11 September 2021 2:08:11.082 PM
VANDERMONDE_APPROX_1D_TEST:
FORTRAN90 version
Test the VANDERMONDE_APPROX_1D library.
The R8LIB library is needed.
The QR_SOLVE library is needed.
The test needs the CONDITION library.
The test needs the TEST_INTERP libary.
TEST01:
Approximate data from TEST_INTERP problem # 1
Number of data points = 18
Using polynomial approximant of degree 0
L2 data approximation error = 0.392837
Normalized length of piecewise linear interpolant = 3.13553
Normalized length of polynomial approximant = 1.00000
TEST01:
Approximate data from TEST_INTERP problem # 1
Number of data points = 18
Using polynomial approximant of degree 1
L2 data approximation error = 0.350074
Normalized length of piecewise linear interpolant = 3.13553
Normalized length of polynomial approximant = 1.08357
TEST01:
Approximate data from TEST_INTERP problem # 1
Number of data points = 18
Using polynomial approximant of degree 2
L2 data approximation error = 0.344057
Normalized length of piecewise linear interpolant = 3.13553
Normalized length of polynomial approximant = 1.12211
TEST01:
Approximate data from TEST_INTERP problem # 1
Number of data points = 18
Using polynomial approximant of degree 3
L2 data approximation error = 0.332868
Normalized length of piecewise linear interpolant = 3.13553
Normalized length of polynomial approximant = 1.31026
TEST01:
Approximate data from TEST_INTERP problem # 1
Number of data points = 18
Using polynomial approximant of degree 4
L2 data approximation error = 0.199123
Normalized length of piecewise linear interpolant = 3.13553
Normalized length of polynomial approximant = 2.51647
TEST01:
Approximate data from TEST_INTERP problem # 1
Number of data points = 18
Using polynomial approximant of degree 5
L2 data approximation error = 0.190907
Normalized length of piecewise linear interpolant = 3.13553
Normalized length of polynomial approximant = 2.60932
TEST01:
Approximate data from TEST_INTERP problem # 1
Number of data points = 18
Using polynomial approximant of degree 9
L2 data approximation error = 0.613776E-01
Normalized length of piecewise linear interpolant = 3.13553
Normalized length of polynomial approximant = 3.22044
TEST01:
Approximate data from TEST_INTERP problem # 1
Number of data points = 18
Using polynomial approximant of degree 12
L2 data approximation error = 0.374634E-01
Normalized length of piecewise linear interpolant = 3.13553
Normalized length of polynomial approximant = 3.37935
TEST01:
Approximate data from TEST_INTERP problem # 2
Number of data points = 18
Using polynomial approximant of degree 0
L2 data approximation error = 2.58162
Normalized length of piecewise linear interpolant = 2.66086
Normalized length of polynomial approximant = 1.00000
TEST01:
Approximate data from TEST_INTERP problem # 2
Number of data points = 18
Using polynomial approximant of degree 1
L2 data approximation error = 2.58162
Normalized length of piecewise linear interpolant = 2.66086
Normalized length of polynomial approximant = 1.00000
TEST01:
Approximate data from TEST_INTERP problem # 2
Number of data points = 18
Using polynomial approximant of degree 2
L2 data approximation error = 1.80946
Normalized length of piecewise linear interpolant = 2.66086
Normalized length of polynomial approximant = 1.88131
TEST01:
Approximate data from TEST_INTERP problem # 2
Number of data points = 18
Using polynomial approximant of degree 3
L2 data approximation error = 1.80946
Normalized length of piecewise linear interpolant = 2.66086
Normalized length of polynomial approximant = 1.88131
TEST01:
Approximate data from TEST_INTERP problem # 2
Number of data points = 18
Using polynomial approximant of degree 4
L2 data approximation error = 1.76341
Normalized length of piecewise linear interpolant = 2.66086
Normalized length of polynomial approximant = 1.90124
TEST01:
Approximate data from TEST_INTERP problem # 2
Number of data points = 18
Using polynomial approximant of degree 5
L2 data approximation error = 1.76341
Normalized length of piecewise linear interpolant = 2.66086
Normalized length of polynomial approximant = 1.90124
TEST01:
Approximate data from TEST_INTERP problem # 2
Number of data points = 18
Using polynomial approximant of degree 9
L2 data approximation error = 1.30404
Normalized length of piecewise linear interpolant = 2.66086
Normalized length of polynomial approximant = 8.90486
TEST01:
Approximate data from TEST_INTERP problem # 2
Number of data points = 18
Using polynomial approximant of degree 12
