octave-nkf: src/DLD-FUNCTIONS/besselj.cc comparison

comparison src/DLD-FUNCTIONS/besselj.cc @ 14426:e28a1723d5a2

besselj: Style fixes on new tests due to Robert T. Short

author	Jordi Gutiérrez Hermoso <jordigh@octave.org>
date	Fri, 02 Mar 2012 14:14:43 -0500
parents	6646031e2450
children	ab4676288414

comparison

equal deleted inserted replaced

-:6646031e2450
+:e28a1723d5a2
 %!assert(besselk(-alpha,x,1), kx*exp(x), 100*eps)
 %!assert(besselh(-alpha,1,x,1), -I*(jx + I*yx)*exp(-I*x), 100*eps)
 %!assert(besselh(-alpha,2,x,1), I*(jx - I*yx)*exp(I*x), 100*eps)
-%  Tests contributed by Robert T. Short.
+Tests contributed by Robert T. Short.
-%  Tests are based on the properties and tables in A&S:
+Tests are based on the properties and tables in A&S:
-%   Abramowitz and Stegun, "Handbook of Mathematical Functions",
+Abramowitz and Stegun, "Handbook of Mathematical Functions",
-%   1972.
+1972.
-%  For regular Bessel functions, there are 3 tests.  These compare
+For regular Bessel functions, there are 3 tests. These compare octave
-%  octave results against Tables 9.1, 9.2, and 9.4 in A&S.  Tables
+results against Tables 9.1, 9.2, and 9.4 in A&S. Tables 9.1 and 9.2
-%  9.1 and 9.2 are good to only a few decimal places, so any
+are good to only a few decimal places, so any failures should be
-%  failures should be considered a broken implementation.  Table
+considered a broken implementation. Table 9.4 is an extended table
-%  9.4 is an extended table for larger orders and arguments.  There
+for larger orders and arguments. There are some differences between
-%  are some differences between octave and Table 9.4, mostly in
+Octave and Table 9.4, mostly in the last decimal place but in a very
-%  the last decimal place but in a very few instances the errors
+few instances the errors are in the last two places. The comparison
-%  are in the last two places.  The comparison tolerance has been
+tolerance has been changed to reflect this.
-%  changed to reflect this.
+Similarly for modifed Bessel functions, there are 3 tests. These
-%  Similarly for modifed Bessel functions, there are 3 tests.
+compare octave results against Tables 9.8, 9.9, and 9.11 in A&S.
-%  These compare octave results against Tables 9.8, 9.9, and
+Tables 9.8 and 9.9 are good to only a few decimal places, so any
-%  9.11 in A&S.  Tables 9.8 and 9.9 are good to only a few
+failures should be considered a broken implementation. Table 9.11 is
-%  decimal places, so any failures should be considered a broken
+an extended table for larger orders and arguments. There are some
-%  implementation.  Table 9.11 is an extended table for larger
+differences between octave and Table 9.11, mostly in the last decimal
-%  orders and arguments.  There are some differences between
+place but in a very few instances the errors are in the last two
-%  octave and Table 9.11, mostly in the last decimal place but
+places. The comparison tolerance has been changed to reflect this.
-%  in a very few instances the errors are in the last two places.
-%  The comparison tolerance has been changed to reflect this.
+For spherical Bessel functions, there are also three tests, comparing
+octave results to Tables 10.1, 10.2, and 10.4 in A&S. Very similar
-%  For spherical Bessel functions, there are also three tests,
+comments may be made here as in the previous lines. At this time,
-%  comparing octave results to Tables 10.1, 10.2, and 10.4 in
+modified spherical Bessel function tests are not included.
-%  A&s.  Very similar comments may be made here as in the previous
-%  lines.  At this time, modified spherical Bessel function
-%  tests are not included - maybe someday when I have some time...
 % Table 9.1 - J and Y for integer orders 0, 1, 2.
 % Compare against excerpts of Table 9.1, Abramowitz and Stegun.
 %!test
 %! n = 0:2;
 %! z = (0:2.5:17.5)';
 %!
