From 03463c45eec3d2417906b637000b1740786e305b Mon Sep 17 00:00:00 2001 From: tsutterley Date: Fri, 25 Oct 2024 16:49:13 -0700 Subject: [PATCH 1/7] feat: added option to use Munk-Cartwright admittance interpolation for minor feat: add Cartwright and Edden (1973) table 1 feat: add Cartwright and Tayler (1971) table 5 --- pyTMD/data/ce1973_tab1.txt | 382 ++++++++++++++++++++++++++++ pyTMD/data/ct1971_tab5.txt | 99 +++++++ pyTMD/predict.py | 86 +++++-- scripts/compute_tidal_currents.py | 5 + scripts/compute_tidal_elevations.py | 5 + 5 files changed, 559 insertions(+), 18 deletions(-) create mode 100644 pyTMD/data/ce1973_tab1.txt create mode 100644 pyTMD/data/ct1971_tab5.txt diff --git a/pyTMD/data/ce1973_tab1.txt b/pyTMD/data/ce1973_tab1.txt new file mode 100644 index 00000000..1cc9e74c --- /dev/null +++ b/pyTMD/data/ce1973_tab1.txt @@ -0,0 +1,382 @@ +0 0 0 0 0 0 -0.31446 -0.31452 -0.31455 055.555 0.73806 0.73869 +0 0 0 0 1 0 0.02794 0.02794 0.02793 055.565 -0.06556 -0.06552 +0 0 0 0 2 0 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185.465 -0.00016 -0.00016 +1 4 -2 0 0 0 -0.00004 -0.00004 -0.00004 193.555 -0.00007 +1 4 0 0 0 0 -0.00006 -0.00005 -0.00005 195.555 -0.00009 +1 4 0 0 1 0 -0.00005 -0.00005 -0.00005 195.565 -0.00008 +2 -4 2 1 0 0 -0.00006 -0.00006 -0.00006 217.655 -0.00008 +2 -3 0 2 0 0 -0.00018 -0.00018 -0.00018 225.755 -0.00027 -0.00027 +2 -3 2 0 -1 0 -0.00003 -0.00003 -0.00003 227.545 -0.00005 +2 -3 2 0 0 0 -0.00019 -0.00018 -0.00018 227.555 -0.00027 -0.00027 +2 -2 0 1 -1 0 -0.00018 -0.00018 -0.00018 235.645 -0.00027 -0.00027 +2 -2 0 1 0 0 -0.00107 -0.00107 -0.00107 235.655 -0.00156 -0.00156 +2 -2 2 -1 -1 0 -0.00003 -0.00003 -0.00003 237.445 -0.00005 +2 -2 2 -1 0 0 -0.00020 -0.00020 -0.00020 237.455 -0.00029 -0.00029 +2 -1 0 0 -2 0 0.00003 0.00004 0.00003 245.535 0.00005 +2 -1 0 0 -1 0 -0.00066 -0.00066 -0.00066 245.545 -0.00097 -0.00097 +2 -1 0 0 0 0 -0.00389 -0.00389 -0.00389 245.555 -0.00569 -0.00569 +2 -1 0 2 0 0 0.00007 0.00007 0.00007 245.755 0.00010 0.00011 +2 -1 2 0 0 0 0.00010 0.00010 0.00010 247.555 0.00014 0.00015 +2 0 -2 1 0 0 0.00005 0.00005 0.00005 253.665 0.00008 +2 0 0 -1 -1 0 0.00004 0.00004 0.00004 255.445 0.00005 +2 0 0 -1 0 0 0.00022 0.00022 0.00022 255.455 0.00032 0.00032 +2 0 0 1 -1 0 -0.00003 -0.00003 -0.00003 255.645 -0.00005 +2 0 0 1 0 0 0.00059 0.00059 0.00059 255.655 0.00086 0.00086 +2 0 0 1 1 0 0.00011 0.00011 0.00011 255.665 0.00016 0.00016 +2 0 2 -1 0 0 0.00011 0.00011 0.00011 257.455 0.00017 0.00017 +2 1 0 0 -1 0 -0.00021 -0.00021 -0.00021 265.545 -0.00031 -0.00031 +2 1 0 0 0 0 0.00359 0.00359 0.00359 265.555 0.00525 0.00525 +2 1 0 0 1 0 0.00068 0.00068 0.00068 265.565 0.00099 0.00099 +2 2 -2 1 0 0 0.00004 0.00004 0.00004 273.655 0.00005 +2 2 0 -1 0 0 0.00019 0.00019 0.00019 275.455 0.00028 0.00028 +2 2 0 -1 1 0 0.00004 0.00004 0.00004 275.465 0.00005 +2 3 -2 0 0 0 0.00004 0.00004 0.00004 283.555 0.00006 +2 3 0 0 0 0 0.00033 0.00033 0.00033 285.555 0.00048 0.00048 +2 3 0 0 1 0 0.00021 0.00021 0.00021 285.565 0.00031 0.00031 +2 3 0 0 2 0 0.00004 0.00004 0.00004 285.575 0.00006 +2 4 0 -1 0 0 0.00005 0.00005 0.00005 295.455 0.00008 +3 -2 0 2 0 0 0.00036 0.00037 0.00037 335.755 -0.00057 -0.00056 +3 -2 2 0 0 0 0.00037 0.00037 0.00037 337.555 -0.00057 -0.00057 +3 -1 0 1 -1 0 -0.00012 -0.00012 -0.00012 345.645 0.00018 0.00018 +3 -1 0 1 0 0 0.00210 0.00210 0.00210 345.655 -0.00326 -0.00326 +3 -1 2 -1 0 0 0.00039 0.00039 0.00039 347.455 -0.00061 -0.00061 +3 0 -2 2 0 0 -0.00005 -0.00005 -0.00005 355.755 0.00007 +3 0 0 0 -1 0 -0.00043 -0.00043 -0.00043 355.545 0.00067 0.00066 +3 0 0 0 0 0 0.00765 0.00765 0.00765 355.555 -0.01188 -0.01188 +3 1 -2 1 0 0 -0.00011 -0.00011 -0.00011 363.655 0.00017 0.00017 +3 1 0 -1 0 0 -0.00043 -0.00043 -0.00043 365.455 0.00067 0.00067 +3 1 0 1 0 0 0.00016 0.00016 0.00016 365.655 -0.00025 -0.00025 +3 1 0 1 1 0 0.00007 0.00007 0.00007 365.665 -0.00011 -0.00011 +3 2 0 0 -1 0 -0.00004 -0.00004 -0.00004 375.545 0.00006 +3 2 0 0 0 0 0.00100 0.00100 0.00100 375.555 -0.00155 -0.00155 +3 2 0 0 1 0 0.00044 0.00044 0.00043 375.565 -0.00068 -0.00068 +3 2 0 0 2 0 0.00005 0.00005 0.00005 375.575 -0.00007 diff --git a/pyTMD/predict.py b/pyTMD/predict.py index fef60c56..14212edd 100644 --- a/pyTMD/predict.py +++ b/pyTMD/predict.py @@ -23,6 +23,7 @@ Updated 10/2024: use PREM as the default Earth model for Love numbers more descriptive error message if cannot infer minor constituents updated calculation of long-period equilibrium tides + added option to use Munk-Cartwright admittance interpolation for minor Updated 09/2024: verify order of minor constituents to infer fix to use case insensitive assertions of string argument values split infer minor function into short and long period calculations @@ -532,6 +533,11 @@ def _infer_semi_diurnal( time correction for converting to Ephemeris Time (days) minor: list or None, default None tidal constituent IDs of minor constituents for inference + method: str, default 'linear' + method for interpolating between major constituents + + * 'linear': linear interpolation + * 'admittance': Munk-Cartwright admittance interpolation raise_exception: bool, default False Raise a ``ValueError`` if major constituents are not found @@ -558,9 +564,12 @@ def _infer_semi_diurnal( """ # set default keyword arguments kwargs.setdefault('deltat', 0.0) + kwargs.setdefault('method', 'linear') kwargs.setdefault('raise_exception', False) # list of minor constituents kwargs.setdefault('minor', None) + # validate interpolation method + assert kwargs['method'].lower() in ('linear', 'admittance') # number of constituents npts, nc = np.shape(zmajor) nt = len(np.atleast_1d(t)) @@ -569,6 +578,7 @@ def _infer_semi_diurnal( # allocate for output elevation correction dh = np.ma.zeros((n)) # major constituents used for inferring semi-diurnal minor tides + # pivot waves listed in Table 6.7 of the 2010 IERS Conventions cindex = ['n2', 'm2', 's2'] # angular frequencies for major constituents omajor = pyTMD.arguments.frequency(cindex, **kwargs) @@ -584,6 +594,7 @@ def _infer_semi_diurnal( j = [j for j,val in enumerate(constituents) if (val.lower() == c)] if j: j1, = j + # "normalize" tide values z[:,i] = zmajor[:,j1]/amajor[i] nz += 1 @@ -639,13 +650,27 @@ def _infer_semi_diurnal( # sum over the minor tidal constituents of interest for k in minor_indices: - # linearly interpolate between major constituents - if (omajor[0] < omajor[1]) and (omega[k] < omajor[1]): - slope = (z[:,1] - z[:,0])/(omajor[1] - omajor[0]) - zmin = amin[k]*(z[:,0] + slope*(omega[k] - omajor[0])) - else: - slope = (z[:,2] - z[:,1])/(omajor[2] - omajor[1]) - zmin = amin[k]*(z[:,1] + slope*(omega[k] - omajor[1])) + # interpolate from major constituents + if (kwargs['method'].lower() == 'linear'): + # linearly interpolate between major constituents + if (omajor[0] < omajor[1]) and (omega[k] < omajor[1]): + slope = (z[:,1] - z[:,0])/(omajor[1] - omajor[0]) + zmin = amin[k]*(z[:,0] + slope*(omega[k] - omajor[0])) + else: + slope = (z[:,2] - z[:,1])/(omajor[2] - omajor[1]) + zmin = amin[k]*(z[:,1] + slope*(omega[k] - omajor[1])) + elif (kwargs['method'].lower() == 'admittance'): + # admittance interpolation using Munk-Cartwright approach + Ainv = np.array([[3.3133, -4.2538, 1.9405], + [-3.3133, 4.2538, -0.9405], + [1.5018, -3.2579, 1.7561]]) + coef = np.inner(Ainv, z) + # convert frequency to cycles per day + f = 2.0*omega[k]*86400.0 + # calculate interpolated values for constituent + interp = coef[0,:] + coef[1,:]*np.cos(f) + coef[2,:]*np.sin(f) + # rescale tide values + zmin = amin[k]*interp # sum over all tides th = G[:,k]*np.pi/180.0 + pu[:,k] dh += zmin.real*pf[:,k]*np.cos(th) - \ @@ -676,6 +701,11 @@ def _infer_diurnal( time correction for converting to Ephemeris Time (days) minor: list or None, default None tidal constituent IDs of minor constituents for inference + method: str, default 'linear' + method for interpolating between major constituents + + * 'linear': linear interpolation + * 'admittance': Munk-Cartwright admittance interpolation raise_exception: bool, default False Raise a ``ValueError`` if major constituents are not found @@ -691,9 +721,10 @@ def _infer_diurnal( Royal Society of London. Series A, Mathematical and Physical Sciences*, 259(1105), 533--581, (1966). `doi: 10.1098/rsta.1966.0024 `_ - .. [2] R. D. Ray, "A global ocean tide model from - Topex/Poseidon altimetry: GOT99.2", - NASA Goddard Space Flight Center, TM-1999-209478, (1999). + .. [2] R. D. Ray, "On Tidal Inference in the Diurnal Band", + Journal of Atmospheric and Oceanic Technology, 34(2), 437--446, + (2017). `doi: 10.1175/jtech-d-16-0142.1 + `_ .. [3] J. M. Wahr and T. Sasao, "A diurnal resonance in the ocean tide and in the Earth's load response due to the resonant free `core nutation`", *Geophysical Journal of the Royal Astronomical @@ -708,9 +739,12 @@ def _infer_diurnal( """ # set default keyword arguments kwargs.setdefault('deltat', 0.0) + kwargs.setdefault('method', 'linear') kwargs.setdefault('raise_exception', False) # list of minor constituents kwargs.setdefault('minor', None) + # validate interpolation method + assert kwargs['method'].lower() in ('linear', 'admittance') # number of constituents npts, nc = np.shape(zmajor) nt = len(np.atleast_1d(t)) @@ -719,6 +753,7 @@ def _infer_diurnal( # allocate for output elevation correction dh = np.ma.zeros((n)) # major constituents used for inferring diurnal minor tides + # pivot waves listed in Table 6.7 of the 2010 IERS Conventions cindex = ['q1', 'o1', 'k1'] # angular frequencies for major constituents omajor = pyTMD.arguments.frequency(cindex, **kwargs) @@ -737,7 +772,7 @@ def _infer_diurnal( # Love numbers of degree 2 for constituent h2, k2, l2 = _body_tide_love_numbers(omajor[i]) gamma_2 = (1.0 + k2 - h2) - # scaled tide + # "normalize" tide values z[:,i] = zmajor[:,j1]/(amajor[i]*gamma_2) nz += 1 @@ -799,13 +834,27 @@ def _infer_diurnal( # Love numbers of degree 2 for constituent h2, k2, l2 = _body_tide_love_numbers(omega[k]) gamma_2 = (1.0 + k2 - h2) - # linearly interpolate between major constituents - if (omajor[0] < omajor[1]) and (omega[k] < omajor[1]): - slope = (z[:,1] - z[:,0])/(omajor[1] - omajor[0]) - zmin = amin[k]*gamma_2*(z[:,0] + slope*(omega[k] - omajor[0])) - else: - slope = (z[:,2] - z[:,1])/(omajor[2] - omajor[1]) - zmin = amin[k]*gamma_2*(z[:,1] + slope*(omega[k] - omajor[1])) + # interpolate from major constituents + if (kwargs['method'].lower() == 'linear'): + # linearly interpolate between major constituents + if (omajor[0] < omajor[1]) and (omega[k] < omajor[1]): + slope = (z[:,1] - z[:,0])/(omajor[1] - omajor[0]) + zmin = amin[k]*gamma_2*(z[:,0] + slope*(omega[k] - omajor[0])) + else: + slope = (z[:,2] - z[:,1])/(omajor[2] - omajor[1]) + zmin = amin[k]*gamma_2*(z[:,1] + slope*(omega[k] - omajor[1])) + elif (kwargs['method'].lower() == 'admittance'): + # admittance interpolation using Munk-Cartwright approach + Ainv = np.array([[3.1214, -3.8494, 1.728], + [-3.1727, 3.9559, -0.7832], + [1.438, -3.0297, 1.5917]]) + coef = np.inner(Ainv, z) + # convert frequency to cycles per day + f = 2.0*omega[k]*86400.0 + # calculate interpolated values for constituent + interp = coef[0,:] + coef[1,:]*np.cos(f) + coef[2,:]*np.sin(f) + # rescale tide values + zmin = amin[k]*gamma_2*interp # sum over all tides th = G[:,k]*np.pi/180.0 + pu[:,k] dh += zmin.real*pf[:,k]*np.cos(th) - \ @@ -873,6 +922,7 @@ def _infer_long_period( # allocate for output elevation correction dh = np.ma.zeros((n)) # major constituents used for inferring long period minor tides + # pivot waves listed in Table 6.7 of the 2010 IERS Conventions cindex = ['node', 'mm', 'mf'] # angular frequencies for major constituents omajor = pyTMD.arguments.frequency(cindex, **kwargs) diff --git a/scripts/compute_tidal_currents.py b/scripts/compute_tidal_currents.py index 31c34388..452f03af 100755 --- a/scripts/compute_tidal_currents.py +++ b/scripts/compute_tidal_currents.py @@ -57,6 +57,11 @@ -E X, --extrapolate X: Extrapolate with nearest-neighbors -c X, --cutoff X: Extrapolation cutoff in kilometers set to inf to extrapolate for all points + --nodal-corrections: Nodal corrections to apply + OTIS + FES + GOT + perth3 --infer-minor: Infer values for minor constituents --minor-constituents: Minor constituents to infer -f X, --fill-value X: Invalid value for spatial fields diff --git a/scripts/compute_tidal_elevations.py b/scripts/compute_tidal_elevations.py index 5e51c9d4..2c9ef0e9 100755 --- a/scripts/compute_tidal_elevations.py +++ b/scripts/compute_tidal_elevations.py @@ -58,6 +58,11 @@ -E X, --extrapolate X: Extrapolate with nearest-neighbors -c X, --cutoff X: Extrapolation cutoff in kilometers set to inf to extrapolate for all points + --nodal-corrections: Nodal corrections to apply + OTIS + FES + GOT + perth3 --infer-minor: Infer values for minor constituents --minor-constituents: Minor constituents to infer --append-node: Append equilibrium amplitudes for node tides From e126ad04114fe9e10c9ba4f84378a65618c3bd60 Mon Sep 17 00:00:00 2001 From: tsutterley Date: Fri, 25 Oct 2024 17:23:24 -0700 Subject: [PATCH 2/7] docs: add citations to included data --- doc/source/getting_started/Citations.rst | 25 ++++++++++++++++++++++++ 1 file changed, 25 insertions(+) diff --git a/doc/source/getting_started/Citations.rst b/doc/source/getting_started/Citations.rst index cd7b8db6..6189c516 100644 --- a/doc/source/getting_started/Citations.rst +++ b/doc/source/getting_started/Citations.rst @@ -23,6 +23,27 @@ If you have used ``pyTMD`` in your work, please consider citing our library: "pyTMD: Python-based tidal prediction software", (2017). `doi: 10.5281/zenodo.5555395 `_ +Data Citations +############## + +Internally, ``pyTMD`` includes datasets from the following: + + D. E. Cartwright and R. J. Tayler, "New Computations of the Tide-generating Potential," + *Geophysical Journal of the Royal Astronomical Society*, 23(1), 45--73. (1971). + `doi: 10.1111/j.1365-246X.1971.tb01803.x `_ + + D. E. Cartwright and A. C. Edden, "Corrected Tables of Tidal Harmonics," + *Geophysical Journal of the Royal Astronomical Society*, 33(3), 253--264, (1973). + `doi: 10.1111/j.1365-246X.1973.tb03420.x `_ + + S. Desai, J. Wahr and B. Beckley "Revisiting the pole tide for and from satellite altimetry", + *Journal of Geodesy*, 89(12), p1233-1243, (2015). + `doi: 10.1007/s00190-015-0848-7 `_ + + *IERS Conventions (2010)*, G. Petit and B. Luzum (eds.), (IERS Technical Note; 36), + Frankfurt am Main: Verlag des Bundesamts f\ |uuml|\ r Kartographie und Geod\ |auml|\ sie, 179 pp. (2010). + `ISBN 3-89888-989-6 `_ + Contributors ############ @@ -89,3 +110,7 @@ of Washington Applied Physics Laboratory (UW-APL). It is not sponsored or maintained by the Universities Space Research Association (USRA), AVISO or NASA. Outputs from