i 9,dZddlZGddeZeddddd d Zd d d d d d d d ddd ZddddddZd d d ddddedzz ddedzedzedz z ddedzedzedz z ddedzedzedz z ddedzedzedz z d Zd d ddd!d!d"d"d#d#d#d$d$d$d%d&Zid'd d(d d)d d*d d+d d,d!d-d!d.d!d/d!d0d!d1d!d2dd3dd4dd5dd6dd7d8id9d8d:d8d;d8dd8d?d8d@d8dAdBdCdBdDdBdEdBdFdBdGdBdHdIdJdIdKd d d d d d dLZ d dedMz dedz dededNzz dOZ d d d dPdQedz dQedz dQedz dedMz dRZ d dSedNedNdTZ eeee e e e dUZ iZe D]'\ZZeD] ZeevsJeee<(dVdWdXdYdZd(d[Zd\Zd]ZdS)^u_ Constants and unit conversion --- :mod:`MDAnalysis.units` =============================================================== The base units of MDAnalysis trajectories are the **Å** (**ångström**) for **length** and **ps** (**pico second**) for **time**. By default, all positions are in Å and all times are in ps, regardless of how the MD code stored trajectory data. By default, MDAnalysis converts automatically to the MDAnalysis units when reading trajectories and converts back when writing. This makes it possible to write scripts that can be agnostic of the specifics of how a particular MD code stores trajectory data. Other base units are listed in the table on :ref:`table-baseunits`. .. _table-baseunits: .. Table:: Base units in MDAnalysis as encoded in :data:`MDANALYSIS_BASE_UNITS` =========== ============== =============================================== quantity unit SI units =========== ============== =============================================== length Å :math:`10^{-10}` m time ps :math:`10^{-12}` s energy kJ/mol :math:`1.66053892103219 \times 10^{-21}` J charge :math:`e` :math:`1.602176565 \times 10^{-19}` As force kJ/(mol·Å) :math:`1.66053892103219 \times 10^{-11}` J/m speed Å/ps :math:`100` m/s =========== ============== =============================================== Implementation notes -------------------- All conversions with :func:`convert` are carried out in a simple fashion: the conversion factor :math:`f_{b,b'}` from the base unit :math:`b` to another unit :math:`b'` is precomputed and stored (see :ref:`Data`). The numerical value of a quantity in unit :math:`b` is :math:`X/b` (e.g. for :math:`X = 1.23\,\mathrm{ps}`, the numerical value is :math:`X/\mathrm{ps} = 1.23`). [#funits]_ The new numerical value :math:`X'/b'` of the quantity (in units of :math:`b'`) is then .. math:: X'/b' = f_{b,b'} X/b The function :func:`get_conversion_factor` returns the appropriate factor :math:`f_{b,b'}`. Conversion between different units is always carried out via the base unit as an intermediate step:: x is in u1: from u1 to b: x' = x / factor[u1] from b to u2: x'' = x' * factor[u2] so f[u1,u2] = factor[u2]/factor[u1] Conversions ~~~~~~~~~~~ Examples for how to calculate some of the conversion factors that are hard-coded in :mod:`~MDAnalysis.units` (see :ref:`Data`). density: Base unit is :math:`\mathrm{Å}^{-3}`:: n/x = n/A**3 * densityUnit_factor[x] Example for how to calculate the conversion factor :math:`f_{\mathrm{Å}^{-3},\mathrm{nm}^{-3}}` from :math:`\mathrm{Å}^{-3}` to :math:`\mathrm{nm}^{-3}`: .. math:: f_{\mathrm{Å}^{-3},\mathrm{nm}^{-3}} = \frac{1\,\mathrm{nm}^{-3}}{1\,\mathrm{Å}^{-3}} = \frac{(10\,\mathrm{Å})^{-3}}{1\,\mathrm{Å}^{-3}} = 10^{-3} concentration: Example for how to convert the conversion factor to Molar (mol/l):: factor = 1 A**-3 / (N_Avogadro * (10**-9 dm)**-3) relative to a density rho0 in :math:`g/cm^3`:: M(H2O) = 18 g/mol Molar mass of water factor = 1/(1e-24 * N_Avogadro / M(H2O)) from :math:`\rho/\rho_0 = n/(N_A * M^{-1}) / \rho_0` where :math:`[n] = 1/Volume`, :math:`[\rho] = mass/Volume` Note ---- In the future we