DREAM data reduction#
We begin with relevant imports. We will be using tutorial data downloaded with pooch. If you get an error about a missing module pooch, you can install it with !pip install pooch:
[1]:
import scipp as sc
from ess import dream, powder
import ess.dream.data # noqa: F401
from ess.powder.types import *
Create and configure the workflow#
We begin by creating the Dream (Geant4) workflow object which is a skeleton for reducing Dream data, with pre-configured steps.
[2]:
workflow = dream.DreamGeant4Workflow(run_norm=powder.RunNormalization.proton_charge)
We then need to set the missing parameters which are specific to each experiment (the keys are types defined in essdiffraction.powder.types):
[3]:
workflow[Filename[SampleRun]] = dream.data.simulated_diamond_sample()
workflow[Filename[VanadiumRun]] = dream.data.simulated_vanadium_sample()
workflow[Filename[BackgroundRun]] = dream.data.simulated_empty_can()
workflow[CalibrationFilename] = None
workflow[NeXusDetectorName] = "mantle"
# The upper bounds mode is not yet implemented.
workflow[UncertaintyBroadcastMode] = UncertaintyBroadcastMode.drop
# Edges for binning in d-spacing
workflow[DspacingBins] = sc.linspace("dspacing", 0.0, 2.3434, 201, unit="angstrom")
# Empty masks by default
workflow[TofMask] = None
workflow[TwoThetaMask] = None
workflow[WavelengthMask] = None
# No pixel masks
workflow = powder.with_pixel_mask_filenames(workflow, [])
# Time-of-flight lookup table
workflow[TimeOfFlightLookupTableFilename] = dream.data.tof_lookup_table_high_flux()
Downloading file 'DREAM_simple_pwd_workflow/data_dream_diamond_vana_container_sample_union.csv.zip' from 'https://public.esss.dk/groups/scipp/ess/dream/1/DREAM_simple_pwd_workflow/data_dream_diamond_vana_container_sample_union.csv.zip' to '/home/runner/.cache/ess/dream/1'.
Downloading file 'DREAM_simple_pwd_workflow/data_dream_vanadium.csv.zip' from 'https://public.esss.dk/groups/scipp/ess/dream/1/DREAM_simple_pwd_workflow/data_dream_vanadium.csv.zip' to '/home/runner/.cache/ess/dream/1'.
Downloading file 'DREAM_simple_pwd_workflow/data_dream_vana_container_sample_union.csv.zip' from 'https://public.esss.dk/groups/scipp/ess/dream/1/DREAM_simple_pwd_workflow/data_dream_vana_container_sample_union.csv.zip' to '/home/runner/.cache/ess/dream/1'.
Downloading file 'DREAM-high-flux-tof-lookup-table.h5' from 'https://public.esss.dk/groups/scipp/ess/dream/1/DREAM-high-flux-tof-lookup-table.h5' to '/home/runner/.cache/ess/dream/1'.
Use the reduction workflow#
We can visualize the graph for computing the final normalized result for intensity as a function of time-of-flight:
[4]:
workflow.visualize([IofTof, ReducedTofCIF], graph_attr={"rankdir": "LR"})
[4]:
We then call compute() to compute the result: (The cif object will later be used to write the result to disk.)
[5]:
results = workflow.compute([IofTof, ReducedTofCIF])
result = results[IofTof]
cif_data = results[ReducedTofCIF]
[6]:
histogram = result.hist()
histogram.plot()
[6]:
We can now save the result to disk:
[7]:
cif_data.comment = """This file was generated with the DREAM data reduction user guide
in the documentation of ESSdiffraction.
See https://scipp.github.io/essdiffraction/
"""
cif_data.save("reduced.cif")
Compute intermediate results#
For inspection and debugging purposes, we can also compute intermediate results. To avoid repeated computation (including costly loading of files), we can request multiple results at once, including the final result, if desired. For example:
[8]:
intermediates = workflow.compute(
(
DataWithScatteringCoordinates[SampleRun],
MaskedData[SampleRun],
)
)
intermediates[DataWithScatteringCoordinates[SampleRun]]
[8]:
scipp.DataArray (185.71 MB)
- module: 14
- segment: 6
- counter: 2
- wire: 32
- strip: 256
- L1()float64mm76550.00007901035
Values:
array(76550.00007901) - L2(module, segment, counter, wire, strip)float64mm1543.532, 1537.244, ..., nan, nan
Values:
array([[[[[1543.53184431, 1537.24446921, 1530.07155038, ..., 1528.81489917, 1532.22281701, 1546.12981627], [1562.11553929, 1552.24823649, 1547.00052107, ..., 1539.05572304, 1560.10595619, 1565.45199794], [1581.57453492, 1562.68486368, 1562.60318059, ..., 1555.0087396 , 1563.58989265, 1570.61617046], ..., [ nan, nan, nan, ..., nan, nan, nan], [2032.32152714, nan, nan, ..., nan, nan, nan], [2034.39169305, nan, nan, ..., nan, nan, nan]], [[1545.62748478, 1540.65632508, 1537.14008199, ..., 1531.05651167, 1534.11436498, 1546.86099944], [1565.84050464, 1554.75820256, 1543.68870778, ..., 1544.7089859 , nan, 1555.90347856], [1579.95431564, 1567.26422742, 1557.30281799, ..., 1561.80768922, 1571.24665546, 1580.89487254], ..., [ nan, nan, nan, ..., nan, nan, nan], [ nan, nan, nan, ..., nan, nan, nan], [ nan, nan, nan, ..., nan, nan, nan]]], [[[1546.66371101, 1535.06174407, 1528.34242771, ..., 1520.52843151, 1536.23161818, 1544.6716277 ], [1567.78194509, 1554.94500537, 1540.3360113 , ..., nan, 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Values:
array([1, 2]) - gravity()vector3m/s^2[ 0. -9.80665 0. ]
Values:
array([ 0. , -9.80665, 0. ]) - incident_beam()vector3mm[3.478e+00 0.000e+00 7.655e+04]
Values:
array([3.478e+00, 0.000e+00, 7.655e+04]) - module(module)int641, 2, ..., 13, 14
Values:
array([ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14]) - position(module, segment, counter, wire, strip)vector3mm[ 943.7585 552.66233333 -1089.20833333], [ 943.48333333 555.36133333 -1079.13555556], ..., [nan nan nan], [nan nan nan]
Values:
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nan, nan, nan], [ nan, nan, nan], ..., [ nan, nan, nan], [ nan, nan, nan], [ nan, nan, nan]], [[ nan, nan, nan], [ nan, nan, nan], [ 760.937 , -1227.1 , -1396.23 ], ..., [ nan, nan, nan], [ nan, nan, nan], [ nan, nan, nan]]], [[[ 531.313 , -956.38975 , -1089.17 ], [ 533.4215 , -953.57925 , -1073.2925 ], [ 530.5145 , -958.12275 , -1061.7575 ], ..., [ 528.432 , -957.681 , 1058.52 ], [ nan, nan, nan], [ 531.055 , -963.04 , 1094.09333333]], [[ nan, nan, nan], [ 542.3512 , -964.207 , -1090.736 ], [ 541.7365 , -966.25 , -1078.21 ], ..., [ nan, nan, nan], [ 543.5225 , -963.978 , 1090.315 ], [ 538.6965 , -964.471 , 1094.68 ]], [[ 547.4695 , -977.21683333, -1114.465 ], [ 548.0585 , -979.87325 , -1104.4125 ], [ 551.46466667, -980.02366667, -1097.29666667], ..., [ nan, nan, nan], [ 551.346 , -973.411 , 1105.57 ], [ 551.53433333, -974.734 , 1114.30666667]], ..., [[ nan, nan, nan], [ nan, nan, nan], [ 749.519 , -1215.74 , -1381.89 ], ..., [ nan, nan, nan], [ nan, nan, nan], [ nan, nan, nan]], [[ nan, nan, nan], [ nan, nan, nan], [ nan, nan, nan], ..., [ nan, nan, nan], [ 754.327 , -1220.94 , 1409.76 ], [ nan, nan, nan]], [[ nan, nan, nan], [ nan, nan, nan], [ nan, nan, nan], ..., [ nan, nan, nan], [ nan, nan, nan], [ nan, nan, nan]]]]]], shape=(14, 6, 2, 32, 256, 3)) - sample_position()vector3mm[0. 0. 0.]
