Grid example¶
In this example we load a HDF5 (test) grid file into a corresponding Grid object, and use the inbuilt functionality to explore the grid.
[1]:
import matplotlib.pyplot as plt
import numpy as np
from unyt import angstrom
from synthesizer.grid import Grid
This object takes the location of the grids on your system (grid_dir) and the name of the grid you wish to load grid_name). Here we load a simple test grid provided with the module (hence the relative path).
[2]:
grid_dir = "../../../tests/test_grid"
grid_name = "test_grid"
grid = Grid(grid_name, grid_dir=grid_dir)
print(grid)
+------------------------------------------------------------------------------------------------+
| GRID |
+-----------------------------+------------------------------------------------------------------+
| Attribute | Value |
+-----------------------------+------------------------------------------------------------------+
| grid_dir | '../../../tests/test_grid' |
+-----------------------------+------------------------------------------------------------------+
| grid_name | 'test_grid' |
+-----------------------------+------------------------------------------------------------------+
| grid_ext | 'hdf5' |
+-----------------------------+------------------------------------------------------------------+
| grid_filename | '../../../tests/test_grid/test_grid.hdf5' |
+-----------------------------+------------------------------------------------------------------+
| reprocessed | True |
+-----------------------------+------------------------------------------------------------------+
| lines_available | True |
+-----------------------------+------------------------------------------------------------------+
| naxes | 2 |
+-----------------------------+------------------------------------------------------------------+
| has_lines | True |
+-----------------------------+------------------------------------------------------------------+
| has_spectra | True |
+-----------------------------+------------------------------------------------------------------+
| lines_available | True |
+-----------------------------+------------------------------------------------------------------+
| reprocessed | True |
+-----------------------------+------------------------------------------------------------------+
| shape | (51, 13, 9244) |
+-----------------------------+------------------------------------------------------------------+
| available_lines | [Al 2 1670.79A, Ar 3 7135.79A, Ar 3 7751.11A, Ar 4 2853.66A, |
| | C 1 1657.91A, C 1 1992.01A, C 1 2582.90A, C 2 1334.53A, |
| | C 2 1335.66A, C 2 1335.71A, C 2 2325.40A, C 2 2326.93A, |
| | C 3 1906.68A, C 3 1908.73A, C 4 1548.19A, C 4 1550.77A, |
| | Ca 2 7291.47A, Ca 2 7323.89A, Cl 2 8578.70A, Fe 2 1.25668m, |
| | Fe 2 1.27877m, Fe 2 1.29427m, Fe 2 1.32055m, Fe 2 1.32777m, |
| | Fe 2 1.37181m, Fe 2 1.53348m, Fe 2 1.59948m, Fe 2 1.64355m, |
| | Fe 2 1.66377m, Fe 2 1.67688m, Fe 2 1.71113m, Fe 2 1.74494m, |
| | Fe 2 1.79711m, Fe 2 1.80002m, Fe 2 1.80940m, Fe 2 1.89541m, |
| | Fe 2 1.95361m, Fe 2 2395.63A, Fe 2 2399.24A, Fe 2 2406.66A, |
