Creating an Interactive Plot using Holoviews()

March 26, 2021

• First, import the modules that we always make use of.

import numpy as np
import matplotlib.pyplot as plt

• Next, we load the contents of "F-H-data.txt" into a variable. Note that you first have to upload this file to your Jupyter Hub file system.

FH = np.loadtxt("F-H-data.txt")

• FH is a 2-dimensional array. It has many rows and three columns.

FH

array([[ 0.000e+00,  8.000e-01, -8.000e-02],
       [ 2.000e-06,  8.000e-01, -8.000e-02],
       [ 4.000e-06,  8.000e-01, -8.000e-02],
       ...,
       [ 4.994e-03,  9.440e+01,  1.072e+01],
       [ 4.996e-03,  9.520e+01,  1.072e+01],
       [ 4.998e-03,  9.520e+01,  1.072e+01]])

The first column is time in seconds, the second column is the accelerating voltage in volts, and the third column is the Franck-Hertz signal in voltage. (The Franck-Hertz signal is a current that is converted into a voltage.)

We are interested in creating a plot of the Franck-Hertz signal as a function of the accelerating voltage.

• Here's how we can select specific columns of data from the 2-D array.

a = FH[:, 1]
sig = FH[:, 2]
a, sig

(array([ 0.8,  0.8,  0.8, ..., 94.4, 95.2, 95.2]),
 array([-0.08, -0.08, -0.08, ..., 10.72, 10.72, 10.72]))

• Here is a plot of the Franck-Hertz signal as a function of the accelerating voltage.

plt.plot(a, sig)
plt.xlabel('Accelerating voltage (V)')
plt.ylabel('Franck-Hertz signal (V)');

• Next, we import a second dataset. It is the visibile part of hydrogen's emission spectrum. This file contains 7 lines of header information that is not data. We can use the skiprows option to omit these rows during the import.

hyd = np.loadtxt("hydrogen spectrum.txt", skiprows = 7)
hyd

array([[3.80000000e+02, 7.09068709e-03],
       [3.81000000e+02, 5.41588042e-03],
       [3.82000000e+02, 5.25715026e-03],
       ...,
       [9.48000000e+02, 0.00000000e+00],
       [9.49000000e+02, 0.00000000e+00],
       [9.50000000e+02, 0.00000000e+00]])

• The first column is wavelength in nm and the second column is relative intensity (unitless).