Values:
array([0., 0., 0.]) - scattered_beam(module, segment, counter, wire, strip)vector3mm[ 943.7585 552.66233333 -1089.20833333], [ 943.48333333 555.36133333 -1079.13555556], ..., [nan nan nan], [nan nan nan]
Values:
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nan, nan, nan], [ nan, nan, nan], ..., [ nan, nan, nan], [ nan, nan, nan], [ nan, nan, nan]], [[ nan, nan, nan], [ nan, nan, nan], [ 760.937 , -1227.1 , -1396.23 ], ..., [ nan, nan, nan], [ nan, nan, nan], [ nan, nan, nan]]], [[[ 531.313 , -956.38975 , -1089.17 ], [ 533.4215 , -953.57925 , -1073.2925 ], [ 530.5145 , -958.12275 , -1061.7575 ], ..., [ 528.432 , -957.681 , 1058.52 ], [ nan, nan, nan], [ 531.055 , -963.04 , 1094.09333333]], [[ nan, nan, nan], [ 542.3512 , -964.207 , -1090.736 ], [ 541.7365 , -966.25 , -1078.21 ], ..., [ nan, nan, nan], [ 543.5225 , -963.978 , 1090.315 ], [ 538.6965 , -964.471 , 1094.68 ]], [[ 547.4695 , -977.21683333, -1114.465 ], [ 548.0585 , -979.87325 , -1104.4125 ], [ 551.46466667, -980.02366667, -1097.29666667], ..., [ nan, nan, nan], [ 551.346 , -973.411 , 1105.57 ], [ 551.53433333, -974.734 , 1114.30666667]], ..., [[ nan, nan, nan], [ nan, nan, nan], [ 749.519 , -1215.74 , -1381.89 ], ..., [ nan, nan, nan], [ nan, nan, nan], [ nan, nan, nan]], [[ nan, nan, nan], [ nan, nan, nan], [ nan, nan, nan], ..., [ nan, nan, nan], [ 754.327 , -1220.94 , 1409.76 ], [ nan, nan, nan]], [[ nan, nan, nan], [ nan, nan, nan], [ nan, nan, nan], ..., [ nan, nan, nan], [ nan, nan, nan], [ nan, nan, nan]]]]]], shape=(14, 6, 2, 32, 256, 3)) - segment(segment)int641, 2, ..., 5, 6
Values:
array([1, 2, 3, 4, 5, 6]) - source_position()vector3mm[-3.478e+00 0.000e+00 -7.655e+04]
Values:
array([-3.478e+00, 0.000e+00, -7.655e+04]) - strip(strip)int641, 2, ..., 255, 256
Values:
array([ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256]) - two_theta(module, segment, counter, wire, strip)float64rad2.354, 2.349, ..., nan, nan
Values:
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nan, nan, ..., nan, nan, nan], [ nan, nan, nan, ..., nan, nan, nan]]]], ..., [[[[2.35457504, 2.34947868, 2.34123046, ..., 0.79692125, 0.79485368, 0.78568186], [2.35425908, 2.34911239, 2.344575 , ..., nan, 0.79064216, 0.7869416 ], [2.35522894, 2.34734449, 2.3427373 , ..., 0.79888204, 0.79299021, 0.78684084], ..., [ nan, nan, 2.34394022, ..., nan, nan, 0.78420285], [2.35739196, nan, 2.33940987, ..., nan, nan, nan], [2.35371569, nan, 2.34063685, ..., nan, nan, nan]], [[2.35450893, 2.34790716, 2.34111446, ..., 0.80141922, nan, 0.78742848], [2.35585311, 2.34699768, 2.3393796 , ..., 0.80076332, 0.79599585, nan], [2.3515635 , 2.34734511, 2.34121542, ..., 0.79721015, 0.79676806, 0.78724801], ..., [ nan, nan, nan, ..., nan, nan, nan], [ nan, nan, nan, ..., nan, nan, nan], [2.3561904 , nan, 2.34081152, ..., nan, nan, nan]]], [[[2.35534659, 2.34686987, 2.34124846, ..., 0.79896619, 0.79507362, 0.78648172], [2.35411397, 2.34909123, 2.34219797, ..., 0.79986197, 0.79633513, 0.78701414], [2.35407724, 2.34828207, 2.34260813, ..., nan, 0.79184334, 0.78920814], ..., [ nan, nan, nan, ..., nan, 0.79224065, nan], [ nan, nan, nan, ..., nan, nan, nan], [ nan, nan, nan, ..., nan, nan, nan]], [[2.35235091, 2.34667372, 2.33998121, ..., 0.79951776, 0.7940407 , 0.78904102], [2.35422072, 2.34705264, 2.33968589, ..., nan, 0.79343835, 0.78824448], [2.35435413, 2.34830445, 2.33767322, ..., 0.80007065, 0.79615596, 0.78786998], ..., [2.35658607, nan, 2.34316486, ..., nan, nan, nan], [ nan, nan, 2.34334845, ..., nan, nan, nan], [ nan, nan, nan, ..., nan, nan, nan]]], [[[2.35475709, 2.34849498, 2.34170979, ..., 0.79815575, 0.79564217, nan], [2.35529288, 2.34662011, 2.34157254, ..., 0.79872101, 0.79512153, 0.78504439], [2.35503776, 2.3473043 , 2.34376638, ..., 0.80170221, 0.79410223, 0.78668313], ..., [ nan, nan, nan, ..., nan, nan, nan], [ nan, nan, nan, ..., nan, nan, nan], [ nan, nan, nan, ..., nan, nan, nan]], [[2.35483872, 2.34683383, 2.34106816, ..., 0.79812782, 0.79574601, 0.78637206], 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2.34135869, ..., 0.79762928, 0.79577597, 0.78522232], [2.35524549, 2.34898427, 2.34001521, ..., 0.80230618, 0.79399863, nan], [2.35582719, 2.34681154, 2.34074028, ..., nan, nan, 0.78682128], ..., [ nan, nan, nan, ..., nan, nan, nan], [ nan, nan, nan, ..., nan, nan, nan], [ nan, nan, nan, ..., 0.79683606, 0.79598766, nan]], [[2.35312628, 2.3476695 , 2.34052282, ..., nan, 0.7923047 , 0.78840886], [2.3530582 , 2.34757994, 2.33888946, ..., nan, 0.79176442, 0.7870269 ], [2.35359128, 2.34666765, 2.34046285, ..., 0.79979411, 0.79574892, 0.78665539], ..., [ nan, nan, nan, ..., nan, nan, nan], [ nan, nan, nan, ..., nan, nan, nan], [ nan, nan, nan, ..., 0.7974848 , nan, nan]]], [[[2.35423314, 2.34878365, 2.34057621, ..., 0.79733719, 0.79647873, 0.78468584], [2.35310805, 2.34761336, 2.34241663, ..., nan, 0.79163379, nan], [2.35340256, 2.34738428, 2.34135509, ..., nan, 0.79244428, 0.78687793], ..., [ nan, nan, nan, ..., nan, nan, nan], [ nan, nan, 2.3404166 , ..., nan, nan, nan], [ nan, nan, nan, 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2.34960918, 2.34131135, ..., nan, 0.79659674, 0.78683598], [2.35558885, 2.34676428, 2.34161452, ..., 0.79704049, 0.79658297, nan], ..., [ nan, nan, nan, ..., nan, nan, nan], [ nan, nan, nan, ..., nan, nan, nan], [ nan, nan, 2.34434109, ..., nan, nan, nan]], [[2.35406013, 2.34652474, 2.34158892, ..., 0.80228696, nan, 0.78576748], [2.35303869, 2.3496428 , 2.34054792, ..., 0.80125932, 0.79550154, 0.78808772], [2.35383932, 2.34616576, 2.34217028, ..., nan, nan, nan], ..., [ nan, nan, nan, ..., nan, nan, nan], [ nan, nan, nan, ..., nan, nan, nan], [ nan, nan, nan, ..., nan, nan, nan]]]], [[[[2.35374611, 2.34969463, 2.34248562, ..., 0.8020957 , nan, 0.78775733], [2.3560148 , 2.3475521 , 2.34111202, ..., nan, 0.79384281, 0.78517139], [2.35309854, 2.34909513, 2.343023 , ..., 0.79741443, 0.79575588, 0.78635492], ..., [ nan, nan, nan, ..., nan, nan, nan], [ nan, nan, nan, ..., nan, nan, nan], [ nan, nan, nan, ..., nan, nan, nan]], [[2.35512651, 2.34791853, 2.34117157, ..., 0.79941037, 0.79297116, 0.7878066 ], [2.35303316, 2.34784235, 2.3405693 , ..., 0.79980211, 0.79350068, 0.78717625], [2.35421369, 2.34620998, 2.34120696, ..., 0.79915636, 0.79616331, 0.78656349], ..., [ nan, nan, nan, ..., nan, nan, nan], [ nan, nan, nan, ..., nan, nan, 0.78565612], [ nan, nan, nan, ..., 0.79928365, nan, nan]]], [[[2.35459373, 2.34880893, 2.34191135, ..., 0.79902904, 0.79458856, 0.78644079], [2.35395066, 2.34748834, 2.34218414, ..., nan, 0.79272576, 0.78503893], [2.35506318, 2.3476248 , 2.34330465, ..., 0.79792852, 0.79122886, nan], ..., [ nan, nan, nan, ..., 0.80117438, nan, nan], [ nan, nan, nan, ..., nan, nan, nan], [ nan, nan, nan, ..., nan, nan, nan]], [[2.35370508, 2.34704486, 2.34107647, ..., 0.79959835, 0.79554683, nan], [2.35373857, 2.34720578, nan, ..., nan, 0.79407281, nan], [2.35383585, 2.34566569, 2.34119756, ..., 0.79797409, 0.79725178, 0.78801874], ..., [ nan, nan, nan, ..., nan, 0.795918 , nan], [ nan, nan, nan, ..., nan, 0.79588174, nan], [ nan, nan, nan, ..., nan, nan, nan]]], [[[2.3541437 , 2.34982399, 2.34124006, ..., 0.80069969, nan, 0.78500579], [2.35478772, 2.34832718, 2.33926921, ..., 0.802078 , 0.79625985, 0.78532084], [ nan, 2.34666813, 2.34375659, ..., 0.80085371, nan, 0.78873496], ..., [ nan, 2.34923363, nan, ..., nan, nan, 0.78589944], [ nan, nan, nan, ..., nan, nan, nan], [ nan, nan, nan, ..., nan, nan, nan]], [[2.3528945 , 2.34674296, 2.34113812, ..., 0.80101256, 0.79125157, 0.79099957], [2.35303176, 2.34612023, 2.34019494, ..., 0.79709146, 0.79499662, 0.78758539], [2.35319867, 2.34722278, 2.34188887, ..., nan, 0.7929278 , 0.78931736], ..., [ nan, nan, nan, ..., nan, 0.79316026, nan], [ nan, nan, nan, ..., nan, nan, nan], [ nan, nan, nan, ..., nan, nan, nan]]], [[[2.35457117, 2.34761892, 2.34135701, ..., 0.79766693, 0.79472339, 0.78659783], [2.3558373 , 2.34818438, 2.34181158, ..., 0.80010779, 0.79029319, 0.78862914], [2.35402451, 2.34834439, 2.33911526, ..., 0.79974196, 0.79146956, 0.78501599], ..., [ nan, nan, nan, ..., nan, nan, nan], [ nan, nan, nan, ..., nan, nan, nan], [ nan, nan, nan, ..., nan, nan, nan]], [[2.35430429, 2.34771182, 2.33848477, ..., nan, nan, 0.78630206], [2.35320529, 2.34810488, 2.34025312, ..., 0.80051919, nan, 0.78859113], [2.35500425, 2.34650251, 2.33965069, ..., 0.80169069, 0.79564914, 0.7881267 ], ..., [ nan, nan, nan, ..., nan, nan, nan], [2.35705734, nan, nan, ..., nan, nan, nan], [2.35703704, nan, nan, ..., nan, nan, nan]]], [[[2.35416911, 2.34785152, 2.3409837 , ..., nan, 0.79429753, 0.78545773], [2.35337787, 2.34889789, 2.34024394, ..., nan, 0.79491954, 0.78670047], [2.35455807, 2.34841565, 2.34002431, ..., 0.80224213, 0.79084635, 0.78730825], ..., [ nan, nan, nan, ..., nan, nan, nan], [ nan, nan, nan, ..., nan, nan, nan], [ nan, nan, nan, ..., nan, 0.79021801, nan]], [[2.35274002, 2.34672014, 2.34163639, ..., 0.80046183, 0.79582759, 0.78609965], [2.35514213, 2.34678917, 2.34155188, ..., 0.80058414, 0.79520091, 0.78575966], [2.35273582, 2.346624 , 2.34165292, ..., nan, 0.79304336, 0.79126268], ..., [2.35552545, nan, 2.33895936, ..., nan, nan, nan], [ nan, nan, nan, ..., nan, nan, nan], [ nan, nan, nan, ..., nan, nan, 0.78978143]]], [[[2.35610792, 2.34778528, 2.3417758 , ..., 0.79984075, nan, 0.78642789], [2.35505724, 2.34699618, 2.34279981, ..., 0.79906757, 0.79632431, 0.78681832], [2.35424702, 2.34973906, 2.3426813 , ..., 0.80076546, 0.79433921, 0.78934006], ..., [2.35453294, nan, nan, ..., nan, nan, nan], [ nan, nan, nan, ..., nan, nan, nan], [ nan, nan, 2.33939339, ..., nan, nan, nan]], [[2.35393105, 2.34724206, 2.34067304, ..., 0.80176528, nan, 0.78795783], [ nan, 2.34910044, 2.34265806, ..., nan, 0.79281017, 0.78993921], [2.35364027, 2.34794842, 2.34391723, ..., nan, 0.7912831 , 0.7879033 ], ..., [ nan, nan, 2.33968645, ..., nan, nan, nan], [ nan, nan, nan, ..., nan, 0.79430461, nan], [ nan, nan, nan, ..., nan, nan, nan]]]]], shape=(14, 6, 2, 32, 256)) - wire(wire)int641, 2, ..., 31, 32
Values:
array([ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32])
- (module, segment, counter, wire, strip)DataArrayViewbinned data [len=12, len=9, ..., len=0, len=0]
dim='event', content=DataArray( dims=(event: 1533595), data=float64[counts], coords={'event_time_offset':float64[µs], 'event_time_zero':float64[µs], 'tof':float64[µs], 'wavelength':float64[Å]})
[9]:
two_theta = sc.linspace("two_theta", 0.8, 2.4, 301, unit="rad")
intermediates[MaskedData[SampleRun]].hist(
two_theta=two_theta, wavelength=300
).plot(norm="log")
[9]:
Grouping by scattering angle#
The above workflow focuses the data by merging all instrument pixels to produce a 1d d-spacing curve. If instead we want to group into \(2\theta\) bins, we can alter the workflow parameters by adding some binning in \(2\theta\):
[10]:
workflow[TwoThetaBins] = sc.linspace(
dim="two_theta", unit="rad", start=0.8, stop=2.4, num=201
)
[11]:
grouped_dspacing = workflow.compute(IofDspacingTwoTheta)
grouped_dspacing
[11]:
scipp.DataArray (48.85 MB)
- two_theta: 200
- dspacing: 200
- L1()float64mm76550.00007901035
Values:
array(76550.00007901) - dspacing(dspacing [bin-edge])float64Å0.0, 0.012, ..., 2.332, 2.343
Values:
array([0. , 0.011717, 0.023434, 0.035151, 0.046868, 0.058585, 0.070302, 0.082019, 0.093736, 0.105453, 0.11717 , 0.128887, 0.140604, 0.152321, 0.164038, 0.175755, 0.187472, 0.199189, 0.210906, 0.222623, 0.23434 , 0.246057, 0.257774, 0.269491, 0.281208, 0.292925, 0.304642, 0.316359, 0.328076, 0.339793, 0.35151 , 0.363227, 0.374944, 0.386661, 0.398378, 0.410095, 0.421812, 0.433529, 0.445246, 0.456963, 0.46868 , 0.480397, 0.492114, 0.503831, 0.515548, 0.527265, 0.538982, 0.550699, 0.562416, 0.574133, 0.58585 , 0.597567, 0.609284, 0.621001, 0.632718, 0.644435, 0.656152, 0.667869, 0.679586, 0.691303, 0.70302 , 0.714737, 0.726454, 0.738171, 0.749888, 0.761605, 0.773322, 0.785039, 0.796756, 0.808473, 0.82019 , 0.831907, 0.843624, 0.855341, 0.867058, 0.878775, 0.890492, 0.902209, 0.913926, 0.925643, 0.93736 , 0.949077, 0.960794, 0.972511, 0.984228, 0.995945, 1.007662, 1.019379, 1.031096, 1.042813, 1.05453 , 1.066247, 1.077964, 1.089681, 1.101398, 1.113115, 1.124832, 1.136549, 1.148266, 1.159983, 1.1717 , 1.183417, 1.195134, 1.206851, 1.218568, 1.230285, 1.242002, 1.253719, 1.265436, 1.277153, 1.28887 , 1.300587, 1.312304, 1.324021, 1.335738, 1.347455, 1.359172, 1.370889, 1.382606, 1.394323, 1.40604 , 1.417757, 1.429474, 1.441191, 1.452908, 1.464625, 1.476342, 1.488059, 1.499776, 1.511493, 1.52321 , 1.534927, 1.546644, 1.558361, 1.570078, 1.581795, 1.593512, 1.605229, 1.616946, 1.628663, 1.64038 , 1.652097, 1.663814, 1.675531, 1.687248, 1.698965, 1.710682, 1.722399, 1.734116, 1.745833, 1.75755 , 1.769267, 1.780984, 1.792701, 1.804418, 1.816135, 1.827852, 1.839569, 1.851286, 1.863003, 1.87472 , 1.886437, 1.898154, 1.909871, 1.921588, 1.933305, 1.945022, 1.956739, 1.968456, 1.980173, 1.99189 , 2.003607, 2.015324, 2.027041, 2.038758, 2.050475, 2.062192, 2.073909, 2.085626, 2.097343, 2.10906 , 2.120777, 2.132494, 2.144211, 2.155928, 2.167645, 2.179362, 2.191079, 2.202796, 2.214513, 2.22623 , 2.237947, 2.249664, 2.261381, 2.273098, 2.284815, 2.296532, 2.308249, 2.319966, 2.331683, 2.3434 ]) - gravity()vector3m/s^2[ 0. -9.80665 0. ]
Values:
array([ 0. , -9.80665, 0. ]) - incident_beam()vector3mm[3.478e+00 0.000e+00 7.655e+04]
Values:
array([3.478e+00, 0.000e+00, 7.655e+04]) - sample_position()vector3mm[0. 0. 0.]
