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comparison libinterp/corefcn/besselj.cc @ 31607:aac27ad79be6 stable

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maint: Re-indent code after switch to using namespace macros. * build-env.h, build-env.in.cc, Cell.h, __betainc__.cc, __eigs__.cc, __ftp__.cc, __ichol__.cc, __ilu__.cc, __isprimelarge__.cc, __magick_read__.cc, __pchip_deriv__.cc, amd.cc, base-text-renderer.cc, base-text-renderer.h, besselj.cc, bitfcns.cc, bsxfun.cc, c-file-ptr-stream.h, call-stack.cc, call-stack.h, ccolamd.cc, cellfun.cc, chol.cc, colamd.cc, dasrt.cc, data.cc, debug.cc, defaults.cc, defaults.h, det.cc, display.cc, display.h, dlmread.cc, dynamic-ld.cc, dynamic-ld.h, ellipj.cc, environment.cc, environment.h, error.cc, error.h, errwarn.h, event-manager.cc, event-manager.h, event-queue.cc, event-queue.h, fcn-info.cc, fcn-info.h, fft.cc, fft2.cc, file-io.cc, filter.cc, find.cc, ft-text-renderer.cc, ft-text-renderer.h, gcd.cc, gl-render.cc, gl-render.h, gl2ps-print.cc, gl2ps-print.h, graphics-toolkit.cc, graphics-toolkit.h, graphics.cc, gsvd.cc, gtk-manager.cc, gtk-manager.h, help.cc, help.h, hook-fcn.cc, hook-fcn.h, input.cc, input.h, interpreter-private.cc, interpreter-private.h, interpreter.cc, interpreter.h, inv.cc, jsondecode.cc, jsonencode.cc, latex-text-renderer.cc, latex-text-renderer.h, load-path.cc, load-path.h, load-save.cc, load-save.h, lookup.cc, ls-hdf5.cc, ls-mat4.cc, ls-mat5.cc, lsode.cc, lu.cc, mappers.cc, matrix_type.cc, max.cc, mex.cc, mexproto.h, mxarray.h, mxtypes.in.h, oct-errno.in.cc, oct-hdf5-types.cc, oct-hist.cc, oct-hist.h, oct-map.cc, oct-map.h, oct-opengl.h, oct-prcstrm.h, oct-process.cc, oct-process.h, oct-stdstrm.h, oct-stream.cc, oct-stream.h, oct-strstrm.h, octave-default-image.h, ordqz.cc, ordschur.cc, pager.cc, pager.h, pinv.cc, pow2.cc, pr-output.cc, psi.cc, qr.cc, quadcc.cc, rand.cc, regexp.cc, settings.cc, settings.h, sighandlers.cc, sighandlers.h, sparse-xpow.cc, sqrtm.cc, stack-frame.cc, stack-frame.h, stream-euler.cc, strfns.cc, svd.cc, syminfo.cc, syminfo.h, symrcm.cc, symrec.cc, symrec.h, symscope.cc, symscope.h, symtab.cc, symtab.h, sysdep.cc, sysdep.h, text-engine.cc, text-engine.h, text-renderer.cc, text-renderer.h, time.cc, toplev.cc, typecast.cc, url-handle-manager.cc, url-handle-manager.h, urlwrite.cc, utils.cc, utils.h, variables.cc, variables.h, xdiv.cc, __delaunayn__.cc, __init_fltk__.cc, __init_gnuplot__.cc, __ode15__.cc, __voronoi__.cc, audioread.cc, convhulln.cc, gzip.cc, cdef-class.cc, cdef-class.h, cdef-fwd.h, cdef-manager.cc, cdef-manager.h, cdef-method.cc, cdef-method.h, cdef-object.cc, cdef-object.h, cdef-package.cc, cdef-package.h, cdef-property.cc, cdef-property.h, cdef-utils.cc, cdef-utils.h, ov-base-diag.cc, ov-base-int.cc, ov-base-mat.cc, ov-base-mat.h, ov-base-scalar.cc, ov-base.cc, ov-base.h, ov-bool-mat.cc, ov-bool-mat.h, ov-bool-sparse.cc, ov-bool.cc, ov-builtin.h, ov-cell.cc, ov-ch-mat.cc, ov-class.cc, ov-class.h, ov-classdef.cc, ov-classdef.h, ov-complex.cc, ov-cx-diag.cc, ov-cx-mat.cc, ov-cx-sparse.cc, ov-dld-fcn.cc, ov-dld-fcn.h, ov-fcn-handle.cc, ov-fcn-handle.h, ov-fcn.h, ov-float.cc, ov-flt-complex.cc, ov-flt-cx-diag.cc, ov-flt-cx-mat.cc, ov-flt-re-diag.cc, ov-flt-re-mat.cc, ov-flt-re-mat.h, ov-intx.h, ov-java.cc, ov-lazy-idx.cc, ov-legacy-range.cc, ov-magic-int.cc, ov-mex-fcn.cc, ov-mex-fcn.h, ov-null-mat.cc, ov-perm.cc, ov-range.cc, ov-re-diag.cc, ov-re-mat.cc, ov-re-mat.h, ov-re-sparse.cc, ov-scalar.cc, ov-str-mat.cc, ov-struct.cc, ov-typeinfo.cc, ov-typeinfo.h, ov-usr-fcn.cc, ov-usr-fcn.h, ov.cc, ov.h, ovl.h, octave.cc, octave.h, op-b-sbm.cc, op-bm-sbm.cc, op-cs-scm.cc, op-fm-fcm.cc, op-fs-fcm.cc, op-s-scm.cc, op-scm-cs.cc, op-scm-s.cc, op-sm-cs.cc, ops.h, anon-fcn-validator.cc, anon-fcn-validator.h, bp-table.cc, bp-table.h, comment-list.cc, comment-list.h, filepos.h, lex.h, oct-lvalue.cc, oct-lvalue.h, parse.h, profiler.cc, profiler.h, pt-anon-scopes.cc, pt-anon-scopes.h, pt-arg-list.cc, pt-arg-list.h, pt-args-block.cc, pt-args-block.h, pt-array-list.cc, pt-array-list.h, pt-assign.cc, pt-assign.h, pt-binop.cc, pt-binop.h, pt-bp.cc, pt-bp.h, pt-cbinop.cc, pt-cbinop.h, pt-cell.cc, pt-cell.h, pt-check.cc, pt-check.h, pt-classdef.cc, pt-classdef.h, pt-cmd.h, pt-colon.cc, pt-colon.h, pt-const.cc, pt-const.h, pt-decl.cc, pt-decl.h, pt-eval.cc, pt-eval.h, pt-except.cc, pt-except.h, pt-exp.cc, pt-exp.h, pt-fcn-handle.cc, pt-fcn-handle.h, pt-id.cc, pt-id.h, pt-idx.cc, pt-idx.h, pt-jump.h, pt-loop.cc, pt-loop.h, pt-mat.cc, pt-mat.h, pt-misc.cc, pt-misc.h, pt-pr-code.cc, pt-pr-code.h, pt-select.cc, pt-select.h, pt-spmd.cc, pt-spmd.h, pt-stmt.cc, pt-stmt.h, pt-tm-const.cc, pt-tm-const.h, pt-unop.cc, pt-unop.h, pt-walk.cc, pt-walk.h, pt.cc, pt.h, token.cc, token.h, Range.cc, Range.h, idx-vector.cc, idx-vector.h, range-fwd.h, CollocWt.cc, CollocWt.h, aepbalance.cc, aepbalance.h, chol.cc, chol.h, gepbalance.cc, gepbalance.h, gsvd.cc, gsvd.h, hess.cc, hess.h, lo-mappers.cc, lo-mappers.h, lo-specfun.cc, lo-specfun.h, lu.cc, lu.h, oct-convn.cc, oct-convn.h, oct-fftw.cc, oct-fftw.h, oct-norm.cc, oct-norm.h, oct-rand.cc, oct-rand.h, oct-spparms.cc, oct-spparms.h, qr.cc, qr.h, qrp.cc, qrp.h, randgamma.cc, randgamma.h, randmtzig.cc, randmtzig.h, randpoisson.cc, randpoisson.h, schur.cc, schur.h, sparse-chol.cc, sparse-chol.h, sparse-lu.cc, sparse-lu.h, sparse-qr.cc, sparse-qr.h, svd.cc, svd.h, child-list.cc, child-list.h, dir-ops.cc, dir-ops.h, file-ops.cc, file-ops.h, file-stat.cc, file-stat.h, lo-sysdep.cc, lo-sysdep.h, lo-sysinfo.cc, lo-sysinfo.h, mach-info.cc, mach-info.h, oct-env.cc, oct-env.h, oct-group.cc, oct-group.h, oct-password.cc, oct-password.h, oct-syscalls.cc, oct-syscalls.h, oct-time.cc, oct-time.h, oct-uname.cc, oct-uname.h, action-container.cc, action-container.h, base-list.h, cmd-edit.cc, cmd-edit.h, cmd-hist.cc, cmd-hist.h, f77-fcn.h, file-info.cc, file-info.h, lo-array-errwarn.cc, lo-array-errwarn.h, lo-hash.cc, lo-hash.h, lo-ieee.h, lo-regexp.cc, lo-regexp.h, lo-utils.cc, lo-utils.h, oct-base64.cc, oct-base64.h, oct-glob.cc, oct-glob.h, oct-inttypes.h, oct-mutex.cc, oct-mutex.h, oct-refcount.h, oct-shlib.cc, oct-shlib.h, oct-sparse.cc, oct-sparse.h, oct-string.h, octave-preserve-stream-state.h, pathsearch.cc, pathsearch.h, quit.cc, quit.h, unwind-prot.cc, unwind-prot.h, url-transfer.cc, url-transfer.h: Re-indent code after switch to using namespace macros.