| | Fe 2 2410.52A, Fe 2 2598.37A, Fe 2 2607.09A, Fe 2 2611.87A, |
| | Fe 2 2613.82A, Fe 2 2625.67A, Fe 2 2628.29A, Fe 2 2631.05A, |
| | Fe 2 2631.32A, Fe 2 4243.97A, Fe 2 4276.84A, Fe 2 4287.39A, |
| | Fe 2 4319.62A, Fe 2 4346.86A, Fe 2 4352.79A, Fe 2 4358.37A, |
| | Fe 2 4359.33A, Fe 2 4413.78A, Fe 2 4416.27A, Fe 2 4452.10A, |
| | Fe 2 4474.90A, Fe 2 4814.54A, Fe 2 4874.50A, Fe 2 4889.62A, |
| | Fe 2 4905.35A, Fe 2 4923.92A, Fe 2 4947.39A, Fe 2 4973.40A, |
| | Fe 2 5005.52A, Fe 2 5018.44A, Fe 2 5020.25A, Fe 2 5049.30A, |
| | Fe 2 5072.41A, Fe 2 5111.64A, Fe 2 5158.01A, Fe 2 5158.79A, |
| | Fe 2 5169.03A, Fe 2 5184.80A, Fe 2 5261.63A, Fe 2 5273.36A, |
| | Fe 2 5284.10A, Fe 2 5333.66A, Fe 2 5376.47A, Fe 2 5412.67A, |
| | Fe 2 5433.15A, Fe 2 5527.36A, Fe 2 6516.08A, Fe 2 7155.17A, |
| | Fe 2 7172.00A, Fe 2 7388.17A, Fe 2 7452.56A, Fe 2 8616.95A, |
| | Fe 2 8891.93A, Fe 2 9051.95A, Fe 2 9226.63A, Fe 2 9267.56A, |
| | Fe 2 9399.04A, Fe 2 9470.94A, Fe 3 4658.05A, Fe 3 4985.87A, |
| | Fe 3 5270.40A, Fe 4 2829.36A, Fe 4 2835.74A, Fe 4 3094.96A, |
| | Fe 5 3891.28A, Fe 6 3662.50A, Fe 6 5176.04A, Fe 7 3586.32A, |
| | Fe 7 3758.92A, Fe 7 5720.71A, Fe 7 6086.97A, H 1 1.00494m, |
| | H 1 1.09381m, H 1 1.28181m, H 1 1.87510m, H 1 1215.67A, |
| | H 1 2.16553m, H 1 3734.37A, H 1 3750.15A, H 1 3770.63A, |
| | H 1 3797.90A, H 1 3835.38A, H 1 3889.05A, H 1 3970.07A, |
| | H 1 4101.73A, H 1 4340.46A, H 1 4861.32A, H 1 6562.80A, |
| | H 1 9229.02A, H 1 9545.97A, He 1 1.08291m, He 1 1.08303m, |
| | He 1 3187.74A, He 1 3888.64A, He 1 5875.61A, He 1 5875.64A, |
| | He 1 6678.15A, He 2 1025.27A, He 2 1084.94A, He 2 1215.13A, |
| | He 2 1640.41A, He 2 4685.68A, Mg 2 2795.53A, Mg 2 2802.71A, |
| | Mg 5 2782.76A, Mg 6 1806.00A, Mg 7 2628.89A, N 2 6548.05A, |
| | N 2 6583.45A, N 3 1749.67A, N 4 1486.50A, N 5 1238.82A, |
| | N 5 1242.80A, Ne 3 3868.76A, Ne 3 3967.47A, Ne 4 1601.45A, |
| | Ne 5 3345.82A, Ne 5 3425.88A, Ni 2 1.19102m, Ni 2 1.93877m, |
| | Ni 2 6666.80A, Ni 2 7377.83A, Ni 2 7411.61A, O 1 1.12863m, |
| | O 1 1.12864m, O 1 1.12869m, O 1 1.12870m, O 1 1.12873m, |
| | O 1 1302.17A, O 1 1304.86A, O 1 1306.03A, O 1 1641.31A, |
| | O 1 6300.30A, O 1 6363.78A, O 1 8446.25A, O 1 8446.36A, |
| | O 1 8446.76A, O 2 3726.03A, O 2 3728.81A, O 3 1660.81A, |
| | O 3 1666.15A, O 3 2320.95A, O 3 4363.21A, O 3 4958.91A, |
| | O 3 5006.84A, O 4 1399.78A, O 4 1401.16A, O 4 1404.81A, |
| | O 4 1407.38A, O 5 1218.34A, O 6 1031.91A, O 6 1037.61A, |
| | S 2 1.02867m, S 2 1.03205m, S 2 1.03364m, S 2 4068.60A, |
| | S 2 4076.35A, S 2 6716.44A, S 2 6730.82A, S 3 9068.62A, |
| | S 3 9530.62A, Si 2 1179.59A, Si 2 1260.42A, Si 2 1264.74A, |
| | Si 2 1265.00A, Si 2 1526.71A, Si 2 1533.43A, Si 3 1206.50A, |
| | Si 3 1882.71A, Si 3 1892.03A, Si 4 1393.75A, Si 4 1402.77A, |
| | Si 6 1.96247m, Si 7 2.48071m, Si 7 2146.64A, ] |
+-----------------------------+------------------------------------------------------------------+
| available_spectra | [incident, linecont, nebular, transmitted, |
| | total, nebular_continuum, ] |
+-----------------------------+------------------------------------------------------------------+
| axes | [log10age, metallicity, ] |