Values:
array([0., 0., 0.]) - source_position()vector3mm[-3.478e+00 0.000e+00 -7.655e+04]
Values:
array([-3.478e+00, 0.000e+00, -7.655e+04]) - two_theta(two_theta [bin-edge])float64rad0.8, 0.808, ..., 2.392, 2.4
Values:
array([0.8 , 0.808, 0.816, 0.824, 0.832, 0.84 , 0.848, 0.856, 0.864, 0.872, 0.88 , 0.888, 0.896, 0.904, 0.912, 0.92 , 0.928, 0.936, 0.944, 0.952, 0.96 , 0.968, 0.976, 0.984, 0.992, 1. , 1.008, 1.016, 1.024, 1.032, 1.04 , 1.048, 1.056, 1.064, 1.072, 1.08 , 1.088, 1.096, 1.104, 1.112, 1.12 , 1.128, 1.136, 1.144, 1.152, 1.16 , 1.168, 1.176, 1.184, 1.192, 1.2 , 1.208, 1.216, 1.224, 1.232, 1.24 , 1.248, 1.256, 1.264, 1.272, 1.28 , 1.288, 1.296, 1.304, 1.312, 1.32 , 1.328, 1.336, 1.344, 1.352, 1.36 , 1.368, 1.376, 1.384, 1.392, 1.4 , 1.408, 1.416, 1.424, 1.432, 1.44 , 1.448, 1.456, 1.464, 1.472, 1.48 , 1.488, 1.496, 1.504, 1.512, 1.52 , 1.528, 1.536, 1.544, 1.552, 1.56 , 1.568, 1.576, 1.584, 1.592, 1.6 , 1.608, 1.616, 1.624, 1.632, 1.64 , 1.648, 1.656, 1.664, 1.672, 1.68 , 1.688, 1.696, 1.704, 1.712, 1.72 , 1.728, 1.736, 1.744, 1.752, 1.76 , 1.768, 1.776, 1.784, 1.792, 1.8 , 1.808, 1.816, 1.824, 1.832, 1.84 , 1.848, 1.856, 1.864, 1.872, 1.88 , 1.888, 1.896, 1.904, 1.912, 1.92 , 1.928, 1.936, 1.944, 1.952, 1.96 , 1.968, 1.976, 1.984, 1.992, 2. , 2.008, 2.016, 2.024, 2.032, 2.04 , 2.048, 2.056, 2.064, 2.072, 2.08 , 2.088, 2.096, 2.104, 2.112, 2.12 , 2.128, 2.136, 2.144, 2.152, 2.16 , 2.168, 2.176, 2.184, 2.192, 2.2 , 2.208, 2.216, 2.224, 2.232, 2.24 , 2.248, 2.256, 2.264, 2.272, 2.28 , 2.288, 2.296, 2.304, 2.312, 2.32 , 2.328, 2.336, 2.344, 2.352, 2.36 , 2.368, 2.376, 2.384, 2.392, 2.4 ])
- (two_theta, dspacing)DataArrayViewbinned data [len=0, len=0, ..., len=0, len=0]
dim='event', content=DataArray( dims=(event: 1264425), data=float64[dimensionless], coords={'event_time_offset':float64[µs], 'event_time_zero':float64[µs], 'dspacing':float64[Å]})
[12]:
grouped_dspacing.hist().plot(norm="log")
[12]:
Normalizing by monitor#
The workflow used above normalizes the detected counts by proton charge. Alternatively, ESSdiffraction can normalize by a monitor. In this example, this is DREAM’s cave monitor.
There are two options for normalizing by monitor:
Normalize by a wavelength-histogram of the monitor counts (normalize_by_monitor_histogram).
Normalized by the integral over all wavelength bins (normalize_by_monitor_integrated).
Here, we use option 1. Option 2 can be chosen by constructing a workflow using run_norm=powder.RunNormalization.monitor_integrated.
Construct a workflow as before but select normalization by monitor histogram:
[13]:
workflow = dream.DreamGeant4Workflow(run_norm=powder.RunNormalization.monitor_histogram)
In addition to the parameters used before, we also need to provide filenames for monitor data and a position of the monitor as that is not saved in the simulation files:
[14]:
workflow[MonitorFilename[SampleRun]] = dream.data.simulated_monitor_diamond_sample()
workflow[MonitorFilename[VanadiumRun]] = dream.data.simulated_monitor_vanadium_sample()
workflow[MonitorFilename[BackgroundRun]] = dream.data.simulated_monitor_empty_can()
workflow[CaveMonitorPosition] = sc.vector([0.0, 0.0, -4220.0], unit="mm")
# These are the same as at the top of the notebook:
workflow[Filename[SampleRun]] = dream.data.simulated_diamond_sample()
workflow[Filename[VanadiumRun]] = dream.data.simulated_vanadium_sample()
workflow[Filename[BackgroundRun]] = dream.data.simulated_empty_can()
workflow[CalibrationFilename] = None
workflow[NeXusDetectorName] = "mantle"
workflow[UncertaintyBroadcastMode] = UncertaintyBroadcastMode.drop
workflow[DspacingBins] = sc.linspace("dspacing", 0.0, 2.3434, 201, unit="angstrom")
workflow[TofMask] = None
workflow[TwoThetaMask] = None
workflow[WavelengthMask] = None
workflow = powder.with_pixel_mask_filenames(workflow, [])
workflow[TimeOfFlightLookupTableFilename] = dream.data.tof_lookup_table_high_flux()
Downloading file 'DREAM_simple_pwd_workflow/Cave_TOF_Monitor_diam_in_can.dat' from 'https://public.esss.dk/groups/scipp/ess/dream/1/DREAM_simple_pwd_workflow/Cave_TOF_Monitor_diam_in_can.dat' to '/home/runner/.cache/ess/dream/1'.
Downloading file 'DREAM_simple_pwd_workflow/Cave_TOF_Monitor_vana_inc_coh.dat' from 'https://public.esss.dk/groups/scipp/ess/dream/1/DREAM_simple_pwd_workflow/Cave_TOF_Monitor_vana_inc_coh.dat' to '/home/runner/.cache/ess/dream/1'.
Downloading file 'DREAM_simple_pwd_workflow/Cave_TOF_Monitor_van_can.dat' from 'https://public.esss.dk/groups/scipp/ess/dream/1/DREAM_simple_pwd_workflow/Cave_TOF_Monitor_van_can.dat' to '/home/runner/.cache/ess/dream/1'.
[15]:
workflow.visualize(IofTof, graph_attr={"rankdir": "LR"})
[15]:
[16]:
results = workflow.compute((IofTof, WavelengthMonitor[SampleRun, CaveMonitor]))
normalized_by_monitor = results[IofTof]
monitor = results[WavelengthMonitor[SampleRun, CaveMonitor]]
monitor
[16]:
scipp.DataArray (23.31 KB)
- wavelength: 681
- Ltotal()float64mm72330.0000836201
Values:
array(72330.00008362) - position()vector3mm[ 0. 0. -4220.]