this software should be used for scientific or technical purposes only. This software should not be used for coastal navigation or any application that may risk life or property. + +.. |auml| unicode:: U+00E4 .. LATIN SMALL LETTER A WITH DIAERESIS +.. |uuml| unicode:: U+00FC .. LATIN SMALL LETTER U WITH DIAERESIS + From b1ec4710c886557f5aef0b54e39711b918de0530 Mon Sep 17 00:00:00 2001 From: tsutterley Date: Sat, 26 Oct 2024 18:00:20 -0700 Subject: [PATCH 3/7] Update Citations.rst --- doc/source/getting_started/Citations.rst | 42 ++++++++++++------------ 1 file changed, 21 insertions(+), 21 deletions(-) diff --git a/doc/source/getting_started/Citations.rst b/doc/source/getting_started/Citations.rst index 6189c516..2f91f468 100644 --- a/doc/source/getting_started/Citations.rst +++ b/doc/source/getting_started/Citations.rst @@ -23,27 +23,6 @@ If you have used ``pyTMD`` in your work, please consider citing our library: "pyTMD: Python-based tidal prediction software", (2017). `doi: 10.5281/zenodo.5555395 `_ -Data Citations -############## - -Internally, ``pyTMD`` includes datasets from the following: - - D. E. Cartwright and R. J. Tayler, "New Computations of the Tide-generating Potential," - *Geophysical Journal of the Royal Astronomical Society*, 23(1), 45--73. (1971). - `doi: 10.1111/j.1365-246X.1971.tb01803.x `_ - - D. E. Cartwright and A. C. Edden, "Corrected Tables of Tidal Harmonics," - *Geophysical Journal of the Royal Astronomical Society*, 33(3), 253--264, (1973). - `doi: 10.1111/j.1365-246X.1973.tb03420.x `_ - - S. Desai, J. Wahr and B. Beckley "Revisiting the pole tide for and from satellite altimetry", - *Journal of Geodesy*, 89(12), p1233-1243, (2015). - `doi: 10.1007/s00190-015-0848-7 `_ - - *IERS Conventions (2010)*, G. Petit and B. Luzum (eds.), (IERS Technical Note; 36), - Frankfurt am Main: Verlag des Bundesamts f\ |uuml|\ r Kartographie und Geod\ |auml|\ sie, 179 pp. (2010). - `ISBN 3-89888-989-6 `_ - Contributors ############ @@ -102,6 +81,27 @@ The NASA Goddard Space Flight Center (GSFC) PREdict Tidal Heights (PERTH3) softw Richard Ray and Remko Scharroo. An updated and more versatile version of the NASA GSFC tidal prediction software (PERTH5) was developed by Richard Ray. +Data Citations +############## + +Internally, ``pyTMD`` includes datasets from the following: + + D. E. Cartwright and R. J. Tayler, "New Computations of the Tide-generating Potential," + *Geophysical Journal of the Royal Astronomical Society*, 23(1), 45--73. (1971). + `doi: 10.1111/j.1365-246X.1971.tb01803.x `_ + + D. E. Cartwright and A. C. Edden, "Corrected Tables of Tidal Harmonics," + *Geophysical Journal of the Royal Astronomical Society*, 33(3), 253--264, (1973). + `doi: 10.1111/j.1365-246X.1973.tb03420.x `_ + + S. Desai, J. Wahr and B. Beckley "Revisiting the pole tide for and from satellite altimetry", + *Journal of Geodesy*, 89(12), p1233-1243, (2015). + `doi: 10.1007/s00190-015-0848-7 `_ + + *IERS Conventions (2010)*, G. Petit and B. Luzum (eds.), (IERS Technical Note; 36), + Frankfurt am Main: Verlag des Bundesamts f\ |uuml|\ r Kartographie und Geod\ |auml|\ sie, 179 pp. (2010). + `ISBN 3-89888-989-6 `_ + Disclaimer ########## From 8372e078c623b38aca2c080c491c800c01bd32db Mon Sep 17 00:00:00 2001 From: tsutterley Date: Mon, 28 Oct 2024 07:45:24 -0700 Subject: [PATCH 4/7] feat: add function to parse Cartwright/Tayler/Edden tables feat: add functions to calculate UKHO Extended Doodson numbers for constituents --- doc/source/api_reference/arguments.rst | 6 ++ pyTMD/arguments.py | 142 +++++++++++++++++++++++-- pyTMD/data/ce1973_tab1.txt | 14 +-- pyTMD/data/ct1971_tab5.txt | 4 +- test/test_arguments.py | 30 +++++- 5 files changed, 177 insertions(+), 19 deletions(-) diff --git a/doc/source/api_reference/arguments.rst b/doc/source/api_reference/arguments.rst index 23bec0ed..0f238502 100644 --- a/doc/source/api_reference/arguments.rst +++ b/doc/source/api_reference/arguments.rst @@ -36,6 +36,12 @@ Calling Sequence .. autofunction:: pyTMD.arguments._constituent_parameters +.. autofunction:: pyTMD.arguments._parse_tide_potential_table + .. autofunction:: pyTMD.arguments._to_doodson_number +.. autofunction:: pyTMD.arguments._to_extended_doodson + .. autofunction:: pyTMD.arguments._from_doodson_number + +.. autofunction:: pyTMD.arguments._from_extended_doodson diff --git a/pyTMD/arguments.py b/pyTMD/arguments.py index 6b75fdea..6935d62f 100755 --- a/pyTMD/arguments.py +++ b/pyTMD/arguments.py @@ -39,6 +39,9 @@ UPDATE HISTORY: Updated 10/2024: can convert Doodson numbers formatted as strings + update Doodson number conversions to follow Cartwright X=10 convention + add function to parse Cartwright/Tayler/Edden tables + add functions to calculate UKHO Extended Doodson numbers for constituents Updated 09/2024: add function to calculate tidal angular frequencies Updated 08/2024: add support for constituents in PERTH5 tables add back nodal arguments from PERTH3 for backwards compatibility @@ -71,8 +74,11 @@ """ from __future__ import annotations +import re +import pathlib import numpy as np import pyTMD.astro +from pyTMD.utilities import get_data_path __all__ = [ "arguments", @@ -84,8 +90,11 @@ "_arguments_table", "_minor_table", "_constituent_parameters", + "_parse_tide_potential_table", "_to_doodson_number", - "_from_doodson_number" + "_to_extended_doodson", + "_from_doodson_number", + "_from_extended_doodson" ] def arguments( @@ -952,6 +961,7 @@ def doodson_number( - ``'Cartwright'`` - ``'Doodson'`` + - ``'Extended'`` raise_error: bool, default True Raise exception if constituent is unsupported @@ -973,7 +983,7 @@ def doodson_number( kwargs.setdefault('formalism', 'Doodson') kwargs.setdefault('raise_error', True) # validate inputs - assert kwargs['formalism'].title() in ('Cartwright', 'Doodson'), \ + assert kwargs['formalism'].title() in ('Cartwright', 'Doodson','Extended'), \ f'Unknown formalism {kwargs["formalism"]}' # get the coefficients of coefficients if isinstance(constituents, str): @@ -992,6 +1002,9 @@ def doodson_number( elif (kwargs['formalism'] == 'Doodson'): # convert from coefficients to Doodson number numbers = _to_doodson_number(coefficients[:,0], **kwargs) + elif (kwargs['formalism'] == 'Extended'): + # convert to extended Doodson number in UKHO format + numbers = _to_extended_doodson(coefficients[:,0], **kwargs) else: # output dictionary with Doodson numbers numbers = {} @@ -1013,6 +1026,9 @@ def doodson_number( elif (kwargs['formalism'] == 'Doodson'): # convert from coefficients to Doodson number numbers[c] = _to_doodson_number(coefficients[:,0], **kwargs) + elif (kwargs['formalism'] == 'Extended'): + # convert to extended Doodson number in UKHO format + numbers[c] = _to_extended_doodson(coefficients[:,0], **kwargs) # return the Doodson or Cartwright number return numbers @@ -1962,6 +1978,64 @@ def _constituent_parameters(c: str, **kwargs): # return the values for the constituent return (amplitude, phase, omega, alpha, species) +# Cartright and Tayler (1971) table with 3rd-degree values +_ct1971_table_5 = get_data_path(['data','ct1971_tab5.txt']) +# Cartwright and Edden (1973) table with updated values +_ce1973_table_1 = get_data_path(['data','ce1973_tab1.txt']) + +def _parse_tide_potential_table(table: str | pathlib.Path): + """Parse tables of tide-generating potential from [1]_ and [2]_ + + Parameters + ---------- + table: str or pathlib.Path + table of tide-generating potentials + + Returns + ------- + CTE: float + Cartwright-Tayler-Edden table values + + References + ---------- + .. [1] D. E. Cartwright and R. J. Tayler, + "New Computations of the Tide-generating Potential," + *Geophysical Journal of the Royal Astronomical Society*, + 23(1), 45--73. (1971). `doi: 10.1111/j.1365-246X.1971.tb01803.x + `_ + .. [2] D. E. Cartwright and A. C. Edden, + "Corrected Tables of Tidal Harmonics," + *Geophysical Journal of the Royal Astronomical Society*, + 33(3), 253--264, (1973). `doi: 10.1111/j.1365-246X.1973.tb03420.x + `_ + """ + # verify table path + table = pathlib.Path(table).expanduser().absolute() + with table.open(mode='r', encoding='utf8') as f: + file_contents = f.readlines() + # number of lines in the file + file_lines = len(file_contents) + # tau: coefficient for mean lunar time + # s: coefficient for mean longitude of moon + # h: coefficient for mean longitude of sun + # p: coefficient for mean longitude of lunar perigee + # n: coefficient for mean longitude of ascending lunar node + # pp: coefficient for mean longitude of solar perigee + # Hs1: amplitude for epoch span 1 (1861-09-21 to 1879-09-22) + # Hs2: amplitude for epoch span 2 (1915-05-16 to 1933-05-22) + # Hs3: amplitude for epoch span 2 (1951-05-23 to 1969-05-22) + # DO: Doodson number for coefficient + # Hs0: Doodson scaled amplitude for 1900 + names = ('tau','s','h','p','n','pp','Hs1','Hs2','Hs3','DO','Hs0') + formats = ('i','i','i','i','i','i','f','f','f','U7','f') + dtype = np.dtype({'names':names, 'formats':formats}) + CTE = np.zeros((file_lines), dtype=dtype) + for i,line in enumerate(file_contents): + # drop last column with values from Doodson (1921) + CTE[i] = np.array(tuple(line.split()[:11]), dtype=dtype) + # return the table values + return CTE + def _to_doodson_number(coef: list | np.ndarray, **kwargs): """ Converts Cartwright numbers into a Doodson number @@ -1975,13 +2049,13 @@ def _to_doodson_number(coef: list | np.ndarray, **kwargs): Returns ------- - DO: float + DO: float or string Doodson number for constituent """ # default keyword arguments kwargs.setdefault('raise_error', True) # assert length and verify array - coef = np.array(coef[:6]) + coef = np.array(coef[:6]).astype(int) # add 5 to values following Doodson convention (prevent negatives) coef[1:] += 5 # check for unsupported constituents @@ -1989,12 +2063,41 @@ def _to_doodson_number(coef: list | np.ndarray, **kwargs): raise ValueError('Unsupported constituent') elif (np.any(coef < 0) or np.any(coef > 10)): return None + elif np.any(coef == 10): + # convert to string and replace 10 with X (Cartwright convention) + DO = [str(v).replace('10','X') for v in coef] + # convert to Doodson number + return np.str_('{0}{1}{2}.{3}{4}{5}'.format(*DO)) else: # convert to single number and round off floating point errors DO = np.sum([v*10**(2-o) for o,v in enumerate(coef)]) return np.round(DO, decimals=3) -def _from_doodson_number(DO: str | float | np.ndarray): +def _to_extended_doodson(coef: list | np.ndarray, **kwargs): + """ + Converts Cartwright numbers into an UKHO Extended Doodson number + + Parameters + ---------- + coef: list or np.ndarray + Doodson coefficients (Cartwright numbers) for constituent + + Returns + ------- + XDO: string + Extended Doodson number for constituent + """ + # assert length and verify array + coef = np.array(coef).astype(int) + # digits for UKHO Extended Doodson number + # Z = 0 + # A - P = 1 to 15 + # R - Y = -8 to -1 + digits = 'RSTUVWXYZABCDEFGHIJKLMNOP' + XDO = ''.join([digits[v+8] for v in coef]) + return np.str_(XDO) + +def _from_doodson_number(DO: str | float | np.ndarray, **kwargs): """ Converts Doodson numbers into Cartwright numbers @@ -2009,10 +2112,31 @@ def _from_doodson_number(DO: str | float | np.ndarray): Doodson coefficients (Cartwright numbers) for constituent """ # convert from Doodson number to Cartwright numbers - # verify Doodson numbers are floating point variables - DO = np.array(DO).astype(float) - # multiply by 1000 to prevent floating point errors - coef = np.array([np.mod(1e3*DO, 10**(6-o))//10**(5-o) for o in range(6)]) + coef = [c.replace('X', '10') for c in re.findall(r'\w', str(DO).zfill(7))] + coef = np.array(coef, dtype=int) # remove 5 from values following Doodson convention coef[1:] -= 5 return coef + +def _from_extended_doodson(XDO: str | np.str_, **kwargs): + """ + Converts UKHO Extended Doodson number into Cartwright numbers + + Parameters + ---------- + XDO: string + Extended Doodson number for constituent + + Returns + ------- + coef: np.ndarray + Doodson coefficients (Cartwright numbers) for constituent + """ + # digits for UKHO Extended Doodson number + # Z = 0 + # A - P = 1 to 15 + # R - Y = -8 to -1 + digits = 'RSTUVWXYZABCDEFGHIJKLMNOP' + # convert from extended Doodson number to Cartwright numbers + coef = np.array([(digits.index(c)-8) for c in str(XDO)], dtype=int) + return coef diff --git a/pyTMD/data/ce1973_tab1.txt b/pyTMD/data/ce1973_tab1.txt index 1cc9e74c..4b7added 100644 --- a/pyTMD/data/ce1973_tab1.txt +++ b/pyTMD/data/ce1973_tab1.txt @@ -6,7 +6,7 @@ 0 0 1 0 0 -1 -0.00493 -0.00493 -0.00492 056.554 0.01156 0.01160 0 0 1 0 0 1 0.00027 0.00026 0.00026 056.556 -0.00062 -0.00061 0 0 1 0 1 -1 0.00005 0.00005 0.00005 056.564 -0.00011 -0 0 -2 -2 -1 0 0.00002 0.00002 0.00002 057.345 -0.00005 +0 0 2 -2 -1 0 0.00002 0.00002 0.00002 057.345 -0.00005 0 0 2 -2 0 0 -0.00031 -0.00031 -0.00032 057.355 0.00074 0.00073 0 0 2 0 0 0 -0.03104 -0.03102 -0.03100 057.555 0.07281 0.07299 0 0 2 0 0 -2 -0.00013 -0.00013 -0.00012 057.553 0.00029 0.00030 @@ -130,7 +130,7 @@ 1 -3 4 0 0 0 0.00008 0.00008 0.00008 129.555 -0.00011 1 -3 4 0 1 0 -0.00003 -0.00003 -0.00003 129.565 0.00005 1 -2 -2 1 -2 0 0.00004 0.00004 0.00004 133.635 -0.00006 -1 -2 -2 3 0 0 0.00016 0.00016 0.00016 135.855 -0.00023 -0.00023 +1 -2 -2 3 0 0 0.00016 0.00016 0.00016 133.855 -0.00023 -0.00023 1 -2 -1 1 -1 1 0.00007 0.00007 0.00007 134.646 -0.00010 1 -2 -1 1 0 1 0.00042 0.00042 0.00042 134.656 -0.00061 -0.00061 1 -2 0 -1 -3 0 0.00004 0.00004 0.00004 135.425 -0.00005 @@ -267,7 +267,7 @@ 2 -4 2 2 0 0 0.00077 0.00078 0.00078 217.755 0.00111 0.00111 2 -4 3 2 0 -1 0.00006 0.00006 0.00006 218.754 0.00009 2 -4 4 0 0 0 0.00048 0.00048 0.00048 219.555 0.00069 0.00069 -2 -4 5 0 0 -1 0.00006 0.00006 0.00006 21X.544 0.00009 +2 -4 5 0 0 -1 0.00006 0.00006 0.00006 21X.554 0.00009 2 -3 0 3 -1 0 -0.00007 -0.00007 -0.00007 225.845 -0.00010 2 -3 0 3 0 0 0.00180 0.00180 0.00180 225.855 0.00259 0.00259 2 -3 1 1 0 1 -0.00009 -0.00009 -0.00009 226.656 -0.00013 -0.00012 @@ -285,14 +285,14 @@ 2 -2 0 2 0 0 0.01601 0.01601 0.01601 235.755 0.02301 0.02301 2 -2 1 0 0 1 -0.00027 -0.00027 -0.00027 236.556 -0.00039 -0.00040 2 -2 1 1 0 0 -0.00017 -0.00017 -0.00017 236.655 -0.00025 -0.00025 -2 -1 1 2 0 -1 0.00025 0.00025 0.00025 236.754 0.00036 0.00036 +2 -2 1 2 0 -1 0.00025 0.00025 0.00025 236.754 0.00036 0.00036 2 -2 2 0 -1 0 -0.00072 -0.00072 -0.00072 237.545 -0.00104 -0.00104 2 -2 2 0 0 0 0.01932 0.01932 0.01932 237.555 0.02776 0.02774 2 -2 3 -1 0 0 -0.00005 -0.00005 -0.00004 238.455 -0.00007 2 -2 3 0 -1 -1 -0.00005 -0.00005 -0.00005 238.544 -0.00007 2 -2 3 0 0 -1 0.00131 0.00131 0.00130 238.554 0.00188 0.00189 2 -2 4 -2 0 0 0.00059 0.00059 0.00059 239.355 0.00085 0.00085 -2 -2 4 0 0 -2 0.00005 0.00005 0.00005 239.554 0.00007 +2 -2 4 0 0 -2 0.00005 0.00005 0.00005 239.553 