 %! Jt = [[ 1.000000000000000,  0.0000000000,  0.0000000000];
 %!       [-0.048383776468198,  0.4970941025,  0.4460590584];
 %!       [-0.177596771314338, -0.3275791376,  0.0465651163];
 %!       [ 0.266339657880378,  0.1352484276, -0.2302734105];
 %!       [-0.245935764451348,  0.0434727462,  0.2546303137];
 %!       [ 0.146884054700421, -0.1654838046, -0.1733614634];
 %!       [-0.014224472826781,  0.2051040386,  0.0415716780];
 %!       [-0.103110398228686, -0.1634199694,  0.0844338303]];
 %!
 %! Yt = [[-Inf,          -Inf,         -Inf         ];
 %!       [ 0.4980703596,  0.1459181380, -0.38133585 ];
 %!       [-0.3085176252,  0.1478631434,  0.36766288 ];
 %!       [ 0.1173132861, -0.2591285105, -0.18641422 ];
 %!       [ 0.0556711673,  0.2490154242, -0.00586808 ];
 %!       [-0.1712143068, -0.1538382565,  0.14660019 ];
 %!       [ 0.2054642960,  0.0210736280, -0.20265448 ];
 %!       [-0.1604111925,  0.0985727987,  0.17167666 ]];
 %!
 %! J = besselj(n,z);
 %! Y = bessely(n,z);
 %! assert(Jt(:,1), J(:,1), 0.5e-10);
 %! assert(Yt(:,1), Y(:,1), 0.5e-10);
 %! assert(Jt(:,2:3), J(:,2:3), 0.5e-10);
-% Table 9.2 - J and Y for integer orders 3-9.
+Table 9.2 - J and Y for integer orders 3-9.
 %!test
 %!  n = (3:9);
 %!  z = (0:2:20).';
 %!
 %!  Jt = [[ 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00];
 %!        [ 1.2894e-01, 3.3996e-02, 7.0396e-03, 1.2024e-03, 1.7494e-04, 2.2180e-05, 2.4923e-06];
 %!        [ 4.3017e-01, 2.8113e-01, 1.3209e-01, 4.9088e-02, 1.5176e-02, 4.0287e-03, 9.3860e-04];
 %!        [ 1.1477e-01, 3.5764e-01, 3.6209e-01, 2.4584e-01, 1.2959e-01, 5.6532e-02, 2.1165e-02];
 %!        [-2.9113e-01,-1.0536e-01, 1.8577e-01, 3.3758e-01, 3.2059e-01, 2.2345e-01, 1.2632e-01];
 %!        [ 1.9514e-01, 1.8250e-01,-7.3471e-02,-2.4372e-01,-1.7025e-01, 4.5095e-02, 2.3038e-01];
 %!        [-1.7681e-01, 7.6244e-02, 2.2038e-01, 8.1168e-02,-1.5080e-01,-2.3197e-01,-1.1431e-01];
 %!        [-4.3847e-02,-2.0264e-01,-5.7473e-02, 1.6672e-01, 1.8251e-01,-7.0211e-03,-1.8953e-01];
 %!        [ 1.8632e-01, 6.9640e-02,-1.5537e-01,-1.5596e-01, 5.1399e-02, 1.9593e-01, 1.2276e-01];
 %!        [-9.8901e-02, 1.3067e-01, 1.5117e-01,-5.5086e-02,-1.8422e-01,-7.3869e-02, 1.2513e-01]];
 %!
 %!  Yt = [[       -Inf,       -Inf,       -Inf,       -Inf,       -Inf,       -Inf,       -Inf];
 %!        [-1.1278e+00,-2.7659e+00,-9.9360e+00,-4.6914e+01,-2.7155e+02,-1.8539e+03,-1.4560e+04];
 %!        [-1.8202e-01,-4.8894e-01,-7.9585e-01,-1.5007e+00,-3.7062e+00,-1.1471e+01,-4.2178e+01];
 %!        [ 3.2825e-01, 9.8391e-02,-1.9706e-01,-4.2683e-01,-6.5659e-01,-1.1052e+00,-2.2907e+00];
 %!        [ 2.6542e-02, 2.8294e-01, 2.5640e-01, 3.7558e-02,-2.0006e-01,-3.8767e-01,-5.7528e-01];
 %!        [ 1.2901e-01,-1.5122e-01,-2.2982e-01,-4.0297e-02, 1.8952e-01, 2.6140e-01, 1.5902e-01];
 %!        [ 1.2350e-01, 2.0393e-01,-6.9717e-03,-2.0891e-01,-1.7209e-01, 3.6816e-02, 2.1417e-01];
 %!        [-1.9637e-01,-7.3222e-05, 1.9633e-01, 1.2278e-01,-1.0425e-01,-2.1399e-01,-1.0975e-01];
 %!        [ 3.3724e-02,-1.7722e-01,-1.1249e-01, 1.1472e-01, 1.8897e-01, 3.2253e-02,-1.6030e-01];
 %!        [ 1.4967e-01, 1.2409e-01,-1.0004e-01,-1.7411e-01,-4.4312e-03, 1.7101e-01, 1.4124e-01]];
 %!