Values:
array([ 0., 0., -4220.]) - source_position()vector3mm[-3.478e+00 0.000e+00 -7.655e+04]
Values:
array([-3.478e+00, 0.000e+00, -7.655e+04]) - tof(wavelength [bin-edge])float64µs4277.011, 4386.413, ..., 7.867e+04, 7.878e+04
Values:
array([ 4277.01076592, 4386.4131861 , 4495.81560628, 4605.21802647, 4714.62044665, 4824.02286683, 4933.42528701, 5042.8277072 , 5152.23012738, 5261.63254756, 5371.03496774, 5480.43738792, 5589.83980811, 5699.24222829, 5808.64464847, 5918.04706865, 6027.44948884, 6136.85190902, 6246.2543292 , 6355.65674938, 6465.05916956, 6574.46158975, 6683.86400993, 6793.26643011, 6902.66885029, 7012.07127047, 7121.47369066, 7230.87611084, 7340.27853102, 7449.6809512 , 7559.08337139, 7668.48579157, 7777.88821175, 7887.29063193, 7996.69305211, 8106.0954723 , 8215.49789248, 8324.90031266, 8434.30273284, 8543.70515303, 8653.10757321, 8762.50999339, 8871.91241357, 8981.31483375, 9090.71725394, 9200.11967412, 9309.5220943 , 9418.92451448, 9528.32693467, 9637.72935485, 9747.13177503, 9856.53419521, 9965.93661539, 10075.33903558, 10184.74145576, 10294.14387594, 10403.54629612, 10512.94871631, 10622.35113649, 10731.75355667, 10841.15597685, 10950.55839703, 11059.96081722, 11169.3632374 , 11278.76565758, 11388.16807776, 11497.57049795, 11606.97291813, 11716.37533831, 11825.77775849, 11935.18017867, 12044.58259886, 12153.98501904, 12263.38743922, 12372.7898594 , 12482.19227959, 12591.59469977, 12700.99711995, 12810.39954013, 12919.80196031, 13029.2043805 , 13138.60680068, 13248.00922086, 13357.41164104, 13466.81406123, 13576.21648141, 13685.61890159, 13795.02132177, 13904.42374195, 14013.82616214, 14123.22858232, 14232.6310025 , 14342.03342268, 14451.43584287, 14560.83826305, 14670.24068323, 14779.64310341, 14889.04552359, 14998.44794378, 15107.85036396, 15217.25278414, 15326.65520432, 15436.0576245 , 15545.46004469, 15654.86246487, 15764.26488505, 15873.66730523, 15983.06972542, 16092.4721456 , 16201.87456578, 16311.27698596, 16420.67940614, 16530.08182633, 16639.48424651, 16748.88666669, 16858.28908687, 16967.69150706, 17077.09392724, 17186.49634742, 17295.8987676 , 17405.30118778, 17514.70360797, 17624.10602815, 17733.50844833, 17842.91086851, 17952.3132887 , 18061.71570888, 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3.71044687, 3.71643055, 3.72241424, 3.72839792, 3.7343816 , 3.74036528, 3.74634896, 3.75233264, 3.75831633, 3.76430001, 3.77028369, 3.77626737, 3.78225105, 3.78823473, 3.79421842, 3.8002021 , 3.80618578, 3.81216946, 3.81815314, 3.82413682, 3.83012051, 3.83610419, 3.84208787, 3.84807155, 3.85405523, 3.86003891, 3.8660226 , 3.87200628, 3.87798996, 3.88397364, 3.88995732, 3.895941 , 3.90192469, 3.90790837, 3.91389205, 3.91987573, 3.92585941, 3.93184309, 3.93782678, 3.94381046, 3.94979414, 3.95577782, 3.9617615 , 3.96774518, 3.97372887, 3.97971255, 3.98569623, 3.99167991, 3.99766359, 4.00364727, 4.00963096, 4.01561464, 4.02159832, 4.027582 , 4.03356568, 4.03954936, 4.04553305, 4.05151673, 4.05750041, 4.06348409, 4.06946777, 4.07545145, 4.08143514, 4.08741882, 4.0934025 , 4.09938618, 4.10536986, 4.11135354, 4.11733722, 4.12332091, 4.12930459, 4.13528827, 4.14127195, 4.14725563, 4.15323931, 4.159223 , 4.16520668, 4.17119036, 4.17717404, 4.18315772, 4.1891414 , 4.19512509, 4.20110877, 4.20709245, 4.21307613, 4.21905981, 4.22504349, 4.23102718, 4.23701086, 4.24299454, 4.24897822, 4.2549619 , 4.26094558, 4.26692927, 4.27291295, 4.27889663, 4.28488031, 4.29086399, 4.29684767, 4.30283136, 4.30881504])
- (wavelength)float64countsnan, nan, ..., nan, nanσ = 0.0, 0.0, ..., 0.0, 0.0
Values:
array([ nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, 3.13149138e-14, 2.13118771e-11, 7.12758424e-10, 2.59580400e-09, 1.19586701e-07, 1.17468665e-06, 1.13515211e-04, 1.24155494e-03, 1.14168427e-02, 5.26914120e-02, 1.94437331e-01, 2.33793109e-01, 1.16250180e+00, 5.93426617e+00, 1.05720506e+01, 3.15087814e+01, 5.36850167e+01, 1.61331822e+02, 2.63047559e+02, 5.26814899e+02, 5.27590891e+02, 1.26388956e+03, 3.34716186e+03, 3.41322372e+03, 5.41295956e+03, 8.04586306e+03, 1.10924084e+04, 1.42767484e+04, 2.14621656e+04, 2.98737120e+04, 4.74979353e+04, 7.09698069e+04, 8.15552112e+04, 9.51363522e+04, 1.38320422e+05, 1.55068164e+05, 1.65123636e+05, 2.05199951e+05, 3.10293363e+05, 2.85346472e+05, 4.50443540e+05, 5.19910125e+05, 5.27711878e+05, 6.04976589e+05, 7.35202803e+05, 8.65799509e+05, 9.17691847e+05, 8.77550687e+05, 1.18384326e+06, 1.06423167e+06, 1.36002864e+06, 1.52709366e+06, 1.67894950e+06, 1.81961042e+06, 1.83721674e+06, 2.10063577e+06, 2.36887090e+06, 2.23956122e+06, 2.56552604e+06, 2.91342759e+06, 3.33107608e+06, 3.38949624e+06, 3.61675571e+06, 3.53310272e+06, 3.94165725e+06, 4.05890198e+06, 4.33580432e+06, 4.97781484e+06, 5.52297060e+06, 5.47041852e+06, 5.86399840e+06, 5.41071453e+06, 6.06627154e+06, 6.74964575e+06, 6.88497432e+06, 7.45688371e+06, 7.63629957e+06, 7.71220596e+06, 8.07443370e+06, 7.85668521e+06, 8.08552241e+06, 7.80961767e+06, 8.44868152e+06, 8.92605268e+06, 9.78893256e+06, 9.64002139e+06, 1.10418024e+07, 1.01504031e+07, 1.10339006e+07, 1.09933295e+07, 1.13305910e+07, 1.06864986e+07, 1.17438219e+07, 1.18220551e+07, 1.29328085e+07, 1.31849114e+07, 1.35953851e+07, 1.23994419e+07, 1.29268523e+07, 1.27599331e+07, 1.41931363e+07, 1.38542030e+07, 1.44516769e+07, 1.39918246e+07, 1.34699845e+07, 1.47575848e+07, 1.43133952e+07, 1.52607088e+07, 1.39811001e+07, 1.44505007e+07, 1.45152919e+07, 1.59567814e+07, 1.44412513e+07, 1.44674454e+07, 1.48657533e+07, 1.58113300e+07, 1.64753961e+07, 1.68972366e+07, 1.52320718e+07, 1.62061065e+07, 1.56825575e+07, 1.60292666e+07, 1.62114852e+07, 1.74287314e+07, 1.50252302e+07, 1.61876168e+07, 1.65388270e+07, 