Sat Apr 18 12:26:44 2015
QUADRULE_TEST
Python version:
Test the QUADRULE library.
BASHFORTH_SET_TEST
BASHFORTH_SET sets the abscissas and weights
for an Adams-Bashforth quadrature rule.
Order W X
1
1 -0
2
1.5 -0
-0.5 -1
3
1.91667 -0
-1.33333 -1
0.416667 -2
4
2.29167 -0
-2.45833 -1
1.54167 -2
-0.375 -3
5
2.64028 -0
-3.85278 -1
3.63333 -2
-1.76944 -3
0.348611 -4
6
2.97014 -0
-5.50208 -1
6.93194 -2
-5.06806 -3
1.99792 -4
-0.329861 -5
7
3.28573 -0
-7.39563 -1
11.6658 -2
-11.3799 -3
6.7318 -4
-2.22341 -5
0.315592 -6
8
3.58996 -0
-9.52521 -1
18.0545 -2
-22.0278 -3
17.3797 -4
-8.61213 -5
2.44516 -6
-0.304225 -7
9
3.88482 -0
-11.8842 -1
26.3108 -2
-38.5404 -3
38.0204 -4
-25.1247 -5
10.7015 -6
-2.66317 -7
0.294868 -8
10
4.1718 -0
-14.4669 -1
36.642 -2
-62.6463 -3
74.1793 -4
-61.2836 -5
34.8074 -6
-12.9943 -7
2.87765 -8
-0.286975 -9
BASHFORTH_SET_TEST:
Normal end of execution.
CHEBYSHEV1_COMPUTE_TEST
CHEBYSHEV1_COMPUTE computes
a Chebyshev Type 1 quadrature rule over [-1,1].
Index X W
0 6.123233995736766e-17 3.141592653589793
0 -0.7071067811865475 1.570796326794897
1 0.7071067811865476 1.570796326794897
0 -0.8660254037844387 1.047197551196598
1 6.123233995736766e-17 1.047197551196598
2 0.8660254037844387 1.047197551196598
0 -0.9238795325112867 0.7853981633974483
1 -0.3826834323650897 0.7853981633974483
2 0.3826834323650898 0.7853981633974483
3 0.9238795325112867 0.7853981633974483
0 -0.9510565162951535 0.6283185307179586
1 -0.587785252292473 0.6283185307179586
2 6.123233995736766e-17 0.6283185307179586
3 0.5877852522924731 0.6283185307179586
4 0.9510565162951535 0.6283185307179586
0 -0.9659258262890682 0.5235987755982988
1 -0.7071067811865475 0.5235987755982988
2 -0.2588190451025206 0.5235987755982988
3 0.2588190451025207 0.5235987755982988
4 0.7071067811865476 0.5235987755982988
5 0.9659258262890683 0.5235987755982988
0 -0.9749279121818237 0.4487989505128276
1 -0.7818314824680295 0.4487989505128276
2 -0.4338837391175581 0.4487989505128276
3 6.123233995736766e-17 0.4487989505128276
4 0.4338837391175582 0.4487989505128276
5 0.7818314824680298 0.4487989505128276
6 0.9749279121818236 0.4487989505128276
0 -0.9807852804032304 0.3926990816987241
1 -0.8314696123025453 0.3926990816987241
2 -0.555570233019602 0.3926990816987241
3 -0.1950903220161282 0.3926990816987241
4 0.1950903220161283 0.3926990816987241
5 0.5555702330196023 0.3926990816987241
6 0.8314696123025452 0.3926990816987241
7 0.9807852804032304 0.3926990816987241
0 -0.984807753012208 0.3490658503988659
1 -0.8660254037844385 0.3490658503988659
2 -0.6427876096865394 0.3490658503988659
3 -0.3420201433256685 0.3490658503988659
4 6.123233995736766e-17 0.3490658503988659
5 0.3420201433256688 0.3490658503988659
6 0.6427876096865394 0.3490658503988659
7 0.8660254037844387 0.3490658503988659
8 0.984807753012208 0.3490658503988659
0 -0.9876883405951377 0.3141592653589793
1 -0.8910065241883678 0.3141592653589793
2 -0.7071067811865475 0.3141592653589793
3 -0.4539904997395467 0.3141592653589793
4 -0.1564344650402306 0.3141592653589793
5 0.1564344650402309 0.3141592653589793
6 0.4539904997395468 0.3141592653589793
7 0.7071067811865476 0.3141592653589793
8 0.8910065241883679 0.3141592653589793
9 0.9876883405951378 0.3141592653589793
CHEBYSHEV1_COMPUTE_TEST:
Normal end of execution.