wavelength = hyd[:, 0]
I = hyd[:, 1]
wavelength, I

(array([380., 381., 382., 383., 384., 385., 386., 387., 388., 389., 390.,
        391., 392., 393., 394., 395., 396., 397., 398., 399., 400., 401.,
        402., 403., 404., 405., 406., 407., 408., 409., 410., 411., 412.,
        413., 414., 415., 416., 417., 418., 419., 420., 421., 422., 423.,
        424., 425., 426., 427., 428., 429., 430., 431., 432., 433., 434.,
        435., 436., 437., 438., 439., 440., 441., 442., 443., 444., 445.,
        446., 447., 448., 449., 450., 451., 452., 453., 454., 455., 456.,
        457., 458., 459., 460., 461., 462., 463., 464., 465., 466., 467.,
        468., 469., 470., 471., 472., 473., 474., 475., 476., 477., 478.,
        479., 480., 481., 482., 483., 484., 485., 486., 487., 488., 489.,
        490., 491., 492., 493., 494., 495., 496., 497., 498., 499., 500.,
        501., 502., 503., 504., 505., 506., 507., 508., 509., 510., 511.,
        512., 513., 514., 515., 516., 517., 518., 519., 520., 521., 522.,
        523., 524., 525., 526., 527., 528., 529., 530., 531., 532., 533.,
        534., 535., 536., 537., 538., 539., 540., 541., 542., 543., 544.,
        545., 546., 547., 548., 549., 550., 551., 552., 553., 554., 555.,
        556., 557., 558., 559., 560., 561., 562., 563., 564., 565., 566.,
        567., 568., 569., 570., 571., 572., 573., 574., 575., 576., 577.,
        578., 579., 580., 581., 582., 583., 584., 585., 586., 587., 588.,
        589., 590., 591., 592., 593., 594., 595., 596., 597., 598., 599.,
        600., 601., 602., 603., 604., 605., 606., 607., 608., 609., 610.,
        611., 612., 613., 614., 615., 616., 617., 618., 619., 620., 621.,
        622., 623., 624., 625., 626., 627., 628., 629., 630., 631., 632.,
        633., 634., 635., 636., 637., 638., 639., 640., 641., 642., 643.,
        644., 645., 646., 647., 648., 649., 650., 651., 652., 653., 654.,
        655., 656., 657., 658., 659., 660., 661., 662., 663., 664., 665.,
        666., 667., 668., 669., 670., 671., 672., 673., 674., 675., 676.,
        677., 678., 679., 680., 681., 682., 683., 684., 685., 686., 687.,
        688., 689., 690., 691., 692., 693., 694., 695., 696., 697., 698.,
        699., 700., 701., 702., 703., 704., 705., 706., 707., 708., 709.,
        710., 711., 712., 713., 714., 715., 716., 717., 718., 719., 720.,
        721., 722., 723., 724., 725., 726., 727., 728., 729., 730., 731.,
        732., 733., 734., 735., 736., 737., 738., 739., 740., 741., 742.,
        743., 744., 745., 746., 747., 748., 749., 750., 751., 752., 753.,
        754., 755., 756., 757., 758., 759., 760., 761., 762., 763., 764.,
        765., 766., 767., 768., 769., 770., 771., 772., 773., 774., 775.,
        776., 777., 778., 779., 780., 781., 782., 783., 784., 785., 786.,
        787., 788., 789., 790., 791., 792., 793., 794., 795., 796., 797.,
        798., 799., 800., 801., 802., 803., 804., 805., 806., 807., 808.,
        809., 810., 811., 812., 813., 814., 815., 816., 817., 818., 819.,
        820., 821., 822., 823., 824., 825., 826., 827., 828., 829., 830.,
        831., 832., 833., 834., 835., 836., 837., 838., 839., 840., 841.,
        842., 843., 844., 845., 846., 847., 848., 849., 850., 851., 852.,
        853., 854., 855., 856., 857., 858., 859., 860., 861., 862., 863.,
        864., 865., 866., 867., 868., 869., 870., 871., 872., 873., 874.,
        875., 876., 877., 878., 879., 880., 881., 882., 883., 884., 885.,
        886., 887., 888., 889., 890., 891., 892., 893., 894., 895., 896.,
        897., 898., 899., 900., 901., 902., 903., 904., 905., 906., 907.,
        908., 909., 910., 911., 912., 913., 914., 915., 916., 917., 918.,
        919., 920., 921., 922., 923., 924., 925., 926., 927., 928., 929.,
        930., 931., 932., 933., 934., 935., 936., 937., 938., 939., 940.,
        941., 942., 943., 944., 945., 946., 947., 948., 949., 950.]),
 array([7.09068709e-03, 5.41588042e-03, 5.25715026e-03, 7.75613276e-03,
        6.44152144e-03, 5.15540016e-03, 6.02231102e-03, 6.98690199e-03,
        1.12726163e-02, 1.35803086e-02, 6.45780146e-03, 6.70607171e-03,
        7.20057720e-03, 7.70322270e-03, 8.90387390e-03, 1.00882451e-02,