0.00007 2 -2 5 -2 0 -1 0.00005 0.00005 0.00005 23X.354 0.00008 2 -1 -2 1 -2 0 -0.00010 -0.00010 -0.00010 243.635 -0.00015 -0.00015 2 -1 -2 3 0 0 -0.00039 -0.00039 -0.00039 243.855 -0.00056 -0.00056 @@ -364,8 +364,8 @@ 2 3 -2 -1 -1 0 0.00006 0.00006 0.00006 283.445 0.00008 2 3 -2 -1 0 0 0.00004 0.00004 0.00004 283.455 0.00006 2 3 -2 1 0 0 0.00086 0.00086 0.00086 283.655 0.00123 0.00123 -3 3 -2 1 1 0 0.00037 0.00037 0.00037 283.665 0.00054 0.00054 -2 3 -2 1 1 0 0.00004 0.00004 0.00004 283.675 0.00006 +2 3 -2 1 1 0 0.00037 0.00037 0.00037 283.665 0.00054 0.00054 +2 3 -2 1 2 0 0.00004 0.00004 0.00004 283.675 0.00006 2 3 0 -1 -1 0 -0.00008 -0.00009 -0.00009 285.445 -0.00012 -0.00012 2 3 0 -1 0 0 0.00447 0.00447 0.00447 285.455 0.00643 0.00643 2 3 0 -1 1 0 0.00195 0.00195 0.00195 285.465 0.00280 0.00280 diff --git a/pyTMD/data/ct1971_tab5.txt b/pyTMD/data/ct1971_tab5.txt index 4f8cc08f..1c46625b 100644 --- a/pyTMD/data/ct1971_tab5.txt +++ b/pyTMD/data/ct1971_tab5.txt @@ -63,7 +63,7 @@ 2 -1 0 0 0 0 -0.00389 -0.00389 -0.00389 245.555 -0.00569 -0.00569 2 -1 0 2 0 0 0.00007 0.00007 0.00007 245.755 0.00010 0.00011 2 -1 2 0 0 0 0.00010 0.00010 0.00010 247.555 0.00014 0.00015 -2 0 -2 1 0 0 0.00005 0.00005 0.00005 253.665 0.00008 +2 0 -2 1 0 0 0.00005 0.00005 0.00005 253.655 0.00008 2 0 0 -1 -1 0 0.00004 0.00004 0.00004 255.445 0.00005 2 0 0 -1 0 0 0.00022 0.00022 0.00022 255.455 0.00032 0.00032 2 0 0 1 -1 0 -0.00003 -0.00003 -0.00003 255.645 -0.00005 @@ -86,7 +86,7 @@ 3 -1 0 1 -1 0 -0.00012 -0.00012 -0.00012 345.645 0.00018 0.00018 3 -1 0 1 0 0 0.00210 0.00210 0.00210 345.655 -0.00326 -0.00326 3 -1 2 -1 0 0 0.00039 0.00039 0.00039 347.455 -0.00061 -0.00061 -3 0 -2 2 0 0 -0.00005 -0.00005 -0.00005 355.755 0.00007 +3 0 -2 2 0 0 -0.00005 -0.00005 -0.00005 353.755 0.00007 3 0 0 0 -1 0 -0.00043 -0.00043 -0.00043 355.545 0.00067 0.00066 3 0 0 0 0 0 0.00765 0.00765 0.00765 355.555 -0.01188 -0.01188 3 1 -2 1 0 0 -0.00011 -0.00011 -0.00011 363.655 0.00017 0.00017 diff --git a/test/test_arguments.py b/test/test_arguments.py index 3dc8a152..92ed303b 100644 --- a/test/test_arguments.py +++ b/test/test_arguments.py @@ -6,6 +6,7 @@ UPDATE HISTORY: Updated 10/2024: add comparisons for formatted Doodson numbers + add function to parse tide potential tables Updated 08/2024: add comparisons for nodal corrections Written 01/2024 """ @@ -17,8 +18,13 @@ doodson_number, _arguments_table, _minor_table, + _parse_tide_potential_table, _to_doodson_number, - _from_doodson_number + _to_extended_doodson, + _from_doodson_number, + _from_extended_doodson, + _ct1971_table_5, + _ce1973_table_1 ) @pytest.mark.parametrize("corrections", ['OTIS', 'GOT']) @@ -714,11 +720,33 @@ def test_doodson(): assert float(val) == test # check conversion to and from Doodson numbers doodson = _to_doodson_number(cartwright[key]) + XDO = _to_extended_doodson(cartwright[key]) # check values when entered as Cartwright assert float(val) == doodson # check values when entered as Doodson coefficients = _from_doodson_number(val) + extended = _from_extended_doodson(XDO) assert np.all(cartwright[key] == coefficients) + assert np.all(cartwright[key] == extended) + +def test_parse_tables(): + """ + Tests the parsing of tables for tide potential coefficients + """ + # Cartright and Tayler (1971) table with 3rd-degree values + # Cartwright and Edden (1973) table with updated values + for table in [_ct1971_table_5, _ce1973_table_1]: + # parse table + CTE = _parse_tide_potential_table(table) + for i, line in enumerate(CTE): + # convert Doodson number to Cartwright numbers + tau, s, h, p, n, pp = _from_doodson_number(line['DO']) + assert tau == line['tau'], line + assert s == line['s'], line + assert h == line['h'], line + assert p == line['p'], line + assert n == line['n'], line + assert pp == line['pp'], line def test_normalize_angle(): """ From 4d4f08206982c02d099f2ef606ea18bca1caf8c6 Mon Sep 17 00:00:00 2001 From: tsutterley Date: Tue, 29 Oct 2024 05:41:30 -0700 Subject: [PATCH 5/7] refactor: convert coefficients table to JSON --- pyTMD/arguments.py | 544 +------------------------------ pyTMD/data/doodson.json | 485 +++++++++++++++++++++++++++ pyproject.toml | 1 + test/_coefficients_to_json.py | 595 ++++++++++++++++++++++++++++++++++ 4 files changed, 1094 insertions(+), 531 deletions(-) create mode 100644 pyTMD/data/doodson.json create mode 100644 test/_coefficients_to_json.py diff --git a/pyTMD/arguments.py b/pyTMD/arguments.py index 6935d62f..874d4690 100755 --- a/pyTMD/arguments.py +++ b/pyTMD/arguments.py @@ -75,6 +75,7 @@ from __future__ import annotations import re +import json import pathlib import numpy as np import pyTMD.astro @@ -348,6 +349,9 @@ def minor_arguments( # return values as tuple return (u, f, arg) +# JSON file of Doodson coefficients +_coefficients_table = get_data_path(['data','coefficients.json']) + def coefficients_table( constituents: list | tuple | np.ndarray | str, **kwargs @@ -361,6 +365,8 @@ def coefficients_table( tidal constituent IDs corrections: str, default 'OTIS' use coefficients from OTIS, FES or GOT models + file: str or pathlib.Path, default `coefficients.json` + JSON file of Doodson coefficients Returns ------- @@ -379,7 +385,10 @@ def coefficients_table( """ # set default keyword arguments kwargs.setdefault('corrections', 'OTIS') + kwargs.setdefault('file', _coefficients_table) + # verify coefficients table path + table = pathlib.Path(kwargs['file']).expanduser().absolute() # modified Doodson coefficients for constituents # using 7 index variables: tau, s, h, p, n, pp, k # tau: mean lunar time @@ -389,542 +398,15 @@ def coefficients_table( # n: mean longitude of ascending lunar node # pp: mean longitude of solar perigee # k: 90-degree phase - coefficients = {} - coefficients['z0'] = [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0] - coefficients['node'] = [0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 2.0] - coefficients['omega0'] = [0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 2.0] - # With p' - coefficients['sa'] = [0.0, 0.0, 1.0, 0.0, 0.0, -1.0, 0.0] + with table.open(mode='r', encoding='utf8') as fid: + coefficients = json.load(fid) + # # Without p' # coefficients['sa'] = [0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0] - coefficients['ssa'] = [0.0, 0.0, 2.0, 0.0, 0.0, 0.0, 0.0] - # With p' - coefficients['sta'] = [0.0, 0.0, 3.0, 0.0, 0.0, -1.0, 0.0] - # # Without p' # coefficients['sta'] = [0.0, 0.0, 3.0, 0.0, 0.0, 0.0, 0.0] - coefficients['st'] = [0.0, 0.0, 3.0, 0.0, 0.0, 0.0, 0.0] - coefficients['msm'] = [0.0, 1.0, -2.0, 1.0, 0.0, 0.0, 0.0] - coefficients['mm'] = [0.0, 1.0, 0.0, -1.0, 0.0, 0.0, 0.0] - # annual sideline - coefficients['msfa'] = [0.0, 2.0, -3.0, 0.0, 0.0, 0.0, 0.0] - coefficients['msf'] = [0.0, 2.0, -2.0, 0.0, 0.0, 0.0, 0.0] - # annual sideline - coefficients['msfb'] = [0.0, 2.0, -1.0, 0.0, 0.0, 0.0, 0.0] - coefficients['mfa'] = [0.0, 2.0, -1.0, 0.0, 0.0, 0.0, 0.0] - coefficients['mf-'] = [0.0, 2.0, 0.0, 0.0, -1.0, 0.0, 0.0] - coefficients['mf'] = [0.0, 2.0, 0.0, 0.0, 0.0, 0.0, 0.0] - # nodal line - coefficients['mf+'] = [0.0, 2.0, 0.0, 0.0, 1.0, 0.0, 0.0] - # nodal line - coefficients['mfn'] = [0.0, 2.0, 0.0, 0.0, 1.0, 0.0, 0.0] - coefficients['mfb'] = [0.0, 2.0, 1.0, 0.0, 0.0, 0.0, 0.0] - coefficients['sn0'] = [0.0, 3.0, -2.0, -1.0, 0.0, 0.0, 0.0] - coefficients['mst'] = [0.0, 3.0, -2.0, 1.0, 0.0, 0.0, 0.0] - coefficients['mt'] = [0.0, 3.0, 0.0, -1.0, 0.0, 0.0, 0.0] - coefficients['mtm'] = [0.0, 3.0, 0.0, -1.0, 0.0, 0.0, 0.0] - coefficients['msqm'] = [0.0, 4.0, -2.0, 0.0, 0.0, 0.0, 0.0] - coefficients['mq'] = [0.0, 4.0, 0.0, -2.0, 0.0, 0.0, 0.0] - coefficients['2smn0'] = [0.0, 5.0, -4.0, -1.0, 0.0, 0.0, 0.0] - coefficients['msp'] = [0.0, 5.0, -2.0, -1.0, 0.0, 0.0, 0.0] - coefficients['mp'] = [0.0, 5.0, 0.0, -3.0, 0.0, 0.0, 0.0] - coefficients['2qj1'] = [1.0, -6.0, 0.0, 3.0, 0.0, 0.0, 1.0] - coefficients['2qk1'] = [1.0, -5.0, 0.0, 2.0, 0.0, 0.0, 1.0] - coefficients['2qs1'] = [1.0, -5.0, 1.0, 2.0, 0.0, 0.0, 0.0] - coefficients['2qp1'] = [1.0, -5.0, 2.0, 2.0, 0.0, 0.0, -1.0] - coefficients['2oj1'] = [1.0, -4.0, 0.0, 1.0, 0.0, 0.0, 1.0] - coefficients['alpha1'] = [1.0, -4.0, 2.0, 1.0, 0.0, 0.0, -1.0] - coefficients['2ok1'] = [1.0, -3.0, 0.0, 0.0, 0.0, 0.0, 1.0] - # 3rd degree terms - coefficients["2q1'"] = [1.0, -3.0, 0.0, 1.0, 0.0, 0.0, 2.0] - coefficients['2q1'] = [1.0, -3.0, 0.0, 2.0, 0.0, 0.0, -1.0] - coefficients['sigma1'] = [1.0, -3.0, 2.0, 0.0, 0.0, 0.0, -1.0] - # 3rd degree terms - coefficients["q1'"] = [1.0, -2.0, 0.0, 0.0, 0.0, 0.0, 2.0] - coefficients['q1'] = [1.0, -2.0, 0.0, 1.0, 0.0, 0.0, -1.0] - coefficients['rho1'] = [1.0, -2.0, 2.0, -1.0, 0.0, 0.0, -1.0] - coefficients['np1'] = [1.0, -2.0, 2.0, 1.0, 0.0, 0.0, 1.0] - coefficients['opk1'] = [1.0, -1.0, -2.0, 0.0, 0.0, 0.0, 1.0] - coefficients['oa1'] = [1.0, -1.0, -1.0, 0.0, 0.0, 0.0, -1.0] - # O1 nodal line - coefficients['o1n'] = [1.0, -1.0, 0.0, 0.0, -1.0, 0.0, -1.0] - # O1 nodal line - coefficients['o1-'] = [1.0, -1.0, 0.0, 0.0, -1.0, 0.0, -1.0] - coefficients['o1'] = [1.0, -1.0, 0.0, 0.0, 0.0, 0.0, -1.0] - # conjugate to nodal line - coefficients['o1+'] = [1.0, -1.0, 0.0, 0.0, 1.0, 0.0, -1.0] - # 3rd degree terms - coefficients["o1'"] = [1.0, -1.0, 0.0, 1.0, 0.0, 0.0, 2.0] - coefficients['ob1'] = [1.0, -1.0, 1.0, 0.0, 0.0, 0.0, -1.0] - coefficients['ms1'] = [1.0, -1.0, 1.0, 0.0, 0.0, 0.0, 2.0] - coefficients['mp1'] = [1.0, -1.0, 2.0, 0.0, 0.0, 0.0, 1.0] - coefficients['tau1'] = [1.0, -1.0, 2.0, 0.0, 0.0, 0.0, 1.0] - coefficients['beta1'] = [1.0, 0.0, -2.0, 1.0, 0.0, 0.0, 1.0] - coefficients['pqo1'] = [1.0, 0.0, -2.0, 1.0, 0.0, 0.0, -1.0] - coefficients['2oq1'] = [1.0, 0.0, 0.0, -1.0, 0.0, 0.0, -1.0] - # 3rd degree terms - coefficients["m1'"] = [1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 2.0] - coefficients['m1'] = [1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0] - coefficients['m1a'] = [1.0, 0.0, 0.0, 1.0, 0.0, 0.0, 1.0] - coefficients['m1b'] = [1.0, 0.0, 0.0, -1.0, 0.0, 0.0, 1.0] - coefficients['no1'] = [1.0, 0.0, 0.0, 1.0, 0.0, 0.0, 1.0] - coefficients['chi1'] = [1.0, 0.0, 2.0, -1.0, 0.0, 0.0, 1.0] - coefficients['2pk1'] = [1.0, 1.0, -4.0, 0.0, 0.0, 0.0, 1.0] - coefficients['pi1'] = [1.0, 1.0, -3.0, 0.0, 0.0, 1.0, -1.0] - coefficients['tk1'] = [1.0, 1.0, -3.0, 0.0, 0.0, 1.0, -1.0] - coefficients['s1-1'] = [1.0, 1.0, -2.0, 0.0, 0.0, 0.0, 2.0] - coefficients['p1'] = [1.0, 1.0, -2.0, 0.0, 0.0, 0.0, -1.0] - coefficients['s1-'] = [1.0, 1.0, -1.0, 0.0, 0.0, -1.0, 1.0] + # set s1 coefficients if kwargs['corrections'] in ('OTIS','ATLAS','TMD3','netcdf'): coefficients['s1'] = [1.0, 1.0, -1.0, 0.0, 0.0, 0.0, 1.0] - else: - # Doodson's phase - coefficients['s1'] = [1.0, 1.0, -1.0, 0.0, 0.0, 0.0, 2.0] - coefficients['s1+'] = [1.0, 1.0, -1.0, 0.0, 0.0, 1.0, 1.0] - coefficients['ojm1'] = [1.0, 1.0, 0.0, -2.0, 0.0, 0.0, -1.0] - # 3rd degree terms - coefficients["k1'"] = [1.0, 1.0, 0.0, -1.0, 0.0, 0.0, 2.0] - coefficients['k1-'] = [1.0, 1.0, 0.0, 0.0, -1.0, 0.0, -1.0] - coefficients['k1'] = [1.0, 1.0, 0.0, 0.0, 0.0, 0.0, 1.0] - coefficients['s1+1'] = [1.0, 1.0, 0.0, 0.0, 0.0, 0.0, 2.0] - coefficients['k1+'] = [1.0, 1.0, 0.0, 0.0, 1.0, 0.0, 1.0] - coefficients['k1n'] = [1.0, 1.0, 0.0, 0.0, 1.0, 0.0, 1.0] - coefficients['k1++'] = [1.0, 1.0, 0.0, 0.0, 2.0, 0.0, -1.0] - coefficients['psi1'] = [1.0, 1.0, 1.0, 0.0, 0.0, -1.0, 1.0] - coefficients['rp1'] = [1.0, 1.0, 1.0, 0.0, 0.0, -1.0, -1.0] - coefficients['phi1'] = [1.0, 1.0, 2.0, 0.0, 0.0, 0.0, 1.0] - coefficients['kp1'] = [1.0, 1.0, 2.0, 0.0, 0.0, 0.0, 1.0] - coefficients['opq1'] = [1.0, 2.0, -2.0, -1.0, 0.0, 0.0, -1.0] - coefficients['the1'] = [1.0, 2.0, -2.0, 1.0, 0.0, 0.0, 1.0] - coefficients['theta1'] = [1.0, 2.0, -2.0, 1.0, 0.0, 0.0, 1.0] - coefficients['mq1'] = [1.0, 2.0, 0.0, -1.0, 0.0, 0.0, 1.0] - coefficients['j1'] = [1.0, 2.0, 0.0, -1.0, 0.0, 0.0, 1.0] - # 3rd degree terms - coefficients["j1'"] = [1.0, 2.0, 0.0, 0.0, 0.0, 0.0, 2.0] - coefficients['2po1'] = [1.0, 3.0, -4.0, 0.0, 0.0, 0.0, -1.0] - coefficients['so1'] = [1.0, 3.0, -2.0, 0.0, 0.0, 0.0, 1.0] - coefficients['oo1'] = [1.0, 3.0, 0.0, 0.0, 0.0, 0.0, 1.0] - coefficients['kpq1'] = [1.0, 4.0, -2.0, -1.0, 0.0, 0.0, 1.0] - coefficients['ups1'] = [1.0, 4.0, 0.0, -1.0, 0.0, 0.0, 1.0] - coefficients['kq1'] = [1.0, 4.0, 0.0, -1.0, 0.0, 0.0, 1.0] - coefficients['2jo1'] = [1.0, 5.0, 0.0, -2.0, 0.0, 0.0, -1.0] - coefficients['kjq1'] = [1.0, 5.0, 0.0, -2.0, 0.0, 0.0, -1.0] - coefficients['2ook1'] = [1.0, 5.0, 0.0, 0.0, 0.0, 0.0, -1.0] - coefficients['2oop1'] = [1.0, 5.0, 2.0, 0.0, 0.0, 0.0, -1.0] - coefficients['2jq1'] = [1.0, 6.0, 0.0, -3.0, 0.0, 0.0, -1.0] - coefficients['2mn2s2'] = [2.0, -5.0, 4.0, 1.0, 0.0, 0.0, 0.0] - coefficients['2nk2'] = [2.0, -4.0, 0.0, 2.0, 0.0, 0.0, 0.0] - coefficients['3m(sk)2'] = [2.0, -4.0, 2.0, 0.0, 0.0, 0.0, 0.0] - coefficients['3mks2'] = [2.0, -4.0, 2.0, 0.0, 0.0, 0.0, 0.0] - coefficients['2ns2'] = [2.0, -4.0, 2.0, 2.0, 0.0, 0.0, 0.0] - coefficients['3m2s2'] = [2.0, -4.0, 4.0, 0.0, 0.0, 0.0, 0.0] - coefficients['oq2'] = [2.0, -3.0, 0.0, 1.0, 0.0, 0.0, 2.0] - coefficients['mnk2'] = [2.0, -3.0, 0.0, 1.0, 0.0, 0.0, 0.0] - coefficients['3n2'] = [2.0, -3.0, 0.0, 3.0, 0.0, 0.0, 0.0] - coefficients['eps2'] = [2.0, -3.0, 2.0, 1.0, 0.0, 0.0, 0.0] - coefficients['mns2'] = [2.0, -3.0, 2.0, 1.0, 0.0, 0.0, 0.0] - # coefficients['mns2'] = [2.0, -3.0, 4.0, -1.0, 0.0, 0.0, 0.0] - coefficients['mnus2'] = [2.0, -3.0, 4.0, -1.0, 0.0, 0.0, 0.0] - coefficients['2ml2s2'] = [2.0, -3.0, 4.0, -1.0, 0.0, 0.0, 2.0] - coefficients['mnk2s2'] = [2.0, -3.0, 4.0, 1.0, 0.0, 0.0, 0.0] - coefficients['2ms2k2'] = [2.0, -2.0, -2.0, 0.0, 0.0, 0.0, 0.0] - coefficients['2mk2'] = [2.0, -2.0, 0.0, 0.0, 0.0, 0.0, 0.0] - coefficients['o2'] = [2.0, -2.0, 0.0, 0.0, 0.0, 0.0, 2.0] - # 3rd degree terms - coefficients["2n2'"] = [2.0, -2.0, 0.0, 1.0, 0.0, 0.0, 1.0] - coefficients['2n2'] = [2.0, -2.0, 0.0, 2.0, 0.0, 0.0, 0.0] - coefficients['2nm2'] = [2.0, -2.0, 0.0, 2.0, 0.0, 0.0, 0.0] - coefficients['2ms2'] = [2.0, -2.0, 2.0, 0.0, 0.0, 0.0, 0.0] - coefficients['mu2'] = [2.0, -2.0, 2.0, 0.0, 0.0, 0.0, 0.0] - coefficients['2mk2s2'] = [2.0, -2.0, 4.0, 0.0, 0.0, 0.0, 0.0] - coefficients['omg2'] = [2.0, -2.0, 3.0, 0.0, 0.0, -1.0, 0.0] - coefficients['nsk2'] = [2.0, -1.0, -2.0, 1.0, 0.0, 0.0, 0.0] - coefficients['snk2'] = [2.0, -1.0, -2.0, 1.0, 0.0, 0.0, 0.0] - coefficients['na2'] = [2.0, -1.0, -1.0, 1.0, 0.0, 0.0, 0.0] - # 3rd degree terms - coefficients["n2'"] = [2.0, -1.0, 0.0, 0.0, 0.0, 0.0, 1.0] - coefficients['n2'] = [2.0, -1.0, 0.0, 1.0, 0.0, 0.0, 0.0] - coefficients['2ml2'] = [2.0, -1.0, 0.0, 1.0, 0.0, 0.0, 2.0] - coefficients['nb2'] = [2.0, -1.0, 1.0, 1.0, 0.0, 0.0, 0.0] - coefficients['nu2'] = [2.0, -1.0, 2.0, -1.0, 0.0, 0.0, 0.0] - coefficients['mmun2'] = [2.0, -1.0, 2.0, -1.0, 0.0, 0.0, 0.0] - coefficients['3m(sn)2'] = [2.0, -1.0, 2.0, -1.0, 0.0, 0.0, 0.0] - coefficients['nks2'] = [2.0, -1.0, 2.0, 1.0, 0.0, 0.0, 0.0] - coefficients['nkp2'] = [2.0, -1.0, 2.0, 1.0, 0.0, 0.0, 2.0] - coefficients['mkl2s2'] = [2.0, -1.0, 4.0, -1.0, 0.0, 0.0, 2.0] - coefficients['2kn2s2'] = [2.0, -1.0, 4.0, 1.0, 0.0, 0.0, 0.0] - coefficients['msk2'] = [2.0, 0.0, -2.0, 0.0, 0.0, 0.0, 0.0] - coefficients['op2'] = [2.0, 0.0, -2.0, 0.0, 0.0, 0.0, 2.0] - coefficients['m2-2'] = [2.0, 0.0, -2.0, 0.0, 0.0, 0.0, 0.0] - coefficients['gamma2'] = [2.0, 0.0, -2.0, 2.0, 0.0, 0.0, 2.0] - coefficients['gam2'] = [2.0, 0.0, -2.0, 2.0, 0.0, 0.0, 2.0] - coefficients['alp2'] = [2.0, 0.0, -1.0, 0.0, 0.0, 1.0, 2.0] - coefficients['alpha2'] = [2.0, 0.0, -1.0, 0.0, 0.0, 1.0, 2.0] - coefficients['m2a'] = [2.0, 0.0, -1.0, 0.0, 0.0, 1.0, 0.0] - coefficients['m2-1'] = [2.0, 0.0, -1.0, 0.0, 0.0, 0.0, 0.0] - coefficients['ma2'] = [2.0, 0.0, -1.0, 0.0, 0.0, 0.0, 0.0] - # M2 nodal line - coefficients['m2-'] = [2.0, 0.0, 0.0, 0.0, -1.0, 0.0, 2.0] - coefficients['m2'] = [2.