CHEBYSHEV3_COMPUTE_TEST
CHEBYSHEV3_COMPUTE computes
a Chebyshev Type 3 quadrature rule over [-1,1].
Index X W
0 0 3.141592653589793
0 1 1.570796326794897
1 -1 1.570796326794897
0 1 0.7853981633974483
1 6.123233995736766e-17 1.570796326794897
2 -1 0.7853981633974483
0 1 0.5235987755982988
1 0.5000000000000001 1.047197551196598
2 -0.4999999999999998 1.047197551196598
3 -1 0.5235987755982988
0 1 0.3926990816987241
1 0.7071067811865476 0.7853981633974483
2 6.123233995736766e-17 0.7853981633974483
3 -0.7071067811865475 0.7853981633974483
4 -1 0.3926990816987241
0 1 0.3141592653589793
1 0.8090169943749475 0.6283185307179586
2 0.3090169943749475 0.6283185307179586
3 -0.3090169943749473 0.6283185307179586
4 -0.8090169943749473 0.6283185307179586
5 -1 0.3141592653589793
0 1 0.2617993877991494
1 0.8660254037844387 0.5235987755982988
2 0.5000000000000001 0.5235987755982988
3 6.123233995736766e-17 0.5235987755982988
4 -0.4999999999999998 0.5235987755982988
5 -0.8660254037844387 0.5235987755982988
6 -1 0.2617993877991494
0 1 0.2243994752564138
1 0.9009688679024191 0.4487989505128276
2 0.6234898018587336 0.4487989505128276
3 0.2225209339563144 0.4487989505128276
4 -0.2225209339563143 0.4487989505128276
5 -0.6234898018587335 0.4487989505128276
6 -0.900968867902419 0.4487989505128276
7 -1 0.2243994752564138
0 1 0.1963495408493621
1 0.9238795325112867 0.3926990816987241
2 0.7071067811865476 0.3926990816987241
3 0.3826834323650898 0.3926990816987241
4 6.123233995736766e-17 0.3926990816987241
5 -0.3826834323650897 0.3926990816987241
6 -0.7071067811865475 0.3926990816987241
7 -0.9238795325112867 0.3926990816987241
8 -1 0.1963495408493621
0 1 0.1745329251994329
1 0.9396926207859084 0.3490658503988659
2 0.766044443118978 0.3490658503988659
3 0.5000000000000001 0.3490658503988659
4 0.1736481776669304 0.3490658503988659
5 -0.1736481776669303 0.3490658503988659
6 -0.4999999999999998 0.3490658503988659
7 -0.7660444431189779 0.3490658503988659
8 -0.9396926207859083 0.3490658503988659
9 -1 0.1745329251994329
CHEBYSHEV3_COMPUTE_TEST:
Normal end of execution.
CLENSHAW_CURTIS_COMPUTE_TEST
CLENSHAW_CURTIS_COMPUTE computes
a Clenshaw-Curtis quadrature rule over [-1,1].
