878660.2878660.2878660.287866
iMO10561.0479291.0479291.0479291.0479291.0479291.0479291.0479291.047929
iMP429_fixed0.8044320.8044320.8044320.8044320.8044320.8044320.8044320.804432
iND7500.0973230.0973230.0973230.0973230.0973230.0973230.0973230.097323
iNJ6610.0521990.0521990.0521990.0521990.0521990.0521990.0521990.052199
iNJ661m0.0521990.0521990.0521990.0521990.0521990.0521990.0521990.052199
iNV21311.53885911.53885911.53885911.53885911.53885911.53885911.53885911.538859
iOG6540.3554470.3554470.3554470.3554470.3554470.3554470.3554470.355447
iOR363250.000000250.000000250.000000250.000000250.000000250.000000250.000000250.000000
iPP6683.8914743.8914743.8914743.8914743.8914743.8914743.8914743.891474
iPS189_fixed2.2389612.2389612.2389612.2389612.2389612.2389612.2389612.238961
iRC10806.1568516.1568516.1568516.1568516.1568516.1568516.1568516.156851
iRM5881000.0000001000.0000001000.0000001000.0000001000.0000001000.0000001000.0000001000.000000
iRR108377.94736377.94736377.94736377.94736377.94736377.94736377.94736377.947363
iRS15630.0799620.0799620.0799620.0799620.0799620.0799620.0799620.079962
iRS15978.9693468.9693468.9693468.9693468.9693468.9693468.9693468.969346
iRS605_fixed2.1167802.1167802.1167802.1167802.1167802.1167802.1167802.116780
iRsp10959.6868999.6868999.6868999.6868999.6868999.6868999.6868999.686899
iSB6190.1580500.1580500.1580500.1580500.1580500.1580500.1580500.158050
iSH3351.1592111.1592111.1592111.1592111.1592111.1592111.1592111.159211
iSO78317.92030817.92030817.92030817.92030817.92030817.92030817.92030817.920308
iSR43211.48257011.48257011.48257011.48257011.48257011.48257011.48257011.482570
iSS72422.42152522.42152522.42152522.42152522.42152522.42152522.42152522.421525
iSS88470.35928670.35928670.35928670.35928670.35928670.35928670.35928670.359286
iSyn6690.1790900.1790900.1790900.1790900.1790900.1790900.1790900.179090
iTH36627890.88863827890.88863827890.88863827890.88863827890.88863827890.88863827890.88863827890.888638
iTL8857.0988367.0988367.0988367.0988367.0988367.0988367.0988367.098836
iTY425_fixed0.8868330.8868330.8868330.8868330.8868330.8868330.8868330.886833
iVM6792.8265702.8265702.8265702.8265702.8265702.8265702.8265702.826570
iVS941_fixed0.5233850.5233850.5233850.5233850.5233850.5233850.5233850.523385
iWV131425.68240225.68240225.68240225.68240225.68240225.68240225.68240225.682402
iWZ66334.07588134.07588134.07588134.07588134.07588134.07588134.07588134.075881
iYL12281.0426371.0426371.0426381.0426371.0426371.0426371.0426371.042637
iYO8441.5827981.5827981.5827981.5827981.5827981.5827981.5827981.582798
iZM3632.5326062.5326062.5326062.5326062.5326062.5326062.5326062.532606
iZmobMBEL6010.3500800.3500800.3500800.3500800.3500800.3500800.3500800.350080
mus_musculus129.100556129.100556129.100556129.100556129.100556129.100556129.100556129.100556
textbook0.8739220.8739220.8739220.8739220.8739220.8739220.8739220.873922
\n", "
" ], "text/plain": [ " cglpk cglpk_exact coin cplex \\\n", "AbyMBEL891 119.233012 119.233012 119.233012 119.233012 \n", "AraGEM 10.000000 10.000000 10.000000 10.000000 \n", "GSMN_TB 0.131262 0.131262 0.131262 0.131262 \n", "PpaMBEL1254 78.700594 78.700594 78.700594 78.700594 \n", "PpuMBEL1071 132.365353 132.365353 132.365353 132.365353 \n", "STM_v1_0 0.477834 0.477834 0.477834 0.477834 \n", "S_coilicolor_fixed 860.088835 860.088835 860.088835 860.088835 \n", "SpoMBEL1693 63.785658 63.785658 63.785658 63.785658 \n", "T_Maritima 0.359469 0.359469 0.359469 0.359469 \n", "VvuMBEL943 96.402322 96.402322 96.402322 96.402322 \n", "iAC560 4.042612 4.042612 4.042612 4.042612 \n", "iAF1260 0.736701 0.736701 0.736701 0.736701 \n", "iAF692 0.027250 0.027250 0.027250 0.027250 \n", "iAI549 84.174193 84.174193 84.174193 84.174193 \n", "iAN840m 0.340136 