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0] - coefficients['ko2'] = [2.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0] - # conjugate to nodal - coefficients['m2+'] = [2.0, 0.0, 0.0, 0.0, 1.0, 0.0, 2.0] - # 3rd degree terms - coefficients["m2'"] = [2.0, 0.0, 0.0, 1.0, 0.0, 0.0, -1.0] - coefficients['mb2'] = [2.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0] - coefficients['m2+1'] = [2.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0] - coefficients['m2b'] = [2.0, 0.0, 1.0, 0.0, 0.0, -1.0, 0.0] - coefficients['beta2'] = [2.0, 0.0, 1.0, 0.0, 0.0, -1.0, 0.0] - coefficients['delta2'] = [2.0, 0.0, 2.0, 0.0, 0.0, 0.0, 0.0] - coefficients['m2+2'] = [2.0, 0.0, 2.0, 0.0, 0.0, 0.0, 0.0] - coefficients['mks2'] = [2.0, 0.0, 2.0, 0.0, 0.0, 0.0, 0.0] - coefficients['m2(ks)2'] = [2.0, 0.0, 4.0, 0.0, 0.0, 0.0, 0.0] - coefficients['2snmk2'] = [2.0, 1.0, -4.0, 1.0, 0.0, 0.0, 0.0] - coefficients['2sn(mk)2'] = [2.0, 1.0, -4.0, 1.0, 0.0, 0.0, 0.0] - coefficients['snm2'] = [2.0, 1.0, -2.0, 1.0, 0.0, 0.0, 0.0] - coefficients['lambda2'] = [2.0, 1.0, -2.0, 1.0, 0.0, 0.0, 2.0] - coefficients['2mn2'] = [2.0, 1.0, 0.0, -1.0, 0.0, 0.0, 0.0] - coefficients['l2'] = [2.0, 1.0, 0.0, -1.0, 0.0, 0.0, 2.0] - coefficients['l2a'] = [2.0, 1.0, 0.0, -1.0, 0.0, 0.0, 2.0] - # 3rd degree terms - coefficients["l2'"] = [2.0, 1.0, 0.0, 0.0, 0.0, 0.0, -1.0] - coefficients['nkm2'] = [2.0, 1.0, 0.0, 1.0, 0.0, 0.0, 0.0] - coefficients['l2b'] = [2.0, 1.0, 0.0, 1.0, 0.0, 0.0, 0.0] - coefficients['lb2'] = [2.0, 1.0, 1.0, -1.0, 0.0, 0.0, 2.0] - coefficients['2sk2'] = [2.0, 2.0, -4.0, 0.0, 0.0, 0.0, 0.0] - coefficients['2t2'] = [2.0, 2.0, -4.0, 0.0, 0.0, 2.0, 0.0] - coefficients['s2-2'] = [2.0, 2.0, -4.0, 0.0, 0.0, 0.0, 0.0] - coefficients['s2-1'] = [2.0, 2.0, -3.0, 0.0, 0.0, 0.0, 0.0] - coefficients['t2'] = [2.0, 2.0, -3.0, 0.0, 0.0, 1.0, 0.0] - coefficients['kp2'] = [2.0, 2.0, -2.0, 0.0, 0.0, 0.0, 0.0] - coefficients['s2r'] = [2.0, 2.0, -2.0, 0.0, 0.0, 0.0, 0.0] - coefficients['s2'] = [2.0, 2.0, -2.0, 0.0, 0.0, 0.0, 0.0] - coefficients['r2'] = [2.0, 2.0, -1.0, 0.0, 0.0, -1.0, 2.0] - coefficients['s2+1'] = [2.0, 2.0, -1.0, 0.0, 0.0, 0.0, 0.0] - coefficients['s2+2'] = [2.0, 2.0, 0.0, 0.0, 0.0, 0.0, 0.0] - coefficients['k2'] = [2.0, 2.0, 0.0, 0.0, 0.0, 0.0, 0.0] - coefficients['kb2'] = [2.0, 2.0, 1.0, 0.0, 0.0, 0.0, 0.0] - coefficients['2ks2'] = [2.0, 2.0, 2.0, 0.0, 0.0, 0.0, 0.0] - coefficients['2pmn2'] = [2.0, 3.0, -4.0, -1.0, 0.0, 0.0, 2.0] - coefficients['msnu2'] = [2.0, 3.0, -4.0, 1.0, 0.0, 0.0, 0.0] - coefficients['msn2'] = [2.0, 3.0, -2.0, -1.0, 0.0, 0.0, 0.0] - coefficients['zeta2'] = [2.0, 3.0, -2.0, 1.0, 0.0, 0.0, 0.0] - coefficients['eta2'] = [2.0, 3.0, 0.0, -1.0, 0.0, 0.0, 0.0] - coefficients['mkn2'] = [2.0, 3.0, 0.0, -1.0, 0.0, 0.0, 0.0] - coefficients['kj2'] = [2.0, 3.0, 0.0, -1.0, 0.0, 0.0, 2.0] - coefficients['2kmsn2'] = [2.0, 3.0, 2.0, -1.0, 0.0, 0.0, 0.0] - coefficients['2km(sn)2'] = [2.0, 3.0, 2.0, -1.0, 0.0, 0.0, 0.0] - coefficients['2sm2'] = [2.0, 4.0, -4.0, 0.0, 0.0, 0.0, 0.0] - coefficients['2ms2n2'] = [2.0, 4.0, -2.0, -2.0, 0.0, 0.0, 0.0] - coefficients['skm2'] = [2.0, 4.0, -2.0, 0.0, 0.0, 0.0, 0.0] - coefficients['2j2'] = [2.0, 4.0, 0.0, -2.0, 0.0, 0.0, 2.0] - coefficients['2k2'] = [2.0, 4.0, 0.0, 0.0, 0.0, 0.0, 0.0] - coefficients['2snu2'] = [2.0, 5.0, -6.0, 1.0, 0.0, 0.0, 0.0] - coefficients['3(sm)n2'] = [2.0, 5.0, -6.0, 1.0, 0.0, 0.0, 0.0] - coefficients['2sn2'] = [2.0, 5.0, -4.0, -1.0, 0.0, 0.0, 0.0] - coefficients['skn2'] = [2.0, 5.0, -2.0, -1.0, 0.0, 0.0, 0.0] - coefficients['2kn2'] = [2.0, 5.0, 0.0, -1.0, 0.0, 0.0, 0.0] - coefficients['3s2m2'] = [2.0, 6.0, -6.0, 0.0, 0.0, 0.0, 0.0] - coefficients['2sk2m2'] = [2.0, 6.0, -4.0, 0.0, 0.0, 0.0, 0.0] - coefficients['2oq3'] = [3.0, -4.0, 0.0, 1.0, 0.0, 0.0, 1.0] - # compound 3 O1 - coefficients['o3'] = [3.0, -3.0, 0.0, 0.0, 0.0, 0.0, 1.0] - coefficients['nq3'] = [3.0, -3.0, 0.0, 2.0, 0.0, 0.0, -1.0] - coefficients['muo3'] = [3.0, -3.0, 2.0, 0.0, 0.0, 0.0, -1.0] - coefficients['mq3'] = [3.0, -2.0, 0.0, 1.0, 0.0, 0.0, -1.0] - coefficients['no3'] = [3.0, -2.0, 0.0, 1.0, 0.0, 0.0, -1.0] - coefficients['mnp3'] = [3.0, -2.0, 2.0, 1.0, 0.0, 0.0, 1.0] - coefficients['2op3'] = [3.0, -1.0, -2.0, 0.0, 0.0, 0.0, 1.0] - coefficients['2os3'] = [3.0, -1.0, -1.0, 0.0, 0.0, 0.0, 0.0] - # Q1+M1+S1 - coefficients['qms3'] = [3.0, -1.0, -1.0, 2.0, 0.0, 0.0, 2.0] - coefficients['mo3-'] = [3.0, -1.0, 0.0, 0.0, -1.0, 0.0, -1.0] - coefficients['mo3'] = [3.0, -1.0, 0.0, 0.0, 0.0, 0.0, -1.0] - coefficients['mo3+'] = [3.0, -1.0, 0.0, 0.0, 1.0, 0.0, -1.0] - coefficients['2mk3'] = [3.0, -1.0, 0.0, 0.0, 0.0, 0.0, -1.0] - coefficients['e3n'] = [3.0, -1.0, 0.0, 1.0, -1.0, 0.0, 0.0] - # 3rd degree terms - coefficients['e3'] = [3.0, -1.0, 0.0, 1.0, 0.0, 0.0, 2.0] - coefficients['2no3'] = [3.0, -1.0, 0.0, 2.0, 0.0, 0.0, 1.0] - coefficients['2nkm3'] = [3.0, -1.0, 0.0, 2.0, 0.0, 0.0, 1.0] - coefficients['2ms3'] = [3.0, -1.0, 1.0, 0.0, 0.0, 0.0, 2.0] - coefficients['2mp3'] = [3.0, -1.0, 2.0, 0.0, 0.0, 0.0, 1.0] - coefficients['ns3'] = [3.0, 0.0, -1.0, 1.0, 0.0, 0.0, 2.0] - coefficients['2oj3'] = [3.0, 0.0, 0.0, -1.0, 0.0, 0.0, -1.0] - # 2M2 - M1 - coefficients['2mm3'] = [3.0, 0.0, 0.0, -1.0, 0.0, 0.0, -1.0] - coefficients['m3'] = [3.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0] - # 3rd degree terms - coefficients["m3'"] = [3.0, 0.0, 0.0, 0.0, 0.0, 0.0, 2.0] - coefficients['nk3'] = [3.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0] - coefficients['mp3'] = [3.0, 1.0, -2.0, 0.0, 0.0, 0.0, -1.0] - coefficients['so3'] = [3.0, 1.0, -2.0, 0.0, 0.0, 0.0, -1.0] - # 3rd degree terms - coefficients['lambda3'] = [3.0, 1.0, -2.0, 1.0, 0.0, 0.0, 0.0] - coefficients['ms3'] = [3.0, 1.0, -1.0, 0.0, 0.0, 0.0, 2.0] - coefficients['pjrho3'] = [3.0, 1.0, 0.0, -2.0, 0.0, 0.0, -1.0] - # 3rd degree terms - coefficients['l3'] = [3.0, 1.0, 0.0, -1.0, 0.0, 0.0, 0.0] - coefficients['mk3-'] = [3.0, 1.0, 0.0, 0.0, -1.0, 0.0, 1.0] - coefficients['mk3'] = [3.0, 1.0, 0.0, 0.0, 0.0, 0.0, 1.0] - coefficients['mk3+'] = [3.0, 1.0, 0.0, 0.0, 1.0, 0.0, 1.0] - # 3rd degree terms - coefficients['l3b'] = [3.0, 1.0, 0.0, 1.0, 0.0, 0.0, 2.0] - coefficients['mks3'] = [3.0, 1.0, 1.0, 0.0, 0.0, 0.0, 2.0] - coefficients['mkp3'] = [3.0, 1.0, 2.0, 0.0, 0.0, 0.0, 1.0] - coefficients['nso3'] = [3.0, 2.0, -2.0, 1.0, 0.0, 0.0, 1.0] - coefficients['2mq3'] = [3.0, 2.0, 0.0, -1.0, 0.0, 0.0, 1.0] - # 3rd degree terms - coefficients['f3'] = [3.0, 2.0, 0.0, 0.0, 0.0, 0.0, 2.0] - # 3rd degree terms - coefficients['j3'] = [3.0, 2.0, 0.0, 0.0, 0.0, 0.0, 2.0] - # s3 perturbation - coefficients['2t3'] = [3.0, 3.0, -5.0, 0.0, 0.0, 0.0, 2.0] - # s3 perturbation - coefficients['t3'] = [3.0, 3.0, -4.0, 0.0, 0.0, 0.0, 2.0] - # = 2SK3 - coefficients['sp3'] = [3.0, 3.0, -4.0, 0.0, 0.0, 0.0, -1.0] - coefficients['s3'] = [3.0, 3.0, -3.0, 0.0, 0.0, 0.0, 0.0] - # 3rd degree terms - coefficients["s3'"] = [3.0, 3.0, -3.0, 0.0, 0.0, 0.0, 2.0] - # s3 perturbation - coefficients['r3'] = [3.0, 3.0, -2.0, 0.0, 0.0, 0.0, 2.0] - coefficients['sk3'] = [3.0, 3.0, -2.0, 0.0, 0.0, 0.0, 1.0] - # s3 perturbation - coefficients['2r3'] = [3.0, 3.0, -1.0, 0.0, 0.0, 0.0, 2.0] - coefficients['k3'] = [3.0, 3.0, 0.0, 0.0, 0.0, 0.0, -1.0] - coefficients['2so3'] = [3.0, 5.0, -4.0, 0.0, 0.0, 0.0, 1.0] - coefficients['2jp3'] = [3.0, 5.0, -2.0, -2.0, 0.0, 0.0, 1.0] - coefficients['kso3'] = [3.0, 5.0, -2.0, 0.0, 0.0, 0.0, 1.0] - coefficients['2jk3'] = [3.0, 5.0, -1.0, -2.0, 0.0, 0.0, 0.0] - coefficients['2ko3'] = [3.0, 5.0, 0.0, 0.0, 0.0, 0.0, 1.0] - coefficients['2sq3'] = [3.0, 6.0, -4.0, -1.0, 0.0, 0.0, 1.0] - coefficients['o4'] = [4.0, -4.0, 0.0, 0.0, 0.0, 0.0, 0.0] - coefficients['2qm4'] = [4.0, -4.0, 0.0, 2.0, 0.0, 0.0, 2.0] - coefficients['4ms4'] = [4.0, -4.0, 4.0, 0.0, 0.0, 0.0, 0.0] - coefficients['4m2s4'] = [4.0, -4.0, 4.0, 0.0, 0.0, 0.0, 0.0] - coefficients['2mnk4'] = [4.0, -3.0, 0.0, 1.0, 0.0, 0.0, 0.0] - coefficients['moq4'] = [4.0, -3.0, 0.0, 1.0, 0.0, 0.0, 2.0] - coefficients['2mns4'] = [4.0, -3.0, 2.0, 1.0, 0.0, 0.0, 0.0] - coefficients['2mns4'] = [4.0, -3.0, 4.0, -1.0, 0.0, 0.0, 0.0] - coefficients['2mnus4'] = [4.0, -3.0, 4.0, -1.0, 0.0, 0.0, 0.0] - coefficients['3mk4'] = [4.0, -2.0, 0.0, 0.0, 0.0, 0.0, 0.0] - coefficients['2om4'] = [4.0, -2.0, 0.0, 0.0, 0.0, 0.0, 2.0] - coefficients['n4'] = [4.0, -2.0, 0.0, 2.0, 0.0, 0.0, 0.0] - coefficients['3ms4'] = [4.0, -2.0, 2.0, 0.0, 0.0, 0.0, 0.0] - coefficients['msnk4'] = [4.0, -1.0, -2.0, 1.0, 0.0, 0.0, 0.0] - coefficients['mpq4'] = [4.0, -1.0, -2.0, 1.0, 0.0, 0.0, 2.0] - coefficients['mn4'] = [4.0, -1.0, 0.0, 1.0, 0.0, 0.0, 0.0] - coefficients['mnu4'] = [4.0, -1.0, 2.0, -1.0, 0.0, 0.0, 0.0] - coefficients['2mls4'] = [4.0, -1.0, 2.0, -1.0, 0.0, 0.0, 2.0] - coefficients['mnks4'] = [4.0, -1.0, 2.0, 1.0, 0.0, 0.0, 0.0] - coefficients['2msk4'] = [4.0, 0.0, -2.0, 0.0, 0.0, 0.0, 0.0] - coefficients['mop4'] = [4.0, 0.0, -2.0, 0.0, 0.0, 0.0, 2.0] - coefficients['ma4'] = [4.0, 0.0, -1.0, 0.0, 0.0, 0.0, 0.0] - coefficients['m4'] = [4.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0] - coefficients['mb4'] = [4.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0] - coefficients['2mks4'] = [4.0, 0.0, 2.0, 0.0, 0.0, 0.0, 0.0] - coefficients['sn4'] = [4.0, 1.0, -2.0, 1.0, 0.0, 0.0, 0.0] - coefficients['3mn4'] = [4.0, 1.0, 0.0, -1.0, 0.0, 0.0, 0.0] - coefficients['ml4'] = [4.0, 1.0, 0.0, -1.0, 0.0, 0.0, 2.0] - coefficients['nk4'] = [4.0, 1.0, 0.0, 1.0, 0.0, 0.0, 0.0] - coefficients['2smk4'] = [4.0, 2.0, -4.0, 0.0, 0.0, 0.0, 0.0] - coefficients['2pm4'] = [4.0, 2.0, -4.0, 0.0, 0.0, 0.0, 2.0] - coefficients['mt4'] = [4.0, 2.0, -3.0, 0.0, 0.0, 1.0, 0.0] - coefficients['ms4'] = [4.0, 2.0, -2.0, 0.0, 0.0, 0.0, 0.0] - coefficients['mr4'] = [4.0, 2.0, -1.0, 0.0, 0.0, -1.0, 2.0] - coefficients['mk4'] = [4.0, 2.0, 0.0, 0.0, 0.0, 0.0, 0.0] - coefficients['2snm4'] = [4.0, 3.0, -4.0, 1.0, 0.0, 0.0, 0.0] - coefficients['2msn4'] = [4.0, 3.0, -2.0, -1.0, 0.0, 0.0, 0.0] - coefficients['sl4'] = [4.0, 3.0, -2.0, -1.0, 0.0, 0.0, 2.0] - coefficients['2mkn4'] = [4.0, 3.0, 0.0, -1.0, 0.0, 0.0, 0.0] - coefficients['mkj4'] = [4.0, 3.0, 0.0, -1.0, 0.0, 0.0, 2.0] - coefficients['2t4'] = [4.0, 4.0, -6.0, 0.0, 0.0, 0.0, 0.0] - coefficients['t4'] = [4.0, 4.0, -5.0, 0.0, 0.0, 0.0, 0.0] - coefficients['st4'] = [4.0, 4.0, -5.0, 0.0, 0.0, 1.0, 0.0] - coefficients['s4'] = [4.0, 4.0, -4.0, 0.0, 0.0, 0.0, 0.0] - coefficients['r4'] = [4.0, 4.0, -3.0, 0.0, 0.0, 0.0, 0.0] - coefficients['2r4'] = [4.0, 4.0, -2.0, 0.0, 0.0, 0.0, 0.0] - coefficients['sk4'] = [4.0, 4.0, -2.0, 0.0, 0.0, 0.0, 0.0] - coefficients['3ks4'] = [4.0, 4.0, -1.0, 0.0, 0.0, 0.0, -1.0] - coefficients['k4'] = [4.0, 4.0, 0.0, 0.0, 0.0, 0.0, 0.0] - coefficients['3sm4'] = [4.0, 6.0, -6.0, 0.0, 0.0, 0.0, 0.0] - coefficients['2(kj)4'] = [4.0, 6.0, 0.0, -2.0, 0.0, 0.0, 2.0] - coefficients['2no5'] = [5.0, -3.0, 0.0, 2.0, 0.0, 0.0, -1.0] - coefficients['mno5'] = [5.0, -2.0, 0.0, 1.0, 0.0, 0.0, -1.0] - coefficients['2mq5'] = [5.0, -2.0, 0.0, 1.0, 0.0, 0.0, -1.0] - coefficients['2nkms5'] = [5.0, -2.0, 2.0, 2.0, 0.0, 0.0, 1.0] - coefficients['2mo5'] = [5.0, -1.0, 0.0, 0.0, 0.0, 0.0, -1.0] - coefficients['mnm5'] = [5.0, -1.0, 0.0, 1.0, 0.0, 0.0, 2.0] - coefficients['2nk5'] = [5.0, -1.0, 0.0, 2.0, 0.0, 0.0, 1.0] - coefficients['3ms5'] = [5.0, -1.0, 1.0, 0.0, 0.0, 0.0, 2.0] - coefficients['3mp5'] = [5.0, -1.0, 2.0, 0.0, 0.0, 0.0, 1.0] - coefficients['nso5'] = [5.0, 0.0, -2.0, 1.0, 0.0, 0.0, -1.0] - coefficients['m5'] = [5.0, 0.0, 0.0, 0.0, 0.0, 0.0, 2.0] - coefficients['mnk5'] = [5.0, 0.0, 0.0, 1.0, 0.0, 0.0, 1.0] - coefficients['mb5'] = [5.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0] - coefficients['mso5'] = [5.0, 1.0, -2.0, 0.0, 0.0, 0.0, -1.0] - coefficients['2mp5'] = [5.0, 1.0, -2.0, 0.0, 0.0, 0.0, -1.0] - coefficients['2ms5'] = [5.0, 1.0, -1.0, 0.0, 0.0, 0.0, 2.0] - coefficients['2mk5'] = [5.0, 1.0, 0.0, 0.0, 0.0, 0.0, 1.0] - # N2 + K2 + S1 - coefficients['nks5'] = [5.0, 2.0, -1.0, 1.0, 0.0, 0.0, 2.0] - coefficients['nsk5'] = [5.0, 2.0, -2.0, -1.0, 0.0, 0.0, 1.0] - coefficients['msm5'] = [5.0, 2.0, -2.0, 0.0, 0.0, 0.0, 2.0] - coefficients['snk5'] = [5.0, 2.0, -2.0, 1.0, 0.0, 0.0, -1.0] - coefficients['3mq5'] = [5.0, 2.0, 0.0, -1.0, 0.0, 0.0, 1.0] - coefficients['msp5'] = [5.0, 3.0, -4.0, 0.0, 0.0, 0.0, -1.0] - coefficients['msk5'] = [5.0, 3.0, -2.0, 0.0, 0.0, 0.0, 1.0] - coefficients['3km5'] = [5.0, 3.0, 0.0, 0.0, 0.0, 0.0, -1.0] - coefficients['2sp5'] = [5.0, 5.0, -6.0, 0.0, 0.0, 0.0, -1.0] - coefficients['t5'] = [5.0, 5.0, -6.0, 0.0, 0.0, 0.0, 0.0] - coefficients['s5'] = [5.0, 5.0, -5.0, 0.0, 0.0, 0.0, 0.0] - coefficients['r5'] = [5.0, 5.0, -4.0, 0.0, 0.0, 0.0, 0.0] - coefficients['2sk5'] = [5.0, 5.0, -4.0, 0.0, 0.0, 0.0, 1.0] - coefficients['k5'] = [5.0, 5.0, 0.0, 0.0, 0.0, 0.0, 1.0] - coefficients['o6'] = [6.0, -6.0, 0.0, 0.0, 0.0, 0.0, 2.0] - coefficients['2(mn)k6'] = [6.0, -4.0, 0.0, 2.0, 0.0, 0.0, 0.0] - coefficients['5mks6'] = [6.0, -4.0, 2.0, 0.0, 0.0, 0.0, 0.0] - coefficients['2(mn)s6'] = [6.0, -4.0, 2.0, 2.0, 0.0, 0.0, 0.0] - coefficients['5m2s6'] = [6.0, -4.0, 4.0, 0.0, 0.0, 0.0, 0.0] - coefficients['3mnk6'] = [6.0, -3.0, 0.0, 1.0, 0.0, 0.0, 0.0] - coefficients['n6'] = [6.0, -3.0, 0.0, 3.0, 0.0, 0.0, 0.0] - coefficients['3mns6'] = [6.0, -3.0, 2.0, 1.0, 0.0, 0.0, 0.0] - coefficients['2nmls6'] = [6.0, -3.0, 2.0, 1.0, 0.0, 0.0, 2.0] - coefficients['3nks6'] = [6.0, -3.0, 2.0, 3.0, 0.0, 0.0, 0.0] - coefficients['3mnus6'] = [6.0, -3.0, 4.0, -1.0, 0.0, 0.0, 0.0] - coefficients['4mk6'] = [6.0, -2.0, 0.0, 0.0, 0.0, 0.0, 0.0] - coefficients['2nm6'] = [6.0, -2.0, 0.0, 2.0, 0.0, 0.0, 0.0] - coefficients['m2n6'] = [6.0, -2.0, 0.0, 2.0, 0.0, 0.0, 0.0] - coefficients['4ms6'] = [6.0, -2.0, 2.0, 0.0, 0.0, 0.0, 0.0] - coefficients['2mlns6'] = [6.0, -2.0, 2.0, 0.0, 0.0, 0.0, 2.0] - coefficients['2mnls6'] = [6.0, -2.0, 2.0, 0.0, 0.0, 0.0, 2.0] - coefficients['2nmks6'] = [6.0, -2.0, 2.0, 2.0, 0.0, 0.0, 0.0] - coefficients['2msnk6'] = [6.0, -1.0, -2.0, 1.0, 0.0, 0.0, 0.0] - coefficients['2mn6'] = [6.0, -1.0, 0.0, 1.0, 0.0, 0.0, 0.0] - coefficients['2mnu6'] = [6.0, -1.0, 2.0, -1.0, 0.0, 0.0, 0.0] - coefficients['2mn6'] = [6.0, -1.0, 2.0, -1.0, 0.0, 0.0, 0.0] - coefficients['3mls6'] = [6.0, -1.0, 2.0, -1.0, 0.0, 0.0, 2.0] - coefficients['2mno6'] = [6.0, -1.0, 2.0, -1.0, 0.0, 0.0, 0.0] - coefficients['2mnks6'] = [6.0, -1.0, 2.0, 1.0, 0.0, 0.0, 0.0] - coefficients['3msk6'] = [6.0, 0.0, -2.0, 0.0, 0.0, 0.0, 0.0] - coefficients['ma6'] = [6.0, 0.0, -1.0, 0.0, 0.0, 0.0, 0.0] - coefficients['m6'] = [6.