author Rik <rik@octave.org>
date Thu, 01 Dec 2022 18:02:15 -0800
parents e88a07dec498
children 597f3ee61a48
comparison
equal deleted inserted replaced
31605:e88a07dec498 31607:aac27ad79be6
159 bool args0_is_row_vector = (dv0(1) == dv0.numel ()); 159 bool args0_is_row_vector = (dv0(1) == dv0.numel ());
160 bool args1_is_col_vector = (dv1(0) == dv1.numel ()); 160 bool args1_is_col_vector = (dv1(0) == dv1.numel ());
161 161
162 if (args0_is_row_vector && args1_is_col_vector) 162 if (args0_is_row_vector && args1_is_col_vector)
163 { 163 {
164 FloatRowVector ralpha = args(0).xfloat_row_vector_value ("%s: ALPHA must be a scalar or matrix", fcn); 164 FloatRowVector ralpha = args(0).xfloat_row_vector_value ("%s: ALPHA must be a scalar or matrix",
165 fcn);
165 166
166 FloatComplexColumnVector cx 167 FloatComplexColumnVector cx
167 = x_arg.xfloat_complex_column_vector_value ("%s: X must be a scalar or matrix", fcn); 168 = x_arg.xfloat_complex_column_vector_value ("%s: X must be a scalar or matrix", fcn);
168 169
169 Array<octave_idx_type> ierr; 170 Array<octave_idx_type> ierr;
793 %!assert (besseli (alpha,x), ix, 100*eps) 794 %!assert (besseli (alpha,x), ix, 100*eps)
794 %!assert (besselk (alpha,x), kx, 100*eps) 795 %!assert (besselk (alpha,x), kx, 100*eps)
795 %!assert (besselh (alpha,1,x), jx + I*yx, 100*eps) 796 %!assert (besselh (alpha,1,x), jx + I*yx, 100*eps)
796 %!assert (besselh (alpha,2,x), jx - I*yx, 100*eps) 797 %!assert (besselh (alpha,2,x), jx - I*yx, 100*eps)
797 %! 798 %!
798 %!assert (besselj (alpha,x,1), jx*exp (-abs (imag (x))), 100*eps) 799 %!assert (besselj (alpha,x,1), jx* exp (-abs (imag (x))), 100*eps)
799 %!assert (bessely (alpha,x,1), yx*exp (-abs (imag (x))), 100*eps) 800 %!assert (bessely (alpha,x,1), yx* exp (-abs (imag (x))), 100*eps)
800 %!assert (besseli (alpha,x,1), ix*exp (-abs (real (x))), 100*eps) 801 %!assert (besseli (alpha,x,1), ix* exp (-abs (real (x))), 100*eps)
801 %!assert (besselk (alpha,x,1), kx*exp (x), 100*eps) 802 %!assert (besselk (alpha,x,1), kx* exp (x), 100*eps)
802 %!assert (besselh (alpha,1,x,1), (jx + I*yx)*exp (-I*x), 100*eps) 803 %!assert (besselh (alpha,1,x,1), (jx + I*yx)* exp (-I*x), 100*eps)
803 %!assert (besselh (alpha,2,x,1), (jx - I*yx)*exp (I*x), 100*eps) 804 %!assert (besselh (alpha,2,x,1), (jx - I*yx)* exp (I*x), 100*eps)
804 %! 805 %!