0.340136 0.340136 0.340136 \n", "iAO358 255.180548 255.180548 255.180548 255.180548 \n", "iAbaylyiV4 12.306545 12.306545 12.306545 12.306545 \n", "iBT721_fixed 0.500000 0.500000 0.500000 0.500000 \n", "iBsu1103 1229.657244 1229.657244 1229.657244 1229.657244 \n", "iCA1273 0.740242 0.740242 0.740242 0.740242 \n", "iCB925 0.119428 0.119428 0.119428 0.119428 \n", "iCR744 41.476742 41.476742 41.476742 41.476742 \n", "iCS291 0.140549 0.140549 0.140549 0.140549 \n", "iCS400 0.215639 0.215639 0.215639 0.215639 \n", "iCac802 0.209597 0.209597 0.209597 0.209597 \n", "iFF708 14.917106 14.917106 14.917106 14.917106 \n", "iGB555_fixed 127.789084 127.789084 127.789084 127.789084 \n", "iHD666_fixed 0.255672 0.255672 0.255672 0.255672 \n", "iIB711 84.688415 84.688415 84.688415 84.688415 \n", "iIT341 0.692813 0.692813 0.692813 0.692813 \n", "iJL432 0.328741 0.328741 0.328741 0.328741 \n", "iJN678 0.063150 0.063150 0.063150 0.063150 \n", "iJN746 3.679412 3.679412 3.679412 3.679412 \n", "iJO1366 0.982372 0.982372 0.982372 0.982372 \n", "iJP815 0.861512 0.861512 0.861512 0.861512 \n", "iJR904 0.921948 0.921948 0.921948 0.921948 \n", "iJS747 34.172662 34.172662 34.172662 34.172662 \n", "iKF1028 0.517807 0.517807 0.517807 0.517807 \n", "iLC915 79.021232 79.021232 79.021232 79.021232 \n", "iLL672 3.475283 3.475283 3.475283 3.475283 \n", "iMA871 27.792976 27.792976 27.792976 27.792976 \n", "iMA945 79.589584 79.589584 79.589584 79.589584 \n", "iMB745 0.030942 0.030942 0.030942 0.030942 \n", "iMH551 0.775081 0.775081 0.775081 0.775081 \n", "iMM1415 1.363428 1.363428 1.363428 1.363428 \n", "iMM904 0.287866 0.287866 0.287866 0.287866 \n", "iMO1056 1.047929 1.047929 1.047929 1.047929 \n", "iMP429_fixed 0.804432 0.804432 0.804432 0.804432 \n", "iND750 0.097323 0.097323 0.097323 0.097323 \n", "iNJ661 0.052199 0.052199 0.052199 0.052199 \n", "iNJ661m 0.052199 0.052199 0.052199 0.052199 \n", "iNV213 11.538859 11.538859 11.538859 11.538859 \n", "iOG654 0.355447 0.355447 0.355447 0.355447 \n", "iOR363 250.000000 250.000000 250.000000 250.000000 \n", "iPP668 3.891474 3.891474 3.891474 3.891474 \n", "iPS189_fixed 2.238961 2.238961 2.238961 2.238961 \n", "iRC1080 6.156851 6.156851 6.156851 6.156851 \n", "iRM588 1000.000000 1000.000000 1000.000000 1000.000000 \n", "iRR1083 77.947363 77.947363 77.947363 77.947363 \n", "iRS1563 0.079962 0.079962 0.079962 0.079962 \n", "iRS1597 8.969346 8.969346 8.969346 8.969346 \n", "iRS605_fixed 2.116780 2.116780 2.116780 2.116780 \n", "iRsp1095 9.686899 9.686899 9.686899 9.686899 \n", "iSB619 0.158050 0.158050 0.158050 0.158050 \n", "iSH335 1.159211 1.159211 1.159211 1.159211 \n", "iSO783 17.920308 17.920308 17.920308 17.920308 \n", "iSR432 11.482570 11.482570 11.482570 11.482570 \n", "iSS724 22.421525 22.421525 22.421525 22.421525 \n", "iSS884 70.359286 70.359286 70.359286 70.359286 \n", "iSyn669 0.179090 0.179090 0.179090 0.179090 \n", "iTH366 27890.888638 27890.888638 27890.888638 27890.888638 \n", "iTL885 7.098836 7.098836 7.098836 7.098836 \n", "iTY425_fixed 0.886833 0.886833 0.886833 0.886833 \n", "iVM679 2.826570 2.826570 2.826570 2.826570 \n", "iVS941_fixed 0.523385 0.523385 0.523385 0.523385 \n", "iWV1314 25.682402 25.682402 25.682402 25.682402 \n", "iWZ663 34.075881 34.075881 34.075881 34.075881 \n", "iYL1228 1.042637 1.042637 1.042638 1.042637 \n", "iYO844 1.582798 1.582798 1.582798 1.582798 \n", "iZM363 2.532606 2.532606 2.532606 2.532606 \n", "iZmobMBEL601 0.350080 0.350080 0.350080 0.350080 \n", "mus_musculus 129.100556 129.100556 129.100556 129.100556 \n", "textbook 0.873922 0.873922 0.873922 0.873922 \n", "\n", " esolver glpk gurobi mosek \n", "AbyMBEL891 119.233012 119.233012 119.233012 119.233012 \n", "AraGEM 10.000000 10.000000 10.000000 