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0] - coefficients['2nk6'] = [6.0, 0.0, 0.0, 2.0, 0.0, 0.0, 0.0] - coefficients['mb6'] = [6.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0] - coefficients['3mks6'] = [6.0, 0.0, 2.0, 0.0, 0.0, 0.0, 0.0] - coefficients['msn6'] = [6.0, 1.0, -2.0, 1.0, 0.0, 0.0, 0.0] - coefficients['4mn6'] = [6.0, 1.0, 0.0, -1.0, 0.0, 0.0, 0.0] - coefficients['2ml6'] = [6.0, 1.0, 0.0, -1.0, 0.0, 0.0, 2.0] - coefficients['mnk6'] = [6.0, 1.0, 0.0, 1.0, 0.0, 0.0, 0.0] - coefficients['mkn6'] = [6.0, 1.0, 0.0, 1.0, 0.0, 0.0, 0.0] - coefficients['mknu6'] = [6.0, 1.0, 2.0, -1.0, 0.0, 0.0, 0.0] - coefficients['2(ms)k6'] = [6.0, 2.0, -4.0, 0.0, 0.0, 0.0, 0.0] - coefficients['2mt6'] = [6.0, 2.0, -3.0, 0.0, 0.0, 1.0, 0.0] - coefficients['2ms6'] = [6.0, 2.0, -2.0, 0.0, 0.0, 0.0, 0.0] - coefficients['2mr6'] = [6.0, 2.0, -1.0, 0.0, 0.0, -1.0, 2.0] - coefficients['2mk6'] = [6.0, 2.0, 0.0, 0.0, 0.0, 0.0, 0.0] - coefficients['2sn6'] = [6.0, 3.0, -4.0, 1.0, 0.0, 0.0, 0.0] - coefficients['3msn6'] = [6.0, 3.0, -2.0, -1.0, 0.0, 0.0, 0.0] - coefficients['msl6'] = [6.0, 3.0, -2.0, -1.0, 0.0, 0.0, 2.0] - coefficients['snk6'] = [6.0, 3.0, -2.0, 1.0, 0.0, 0.0, 0.0] - coefficients['mkl6'] = [6.0, 3.0, 0.0, -1.0, 0.0, 0.0, 2.0] - coefficients['3mkn6'] = [6.0, 3.0, 0.0, -1.0, 0.0, 0.0, 0.0] - coefficients['2sm6'] = [6.0, 4.0, -4.0, 0.0, 0.0, 0.0, 0.0] - coefficients['msk6'] = [6.0, 4.0, -2.0, 0.0, 0.0, 0.0, 0.0] - coefficients['2km6'] = [6.0, 4.0, 0.0, 0.0, 0.0, 0.0, 0.0] - coefficients['2(ms)n6'] = [6.0, 5.0, -4.0, -1.0, 0.0, 0.0, 0.0] - coefficients['2mskn6'] = [6.0, 5.0, -2.0, -1.0, 0.0, 0.0, 0.0] - coefficients['2t6'] = [6.0, 6.0, -8.0, 0.0, 0.0, 0.0, 0.0] - coefficients['t6'] = [6.0, 6.0, -7.0, 0.0, 0.0, 0.0, 0.0] - coefficients['s6'] = [6.0, 6.0, -6.0, 0.0, 0.0, 0.0, 0.0] - coefficients['r6'] = [6.0, 6.0, -5.0, 0.0, 0.0, 0.0, 0.0] - coefficients['2r6'] = [6.0, 6.0, -4.0, 0.0, 0.0, 0.0, 0.0] - coefficients['2sk6'] = [6.0, 6.0, -4.0, 0.0, 0.0, 0.0, 0.0] - coefficients['k6'] = [6.0, 6.0, 0.0, 0.0, 0.0, 0.0, 0.0] - coefficients['4sm6'] = [6.0, 8.0, -8.0, 0.0, 0.0, 0.0, 0.0] - coefficients['2mno7'] = [7.0, -2.0, 0.0, 1.0, 0.0, 0.0, -1.0] - coefficients['4mk7'] = [7.0, -1.0, 0.0, 0.0, 0.0, 0.0, -1.0] - coefficients['3mo7'] = [7.0, -1.0, 0.0, 0.0, 0.0, 0.0, -1.0] - coefficients['2nmk7'] = [7.0, -1.0, 0.0, 2.0, 0.0, 0.0, 1.0] - # = 2MNK7 = MNKO7 - coefficients['m7'] = [7.0, 0.0, 0.0, 1.0, 0.0, 0.0, 1.0] - coefficients['3mp7'] = [7.0, 1.0, -2.0, 0.0, 0.0, 0.0, -1.0] - coefficients['2mso7'] = [7.0, 1.0, -2.0, 0.0, 0.0, 0.0, -1.0] - coefficients['3mk7'] = [7.0, 1.0, 0.0, 0.0, 0.0, 0.0, 1.0] - # = MSKO7 (noaa) - coefficients['2msk7'] = [7.0, 3.0, -2.0, 0.0, 0.0, 0.0, 1.0] - coefficients['msko7'] = [7.0, 3.0, -2.0, 0.0, 0.0, 0.0, -1.0] - coefficients['2t7'] = [7.0, 7.0, -9.0, 0.0, 0.0, 0.0, 0.0] - coefficients['3sp7'] = [7.0, 7.0, -8.0, 0.0, 0.0, 0.0, -1.0] - coefficients['t7'] = [7.0, 7.0, -8.0, 0.0, 0.0, 0.0, 0.0] - coefficients['s7'] = [7.0, 7.0, -7.0, 0.0, 0.0, 0.0, 0.0] - coefficients['r7'] = [7.0, 7.0, -6.0, 0.0, 0.0, 0.0, 0.0] - coefficients['3sk7'] = [7.0, 7.0, -6.0, 0.0, 0.0, 0.0, 1.0] - coefficients['2r7'] = [7.0, 7.0, -5.0, 0.0, 0.0, 0.0, 0.0] - coefficients['3r7'] = [7.0, 7.0, -4.0, 0.0, 0.0, 0.0, 0.0] - coefficients['4r7'] = [7.0, 7.0, -3.0, 0.0, 0.0, 0.0, 0.0] - coefficients['k7'] = [7.0, 7.0, 0.0, 0.0, 0.0, 0.0, 1.0] - coefficients['3m2ns8'] = [8.0, -4.0, 2.0, 2.0, 0.0, 0.0, 0.0] - coefficients['4mns8'] = [8.0, -3.0, 2.0, 1.0, 0.0, 0.0, 0.0] - coefficients['5mk8'] = [8.0, -2.0, 0.0, 0.0, 0.0, 0.0, 0.0] - coefficients['2mn8'] = [8.0, -2.0, 0.0, 2.0, 0.0, 0.0, 0.0] - coefficients['2(mn)8'] = [8.0, -2.0, 0.0, 2.0, 0.0, 0.0, 0.0] - coefficients['5ms8'] = [8.0, -2.0, 2.0, 0.0, 0.0, 0.0, 0.0] - coefficients['3mn8'] = [8.0, -1.0, 0.0, 1.0, 0.0, 0.0, 0.0] - coefficients['3mnu8'] = [8.0, -1.0, 2.0, -1.0, 0.0, 0.0, 0.0] - coefficients['3mn8'] = [8.0, -1.0, 2.0, -1.0, 0.0, 0.0, 0.0] - coefficients['4mls8'] = [8.0, -1.0, 2.0, -1.0, 0.0, 0.0, 2.0] - coefficients['ma8'] = [8.0, 0.0, -1.0, 0.0, 0.0, 0.0, 0.0] - coefficients['m8'] = [8.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0] - coefficients['mb8'] = [8.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0] - coefficients['2msn8'] = [8.0, 1.0, -2.0, 1.0, 0.0, 0.0, 0.0] - coefficients['3ml8'] = [8.0, 1.0, 0.0, -1.0, 0.0, 0.0, 2.0] - coefficients['2mnk8'] = [8.0, 1.0, 0.0, 1.0, 0.0, 0.0, 0.0] - coefficients['3mt8'] = [8.0, 2.0, -3.0, 0.0, 0.0, 1.0, 0.0] - coefficients['3ms8'] = [8.0, 2.0, -2.0, 0.0, 0.0, 0.0, 0.0] - coefficients['3mk8'] = [8.0, 2.0, 0.0, 0.0, 0.0, 0.0, 0.0] - coefficients['2smn8'] = [8.0, 3.0, -4.0, 1.0, 0.0, 0.0, 0.0] - coefficients['2msl8'] = [8.0, 3.0, -2.0, -1.0, 0.0, 0.0, 2.0] - coefficients['msnk8'] = [8.0, 3.0, -2.0, 1.0, 0.0, 0.0, 0.0] - coefficients['4msn8'] = [8.0, 3.0, 0.0, -1.0, 0.0, 0.0, 0.0] - coefficients['2(ms)8'] = [8.0, 4.0, -4.0, 0.0, 0.0, 0.0, 0.0] - coefficients['2msk8'] = [8.0, 4.0, -2.0, 0.0, 0.0, 0.0, 0.0] - coefficients['2(mk)8'] = [8.0, 4.0, 0.0, 0.0, 0.0, 0.0, 0.0] - coefficients['s8'] = [8.0, 8.0, -8.0, 0.0, 0.0, 0.0, 0.0] - coefficients['k8'] = [8.0, 8.0, 0.0, 0.0, 0.0, 0.0, 0.0] - coefficients['4mo9'] = [9.0, -1.0, 0.0, 0.0, 0.0, 0.0, -1.0] - coefficients['2(mn)k9'] = [9.0, -1.0, 0.0, 2.0, 0.0, 0.0, 1.0] - coefficients['2m2nk9'] = [9.0, -1.0, 0.0, 2.0, 0.0, 0.0, 1.0] - coefficients['3mnk9'] = [9.0, 0.0, 0.0, 1.0, 0.0, 0.0, 1.0] - coefficients['4mp9'] = [9.0, 1.0, -2.0, 0.0, 0.0, 0.0, -1.0] - coefficients['4ms9'] = [9.0, 1.0, -1.0, 0.0, 0.0, 0.0, 2.0] - coefficients['4mk9'] = [9.0, 1.0, 0.0, 0.0, 0.0, 0.0, 1.0] - coefficients['3msk9'] = [9.0, 3.0, -2.0, 0.0, 0.0, 0.0, 1.0] - coefficients['s9'] = [9.0, 9.0, -9.0, 0.0, 0.0, 0.0, 0.0] - coefficients['k9'] = [9.0, 9.0, 0.0, 0.0, 0.0, 0.0, 1.0] - coefficients['4mn10'] = [10.0, -1, 0.0, 1.0, 0.0, 0.0, 0.0] - coefficients['m10'] = [10.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0] - coefficients['3msn10'] = [10.0, 1.0, -2, 1.0, 0.0, 0.0, 0.0] - coefficients['4ms10'] = [10.0, 2.0, -2, 0.0, 0.0, 0.0, 0.0] - coefficients['4mk10'] = [10.0, 2.0, 0.0, 0.0, 0.0, 0.0, 0.0] - coefficients['3msl10'] = [10.0, 3.0, -2, -1.0, 0.0, 0.0, 2.0] - coefficients['3m2s10'] = [10.0, 4.0, -4, 0.0, 0.0, 0.0, 0.0] - coefficients['3msk10'] = [10.0, 4.0, -2, 0.0, 0.0, 0.0, 0.0] - coefficients['s10'] = [10.0, 10.0, -10.0, 0.0, 0.0, 0.0, 0.0] - coefficients['4msk11'] = [11.0, 3.0, -2, 0.0, 0.0, 0.0, 1.0] - coefficients['s11'] = [11.0, 11.0, -11.0, 0.0, 0.0, 0.0, 0.0] - coefficients['5mn12'] = [12.0, -1, 0.0, 1.0, 0.0, 0.0, 0.0] - coefficients['m12'] = [12.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0] - coefficients['4msn12'] = [12.0, 1.0, -2, 1.0, 0.0, 0.0, 0.0] - coefficients['4mns12'] = [12.0, 1.0, -2, 1.0, 0.0, 0.0, 0.0] - coefficients['5ms12'] = [12.0, 2.0, -2, 0.0, 0.0, 0.0, 0.0] - coefficients['4msl12'] = [12.0, 3.0, -2, -1.0, 0.0, 0.0, 2.0] - coefficients['4m2s12'] = [12.0, 4.0, -4, 0.0, 0.0, 0.0, 0.0] - coefficients['s12'] = [12.0, 12.0, -12.0, 0.0, 0.0, 0.0, 0.0] - coefficients['m14'] = [14.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0] - coefficients['5msn14'] = [14.0, 1.0, -2.0, 1.0, 0.0, 0.0, 0.0] - coefficients['6ms14'] = [14.0, 2.0, -2.0, 0.0, 0.0, 0.0, 0.0] - coefficients['5m2s14'] = [14.0, 4.0, -4.0, 0.0, 0.0, 0.0, 0.0] # set constituents to be iterable if isinstance(constituents, str): diff --git a/pyTMD/data/doodson.json b/pyTMD/data/doodson.json new file mode 100644 index 00000000..aca114f6 --- /dev/null +++ b/pyTMD/data/doodson.json @@ -0,0 +1,485 @@ +{ + "z0": [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], + "node": [0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 2.0], + "omega0": [0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 2.0], + "sa": [0.0, 0.0, 1.0, 0.0, 0.0, -1.0, 0.0], + "ssa": [0.0, 0.0, 2.0, 0.0, 0.0, 0.0, 0.0], + "sta": [0.0, 0.0, 3.0, 0.0, 0.0, -1.0, 0.0], + "st": [0.0, 0.0, 3.0, 0.0, 0.0, 0.0, 0.0], + "msm": [0.0, 1.0, -2.0, 1.0, 0.0, 0.0, 0.0], + "mm": [0.0, 1.0, 0.0, -1.0, 0.0, 0.0, 0.0], + "msfa": [0.0, 2.0, -3.0, 0.0, 0.0, 0.0, 0.0], + "msf": [0.0, 2.0, -2.0, 0.0, 0.0, 0.0, 0.0], + "msfb": [0.0, 2.0, -1.0, 0.0, 0.0, 0.0, 0.0], + "mfa": [0.0, 2.0, -1.0, 0.0, 0.0, 0.0, 0.0], + "mf-": [0.0, 2.0, 0.0, 0.0, -1.0, 0.0, 0.0], + "mf": [0.0, 2.0, 0.0, 0.0, 0.0, 0.0, 0.0], + "mf+": [0.0, 2.0, 0.0, 0.0, 1.0, 0.0, 0.0], + "mfn": [0.0, 2.0, 0.0, 0.0, 1.0, 0.0, 0.0], + "mfb": [0.0, 2.0, 1.0, 0.0, 0.0, 0.0, 0.0], + "sn0": [0.0, 3.0, -2.0, -1.0, 0.0, 0.0, 0.0], + "mst": [0.0, 3.0, -2.0, 1.0, 0.0, 0.0, 0.0], + "mt": [0.0, 3.0, 0.0, -1.0, 0.0, 0.0, 0.0], + "mtm": [0.0, 3.0, 0.0, -1.0, 0.0, 0.0, 0.0], + "msqm": [0.0, 4.0, -2.0, 0.0, 0.0, 0.0, 0.0], + "mq": [0.0, 4.0, 0.0, -2.0, 0.0, 0.0, 0.0], + "2smn0": [0.0, 5.0, -4.0, -1.0, 0.0, 0.0, 0.0], + "msp": [0.0, 5.0, -2.0, -1.0, 0.0, 0.0, 0.0], + "mp": [0.0, 5.0, 0.0, -3.0, 0.0, 0.0, 0.0], + "2qj1": [1.0, -6.0, 0.0, 3.0, 0.0, 0.0, 1.0], + "2qk1": [1.0, -5.0, 0.0, 2.0, 0.0, 0.0, 1.0], + "2qs1": [1.0, -5.0, 1.0, 2.0, 0.0, 0.0, 0.0], + "2qp1": [1.0, -5.0, 2.0, 2.0, 0.0, 0.0, -1.0], + "2oj1": [1.0, -4.0, 0.0, 1.0, 0.0, 0.0, 1.0], + "alpha1": [1.0, -4.0, 2.0, 1.0, 0.0, 0.0, -1.0], + "2ok1": [1.0, -3.0, 0.0, 0.0, 0.0, 0.0, 1.0], + "2q1'": [1.0, -3.0, 0.0, 1.0, 0.0, 0.0, 2.0], + "2q1": [1.0, -3.0, 0.0, 2.0, 0.0, 0.0, -1.0], + "sigma1": [1.0, -3.0, 2.0, 0.0, 0.0, 0.0, -1.0], + "q1'": [1.0, -2.0, 0.0, 0.0, 0.0, 0.0, 2.0], + "q1": [1.0, -2.0, 0.0, 1.0, 0.0, 0.0, -1.0], + "rho1": [1.0, -2.0, 2.0, -1.0, 0.0, 0.0, -1.0], + "np1": [1.0, -2.0, 2.0, 1.0, 0.0, 0.0, 1.0], + "opk1": [1.0, -1.0, -2.0, 0.0, 0.0, 0.0, 1.0], + "oa1": [1.0, -1.0, -1.0, 0.0, 0.0, 0.0, -1.0], + "o1n": [1.0, -1.0, 0.0, 0.0, -1.0, 0.0, -1.0], + "o1-": [1.0, -1.0, 0.0, 0.0, -1.0, 0.0, -1.0], + "o1": [1.0, -1.0, 0.0, 0.0, 0.0, 0.0, -1.0], + "o1+": [1.0, -1.0, 0.0, 0.0, 1.0, 0.0, -1.0], + "o1'": [1.0, -1.0, 0.0, 1.0, 0.0, 0.0, 2.0], + "ob1": [1.0, -1.0, 1.0, 0.0, 0.0, 0.0, -1.0], + "ms1": [1.0, -1.0, 1.0, 0.0, 0.0, 0.0, 2.0], + "mp1": [1.0, -1.0, 2.0, 0.0, 0.0, 0.0, 1.0], + "tau1": [1.0, -1.0, 2.0, 0.0, 0.0, 0.0, 1.0], + 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0.0], + "mop4": [4.0, 0.0, -2.0, 0.0, 0.0, 0.0, 2.0], + "ma4": [4.0, 0.0, -1.0, 0.0, 0.0, 0.0, 0.0], + "m4": [4.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], + "mb4": [4.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0], + "2mks4": [4.0, 0.0, 2.0, 0.0, 0.0, 0.0, 0.0], + "sn4": [4.0, 1.0, -2.0, 1.0, 0.0, 0.0, 0.0], + "3mn4": [4.0, 1.0, 0.0, -1.0, 0.0, 0.0, 0.0], + "ml4": [4.0, 1.0, 0.0, -1.0, 0.0, 0.0, 2.0], + "nk4": [4.0, 1.0, 0.0, 1.0, 0.0, 0.0, 0.0], + "2smk4": [4.0, 2.0, -4.0, 0.0, 0.0, 0.0, 0.0], + "2pm4": [4.0, 2.0, -4.0, 0.0, 0.0, 0.0, 2.0], + "mt4": [4.0, 2.0, -3.0, 0.0, 0.0, 1.0, 0.0], + "ms4": [4.0, 2.0, -2.0, 0.0, 0.0, 0.0, 0.0], + "mr4": [4.0, 2.0, -1.0, 0.0, 0.0, -1.0, 2.0], + "mk4": [4.0, 2.0, 0.0, 0.0, 0.0, 0.0, 0.0], + "2snm4": [4.0, 3.0, -4.0, 1.0, 0.0, 0.0, 0.0], + "2msn4": [4.0, 3.0, -2.0, -1.0, 0.0, 0.0, 0.0], + "sl4": [4.0, 3.0, -2.0, -1.0, 0.0, 0.0, 2.0], + "2mkn4": [4.0, 3.0, 0.0, -1.0, 0.0, 0.0, 0.0], + "mkj4": [4.0, 3.0, 0.0, -1.0, 0.0, 0.0, 2.0], + "2t4": [4.0, 4.0, -6.0, 0.0, 0.0, 0.0, 0.0], + "t4": [4.0, 4.0, -5.0, 0.0, 0.0, 0.0, 0.0], + "st4": [4.0, 4.0, -5.0, 0.0, 0.0, 1.0, 0.0], + "s4": [4.0, 4.0, -4.0, 0.0, 0.0, 0.0, 0.0], + "r4": [4.0, 4.0, -3.0, 0.0, 0.0, 0.0, 0.0], + "2r4": [4.0, 4.0, -2.0, 0.0, 0.0, 0.0, 0.0], + "sk4": [4.0, 4.0, -2.0, 0.0, 0.0, 0.0, 0.0], + "3ks4": [4.0, 4.0, -1.0, 0.0, 0.0, 0.0, -1.0], + "k4": [4.0, 4.0, 0.0, 0.0, 0.0, 0.0, 0.0], + "3sm4": [4.0, 6.0, -6.0, 0.0, 0.0, 0.0, 0.0], + "2(kj)4": [4.0, 6.0, 0.0, -2.0, 0.0, 0.0, 2.0], + "2no5": [5.0, -3.0, 0.0, 2.0, 0.0, 0.0, -1.0], + "mno5": [5.0, -2.0, 0.0, 1.0, 0.0, 0.0, -1.0], + "2mq5": [5.0, -2.0, 0.0, 1.0, 0.0, 0.0, -1.0], + "2nkms5": [5.0, -2.0, 2.0, 2.0, 0.0, 0.0, 1.0], + "2mo5": [5.0, -1.0, 0.0, 0.0, 0.0, 0.0, -1.0], + "mnm5": [5.0, -1.0, 0.0, 1.0, 0.0, 0.0, 2.0], + "2nk5": [5.0, -1.0, 0.0, 2.0, 0.0, 0.0, 1.0], + "3ms5": [5.0, -1.0, 1.0, 0.0, 0.0, 0.0, 2.0], + "3mp5": [5.0, -1.0, 2.0, 0.0, 0.0, 0.0, 1.0], + "nso5": [5.0, 0.0, -2.0, 1.0, 0.0, 0.0, -1.0], + "m5": [5.0, 0.0, 0.0, 0.0, 0.0, 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0.0, 2.0], + "2(mn)k6": [6.0, -4.0, 0.0, 2.0, 0.0, 0.0, 0.0], + "5mks6": [6.0, -4.0, 2.0, 0.0, 0.0, 0.0, 0.0], + "2(mn)s6": [6.0, -4.0, 2.0, 2.0, 0.0, 0.0, 0.0], + "5m2s6": [6.0, -4.0, 4.0, 0.0, 0.0, 0.0, 0.0], + "3mnk6": [6.0, -3.0, 0.0, 1.0, 0.0, 0.0, 0.0], + "n6": [6.0, -3.0, 0.0, 3.0, 0.0, 0.0, 0.0], + "3mns6": [6.0, -3.0, 2.0, 1.0, 0.0, 0.0, 0.0], + "2nmls6": [6.0, -3.0, 2.0, 1.0, 0.0, 0.0, 2.0], + "3nks6": [6.0, -3.0, 2.0, 3.0, 0.0, 0.0, 0.0], + "3mnus6": [6.0, -3.0, 4.0, -1.0, 0.0, 0.0, 0.0], + "4mk6": [6.0, -2.0, 0.0, 0.0, 0.0, 0.0, 0.0], + "2nm6": [6.0, -2.0, 0.0, 2.0, 0.0, 0.0, 0.0], + "m2n6": [6.0, -2.0, 0.0, 2.0, 0.0, 0.0, 0.0], + "4ms6": [6.0, -2.0, 2.0, 0.0, 0.0, 0.0, 0.0], + "2mlns6": [6.0, -2.0, 2.0, 0.0, 0.0, 0.0, 2.0], + "2mnls6": [6.0, -2.0, 2.0, 0.0, 0.0, 0.0, 2.0], + "2nmks6": [6.0, -2.0, 2.0, 2.0, 0.0, 0.0, 0.0], + "2msnk6": [6.0, -1.0, -2.0, 1.0, 0.0, 0.0, 0.0], + "2mn6": [6.0, -1.0, 2.0, -1.0, 0.0, 0.0, 0.0], + "2mnu6": [6.0, -1.0, 2.0, -1.0, 0.0, 0.0, 0.0], + "3mls6": [6.0, -1.0, 2.0, -1.0, 0.0, 0.0, 2.0], + "2mno6": [6.0, -1.0, 2.0, -1.0, 0.0, 0.0, 0.0], + "2mnks6": [6.0, -1.0, 2.0, 1.0, 0.0, 0.0, 0.0], + "3msk6": [6.0, 0.0, -2.0, 0.0, 0.0, 0.0, 0.0], + "ma6": [6.0, 0.0, -1.0, 0.0, 0.0, 0.0, 0.0], + "m6": [6.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], + "2nk6": [6.0, 0.0, 0.0, 2.0, 0.0, 0.0, 0.0], + "mb6": [6.