805 %!assert (besselj (-alpha,x), jx, 100*eps) 806 %!assert (besselj (-alpha,x), jx, 100*eps)
806 %!assert (bessely (-alpha,x), yx, 100*eps) 807 %!assert (bessely (-alpha,x), yx, 100*eps)
807 %!assert (besseli (-alpha,x), ix, 100*eps) 808 %!assert (besseli (-alpha,x), ix, 100*eps)
808 %!assert (besselk (-alpha,x), kx, 100*eps) 809 %!assert (besselk (-alpha,x), kx, 100*eps)
809 %!assert (besselh (-alpha,1,x), jx + I*yx, 100*eps) 810 %!assert (besselh (-alpha,1,x), jx + I*yx, 100*eps)
810 %!assert (besselh (-alpha,2,x), jx - I*yx, 100*eps) 811 %!assert (besselh (-alpha,2,x), jx - I*yx, 100*eps)
811 %! 812 %!
812 %!assert (besselj (-alpha,x,1), jx*exp (-abs (imag (x))), 100*eps) 813 %!assert (besselj (-alpha,x,1), jx* exp (-abs (imag (x))), 100*eps)
813 %!assert (bessely (-alpha,x,1), yx*exp (-abs (imag (x))), 100*eps) 814 %!assert (bessely (-alpha,x,1), yx* exp (-abs (imag (x))), 100*eps)
814 %!assert (besseli (-alpha,x,1), ix*exp (-abs (real (x))), 100*eps) 815 %!assert (besseli (-alpha,x,1), ix* exp (-abs (real (x))), 100*eps)
815 %!assert (besselk (-alpha,x,1), kx*exp (x), 100*eps) 816 %!assert (besselk (-alpha,x,1), kx* exp (x), 100*eps)
816 %!assert (besselh (-alpha,1,x,1), (jx + I*yx)*exp (-I*x), 100*eps) 817 %!assert (besselh (-alpha,1,x,1), (jx + I*yx)* exp (-I*x), 100*eps)
817 %!assert (besselh (-alpha,2,x,1), (jx - I*yx)*exp (I*x), 100*eps) 818 %!assert (besselh (-alpha,2,x,1), (jx - I*yx)* exp (I*x), 100*eps)
818 %! 819 %!
819 %! x *= -1; 820 %! x *= -1;
820 %! yx = -1.193199310178553861283790424 + 0.3421822624810469647226182835*I; 821 %! yx = -1.193199310178553861283790424 + 0.3421822624810469647226182835*I;
821 %! kx = 0.9410016167388185767085460540 - 0.6974915263814386815610060884*I; 822 %! kx = 0.9410016167388185767085460540 - 0.6974915263814386815610060884*I;
822 %! 823 %!
825 %!assert (besseli (alpha,x), ix, 100*eps) 826 %!assert (besseli (alpha,x), ix, 100*eps)
826 %!assert (besselk (alpha,x), kx, 100*eps) 827 %!assert (besselk (alpha,x), kx, 100*eps)
827 %!assert (besselh (alpha,1,x), jx + I*yx, 100*eps) 828 %!assert (besselh (alpha,1,x), jx + I*yx, 100*eps)
828 %!assert (besselh (alpha,2,x), jx - I*yx, 100*eps) 829 %!assert (besselh (alpha,2,x), jx - I*yx, 100*eps)
829 %! 830 %!
830 %!assert (besselj (alpha,x,1), jx*exp (-abs (imag (x))), 100*eps) 831 %!assert (besselj (alpha,x,1), jx* exp (-abs (imag (x))), 100*eps)
831 %!assert (bessely (alpha,x,1), yx*exp (-abs (imag (x))), 100*eps) 832 %!assert (bessely (alpha,x,1), yx* exp (-abs (imag (x))), 100*eps)
832 %!assert (besseli (alpha,x,1), ix*exp (-abs (real (x))), 100*eps) 833 %!assert (besseli (alpha,x,1), ix* exp (-abs (real (x))), 100*eps)
833 %!assert (besselk (alpha,x,1), kx*exp (x), 100*eps) 834 %!assert (besselk (alpha,x,1), kx* exp (x), 100*eps)
834 %!assert (besselh (alpha,1,x,1), (jx + I*yx)*exp (-I*x), 100*eps) 835 %!assert (besselh (alpha,1,x,1), (jx + I*yx)* exp (-I*x), 100*eps)
835 %!assert (besselh (alpha,2,x,1), (jx - I*yx)*exp (I*x), 100*eps) 836 %!assert (besselh (alpha,2,x,1), (jx - I*yx)* exp (I*x), 100*eps)
836 %! 837 %!
