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6 Testing the BsplineEval library vs DASL

Testing was performed by comparing the results given by the dasl and the optimized algorithm C. The paragraphs to follow show the results of two different input files, one with `large' rms deformation ( p6.spl ) and one with `small' rms deformation ( p6_low_31_72.SPL ). The results agree to within roundoff errors, this was done by running the following command:

     The file ./test/p6.spl with the following characteristics:
     
     # spline deformation amplitudes
     # z_order         4
     # theta_order     4
     # qz              421
     # num_z_knots     417
     # num_theta_knots 144
     # zmin zmax       -1.000000e+00 1.000000e+00
     # tmin tmax       0.000000e+00 6.283185e+00
     # rms amplitude   129188.64688685712463
     #
     
     yield the following results:
     
     futile-90: objs/sun4u-SunOS-5/evalbspline num=100 test=5 \
     	| column -v -a deltas N - | column -v -a deltadt N \
     	| column -v -a deltadz N \
             | compute deltas = \( dasl - algoc \) \/ dasl \
             | compute deltadz = \( ddasldz - dalgocdz \) \/ ddasldz \
             | compute deltadt = \( ddasldt - dalgocdt \) \/ ddasldt \
             | rdbstats deltas deltadz deltadt | tbl2lst
     
          deltas_n | N
        deltas_sum | N
        deltas_ave | N
        deltas_dev | N
        deltas_min | N
        deltas_max | N
         deltadz_n | N
       deltadz_sum | N
       deltadz_ave | N
       deltadz_dev | N
       deltadz_min | N
       deltadz_max | N
         deltadt_n | N
       deltadt_sum | N
       deltadt_ave | N
       deltadt_dev | N
       deltadt_min | N
       deltadt_max | N
     
          deltas_n | 10000
        deltas_sum | -1.29628283548978e-13
        deltas_ave | -1.29628283548978e-17
        deltas_dev | 1.10245039134638e-16
        deltas_min | -5.83761910253855e-16
        deltas_max | 5.3919301269975e-16
         deltadz_n | 10000
       deltadz_sum | -9.28799965664604e-14
       deltadz_ave | -9.28799965664602e-18
       deltadz_dev | 1.33699222283282e-16
       deltadz_min | -3.90195209692813e-15
       deltadz_max | 3.74917737998133e-15
         deltadt_n | 10000
       deltadt_sum | -1.46179231627943e-13
       deltadt_ave | -1.46179231627943e-17
       deltadt_dev | 1.07162272062163e-16
       deltadt_min | -6.82814047720486e-16
       deltadt_max | 7.42207044201643e-16
     
     
     The file ./test/p6_low_31_72.SPL with the following characteristics:
     
     # spline deformation amplitudes
     # z_order         4
     # theta_order     4
     # qz              33
     # num_z_knots     29
     # num_theta_knots 71
     # zmin zmax       -1.000000e+00 1.000000e+00
     # tmin tmax       0.000000e+00 6.283185e+00
     # rms amplitude   0.00101284258284
     
     yield the following results:
     
     futile-93: objs/sun4u-SunOS-5/evalbspline num=100 test=5 \
     	input=p6_low_31_72.SPL	\
     	| column -v -a deltas N - | column -v -a deltadt N \
     	| column -v -a deltadz N \
             | compute deltas = \( dasl - algoc \) \/ dasl \
             | compute deltadz = \( ddasldz - dalgocdz \) \/ ddasldz \
             | compute deltadt = \( ddasldt - dalgocdt \) \/ ddasldt \
             | rdbstats deltas deltadz deltadt | tbl2lst
     
     
          deltas_n | N
        deltas_sum | N
        deltas_ave | N
        deltas_dev | N
        deltas_min | N
        deltas_max | N
         deltadz_n | N
       deltadz_sum | N
       deltadz_ave | N
       deltadz_dev | N
       deltadz_min | N
       deltadz_max | N
         deltadt_n | N
       deltadt_sum | N
       deltadt_ave | N
       deltadt_dev | N
       deltadt_min | N
       deltadt_max | N
     
          deltas_n | 10000
        deltas_sum | -0
        deltas_ave | 0
        deltas_dev | 0
        deltas_min | -0
        deltas_max | -0
         deltadz_n | 10000
       deltadz_sum | 0
       deltadz_ave | 0
       deltadz_dev | 0
       deltadz_min | 0
       deltadz_max | 0
         deltadt_n | 10000
       deltadt_sum | 0
       deltadt_ave | 0
       deltadt_dev | 0
       deltadt_min | -0
       deltadt_max | -0