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0], + "3mks6": [6.0, 0.0, 2.0, 0.0, 0.0, 0.0, 0.0], + "msn6": [6.0, 1.0, -2.0, 1.0, 0.0, 0.0, 0.0], + "4mn6": [6.0, 1.0, 0.0, -1.0, 0.0, 0.0, 0.0], + "2ml6": [6.0, 1.0, 0.0, -1.0, 0.0, 0.0, 2.0], + "mnk6": [6.0, 1.0, 0.0, 1.0, 0.0, 0.0, 0.0], + "mkn6": [6.0, 1.0, 0.0, 1.0, 0.0, 0.0, 0.0], + "mknu6": [6.0, 1.0, 2.0, -1.0, 0.0, 0.0, 0.0], + "2(ms)k6": [6.0, 2.0, -4.0, 0.0, 0.0, 0.0, 0.0], + "2mt6": [6.0, 2.0, -3.0, 0.0, 0.0, 1.0, 0.0], + "2ms6": [6.0, 2.0, -2.0, 0.0, 0.0, 0.0, 0.0], + "2mr6": [6.0, 2.0, -1.0, 0.0, 0.0, -1.0, 2.0], + "2mk6": [6.0, 2.0, 0.0, 0.0, 0.0, 0.0, 0.0], + "2sn6": [6.0, 3.0, -4.0, 1.0, 0.0, 0.0, 0.0], + "3msn6": [6.0, 3.0, -2.0, -1.0, 0.0, 0.0, 0.0], + "msl6": [6.0, 3.0, -2.0, -1.0, 0.0, 0.0, 2.0], + "snk6": [6.0, 3.0, -2.0, 1.0, 0.0, 0.0, 0.0], + "mkl6": [6.0, 3.0, 0.0, -1.0, 0.0, 0.0, 2.0], + "3mkn6": [6.0, 3.0, 0.0, -1.0, 0.0, 0.0, 0.0], + "2sm6": [6.0, 4.0, -4.0, 0.0, 0.0, 0.0, 0.0], + "msk6": [6.0, 4.0, -2.0, 0.0, 0.0, 0.0, 0.0], + "2km6": [6.0, 4.0, 0.0, 0.0, 0.0, 0.0, 0.0], + "2(ms)n6": [6.0, 5.0, -4.0, -1.0, 0.0, 0.0, 0.0], + "2mskn6": [6.0, 5.0, -2.0, -1.0, 0.0, 0.0, 0.0], + "2t6": [6.0, 6.0, -8.0, 0.0, 0.0, 0.0, 0.0], + "t6": [6.0, 6.0, -7.0, 0.0, 0.0, 0.0, 0.0], + "s6": [6.0, 6.0, -6.0, 0.0, 0.0, 0.0, 0.0], + "r6": [6.0, 6.0, -5.0, 0.0, 0.0, 0.0, 0.0], + "2r6": [6.0, 6.0, -4.0, 0.0, 0.0, 0.0, 0.0], + "2sk6": [6.0, 6.0, -4.0, 0.0, 0.0, 0.0, 0.0], + "k6": [6.0, 6.0, 0.0, 0.0, 0.0, 0.0, 0.0], + "4sm6": [6.0, 8.0, -8.0, 0.0, 0.0, 0.0, 0.0], + "2mno7": [7.0, -2.0, 0.0, 1.0, 0.0, 0.0, -1.0], + "4mk7": [7.0, -1.0, 0.0, 0.0, 0.0, 0.0, -1.0], + "3mo7": [7.0, -1.0, 0.0, 0.0, 0.0, 0.0, -1.0], + "2nmk7": [7.0, -1.0, 0.0, 2.0, 0.0, 0.0, 1.0], + "m7": [7.0, 0.0, 0.0, 1.0, 0.0, 0.0, 1.0], + "3mp7": [7.0, 1.0, -2.0, 0.0, 0.0, 0.0, -1.0], + "2mso7": [7.0, 1.0, -2.0, 0.0, 0.0, 0.0, -1.0], + "3mk7": [7.0, 1.0, 0.0, 0.0, 0.0, 0.0, 1.0], + "2msk7": [7.0, 3.0, -2.0, 0.0, 0.0, 0.0, 1.0], + "msko7": [7.0, 3.0, -2.0, 0.0, 0.0, 0.0, -1.0], + "2t7": [7.0, 7.0, -9.0, 0.0, 0.0, 0.0, 0.0], + "3sp7": [7.0, 7.0, -8.0, 0.0, 0.0, 0.0, -1.0], + "t7": [7.0, 7.0, -8.0, 0.0, 0.0, 0.0, 0.0], + "s7": [7.0, 7.0, -7.0, 0.0, 0.0, 0.0, 0.0], + "r7": [7.0, 7.0, -6.0, 0.0, 0.0, 0.0, 0.0], + "3sk7": [7.0, 7.0, -6.0, 0.0, 0.0, 0.0, 1.0], + "2r7": [7.0, 7.0, -5.0, 0.0, 0.0, 0.0, 0.0], + "3r7": [7.0, 7.0, -4.0, 0.0, 0.0, 0.0, 0.0], + "4r7": [7.0, 7.0, -3.0, 0.0, 0.0, 0.0, 0.0], + "k7": [7.0, 7.0, 0.0, 0.0, 0.0, 0.0, 1.0], + "3m2ns8": [8.0, -4.0, 2.0, 2.0, 0.0, 0.0, 0.0], + "4mns8": [8.0, -3.0, 2.0, 1.0, 0.0, 0.0, 0.0], + "5mk8": [8.0, -2.0, 0.0, 0.0, 0.0, 0.0, 0.0], + "2mn8": [8.0, -2.0, 0.0, 2.0, 0.0, 0.0, 0.0], + "2(mn)8": [8.0, -2.0, 0.0, 2.0, 0.0, 0.0, 0.0], + "5ms8": [8.0, -2.0, 2.0, 0.0, 0.0, 0.0, 0.0], + "3mn8": [8.0, -1.0, 2.0, -1.0, 0.0, 0.0, 0.0], + "3mnu8": [8.0, -1.0, 2.0, -1.0, 0.0, 0.0, 0.0], + "4mls8": [8.0, -1.0, 2.0, -1.0, 0.0, 0.0, 2.0], + "ma8": [8.0, 0.0, -1.0, 0.0, 0.0, 0.0, 0.0], + "m8": [8.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], + "mb8": [8.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0], + "2msn8": [8.0, 1.0, -2.0, 1.0, 0.0, 0.0, 0.0], + "3ml8": [8.0, 1.0, 0.0, -1.0, 0.0, 0.0, 2.0], + "2mnk8": [8.0, 1.0, 0.0, 1.0, 0.0, 0.0, 0.0], + "3mt8": [8.0, 2.0, -3.0, 0.0, 0.0, 1.0, 0.0], + "3ms8": [8.0, 2.0, -2.0, 0.0, 0.0, 0.0, 0.0], + "3mk8": [8.0, 2.0, 0.0, 0.0, 0.0, 0.0, 0.0], + "2smn8": [8.0, 3.0, -4.0, 1.0, 0.0, 0.0, 0.0], + "2msl8": [8.0, 3.0, -2.0, -1.0, 0.0, 0.0, 2.0], + "msnk8": [8.0, 3.0, -2.0, 1.0, 0.0, 0.0, 0.0], + "4msn8": [8.0, 3.0, 0.0, -1.0, 0.0, 0.0, 0.0], + "2(ms)8": [8.0, 4.0, -4.0, 0.0, 0.0, 0.0, 0.0], + "2msk8": [8.0, 4.0, -2.0, 0.0, 0.0, 0.0, 0.0], + "2(mk)8": [8.0, 4.0, 0.0, 0.0, 0.0, 0.0, 0.0], + "s8": [8.0, 8.0, -8.0, 0.0, 0.0, 0.0, 0.0], + "k8": [8.0, 8.0, 0.0, 0.0, 0.0, 0.0, 0.0], + "4mo9": [9.0, -1.0, 0.0, 0.0, 0.0, 0.0, -1.0], + "2(mn)k9": [9.0, -1.0, 0.0, 2.0, 0.0, 0.0, 1.0], + "2m2nk9": [9.0, -1.0, 0.0, 2.0, 0.0, 0.0, 1.0], + "3mnk9": [9.0, 0.0, 0.0, 1.0, 0.0, 0.0, 1.0], + "4mp9": [9.0, 1.0, -2.0, 0.0, 0.0, 0.0, -1.0], + "4ms9": [9.0, 1.0, -1.0, 0.0, 0.0, 0.0, 2.0], + "4mk9": [9.0, 1.0, 0.0, 0.0, 0.0, 0.0, 1.0], + "3msk9": [9.0, 3.0, -2.0, 0.0, 0.0, 0.0, 1.0], + "s9": [9.0, 9.0, -9.0, 0.0, 0.0, 0.0, 0.0], + "k9": [9.0, 9.0, 0.0, 0.0, 0.0, 0.0, 1.0], + "4mn10": [10.0, -1, 0.0, 1.0, 0.0, 0.0, 0.0], + "m10": [10.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], + "3msn10": [10.0, 1.0, -2, 1.0, 0.0, 0.0, 0.0], + "4ms10": [10.0, 2.0, -2, 0.0, 0.0, 0.0, 0.0], + "4mk10": [10.0, 2.0, 0.0, 0.0, 0.0, 0.0, 0.0], + "3msl10": [10.0, 3.0, -2, -1.0, 0.0, 0.0, 2.0], + "3m2s10": [10.0, 4.0, -4, 0.0, 0.0, 0.0, 0.0], + "3msk10": [10.0, 4.0, -2, 0.0, 0.0, 0.0, 0.0], + "s10": [10.0, 10.0, -10.0, 0.0, 0.0, 0.0, 0.0], + "4msk11": [11.0, 3.0, -2, 0.0, 0.0, 0.0, 1.0], + "s11": [11.0, 11.0, -11.0, 0.0, 0.0, 0.0, 0.0], + "5mn12": [12.0, -1, 0.0, 1.0, 0.0, 0.0, 0.0], + "m12": [12.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], + "4msn12": [12.0, 1.0, -2, 1.0, 0.0, 0.0, 0.0], + "4mns12": [12.0, 1.0, -2, 1.0, 0.0, 0.0, 0.0], + "5ms12": [12.0, 2.0, -2, 0.0, 0.0, 0.0, 0.0], + "4msl12": [12.0, 3.0, -2, -1.0, 0.0, 0.0, 2.0], + "4m2s12": [12.0, 4.0, -4, 0.0, 0.0, 0.0, 0.0], + "s12": [12.0, 12.0, -12.0, 0.0, 0.0, 0.0, 0.0], + "m14": [14.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], + "5msn14": [14.0, 1.0, -2.0, 1.0, 0.0, 0.0, 0.0], + "6ms14": [14.0, 2.0, -2.0, 0.0, 0.0, 0.0, 0.0], + "5m2s14": [14.0, 4.0, -4.0, 0.0, 0.0, 0.0, 0.0] +} \ No newline at end of file diff --git a/pyproject.toml b/pyproject.toml index e1d75c62..c0916fe3 100644 --- a/pyproject.toml +++ b/pyproject.toml @@ -92,6 +92,7 @@ omit = [ "pyTMD/convert_ll_xy.py", "pyTMD/load_constituent.py", "pyTMD/load_nodal_corrections.py", + "test/_coefficients_to_json.py", "test/_def_to_json.py", "providers/*.py", ] diff --git a/test/_coefficients_to_json.py b/test/_coefficients_to_json.py new file mode 100644 index 00000000..9a6aa1d8 --- /dev/null +++ b/test/_coefficients_to_json.py @@ -0,0 +1,595 @@ +""" +coefficients_to_json.py (10/2024) +Converts the coefficients table to a json file +""" +import re +import copy +import json +import inspect +import pathlib +import argparse +import pyTMD.utilities +from collections import OrderedDict + +# current file path +filename = inspect.getframeinfo(inspect.currentframe()).filename +filepath = pathlib.Path(filename).absolute().parent + +def coefficients_table(): + coefficients = OrderedDict() + coefficients['z0'] = [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0] + coefficients['node'] = [0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 2.0] + coefficients['omega0'] = [0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 2.0] + # With p' + coefficients['sa'] = [0.0, 0.0, 1.0, 0.0, 0.0, -1.0, 0.0] + # # Without p' + # coefficients['sa'] = [0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0] + coefficients['ssa'] = [0.0, 0.0, 2.0, 0.0, 0.0, 0.0, 0.0] + # With p' + coefficients['sta'] = [0.0, 0.0, 3.0, 0.0, 0.0, -1.0, 0.0] + # # Without p' + # coefficients['sta'] = [0.0, 0.0, 3.0, 0.0, 0.0, 0.0, 0.0] + coefficients['st'] = [0.0, 0.0, 3.0, 0.0, 0.0, 0.0, 0.0] + coefficients['msm'] = [0.0, 1.0, -2.0, 1.0, 0.0, 0.0, 0.0] + coefficients['mm'] = [0.0, 1.0, 0.0, -1.0, 0.0, 0.0, 0.0] + # annual sideline + coefficients['msfa'] = [0.0, 2.0, -3.0, 0.0, 0.0, 0.0, 0.0] + coefficients['msf'] = [0.0, 2.0, -2.0, 0.0, 0.0, 0.0, 0.0] + # annual sideline + coefficients['msfb'] = [0.0, 2.0, -1.0, 0.0, 0.0, 0.0, 0.0] + coefficients['mfa'] = [0.0, 2.0, -1.0, 0.0, 0.0, 0.0, 0.0] + coefficients['mf-'] = [0.0, 2.0, 0.0, 0.0, -1.0, 0.0, 0.0] + coefficients['mf'] = [0.0, 2.0, 0.0, 0.0, 0.0, 0.0, 0.0] + # nodal line + coefficients['mf+'] = [0.0, 2.0, 0.0, 0.0, 1.0, 0.0, 0.0] + # nodal line + coefficients['mfn'] = [0.0, 2.0, 0.0, 0.0, 1.0, 0.0, 0.0] + coefficients['mfb'] = [0.0, 2.0, 1.0, 0.0, 0.0, 0.0, 0.0] + coefficients['sn0'] = [0.0, 3.0, -2.0, -1.0, 0.0, 0.0, 0.0] + coefficients['mst'] = [0.0, 3.0, -2.0, 1.0, 0.0, 0.0, 0.0] + coefficients['mt'] = [0.0, 3.0, 0.0, -1.0, 0.0, 0.0, 0.0] + coefficients['mtm'] = [0.0, 3.0, 0.0, -1.0, 0.0, 0.0, 0.0] + coefficients['msqm'] = [0.0, 4.0, -2.0, 0.0, 0.0, 0.0, 0.0] + coefficients['mq'] = [0.0, 4.0, 0.0, -2.0, 0.0, 0.0, 0.0] + coefficients['2smn0'] = [0.0, 5.0, -4.0, -1.0, 0.0, 0.0, 0.0] + coefficients['msp'] = [0.0, 5.0, -2.0, -1.0, 0.0, 0.0, 0.0] + coefficients['mp'] = [0.0, 5.0, 0.0, -3.0, 0.0, 0.0, 0.0] + coefficients['2qj1'] = [1.0, -6.0, 0.0, 3.0, 0.0, 0.0, 1.0] + coefficients['2qk1'] = [1.0, -5.0, 0.0, 2.0, 0.0, 0.0, 1.0] + coefficients['2qs1'] = [1.0, -5.0, 1.0, 2.0, 0.0, 0.0, 0.0] + coefficients['2qp1'] = [1.0, -5.0, 2.0, 2.0, 0.0, 0.0, -1.0] + coefficients['2oj1'] = [1.0, -4.0, 0.0, 1.0, 0.0, 0.0, 1.0] + coefficients['alpha1'] = [1.0, -4.0, 2.0, 1.0, 0.0, 0.0, -1.0] + coefficients['2ok1'] = [1.0, -3.0, 0.0, 0.0, 0.0, 0.0, 1.0] + # 3rd degree terms + coefficients["2q1'"] = [1.0, -3.0, 0.0, 1.0, 0.0, 0.0, 2.0] + coefficients['2q1'] = [1.0, -3.0, 0.0, 2.0, 0.0, 0.0, -1.0] + coefficients['sigma1'] = [1.0, -3.0, 2.0, 0.0, 0.0, 0.0, -1.0] + # 3rd degree terms + coefficients["q1'"] = [1.0, -2.0, 0.0, 0.0, 0.0, 0.0, 2.0] + coefficients['q1'] = [1.0, -2.0, 0.0, 1.0, 0.0, 0.0, -1.0] + coefficients['rho1'] = [1.0, -2.0, 2.0, -1.0, 0.0, 0.0, -1.0] + coefficients['np1'] = [1.0, -2.0, 2.0, 1.0, 0.0, 0.0, 1.0] + coefficients['opk1'] = [1.0, -1.0, -2.0, 0.0, 0.0, 0.0, 1.0] + coefficients['oa1'] = [1.0, -1.0, -1.0, 0.0, 0.0, 0.0, -1.0] + # O1 nodal line + coefficients['o1n'] = [1.0, -1.0, 0.0, 0.0, -1.0, 0.0, -1.0] + # O1 nodal line + coefficients['o1-'] = [1.0, -1.0, 0.0, 0.0, -1.0, 0.0, -1.0] + coefficients['o1'] = [1.0, -1.0, 0.0, 0.0, 0.0, 0.0, -1.0] + # conjugate to nodal line + coefficients['o1+'] = [1.0, -1.0, 0.0, 0.0, 1.0, 0.0, -1.0] + # 3rd degree terms + coefficients["o1'"] = [1.0, -1.0, 0.0, 1.0, 0.0, 0.0, 2.0] + coefficients['ob1'] = [1.0, -1.0, 1.0, 0.0, 0.0, 0.0, -1.0] + coefficients['ms1'] = [1.0, -1.0, 1.0, 0.0, 0.0, 0.0, 2.0] + coefficients['mp1'] = [1.0, -1.0, 2.0, 0.0, 0.0, 0.0, 1.0] + coefficients['tau1'] = [1.0, -1.0, 2.0, 0.0, 0.0, 0.0, 1.0] + coefficients['beta1'] = [1.0, 0.0, -2.0, 1.0, 0.0, 0.0, 1.0] + coefficients['pqo1'] = [1.0, 0.0, -2.0, 1.0, 0.0, 0.0, -1.0] + coefficients['2oq1'] = [1.0, 0.0, 0.0, -1.0, 0.0, 0.0, -1.0] + # 3rd degree terms + coefficients["m1'"] = [1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 2.0] + coefficients['m1'] = [1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0] + coefficients['m1a'] = [1.0, 0.0, 0.0, 1.0, 0.0, 0.0, 1.0] + coefficients['m1b'] = [1.0, 0.0, 0.0, -1.0, 0.0, 0.0, 1.0] + coefficients['no1'] = [1.0, 0.0, 0.0, 1.0, 0.0, 0.0, 1.0] + coefficients['chi1'] = [1.0, 0.0, 2.0, -1.0, 0.0, 0.0, 1.0] + coefficients['2pk1'] = [1.0, 1.0, -4.0, 0.0, 0.0, 0.0, 1.0] + coefficients['pi1'] = [1.0, 1.0, -3.0, 0.0, 0.0, 1.0, -1.0] + coefficients['tk1'] = [1.0, 1.0, -3.0, 0.0, 0.0, 1.0, -1.0] + coefficients['s1-1'] = [1.0, 1.0, -2.0, 0.0, 0.0, 0.0, 2.0] + coefficients['p1'] = [1.0, 1.0, -2.0, 0.0, 0.0, 0.0, -1.0] + coefficients['s1-'] = [1.0, 1.0, -1.0, 0.0, 0.0, -1.0, 1.0] + # Doodson's phase + coefficients['s1'] = [1.0, 1.0, -1.0, 0.0, 0.0, 0.0, 2.0] + coefficients['s1+'] = [1.0, 1.0, -1.0, 0.0, 0.0, 1.0, 1.0] + coefficients['ojm1'] = [1.0, 1.0, 0.0, -2.0, 0.0, 0.0, -1.0] + # 3rd degree terms + coefficients["k1'"] = [1.0, 1.0, 0.0, -1.0, 0.0, 0.0, 2.0] + coefficients['k1-'] = [1.0, 1.0, 0.0, 0.0, -1.0, 0.0, -1.0] + coefficients['k1'] = [1.0, 1.0, 0.0, 0.0, 0.0, 0.0, 1.0] + coefficients['s1+1'] = [1.0, 1.0, 0.0, 0.0, 0.0, 0.0, 2.0] + coefficients['k1+'] = [1.0, 1.0, 0.0, 0.0, 1.0, 0.0, 1.0] + coefficients['k1n'] = [1.0, 1.0, 0.0, 0.0, 1.0, 0.0, 1.0] + coefficients['k1++'] = [1.0, 1.0, 0.0, 0.0, 2.0, 0.0, -1.0] + coefficients['psi1'] = [1.0, 1.0, 1.0, 0.0, 0.0, -1.0, 1.0] + coefficients['rp1'] = [1.0, 1.0, 1.0, 0.0, 0.0, -1.0, -1.0] + coefficients['phi1'] = [1.0, 1.0, 2.0, 0.0, 0.0, 0.0, 1.0] + coefficients['kp1'] = [1.0, 1.0, 2.0, 0.0, 0.0, 0.0, 1.0] + coefficients['opq1'] = [1.0, 2.0, -2.0, -1.0, 0.0, 0.0, -1.0] + coefficients['the1'] = [1.0, 2.0, -2.0, 1.0, 0.0, 0.0, 1.0] + coefficients['theta1'] = [1.0, 2.0, -2.0, 1.0, 0.0, 0.0, 1.0] + coefficients['mq1'] = [1.0, 2.0, 0.0, -1.0, 0.0, 0.0, 1.0] + coefficients['j1'] = [1.0, 2.0, 0.0, -1.0, 0.0, 0.0, 1.0] + # 3rd degree terms + coefficients["j1'"] = [1.0, 2.0, 0.0, 0.0, 0.0, 0.0, 2.0] + coefficients['2po1'] = [1.0, 3.0, -4.0, 0.0, 0.0, 0.0, -1.0] + coefficients['so1'] = [1.0, 3.0, -2.0, 0.0, 0.0, 0.0, 1.0] + coefficients['oo1'] = [1.0, 3.0, 0.0, 0.0, 0.0, 0.0, 1.0] + coefficients['kpq1'] = [1.0, 4.0, -2.0, -1.0, 0.0, 0.0, 1.0] + coefficients['ups1'] = [1.0, 4.0, 0.0, -1.0, 0.0, 0.0, 1.0] + coefficients['kq1'] = [1.0, 4.0, 0.0, -1.0, 0.0, 0.0, 1.0] + coefficients['2jo1'] = [1.0, 5.0, 0.0, -2.0, 0.0, 0.0, -1.0] + coefficients['kjq1'] = [1.0, 5.0, 0.0, -2.0, 0.0, 0.0, -1.0] + coefficients['2ook1'] = [1.0, 5.0, 0.0, 0.0, 0.0, 0.0, -1.0] + coefficients['2oop1'] = [1.0, 5.0, 2.0, 0.0, 0.0, 0.0, -1.0] + coefficients['2jq1'] = [1.0, 6.0, 0.0, -3.0, 0.0, 0.0, -1.0] + coefficients['2mn2s2'] = [2.0, -5.0, 4.0, 1.0, 0.0, 0.0, 0.0] + coefficients['2nk2'] = [2.0, -4.0, 0.0, 2.0, 0.0, 0.0, 0.0] + coefficients['3m(sk)2'] = [2.0, -4.0, 2.0, 0.0, 0.0, 0.0, 0.0] + coefficients['3mks2'] = [2.0, -4.0, 2.0, 0.0, 0.0, 0.0, 0.0] + coefficients['2ns2'] = [2.0, -4.0, 2.0, 2.0, 0.0, 0.0, 0.0] + coefficients['3m2s2'] = [2.0, -4.0, 4.0, 0.0, 0.0, 0.0, 0.0] + coefficients['oq2'] = [2.0, -3.0, 0.0, 1.0, 0.0, 0.0, 2.0] + coefficients['mnk2'] = [2.0, -3.0, 0.0, 1.0, 0.0, 0.0, 0.0] + coefficients['3n2'] = [2.0, -3.0, 0.0, 3.0, 0.0, 0.0, 0.0] + coefficients['eps2'] = [2.0, -3.0, 2.0, 1.0, 0.0, 0.0, 0.0] + coefficients['mns2'] = [2.0, -3.0, 2.0, 1.0, 0.0, 0.0, 0.0] + # coefficients['mns2'] = [2.0, -3.0, 4.0, -1.0, 0.0, 0.0, 0.0] + coefficients['mnus2'] = [2.0, -3.0, 4.0, -1.0, 0.0, 0.0, 0.0] + coefficients['2ml2s2'] = [2.0, -3.0, 4.0, -1.0, 0.0, 0.0, 2.0] + coefficients['mnk2s2'] = [2.0, -3.0, 4.0, 1.0, 0.0, 0.0, 0.0] + coefficients['2ms2k2'] = [2.0, -2.0, -2.0, 0.0, 0.0, 0.0, 0.0] + coefficients['2mk2'] = [2.0, -2.0, 0.0, 0.0, 0.0, 0.0, 0.0] + coefficients['o2'] = [2.0, -2.0, 0.0, 0.0, 0.0, 0.0, 2.0] + # 3rd degree terms + coefficients["2n2'"] = [2.0, -2.0, 0.0, 1.0, 0.0, 0.0, 1.0] + coefficients['2n2'] = [2.0, -2.0, 0.0, 2.0, 0.0, 0.0, 0.0] + coefficients['2nm2'] = [2.0, -2.0, 0.0, 2.0, 0.0, 0.0, 0.0] + coefficients['2ms2'] = [2.0, -2.0, 2.0, 0.0, 0.0, 0.0, 0.0] + coefficients['mu2'] = [2.0, -2.0, 2.0, 0.0, 0.0, 0.0, 0.0] + coefficients['2mk2s2'] = [2.0, -2.0, 4.0, 0.0, 0.0, 0.0, 0.0] + coefficients['omg2'] = [2.0, -2.0, 3.0, 0.0, 0.0, -1.0, 0.0] + coefficients['nsk2'] = [2.0, -1.0, -2.0, 1.0, 0.0, 0.0, 0.0] + coefficients['snk2'] = [2.0, -1.0, -2.0, 1.0, 0.0, 0.0, 0.0] + coefficients['na2'] = [2.0, -1.0, -1.0, 1.0, 0.0, 0.0, 0.0] + # 3rd degree terms + coefficients["n2'"] = [2.0, -1.0, 0.0, 0.0, 0.0, 0.0, 1.0] + coefficients['n2'] = [2.0, -1.0, 0.0, 1.0, 0.0, 0.0, 0.0] + coefficients['2ml2'] = [2.0, -1.0, 0.0, 1.0, 0.0, 0.0, 2.0] + coefficients['nb2'] = [2.0, -1.0, 1.0, 1.0, 0.0, 0.0, 0.0] + coefficients['nu2'] = [2.0, -1.0, 2.0, -1.0, 0.0, 0.0, 0.0] + coefficients['mmun2'] = [2.0, -1.0, 2.0, -1.0, 0.0, 0.0, 0.0] + coefficients['3m(sn)2'] = [2.0, -1.0, 2.0, -1.0, 0.0, 0.0, 0.0] + coefficients['nks2'] = [2.0, -1.0, 2.0, 1.0, 0.0, 0.0, 0.0] + coefficients['nkp2'] = [2.0, -1.0, 2.0, 1.0, 0.0, 0.0, 2.0] + coefficients['mkl2s2'] = [2.0, -1.0, 4.0, -1.0, 0.0, 0.0, 2.0] + coefficients['2kn2s2'] = [2.0, -1.0, 4.0, 1.0, 0.0, 0.0, 0.0] + coefficients['msk2'] = [2.0, 0.0, -2.0, 0.0, 0.0, 0.0, 0.0] + coefficients['op2'] = [2.0, 0.0, -2.0, 0.0, 0.0, 0.0, 2.0] + coefficients['m2-2'] = [2.0, 0.0, -2.0, 0.0, 0.0, 0.0, 0.0] + coefficients['gamma2'] = [2.0, 0.0, -2.0, 2.0, 0.0, 0.0, 2.0] + coefficients['gam2'] = [2.0, 0.0, -2.0, 2.0, 0.0, 0.0, 2.0] + coefficients['alp2'] = [2.0, 0.0, -1.0, 0.0, 0.0, 1.0, 2.0] + coefficients['alpha2'] = [2.0, 0.0, -1.0, 0.0, 0.0, 1.0, 2.0] + coefficients['m2a'] = [2.0, 0.0, -1.0, 0.0, 0.0, 1.0, 0.0] + coefficients['m2-1'] = [2.0, 0.0, -1.0, 0.0, 0.0, 0.0, 0.0] + coefficients['ma2'] = [2.0, 0.0, -1.0, 0.0, 0.0, 0.0, 0.0] + # M2 nodal line + coefficients['m2-'] = [2.0, 0.0, 0.0, 0.0, -1.0, 0.0, 2.0] + coefficients['m2'] = [2.