+-----------------------------+------------------------------------------------------------------+
| log10age (51,) | 6.00e+00 -> 1.10e+01 (Mean: 8.50e+00) |
+-----------------------------+------------------------------------------------------------------+
| metallicity (13,) | 1.00e-05 -> 4.00e-02 (Mean: 1.06e-02) |
+-----------------------------+------------------------------------------------------------------+
| lam (9244,) | 1.30e-04 Å -> 2.99e+11 Å (Mean: 9.73e+09 Å) |
+-----------------------------+------------------------------------------------------------------+
| log10ages (51,) | 6.00e+00 -> 1.10e+01 (Mean: 8.50e+00) |
+-----------------------------+------------------------------------------------------------------+
| log10metallicities (13,) | -5.00e+00 -> -1.40e+00 (Mean: -2.49e+00) |
+-----------------------------+------------------------------------------------------------------+
| spectra | incident: ndarray |
| | linecont: ndarray |
| | nebular: ndarray |
| | transmitted: ndarray |
| | total: ndarray |
| | nebular_continuum: ndarray |
+-----------------------------+------------------------------------------------------------------+
| line_lams | Al 2 1670.79A: float64 |
| | Ar 3 7135.79A: float64 |
| | Ar 3 7751.11A: float64 |
| | Ar 4 2853.66A: float64 |
| | C 1 1657.91A: float64 |
| | C 1 1992.01A: float64 |
| | C 1 2582.90A: float64 |
| | C 2 1334.53A: float64 |
| | C 2 1335.66A: float64 |
| | C 2 1335.71A: float64 |
| | C 2 2325.40A: float64 |
| | C 2 2326.93A: float64 |
| | C 3 1906.68A: float64 |
| | C 3 1908.73A: float64 |
| | C 4 1548.19A: float64 |
| | C 4 1550.77A: float64 |
| | Ca 2 7291.47A: float64 |
| | Ca 2 7323.89A: float64 |
| | Cl 2 8578.70A: float64 |
| | Fe 2 1.25668m: float64 |
| | Fe 2 1.27877m: float64 |
| | Fe 2 1.29427m: float64 |
| | Fe 2 1.32055m: float64 |
| | Fe 2 1.32777m: float64 |
| | Fe 2 1.37181m: float64 |
| | Fe 2 1.53348m: float64 |
| | Fe 2 1.59948m: float64 |
| | Fe 2 1.64355m: float64 |
| | Fe 2 1.66377m: float64 |
| | Fe 2 1.67688m: float64 |
| | Fe 2 1.71113m: float64 |
| | Fe 2 1.74494m: float64 |
| | Fe 2 1.79711m: float64 |
| | Fe 2 1.80002m: float64 |
| | Fe 2 1.80940m: float64 |
| | Fe 2 1.89541m: float64 |
| | Fe 2 1.95361m: float64 |
| | Fe 2 2395.63A: float64 |
| | Fe 2 2399.24A: float64 |
| | Fe 2 2406.66A: float64 |
| | Fe 2 2410.52A: float64 |
| | Fe 2 2598.37A: float64 |
| | Fe 2 2607.09A: float64 |
| | Fe 2 2611.87A: float64 |
| | Fe 2 2613.82A: float64 |
| | Fe 2 2625.67A: float64 |
| | Fe 2 2628.29A: float64 |
| | Fe 2 2631.05A: float64 |
| | Fe 2 2631.32A: float64 |
| | Fe 2 4243.97A: float64 |
| | Fe 2 4276.84A: float64 |
| | Fe 2 4287.39A: float64 |
| | Fe 2 4319.62A: float64 |
| | Fe 2 4346.86A: float64 |
| | Fe 2 4352.79A: float64 |
| | Fe 2 4358.37A: float64 |
| | Fe 2 4359.33A: float64 |
| | Fe 2 4413.78A: float64 |
| | Fe 2 4416.27A: float64 |
| | Fe 2 4452.10A: float64 |
| | Fe 2 4474.90A: float64 |
| | Fe 2 4814.54A: float64 |
| | Fe 2 4874.50A: float64 |
| | Fe 2 4889.62A: float64 |
| | Fe 2 4905.35A: float64 |
| | Fe 2 4923.92A: float64 |
| | Fe 2 4947.39A: float64 |
| | Fe 2 4973.40A: float64 |
| | Fe 2 5005.52A: float64 |