10.000000 \n", "GSMN_TB 0.131262 0.131262 0.131262 0.131262 \n", "PpaMBEL1254 78.700594 78.700594 78.700594 78.700594 \n", "PpuMBEL1071 132.365353 132.365353 132.365353 132.365353 \n", "STM_v1_0 0.477834 0.477834 0.477834 0.477834 \n", "S_coilicolor_fixed 860.088835 860.088835 860.088835 860.088835 \n", "SpoMBEL1693 63.785658 63.785658 63.785658 63.785658 \n", "T_Maritima 0.359469 0.359469 0.359469 0.359469 \n", "VvuMBEL943 96.402322 96.402322 96.402322 96.402322 \n", "iAC560 4.042612 4.042612 4.042612 4.042612 \n", "iAF1260 0.736701 0.736701 0.736701 0.736701 \n", "iAF692 0.027250 0.027250 0.027250 0.027250 \n", "iAI549 84.174193 84.174193 84.174193 84.174193 \n", "iAN840m 0.340136 0.340136 0.340136 0.340136 \n", "iAO358 255.180548 255.180548 255.180548 255.180548 \n", "iAbaylyiV4 12.306545 12.306545 12.306545 12.306545 \n", "iBT721_fixed 0.500000 0.500000 0.500000 0.500000 \n", "iBsu1103 1229.657244 1229.657244 1229.657244 1229.657244 \n", "iCA1273 0.740242 0.740242 0.740242 0.740242 \n", "iCB925 0.119428 0.119428 0.119428 0.119428 \n", "iCR744 41.476742 41.476742 41.476742 41.476742 \n", "iCS291 0.140549 0.140549 0.140549 0.140549 \n", "iCS400 0.215639 0.215639 0.215639 0.215639 \n", "iCac802 0.209597 0.209597 0.209597 0.209597 \n", "iFF708 14.917106 14.917106 14.917106 14.917106 \n", "iGB555_fixed 127.789084 127.789084 127.789084 127.789084 \n", "iHD666_fixed 0.255672 0.255672 0.255672 0.255672 \n", "iIB711 84.688415 84.688415 84.688415 84.688415 \n", "iIT341 0.692813 0.692813 0.692813 0.692813 \n", "iJL432 0.328741 0.328741 0.328741 0.328741 \n", "iJN678 0.063150 0.063150 0.063150 0.063150 \n", "iJN746 3.679412 3.679412 3.679412 3.679412 \n", "iJO1366 0.982372 0.982372 0.982372 0.982372 \n", "iJP815 0.861512 0.861512 0.861512 0.861512 \n", "iJR904 0.921948 0.921948 0.921948 0.921948 \n", "iJS747 34.172662 34.172662 34.172662 34.172662 \n", "iKF1028 0.517807 0.517807 0.517807 0.517807 \n", "iLC915 79.021232 79.021232 79.021232 79.021232 \n", "iLL672 3.475283 3.475283 3.475283 3.475283 \n", "iMA871 27.792976 27.792976 27.792976 27.792976 \n", "iMA945 79.589584 79.589584 79.589584 79.589584 \n", "iMB745 0.030942 0.030942 0.030942 0.030942 \n", "iMH551 0.775081 0.775081 0.775081 0.775081 \n", "iMM1415 1.363428 1.363428 1.363428 1.363428 \n", "iMM904 0.287866 0.287866 0.287866 0.287866 \n", "iMO1056 1.047929 1.047929 1.047929 1.047929 \n", "iMP429_fixed 0.804432 0.804432 0.804432 0.804432 \n", "iND750 0.097323 0.097323 0.097323 0.097323 \n", "iNJ661 0.052199 0.052199 0.052199 0.052199 \n", "iNJ661m 0.052199 0.052199 0.052199 0.052199 \n", "iNV213 11.538859 11.538859 11.538859 11.538859 \n", "iOG654 0.355447 0.355447 0.355447 0.355447 \n", "iOR363 250.000000 250.000000 250.000000 250.000000 \n", "iPP668 3.891474 3.891474 3.891474 3.891474 \n", "iPS189_fixed 2.238961 2.238961 2.238961 2.238961 \n", "iRC1080 6.156851 6.156851 6.156851 6.156851 \n", "iRM588 1000.000000 1000.000000 1000.000000 1000.000000 \n", "iRR1083 77.947363 77.947363 77.947363 77.947363 \n", "iRS1563 0.079962 0.079962 0.079962 0.079962 \n", "iRS1597 8.969346 8.969346 8.969346 8.969346 \n", "iRS605_fixed 2.116780 2.116780 2.116780 2.116780 \n", "iRsp1095 9.686899 9.686899 9.686899 9.686899 \n", "iSB619 0.158050 0.158050 0.158050 0.158050 \n", "iSH335 1.159211 1.159211 1.159211 1.159211 \n", "iSO783 17.920308 17.920308 17.920308 17.920308 \n", "iSR432 11.482570 11.482570 11.482570 11.482570 \n", "iSS724 22.421525 22.421525 22.421525 22.421525 \n", "iSS884 70.359286 70.359286 70.359286 70.359286 \n", "iSyn669 0.179090 0.179090 0.179090 0.179090 \n", "iTH366 27890.888638 27890.888638 27890.888638 27890.888638 \n", "iTL885 7.098836 7.098836 7.098836 7.098836 \n", "iTY425_fixed 0.886833 0.886833 