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0] + coefficients['ko2'] = [2.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0] + # conjugate to nodal + coefficients['m2+'] = [2.0, 0.0, 0.0, 0.0, 1.0, 0.0, 2.0] + # 3rd degree terms + coefficients["m2'"] = [2.0, 0.0, 0.0, 1.0, 0.0, 0.0, -1.0] + coefficients['mb2'] = [2.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0] + coefficients['m2+1'] = [2.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0] + coefficients['m2b'] = [2.0, 0.0, 1.0, 0.0, 0.0, -1.0, 0.0] + coefficients['beta2'] = [2.0, 0.0, 1.0, 0.0, 0.0, -1.0, 0.0] + coefficients['delta2'] = [2.0, 0.0, 2.0, 0.0, 0.0, 0.0, 0.0] + coefficients['m2+2'] = [2.0, 0.0, 2.0, 0.0, 0.0, 0.0, 0.0] + coefficients['mks2'] = [2.0, 0.0, 2.0, 0.0, 0.0, 0.0, 0.0] + coefficients['m2(ks)2'] = [2.0, 0.0, 4.0, 0.0, 0.0, 0.0, 0.0] + coefficients['2snmk2'] = [2.0, 1.0, -4.0, 1.0, 0.0, 0.0, 0.0] + coefficients['2sn(mk)2'] = [2.0, 1.0, -4.0, 1.0, 0.0, 0.0, 0.0] + coefficients['snm2'] = [2.0, 1.0, -2.0, 1.0, 0.0, 0.0, 0.0] + coefficients['lambda2'] = [2.0, 1.0, -2.0, 1.0, 0.0, 0.0, 2.0] + coefficients['2mn2'] = [2.0, 1.0, 0.0, -1.0, 0.0, 0.0, 0.0] + coefficients['l2'] = [2.0, 1.0, 0.0, -1.0, 0.0, 0.0, 2.0] + coefficients['l2a'] = [2.0, 1.0, 0.0, -1.0, 0.0, 0.0, 2.0] + # 3rd degree terms + coefficients["l2'"] = [2.0, 1.0, 0.0, 0.0, 0.0, 0.0, -1.0] + coefficients['nkm2'] = [2.0, 1.0, 0.0, 1.0, 0.0, 0.0, 0.0] + coefficients['l2b'] = [2.0, 1.0, 0.0, 1.0, 0.0, 0.0, 0.0] + coefficients['lb2'] = [2.0, 1.0, 1.0, -1.0, 0.0, 0.0, 2.0] + coefficients['2sk2'] = [2.0, 2.0, -4.0, 0.0, 0.0, 0.0, 0.0] + coefficients['2t2'] = [2.0, 2.0, -4.0, 0.0, 0.0, 2.0, 0.0] + coefficients['s2-2'] = [2.0, 2.0, -4.0, 0.0, 0.0, 0.0, 0.0] + coefficients['s2-1'] = [2.0, 2.0, -3.0, 0.0, 0.0, 0.0, 0.0] + coefficients['t2'] = [2.0, 2.0, -3.0, 0.0, 0.0, 1.0, 0.0] + coefficients['kp2'] = [2.0, 2.0, -2.0, 0.0, 0.0, 0.0, 0.0] + coefficients['s2r'] = [2.0, 2.0, -2.0, 0.0, 0.0, 0.0, 0.0] + coefficients['s2'] = [2.0, 2.0, -2.0, 0.0, 0.0, 0.0, 0.0] + coefficients['r2'] = [2.0, 2.0, -1.0, 0.0, 0.0, -1.0, 2.0] + coefficients['s2+1'] = [2.0, 2.0, -1.0, 0.0, 0.0, 0.0, 0.0] + coefficients['s2+2'] = [2.0, 2.0, 0.0, 0.0, 0.0, 0.0, 0.0] + coefficients['k2'] = [2.0, 2.0, 0.0, 0.0, 0.0, 0.0, 0.0] + coefficients['kb2'] = [2.0, 2.0, 1.0, 0.0, 0.0, 0.0, 0.0] + coefficients['2ks2'] = [2.0, 2.0, 2.0, 0.0, 0.0, 0.0, 0.0] + coefficients['2pmn2'] = [2.0, 3.0, -4.0, -1.0, 0.0, 0.0, 2.0] + coefficients['msnu2'] = [2.0, 3.0, -4.0, 1.0, 0.0, 0.0, 0.0] + coefficients['msn2'] = [2.0, 3.0, -2.0, -1.0, 0.0, 0.0, 0.0] + coefficients['zeta2'] = [2.0, 3.0, -2.0, 1.0, 0.0, 0.0, 0.0] + coefficients['eta2'] = [2.0, 3.0, 0.0, -1.0, 0.0, 0.0, 0.0] + coefficients['mkn2'] = [2.0, 3.0, 0.0, -1.0, 0.0, 0.0, 0.0] + coefficients['kj2'] = [2.0, 3.0, 0.0, -1.0, 0.0, 0.0, 2.0] + coefficients['2kmsn2'] = [2.0, 3.0, 2.0, -1.0, 0.0, 0.0, 0.0] + coefficients['2km(sn)2'] = [2.0, 3.0, 2.0, -1.0, 0.0, 0.0, 0.0] + coefficients['2sm2'] = [2.0, 4.0, -4.0, 0.0, 0.0, 0.0, 0.0] + coefficients['2ms2n2'] = [2.0, 4.0, -2.0, -2.0, 0.0, 0.0, 0.0] + coefficients['skm2'] = [2.0, 4.0, -2.0, 0.0, 0.0, 0.0, 0.0] + coefficients['2j2'] = [2.0, 4.0, 0.0, -2.0, 0.0, 0.0, 2.0] + coefficients['2k2'] = [2.0, 4.0, 0.0, 0.0, 0.0, 0.0, 0.0] + coefficients['2snu2'] = [2.0, 5.0, -6.0, 1.0, 0.0, 0.0, 0.0] + coefficients['3(sm)n2'] = [2.0, 5.0, -6.0, 1.0, 0.0, 0.0, 0.0] + coefficients['2sn2'] = [2.0, 5.0, -4.0, -1.0, 0.0, 0.0, 0.0] + coefficients['skn2'] = [2.0, 5.0, -2.0, -1.0, 0.0, 0.0, 0.0] + coefficients['2kn2'] = [2.0, 5.0, 0.0, -1.0, 0.0, 0.0, 0.0] + coefficients['3s2m2'] = [2.0, 6.0, -6.0, 0.0, 0.0, 0.0, 0.0] + coefficients['2sk2m2'] = [2.0, 6.0, -4.0, 0.0, 0.0, 0.0, 0.0] + coefficients['2oq3'] = [3.0, -4.0, 0.0, 1.0, 0.0, 0.0, 1.0] + # compound 3 O1 + coefficients['o3'] = [3.0, -3.0, 0.0, 0.0, 0.0, 0.0, 1.0] + coefficients['nq3'] = [3.0, -3.0, 0.0, 2.0, 0.0, 0.0, -1.0] + coefficients['muo3'] = [3.0, -3.0, 2.0, 0.0, 0.0, 0.0, -1.0] + coefficients['mq3'] = [3.0, -2.0, 0.0, 1.0, 0.0, 0.0, -1.0] + coefficients['no3'] = [3.0, -2.0, 0.0, 1.0, 0.0, 0.0, -1.0] + coefficients['mnp3'] = [3.0, -2.0, 2.0, 1.0, 0.0, 0.0, 1.0] + coefficients['2op3'] = [3.0, -1.0, -2.0, 0.0, 0.0, 0.0, 1.0] + coefficients['2os3'] = [3.0, -1.0, -1.0, 0.0, 0.0, 0.0, 0.0] + # Q1+M1+S1 + coefficients['qms3'] = [3.0, -1.0, -1.0, 2.0, 0.0, 0.0, 2.0] + coefficients['mo3-'] = [3.0, -1.0, 0.0, 0.0, -1.0, 0.0, -1.0] + coefficients['mo3'] = [3.0, -1.0, 0.0, 0.0, 0.0, 0.0, -1.0] + coefficients['mo3+'] = [3.0, -1.0, 0.0, 0.0, 1.0, 0.0, -1.0] + coefficients['2mk3'] = [3.0, -1.0, 0.0, 0.0, 0.0, 0.0, -1.0] + coefficients['e3n'] = [3.0, -1.0, 0.0, 1.0, -1.0, 0.0, 0.0] + # 3rd degree terms + coefficients['e3'] = [3.0, -1.0, 0.0, 1.0, 0.0, 0.0, 2.0] + coefficients['2no3'] = [3.0, -1.0, 0.0, 2.0, 0.0, 0.0, 1.0] + coefficients['2nkm3'] = [3.0, -1.0, 0.0, 2.0, 0.0, 0.0, 1.0] + coefficients['2ms3'] = [3.0, -1.0, 1.0, 0.0, 0.0, 0.0, 2.0] + coefficients['2mp3'] = [3.0, -1.0, 2.0, 0.0, 0.0, 0.0, 1.0] + coefficients['ns3'] = [3.0, 0.0, -1.0, 1.0, 0.0, 0.0, 2.0] + coefficients['2oj3'] = [3.0, 0.0, 0.0, -1.0, 0.0, 0.0, -1.0] + # 2M2 - M1 + coefficients['2mm3'] = [3.0, 0.0, 0.0, -1.0, 0.0, 0.0, -1.0] + coefficients['m3'] = [3.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0] + # 3rd degree terms + coefficients["m3'"] = [3.0, 0.0, 0.0, 0.0, 0.0, 0.0, 2.0] + coefficients['nk3'] = [3.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0] + coefficients['mp3'] = [3.0, 1.0, -2.0, 0.0, 0.0, 0.0, -1.0] + coefficients['so3'] = [3.0, 1.0, -2.0, 0.0, 0.0, 0.0, -1.0] + # 3rd degree terms + coefficients['lambda3'] = [3.0, 1.0, -2.0, 1.0, 0.0, 0.0, 0.0] + coefficients['ms3'] = [3.0, 1.0, -1.0, 0.0, 0.0, 0.0, 2.0] + coefficients['pjrho3'] = [3.0, 1.0, 0.0, -2.0, 0.0, 0.0, -1.0] + # 3rd degree terms + coefficients['l3'] = [3.0, 1.0, 0.0, -1.0, 0.0, 0.0, 0.0] + coefficients['mk3-'] = [3.0, 1.0, 0.0, 0.0, -1.0, 0.0, 1.0] + coefficients['mk3'] = [3.0, 1.0, 0.0, 0.0, 0.0, 0.0, 1.0] + coefficients['mk3+'] = [3.0, 1.0, 0.0, 0.0, 1.0, 0.0, 1.0] + # 3rd degree terms + coefficients['l3b'] = [3.0, 1.0, 0.0, 1.0, 0.0, 0.0, 2.0] + coefficients['mks3'] = [3.0, 1.0, 1.0, 0.0, 0.0, 0.0, 2.0] + coefficients['mkp3'] = [3.0, 1.0, 2.0, 0.0, 0.0, 0.0, 1.0] + coefficients['nso3'] = [3.0, 2.0, -2.0, 1.0, 0.0, 0.0, 1.0] + coefficients['2mq3'] = [3.0, 2.0, 0.0, -1.0, 0.0, 0.0, 1.0] + # 3rd degree terms + coefficients['f3'] = [3.0, 2.0, 0.0, 0.0, 0.0, 0.0, 2.0] + # 3rd degree terms + coefficients['j3'] = [3.0, 2.0, 0.0, 0.0, 0.0, 0.0, 2.0] + # s3 perturbation + coefficients['2t3'] = [3.0, 3.0, -5.0, 0.0, 0.0, 0.0, 2.0] + # s3 perturbation + coefficients['t3'] = [3.0, 3.0, -4.0, 0.0, 0.0, 0.0, 2.0] + # = 2SK3 + coefficients['sp3'] = [3.0, 3.0, -4.0, 0.0, 0.0, 0.0, -1.0] + coefficients['s3'] = [3.0, 3.0, -3.0, 0.0, 0.0, 0.0, 0.0] + # 3rd degree terms + coefficients["s3'"] = [3.0, 3.0, -3.0, 0.0, 0.0, 0.0, 2.0] + # s3 perturbation + coefficients['r3'] = [3.0, 3.0, -2.0, 0.0, 0.0, 0.0, 2.0] + coefficients['sk3'] = [3.0, 3.0, -2.0, 0.0, 0.0, 0.0, 1.0] + # s3 perturbation + coefficients['2r3'] = [3.0, 3.0, -1.0, 0.0, 0.0, 0.0, 2.0] + coefficients['k3'] = [3.0, 3.0, 0.0, 0.0, 0.0, 0.0, -1.0] + coefficients['2so3'] = [3.0, 5.0, -4.0, 0.0, 0.0, 0.0, 1.0] + coefficients['2jp3'] = [3.0, 5.0, -2.0, -2.0, 0.0, 0.0, 1.0] + coefficients['kso3'] = [3.0, 5.0, -2.0, 0.0, 0.0, 0.0, 1.0] + coefficients['2jk3'] = [3.0, 5.0, -1.0, -2.0, 0.0, 0.0, 0.0] + coefficients['2ko3'] = [3.0, 5.0, 0.0, 0.0, 0.0, 0.0, 1.0] + coefficients['2sq3'] = [3.0, 6.0, -4.0, -1.0, 0.0, 0.0, 1.0] + coefficients['o4'] = [4.0, -4.0, 0.0, 0.0, 0.0, 0.0, 0.0] + coefficients['2qm4'] = [4.0, -4.0, 0.0, 2.0, 0.0, 0.0, 2.0] + coefficients['4ms4'] = [4.0, -4.0, 4.0, 0.0, 0.0, 0.0, 0.0] + coefficients['4m2s4'] = [4.0, -4.0, 4.0, 0.0, 0.0, 0.0, 0.0] + coefficients['2mnk4'] = [4.0, -3.0, 0.0, 1.0, 0.0, 0.0, 0.0] + coefficients['moq4'] = [4.0, -3.0, 0.0, 1.0, 0.0, 0.0, 2.0] + coefficients['2mns4'] = [4.0, -3.0, 2.0, 1.0, 0.0, 0.0, 0.0] + coefficients['2mns4'] = [4.0, -3.0, 4.0, -1.0, 0.0, 0.0, 0.0] + coefficients['2mnus4'] = [4.0, -3.0, 4.0, -1.0, 0.0, 0.0, 0.0] + coefficients['3mk4'] = [4.0, -2.0, 0.0, 0.0, 0.0, 0.0, 0.0] + coefficients['2om4'] = [4.0, -2.0, 0.0, 0.0, 0.0, 0.0, 2.0] + coefficients['n4'] = [4.0, -2.0, 0.0, 2.0, 0.0, 0.0, 0.0] + coefficients['3ms4'] = [4.0, -2.0, 2.0, 0.0, 0.0, 0.0, 0.0] + coefficients['msnk4'] = [4.0, -1.0, -2.0, 1.0, 0.0, 0.0, 0.0] + coefficients['mpq4'] = [4.0, -1.0, -2.0, 1.0, 0.0, 0.0, 2.0] + coefficients['mn4'] = [4.0, -1.0, 0.0, 1.0, 0.0, 0.0, 0.0] + coefficients['mnu4'] = [4.0, -1.0, 2.0, -1.0, 0.0, 0.0, 0.0] + coefficients['2mls4'] = [4.0, -1.0, 2.0, -1.0, 0.0, 0.0, 2.0] + coefficients['mnks4'] = [4.0, -1.0, 2.0, 1.0, 0.0, 0.0, 0.0] + coefficients['2msk4'] = [4.0, 0.0, -2.0, 0.0, 0.0, 0.0, 0.0] + coefficients['mop4'] = [4.0, 0.0, -2.0, 0.0, 0.0, 0.0, 2.0] + coefficients['ma4'] = [4.0, 0.0, -1.0, 0.0, 0.0, 0.0, 0.0] + coefficients['m4'] = [4.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0] + coefficients['mb4'] = [4.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0] + coefficients['2mks4'] = [4.0, 0.0, 2.0, 0.0, 0.0, 0.0, 0.0] + coefficients['sn4'] = [4.0, 1.0, -2.0, 1.0, 0.0, 0.0, 0.0] + coefficients['3mn4'] = [4.0, 1.0, 0.0, -1.0, 0.0, 0.0, 0.0] + coefficients['ml4'] = [4.0, 1.0, 0.0, -1.0, 0.0, 0.0, 2.0] + coefficients['nk4'] = [4.0, 1.0, 0.0, 1.0, 0.0, 0.0, 0.0] + coefficients['2smk4'] = [4.0, 2.0, -4.0, 0.0, 0.0, 0.0, 0.0] + coefficients['2pm4'] = [4.0, 2.0, -4.0, 0.0, 0.0, 0.0, 2.0] + coefficients['mt4'] = [4.0, 2.0, -3.0, 0.0, 0.0, 1.0, 0.0] + coefficients['ms4'] = [4.0, 2.0, -2.0, 0.0, 0.0, 0.0, 0.0] + coefficients['mr4'] = [4.0, 2.0, -1.0, 0.0, 0.0, -1.0, 2.0] + coefficients['mk4'] = [4.0, 2.0, 0.0, 0.0, 0.0, 0.0, 0.0] + coefficients['2snm4'] = [4.0, 3.0, -4.0, 1.0, 0.0, 0.0, 0.0] + coefficients['2msn4'] = [4.0, 3.0, -2.0, -1.0, 0.0, 0.0, 0.0] + coefficients['sl4'] = [4.0, 3.0, -2.0, -1.0, 0.0, 0.0, 2.0] + coefficients['2mkn4'] = [4.0, 3.0, 0.0, -1.0, 0.0, 0.0, 0.0] + coefficients['mkj4'] = [4.0, 3.0, 0.0, -1.0, 0.0, 0.0, 2.0] + coefficients['2t4'] = [4.0, 4.0, -6.0, 0.0, 0.0, 0.0, 0.0] + coefficients['t4'] = [4.0, 4.0, -5.0, 0.0, 0.0, 0.0, 0.0] + coefficients['st4'] = [4.0, 4.0, -5.0, 0.0, 0.0, 1.0, 0.0] + coefficients['s4'] = [4.0, 4.0, -4.0, 0.0, 0.0, 0.0, 0.0] + coefficients['r4'] = [4.0, 4.0, -3.0, 0.0, 0.0, 0.0, 0.0] + coefficients['2r4'] = [4.0, 4.0, -2.0, 0.0, 0.0, 0.0, 0.0] + coefficients['sk4'] = [4.0, 4.0, -2.0, 0.0, 0.0, 0.0, 0.0] + coefficients['3ks4'] = [4.0, 4.0, -1.0, 0.0, 0.0, 0.0, -1.0] + coefficients['k4'] = [4.0, 4.0, 0.0, 0.0, 0.0, 0.0, 0.0] + coefficients['3sm4'] = [4.0, 6.0, -6.0, 0.0, 0.0, 0.0, 0.0] + coefficients['2(kj)4'] = [4.0, 6.0, 0.0, -2.0, 0.0, 0.0, 2.0] + coefficients['2no5'] = [5.0, -3.0, 0.0, 2.0, 0.0, 0.0, -1.0] + coefficients['mno5'] = [5.0, -2.0, 0.0, 1.0, 0.0, 0.0, -1.0] + coefficients['2mq5'] = [5.0, -2.0, 0.0, 1.0, 0.0, 0.0, -1.0] + coefficients['2nkms5'] = [5.0, -2.0, 2.0, 2.0, 0.0, 0.0, 1.0] + coefficients['2mo5'] = [5.0, -1.0, 0.0, 0.0, 0.0, 0.0, -1.0] + coefficients['mnm5'] = [5.0, -1.0, 0.0, 1.0, 0.0, 0.0, 2.0] + coefficients['2nk5'] = [5.0, -1.0, 0.0, 2.0, 0.0, 0.0, 1.0] + coefficients['3ms5'] = [5.0, -1.0, 1.0, 0.0, 0.0, 0.0, 2.0] + coefficients['3mp5'] = [5.0, -1.0, 2.0, 0.0, 0.0, 0.0, 1.0] + coefficients['nso5'] = [5.0, 0.0, -2.0, 1.0, 0.0, 0.0, -1.0] + coefficients['m5'] = [5.0, 0.0, 0.0, 0.0, 0.0, 0.0, 2.0] + coefficients['mnk5'] = [5.0, 0.0, 0.0, 1.0, 0.0, 0.0, 1.0] + coefficients['mb5'] = [5.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0] + coefficients['mso5'] = [5.0, 1.0, -2.0, 0.0, 0.0, 0.0, -1.0] + coefficients['2mp5'] = [5.0, 1.0, -2.0, 0.0, 0.0, 0.0, -1.0] + coefficients['2ms5'] = [5.0, 1.0, -1.0, 0.0, 0.0, 0.0, 2.0] + coefficients['2mk5'] = [5.0, 1.0, 0.0, 0.0, 0.0, 0.0, 1.0] + # N2 + K2 + S1 + coefficients['nks5'] = [5.0, 2.0, -1.0, 1.0, 0.0, 0.0, 2.0] + coefficients['nsk5'] = [5.0, 2.0, -2.0, -1.0, 0.0, 0.0, 1.0] + coefficients['msm5'] = [5.0, 2.0, -2.0, 0.0, 0.0, 0.0, 2.0] + coefficients['snk5'] = [5.0, 2.0, -2.0, 1.0, 0.0, 0.0, -1.0] + coefficients['3mq5'] = [5.0, 2.0, 0.0, -1.0, 0.0, 0.0, 1.0] + coefficients['msp5'] = [5.0, 3.0, -4.0, 0.0, 0.0, 0.0, -1.0] + coefficients['msk5'] = [5.0, 3.0, -2.0, 0.0, 0.0, 0.0, 1.0] + coefficients['3km5'] = [5.0, 3.0, 0.0, 0.0, 0.0, 0.0, -1.0] + coefficients['2sp5'] = [5.0, 5.0, -6.0, 0.0, 0.0, 0.0, -1.0] + coefficients['t5'] = [5.0, 5.0, -6.0, 0.0, 0.0, 0.0, 0.0] + coefficients['s5'] = [5.0, 5.0, -5.0, 0.0, 0.0, 0.0, 0.0] + coefficients['r5'] = [5.0, 5.0, -4.0, 0.0, 0.0, 0.0, 0.0] + coefficients['2sk5'] = [5.0, 5.0, -4.0, 0.0, 0.0, 0.0, 1.0] + coefficients['k5'] = [5.0, 5.0, 0.0, 0.0, 0.0, 0.0, 1.0] + coefficients['o6'] = [6.0, -6.0, 0.0, 0.0, 0.0, 0.0, 2.0] + coefficients['2(mn)k6'] = [6.0, -4.0, 0.0, 2.0, 0.0, 0.0, 0.0] + coefficients['5mks6'] = [6.0, -4.0, 2.0, 0.0, 0.0, 0.0, 0.0] + coefficients['2(mn)s6'] = [6.0, -4.0, 2.0, 2.0, 0.0, 0.0, 0.0] + coefficients['5m2s6'] = [6.0, -4.0, 4.0, 0.0, 0.0, 0.0, 0.0] + coefficients['3mnk6'] = [6.0, -3.0, 0.0, 1.0, 0.0, 0.0, 0.0] + coefficients['n6'] = [6.0, -3.0, 0.0, 3.0, 0.0, 0.0, 0.0] + coefficients['3mns6'] = [6.0, -3.0, 2.0, 1.0, 0.0, 0.0, 0.0] + coefficients['2nmls6'] = [6.0, -3.0, 2.0, 1.0, 0.0, 0.0, 2.0] + coefficients['3nks6'] = [6.0, -3.0, 2.0, 3.0, 0.0, 0.0, 0.0] + coefficients['3mnus6'] = [6.0, -3.0, 4.0, -1.0, 0.0, 0.0, 0.0] + coefficients['4mk6'] = [6.0, -2.0, 0.0, 0.0, 0.0, 0.0, 0.0] + coefficients['2nm6'] = [6.0, -2.0, 0.0, 2.0, 0.0, 0.0, 0.0] + coefficients['m2n6'] = [6.0, -2.0, 0.0, 2.0, 0.0, 0.0, 0.0] + coefficients['4ms6'] = [6.0, -2.0, 2.0, 0.0, 0.0, 0.0, 0.0] + coefficients['2mlns6'] = [6.0, -2.0, 2.0, 0.0, 0.0, 0.0, 2.0] + coefficients['2mnls6'] = [6.0, -2.0, 2.0, 0.0, 0.0, 0.0, 2.0] + coefficients['2nmks6'] = [6.0, -2.0, 2.0, 2.0, 0.0, 0.0, 0.0] + coefficients['2msnk6'] = [6.0, -1.0, -2.0, 1.0, 0.0, 0.0, 0.0] + coefficients['2mn6'] = [6.0, -1.0, 0.0, 1.0, 0.0, 0.0, 0.0] + coefficients['2mnu6'] = [6.0, -1.0, 2.0, -1.0, 0.0, 0.0, 0.0] + coefficients['2mn6'] = [6.0, -1.0, 2.0, -1.0, 0.0, 0.0, 0.0] + coefficients['3mls6'] = [6.0, -1.0, 2.0, -1.0, 0.0, 0.0, 2.0] + coefficients['2mno6'] = [6.0, -1.0, 2.0, -1.0, 0.0, 0.0, 0.0] + coefficients['2mnks6'] = [6.0, -1.0, 2.0, 1.0, 0.0, 0.0, 0.0] + coefficients['3msk6'] = [6.0, 0.0, -2.0, 0.0, 0.0, 0.0, 0.0] + coefficients['ma6'] = [6.0, 0.0, -1.0, 0.0, 0.0, 0.0, 0.0] + coefficients['m6'] = [6.