837 %! ## Bessel functions, odd order, positive and negative x 838 %! ## Bessel functions, odd order, positive and negative x
838 %! alpha = 3; x = 2.5; 839 %! alpha = 3; x = 2.5;
839 %! jx = 0.2166003910391135247666890035; 840 %! jx = 0.2166003910391135247666890035;
840 %! yx = -0.7560554967536709968379029772; 841 %! yx = -0.7560554967536709968379029772;
846 %!assert (besseli (alpha,x), ix, 100*eps) 847 %!assert (besseli (alpha,x), ix, 100*eps)
847 %!assert (besselk (alpha,x), kx, 100*eps) 848 %!assert (besselk (alpha,x), kx, 100*eps)
848 %!assert (besselh (alpha,1,x), jx + I*yx, 100*eps) 849 %!assert (besselh (alpha,1,x), jx + I*yx, 100*eps)
849 %!assert (besselh (alpha,2,x), jx - I*yx, 100*eps) 850 %!assert (besselh (alpha,2,x), jx - I*yx, 100*eps)
850 %! 851 %!
851 %!assert (besselj (alpha,x,1), jx*exp (-abs (imag (x))), 100*eps) 852 %!assert (besselj (alpha,x,1), jx* exp (-abs (imag (x))), 100*eps)
852 %!assert (bessely (alpha,x,1), yx*exp (-abs (imag (x))), 100*eps) 853 %!assert (bessely (alpha,x,1), yx* exp (-abs (imag (x))), 100*eps)
853 %!assert (besseli (alpha,x,1), ix*exp (-abs (real (x))), 100*eps) 854 %!assert (besseli (alpha,x,1), ix* exp (-abs (real (x))), 100*eps)
854 %!assert (besselk (alpha,x,1), kx*exp (x), 100*eps) 855 %!assert (besselk (alpha,x,1), kx* exp (x), 100*eps)
855 %!assert (besselh (alpha,1,x,1), (jx + I*yx)*exp (-I*x), 100*eps) 856 %!assert (besselh (alpha,1,x,1), (jx + I*yx)* exp (-I*x), 100*eps)
856 %!assert (besselh (alpha,2,x,1), (jx - I*yx)*exp (I*x), 100*eps) 857 %!assert (besselh (alpha,2,x,1), (jx - I*yx)* exp (I*x), 100*eps)
857 %! 858 %!
858 %!assert (besselj (-alpha,x), -jx, 100*eps) 859 %!assert (besselj (-alpha,x), -jx, 100*eps)
859 %!assert (bessely (-alpha,x), -yx, 100*eps) 860 %!assert (bessely (-alpha,x), -yx, 100*eps)
860 %!assert (besseli (-alpha,x), ix, 100*eps) 861 %!assert (besseli (-alpha,x), ix, 100*eps)
861 %!assert (besselk (-alpha,x), kx, 100*eps) 862 %!assert (besselk (-alpha,x), kx, 100*eps)
862 %!assert (besselh (-alpha,1,x), -(jx + I*yx), 100*eps) 863 %!assert (besselh (-alpha,1,x), -(jx + I*yx), 100*eps)
863 %!assert (besselh (-alpha,2,x), -(jx - I*yx), 100*eps) 864 %!assert (besselh (-alpha,2,x), -(jx - I*yx), 100*eps)
864 %! 865 %!