        3.35680986e-02, 5.09063159e-02, 1.16511267e-02, 1.22372072e-02,
        1.05115255e-02, 9.20301920e-03, 8.76956377e-03, 8.72072372e-03,
        8.21604322e-03, 8.50908351e-03, 1.20825471e-02, 1.22433122e-02,
        1.23755874e-02, 7.66328116e-02, 1.92157842e-01, 2.03283753e-02,
        1.04789655e-02, 1.17060717e-02, 1.29128279e-02, 1.51309801e-02,
        1.76279276e-02, 2.21965072e-02, 2.24854775e-02, 1.83605284e-02,
        2.20011470e-02, 2.04504755e-02, 1.69746920e-02, 1.43658194e-02,
        1.13662264e-02, 1.06376956e-02, 1.02388352e-02, 1.02958153e-02,
        1.26218226e-02, 1.26767677e-02, 1.33157583e-02, 1.73226773e-02,
        3.13051763e-02, 4.78724794e-01, 8.87043882e-01, 1.91785992e-02,
        1.57211307e-02, 1.49193399e-02, 1.44044844e-02, 1.53670404e-02,
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        1.57781108e-02, 1.71273171e-02, 1.86230436e-02, 1.95347245e-02,
        1.83788434e-02, 1.18220668e-02, 1.23023273e-02, 1.34948385e-02,
        1.00353350e-02, 8.97102897e-03, 9.83183483e-03, 1.01981352e-02,
        9.85218485e-03, 1.01187701e-02, 9.38413438e-03, 1.08045658e-02,
        9.73822474e-03, 9.03818404e-03, 1.07842158e-02, 9.14400414e-03,
        8.65560366e-03, 1.04179154e-02, 1.45082695e-02, 1.23877974e-02,
        1.02388352e-02, 1.09632960e-02, 1.23104673e-02, 1.07720058e-02,
        1.23511674e-02, 1.34052984e-02, 1.06560107e-02, 1.11057461e-02,
        1.28029378e-02, 1.29372479e-02, 1.63723314e-02, 1.70418470e-02,
        1.49396899e-02, 1.65514116e-02, 2.19075369e-02, 1.65961816e-02,
        1.13295963e-02, 1.08574759e-02, 1.13784364e-02, 1.10243460e-02,
        1.04850705e-02, 1.11138861e-02, 1.24162874e-02, 9.97021497e-03,
        9.18877419e-03, 1.25851926e-02, 1.31203981e-02, 1.03853554e-02,
        8.48466348e-03, 7.15173715e-03, 7.00318200e-03, 8.99748400e-03,
        1.07475857e-02, 9.91323491e-03, 9.81962482e-03, 1.06906057e-02,
        9.81555482e-03, 1.23837274e-02, 1.30105080e-02, 1.21334221e-02,
        1.91236541e-02, 2.18953269e-02, 2.03731454e-02, 1.61199911e-02,
        2.17610168e-02, 3.35803086e-02, 2.14191364e-02, 2.54647205e-02,
        2.99132349e-02, 3.35111185e-02, 4.08269508e-02, 3.80858031e-02,
        4.47646798e-02, 6.99091649e-02, 4.60792911e-02, 4.79820180e-02,
        3.41094091e-02, 2.57211307e-02, 3.29657380e-02, 4.07109557e-02,
        5.21354571e-02, 3.48562549e-02, 2.42884893e-02, 3.39628890e-02,
        4.24529175e-02, 5.29738780e-02, 4.51554002e-02, 3.47117697e-02,
        3.66246716e-02, 4.88102638e-02, 3.63804714e-02, 2.64659415e-02,
        2.30919081e-02, 3.61525512e-02, 5.63560514e-02, 4.49478299e-02,
        2.50048100e-02, 2.45652496e-02, 3.05522256e-02, 3.18281718e-02,
        3.23145373e-02, 3.18627669e-02, 1.70560921e-02, 2.23552374e-02,
        3.46751397e-02, 3.41847042e-02, 2.28721279e-02, 2.92620343e-02,
        2.76991527e-02, 2.23918674e-02, 1.86352536e-02, 2.49926000e-02,
        1.96059496e-02, 1.44960595e-02, 2.79759130e-02, 2.89608540e-02,
        1.98562549e-02, 1.72433122e-02, 2.05807156e-02, 2.40381840e-02,
        2.37675288e-02, 2.54606505e-02, 2.54280904e-02, 2.41297591e-02,
        3.52775003e-02, 3.30674881e-02, 2.70601621e-02, 2.63458763e-02,
        2.92620343e-02, 3.13458763e-02, 3.12644763e-02, 3.65514116e-02,
        3.97789248e-02, 9.31041181e-02, 1.66368261e-01, 1.58934399e-01,
        1.48582344e-01, 1.47601473e-01, 2.07288082e-01, 2.10751656e-01,
        1.78175343e-01, 1.51366226e-01, 1.29644615e-01, 1.21571762e-01,
        2.54048359e-01, 2.38586414e-01, 3.13205868e-01, 9.59184704e-01,
        9.59184704e-01, 9.59184704e-01, 9.59184704e-01, 4.42546528e-01,
        9.22209272e-02, 6.02775003e-02, 4.45123395e-02, 3.32913383e-02,
        2.48216598e-02, 1.87410737e-02, 1.62583713e-02, 1.42111592e-02,
        1.26849077e-02, 1.23796574e-02, 1.06987457e-02, 9.90509491e-03,
        9.11754912e-03, 8.15092315e-03, 7.16598217e-03, 6.95434195e-03,
        5.94498094e-03, 4.84607985e-03, 4.40559441e-03, 4.32696933e-03,
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        3.55255855e-03, 2.92966293e-03, 2.30547231e-03, 2.64901765e-03,