1.72731823e+07, 1.61898428e+07, 1.60588877e+07, 1.64819013e+07, 1.59747462e+07, 1.54904088e+07, 1.55531911e+07, 1.76629105e+07, 1.61743327e+07, 1.66825947e+07, 1.56342892e+07, 1.70910923e+07, 1.66339127e+07, 1.49456446e+07, 1.60650540e+07, 1.56638116e+07, 1.67608206e+07, 1.70639050e+07, 1.74095343e+07, 1.77272557e+07, 1.58488414e+07, 1.58368849e+07, 1.63842302e+07, 1.68746144e+07, 1.69868243e+07, 1.58497331e+07, 1.65117490e+07, 1.60958844e+07, 1.54317881e+07, 1.44234331e+07, 1.56217452e+07, 1.56616727e+07, 1.48222156e+07, 1.55335343e+07, 1.54468441e+07, 1.57871630e+07, 1.39625955e+07, 1.55647164e+07, 1.39542174e+07, 1.42331936e+07, 1.31142042e+07, 1.35256871e+07, 1.36614357e+07, 1.39127967e+07, 1.34787141e+07, 1.32436498e+07, 1.44818716e+07, 1.40766736e+07, 1.37598174e+07, 1.36748448e+07, 1.33071067e+07, 1.37951322e+07, 1.34207308e+07, 1.38102333e+07, 1.31911312e+07, 1.27878728e+07, 1.28212255e+07, 1.23601094e+07, 1.24874040e+07, 1.25470257e+07, 1.27130831e+07, 1.32108710e+07, 1.25319700e+07, 1.14181461e+07, 1.21430368e+07, 1.26226342e+07, 1.25565222e+07, 1.17379160e+07, 1.12722964e+07, 1.10527049e+07, 1.07436688e+07, 1.08324044e+07, 1.04466451e+07, 1.19873715e+07, 1.07411962e+07, 1.18560758e+07, 1.19117145e+07, 1.05897521e+07, 1.13946709e+07, 1.06527725e+07, 1.01927993e+07, 1.05408153e+07, 1.02660823e+07, 1.01051596e+07, 1.07644161e+07, 9.33272079e+06, 9.94720244e+06, 1.00103426e+07, 9.13679236e+06, 1.00613764e+07, 9.42204477e+06, 8.86365990e+06, 9.45305819e+06, 9.38729328e+06, 9.85180457e+06, 9.89584115e+06, 8.87900888e+06, 8.81483414e+06, 9.08857393e+06, 9.50543393e+06, 8.78036210e+06, 8.36291216e+06, 8.86746893e+06, 8.48368195e+06, 9.12576983e+06, 9.33148009e+06, 8.64899049e+06, 8.75626919e+06, 8.96589342e+06, 8.19416473e+06, 8.04483940e+06, 8.22360981e+06, 7.93395507e+06, 8.40317979e+06, 8.28013264e+06, 8.01671802e+06, 8.19273313e+06, 7.53783220e+06, 7.64492418e+06, 8.43413473e+06, 8.01683768e+06, 7.76947226e+06, 8.02362890e+06, 7.73577591e+06, 7.90539072e+06, 8.18125895e+06, 7.26879861e+06, 7.84823702e+06, 7.96014533e+06, 7.64722692e+06, 7.35599872e+06, 7.43263598e+06, 7.33994813e+06, 7.62046125e+06, 7.38819489e+06, 7.94056189e+06, 6.95473778e+06, 7.30084887e+06, 6.52048709e+06, 6.79461093e+06, 7.06189380e+06, 7.04440870e+06, 7.05924119e+06, 7.36376701e+06, 6.64442257e+06, 7.15613861e+06, 6.45854891e+06, 6.88600144e+06, 7.47274628e+06, 6.93226937e+06, 6.95737980e+06, 6.94561383e+06, 6.54813702e+06, 6.49791808e+06, 6.92031135e+06, 7.09216401e+06, 7.07412520e+06, 6.45610367e+06, 6.56676541e+06, 7.06650448e+06, 6.15872789e+06, 6.78069140e+06, 6.75428592e+06, 6.42660074e+06, 6.40410457e+06, 5.88474097e+06, 6.58662421e+06, 6.31665416e+06, 6.10089110e+06, 6.02886179e+06, 5.67782766e+06, 5.79348104e+06, 5.20177205e+06, 5.73612035e+06, 5.86888994e+06, 6.02915754e+06, 5.91107954e+06, 5.61299789e+06, 5.20846316e+06, 4.99522503e+06, 4.80470083e+06, 5.02620347e+06, 5.38219600e+06, 4.54467510e+06, 4.72029883e+06, 5.10652840e+06, 4.72664157e+06, 4.50018945e+06, 3.96672496e+06, 4.37505084e+06, 5.09618719e+06, 5.13274606e+06, 4.18763426e+06, 3.89869159e+06, 3.60427402e+06, 4.03015628e+06, 3.98246809e+06, 4.09093345e+06, 6.28693791e+05, 1.38222327e+06, 1.92683043e+06, 1.79178661e+06, 2.08955237e+06, 2.12649935e+06, 2.18087402e+06, 2.35429721e+06, 2.61203750e+06, 2.39601974e+06, 2.61877217e+06, 2.98602917e+06, 3.42394551e+06, 3.56369690e+06, 3.92624856e+06, 4.08799536e+06, 3.61591310e+06, 4.43012272e+06, 4.89951911e+06, 5.00164386e+06, 5.26888217e+06, 5.10300279e+06, 5.27497868e+06, 5.66015647e+06, 6.05007909e+06, 5.46545005e+06, 5.96686848e+06, 6.81402293e+06, 6.92649225e+06, 7.36644149e+06, 7.46533661e+06, 7.71881299e+06, 7.31424868e+06, 7.72589078e+06, 8.20737742e+06, 8.72915936e+06, 8.76680391e+06, 8.78277926e+06, 8.55417543e+06, 9.46949659e+06, 8.92819515e+06, 9.26556356e+06, 8.99652407e+06, 8.91112066e+06, 9.36134127e+06, 1.00844651e+07, 9.58943185e+06, 9.71309415e+06, 9.92927781e+06, 1.00194919e+07, 1.11226442e+07, 1.05968863e+07, 1.05389885e+07, 9.71345446e+06, 1.13400672e+07, 9.65944937e+06, 1.10710181e+07, 1.02079368e+07, 9.95517716e+06, 1.13434513e+07, 9.96326220e+06, 1.03326360e+07, 1.17019469e+07, 1.05192846e+07, 1.08775661e+07, 1.09015948e+07, 1.13961404e+07, 1.10312675e+07, 1.04066006e+07, 9.82076495e+06, 1.10181660e+07, 1.08428517e+07, 1.08296663e+07, 1.10005911e+07, 9.63880944e+06, 1.19630043e+07, 1.02949480e+07, 1.03580750e+07, 1.06776158e+07, 1.07397585e+07, 1.04328991e+07, 1.14090395e+07, 1.03383028e+07, 1.09839953e+07, 1.15501381e+07, 1.02991551e+07, 1.02047204e+07, 1.02476718e+07, 1.10014754e+07, 9.51191521e+06, 1.07861489e+07, 1.11761843e+07, 1.00200980e+07, 1.10634440e+07, 9.43239515e+06, 9.25722279e+06, 1.00317783e+07, 9.86520794e+06, 9.53323830e+06, 9.40675063e+06, 1.03198258e+07, 1.03386151e+07, 9.98977819e+06, 9.57277119e+06, 9.69996137e+06, 8.81230337e+06, 9.42012848e+06, 9.63951140e+06, 9.61104039e+06, 8.73216358e+06, 9.74758971e+06, 9.45008824e+06, 9.99298468e+06, 9.90578026e+06, 8.76389003e+06, 9.42566458e+06, 9.87795581e+06, 9.20817011e+06, 1.01026255e+07, 8.95242574e+06, 8.61097324e+06, 8.29667890e+06, 8.81112559e+06, 8.80634089e+06, 9.53506809e+06, 8.65429481e+06, 8.66520410e+06, 8.23817698e+06, 8.76649555e+06, 8.30790075e+06, 8.07896979e+06, 8.29989045e+06, 9.01164936e+06, 8.57960794e+06, 8.52989313e+06, 7.78341392e+06, 9.42973128e+06, 8.27401849e+06, 7.65298603e+06, 8.11151055e+06, 7.59688403e+06, 7.89811418e+06, 7.50672962e+06, 8.20830346e+06, 7.75842241e+06, 8.54573909e+06, 7.90416891e+06, 8.25506452e+06, 7.78840797e+06, 8.22021017e+06, 7.99325401e+06, 7.54524393e+06, 7.43397139e+06, 7.47115647e+06, 8.06383634e+06, 8.57822146e+06, 