L2 data approximation error = 0.894360
Normalized length of piecewise linear interpolant = 2.66086
Normalized length of polynomial approximant = 7153.58
TEST01:
Approximate data from TEST_INTERP problem # 3
Number of data points = 11
Using polynomial approximant of degree 0
L2 data approximation error = 7.87737
Normalized length of piecewise linear interpolant = 1.68472
Normalized length of polynomial approximant = 1.00000
TEST01:
Approximate data from TEST_INTERP problem # 3
Number of data points = 11
Using polynomial approximant of degree 1
L2 data approximation error = 4.46790
Normalized length of piecewise linear interpolant = 1.68472
Normalized length of polynomial approximant = 1.28026
TEST01:
Approximate data from TEST_INTERP problem # 3
Number of data points = 11
Using polynomial approximant of degree 2
L2 data approximation error = 2.59431
Normalized length of piecewise linear interpolant = 1.68472
Normalized length of polynomial approximant = 1.48631
TEST01:
Approximate data from TEST_INTERP problem # 3
Number of data points = 11
Using polynomial approximant of degree 3
L2 data approximation error = 1.74627
Normalized length of piecewise linear interpolant = 1.68472
Normalized length of polynomial approximant = 1.58943
TEST01:
Approximate data from TEST_INTERP problem # 3
Number of data points = 11
Using polynomial approximant of degree 4
L2 data approximation error = 1.68297
Normalized length of piecewise linear interpolant = 1.68472
Normalized length of polynomial approximant = 1.61226
TEST01:
Approximate data from TEST_INTERP problem # 3
Number of data points = 11
Using polynomial approximant of degree 5
L2 data approximation error = 1.66663
Normalized length of piecewise linear interpolant = 1.68472
Normalized length of polynomial approximant = 1.59507
TEST01:
Approximate data from TEST_INTERP problem # 3
Number of data points = 11
Using polynomial approximant of degree 9
L2 data approximation error = 0.328589
Normalized length of piecewise linear interpolant = 1.68472
Normalized length of polynomial approximant = 3.28924
TEST01:
Approximate data from TEST_INTERP problem # 3
Number of data points = 11
Using polynomial approximant of degree 12
L2 data approximation error = 0.324433E-09
Normalized length of piecewise linear interpolant = 1.68472
Normalized length of polynomial approximant = 3.88345
TEST01:
Approximate data from TEST_INTERP problem # 4
Number of data points = 8
Using polynomial approximant of degree 0
L2 data approximation error = 0.149984
Normalized length of piecewise linear interpolant = 3.25908
Normalized length of polynomial approximant = 1.00000
TEST01:
Approximate data from TEST_INTERP problem # 4
Number of data points = 8
Using polynomial approximant of degree 1
L2 data approximation error = 0.146011
Normalized length of piecewise linear interpolant = 3.25908
Normalized length of polynomial approximant = 1.02803
TEST01:
Approximate data from TEST_INTERP problem # 4
Number of data points = 8
Using polynomial approximant of degree 2
L2 data approximation error = 0.145980
Normalized length of piecewise linear interpolant = 3.25908
Normalized length of polynomial approximant = 1.03194
TEST01:
Approximate data from TEST_INTERP problem # 4
Number of data points = 8
Using polynomial approximant of degree 3
L2 data approximation error = 0.559589E-01
Normalized length of piecewise linear interpolant = 3.25908
Normalized length of polynomial approximant = 3.33040
TEST01:
Approximate data from TEST_INTERP problem # 4
Number of data points = 8
Using polynomial approximant of degree 4
L2 data approximation error = 0.559577E-01
Normalized length of piecewise linear interpolant = 3.25908
Normalized length of polynomial approximant = 3.32957
TEST01:
Approximate data from TEST_INTERP problem # 4
Number of data points = 8
Using polynomial approximant of degree 5
L2 data approximation error = 0.829484E-02
Normalized length of piecewise linear interpolant = 3.25908
Normalized length of polynomial approximant = 3.58478
TEST01:
Approximate data from TEST_INTERP problem # 4
Number of data points = 8
Using polynomial approximant of degree 9
L2 data approximation error = 0.177715E-13
Normalized length of piecewise linear interpolant = 3.25908
Normalized length of polynomial approximant = 4.81669
TEST01:
Approximate data from TEST_INTERP problem # 4
Number of data points = 8
Using polynomial approximant of degree 12
L2 data approximation error = 0.651592E-14
Normalized length of piecewise linear interpolant = 3.25908