 %!  n = (3:9);
 %!  z = (0:2:20).';
 %!  J=besselj(n,z);
 %!  Y=bessely(n,z);
 %!
-%!  assert(max(abs(J(1,:)))==0);
+%!  assert(J(1,:), zeros (1, columns (J)));
-%!  assert(max(max(J(2:end,:)./Jt(2:end,:)-1))<5e-5);
+%!  assert(J(2:end,:), Jt(2:end,:), -5e-5);
-%!  assert(Yt(1,:)==Y(1,:));
+%!  assert(Yt(1,:), Y(1,:));
-%!  assert(max(max(Y(2:end,:)./Yt(2:end,:)-1))<5e-5);
+%!  assert(Y(2:end,:), Yt(2:end,:), -5e-5);
-% Table 9.4 - J and Y for various integer orders and arguments.
+Table 9.4 - J and Y for various integer orders and arguments.
-%!test
+%!xtest
 %! Jt = [[7.651976866e-01,   2.238907791e-01,  -1.775967713e-01,  -2.459357645e-01,  5.581232767e-02,  1.998585030e-02];
 %!       [2.497577302e-04,   7.039629756e-03,   2.611405461e-01,  -2.340615282e-01, -8.140024770e-02, -7.419573696e-02];
 %!       [2.630615124e-10,   2.515386283e-07,   1.467802647e-03,   2.074861066e-01, -1.138478491e-01, -5.473217694e-02];
 %!       [2.297531532e-17,   7.183016356e-13,   4.796743278e-07,   4.507973144e-03, -1.082255990e-01,  1.519812122e-02];
 %!       [3.873503009e-25,   3.918972805e-19,   2.770330052e-11,   1.151336925e-05, -1.167043528e-01,  6.221745850e-02];
 %!       [3.482869794e-42,   3.650256266e-33,   2.671177278e-21,   1.551096078e-12,  4.843425725e-02,  8.146012958e-02];
 %!       [1.107915851e-60,   1.196077458e-48,   8.702241617e-33,   6.030895312e-21, -1.381762812e-01,  7.270175482e-02];
 %!       [2.906004948e-80,   3.224095839e-65,   2.294247616e-45,   1.784513608e-30,  1.214090219e-01, -3.869833973e-02];
 %!       [8.431828790e-189,  1.060953112e-158,  6.267789396e-119,  6.597316064e-89,  1.115927368e-21,  9.636667330e-02]];
 %!
 %! Yt = [[8.825696420e-02,   5.103756726e-01,  -3.085176252e-01,   5.567116730e-02, -9.806499547e-02, -7.724431337e-02]
 %!       [2.604058666e+02,  -9.935989128e+00,  -4.536948225e-01,   1.354030477e-01, -7.854841391e-02, -2.948019628e-02]
 %!       [1.216180143e+08,  -1.291845422e+05,  -2.512911010e+01,  -3.598141522e-01,  5.723897182e-03,  5.833157424e-02]
 %!       [9.256973276e+14,  -2.981023646e+10,  -4.694049564e+04,  -6.364745877e+00,  4.041280205e-02,  7.879068695e-02]
 %!       [4.113970315e+22,  -4.081651389e+16,  -5.933965297e+08,  -1.597483848e+03,  1.644263395e-02,  5.124797308e-02]
 %!
 %! n = [(0:5:20).';30;40;50;100];
 %! z = [1,2,5,10,50,100];
 %! J = besselj(n.',z.').';
 %! Y = bessely(n.',z.').';
-%!  assert(max(max(J./Jt-1))<1e-9);
+%!  assert(J, Jt, -1e-9);
-%!  assert(max(max(Y./Yt-1))<1e-9);
+%!  assert(Y, Yt, -1e-9);
-% Table 9.8 - I and K for integer orders 0, 1, 2.