865 %!assert (besselj (-alpha,x,1), -jx*exp (-abs (imag (x))), 100*eps) 866 %!assert (besselj (-alpha,x,1), -jx* exp (-abs (imag (x))), 100*eps)
866 %!assert (bessely (-alpha,x,1), -yx*exp (-abs (imag (x))), 100*eps) 867 %!assert (bessely (-alpha,x,1), -yx* exp (-abs (imag (x))), 100*eps)
867 %!assert (besseli (-alpha,x,1), ix*exp (-abs (real (x))), 100*eps) 868 %!assert (besseli (-alpha,x,1), ix* exp (-abs (real (x))), 100*eps)
868 %!assert (besselk (-alpha,x,1), kx*exp (x), 100*eps) 869 %!assert (besselk (-alpha,x,1), kx* exp (x), 100*eps)
869 %!assert (besselh (-alpha,1,x,1), -(jx + I*yx)*exp (-I*x), 100*eps) 870 %!assert (besselh (-alpha,1,x,1), -(jx + I*yx)* exp (-I*x), 100*eps)
870 %!assert (besselh (-alpha,2,x,1), -(jx - I*yx)*exp (I*x), 100*eps) 871 %!assert (besselh (-alpha,2,x,1), -(jx - I*yx)* exp (I*x), 100*eps)
871 %! 872 %!
872 %! x *= -1; 873 %! x *= -1;
873 %! jx = -jx; 874 %! jx = -jx;
874 %! yx = 0.7560554967536709968379029772 - 0.4332007820782270495333780070*I; 875 %! yx = 0.7560554967536709968379029772 - 0.4332007820782270495333780070*I;
875 %! ix = -ix; 876 %! ix = -ix;
880 %!assert (besseli (alpha,x), ix, 100*eps) 881 %!assert (besseli (alpha,x), ix, 100*eps)
881 %!assert (besselk (alpha,x), kx, 100*eps) 882 %!assert (besselk (alpha,x), kx, 100*eps)
882 %!assert (besselh (alpha,1,x), jx + I*yx, 100*eps) 883 %!assert (besselh (alpha,1,x), jx + I*yx, 100*eps)
883 %!assert (besselh (alpha,2,x), jx - I*yx, 100*eps) 884 %!assert (besselh (alpha,2,x), jx - I*yx, 100*eps)
884 %! 885 %!
885 %!assert (besselj (alpha,x,1), jx*exp (-abs (imag (x))), 100*eps) 886 %!assert (besselj (alpha,x,1), jx* exp (-abs (imag (x))), 100*eps)
886 %!assert (bessely (alpha,x,1), yx*exp (-abs (imag (x))), 100*eps) 887 %!assert (bessely (alpha,x,1), yx* exp (-abs (imag (x))), 100*eps)
887 %!assert (besseli (alpha,x,1), ix*exp (-abs (real (x))), 100*eps) 888 %!assert (besseli (alpha,x,1), ix* exp (-abs (real (x))), 100*eps)
888 %!assert (besselk (alpha,x,1), kx*exp (x), 100*eps) 889 %!assert (besselk (alpha,x,1), kx* exp (x), 100*eps)
889 %!assert (besselh (alpha,1,x,1), (jx + I*yx)*exp (-I*x), 100*eps) 890 %!assert (besselh (alpha,1,x,1), (jx + I*yx)* exp (-I*x), 100*eps)
890 %!assert (besselh (alpha,2,x,1), (jx - I*yx)*exp (I*x), 100*eps) 891 %!assert (besselh (alpha,2,x,1), (jx - I*yx)* exp (I*x), 100*eps)
891 %! 892 %!
892 %! ## Bessel functions, fractional order, positive and negative x 893 %! ## Bessel functions, fractional order, positive and negative x
893 %! 894 %!
894 %! alpha = 3.5; x = 2.75; 895 %! alpha = 3.5; x = 2.75;
895 %! jx = 0.1691636439842384154644784389; 896 %! jx = 0.1691636439842384154644784389;
902 %!assert (besseli (alpha,x), ix, 100*eps) 903 %!assert (besseli (alpha,x), ix, 100*eps)
903 %!assert (besselk (alpha,x), kx, 100*eps) 904 %!assert (besselk (alpha,x), kx, 100*eps)
904 %!assert (besselh (alpha,1,x), jx + I*yx, 100*eps) 905 %!assert (besselh (alpha,1,x), jx + I*yx, 100*eps)
905 %!assert (besselh (alpha,2,x), jx - I*yx, 100*eps) 906 %!assert (besselh (alpha,2,x), jx - I*yx, 100*eps)
906 %! 907 %!