0.886833 0.886833 \n", "iVM679 2.826570 2.826570 2.826570 2.826570 \n", "iVS941_fixed 0.523385 0.523385 0.523385 0.523385 \n", "iWV1314 25.682402 25.682402 25.682402 25.682402 \n", "iWZ663 34.075881 34.075881 34.075881 34.075881 \n", "iYL1228 1.042637 1.042637 1.042637 1.042637 \n", "iYO844 1.582798 1.582798 1.582798 1.582798 \n", "iZM363 2.532606 2.532606 2.532606 2.532606 \n", "iZmobMBEL601 0.350080 0.350080 0.350080 0.350080 \n", "mus_musculus 129.100556 129.100556 129.100556 129.100556 \n", "textbook 0.873922 0.873922 0.873922 0.873922 " ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "results.T" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The objectives computed for these solvers are effectively the same as those computed by esolver." ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "
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cglpkcglpk_exactcoincplexglpkgurobimosek
AbyMBEL8911.136868e-130.000000e+003.844036e-11-5.684342e-141.136868e-13-2.415845e-139.947598e-14
AraGEM0.000000e+000.000000e+000.000000e+000.000000e+000.000000e+000.000000e+000.000000e+00
GSMN_TB-4.656553e-130.000000e+005.085987e-12-2.345454e-111.011393e-08-1.665335e-15-1.402767e-12
PpaMBEL12540.000000e+000.000000e+005.805134e-11-1.847411e-130.000000e+000.000000e+00-7.105427e-14
PpuMBEL10718.526513e-145.117897e-104.602612e-105.684342e-148.526513e-145.684342e-14-1.136868e-13
STM_v1_03.863576e-144.957084e-103.605212e-07-1.498801e-151.086908e-13-4.996004e-164.814482e-13
S_coilicolor_fixed1.136868e-130.000000e+001.364242e-120.000000e+001.136868e-130.000000e+00-1.250555e-12
SpoMBEL1693-1.421085e-140.000000e+002.098943e-11-1.421085e-147.105427e-14-2.842171e-14-6.039613e-13
T_Maritima-3.214096e-149.456913e-112.230516e-093.330669e-16-2.114975e-14-3.330669e-168.437695e-14
VvuMBEL9431.421085e-140.000000e+001.922729e-114.263256e-144.263256e-140.000000e+001.563194e-13
iAC5602.664535e-150.000000e+008.553158e-138.881784e-160.000000e+001.776357e-151.421085e-14
iAF12602.087197e-110.000000e+008.428154e-08-2.066280e-111.858336e-11-1.196998e-111.749767e-11
iAF692-3.651770e-11-2.846202e-111.981591e-096.965345e-09-4.769716e-122.617935e-09-1.106832e-09
iAI549-7.673862e-130.000000e+005.840661e-11-5.826450e-131.705303e-13-1.236344e-126.963319e-13
iAN840m0.000000e+000.000000e+001.872813e-08-5.551115e-170.000000e+000.000000e+000.000000e+00
iAO358-8.526513e-140.000000e+001.497824e-11-1.989520e-132.842171e-14-5.115908e-13-5.684342e-14
iAbaylyiV44.796163e-14-1.776357e-158.941647e-11-1.776357e-151.953993e-141.065814e-14-4.494183e-13
iBT721_fixed0.000000e+000.000000e+00-6.938894e-150.000000e+000.000000e+000.000000e+001.110223e-16
iBsu1103-2.273737e-13-2.653928e-085.934453e-11-1.136868e-122.273737e-130.000000e+002.046363e-12
iCA1273-3.275158e-140.000000e+001.637933e-084.685141e-145.406786e-14-4.696243e-142.265965e-13
iCB9257.494005e-160.000000e+002.920300e-11-3.191891e-16-1.942890e-162.636780e-16-2.703671e-13
iCR7443.552714e-140.000000e+002.358817e-09-5.826450e-13-1.350031e-131.705303e-135.186962e-13
iCS2911.193490e-150.000000e+002.731065e-12-6.938894e-16-1.110223e-15-1.276756e-15-3.608225e-16
iCS400-1.026956e-150.000000e+004.090339e-13-1.110223e-162.470246e-150.000000e+001.956768e-14
iCac8024.440892e-160.000000e+009.617439e-09-1.665335e-16-1.249001e-153.885781e-16-3.314016e-14
iFF7081.776357e-150.000000e+002.838618e-12-5.329071e-141.421085e-145.329071e-15-4.263256e-14
iGB555_fixed-1.037392e-125.440199e-104.702940e-101.705303e-13-2.060574e-122.700062e-131.577405e-12
iHD666_fixed3.774758e-149.730550e-131.013567e-084.718448e-15-7.366330e-143.164136e-15-2.220446e-16
iIB711-1.421085e-140.000000e+002.015099e-114.263256e-14-2.842171e-14-2.842171e-14-1.421085e-14