+Table 9.8 - I and K for integer orders 0, 1, 2.
-%!test
+%!xtest
 %! n  = 0:2;
 %! z1 = [0.1;2.5;5.0];
 %! z2 = [7.5;10.0;15.0;20.0];
 %! rtbl = [ [ 0.9071009258   0.0452984468   0.1251041992   2.6823261023  10.890182683    1.995039646  ];
 %!          [ 0.2700464416   0.2065846495   0.2042345837   0.7595486903   0.9001744239   0.759126289  ];
 %!          [ 0.1835408126   0.1639722669   0.7002245988   0.5478075643   0.6002738588   0.132723593  ];
 %!          [ 0.1483158301   0.1380412115   0.111504840    0.4505236991   0.4796689336   0.57843541   ];
 %!          [ 0.1278333372   0.1212626814   0.103580801    0.3916319344   0.4107665704   0.47378525   ];
 %!          [ 0.1038995314   0.1003741751   0.090516308    0.3210023535   0.3315348950   0.36520701   ];
 %!          [ 0.0897803119   0.0875062222   0.081029690    0.2785448768   0.2854254970   0.30708743   ]];
 %!
 %! tbl = [besseli(n,z1,1), besselk(n,z1)];
 %! tbl(:,3) = tbl(:,3).*(exp(z1).*z1.^(-2));
 %! tbl(:,6) = tbl(:,6).*(exp(-z1).*z1.^(2));
 %! tbl = [tbl;[besseli(n,z2,1),besselk(n,z2,1)]];
 %!
-%! assert(max(max((tbl-rtbl)./rtbl)<1e-8));
+%! assert(tbl, rtbl, -1e-8);
-% Table 9.9 - I and K for orders 3-9.
+Table 9.9 - I and K for orders 3-9.
 %!test
 %! It = [[  0.0000e+00  0.0000e+00  0.0000e+00  0.0000e+00  0.0000e+00  0.0000e+00  0.0000e+00];
 %!       [  2.8791e-02  6.8654e-03  1.3298e-03  2.1656e-04  3.0402e-05  3.7487e-06  4.1199e-07];
 %!       [  6.1124e-02  2.5940e-02  9.2443e-03  2.8291e-03  7.5698e-04  1.7968e-04  3.8284e-05];
 %!       [  7.4736e-02  4.1238e-02  1.9752e-02  8.3181e-03  3.1156e-03  1.0484e-03  3.1978e-04];
 %!       [  7.8848e-02  5.8425e-02  3.9898e-02  2.5176e-02  1.4722e-02  8.0010e-03  4.0537e-03];
 %!       [  7.7183e-02  5.9723e-02  4.3056e-02  2.8969e-02  1.8225e-02  1.0744e-02  5.9469e-03];
 %!       [  7.5256e-02  6.0155e-02  4.5179e-02  3.1918e-02  2.1240e-02  1.3333e-02  7.9071e-03];
 %!       [  7.3263e-02  6.0059e-02  4.6571e-02  3.4186e-02  2.3780e-02  1.5691e-02  9.8324e-03];
 %!       [  7.1300e-02  5.9640e-02  4.7444e-02  3.5917e-02  2.5894e-02  1.7792e-02  1.1661e-02]];
 %!
 %! Kt = [
 %!      [         Inf         Inf         Inf         Inf         Inf         Inf         Inf];
 %!      [  4.7836e+00  1.6226e+01  6.9687e+01  3.6466e+02  2.2576e+03  1.6168e+04  1.3160e+05];
 %!      [  1.6317e+00  3.3976e+00  8.4268e+00  2.4465e+01  8.1821e+01  3.1084e+02  1.3252e+03];
 %!      [  9.9723e-01  1.6798e+00  3.2370e+00  7.0748e+00  1.7387e+01  4.7644e+01  1.4444e+02];
 %!      [  5.1294e-01  6.7680e-01  9.6415e-01  1.4803e+00  2.4444e+00  4.3321e+00  8.2205e+00];
 %!      [  4.5266e-01  5.7519e-01  7.8133e-01  1.1333e+00  1.7527e+00  2.8860e+00  5.0510e+00];
 %!      [  4.0829e-01  5.0414e-01  6.6036e-01  9.1686e-01  1.3480e+00  2.0964e+00  3.4444e+00];
 %!      [  3.7411e-01  4.5162e-01  5.7483e-01  7.7097e-01  1.0888e+00  1.6178e+00  2.5269e+00];
 %!      [  3.4684e-01  4.1114e-01  5.1130e-01  6.6679e-01  9.1137e-01  1.3048e+00  1.9552e+00]];
 %!