| | Fe 2 5018.44A: float64 |
| | Fe 2 5020.25A: float64 |
| | Fe 2 5049.30A: float64 |
| | Fe 2 5072.41A: float64 |
| | Fe 2 5111.64A: float64 |
| | Fe 2 5158.01A: float64 |
| | Fe 2 5158.79A: float64 |
| | Fe 2 5169.03A: float64 |
| | Fe 2 5184.80A: float64 |
| | Fe 2 5261.63A: float64 |
| | Fe 2 5273.36A: float64 |
| | Fe 2 5284.10A: float64 |
| | Fe 2 5333.66A: float64 |
| | Fe 2 5376.47A: float64 |
| | Fe 2 5412.67A: float64 |
| | Fe 2 5433.15A: float64 |
| | Fe 2 5527.36A: float64 |
| | Fe 2 6516.08A: float64 |
| | Fe 2 7155.17A: float64 |
| | Fe 2 7172.00A: float64 |
| | Fe 2 7388.17A: float64 |
| | Fe 2 7452.56A: float64 |
| | Fe 2 8616.95A: float64 |
| | Fe 2 8891.93A: float64 |
| | Fe 2 9051.95A: float64 |
| | Fe 2 9226.63A: float64 |
| | Fe 2 9267.56A: float64 |
| | Fe 2 9399.04A: float64 |
| | Fe 2 9470.94A: float64 |
| | Fe 3 4658.05A: float64 |
| | Fe 3 4985.87A: float64 |
| | Fe 3 5270.40A: float64 |
| | Fe 4 2829.36A: float64 |
| | Fe 4 2835.74A: float64 |
| | Fe 4 3094.96A: float64 |
| | Fe 5 3891.28A: float64 |
| | Fe 6 3662.50A: float64 |
| | Fe 6 5176.04A: float64 |
| | Fe 7 3586.32A: float64 |
| | Fe 7 3758.92A: float64 |
| | Fe 7 5720.71A: float64 |
| | Fe 7 6086.97A: float64 |
| | H 1 1.00494m: float64 |
| | H 1 1.09381m: float64 |
| | H 1 1.28181m: float64 |
| | H 1 1.87510m: float64 |
| | H 1 1215.67A: float64 |
| | H 1 2.16553m: float64 |
| | H 1 3734.37A: float64 |
| | H 1 3750.15A: float64 |
| | H 1 3770.63A: float64 |
| | H 1 3797.90A: float64 |
| | H 1 3835.38A: float64 |
| | H 1 3889.05A: float64 |
| | H 1 3970.07A: float64 |
| | H 1 4101.73A: float64 |
| | H 1 4340.46A: float64 |
| | H 1 4861.32A: float64 |
| | H 1 6562.80A: float64 |
| | H 1 9229.02A: float64 |
| | H 1 9545.97A: float64 |
| | He 1 1.08291m: float64 |
| | He 1 1.08303m: float64 |
| | He 1 3187.74A: float64 |
| | He 1 3888.64A: float64 |
| | He 1 5875.61A: float64 |
| | He 1 5875.64A: float64 |
| | He 1 6678.15A: float64 |
| | He 2 1025.27A: float64 |
| | He 2 1084.94A: float64 |
| | He 2 1215.13A: float64 |
| | He 2 1640.41A: float64 |
| | He 2 4685.68A: float64 |
| | Mg 2 2795.53A: float64 |
| | Mg 2 2802.71A: float64 |
| | Mg 5 2782.76A: float64 |
| | Mg 6 1806.00A: float64 |
| | Mg 7 2628.89A: float64 |
| | N 2 6548.05A: float64 |
| | N 2 6583.45A: float64 |
| | N 3 1749.67A: float64 |
| | N 4 1486.50A: float64 |
| | N 5 1238.82A: float64 |
| | N 5 1242.80A: float64 |
| | Ne 3 3868.76A: float64 |
| | Ne 3 3967.47A: float64 |
| | Ne 4 1601.45A: float64 |
| | Ne 5 3345.82A: float64 |
| | Ne 5 3425.88A: float64 |
| | Ni 2 1.19102m: float64 |
| | Ni 2 1.93877m: float64 |
| | Ni 2 6666.80A: float64 |
| | Ni 2 7377.83A: float64 |
| | Ni 2 7411.61A: float64 |
| | O 1 1.12863m: float64 |
| | O 1 1.12864m: float64 |
| | O 1 1.12869m: float64 |
| | O 1 1.12870m: float64 |
| | O 1 1.12873m: float64 |
| | O 1 1302.17A: float64 |
| | O 1 1304.86A: float64 |
| | O 1 1306.03A: float64 |
| | O 1 1641.31A: float64 |
| | O 1 6300.30A: float64 |
| | O 1 6363.78A: float64 |
| | O 1 8446.25A: float64 |
| | O 1 8446.36A: float64 |
| | O 1 8446.76A: float64 |
| | O 2 3726.03A: float64 |
| | O 2 3728.81A: float64 |
