.. _visualizing-fields: How to convert your coefficients back to physical fields ======================================================== Now that we have our new coefficients, we can use the ``FieldGenerator`` to view the BFE representation of the underlying fields. Here is an example: .. code:: python # Now try some slices for rendering # times = coefs.Times()[0:3] pmin = [-1.0, -1.0, 0.0] pmax = [ 1.0, 1.0, 0.0] grid = [ 40, 40, 0] fields = pyEXP.field.FieldGenerator(times, pmin, pmax, grid) surfaces = fields.slices(basis, coefs) print("We now have the following [time field] pairs") for v in surfaces: print('-'*40) for u in surfaces[v]: print("{:8.4f} {}".format(v, u)) print("\nHere is the first one:") for v in surfaces: for u in surfaces[v]: print('-'*40) print('----', u) print('-'*40) print(surfaces[v][u]) break .. parsed-literal:: We now have the following [time field] pairs ---------------------------------------- 0.0050 d 0.0050 d0 0.0050 d1 0.0050 dd 0.0050 fp 0.0050 fr 0.0050 ft 0.0050 p 0.0050 p0 0.0050 p1 ---------------------------------------- 0.0100 d 0.0100 d0 0.0100 d1 0.0100 dd 0.0100 fp 0.0100 fr 0.0100 ft 0.0100 p 0.0100 p0 0.0100 p1 ---------------------------------------- 0.0150 d 0.0150 d0 0.0150 d1 0.0150 dd 0.0150 fp 0.0150 fr 0.0150 ft 0.0150 p 0.0150 p0 0.0150 p1 Here is the first one: ---------------------------------------- ---- d ---------------------------------------- [[0.01466935 0.01572764 0.01683037 ... 0.01691943 0.01569578 0.01454976] [0.01579922 0.01698843 0.01823976 ... 0.01824065 0.01685886 0.01557862] [0.01700229 0.01834482 0.01977141 ... 0.01965588 0.01809046 0.01665567] ... [0.01620709 0.01764648 0.01922052 ... 0.01933605 0.01790085 0.0165537 ] [0.01512669 0.01641221 0.01780488 ... 0.01780399 0.01654179 0.01534729] [0.01409477 0.0152446 0.0164784 ... 0.01638934 0.01527646 0.01421436]] ---------------------------------------- ---- d0 ---------------------------------------- [[0.01437625 0.01548706 0.01666514 ... 0.01666514 0.01548706 0.01437625] [0.01548706 0.01673475 0.01807075 ... 0.01807075 0.01673475 0.01548706] [0.01666514 0.01807075 0.01959023 ... 0.01959023 0.01807075 0.01666514] ... [0.01666514 0.01807075 0.01959023 ... 0.01959023 0.01807075 0.01666514] [0.01548706 0.01673475 0.01807075 ... 0.01807075 0.01673475 0.01548706] [0.01437625 0.01548706 0.01666514 ... 0.01666514 0.01548706 0.01437625]] ---------------------------------------- ---- d1 ---------------------------------------- [[ 2.9310214e-04 2.4057881e-04 1.6522847e-04 ... 2.5428724e-04 2.0872064e-04 1.7351801e-04] [ 3.1216009e-04 2.5367373e-04 1.6900530e-04 ... 1.6989630e-04 1.2410045e-04 9.1563532e-05] [ 3.3714369e-04 2.7406731e-04 1.8118456e-04 ... 6.5652450e-05 1.9704208e-05 -9.4723200e-06] ... [-4.5805585e-04 -4.2427101e-04 -3.6970933e-04 ... -2.5417723e-04 -1.6990790e-04 -1.1143985e-04] [-3.6036380e-04 -3.2254297e-04 -2.6587487e-04 ... -2.6676588e-04 -1.9296970e-04 -1.3976726e-04] [-2.8147074e-04 -2.4245947e-04 -1.8674540e-04 ... -2.7580417e-04 -2.1060130e-04 -1.6188661e-04]] ---------------------------------------- ---- dd ---------------------------------------- [[ 0.02038795 0.01553419 0.00991461 ... 0.01525863 0.0134771 0.01206977] [ 0.02015619 0.0151585 0.00935242 ... 0.00940173 0.00741573 0.00591226] [ 0.02023047 0.01516635 0.00924872 ... 