 %! n = (3:9);
 %! z = (0:2:20).';
 %! I=besseli(n,z,1);
 %! K=besselk(n,z,1);
 %!
-%! assert(max(abs(I(1,:)))==0);
+%! assert(abs (I(1,:)), zeros(1, columns(I)));
-%! assert(max(max(I(2:end,:)./It(2:end,:)-1))<5e-5);
+%! assert(I(2:end,:), It(2:end,:), -5e-5);
-%! assert(Kt(1,:)==K(1,:));
+%! assert(Kt(1,:), K(1,:));
-%! assert(max(max(K(2:end,:)./Kt(2:end,:)-1))<5e-5);
+%! assert(K(2:end,:), Kt(2:end,:), -5e-5);
-% Table 9.11 - I and K for various integer orders and arguments.
+Table 9.11 - I and K for various integer orders and arguments.
 %!test
 %! It = [[   1.266065878e+00    2.279585302e+00    2.723987182e+01    2.815716628e+03     2.93255378e+20     1.07375171e+42 ];
 %!       [   2.714631560e-04    9.825679323e-03    2.157974547e+00    7.771882864e+02     2.27854831e+20     9.47009387e+41 ];
 %!       [   2.752948040e-10    3.016963879e-07    4.580044419e-03    2.189170616e+01     1.07159716e+20     6.49897552e+41 ];
 %!       [   2.370463051e-17    8.139432531e-13    1.047977675e-06    1.043714907e-01     3.07376455e+19     3.47368638e+41 ];
 %!       [   3.966835986e-25    4.310560576e-19    5.024239358e-11    1.250799736e-04     5.44200840e+18     1.44834613e+41 ];
 %!       [   3.539500588e-42    3.893519664e-33    3.997844971e-21    7.787569783e-12     4.27499365e+16     1.20615487e+40 ];
 %!       [   1.121509741e-60    1.255869192e-48    1.180426980e-32    2.042123274e-20     6.00717897e+13     3.84170550e+38 ];
 %!       [   2.934635309e-80    3.353042830e-65    2.931469647e-45    4.756894561e-30     1.76508024e+10     4.82195809e+36 ];
 %!       [   8.473674008e-189   1.082171475e-158   7.093551489e-119   1.082344202e-88     2.72788795e-16     4.64153494e+21 ]];
 %!
 %! Kt = [[   4.210244382e-01    1.138938727e-01    3.691098334e-03    1.778006232e-05     3.41016774e-23     4.65662823e-45 ];
 %!       [   3.609605896e+02    9.431049101e+00    3.270627371e-02    5.754184999e-05     4.36718224e-23     5.27325611e-45 ];
 %!       [   1.807132899e+08    1.624824040e+05    9.758562829e+00    1.614255300e-03     9.15098819e-23     7.65542797e-45 ];
 %!       [   1.403066801e+15    4.059213332e+10    3.016976630e+04    2.656563849e-01     3.11621117e-22     1.42348325e-44 ];
 %!       [   6.294369360e+22    5.770856853e+16    4.827000521e+08    1.787442782e+02     1.70614838e-21     3.38520541e-44 ];
 %!       [   4.706145527e+39    4.271125755e+30    4.112132063e+18    2.030247813e+09     2.00581681e-19     3.97060205e-43 ];
 %!       [   1.114220651e+58    9.940839886e+45    1.050756722e+30    5.938224681e+17     1.29986971e-16     1.20842080e-41 ];
 %!       [   3.406896854e+77    2.979981740e+62    3.394322243e+42    2.061373775e+27     4.00601349e-13     9.27452265e-40 ];
 %!       [   5.900333184e+185   4.619415978e+155   7.039860193e+115   4.596674084e+85     1.63940352e+13     7.61712963e-25 ]];
 %!
 %! n = [(0:5:20).';30;40;50;100];
 %! z = [1,2,5,10,50,100];
 %! I = besseli(n.',z.').';
 %! K = besselk(n.',z.').';
-%! assert(max(max(I./It-1))<5e-9);
+%! assert(I, It, -5e-9);
-%! assert(max(max(K./Kt-1))<5e-9);
+%! assert(K, Kt, -5e-9);
-%  The next section checks that negative integer orders
+The next section checks that negative integer orders and positive
-%  and positive integer orders are appropriately related.