| | O 3 1660.81A: float64 |
| | O 3 1666.15A: float64 |
| | O 3 2320.95A: float64 |
| | O 3 4363.21A: float64 |
| | O 3 4958.91A: float64 |
| | O 3 5006.84A: float64 |
| | O 4 1399.78A: float64 |
| | O 4 1401.16A: float64 |
| | O 4 1404.81A: float64 |
| | O 4 1407.38A: float64 |
| | O 5 1218.34A: float64 |
| | O 6 1031.91A: float64 |
| | O 6 1037.61A: float64 |
| | S 2 1.02867m: float64 |
| | S 2 1.03205m: float64 |
| | S 2 1.03364m: float64 |
| | S 2 4068.60A: float64 |
| | S 2 4076.35A: float64 |
| | S 2 6716.44A: float64 |
| | S 2 6730.82A: float64 |
| | S 3 9068.62A: float64 |
| | S 3 9530.62A: float64 |
| | Si 2 1179.59A: float64 |
| | Si 2 1260.42A: float64 |
| | Si 2 1264.74A: float64 |
| | Si 2 1265.00A: float64 |
| | Si 2 1526.71A: float64 |
| | Si 2 1533.43A: float64 |
| | Si 3 1206.50A: float64 |
| | Si 3 1882.71A: float64 |
| | Si 3 1892.03A: float64 |
| | Si 4 1393.75A: float64 |
| | Si 4 1402.77A: float64 |
| | Si 6 1.96247m: float64 |
| | Si 7 2.48071m: float64 |
| | Si 7 2146.64A: float64 |
+-----------------------------+------------------------------------------------------------------+
| line_lums | incident: dict |
| | linecont: dict |
| | nebular: dict |
| | transmitted: dict |
| | total: dict |
| | nebular_continuum: dict |
+-----------------------------+------------------------------------------------------------------+
| line_conts | incident: dict |
| | linecont: dict |
| | nebular: dict |
| | transmitted: dict |
| | total: dict |
| | nebular_continuum: dict |
+-----------------------------+------------------------------------------------------------------+
| parameters | CMB: str |
| | T_floor: int64 |
| | abundance_scalings_carbon: str |
| | abundance_scalings_nitrogen: str |
| | alpha: float64 |
| | axes: ndarray |
| | axes_alternative: ndarray |
| | cloudy_version: str |
| | constant_density: bool |
| | cosmic_rays: bool |
| | depletion_model: str |
| | depletion_scale: float64 |
| | geometry: str |
| | grains: str |
| | hydrogen_density: float64 |
| | incident_axes: ndarray |
| | ionisation_parameter_model: str |
| | iterate_to_convergence: bool |
| | log10age: ndarray |
| | metallicity: ndarray |
| | output_cont: bool |
| | output_linelist: str |
| | parameter_file: str |
| | radius: float64 |
| | reference_abundance: str |
| | reference_ionisation_parameter: float64 |
| | reference_log10age: float64 |
| | reference_log10age_index: int64 |
| | reference_metallicity: float64 |
| | reference_metallicity_index: int64 |
| | resolution: float64 |
| | stop_T: int64 |
| | stop_efrac: int64 |
| | turbulence: int64 |
| | z: float64 |
+-----------------------------+------------------------------------------------------------------+
| log10_specific_ionising_lum | HI: ndarray |
| | HeII: ndarray |
+-----------------------------+------------------------------------------------------------------+
A Grid can also take various arguments to limit the size of the grid, e.g. by isolating the Grid to a wavelength region of interest. This is particularly useful when making a large number of spectra from a high resolution Grid, where the memory footprint can become large.