        2.06016206e-03, 2.29973730e-03, 2.84400784e-03, 2.58408258e-03,
        1.60302660e-03, 1.57749658e-03, 1.78044178e-03, 1.63299663e-03,
        1.52736153e-03, 1.46427646e-03, 1.31109631e-03, 2.10937211e-03,
        2.11399711e-03, 1.44781145e-03, 1.42487142e-03, 1.44170644e-03,
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        1.11259111e-03, 8.90220890e-04, 9.95115995e-04, 6.55825656e-04,
        1.50090650e-03, 2.52395752e-03, 2.62755763e-03, 2.04832205e-03,
        1.46594147e-03, 1.15569616e-03, 1.87257187e-03, 2.88008288e-03,
        4.11033411e-03, 5.18389018e-03, 4.82979983e-03, 2.64161764e-03,
        3.05213305e-03, 3.20993821e-03, 4.09923410e-03, 3.99137899e-03,
        2.82754283e-03, 1.41839642e-03, 1.69552670e-03, 3.40122840e-03,
        2.14452214e-03, 1.33810634e-03, 6.01435601e-04, 8.17700818e-04,
        7.77370777e-04, 3.37810338e-04, 3.31890332e-04, 7.17800718e-04,
        1.69441669e-03, 2.55263255e-03, 2.19299219e-03, 2.04425204e-03,
        1.26281126e-03, 9.45720946e-04, 6.47870648e-04, 5.18333518e-03,
        2.51817627e-03, 3.33573834e-03, 1.92696193e-03, 9.99741000e-04,
        7.33155733e-04, 9.86235986e-04, 1.19140119e-03, 3.07137307e-03,
        2.69156769e-03, 9.86975987e-04, 6.05875606e-04, 1.60395160e-04,
        1.12609613e-03, 2.05054205e-03, 1.64261664e-03, 9.52195952e-04,
        1.56066156e-03, 1.61616162e-03, 7.56835757e-04, 7.29640730e-04,
        5.39275539e-04, 4.47145447e-04, 2.23110223e-04, 2.89895290e-04,
        3.15880416e-02, 9.03650054e-02, 3.82648833e-02, 1.07516558e-02,
        1.77766678e-03, 5.50560551e-04, 8.30650831e-05, 4.68050468e-05,
        2.68250268e-05, 0.00000000e+00, 0.00000000e+00, 1.40600141e-05,
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        8.39438339e-05, 4.23650424e-05, 8.63950864e-05, 2.59000259e-05,
        3.75550376e-05, 2.64550265e-05, 0.00000000e+00, 3.58900359e-05,
        1.35050135e-05, 3.03400303e-05, 1.12850113e-05, 0.00000000e+00,
        3.33000333e-06, 9.25000925e-07, 0.00000000e+00, 0.00000000e+00,
        2.20150220e-05, 4.25500425e-06, 2.10900211e-05, 0.00000000e+00,
        1.48000148e-05, 4.16250416e-06, 0.00000000e+00, 0.00000000e+00,
        0.00000000e+00, 1.33200133e-05, 2.64550265e-05, 5.55000555e-06,
        2.66400266e-05, 6.47500648e-06, 3.46875347e-06, 3.44100344e-05,
        0.00000000e+00, 1.11000111e-06, 9.25000925e-07, 0.00000000e+00,
        0.00000000e+00, 2.49750250e-06, 1.33200133e-05, 1.18400118e-05,
        2.46050246e-05, 4.08850409e-05, 2.09050209e-05, 0.00000000e+00,
        3.46875347e-06, 3.88500388e-06, 3.88500388e-06, 2.89895290e-03,
        3.70764421e-02, 2.29494579e-02, 7.53635254e-03, 5.85109335e-04,
        0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 1.85000185e-06,
        5.95700596e-05, 1.47075147e-05, 1.00455100e-04, 3.88500388e-06,
        0.00000000e+00, 0.00000000e+00, 4.62500462e-06, 2.41425241e-05,
        0.00000000e+00, 6.10500611e-06, 3.33000333e-06, 0.00000000e+00,
        0.00000000e+00, 0.00000000e+00, 5.10600511e-05, 1.83150183e-05,
        0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 1.40600141e-05,
        5.92000592e-06, 2.40500240e-06, 0.00000000e+00, 0.00000000e+00,
        2.03500203e-06, 0.00000000e+00, 0.00000000e+00, 1.65945166e-04,
        6.88200688e-05, 2.64550265e-05, 0.00000000e+00, 0.00000000e+00,
        0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 9.17600918e-05,
        1.88838939e-04, 5.00610501e-04, 4.95985496e-04, 6.10500611e-06,
        4.57875458e-06, 0.00000000e+00, 0.00000000e+00, 3.33000333e-06,
        0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
        0.00000000e+00, 1.55400155e-05, 0.00000000e+00, 1.11000111e-06,
        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,
        5.55000555e-07, 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, 1.00885226e-03, 3.48725349e-04,
        0.00000000e+00, 0.00000000e+00, 1.48000148e-06, 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, 1.42450142e-05,
        0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
        0.00000000e+00, 0.00000000e+00, 0.00000000e+00]))