Normalized length of polynomial approximant = 4.89584
TEST01:
Approximate data from TEST_INTERP problem # 5
Number of data points = 9
Using polynomial approximant of degree 0
L2 data approximation error = 0.143324
Normalized length of piecewise linear interpolant = 3.22180
Normalized length of polynomial approximant = 1.00000
TEST01:
Approximate data from TEST_INTERP problem # 5
Number of data points = 9
Using polynomial approximant of degree 1
L2 data approximation error = 0.143322
Normalized length of piecewise linear interpolant = 3.22180
Normalized length of polynomial approximant = 1.00003
TEST01:
Approximate data from TEST_INTERP problem # 5
Number of data points = 9
Using polynomial approximant of degree 2
L2 data approximation error = 0.135170
Normalized length of piecewise linear interpolant = 3.22180
Normalized length of polynomial approximant = 1.31038
TEST01:
Approximate data from TEST_INTERP problem # 5
Number of data points = 9
Using polynomial approximant of degree 3
L2 data approximation error = 0.717904E-01
Normalized length of piecewise linear interpolant = 3.22180
Normalized length of polynomial approximant = 3.05546
TEST01:
Approximate data from TEST_INTERP problem # 5
Number of data points = 9
Using polynomial approximant of degree 4
L2 data approximation error = 0.391096E-01
Normalized length of piecewise linear interpolant = 3.22180
Normalized length of polynomial approximant = 3.42544
TEST01:
Approximate data from TEST_INTERP problem # 5
Number of data points = 9
Using polynomial approximant of degree 5
L2 data approximation error = 0.358900E-01
Normalized length of piecewise linear interpolant = 3.22180
Normalized length of polynomial approximant = 3.41454
TEST01:
Approximate data from TEST_INTERP problem # 5
Number of data points = 9
Using polynomial approximant of degree 9
L2 data approximation error = 0.199908E-11
Normalized length of piecewise linear interpolant = 3.22180
Normalized length of polynomial approximant = 47.9536
TEST01:
Approximate data from TEST_INTERP problem # 5
Number of data points = 9
Using polynomial approximant of degree 12
L2 data approximation error = 0.615052E-12
Normalized length of piecewise linear interpolant = 3.22180
Normalized length of polynomial approximant = 125.388
TEST01:
Approximate data from TEST_INTERP problem # 6
Number of data points = 49
Using polynomial approximant of degree 0
L2 data approximation error = 0.530251E-01
Normalized length of piecewise linear interpolant = 2.68209
Normalized length of polynomial approximant = 1.00000
TEST01:
Approximate data from TEST_INTERP problem # 6
Number of data points = 49
Using polynomial approximant of degree 1
L2 data approximation error = 0.525121E-01
Normalized length of piecewise linear interpolant = 2.68209
Normalized length of polynomial approximant = 1.00620
TEST01:
Approximate data from TEST_INTERP problem # 6
Number of data points = 49
Using polynomial approximant of degree 2
L2 data approximation error = 0.473605E-01
Normalized length of piecewise linear interpolant = 2.68209
Normalized length of polynomial approximant = 1.24020
TEST01:
Approximate data from TEST_INTERP problem # 6
Number of data points = 49
Using polynomial approximant of degree 3
L2 data approximation error = 0.437687E-01
Normalized length of piecewise linear interpolant = 2.68209
Normalized length of polynomial approximant = 1.43902
TEST01:
Approximate data from TEST_INTERP problem # 6
Number of data points = 49
Using polynomial approximant of degree 4
L2 data approximation error = 0.424429E-01
Normalized length of piecewise linear interpolant = 2.68209
Normalized length of polynomial approximant = 1.51608
TEST01:
Approximate data from TEST_INTERP problem # 6
Number of data points = 49
Using polynomial approximant of degree 5
L2 data approximation error = 0.363054E-01
Normalized length of piecewise linear interpolant = 2.68209
Normalized length of polynomial approximant = 1.97702
TEST01:
Approximate data from TEST_INTERP problem # 6
Number of data points = 49
Using polynomial approximant of degree 9
L2 data approximation error = 0.272317E-01
Normalized length of piecewise linear interpolant = 2.68209
Normalized length of polynomial approximant = 2.51535
TEST01:
Approximate data from TEST_INTERP problem # 6
Number of data points = 49
Using polynomial approximant of degree 12
L2 data approximation error = 0.187600E-01
Normalized length of piecewise linear interpolant = 2.68209
Normalized length of polynomial approximant = 2.95947
TEST01:
Approximate data from TEST_INTERP problem # 7
Number of data points = 4
Using polynomial approximant of degree 0
L2 data approximation error = 0.250000
Normalized length of piecewise linear interpolant = 2.63961
Normalized length of polynomial approximant = 1.00000
TEST01:
Approximate data from TEST_INTERP problem # 7
Number of data points = 4
Using polynomial approximant of degree 1
L2 data approximation error = 0.250000
Normalized length of piecewise linear interpolant = 2.63961
Normalized length of polynomial approximant = 1.00000
TEST01:
Approximate data from TEST_INTERP problem # 7
Number of data points = 4
Using polynomial approximant of degree 2
L2 data approximation error = 0.590092E-15
Normalized length of piecewise linear interpolant = 2.63961
Normalized length of polynomial approximant = 3.36731
TEST01:
Approximate data from TEST_INTERP problem # 7
Number of data points = 4
Using polynomial approximant of degree 3
L2 data approximation error = 0.235514E-15
Normalized length of piecewise linear interpolant = 2.63961
Normalized length of polynomial approximant = 3.36731
TEST01:
Approximate data from TEST_INTERP problem # 7
Number of data points = 4
Using polynomial approximant of degree 4
L2 data approximation error = 0.101829E-14
Normalized length of piecewise linear interpolant = 2.63961
Normalized length of polynomial approximant = 3.58258
TEST01:
Approximate data from TEST_INTERP problem # 7
Number of data points = 4
Using polynomial approximant of degree 5
L2 data approximation error = 0.129235E-14
Normalized length of piecewise linear interpolant = 2.63961
Normalized length of polynomial approximant = 3.90825
TEST01:
Approximate data from TEST_INTERP problem # 7
Number of data points = 4
Using polynomial approximant of degree 9
L2 data approximation error = 0.534437E-14
Normalized length of piecewise linear interpolant = 2.63961
Normalized length of polynomial approximant = 6.52763
TEST01:
Approximate data from TEST_INTERP problem # 7
Number of data points = 4
Using polynomial approximant of degree 12
L2 data approximation error = 0.216022E-13
Normalized length of piecewise linear interpolant = 2.63961
Normalized length of polynomial approximant = 10.4248
TEST01:
Approximate data from TEST_INTERP problem # 8
Number of data points = 12
Using polynomial approximant of degree 0
L2 data approximation error = 0.101554
Normalized length of piecewise linear interpolant = 2.31939
Normalized length of polynomial approximant = 1.00000
TEST01:
Approximate data from TEST_INTERP problem # 8
Number of data points = 12
Using polynomial approximant of degree 1
L2 data approximation error = 0.101522
Normalized length of piecewise linear interpolant = 2.31939
Normalized length of polynomial approximant = 1.00042
TEST01:
Approximate data from TEST_INTERP problem # 8
Number of data points = 12
Using polynomial approximant of degree 2
L2 data approximation error = 0.762201E-03
Normalized length of piecewise linear interpolant = 2.31939
Normalized length of polynomial approximant = 2.31944
TEST01:
Approximate data from TEST_INTERP problem # 8
Number of data points = 12
Using polynomial approximant of degree 3
L2 data approximation error = 0.748027E-03
Normalized length of piecewise linear interpolant = 2.31939
Normalized length of polynomial approximant = 2.31959
TEST01:
Approximate data from TEST_INTERP problem # 8
Number of data points = 12
Using polynomial approximant of degree 4
L2 data approximation error = 0.731706E-03
Normalized length of piecewise linear interpolant = 2.31939
Normalized length of polynomial approximant = 2.32028
TEST01:
Approximate data from TEST_INTERP problem # 8
Number of data points = 12
Using polynomial approximant of degree 5
L2 data approximation error = 0.704364E-03
Normalized length of piecewise linear interpolant = 2.31939
Normalized length of polynomial approximant = 2.32052
TEST01:
Approximate data from TEST_INTERP problem # 8
Number of data points = 12
Using polynomial approximant of degree 9
L2 data approximation error = 0.627667E-03
Normalized length of piecewise linear interpolant = 2.31939
Normalized length of polynomial approximant = 2.32096
TEST01:
Approximate data from TEST_INTERP problem # 8
Number of data points = 12
Using polynomial approximant of degree 12
L2 data approximation error = 0.591022E-10
Normalized length of piecewise linear interpolant = 2.31939
Normalized length of polynomial approximant = 23167.0
VANDERMONDE_APPROX_1D_TEST:
Normal end of execution.
11 September 2021 2:08:11.084 PM