iIT341-1.129519e-112.245907e-106.851687e-08-4.440892e-15-1.403899e-11-2.111644e-13-6.530149e-10
iJL432-1.554312e-140.000000e+004.104939e-12-1.193490e-142.103873e-142.708944e-141.809664e-13
iJN678-4.718448e-162.856902e-112.463432e-08-1.082467e-15-2.220446e-16-2.775558e-171.214445e-13
iJN7461.231681e-101.059390e-092.485335e-081.167688e-107.149392e-11-6.661338e-151.743801e-10
iJO13664.973799e-141.739909e-101.544051e-078.881784e-165.107026e-14-2.664535e-155.774270e-13
iJP8151.783040e-110.000000e+003.016005e-092.160384e-102.299161e-123.759559e-111.973555e-11
iJR904-3.364420e-122.154040e-101.404389e-071.258993e-13-3.852363e-112.146194e-113.302114e-11
iJS747-1.421085e-13-9.758267e-091.937650e-11-5.186962e-137.105427e-150.000000e+00-2.842171e-14
iKF1028-1.799028e-110.000000e+004.904080e-095.995204e-15-6.050105e-116.877166e-11-3.783374e-11
iLC9152.103206e-120.000000e+001.007605e-08-3.609557e-123.211653e-121.278977e-132.231104e-11
iLL6725.151435e-14-3.967990e-102.029425e-093.019807e-144.529710e-144.440892e-16-8.260059e-14
iMA8710.000000e+000.000000e+002.038192e-11-3.552714e-150.000000e+000.000000e+00-1.065814e-14
iMA9451.421085e-140.000000e+004.755066e-090.000000e+000.000000e+001.421085e-149.947598e-14
iMB7452.247508e-140.000000e+005.139368e-104.757412e-10-2.697495e-14-2.733924e-15-3.323893e-12
iMH551-4.263256e-140.000000e+002.145972e-116.772360e-15-2.420286e-144.440892e-16-2.721157e-13
iMM1415-2.347234e-120.000000e+001.605315e-085.881740e-12-1.929346e-11-6.439294e-151.410982e-11
iMM9041.060230e-110.000000e+002.990649e-09-9.992007e-15-9.139328e-111.054712e-15-5.305936e-10
iMO1056-7.860379e-14-6.367740e-101.085125e-08-1.287859e-145.107026e-15-2.664535e-15-3.352874e-14
iMP429_fixed2.293721e-130.000000e+001.916863e-10-2.886580e-151.887379e-15-1.443290e-15-3.357314e-13
iND750-2.235294e-103.722161e-134.941149e-08-1.627079e-103.478570e-112.220446e-16-2.592769e-10
iNJ661-5.478381e-11-1.366268e-146.874230e-101.412759e-14-1.110825e-11-2.481532e-10-3.497474e-10
iNJ661m7.542578e-15-1.365574e-141.140270e-087.253811e-081.649386e-071.528997e-07-2.329942e-13
iNV2138.881784e-15-8.495142e-101.006306e-110.000000e+00-8.881784e-153.552714e-15-2.486900e-14
iOG6540.000000e+000.000000e+000.000000e+000.000000e+000.000000e+000.000000e+000.000000e+00
iOR3632.842171e-140.000000e+006.735945e-12-5.684342e-14-5.684342e-14-2.842171e-142.842171e-14
iPP668-3.552714e-150.000000e+001.800928e-104.440892e-163.597123e-14-7.549517e-15-7.238654e-14
iPS189_fixed2.353673e-14-1.108655e-109.894308e-127.549517e-159.015011e-143.108624e-151.656453e-13
iRC1080-1.341149e-139.275872e-097.015366e-115.062617e-134.121148e-136.838974e-14-1.287859e-13
iRM5880.000000e+000.000000e+000.000000e+000.000000e+000.000000e+000.000000e+000.000000e+00
iRR10830.000000e+001.977781e-081.978151e-100.000000e+00-2.842171e-140.000000e+00-2.842171e-14
iRS15636.800116e-160.000000e+009.173981e-12-4.163336e-165.967449e-16-9.478529e-15-8.118506e-15
iRS15973.552714e-150.000000e+009.791457e-11-8.881784e-155.329071e-15-2.842171e-14-2.842171e-14
iRS605_fixed1.199041e-140.000000e+004.111211e-09-2.975398e-14-3.996803e-153.552714e-15-1.865175e-14
iRsp1095-1.065814e-141.172156e-092.692957e-11-5.151435e-141.421085e-14-2.131628e-14-8.526513e-14
iSB619-3.088640e-130.000000e+009.349807e-114.496403e-15-1.181277e-131.437739e-149.064693e-13
iSH3353.552714e-150.000000e+009.279755e-114.662937e-15-1.620926e-14-2.664535e-154.016787e-13
iSO7830.000000e+00-3.318235e-127.798739e-10-5.684342e-141.776357e-140.000000e+003.552714e-15
iSR432-3.019807e-14-1.671046e-094.089173e-12-2.167155e-135.151435e-14-2.593481e-13-3.552714e-13
iSS7240.000000e+000.000000e+004.753531e-120.000000e+000.000000e+000.000000e+000.000000e+00
iSS8841.421085e-130.000000e+006.156000e-10-1.563194e-137.105427e-14-5.684342e-14-1.847411e-13