Index X W
0 0 2
0 -1 1
1 1 1
0 -1 0.3333333333333334
1 6.123233995736766e-17 1.333333333333333
2 1 0.3333333333333334
0 -1 0.1111111111111111
1 -0.4999999999999998 0.8888888888888892
2 0.5000000000000001 0.8888888888888888
3 1 0.1111111111111111
0 -1 0.06666666666666668
1 -0.7071067811865475 0.5333333333333334
2 6.123233995736766e-17 0.7999999999999999
3 0.7071067811865476 0.5333333333333333
4 1 0.06666666666666668
0 -1 0.04000000000000001
1 -0.8090169943749473 0.3607430412000113
2 -0.3090169943749473 0.5992569587999887
3 0.3090169943749475 0.5992569587999889
4 0.8090169943749475 0.3607430412000112
5 1 0.04000000000000001
0 -1 0.02857142857142858
1 -0.8660254037844387 0.2539682539682539
2 -0.4999999999999998 0.4571428571428573
3 6.123233995736766e-17 0.5206349206349206
4 0.5000000000000001 0.4571428571428571
5 0.8660254037844387 0.2539682539682539
6 1 0.02857142857142858
0 -1 0.02040816326530613
1 -0.900968867902419 0.1901410072182084
2 -0.6234898018587335 0.3522424237181591
3 -0.2225209339563143 0.4372084057983264
4 0.2225209339563144 0.4372084057983264
5 0.6234898018587336 0.3522424237181591
6 0.9009688679024191 0.1901410072182084
7 1 0.02040816326530613
0 -1 0.01587301587301588
1 -0.9238795325112867 0.1462186492160182
2 -0.7071067811865475 0.2793650793650794
3 -0.3826834323650897 0.3617178587204898
4 6.123233995736766e-17 0.3936507936507936
5 0.3826834323650898 0.3617178587204897
6 0.7071067811865476 0.2793650793650794
7 0.9238795325112867 0.1462186492160181
8 1 0.01587301587301588
0 -1 0.01234567901234569
1 -0.9396926207859083 0.1165674565720372
2 -0.7660444431189779 0.2252843233381044
3 -0.4999999999999998 0.3019400352733687
4 -0.1736481776669303 0.3438625058041442
5 0.1736481776669304 0.3438625058041442
6 0.5000000000000001 0.3019400352733685
7 0.766044443118978 0.2252843233381044
8 0.9396926207859084 0.1165674565720371
9 1 0.01234567901234569
CLENSHAW_CURTIS_COMPUTE_TEST:
Normal end of execution.
CLENSHAW_CURTIS_SET_TEST
CLENSHAW_CURTIS_SET sets up a Clenshaw Curtis
quadrature rule over [-1,1].
Estimate the integral of sqrt(abs(x)) over [-1,+1].
N Estimate Error
1 0 1.333333e+00
2 2 6.666667e-01
3 0.6666666666666666 6.666667e-01
4 1.47930094433164 1.459676e-01
5 1.030289509603962 3.030438e-01
6 1.395188802266437 6.185547e-02
7 1.176328668057338 1.570047e-01
8 1.370529534325666 3.719620e-02
9 1.230194560888044 1.031388e-01
10 1.358632996768151 2.529966e-02
CLENSHAW_CURTIS_SET_TEST:
Normal end of execution.
FEJER1_COMPUTE_TEST
FEJER1_COMPUTE computes the abscissas and weights
of a Fejer type 1 quadrature rule.
Order W X
1
2 6.12323e-17
2
1 -0.707107
1 0.707107
3
0.444444 -0.866025
1.11111 6.12323e-17
0.444444 0.866025
4
0.264298 -0.92388
0.735702 -0.382683
0.735702 0.382683
0.264298 0.92388
5
0.167781 -0.951057
0.525552 -0.587785
0.613333 6.12323e-17
0.525552 0.587785
0.167781 0.951057
6
0.118661 -0.965926
0.377778 -0.707107
0.503561 -0.258819
0.503561 0.258819
0.377778 0.707107
0.118661 0.965926
7
0.0867162 -0.974928
0.287831 -0.781831
0.398242 -0.433884
0.454422 6.12323e-17
0.398242 0.433884
0.287831 0.781831
0.0867162 0.974928
8
0.0669829 -0.980785
0.222988 -0.83147
0.324153 -0.55557
0.385877 -0.19509
0.385877 0.19509
0.324153 0.55557
0.222988 0.83147
0.0669829 0.980785
9
0.0527366 -0.984808
0.179189 -0.866025
0.264037 -0.642788
0.330845 -0.34202
0.346384 6.12323e-17
0.330845 0.34202
0.264037 0.642788
0.179189 0.866025
0.0527366 0.984808
10
0.0429391 -0.987688
0.145875 -0.891007
0.220317 -0.707107
0.280879 -0.45399
0.309989 -0.156434
0.309989 0.156434
0.280879 0.45399
0.220317 0.707107
0.145875 0.891007
0.0429391 0.987688
FEJER1_COMPUTE_TEST:
Normal end of execution.