907 %!assert (besselj (alpha,x,1), jx*exp (-abs (imag (x))), 100*eps) 908 %!assert (besselj (alpha,x,1), jx* exp (-abs (imag (x))), 100*eps)
908 %!assert (bessely (alpha,x,1), yx*exp (-abs (imag (x))), 100*eps) 909 %!assert (bessely (alpha,x,1), yx* exp (-abs (imag (x))), 100*eps)
909 %!assert (besseli (alpha,x,1), ix*exp (-abs (real (x))), 100*eps) 910 %!assert (besseli (alpha,x,1), ix* exp (-abs (real (x))), 100*eps)
910 %!assert (besselk (alpha,x,1), kx*exp (x), 100*eps) 911 %!assert (besselk (alpha,x,1), kx* exp (x), 100*eps)
911 %!assert (besselh (alpha,1,x,1), (jx + I*yx)*exp (-I*x), 100*eps) 912 %!assert (besselh (alpha,1,x,1), (jx + I*yx)* exp (-I*x), 100*eps)
912 %!assert (besselh (alpha,2,x,1), (jx - I*yx)*exp (I*x), 100*eps) 913 %!assert (besselh (alpha,2,x,1), (jx - I*yx)* exp (I*x), 100*eps)
913 %! 914 %!
914 %! nix = 0.2119931212254662995364461998; 915 %! nix = 0.2119931212254662995364461998;
915 %! 916 %!
916 %!assert (besselj (-alpha,x), yx, 100*eps) 917 %!assert (besselj (-alpha,x), yx, 100*eps)
917 %!assert (bessely (-alpha,x), -jx, 100*eps) 918 %!assert (bessely (-alpha,x), -jx, 100*eps)
918 %!assert (besseli (-alpha,x), nix, 100*eps) 919 %!assert (besseli (-alpha,x), nix, 100*eps)
919 %!assert (besselk (-alpha,x), kx, 100*eps) 920 %!assert (besselk (-alpha,x), kx, 100*eps)
920 %!assert (besselh (-alpha,1,x), -I*(jx + I*yx), 100*eps) 921 %!assert (besselh (-alpha,1,x), -I*(jx + I*yx), 100*eps)
921 %!assert (besselh (-alpha,2,x), I*(jx - I*yx), 100*eps) 922 %!assert (besselh (-alpha,2,x), I*(jx - I*yx), 100*eps)
922 %! 923 %!
923 %!assert (besselj (-alpha,x,1), yx*exp (-abs (imag (x))), 100*eps) 924 %!assert (besselj (-alpha,x,1), yx* exp (-abs (imag (x))), 100*eps)
924 %!assert (bessely (-alpha,x,1), -jx*exp (-abs (imag (x))), 100*eps) 925 %!assert (bessely (-alpha,x,1), -jx* exp (-abs (imag (x))), 100*eps)
925 %!assert (besseli (-alpha,x,1), nix*exp (-abs (real (x))), 100*eps) 926 %!assert (besseli (-alpha,x,1), nix* exp (-abs (real (x))), 100*eps)
926 %!assert (besselk (-alpha,x,1), kx*exp (x), 100*eps) 927 %!assert (besselk (-alpha,x,1), kx* exp (x), 100*eps)
927 %!assert (besselh (-alpha,1,x,1), -I*(jx + I*yx)*exp (-I*x), 100*eps) 928 %!assert (besselh (-alpha,1,x,1), -I*(jx + I*yx)* exp (-I*x), 100*eps)
928 %!assert (besselh (-alpha,2,x,1), I*(jx - I*yx)*exp (I*x), 100*eps) 929 %!assert (besselh (-alpha,2,x,1), I*(jx - I*yx)* exp (I*x), 100*eps)
929 %! 930 %!
930 %! x *= -1; 931 %! x *= -1;
931 %! jx *= -I; 932 %! jx *= -I;
932 %! yx = -0.8301381935499356070267953387*I; 933 %! yx = -0.8301381935499356070267953387*I;
933 %! ix *= -I; 934 %! ix *= -I;
938 %!assert (besseli (alpha,x), ix, 100*eps) 939 %!assert (besseli (alpha,x), ix, 100*eps)
939 %!assert (besselk (alpha,x), kx, 100*eps) 940 %!assert (besselk (alpha,x), kx, 100*eps)
940 %!assert (besselh (alpha,1,x), jx + I*yx, 100*eps) 941 %!assert (besselh (alpha,1,x), jx + I*yx, 100*eps)
941 %!assert (besselh (alpha,2,x), jx - I*yx, 100*eps) 942 %!assert (besselh (alpha,2,x), jx - I*yx, 100*eps)
942 %! 943 %!