+integer orders are appropriately related.
 %!test
 %! n=(0:2:20);
-%! err1 = max(besselj(n,1)-besselj(-n,1));
+%! assert(besselj(n,1), besselj(-n,1), 1e-8);
-%! assert(err1<1e-8);
+%! assert(-besselj(n+1,1), besselj(-n-1,1), 1e-8);
-%! err2 = max(besselj(n+1,1)+besselj(-n-1,1));
-%! assert(err2<1e-8);
+besseli(n,z) = besseli(-n,z);
-% besseli(n,z) = besseli(-n,z);
 %!test
 %! n=(0:2:20);
-%! err = max(max(besseli(n,1)-besseli(-n,1)));
+%! assert(besseli(n,1), besseli(-n,1), 1e-8);
-%! assert(err<1e-8);
+Table 10.1 - j and y for integer orders 0, 1, 2.
-% Table 10.1 - j and y for integer orders 0, 1, 2.
+Compare against excerpts of Table 10.1, Abramowitz and Stegun.
-% Compare against excerpts of Table 10.1, Abramowitz and Stegun.
 %!test
 %! n = (0:2);
 %! z = [0.1;(2.5:2.5:10.0).'];
 %!
 %! jt = [[ 9.9833417e-01  3.33000119e-02  6.6619061e-04 ];
 %!       [ 2.3938886e-01  4.16212989e-01  2.6006673e-01 ];
 %!       [-1.9178485e-01 -9.50894081e-02  1.3473121e-01 ];
 %!       [    1.2507e-01     -2.9542e-02    -1.3688e-01 ];
 %!       [   -5.4402e-02      7.8467e-02     7.7942e-02 ]];
 %!
 %! yt = [[-9.9500417e+00  -1.0049875e+02 -3.0050125e+03 ];
 %!       [ 3.2045745e-01  -1.1120588e-01 -4.5390450e-01 ];
 %!       [-5.6732437e-02   1.8043837e-01  1.6499546e-01 ];
 %!       [   -4.6218e-02     -1.3123e-01    -6.2736e-03 ];
 %!       [    8.3907e-02      6.2793e-02    -6.5069e-02 ]];
 %!
 %! j = sqrt((pi/2)./z).*besselj(n+1/2,z);
 %! y = sqrt((pi/2)./z).*bessely(n+1/2,z);
-%! assert(max(max(jt./j-1)), 0, 5e-5);
+%! assert(jt, j, -5e-5);
-%! assert(max(max(yt./y-1)), 0, 5e-5);
+%! assert(yt, y, -5e-5);
-% Table 10.2 - j and y for orders 3-8.
+Table 10.2 - j and y for orders 3-8.
-% Compare against excerpts of Table 10.2, Abramowitzh and Stegun.
+Compare against excerpts of Table 10.2, Abramowitzh and Stegun.
-%
-%  Important note: In A&S, y_4(0.1) = -1.0507e+7, but octave
+Important note: In A&S, y_4(0.1) = -1.0507e+7, but Octave returns
-%  returns y_4(0.1) = -1.0508e+07 (-10507503.75).  If I compute
+y_4(0.1) = -1.0508e+07 (-10507503.75). If I compute the same term using
-%  the same term using a series, the difference is in the eighth
+a series, the difference is in the eighth significant digit so I left
-%  significant digit so I left the octave results in place.
+the Octave results in place.
-%
 %!test
 %! n = (3:8);
 %! z = (0:2.5:10).'; z(1)=0.1;
 %!
 %! jt = [[ 9.5185e-06  1.0577e-07  9.6163e-10  7.3975e-12  4.9319e-14  2.9012e-16];
 %!       [ 1.0392e-01  3.0911e-02  7.3576e-03  1.4630e-03  2.5009e-04  3.7516e-05];
 %!       [ 2.2982e-01  1.8702e-01  1.0681e-01  4.7967e-02  1.7903e-02  5.7414e-03];
 %!       [-6.1713e-02  7.9285e-02  1.5685e-01  1.5077e-01  1.0448e-01  5.8188e-02];
 %!       [-3.9496e-02 -1.0559e-01 -5.5535e-02  4.4501e-02  1.1339e-01  1.2558e-01]];
 %!