FEJER1_SET_TEST
FEJER1_SET sets the abscissas and weights
of a Fejer type 1 quadrature rule.
Order W X
1
2 0
2
1 -0.707107
1 0.707107
3
0.444444 -0.866025
1.11111 0
0.444444 0.866025
4
0.264298 -0.92388
0.735702 -0.382683
0.735702 0.382683
0.264298 0.92388
5
0.167781 -0.951057
0.525552 -0.587785
0.613333 0
0.525552 0.587785
0.167781 0.951057
6
0.118661 -0.965926
0.377778 -0.707107
0.503561 -0.258819
0.503561 0.258819
0.377778 0.707107
0.118661 0.965926
7
0.0867162 -0.974928
0.287831 -0.781831
0.398242 -0.433884
0.454422 0
0.398242 0.433884
0.287831 0.781831
0.0867162 0.974928
8
0.0669829 -0.980785
0.222988 -0.83147
0.324153 -0.55557
0.385877 -0.19509
0.385877 0.19509
0.324153 0.55557
0.222988 0.83147
0.0669829 0.980785
9
0.0527366 -0.984808
0.179189 -0.866025
0.264037 -0.642788
0.330845 -0.34202
0.346384 0
0.330845 0.34202
0.264037 0.642788
0.179189 0.866025
0.0527366 0.984808
10
0.0429391 -0.987688
0.145875 -0.891007
0.220317 -0.707107
0.280879 -0.45399
0.309989 -0.156434
0.309989 0.156434
0.280879 0.45399
0.220317 0.707107
0.145875 0.891007
0.0429391 0.987688
FEJER1_SET_TEST:
Normal end of execution.
FEJER2_COMPUTE_TEST
FEJER2_COMPUTE computes the abscissas and weights
of a Fejer type 2 quadrature rule.
Order W X
1
2 0
2
1 -0.5
1 0.5
3
0.666667 -0.707107
0.666667 6.12323e-17
0.666667 0.707107
4
0.425464 -0.809017
0.574536 -0.309017
0.574536 0.309017
0.425464 0.809017
5
0.311111 -0.866025
0.4 -0.5
0.577778 6.12323e-17
0.4 0.5
0.311111 0.866025
6
0.226915 -0.900969
0.326794 -0.62349
0.446291 -0.222521
0.446291 0.222521
0.326794 0.62349
0.226915 0.900969
7
0.177965 -0.92388
0.247619 -0.707107
0.393464 -0.382683
0.361905 6.12323e-17
0.393464 0.382683
0.247619 0.707107
0.177965 0.92388
8
0.13977 -0.939693
0.20637 -0.766044
0.314286 -0.5
0.339575 -0.173648
0.339575 0.173648
0.314286 0.5
0.20637 0.766044
0.13977 0.939693
9
0.114781 -0.951057
0.165433 -0.809017
0.27379 -0.587785
0.279011 -0.309017
0.333968 6.12323e-17
0.279011 0.309017
0.27379 0.587785
0.165433 0.809017
0.114781 0.951057
10
0.0944195 -0.959493
0.141135 -0.841254
0.226387 -0.654861
0.253051 -0.415415
0.285007 -0.142315
0.285007 0.142315
0.253051 0.415415
0.226387 0.654861
0.141135 0.841254
0.0944195 0.959493
FEJER2_COMPUTE_TEST:
Normal end of execution.
FEJER2_SET_TEST
FEJER2_SET sets the abscissas and weights
of a Fejer type 2 quadrature rule.