Passing a wavelength array¶
If you only care about a grid of specific wavelength values, you can pass this array and the Grid will automatically be interpolated onto the new wavelength array using spectres:
[3]:
# Define a new set of wavelengths
new_lams = np.logspace(2, 5, 1000) * angstrom
# Create a new grid
grid = Grid(grid_name, grid_dir=grid_dir, new_lam=new_lams)
print(grid.shape)
(51, 13, 1000)
Passing wavelength limits¶
If you don’t want to modify the underlying grid resolution, but only care about a specific wavelength range, you can pass limits to truncate the grid at:
[4]:
# Create a new grid
grid = Grid(
grid_name, grid_dir=grid_dir, lam_lims=(10**3 * angstrom, 10**4 * angstrom)
)
print(grid.shape)
(51, 13, 691)
Plot a single grid point¶
We can plot the spectra at the location of a single point in our grid. First, we choose some age and metallicity
[5]:
# Return to the unmodified grid
grid = Grid(grid_name, grid_dir=grid_dir)
log10age = 6.0 # log10(age/yr)
Z = 0.01 # metallicity
We then get the index location of that grid point for this age and metallicity
[6]:
grid_point = grid.get_grid_point(log10ages=log10age, metallicity=Z)
We can then loop over the available spectra (contained in grid.spec_names) and plot
[7]:
for spectra_id in grid.available_spectra:
# Get `Sed` object
sed = grid.get_spectra(grid_point, spectra_id=spectra_id)
# Mask zero valued elements
mask = sed.lnu > 0
plt.plot(
np.log10(sed.lam[mask]),
np.log10(sed.lnu[mask]),
lw=1,
alpha=0.8,
label=spectra_id,
)
plt.legend(fontsize=8, labelspacing=0.0)
plt.xlabel(r"$\rm log_{10}(\lambda/\AA)$")
plt.ylabel(r"$\rm log_{10}(L_{\nu}/erg\ s^{-1}\ Hz^{-1} M_{\odot}^{-1})$")
[7]:
Text(0, 0.5, '$\\rm log_{10}(L_{\\nu}/erg\\ s^{-1}\\ Hz^{-1} M_{\\odot}^{-1})$')
Plot ionising luminosities¶
We can also plot properties over the entire age and metallicity grid, such as the ionising luminosity.
In the examples below we plot ionising luminosities for HI and HeII
[8]:
fig, ax = grid.plot_specific_ionising_lum(ion="HI")
[9]:
fig, ax = grid.plot_specific_ionising_lum(ion="HeII")
Resampling Grids¶
If you want to resample a grid after instantiation, you can apply the intrep_spectra method:
[10]:
# Define a new set of wavelengths
new_lams = np.logspace(2, 5, 10000) * angstrom
print("The old grid had dimensions:", grid.spectra["incident"].shape)
# Get the grid interpolated onto the new wavelength array
grid.interp_spectra(new_lam=new_lams)
print("The interpolated grid has dimensions:", grid.spectra["incident"].shape)
The old grid had dimensions: (51, 13, 9244)
The interpolated grid has dimensions: (51, 13, 10000)
Note that this will overwrite the spectra and wavelengths read from the file in place. To get back to the original arrays, a separate Grid can be instatiated without the modified wavelength array.
Converting a Grid into an Sed¶
Any of the spectra arrays stored within a Grid can be returned as Sed objects (see the Sed docs). This enables all of the analysis methods provide on an Sed to be used on the whole spectra grid. To do this we simply call get_sed with the spectra type we want to extract, and then use any of the included methods.
[11]:
# Get the sed object
sed = grid.get_sed(spectra_type="incident")
# Measure the balmer break for all spectra in the grid (limiting the output)
sed.measure_balmer_break()[5:10, 5:10]
[11]:
array([[0.99095578, 1.00851607, 1.00394175, 0.99979438, 0.94348793],
[1.01696748, 1.01627346, 1.0026636 , 0.97766383, 0.97755911],
[1.04712358, 1.03816692, 1.02788439, 1.0014771 , 0.9827252 ],
[1.12597668, 1.08081315, 1.05479005, 1.02042145, 1.01481675],
[1.09623435, 1.06834097, 1.05297887, 1.04633496, 1.03886266]])