• Here is a plot of the emission spectrum which should correspond to the Balmer series.

plt.plot(wavelength, I)
plt.xlabel('Wavelength (nm)')
plt.ylabel('Relative intensity (a.u.)');

To make interactive plots that can be zoomed and panned to examine the features of these plots in detail, we will need two new modules. There modules are not 'standard', so we will have to install them first.

• The first module to install is xarray. Here is the install command.

!pip install xarray

Requirement already satisfied: xarray in /opt/conda/lib/python3.8/site-packages (0.17.0)
Requirement already satisfied: numpy>=1.15 in /opt/conda/lib/python3.8/site-packages (from xarray) (1.19.4)
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• The second module to install is holoviews.

!pip install holoviews

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• We can now import these modules. We will also make use of an extension to holoviews.

import xarray as xr
import holoviews as hv
hv.extension('bokeh')

We can now construct our interactive plots. The syntax is a little unintuitive. We first have to use xarray to create the proper data structure to use in holoviews

• Here's the data structure for the Franck-Hertz plot.

FHdata = xr.DataArray(sig, dims=['acceleration voltage (V)'], 
                      coords = {'acceleration voltage (V)': a}, 
                      name='Franck-Hertz signal (V)')

• Now we can create the plot. We get a set of controls on the right that can be used to pan and zoom. We can also create png images of the desired views. The option on the bottom allow the graph to ne reset.

hv.Curve(FHdata).opts(width = 800, height = 500)

• Here's an interactive plot of the hydrogen emission spectrum.

HydrogenData = xr.DataArray(I, dims=['Wavelength (nm)'], 
                      coords = {'Wavelength (nm)': wavelength}, 
                      name='Relative intensity (a.u.)')
hv.Curve(HydrogenData).opts(width = 800, height = 500)