Order W X
1
2 0
2
1 -0.5
1 0.5
3
0.666667 -0.707107
0.666667 0
0.666667 0.707107
4
0.425464 -0.809017
0.574536 -0.309017
0.574536 0.309017
0.425464 0.809017
5
0.311111 -0.866025
0.4 -0.5
0.577778 0
0.4 0.5
0.311111 0.866025
6
0.226915 -0.900969
0.326794 -0.62349
0.446291 -0.222521
0.446291 0.222521
0.326794 0.62349
0.226915 0.900969
7
0.177965 -0.92388
0.247619 -0.707107
0.393464 -0.382683
0.361905 0
0.393464 0.382683
0.247619 0.707107
0.177965 0.92388
8
0.13977 -0.939693
0.20637 -0.766044
0.314286 -0.5
0.339575 -0.173648
0.339575 0.173648
0.314286 0.5
0.20637 0.766044
0.13977 0.939693
9
0.114781 -0.951057
0.165433 -0.809017
0.27379 -0.587785
0.279011 -0.309017
0.333968 0
0.279011 0.309017
0.27379 0.587785
0.165433 0.809017
0.114781 0.951057
10
0.0944195 -0.959493
0.141135 -0.841254
0.226387 -0.654861
0.253051 -0.415415
0.285007 -0.142315
0.285007 0.142315
0.253051 0.415415
0.226387 0.654861
0.141135 0.841254
0.0944195 0.959493
FEJER2_SET_TEST:
Normal end of execution.
LEGENDRE_SET_TEST01:
LEGENDRE_SET returns points and weights of a Gauss-Legendre quadrature rule.
Gauss-Legendre rule of order 3:
Index X W
0 -0.7745966692414834 0.5555555555555556
1 0.0000000000000000 0.8888888888888888
2 0.7745966692414834 0.5555555555555556
Gauss-Legendre rule of order 6:
Index X W
0 -0.9324695142031521 0.1713244923791704
1 -0.6612093864662645 0.3607615730481386
2 -0.2386191860831969 0.4679139345726910
3 0.2386191860831969 0.4679139345726910
4 0.6612093864662645 0.3607615730481386
5 0.9324695142031521 0.1713244923791704
Gauss-Legendre rule of order 11:
Index X W
0 -0.9782286581460570 0.0556685671161737
1 -0.8870625997680953 0.1255803694649046
2 -0.7301520055740494 0.1862902109277343
3 -0.5190961292068118 0.2331937645919905
4 -0.2695431559523450 0.2628045445102467
5 0.0000000000000000 0.2729250867779006
6 0.2695431559523450 0.2628045445102467
7 0.5190961292068118 0.2331937645919905
8 0.7301520055740494 0.1862902109277343
9 0.8870625997680953 0.1255803694649046
10 0.9782286581460570 0.0556685671161737
LEGENDRE_SET_TEST01:
Normal end of execution.
MOULTON_SET_TEST
MOULTON_SET sets the abscissas and weights
for an Adams-Moulton quadrature rule.
Order W X
1
1 1
2
0.5 1
0.5 0
3
0.416667 1
0.666667 0
-0.0833333 -1
4
0.375 1
0.791667 0
-0.208333 -1
0.0416667 -2
5
0.348611 1
0.897222 0
-0.366667 -1
0.147222 -2
-0.0263889 -3
6
0.329861 1
0.990972 0
-0.554167 -1
0.334722 -2
-0.120139 -3
0.01875 -4
7
0.315592 1
1.07659 0
-0.768204 -1
0.620106 -2
-0.334177 -3
0.104365 -4
-0.0142692 -5
8
0.304225 1
1.15616 0
-1.00692 -1
1.01796 -2
-0.732035 -3
0.34308 -4
-0.0938409 -5
0.0113674 -6
9
0.294868 1
1.23101 0
-1.2689 -1
1.54193 -2
-1.38699 -3
0.867046 -4
-0.355824 -5
0.0862197 -6
-0.00935654 -7
10
0.286975 1
1.30204 0
-1.55303 -1
2.20491 -2
-2.38145 -3
1.86151 -4
-1.0188 -5
0.370352 -6
-0.0803895 -7
0.00789255 -8
MOULTON_SET_TEST:
Normal end of execution.
TIMESTAMP_TEST:
Python version:
TIMESTAMP prints a timestamp of the current date and time.
Sat Apr 18 12:26:44 2015
TIMESTAMP_TEST:
Normal end of execution.
QUADRULE_TEST:
Normal end of execution.
Sat Apr 18 12:26:44 2015