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0] + coefficients['2nk6'] = [6.0, 0.0, 0.0, 2.0, 0.0, 0.0, 0.0] + coefficients['mb6'] = [6.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0] + coefficients['3mks6'] = [6.0, 0.0, 2.0, 0.0, 0.0, 0.0, 0.0] + coefficients['msn6'] = [6.0, 1.0, -2.0, 1.0, 0.0, 0.0, 0.0] + coefficients['4mn6'] = [6.0, 1.0, 0.0, -1.0, 0.0, 0.0, 0.0] + coefficients['2ml6'] = [6.0, 1.0, 0.0, -1.0, 0.0, 0.0, 2.0] + coefficients['mnk6'] = [6.0, 1.0, 0.0, 1.0, 0.0, 0.0, 0.0] + coefficients['mkn6'] = [6.0, 1.0, 0.0, 1.0, 0.0, 0.0, 0.0] + coefficients['mknu6'] = [6.0, 1.0, 2.0, -1.0, 0.0, 0.0, 0.0] + coefficients['2(ms)k6'] = [6.0, 2.0, -4.0, 0.0, 0.0, 0.0, 0.0] + coefficients['2mt6'] = [6.0, 2.0, -3.0, 0.0, 0.0, 1.0, 0.0] + coefficients['2ms6'] = [6.0, 2.0, -2.0, 0.0, 0.0, 0.0, 0.0] + coefficients['2mr6'] = [6.0, 2.0, -1.0, 0.0, 0.0, -1.0, 2.0] + coefficients['2mk6'] = [6.0, 2.0, 0.0, 0.0, 0.0, 0.0, 0.0] + coefficients['2sn6'] = [6.0, 3.0, -4.0, 1.0, 0.0, 0.0, 0.0] + coefficients['3msn6'] = [6.0, 3.0, -2.0, -1.0, 0.0, 0.0, 0.0] + coefficients['msl6'] = [6.0, 3.0, -2.0, -1.0, 0.0, 0.0, 2.0] + coefficients['snk6'] = [6.0, 3.0, -2.0, 1.0, 0.0, 0.0, 0.0] + coefficients['mkl6'] = [6.0, 3.0, 0.0, -1.0, 0.0, 0.0, 2.0] + coefficients['3mkn6'] = [6.0, 3.0, 0.0, -1.0, 0.0, 0.0, 0.0] + coefficients['2sm6'] = [6.0, 4.0, -4.0, 0.0, 0.0, 0.0, 0.0] + coefficients['msk6'] = [6.0, 4.0, -2.0, 0.0, 0.0, 0.0, 0.0] + coefficients['2km6'] = [6.0, 4.0, 0.0, 0.0, 0.0, 0.0, 0.0] + coefficients['2(ms)n6'] = [6.0, 5.0, -4.0, -1.0, 0.0, 0.0, 0.0] + coefficients['2mskn6'] = [6.0, 5.0, -2.0, -1.0, 0.0, 0.0, 0.0] + coefficients['2t6'] = [6.0, 6.0, -8.0, 0.0, 0.0, 0.0, 0.0] + coefficients['t6'] = [6.0, 6.0, -7.0, 0.0, 0.0, 0.0, 0.0] + coefficients['s6'] = [6.0, 6.0, -6.0, 0.0, 0.0, 0.0, 0.0] + coefficients['r6'] = [6.0, 6.0, -5.0, 0.0, 0.0, 0.0, 0.0] + coefficients['2r6'] = [6.0, 6.0, -4.0, 0.0, 0.0, 0.0, 0.0] + coefficients['2sk6'] = [6.0, 6.0, -4.0, 0.0, 0.0, 0.0, 0.0] + coefficients['k6'] = [6.0, 6.0, 0.0, 0.0, 0.0, 0.0, 0.0] + coefficients['4sm6'] = [6.0, 8.0, -8.0, 0.0, 0.0, 0.0, 0.0] + coefficients['2mno7'] = [7.0, -2.0, 0.0, 1.0, 0.0, 0.0, -1.0] + coefficients['4mk7'] = [7.0, -1.0, 0.0, 0.0, 0.0, 0.0, -1.0] + coefficients['3mo7'] = [7.0, -1.0, 0.0, 0.0, 0.0, 0.0, -1.0] + coefficients['2nmk7'] = [7.0, -1.0, 0.0, 2.0, 0.0, 0.0, 1.0] + # = 2MNK7 = MNKO7 + coefficients['m7'] = [7.0, 0.0, 0.0, 1.0, 0.0, 0.0, 1.0] + coefficients['3mp7'] = [7.0, 1.0, -2.0, 0.0, 0.0, 0.0, -1.0] + coefficients['2mso7'] = [7.0, 1.0, -2.0, 0.0, 0.0, 0.0, -1.0] + coefficients['3mk7'] = [7.0, 1.0, 0.0, 0.0, 0.0, 0.0, 1.0] + # = MSKO7 (noaa) + coefficients['2msk7'] = [7.0, 3.0, -2.0, 0.0, 0.0, 0.0, 1.0] + coefficients['msko7'] = [7.0, 3.0, -2.0, 0.0, 0.0, 0.0, -1.0] + coefficients['2t7'] = [7.0, 7.0, -9.0, 0.0, 0.0, 0.0, 0.0] + coefficients['3sp7'] = [7.0, 7.0, -8.0, 0.0, 0.0, 0.0, -1.0] + coefficients['t7'] = [7.0, 7.0, -8.0, 0.0, 0.0, 0.0, 0.0] + coefficients['s7'] = [7.0, 7.0, -7.0, 0.0, 0.0, 0.0, 0.0] + coefficients['r7'] = [7.0, 7.0, -6.0, 0.0, 0.0, 0.0, 0.0] + coefficients['3sk7'] = [7.0, 7.0, -6.0, 0.0, 0.0, 0.0, 1.0] + coefficients['2r7'] = [7.0, 7.0, -5.0, 0.0, 0.0, 0.0, 0.0] + coefficients['3r7'] = [7.0, 7.0, -4.0, 0.0, 0.0, 0.0, 0.0] + coefficients['4r7'] = [7.0, 7.0, -3.0, 0.0, 0.0, 0.0, 0.0] + coefficients['k7'] = [7.0, 7.0, 0.0, 0.0, 0.0, 0.0, 1.0] + coefficients['3m2ns8'] = [8.0, -4.0, 2.0, 2.0, 0.0, 0.0, 0.0] + coefficients['4mns8'] = [8.0, -3.0, 2.0, 1.0, 0.0, 0.0, 0.0] + coefficients['5mk8'] = [8.0, -2.0, 0.0, 0.0, 0.0, 0.0, 0.0] + coefficients['2mn8'] = [8.0, -2.0, 0.0, 2.0, 0.0, 0.0, 0.0] + coefficients['2(mn)8'] = [8.0, -2.0, 0.0, 2.0, 0.0, 0.0, 0.0] + coefficients['5ms8'] = [8.0, -2.0, 2.0, 0.0, 0.0, 0.0, 0.0] + coefficients['3mn8'] = [8.0, -1.0, 0.0, 1.0, 0.0, 0.0, 0.0] + coefficients['3mnu8'] = [8.0, -1.0, 2.0, -1.0, 0.0, 0.0, 0.0] + coefficients['3mn8'] = [8.0, -1.0, 2.0, -1.0, 0.0, 0.0, 0.0] + coefficients['4mls8'] = [8.0, -1.0, 2.0, -1.0, 0.0, 0.0, 2.0] + coefficients['ma8'] = [8.0, 0.0, -1.0, 0.0, 0.0, 0.0, 0.0] + coefficients['m8'] = [8.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0] + coefficients['mb8'] = [8.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0] + coefficients['2msn8'] = [8.0, 1.0, -2.0, 1.0, 0.0, 0.0, 0.0] + coefficients['3ml8'] = [8.0, 1.0, 0.0, -1.0, 0.0, 0.0, 2.0] + coefficients['2mnk8'] = [8.0, 1.0, 0.0, 1.0, 0.0, 0.0, 0.0] + coefficients['3mt8'] = [8.0, 2.0, -3.0, 0.0, 0.0, 1.0, 0.0] + coefficients['3ms8'] = [8.0, 2.0, -2.0, 0.0, 0.0, 0.0, 0.0] + coefficients['3mk8'] = [8.0, 2.0, 0.0, 0.0, 0.0, 0.0, 0.0] + coefficients['2smn8'] = [8.0, 3.0, -4.0, 1.0, 0.0, 0.0, 0.0] + coefficients['2msl8'] = [8.0, 3.0, -2.0, -1.0, 0.0, 0.0, 2.0] + coefficients['msnk8'] = [8.0, 3.0, -2.0, 1.0, 0.0, 0.0, 0.0] + coefficients['4msn8'] = [8.0, 3.0, 0.0, -1.0, 0.0, 0.0, 0.0] + coefficients['2(ms)8'] = [8.0, 4.0, -4.0, 0.0, 0.0, 0.0, 0.0] + coefficients['2msk8'] = [8.0, 4.0, -2.0, 0.0, 0.0, 0.0, 0.0] + coefficients['2(mk)8'] = [8.0, 4.0, 0.0, 0.0, 0.0, 0.0, 0.0] + coefficients['s8'] = [8.0, 8.0, -8.0, 0.0, 0.0, 0.0, 0.0] + coefficients['k8'] = [8.0, 8.0, 0.0, 0.0, 0.0, 0.0, 0.0] + coefficients['4mo9'] = [9.0, -1.0, 0.0, 0.0, 0.0, 0.0, -1.0] + coefficients['2(mn)k9'] = [9.0, -1.0, 0.0, 2.0, 0.0, 0.0, 1.0] + coefficients['2m2nk9'] = [9.0, -1.0, 0.0, 2.0, 0.0, 0.0, 1.0] + coefficients['3mnk9'] = [9.0, 0.0, 0.0, 1.0, 0.0, 0.0, 1.0] + coefficients['4mp9'] = [9.0, 1.0, -2.0, 0.0, 0.0, 0.0, -1.0] + coefficients['4ms9'] = [9.0, 1.0, -1.0, 0.0, 0.0, 0.0, 2.0] + coefficients['4mk9'] = [9.0, 1.0, 0.0, 0.0, 0.0, 0.0, 1.0] + coefficients['3msk9'] = [9.0, 3.0, -2.0, 0.0, 0.0, 0.0, 1.0] + coefficients['s9'] = [9.0, 9.0, -9.0, 0.0, 0.0, 0.0, 0.0] + coefficients['k9'] = [9.0, 9.0, 0.0, 0.0, 0.0, 0.0, 1.0] + coefficients['4mn10'] = [10.0, -1, 0.0, 1.0, 0.0, 0.0, 0.0] + coefficients['m10'] = [10.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0] + coefficients['3msn10'] = [10.0, 1.0, -2, 1.0, 0.0, 0.0, 0.0] + coefficients['4ms10'] = [10.0, 2.0, -2, 0.0, 0.0, 0.0, 0.0] + coefficients['4mk10'] = [10.0, 2.0, 0.0, 0.0, 0.0, 0.0, 0.0] + coefficients['3msl10'] = [10.0, 3.0, -2, -1.0, 0.0, 0.0, 2.0] + coefficients['3m2s10'] = [10.0, 4.0, -4, 0.0, 0.0, 0.0, 0.0] + coefficients['3msk10'] = [10.0, 4.0, -2, 0.0, 0.0, 0.0, 0.0] + coefficients['s10'] = [10.0, 10.0, -10.0, 0.0, 0.0, 0.0, 0.0] + coefficients['4msk11'] = [11.0, 3.0, -2, 0.0, 0.0, 0.0, 1.0] + coefficients['s11'] = [11.0, 11.0, -11.0, 0.0, 0.0, 0.0, 0.0] + coefficients['5mn12'] = [12.0, -1, 0.0, 1.0, 0.0, 0.0, 0.0] + coefficients['m12'] = [12.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0] + coefficients['4msn12'] = [12.0, 1.0, -2, 1.0, 0.0, 0.0, 0.0] + coefficients['4mns12'] = [12.0, 1.0, -2, 1.0, 0.0, 0.0, 0.0] + coefficients['5ms12'] = [12.0, 2.0, -2, 0.0, 0.0, 0.0, 0.0] + coefficients['4msl12'] = [12.0, 3.0, -2, -1.0, 0.0, 0.0, 2.0] + coefficients['4m2s12'] = [12.0, 4.0, -4, 0.0, 0.0, 0.0, 0.0] + coefficients['s12'] = [12.0, 12.0, -12.0, 0.0, 0.0, 0.0, 0.0] + coefficients['m14'] = [14.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0] + coefficients['5msn14'] = [14.0, 1.0, -2.0, 1.0, 0.0, 0.0, 0.0] + coefficients['6ms14'] = [14.0, 2.0, -2.0, 0.0, 0.0, 0.0, 0.0] + coefficients['5m2s14'] = [14.0, 4.0, -4.0, 0.0, 0.0, 0.0, 0.0] + # return the coefficients table + return coefficients + +def replace_and_join(match): + return " ".join(match.group().split()) + +# PURPOSE: create argument parser +def arguments(): + parser = argparse.ArgumentParser( + description="""Converts the coefficients table to a json file" + """, + fromfile_prefix_chars="@" + ) + # command line parameters + parser.add_argument('--pretty', '-p', + action='store_true', + help='Pretty print the json file') + parser.add_argument('--verbose', '-v', + action='store_true', + help='Verbose output') + return parser + +def main(): + # Read the system arguments listed after the program + parser = arguments() + args,_ = parser.parse_known_args() + + # coefficients dictionary + coefficients = coefficients_table() + # writing coefficients to JSON file + json_file = pyTMD.utilities.get_data_path(['data','doodson.json']) + print(f'\t{json_file}') if args.verbose else None + with open(json_file, 'w') as fid: + indent = 4 if args.pretty else None + temp1 = json.dumps(coefficients, indent=indent) + temp2 = re.sub(r"(?<=\[)[^\[\]]+(?=\])", replace_and_join, temp1) + fid.write(temp2) + # verify outputs + with open(json_file, 'r') as fid: + test = json.load(fid) + assert test == coefficients, 'Error in coefficients table' + +if __name__ == '__main__': + main() \ No newline at end of file From 774f35c85f826103af18b1c0a48dec264ffd0ba2 Mon Sep 17 00:00:00 2001 From: Tyler Sutterley Date: Tue, 29 Oct 2024 09:42:40 -0700 Subject: [PATCH 6/7] Update arguments.py --- pyTMD/arguments.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/pyTMD/arguments.py b/pyTMD/arguments.py index 874d4690..1b1e9482 100755 --- a/pyTMD/arguments.py +++ b/pyTMD/arguments.py @@ -350,7 +350,7 @@ def minor_arguments( return (u, f, arg) # JSON file of Doodson coefficients -_coefficients_table = get_data_path(['data','coefficients.json']) +_coefficients_table = get_data_path(['data','doodson.json']) def coefficients_table( constituents: list | tuple | np.ndarray | str, From 5d1be5550a0dee7963538709a43bc3a021a28750 Mon Sep 17 00:00:00 2001 From: tsutterley Date: Tue, 29 Oct 2024 12:53:47 -0700 Subject: [PATCH 7/7] test: add test for extended doodson --- pyTMD/arguments.py | 2 +- test/test_arguments.py | 105 +++++++++++++++++++++++++++++++++++------ 2 files changed, 91 insertions(+), 16 deletions(-) diff --git a/pyTMD/arguments.py b/pyTMD/arguments.py index 1b1e9482..52843f21 100755 --- a/pyTMD/arguments.py +++ b/pyTMD/arguments.py @@ -1460,7 +1460,7 @@ def _constituent_parameters(c: str, **kwargs): # return the values for the constituent return (amplitude, phase, omega, alpha, species) -# Cartright and Tayler (1971) table with 3rd-degree values +# Cartwright and Tayler (1971) table with 3rd-degree values _ct1971_table_5 = get_data_path(['data','ct1971_tab5.txt']) # Cartwright and Edden (1973) table with updated values _ce1973_table_1 = get_data_path(['data','ce1973_tab1.txt']) diff --git a/test/test_arguments.py b/test/test_arguments.py index 92ed303b..0ff77f37 100644 --- a/test/test_arguments.py +++ b/test/test_arguments.py @@ -697,43 +697,118 @@ def test_doodson(): exp['2q1'] = 125.755 exp['p1'] = 163.555 # long-period species - exp['mm'] = '065.455' - exp['ssa'] = '057.555' - exp['msf'] = '073.555' - exp['mf'] = '075.555' - exp['msqm'] = '093.555' - exp['mtm'] = '085.455' - exp['node'] = '055.565' + exp['mm'] = 065.455 + exp['ssa'] = 057.555 + exp['msf'] = 073.555 + exp['mf'] = 075.555 + exp['msqm'] = 093.555 + exp['mtm'] = 085.455 + exp['node'] = 055.565 # short-period species exp['m3'] = 355.555 exp['m4'] = 455.555 exp['m6'] = 655.555 exp['m8'] = 855.555 + # shallow water species + exp['2so3'] = '3X1.555' + exp['2jp3'] = '3X3.355' + exp['kso3'] = '3X3.555' + exp['2jk3'] = '3X4.355' + exp['2ko3'] = '3X5.555' + # 3rd degree terms + exp["2q1'"] = 125.655 + exp["q1'"] = 135.555 + exp["o1'"] = 145.655 + exp["m1'"] = 155.555 + exp["k1'"] = 165.455 + exp["j1'"] = 175.555 + exp["2n2'"] = 235.655 + exp["n2'"] = 245.555 + exp["m2'"] = 255.655 + exp["l2'"] = 265.555 + exp["m3'"] = 355.555 + exp['lambda3'] = 363.655 + exp["l3"] = 365.455 + exp["l3b"] = 365.655 + exp["f3"] = 375.555 + exp["j3"] = 375.555 + exp["s3'"] = 382.555 # get observed values for constituents obs = doodson_number(exp.keys()) cartwright = doodson_number(exp.keys(), formalism='Cartwright') # check values for key,val in exp.items(): - assert float(val) == obs[key] + assert val == obs[key] # check values when entered as string test = doodson_number(key) - assert float(val) == test - # check conversion to and from Doodson numbers + assert val == test + # check conversion to Doodson numbers doodson = _to_doodson_number(cartwright[key]) - XDO = _to_extended_doodson(cartwright[key]) # check values when entered as Cartwright - assert float(val) == doodson + assert val == doodson # check values when entered as Doodson coefficients = _from_doodson_number(val) - extended = _from_extended_doodson(XDO) assert np.all(cartwright[key] == coefficients) - assert np.all(cartwright[key] == extended) + +def test_extended(): + """ + Tests the calculation of UKHO Extended Doodson numbers + """ + # expected values + exp = {} + # semi-diurnal species + exp['m2'] = 'BZZZZZZ' + exp['s2'] = 'BBXZZZZ' + exp['n2'] = 'BYZAZZZ' + exp['nu2'] = 'BYBYZZZ' + exp['mu2'] = 'BXBZZZZ' + exp['2n2'] = 'BXZBZZZ' + exp['lambda2'] = 'BAXAZZB' + exp['l2'] = 'BAZYZZB' + exp['k2'] = 'BBZZZZZ' + # diurnal species + exp['m1'] = 'AZZZZZA' + exp['s1'] = 'AAYZZZA' + exp['o1'] = 'AYZZZZY' + exp['oo1'] = 'ACZZZZA' + exp['k1'] = 'AAZZZZA' + exp['q1'] = 'AXZAZZY' + exp['2q1'] = 'AWZBZZY' + exp['p1'] = 'AAXZZZY' + # long-period species + exp['mm'] = 'ZAZYZZZ' + exp['ssa'] = 'ZZBZZZZ' + exp['msf'] = 'ZBXZZZZ' + exp['mf'] = 'ZBZZZZZ' + exp['msqm'] = 'ZDXZZZZ' + exp['mtm'] = 'ZCZYZZZ' + exp['node'] = 'ZZZZAZB' + # short-period species + exp['m3'] = 'CZZZZZZ' + exp['m4'] = 'DZZZZZZ' + exp['n4'] = 'DXZBZZZ' + exp['m6'] = 'FZZZZZZ' + exp['n6'] = 'FWZCZZZ' + exp['m8'] = 'HZZZZZZ' + exp['m10'] = 'JZZZZZZ' + exp['m12'] = 'LZZZZZZ' + # shallow water species + exp['2so3'] = 'CEVZZZA' + exp['2jp3'] = 'CEXXZZA' + exp['kso3'] = 'CEXZZZA' + exp['2jk3'] = 'CEYXZZZ' + exp['2ko3'] = 'CEZZZZA' + # get observed values for constituents + obs = doodson_number(exp.keys(), formalism='Extended') + # check values + for key,val in exp.items(): + assert val == obs[key] def test_parse_tables(): """ Tests the parsing of tables for tide potential coefficients """ - # Cartright and Tayler (1971) table with 3rd-degree values + # Cartwright and Tayler (1971) table with 3rd-degree values # Cartwright and Edden (1973) table with updated values for table in [_ct1971_table_5, _ce1973_table_1]: # parse table