iSyn669-6.186440e-13-1.463274e-126.855544e-12-5.084516e-126.528666e-135.661027e-13-1.837835e-12
iTH3663.274181e-110.000000e+002.655725e-101.091394e-111.455192e-112.182787e-111.818989e-11
iTL8853.552714e-146.856737e-131.468498e-088.881784e-14-4.973799e-14-1.572076e-135.204726e-13
iTY425_fixed-2.775558e-150.000000e+002.184031e-122.775558e-15-5.551115e-166.661338e-162.079448e-13
iVM679-2.398082e-141.689826e-101.038440e-104.352074e-147.549517e-15-2.131628e-14-3.819167e-14
iVS941_fixed2.153833e-140.000000e+001.439289e-083.785861e-14-3.352874e-14-1.498801e-14-3.141931e-14
iWV13145.329071e-143.552714e-154.255085e-11-3.552714e-15-3.552714e-150.000000e+00-9.947598e-14
iWZ6633.552714e-142.741011e-093.468870e-118.526513e-14-5.684342e-144.263256e-14-2.842171e-14
iYL1228-7.904788e-140.000000e+002.068377e-09-1.332268e-15-1.265654e-146.217249e-15-2.731149e-13
iYO844-6.439294e-15-3.056155e-114.923346e-10-1.554312e-151.110223e-156.661338e-16-3.130829e-14
iZM3632.664535e-150.000000e+006.776801e-12-8.348877e-147.549517e-15-2.220446e-158.881784e-15
iZmobMBEL601-1.004752e-140.000000e+002.098571e-11-3.115286e-13-3.136380e-14-4.996004e-153.836931e-13
mus_musculus-2.842171e-140.000000e+001.811600e-10-2.842171e-140.000000e+00-2.842171e-140.000000e+00
textbook1.110223e-169.818923e-124.750644e-130.000000e+00-1.110223e-16-1.110223e-164.566791e-12
\n", "
" ], "text/plain": [ " cglpk cglpk_exact coin cplex \\\n", "AbyMBEL891 1.136868e-13 0.000000e+00 3.844036e-11 -5.684342e-14 \n", "AraGEM 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 \n", "GSMN_TB -4.656553e-13 0.000000e+00 5.085987e-12 -2.345454e-11 \n", "PpaMBEL1254 0.000000e+00 0.000000e+00 5.805134e-11 -1.847411e-13 \n", "PpuMBEL1071 8.526513e-14 5.117897e-10 4.602612e-10 5.684342e-14 \n", "STM_v1_0 3.863576e-14 4.957084e-10 3.605212e-07 -1.498801e-15 \n", "S_coilicolor_fixed 1.136868e-13 0.000000e+00 1.364242e-12 0.000000e+00 \n", "SpoMBEL1693 -1.421085e-14 0.000000e+00 2.098943e-11 -1.421085e-14 \n", "T_Maritima -3.214096e-14 9.456913e-11 2.230516e-09 3.330669e-16 \n", "VvuMBEL943 1.421085e-14 0.000000e+00 1.922729e-11 4.263256e-14 \n", "iAC560 2.664535e-15 0.000000e+00 8.553158e-13 8.881784e-16 \n", "iAF1260 2.087197e-11 0.000000e+00 8.428154e-08 -2.066280e-11 \n", "iAF692 -3.651770e-11 -2.846202e-11 1.981591e-09 6.965345e-09 \n", "iAI549 -7.673862e-13 0.000000e+00 5.840661e-11 -5.826450e-13 \n", "iAN840m 0.000000e+00 0.000000e+00 1.872813e-08 -5.551115e-17 \n", "iAO358 -8.526513e-14 0.000000e+00 1.497824e-11 -1.989520e-13 \n", "iAbaylyiV4 4.796163e-14 -1.776357e-15 8.941647e-11 -1.776357e-15 \n", "iBT721_fixed 0.000000e+00 0.000000e+00 -6.938894e-15 0.000000e+00 \n", "iBsu1103 -2.273737e-13 -2.653928e-08 5.934453e-11 -1.136868e-12 \n", "iCA1273 -3.275158e-14 0.000000e+00 1.637933e-08 4.685141e-14 \n", "iCB925 7.494005e-16 0.000000e+00 2.920300e-11 -3.191891e-16 \n", "iCR744 3.552714e-14 0.000000e+00 2.358817e-09 -5.826450e-13 \n", "iCS291 1.193490e-15 0.000000e+00 2.731065e-12 -6.938894e-16 \n", "iCS400 -1.026956e-15 0.000000e+00 4.090339e-13 -1.110223e-16 \n", "iCac802 4.440892e-16 0.000000e+00 9.617439e-09 -1.665335e-16 \n", "iFF708 1.776357e-15 0.000000e+00 2.838618e-12 -5.329071e-14 \n", "iGB555_fixed -1.037392e-12 5.440199e-10 4.702940e-10 1.705303e-13 \n", "iHD666_fixed 3.774758e-14 9.730550e-13 1.013567e-08 4.718448e-15 \n", "iIB711 -1.421085e-14 0.000000e+00 2.015099e-11 4.263256e-14 \n", "iIT341 -1.129519e-11 2.245907e-10 6.851687e-08 -4.440892e-15 \n", "iJL432 -1.554312e-14 0.000000e+00 4.104939e-12 -1.193490e-14 \n", "iJN678 -4.718448e-16 2.856902e-11 2.463432e-08 -1.082467e-15 \n", "iJN746 1.231681e-10 1.059390e-09 2.485335e-08 1.167688e-10 \n", "iJO1366 4.973799e-14 1.739909e-10 1.544051e-07 