7.33117105e+06, 7.37730636e+06, 7.81271306e+06, 7.31899389e+06, 7.68112494e+06, 7.18017594e+06, 7.24257112e+06, 7.70650211e+06, 6.91822060e+06, 7.07927977e+06, 7.23551068e+06, 7.25964275e+06, 6.98250287e+06, 6.84143594e+06, 6.92264102e+06, 6.55288641e+06, 6.34356408e+06, 6.87989599e+06, 6.74849114e+06, 6.58469952e+06, 6.75690348e+06, 6.71746277e+06, 6.87362850e+06, 6.99469566e+06, 7.11474936e+06, 6.47265111e+06, 6.62943021e+06, 6.30454845e+06, 6.48906581e+06, 6.86579928e+06, 6.21362931e+06, 6.36914934e+06, 6.37209951e+06, 6.91891156e+06, 6.70278141e+06, 6.51731643e+06, 6.74880512e+06, 6.09121776e+06, 6.95478357e+06, 5.33802109e+06, 5.92350590e+06, 5.66546617e+06, 6.41234443e+06, 6.05589270e+06, 5.83792621e+06, 5.66004434e+06, 6.53874792e+06, 6.05769946e+06, 5.86145178e+06, 5.68025561e+06, 5.87671474e+06, 5.70633929e+06, 6.44364478e+06, 6.05513557e+06, 5.49147785e+06, 5.71712194e+06, 5.87190854e+06, 5.95028079e+06, 5.78201344e+06, 5.67092859e+06, 5.16573742e+06, 5.38067064e+06, 5.45451359e+06, 5.68948900e+06, 5.34603739e+06, 5.76744547e+06, 5.30257864e+06, 4.93834613e+06, 5.58068600e+06, 5.48853050e+06, 5.53325631e+06, 5.32784647e+06, 5.49229983e+06, 5.40929310e+06, 5.50446880e+06, 4.86518836e+06, 5.49052358e+06, 5.85450387e+06, 5.77312082e+06, 5.21283127e+06, 5.06349891e+06, 5.13344843e+06, 4.89833777e+06, 4.99975959e+06, 4.64694694e+06, 4.73302427e+06, 4.65583816e+06, 4.66423695e+06, 4.39489462e+06, 4.75246842e+06, 4.94727933e+06, 5.04590159e+06, 4.68464725e+06, 4.38348490e+06, 3.77739241e+06, 4.01317282e+06, 4.23544200e+06, 4.18897725e+06, 4.02094889e+06, 2.87832053e+06, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan])
Variances (σ²):
array([0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 1.88861751e-27, 7.11249759e-22, 1.55438146e-18, 4.86940401e-18, 4.56900986e-14, 4.61936952e-13, 4.19616090e-09, 1.32108893e-06, 1.41655466e-04, 2.14527827e-03, 1.61384697e-02, 6.07466006e-03, 2.53883865e-01, 3.55742084e+00, 1.21402340e+01, 1.58478768e+02, 2.57730715e+02, 2.88118143e+03, 7.63238217e+03, 3.98624813e+04, 2.52120218e+04, 8.35339186e+04, 6.24042989e+05, 5.89184146e+05, 1.65617298e+06, 2.60026890e+06, 5.23231431e+06, 7.82013596e+06, 1.36541645e+07, 2.59546196e+07, 5.96796727e+07, 1.17754904e+08, 1.66371915e+08, 2.28547824e+08, 3.66506940e+08, 4.79068573e+08, 5.36536462e+08, 7.86270118e+08, 1.53563729e+09, 1.26399962e+09, 2.66288048e+09, 3.52330434e+09, 3.64600023e+09, 4.59580650e+09, 5.64949346e+09, 6.89716866e+09, 7.73825842e+09, 6.83181476e+09, 1.05008527e+10, 9.82351169e+09, 1.37345295e+10, 1.60654936e+10, 1.82844111e+10, 2.09100211e+10, 2.14839149e+10, 2.58089767e+10, 3.23428221e+10, 3.10024745e+10, 3.69594572e+10, 4.41363620e+10, 5.28953570e+10, 5.44660606e+10, 6.16278082e+10, 6.12306234e+10, 7.04749877e+10, 7.48384099e+10, 8.21935407e+10, 9.96513424e+10, 1.13960246e+11, 1.13984266e+11, 1.26553104e+11, 1.21855835e+11, 1.40120064e+11, 1.60207276e+11, 1.65775194e+11, 1.83211007e+11, 1.92943471e+11, 1.93956746e+11, 2.06656184e+11, 2.08977237e+11, 2.19681678e+11, 2.15848638e+11, 2.33186011e+11, 2.52510437e+11, 2.81335220e+11, 2.84547984e+11, 3.38093233e+11, 3.15240605e+11, 3.46053947e+11, 3.50212746e+11, 3.64045508e+11, 3.43379651e+11, 3.85460793e+11, 3.93705384e+11, 4.32672776e+11, 4.49917310e+11, 4.71314294e+11, 4.29544923e+11, 4.39178877e+11, 4.34396223e+11, 4.95734503e+11, 4.89825503e+11, 5.05334075e+11, 4.94143153e+11, 4.83488237e+11, 5.32360530e+11, 5.23489417e+11, 5.64477777e+11, 5.12280498e+11, 5.20962996e+11, 5.32414301e+11, 5.94789127e+11, 5.32234869e+11, 5.34252728e+11, 5.56800779e+11, 5.91449656e+11, 6.09058816e+11, 6.24201069e+11, 5.64489584e+11, 6.06640664e+11, 5.88460877e+11, 5.96638966e+11, 6.02176445e+11, 6.47077539e+11, 5.55419764e+11, 5.95457372e+11, 6.16451995e+11, 6.49859534e+11, 5.96588991e+11, 5.86798571e+11, 6.07223384e+11, 5.87082673e+11, 5.61411455e+11, 5.64606441e+11, 6.39961236e+11, 5.82076791e+11, 5.92518821e+11, 5.62783271e+11, 6.15235317e+11, 5.96179618e+11, 5.30840466e+11, 5.64708434e+11, 5.45867598e+11, 5.83579093e+11, 5.94042077e+11, 6.02155696e+11, 6.04017043e+11, 5.41251953e+11, 5.33288009e+11, 5.51430184e+11, 5.71323798e+11, 5.66133313e+11, 5.27910527e+11, 5.45074568e+11, 5.23781479e+11, 4.99052175e+11, 4.61219581e+11, 4.93397685e+11, 4.96806363e+11, 4.71450366e+11, 4.87298689e+11, 4.77634184e+11, 4.82965709e+11, 4.21808274e+11, 4.68986188e+11, 4.18808157e+11, 4.24305742e+11, 3.86564016e+11, 3.92381926e+11, 3.94758087e+11, 4.07940908e+11, 3.84245042e+11, 3.74604989e+11, 4.07644139e+11, 3.94149148e+11, 3.80777701e+11, 3.72195585e+11, 3.58090084e+11, 3.69051858e+11, 3.55439458e+11, 3.61970057e+11, 3.43811229e+11, 3.31006894e+11, 3.21672907e+11, 3.14083786e+11, 3.16461097e+11, 3.15883280e+11, 3.13259731e+11, 3.18515975e+11, 3.00624015e+11, 2.71077817e+11, 2.83268965e+11, 2.89999572e+11, 2.88841198e+11, 2.66923250e+11, 2.54662924e+11, 2.44373374e+11, 2.34932369e+11, 2.31625017e+11, 2.27349488e+11, 2.57441108e+11, 2.25982573e+11, 2.48016641e+11, 2.47494597e+11, 2.16713470e+11, 2.28956101e+11, 2.13581884e+11, 1.99993662e+11, 2.05365209e+11, 1.98217571e+11, 1.92694715e+11, 2.02608965e+11, 1.74639378e+11, 1.85189305e+11, 1.84558867e+11, 1.64608810e+11, 1.79382496e+11, 1.67927359e+11, 1.55026832e+11, 1.65274831e+11, 1.64270373e+11, 1.65704006e+11, 1.64711941e+11, 1.49923059e+11, 1.47099847e+11, 1.51344965e+11, 1.56124174e+11, 1.41018652e+11, 1.31779216e+11, 1.39052562e+11, 1.32236208e+11, 1.41530686e+11, 1.44373857e+11, 1.32222902e+11, 1.33402909e+11, 1.35136325e+11, 1.22450910e+11, 1.18287830e+11, 1.19956412e+11, 1.15403405e+11, 1.22910503e+11, 1.19089369e+11, 1.15271875e+11, 1.16593820e+11, 1.06581233e+11, 