0.00335129 0.00109039 -0.00056839] ... [-0.02748586 -0.02347832 -0.01887213 ... -0.01297469 -0.00940237 -0.006687 ] [-0.02326871 -0.01927384 -0.01471299 ... -0.0147623 -0.01153107 -0.00902478] [-0.01957888 -0.01565562 -0.01120575 ... -0.01654976 -0.01359854 -0.0112607 ]] ---------------------------------------- ---- fp ---------------------------------------- [[ 2.3523889e-05 -2.7494747e-05 -4.6142261e-05 ... -2.3744381e-03 -2.4765318e-03 -2.5420913e-03] [ 2.8253578e-05 -3.1490850e-05 -5.5665809e-05 ... -2.5630798e-03 -2.6640687e-03 -2.7256690e-03] [ 4.6333553e-05 -2.1516280e-05 -5.0185608e-05 ... -2.7228037e-03 -2.8249177e-03 -2.8843500e-03] ... [-2.1641932e-03 -2.2813964e-03 -2.3770637e-03 ... -3.9592560e-04 -5.6503766e-04 -6.7382312e-04] [-2.0946811e-03 -2.1986777e-03 -2.2811126e-03 ... -3.3763298e-04 -4.9688172e-04 -6.0273433e-04] [-1.9825757e-03 -2.0702051e-03 -2.1361131e-03 ... -2.8446739e-04 -4.3382143e-04 -5.3599157e-04]] ---------------------------------------- ---- fr ---------------------------------------- [[0.58427083 0.6082849 0.63328177 ... 0.6348349 0.6097044 0.5855306 ] [0.6083254 0.6327109 0.66183424 ... 0.663443 0.6341739 0.6096149 ] [0.63334346 0.66184974 0.6909387 ... 0.6926467 0.6633966 0.63469154] ... [0.6335817 0.6622526 0.6914552 ... 0.6897473 0.66070575 0.6322336 ] [0.60857403 0.6331353 0.6623904 ... 0.6607817 0.63167226 0.6072846 ] [0.58453256 0.6087315 0.6338822 ... 0.63232917 0.6073121 0.5832728 ]] ---------------------------------------- ---- ft ---------------------------------------- [[ 0.0012785 0.00119742 0.0011111 ... 0.00318776 0.00310654 0.00301686] [ 0.00131722 0.00122571 0.00112941 ... 0.00322231 0.00313888 0.0030473 ] [ 0.0013581 0.00125646 0.00115072 ... 0.00324172 0.00315533 0.0030613 ] ... [-0.00032756 -0.00041616 -0.00050753 ... 0.00158347 0.00148271 0.00137564] [-0.00043507 -0.00052673 -0.00062107 ... 0.00147183 0.00138643 0.00129502] [-0.00051574 -0.00060837 -0.00070339 ... 0.00137327 0.00130075 0.00122262]] ---------------------------------------- ---- p ---------------------------------------- [[-0.9201083 -0.94142485 -0.96298295 ... -0.9640897 -0.9424115 -0.9209808 ] [-0.9414251 -0.9642257 -0.987366 ... -0.988466 -0.9651967 -0.9422744 ] [-0.9629851 -0.98736846 -1.0122092 ... -1.013295 -0.98831606 -0.9638034 ] ... [-0.9620315 -0.9864852 -1.0114089 ... -1.0103232 -0.9855376 -0.96121323] [-0.94052106 -0.96339077 -0.9866123 ... -0.9855123 -0.96241975 -0.9396718 ] [-0.9192482 -0.94063103 -0.9622668 ... -0.96116006 -0.9396444 -0.9183758 ]] ---------------------------------------- ---- p0 ---------------------------------------- [[-0.91991323 -0.9412575 -0.96284693 ... -0.96284693 -0.9412575 -0.91991323] [-0.9412575 -0.9640891 -0.9872643 ... -0.9872643 -0.9640891 -0.9412575 ] [-0.96284693 -0.9872643 -1.012143 ... -1.012143 -0.9872643 -0.96284693] ... [-0.96284693 -0.9872643 -1.012143 ... -1.012143 -0.9872643 -0.96284693] [-0.9412575 -0.9640891 -0.9872643 ... -0.9872643 -0.9640891 -0.9412575 ] [-0.91991323 -0.9412575 -0.96284693 ... -0.96284693 -0.9412575 -0.91991323]] ---------------------------------------- ---- p1 ---------------------------------------- [[-1.9506646e-04 -1.6740267e-04 -1.3601784e-04 ... -1.2427544e-03 -1.1540418e-03 -1.0675343e-03] [-1.6762824e-04 -1.3661387e-04 -1.0173081e-04 ... -1.2017373e-03 -1.1076175e-03 -1.0169116e-03] [-1.3819906e-04 -1.0418223e-04 -6.6171742e-05 ... -1.1519545e-03 -1.0517898e-03 -9.5646293e-04] ... [ 8.1542262e-04 7.7908312e-04 7.3413475e-04 ... 1.8199176e-03 1.7266908e-03 1.6336865e-03] [ 7.3637860e-04 6.9830474e-04 6.5194303e-04 ... 1.7519495e-03 1.6693083e-03 1.5856619e-03] [ 6.6501868e-04 6.2645477e-04 5.8010087e-04 ... 1.6868374e-03 1.6130940e-03 1.5374866e-03]] These could be made into images and so forth. We’ll do this in another example notebook.