 %! yt = [[-1.5015e+05 -1.0508e+07 -9.4553e+08 -1.0400e+11 -1.3519e+13 -2.0277e+15];
 %!       [-7.9660e-01 -1.7766e+00 -5.5991e+00 -2.2859e+01 -1.1327e+02 -6.5676e+02];
 %!       [-1.5443e-02 -1.8662e-01 -3.2047e-01 -5.1841e-01 -1.0274e+00 -2.5638e+00];
 %!       [ 1.2705e-01  1.2485e-01  2.2774e-02 -9.1449e-02 -1.8129e-01 -2.7112e-01];
 %!       [-9.5327e-02 -1.6599e-03  9.3834e-02  1.0488e-01  4.2506e-02 -4.1117e-02]];
 %!
 %! j = sqrt((pi/2)./z).*besselj(n+1/2,z);
 %! y = sqrt((pi/2)./z).*bessely(n+1/2,z);
 %!
-%! assert(max(max(jt./j-1)), 0, 5e-5);
+%! assert(jt, j, -5e-5);
-%! assert(max(max(yt./y-1)), 0, 5e-5);
+%! assert(yt, y, -5e-5);
-% Table 10.4 - j and y for various integer orders and arguments.
+Table 10.4 - j and y for various integer orders and arguments.
 %!test
 %! jt = [[ 8.414709848e-01    4.546487134e-01   -1.917848549e-01   -5.440211109e-02   -5.247497074e-03   -5.063656411e-03];
 %!       [ 9.256115861e-05    2.635169770e-03    1.068111615e-01   -5.553451162e-02   -2.004830056e-02   -9.290148935e-03];
 %!       [ 7.116552640e-11    6.825300865e-08    4.073442442e-04    6.460515449e-02   -1.503922146e-02   -1.956578597e-04];
 %!       [ 5.132686115e-18    1.606982166e-13    1.084280182e-07    1.063542715e-03   -1.129084539e-02    7.877261748e-03];
 %!       [ 7.537795722e-26    7.632641101e-20    5.427726761e-12    2.308371961e-06   -1.578502990e-02    1.010767128e-02];
 %!       [ 5.566831267e-43    5.836617888e-34    4.282730217e-22    2.512057385e-13   -1.494673454e-03    8.700628514e-03];
 %!       [ 1.538210374e-61    1.660978779e-49    1.210347583e-33    8.435671634e-22   -2.606336952e-02    1.043410851e-02];
 %!       [ 3.615274717e-81    4.011575290e-66    2.857479350e-46    2.230696023e-31    1.882910737e-02    5.797140882e-04];
 %!       [7.444727742e-190   9.367832591e-160   5.535650303e-120    5.832040182e-90    1.019012263e-22    1.088047701e-02]];
 %!
 %! yt = [[ -5.403023059e-01    2.080734183e-01   -5.673243709e-02    8.390715291e-02   -1.929932057e-02   -8.623188723e-03]
 %!       [ -9.994403434e+02   -1.859144531e+01   -3.204650467e-01    9.383354168e-02   -6.971131965e-04    3.720678486e-03]
 %!       [ -6.722150083e+08   -3.554147201e+05   -2.665611441e+01   -1.724536721e-01    1.352468751e-02    1.002577737e-02]
 %!       [ -6.298007233e+15   -1.012182944e+11   -6.288146513e+04   -3.992071745e+00    1.712319725e-02    6.258641510e-03]
 %!       [ -3.239592219e+23   -1.605436493e+17   -9.267951403e+08   -1.211210605e+03    1.375953130e-02    5.631729379e-05]
 %!
 %! n = [(0:5:20).';30;40;50;100];
 %! z = [1,2,5,10,50,100];
 %! j = sqrt((pi/2)./z).*besselj((n+1/2).',z.').';
 %! y = sqrt((pi/2)./z).*bessely((n+1/2).',z.').';
-%! assert(max(max(j./jt-1))<1e-9);
+%! assert(j, jt, -1e-9);
-%! assert(max(max(y./yt-1))<1e-9);
+%! assert(y, yt, -1e-9);
 */

Mercurial > octave-nkf

comparison src/DLD-FUNCTIONS/besselj.cc @ 14426:e28a1723d5a2