1.07333711e+11, 1.17773602e+11, 1.11735062e+11, 1.07538057e+11, 1.10643000e+11, 1.06316113e+11, 1.07128434e+11, 1.11076559e+11, 9.80468966e+10, 1.06500296e+11, 1.07943495e+11, 1.03940354e+11, 9.90715881e+10, 1.00895939e+11, 9.91454311e+10, 1.02648197e+11, 9.77919357e+10, 1.04664429e+11, 9.27750552e+10, 9.79116029e+10, 8.74109333e+10, 9.00336957e+10, 9.52373006e+10, 9.59857381e+10, 9.48866815e+10, 9.85639002e+10, 8.94989128e+10, 9.73826387e+10, 8.69319812e+10, 9.42409199e+10, 1.02982972e+11, 9.58394346e+10, 9.51995499e+10, 9.77925643e+10, 9.30492951e+10, 8.99457441e+10, 9.68316817e+10, 1.01349105e+11, 1.00382125e+11, 9.09420037e+10, 9.55028800e+10, 1.03633579e+11, 8.80184421e+10, 1.01029941e+11, 9.89216065e+10, 9.60079082e+10, 9.42423016e+10, 8.59801405e+10, 1.00831068e+11, 9.49678653e+10, 9.01643247e+10, 9.07196780e+10, 8.46637095e+10, 8.76861265e+10, 7.91373181e+10, 8.79906856e+10, 9.25132238e+10, 9.18032259e+10, 9.34893250e+10, 8.40448630e+10, 7.84245518e+10, 7.75820159e+10, 7.69260929e+10, 8.01805693e+10, 8.49779585e+10, 7.05635424e+10, 7.28372380e+10, 8.15663562e+10, 7.69846957e+10, 7.22422033e+10, 6.17980887e+10, 6.81712488e+10, 7.84193616e+10, 8.18515670e+10, 6.50432128e+10, 5.92638590e+10, 5.27567977e+10, 5.86966731e+10, 5.73209261e+10, 5.99087435e+10, 9.14448817e+09, 1.24210169e+10, 1.67741478e+10, 1.69622015e+10, 2.28564789e+10, 2.46989026e+10, 2.55273099e+10, 2.90144799e+10, 3.35247169e+10, 3.23754466e+10, 3.84627167e+10, 4.80181144e+10, 5.66305270e+10, 6.16312068e+10, 7.38508626e+10, 7.94290054e+10, 7.05626583e+10, 9.10064661e+10, 1.07052230e+11, 1.13743075e+11, 1.24889016e+11, 1.21019776e+11, 1.24903446e+11, 1.38737714e+11, 1.53106454e+11, 1.38647575e+11, 1.60453424e+11, 1.91605005e+11, 2.02721710e+11, 2.17400410e+11, 2.20460390e+11, 2.27369209e+11, 2.16675523e+11, 2.37304251e+11, 2.58130838e+11, 2.78166702e+11, 2.69209401e+11, 2.67986504e+11, 2.64420672e+11, 3.05330076e+11, 2.84312616e+11, 2.97745048e+11, 2.94323045e+11, 2.79823160e+11, 3.00720337e+11, 3.15457898e+11, 3.03655037e+11, 3.10171533e+11, 3.25815890e+11, 3.26324154e+11, 3.65066755e+11, 3.46308701e+11, 3.38642997e+11, 3.15467566e+11, 3.70775861e+11, 3.16016373e+11, 3.60178817e+11, 3.26874950e+11, 3.16870223e+11, 3.68363394e+11, 3.21686787e+11, 3.36353486e+11, 3.79087466e+11, 3.36264695e+11, 3.54827395e+11, 3.54365213e+11, 3.63510502e+11, 3.53928382e+11, 3.32258812e+11, 3.07457560e+11, 3.49373577e+11, 3.43873461e+11, 3.38819321e+11, 3.47225205e+11, 3.00928251e+11, 3.76414269e+11, 3.22697826e+11, 3.20047527e+11, 3.31544095e+11, 3.32239099e+11, 3.21891331e+11, 3.55276893e+11, 3.21405171e+11, 3.37259371e+11, 3.55677576e+11, 3.14046920e+11, 3.10471793e+11, 3.09880497e+11, 3.31790034e+11, 2.85277223e+11, 3.21085935e+11, 3.32972492e+11, 2.97693555e+11, 3.25190003e+11, 2.75499970e+11, 2.70562652e+11, 2.93798748e+11, 2.85972132e+11, 2.74286065e+11, 2.70559309e+11, 2.97903474e+11, 2.92417186e+11, 2.82845979e+11, 2.68773459e+11, 2.72423405e+11, 2.45734247e+11, 2.64237394e+11, 2.69291294e+11, 2.67942326e+11, 2.41913033e+11, 2.69615619e+11, 2.58439056e+11, 2.76208814e+11, 2.70113579e+11, 2.35402268e+11, 2.53923208e+11, 2.65762764e+11, 2.46346182e+11, 2.71895726e+11, 2.38511042e+11, 2.27558944e+11, 2.16964413e+11, 2.27747947e+11, 2.29887681e+11, 2.49950248e+11, 2.24832625e+11, 2.24717906e+11, 2.12075113e+11, 2.24860438e+11, 2.12180218e+11, 2.01653983e+11, 2.07646565e+11, 2.25143054e+11, 2.15038325e+11, 2.13604644e+11, 1.92183522e+11, 2.34066199e+11, 2.03679822e+11, 1.86412319e+11, 1.98277962e+11, 1.84427929e+11, 1.91063379e+11, 1.81087647e+11, 1.97255442e+11, 1.87644021e+11, 2.05017953e+11, 1.87630755e+11, 1.96732170e+11, 1.85391971e+11, 1.93421159e+11, 1.87788692e+11, 1.75097703e+11, 1.72368597e+11, 1.71477354e+11, 1.84363543e+11, 1.98238379e+11, 1.67806850e+11, 1.67298216e+11, 1.76983280e+11, 1.65381628e+11, 1.72130802e+11, 1.60674230e+11, 1.62033356e+11, 1.70007733e+11, 1.51698506e+11, 1.55397678e+11, 1.57177712e+11, 1.58018263e+11, 1.51958117e+11, 1.48079555e+11, 1.49601697e+11, 1.39970883e+11, 1.35015019e+11, 1.46280030e+11, 1.41452169e+11, 1.38113780e+11, 1.41288254e+11, 1.40183297e+11, 1.43071216e+11, 1.45385652e+11, 1.46606001e+11, 1.32551441e+11, 1.35341506e+11, 1.26984136e+11, 1.30678050e+11, 1.38751741e+11, 1.24889942e+11, 1.27605986e+11, 1.27232890e+11, 1.37645733e+11, 1.33138697e+11, 1.29244345e+11, 1.32667250e+11, 1.18727100e+11, 1.34703038e+11, 1.03047036e+11, 1.13265024e+11, 1.07714253e+11, 1.21973275e+11, 1.15232019e+11, 1.09427552e+11, 1.06108483e+11, 1.22727615e+11, 1.13019417e+11, 1.08337000e+11, 1.04569068e+11, 1.07899054e+11, 1.04399175e+11, 1.17659392e+11, 1.10002416e+11, 9.86711862e+10, 1.02976185e+11, 1.06038646e+11, 1.06928893e+11, 1.02697823e+11, 9.96542280e+10, 8.99837762e+10, 9.31575396e+10, 9.41623657e+10, 9.77390732e+10, 9.07332799e+10, 9.81374279e+10, 8.99168986e+10, 8.27506012e+10, 9.39927248e+10, 9.20791336e+10, 9.25855349e+10, 8.87750241e+10, 9.06870996e+10, 8.85634520e+10, 8.97210483e+10, 7.89687177e+10, 8.89726183e+10, 9.46174831e+10, 9.22415773e+10, 8.30042760e+10, 8.05421518e+10, 8.10899796e+10, 7.69100620e+10, 7.75119559e+10, 7.16605995e+10, 7.28222526e+10, 7.08378887e+10, 7.08303399e+10, 6.67746040e+10, 7.14362059e+10, 7.34267302e+10, 7.49345750e+10, 6.89431650e+10, 6.32610464e+10, 5.41271783e+10, 5.75967901e+10, 6.03252322e+10, 5.90589205e+10, 5.66227628e+10, 4.04795513e+10, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00])
[17]:
monitor.plot()
[17]:
Comparing the final, normalized result shows that it agrees with the data that was normalized by proton-charge:
[18]:
sc.plot({"By proton charge": histogram, "By monitor": normalized_by_monitor.hist()})
[18]:
