@@ -52,17 +52,17 @@ The library is compiled by Apple LLVM version 10.0.1 as above with the compiler
5252| ----------------: | -------: | -------: | -------: | -------: | -------: | -------: | -------: | -------: |
5353| ** Forward** | 0.000101 | 0.000446 | 0.001952 | 0.006277 | 0.026590 | 0.141962 | 0.775724 | 4.870621 |
5454| ** Backward** | 0.000101 | 0.000448 | 0.001918 | 0.006357 | 0.027123 | 0.145149 | 0.815881 | 5.040577 |
55- | ** ϵ<sub >2</sub >** | 5.42e-16 | 7.79e-16 | 9.23e-16 | 1.27e-15 | 1.80e-15 | 2.52e-15 | 3.54e-15 | 4.98e-15 |
56- | ** ϵ<sub >∞</sub >** | 1.33e-15 | 2.55e-15 | 4.55e-15 | 5.22e-15 | 9.33e-15 | 1.11e-14 | 1.81e-14 | 3.80e-14 |
55+ | < b > ϵ<sub >2</sub ></ b > | 5.42e-16 | 7.79e-16 | 9.23e-16 | 1.27e-15 | 1.80e-15 | 2.52e-15 | 3.54e-15 | 4.98e-15 |
56+ | < b > ϵ<sub >∞</sub ></ b > | 1.33e-15 | 2.55e-15 | 4.55e-15 | 5.22e-15 | 9.33e-15 | 1.11e-14 | 1.81e-14 | 3.80e-14 |
5757
5858### Proriol series to bivariate Chebyshev series (` tri2cheb ` ) with (α, β, γ) = (0, 0, 0)
5959
6060| Degree | 63 | 127 | 255 | 511 | 1023 | 2047 | 4095 | 8191 |
6161| ----------------: | -------: | -------: | -------: | -------: | -------: | -------: | -------: | -------: |
6262| ** Forward** | 0.000063 | 0.000300 | 0.001048 | 0.003886 | 0.019123 | 0.113299 | 0.699465 | 4.555086 |
6363| ** Backward** | 0.000065 | 0.000289 | 0.000987 | 0.003837 | 0.019529 | 0.114718 | 0.699051 | 4.697958 |
64- | ** ϵ<sub >2</sub >** | 2.30e-15 | 3.94e-15 | 8.14e-15 | 1.68e-14 | 3.55e-14 | 7.30e-14 | 1.44e-13 | 2.97e-13 |
65- | ** ϵ<sub >∞</sub >** | 1.09e-14 | 1.84e-14 | 5.49e-14 | 1.49e-13 | 9.06e-13 | 1.95e-12 | 3.73e-12 | 1.05e-11 |
64+ | < b > ϵ<sub >2</sub ></ b > | 2.30e-15 | 3.94e-15 | 8.14e-15 | 1.68e-14 | 3.55e-14 | 7.30e-14 | 1.44e-13 | 2.97e-13 |
65+ | < b > ϵ<sub >∞</sub ></ b > | 1.09e-14 | 1.84e-14 | 5.49e-14 | 1.49e-13 | 9.06e-13 | 1.95e-12 | 3.73e-12 | 1.05e-11 |
6666
6767The error growth rate is significantly reduced if (α, β, γ) = (-0.5, -0.5, -0.5).
6868
@@ -72,16 +72,16 @@ The error growth rate is significantly reduced if (α, β, γ) = (-0.5, -0.5, -0
7272| ----------------: | -------: | -------: | -------: | -------: | -------: | -------: | -------: | -------: |
7373| ** Forward** | 0.000209 | 0.001077 | 0.003618 | 0.013243 | 0.064321 | 0.369272 | 2.182001 | 16.15872 |
7474| ** Backward** | 0.000208 | 0.001027 | 0.003487 | 0.012903 | 0.064544 | 0.372493 | 2.191747 | 16.43340 |
75- | ** ϵ<sub >2</sub >** | 7.60e-16 | 9.35e-16 | 1.31e-15 | 1.84e-15 | 2.56e-15 | 3.59e-15 | 5.05e-15 | 7.15e-15 |
76- | ** ϵ<sub >∞</sub >** | 1.78e-15 | 2.66e-15 | 5.33e-15 | 7.11e-15 | 1.27e-14 | 1.79e-14 | 2.91e-14 | 1.66e-13 |
75+ | < b > ϵ<sub >2</sub ></ b > | 7.60e-16 | 9.35e-16 | 1.31e-15 | 1.84e-15 | 2.56e-15 | 3.59e-15 | 5.05e-15 | 7.15e-15 |
76+ | < b > ϵ<sub >∞</sub ></ b > | 1.78e-15 | 2.66e-15 | 5.33e-15 | 7.11e-15 | 1.27e-14 | 1.79e-14 | 2.91e-14 | 1.66e-13 |
7777
7878### Rotation of a spherical harmonic series (` sph_rotation ` ) with ZYZ Euler angles (α, β, γ) = (0.1, 0.2, 0.3)
7979
8080| Degree | 63 | 127 | 255 | 511 | 1023 | 2047 | 4095 | 8191 |
8181| ----------------: | -------: | -------: | -------: | -------: | -------: | -------: | -------: | -------: |
8282| ** Time** | 0.000141 | 0.000453 | 0.001598 | 0.006742 | 0.031256 | 0.170632 | 1.082894 | 10.35029 |
83- | ** ϵ<sub >2</sub >** | 7.75e-15 | 8.29e-15 | 1.08e-14 | 1.77e-14 | 2.93e-14 | 5.12e-14 | 1.09e-13 | 1.87e-13 |
84- | ** ϵ<sub >∞</sub >** | 1.47e-14 | 2.55e-14 | 8.01e-14 | 2.59e-13 | 7.36e-13 | 2.45e-12 | 6.74e-12 | 1.55e-11 |
83+ | < b > ϵ<sub >2</sub ></ b > | 7.75e-15 | 8.29e-15 | 1.08e-14 | 1.77e-14 | 2.93e-14 | 5.12e-14 | 1.09e-13 | 1.87e-13 |
84+ | < b > ϵ<sub >∞</sub ></ b > | 1.47e-14 | 2.55e-14 | 8.01e-14 | 2.59e-13 | 7.36e-13 | 2.45e-12 | 6.74e-12 | 1.55e-11 |
8585
8686## References
8787
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