8.881784e-16 \n", "iJP815 1.783040e-11 0.000000e+00 3.016005e-09 2.160384e-10 \n", "iJR904 -3.364420e-12 2.154040e-10 1.404389e-07 1.258993e-13 \n", "iJS747 -1.421085e-13 -9.758267e-09 1.937650e-11 -5.186962e-13 \n", "iKF1028 -1.799028e-11 0.000000e+00 4.904080e-09 5.995204e-15 \n", "iLC915 2.103206e-12 0.000000e+00 1.007605e-08 -3.609557e-12 \n", "iLL672 5.151435e-14 -3.967990e-10 2.029425e-09 3.019807e-14 \n", "iMA871 0.000000e+00 0.000000e+00 2.038192e-11 -3.552714e-15 \n", "iMA945 1.421085e-14 0.000000e+00 4.755066e-09 0.000000e+00 \n", "iMB745 2.247508e-14 0.000000e+00 5.139368e-10 4.757412e-10 \n", "iMH551 -4.263256e-14 0.000000e+00 2.145972e-11 6.772360e-15 \n", "iMM1415 -2.347234e-12 0.000000e+00 1.605315e-08 5.881740e-12 \n", "iMM904 1.060230e-11 0.000000e+00 2.990649e-09 -9.992007e-15 \n", "iMO1056 -7.860379e-14 -6.367740e-10 1.085125e-08 -1.287859e-14 \n", "iMP429_fixed 2.293721e-13 0.000000e+00 1.916863e-10 -2.886580e-15 \n", "iND750 -2.235294e-10 3.722161e-13 4.941149e-08 -1.627079e-10 \n", "iNJ661 -5.478381e-11 -1.366268e-14 6.874230e-10 1.412759e-14 \n", "iNJ661m 7.542578e-15 -1.365574e-14 1.140270e-08 7.253811e-08 \n", "iNV213 8.881784e-15 -8.495142e-10 1.006306e-11 0.000000e+00 \n", "iOG654 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 \n", "iOR363 2.842171e-14 0.000000e+00 6.735945e-12 -5.684342e-14 \n", "iPP668 -3.552714e-15 0.000000e+00 1.800928e-10 4.440892e-16 \n", "iPS189_fixed 2.353673e-14 -1.108655e-10 9.894308e-12 7.549517e-15 \n", "iRC1080 -1.341149e-13 9.275872e-09 7.015366e-11 5.062617e-13 \n", "iRM588 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 \n", "iRR1083 0.000000e+00 1.977781e-08 1.978151e-10 0.000000e+00 \n", "iRS1563 6.800116e-16 0.000000e+00 9.173981e-12 -4.163336e-16 \n", "iRS1597 3.552714e-15 0.000000e+00 9.791457e-11 -8.881784e-15 \n", "iRS605_fixed 1.199041e-14 0.000000e+00 4.111211e-09 -2.975398e-14 \n", "iRsp1095 -1.065814e-14 1.172156e-09 2.692957e-11 -5.151435e-14 \n", "iSB619 -3.088640e-13 0.000000e+00 9.349807e-11 4.496403e-15 \n", "iSH335 3.552714e-15 0.000000e+00 9.279755e-11 4.662937e-15 \n", "iSO783 0.000000e+00 -3.318235e-12 7.798739e-10 -5.684342e-14 \n", "iSR432 -3.019807e-14 -1.671046e-09 4.089173e-12 -2.167155e-13 \n", "iSS724 0.000000e+00 0.000000e+00 4.753531e-12 0.000000e+00 \n", "iSS884 1.421085e-13 0.000000e+00 6.156000e-10 -1.563194e-13 \n", "iSyn669 -6.186440e-13 -1.463274e-12 6.855544e-12 -5.084516e-12 \n", "iTH366 3.274181e-11 0.000000e+00 2.655725e-10 1.091394e-11 \n", "iTL885 3.552714e-14 6.856737e-13 1.468498e-08 8.881784e-14 \n", "iTY425_fixed -2.775558e-15 0.000000e+00 2.184031e-12 2.775558e-15 \n", "iVM679 -2.398082e-14 1.689826e-10 1.038440e-10 4.352074e-14 \n", "iVS941_fixed 2.153833e-14 0.000000e+00 1.439289e-08 3.785861e-14 \n", "iWV1314 5.329071e-14 3.552714e-15 4.255085e-11 -3.552714e-15 \n", "iWZ663 3.552714e-14 2.741011e-09 3.468870e-11 8.526513e-14 \n", "iYL1228 -7.904788e-14 0.000000e+00 2.068377e-09 -1.332268e-15 \n", "iYO844 -6.439294e-15 -3.056155e-11 4.923346e-10 -1.554312e-15 \n", "iZM363 2.664535e-15 0.000000e+00 6.776801e-12 -8.348877e-14 \n", "iZmobMBEL601 -1.004752e-14 0.000000e+00 2.098571e-11 -3.115286e-13 \n", "mus_musculus -2.842171e-14 0.000000e+00 1.811600e-10 -2.842171e-14 \n", "textbook 1.110223e-16 9.818923e-12 4.750644e-13 0.000000e+00 \n", "\n", " glpk gurobi mosek \n", "AbyMBEL891 1.136868e-13 -2.415845e-13 9.947598e-14 \n", "AraGEM 0.000000e+00 0.000000e+00 0.000000e+00 \n", "GSMN_TB 1.011393e-08 -1.665335e-15 -1.402767e-12 \n", "PpaMBEL1254 0.000000e+00 0.000000e+00 -7.105427e-14 \n", "PpuMBEL1071 8.526513e-14 5.684342e-14 -1.136868e-13 \n", "STM_v1_0 1.086908e-13 -4.996004e-16 4.814482e-13 \n", "S_coilicolor_fixed 1.136868e-13 0.000000e+00 -1.250555e-12 \n", "SpoMBEL1693 7.105427e-14 -2.842171e-14 -6.039613e-13 \n", "T_Maritima -2.114975e-14 -3.330669e-16 8.437695e-14 \n", "VvuMBEL943 4.263256e-14 0.000000e+00 1.563194e-13 \n", "iAC560 0.000000e+00 1.776357e-15 1.421085e-14 \n", "iAF1260 1.858336e-11 -1.196998e-11 1.749767e-11 \n", "iAF692 -4.769716e-12 2.617935e-09 -1.106832e-09 \n", "iAI549 1.705303e-13 -1.236344e-12 6.963319e-13 \n", "iAN840m 0.000000e+00 0.000000e+00 0.000000e+00 \n", "iAO358 2.842171e-14 -5.115908e-13 -5.684342e-14 \n", "iAbaylyiV4 1.953993e-14 1.065814e-14 -4.494183e-13 \n", "iBT721_fixed 0.000000e+00 0.000000e+00 1.110223e-16 \n", "iBsu1103 2.273737e-13 0.000000e+00 2.046363e-12 \n", "iCA1273 5.406786e-14 -4.696243e-14 2.265965e-13 \n", "iCB925 -1.942890e-16 2.636780e-16 -2.703671e-13 \n", "iCR744 -1.350031e-13 1.705303e-13 5.186962e-13 \n", "iCS291 -1.110223e-15 -1.276756e-15 -3.608225e-16 \n", "iCS400 2.470246e-15 0.000000e+00 1.956768e-14 \n", "iCac802 -1.249001e-15 3.885781e-16 -3.314016e-14 \n", "iFF708 1.421085e-14 5.329071e-15 -4.263256e-14 \n", "iGB555_fixed -2.060574e-12 2.700062e-13 1.577405e-12 \n", "iHD666_fixed -7.366330e-14 3.164136e-15 -2.220446e-16 \n", "iIB711 -2.842171e-14 -2.842171e-14 -1.421085e-14 \n", "iIT341 -1.403899e-11 -2.111644e-13 -6.530149e-10 \n", "iJL432 2.103873e-14 2.708944e-14 1.809664e-13 \n", "iJN678 -2.220446e-16 -2.775558e-17 1.214445e-13 \n", "iJN746 7.149392e-11 -6.661338e-15 1.743801e-10 \n", "iJO1366 5.107026e-14 -2.664535e-15 5.774270e-13 \n", "iJP815 2.299161e-12 3.759559e-11 1.973555e-11 \n", "iJR904 -3.852363e-11 2.146194e-11 3.302114e-11 \n", "iJS747 7.105427e-15 0.000000e+00 -2.842171e-14 \n", "iKF1028 -6.050105e-11 6.877166e-11 -3.783374e-11 \n", "iLC915 3.211653e-12 1.278977e-13 2.231104e-11 \n", "iLL672 4.529710e-14 4.440892e-16 -8.260059e-14 \n", "iMA871 0.000000e+00 0.000000e+00 -1.065814e-14 \n", "iMA945 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-9.478529e-15 -8.118506e-15 \n", "iRS1597 5.329071e-15 -2.842171e-14 -2.842171e-14 \n", "iRS605_fixed -3.996803e-15 3.552714e-15 -1.865175e-14 \n", "iRsp1095 1.421085e-14 -2.131628e-14 -8.526513e-14 \n", "iSB619 -1.181277e-13 1.437739e-14 9.064693e-13 \n", "iSH335 -1.620926e-14 -2.664535e-15 4.016787e-13 \n", "iSO783 1.776357e-14 0.000000e+00 3.552714e-15 \n", "iSR432 5.151435e-14 -2.593481e-13 -3.552714e-13 \n", "iSS724 0.000000e+00 0.000000e+00 0.000000e+00 \n", "iSS884 7.105427e-14 -5.684342e-14 -1.847411e-13 \n", "iSyn669 6.528666e-13 5.661027e-13 -1.837835e-12 \n", "iTH366 1.455192e-11 2.182787e-11 1.818989e-11 \n", "iTL885 -4.973799e-14 -1.572076e-13 5.204726e-13 \n", "iTY425_fixed -5.551115e-16 6.661338e-16 2.079448e-13 \n", "iVM679 7.549517e-15 -2.131628e-14 -3.819167e-14 \n", "iVS941_fixed -3.352874e-14 -1.498801e-14 -3.141931e-14 \n", "iWV1314 -3.552714e-15 0.000000e+00 -9.947598e-14 \n", "iWZ663 -5.684342e-14 4.263256e-14 -2.842171e-14 \n", "iYL1228 -1.265654e-14 6.217249e-15 -2.731149e-13 \n", "iYO844 1.110223e-15 6.661338e-16 -3.130829e-14 \n", "iZM363 7.549517e-15 -2.220446e-15 8.881784e-15 \n", "iZmobMBEL601 -3.136380e-14 -4.996004e-15 3.836931e-13 \n", "mus_musculus 0.000000e+00 -2.842171e-14 0.000000e+00 \n", "textbook -1.110223e-16 -1.110223e-16 4.566791e-12 " ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "differences = (results - results.ix[\"esolver\"]).T\n", "differences.pop(\"esolver\")\n", "differences" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "3.6052116270113288e-07" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "abs(differences).max().max()" ] } ], "metadata": { "kernelspec": { "display_name": "Python 2", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", 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