might move towards using the Quantities_ package or :mod:`scipy.constants`. .. _Quantities: http://packages.python.org/quantities/ Functions --------- .. autofunction:: get_conversion_factor .. autofunction:: convert .. _Data: Data ---- .. autodata:: MDANALYSIS_BASE_UNITS .. autodata:: constants .. autodata:: lengthUnit_factor .. autodata:: water .. autodata:: densityUnit_factor .. autodata:: timeUnit_factor .. autodata:: speedUnit_factor .. autodata:: forceUnit_factor .. autodata:: chargeUnit_factor .. autodata:: conversion_factor .. autodata:: unit_types References and footnotes ------------------------ .. footbibliography:: .. _AKMA: http://www.charmm.org/documentation/c37b1/usage.html#%20AKMA .. _electron charge: http://physics.nist.gov/cgi-bin/cuu/Value?e .. _`Avogadro's constant`: http://physics.nist.gov/cgi-bin/cuu/Value?na .. Rubric:: Footnotes .. [#funits] One can also consider the conversion factor to carry units :math:`b'/b`, in which case the conversion formula would become .. math:: X' = f_{b,b'} X Nc"eZdZdZfdZxZS)DeprecatedKeyAccessDictBoltzman_constantc||jkrd}tj|td}t |S)Nz{Please use 'Boltzmann_constant' henceforth. The key 'Boltzman_constant' was a typo and will be removed in MDAnalysis 2.8.0.Boltzmann_constant) deprecated_kBwarningswarnDeprecationWarningsuper __getitem__)selfkeywmsg __class__s Z/srv/www/vhosts/g4struct/public_html/venv/lib/python3.11/site-packages/MDAnalysis/units.pyr z#DeprecatedKeyAccessDict.__getitem__sM $$ $ $'  M$ 2 3 3 3&Cww""3''')__name__ __module__ __qualname__rr __classcell__)rs@rrrs='M ( ( ( ( ( ( ( ( (rrgjDgQڤgư>g-q=g9ot4@)ps picosecondfs femtosecondns nanosecondms millisecondus microseconduμssecondsecsAKMAz Angstrom/pszA/psuÅ/pszAngstrom/picosecondzangstrom/picosecondz Angstrom/fszAngstrom/femtosecondzangstrom/femtosecondz angstrom/fszA/fsuÅ/fsz Angstrom/nszA/nsuÅ/nszAngstrom/nanosecondzangstrom/nanosecondz Angstrom/usg.Az angstrom/uszA/usuA/μsuÅ/μszAngstrom/microsecondzangstrom/microsecondu Angstrom/μsu angstrom/μsz Angstrom/msgeAzAngstrom/millisecondzangstrom/millisecondz angstrom/mszA/msuÅ/msz Angstrom/AKMAgRO8?zA/AKMAznm/ps)z nanometer/psznanometer/picosecondznm/nszpm/pszm/srr)kJ/molzkcal/molJeVg$@g@0B)zkJ/(mol*Angstrom) kJ/(mol*A)u kJ/(mol*Å)z kJ/(mol*nm)NewtonNzJ/mzkcal/(mol*Angstrom)g82@)eAmberCAs)lengthdensitytimechargespeedforceenergyrr-r;rAr>)rErGrKrHrJrIcPt||t||z S)zgenerate the conversion factor u1 -> u2 by using the base unit as an intermediate f[u1 -> u2] = factor[u2]/factor[u1] Conversion of :math:`X` (in u1) to :math:`X'` (in u2): :math:`X'` = conversion_factor * :math:`X` )conversion_factor) unit_typeu1u2s rget_conversion_factorrQs$ Y ' +.? .J2.N NNrc t|}n?#t$r2d|ddtd}t|dwxYw t|}n?#t$r2d|ddtd}t|dwxYw||kr#td|||t |||zS)zConvert value *x* in unit *u1* to new value in *u2*. Returns ------- float Converted value. Raises ------ ValueError The units are not known or if one attempts to convert between incompatible units. zunit 'z$' not recognized. It must be one of z, .Nz-Cannot convert between unit types {0} --> {1}) unit_typesKeyErrorjoin ValueErrorformatrQ)xrOrPut1errmsgut2s rconvertr]s.+n +++ :R : :!%:!6!6 : : :   d* ++n +++ :R : :!%:!6!6 : : :   d* +  czz > E Eb" M M    $S"b11 11s ros'0QQf ( ( ( ( (d ( ( (@ $ ##,,(          4        %)L11 2  y&&u5k8JJ L  y&&w7% :LLN  y&&w7% :LLN  y&&u5k8JJL*        ((3( C((3 ( 3 ( : (J(J(:( J((9( I((9( 9!("9#(($9%(& I'(()(*i+(,I-(.I/(0 1(2 3(495(6I7(8I9(:9;(< I=(>?(@[A(B kC(D SE((F   O(((ZIi(( y& & <(95H+II J Y|,, ,' ' )L) )y33  .  & ' ' (  !    '--//!!NE7 !!:%%%% 4!      O O O#2#2#2#2#2r