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Refactor: optimized cubic spline (#4081)
* redesign eval to enable potential vectorization * fix interface * refactored version init commit * clean up * clean up * fix & a few tests * theoretical error bound test * clean up * better unit test for cross-check * systematic cross-check * minor change * clean up * clean up * minor internal change * add explanation --------- Co-authored-by: Mohan Chen <[email protected]>
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,7 @@ | ||
| periodic periodic | ||
| 0.00000000000000000e+00 1.00000000000000006e-01 1.00000000000000000e+00 1.50000000000000000e+00 3.00000000000000000e+00 6.28318530717958623e+00 | ||
| 1.00000000000000000e+00 9.95004165278025821e-01 5.40302305868139765e-01 7.07372016677029064e-02 -9.89992496600445415e-01 1.00000000000000000e+00 | ||
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,7 @@ | ||
| first_deriv:1.10517091807564771e+00 first_deriv:2.71828182845904509e+00 | ||
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,64 @@ | ||
| ''' | ||
| This script generates reference data for the cross-check in cubic_spline_test.cpp. | ||
| To add more tests, append a new Case object to the cases list. | ||
| ''' | ||
| import numpy as np | ||
| from scipy.interpolate import CubicSpline | ||
|
|
||
| class Case: | ||
| def __init__(self, f, x, bc, fname): | ||
| self.x = x | ||
| self.y = f(x) | ||
| self.bc = bc | ||
| self.fname = fname | ||
| if bc == 'periodic': | ||
| self.y[-1] = self.y[0] | ||
|
|
||
| cases = [ | ||
| Case(np.sin, np.logspace(-1, 0, 10), 'not-a-knot', | ||
| 'sin_not_a_knot.dat'), | ||
| Case(np.cos, [0, 0.1, 1, 1.5, 3, 2*np.pi], 'periodic', | ||
| 'cos_periodic.dat'), | ||
| Case(np.exp, np.logspace(-1, 0, 10), ((1, np.exp(0.1)), (1, np.exp(1))), | ||
| 'exp_first_deriv.dat'), | ||
| Case(np.log, np.logspace(0, 1, 10), ((2, -1), (2, -0.01)), | ||
| 'log_second_deriv.dat'), | ||
| Case(np.sqrt, np.logspace(0, 1, 10), ((1, 0.5), 'not-a-knot'), | ||
| 'sqrt_mix_bc.dat'), | ||
| Case(lambda x: np.ones_like(x), [0, 1], 'periodic', | ||
| 'two_points_periodic.dat'), | ||
| Case(np.arccos, [0, 0.5], ((1, -1), (1, -2/np.sqrt(3))), | ||
| 'two_points_first_deriv.dat'), | ||
| Case(np.sqrt, [1, 4], ((2, 0.5), (2, 0.25)), | ||
| 'two_points_second_deriv.dat'), | ||
| Case(np.sin, [0, 0.3, 1], 'not-a-knot', | ||
| 'three_points_not_a_knot.dat'), | ||
| ] | ||
|
|
||
| n_interp = 37 | ||
|
|
||
| for case in cases: | ||
| cubspl = CubicSpline(case.x, case.y, bc_type=case.bc) | ||
| x_interp = np.linspace(case.x[0], case.x[-1], n_interp) | ||
| y_interp = cubspl(x_interp) | ||
| dy_interp = cubspl(x_interp, 1) | ||
| d2y_interp = cubspl(x_interp, 2) | ||
|
|
||
| with open(case.fname, 'w') as f: | ||
| if case.bc == 'periodic' or case.bc == 'not-a-knot': | ||
| f.write('{bc} {bc}\n'.format(bc=case.bc)) | ||
| else: | ||
| for b in case.bc: | ||
| if b == 'not-a-knot': | ||
| f.write('not-a-knot ') | ||
| else: | ||
| tag = 'first_deriv' if b[0] == 1 else 'second_deriv' | ||
| f.write('{tag}:{val:<24.17e} '.format(tag=tag, val=b[1])) | ||
| f.write('\n') | ||
|
|
||
| for data in [case.x, case.y, x_interp, y_interp, dy_interp, d2y_interp]: | ||
| for elem in data: | ||
| f.write('% 24.17e '%(elem)) | ||
| f.write('\n') | ||
|
|
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,7 @@ | ||
| second_deriv:-1.00000000000000000e+00 second_deriv:-1.00000000000000002e-02 | ||
| 1.00000000000000000e+00 1.29154966501488389e+00 1.66810053720005880e+00 2.15443469003188381e+00 2.78255940220712450e+00 3.59381366380462763e+00 4.64158883361277841e+00 5.99484250318940859e+00 7.74263682681126930e+00 1.00000000000000000e+01 | ||
| 0.00000000000000000e+00 2.55842788110449526e-01 5.11685576220899052e-01 7.67528364331348634e-01 1.02337115244179810e+00 1.27921394055224780e+00 1.53505672866269705e+00 1.79089951677314629e+00 2.04674230488359621e+00 2.30258509299404590e+00 | ||
| 1.00000000000000000e+00 1.25000000000000000e+00 1.50000000000000000e+00 1.75000000000000000e+00 2.00000000000000000e+00 2.25000000000000000e+00 2.50000000000000000e+00 2.75000000000000000e+00 3.00000000000000000e+00 3.25000000000000000e+00 3.50000000000000000e+00 3.75000000000000000e+00 4.00000000000000000e+00 4.25000000000000000e+00 4.50000000000000000e+00 4.75000000000000000e+00 5.00000000000000000e+00 5.25000000000000000e+00 5.50000000000000000e+00 5.75000000000000000e+00 6.00000000000000000e+00 6.25000000000000000e+00 6.50000000000000000e+00 6.75000000000000000e+00 7.00000000000000000e+00 7.25000000000000000e+00 7.50000000000000000e+00 7.75000000000000000e+00 8.00000000000000000e+00 8.25000000000000000e+00 8.50000000000000000e+00 8.75000000000000000e+00 9.00000000000000000e+00 9.25000000000000000e+00 9.50000000000000000e+00 9.75000000000000000e+00 1.00000000000000000e+01 | ||
| 0.00000000000000000e+00 2.23201685990528503e-01 4.05482161721055334e-01 5.59647381157334922e-01 6.93212288502453533e-01 8.10938183318088091e-01 9.16348065656249267e-01 1.01160453727708877e+00 1.09865227971226798e+00 1.17872100366669685e+00 1.25277767969836296e+00 1.32176777395878364e+00 1.38635002079692837e+00 1.44697637249515854e+00 1.50409420887274625e+00 1.55814764821316754e+00 1.60947600084362952e+00 1.65829393447507156e+00 1.70480885095700785e+00 1.74922815213895189e+00 1.79175923970966466e+00 1.83259005049654222e+00 1.87183533226151133e+00 1.90959263384970646e+00 1.94595950410626362e+00 1.98103349187631750e+00 2.01491214600500346e+00 2.04769301510038781e+00 2.07946352550178926e+00 2.11027403528676105e+00 2.14016641953235709e+00 2.16918255331563126e+00 2.19736431171363611e+00 2.22475356980342642e+00 2.25139220266205564e+00 2.27732208536657810e+00 2.30258509299404635e+00 | ||
| 1.00254261613056794e+00 7.98334999625206598e-01 6.66752209256807338e-01 5.71952135021786212e-01 4.99597454958138398e-01 4.44699888470842797e-01 3.99955939076224509e-01 3.63472602732268946e-01 3.33587746439520605e-01 3.07606422584049077e-01 2.85491363057420178e-01 2.66837284058103641e-01 2.50118943859901521e-01 2.35190122938787882e-01 2.22050821294762640e-01 2.10610784319237826e-01 2.00154304624132307e-01 1.90527432327081331e-01 1.81730167428084816e-01 1.73762509927142816e-01 1.66624366318174705e-01 1.60087152540269423e-01 1.53940134142904944e-01 1.48183311126081213e-01 1.42816683489798313e-01 1.37840251234056188e-01 1.33254014358854894e-01 1.29057876274537020e-01 1.25134123654711077e-01 1.21377871343099950e-01 1.17789119339703638e-01 1.14367867644522142e-01 1.11114116257555462e-01 1.08027865178803598e-01 1.05109114408266549e-01 1.02357863945944316e-01 9.97741137918368992e-02 | ||
| -1.00000000000000377e+00 -6.33660932042887648e-01 -4.49235132334255161e-01 -3.25782694882304436e-01 -2.53054745626878019e-01 -1.95497023679798904e-01 -1.62454571477147702e-01 -1.29412119274496529e-01 -1.11657824079571477e-01 -9.61927667642009099e-02 -8.07277094488303704e-02 -7.04523993469851478e-02 -6.32943222386314758e-02 -5.61362451302777968e-02 -4.89781680219241247e-02 -4.34851335765309294e-02 -4.01667039843129556e-02 -3.68482743920949818e-02 -3.35298447998770149e-02 -3.02114152076590411e-02 -2.69292458727027513e-02 -2.53684643505395734e-02 -2.38076828283763989e-02 -2.22469013062132209e-02 -2.06861197840500430e-02 -1.91253382618868650e-02 -1.75645567397236871e-02 -1.60300110957334006e-02 -1.53600098628741376e-02 -1.46900086300148763e-02 -1.40200073971556132e-02 -1.33500061642963519e-02 -1.26800049314370888e-02 -1.20100036985778258e-02 -1.13400024657185645e-02 -1.06700012328593032e-02 -1.00000000000000401e-02 |
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,7 @@ | ||
| not-a-knot not-a-knot | ||
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