943 %!assert (besselj (alpha,x,1), jx*exp (-abs (imag (x))), 100*eps) 944 %!assert (besselj (alpha,x,1), jx* exp (-abs (imag (x))), 100*eps)
944 %!assert (bessely (alpha,x,1), yx*exp (-abs (imag (x))), 100*eps) 945 %!assert (bessely (alpha,x,1), yx* exp (-abs (imag (x))), 100*eps)
945 %!assert (besseli (alpha,x,1), ix*exp (-abs (real (x))), 100*eps) 946 %!assert (besseli (alpha,x,1), ix* exp (-abs (real (x))), 100*eps)
946 %!assert (besselk (alpha,x,1), kx*exp (x), 100*eps) 947 %!assert (besselk (alpha,x,1), kx* exp (x), 100*eps)
947 %!assert (besselh (alpha,1,x,1), (jx + I*yx)*exp (-I*x), 100*eps) 948 %!assert (besselh (alpha,1,x,1), (jx + I*yx)* exp (-I*x), 100*eps)
948 %!assert (besselh (alpha,2,x,1), (jx - I*yx)*exp (I*x), 100*eps) 949 %!assert (besselh (alpha,2,x,1), (jx - I*yx)* exp (I*x), 100*eps)
949 %! 950 %!
950 %! ## Bessel functions, even order, complex x 951 %! ## Bessel functions, even order, complex x
951 %! 952 %!
952 %! alpha = 2; x = 1.25 + 3.625 * I; 953 %! alpha = 2; x = 1.25 + 3.625 * I;
953 %! jx = -1.299533366810794494030065917 + 4.370833116012278943267479589*I; 954 %! jx = -1.299533366810794494030065917 + 4.370833116012278943267479589*I;
960 %!assert (besseli (alpha,x), ix, 100*eps) 961 %!assert (besseli (alpha,x), ix, 100*eps)
961 %!assert (besselk (alpha,x), kx, 100*eps) 962 %!assert (besselk (alpha,x), kx, 100*eps)
962 %!assert (besselh (alpha,1,x), jx + I*yx, 100*eps) 963 %!assert (besselh (alpha,1,x), jx + I*yx, 100*eps)
963 %!assert (besselh (alpha,2,x), jx - I*yx, 100*eps) 964 %!assert (besselh (alpha,2,x), jx - I*yx, 100*eps)
964 %! 965 %!
965 %!assert (besselj (alpha,x,1), jx*exp (-abs (imag (x))), 100*eps) 966 %!assert (besselj (alpha,x,1), jx* exp (-abs (imag (x))), 100*eps)
966 %!assert (bessely (alpha,x,1), yx*exp (-abs (imag (x))), 100*eps) 967 %!assert (bessely (alpha,x,1), yx* exp (-abs (imag (x))), 100*eps)
967 %!assert (besseli (alpha,x,1), ix*exp (-abs (real (x))), 100*eps) 968 %!assert (besseli (alpha,x,1), ix* exp (-abs (real (x))), 100*eps)
968 %!assert (besselk (alpha,x,1), kx*exp (x), 100*eps) 969 %!assert (besselk (alpha,x,1), kx* exp (x), 100*eps)
969 %!assert (besselh (alpha,1,x,1), (jx + I*yx)*exp (-I*x), 100*eps) 970 %!assert (besselh (alpha,1,x,1), (jx + I*yx)* exp (-I*x), 100*eps)
970 %!assert (besselh (alpha,2,x,1), (jx - I*yx)*exp (I*x), 100*eps) 971 %!assert (besselh (alpha,2,x,1), (jx - I*yx)* exp (I*x), 100*eps)
971 %! 972 %!
972 %!assert (besselj (-alpha,x), jx, 100*eps) 973 %!assert (besselj (-alpha,x), jx, 100*eps)
973 %!assert (bessely (-alpha,x), yx, 100*eps) 974 %!assert (bessely (-alpha,x), yx, 100*eps)
974 %!assert (besseli (-alpha,x), ix, 100*eps) 975 %!assert (besseli (-alpha,x), ix, 100*eps)
975 %!assert (besselk (-alpha,x), kx, 100*eps) 976 %!assert (besselk (-alpha,x), kx, 100*eps)
976 %!assert (besselh (-alpha,1,x), jx + I*yx, 100*eps) 977 %!assert (besselh (-alpha,1,x), jx + I*yx, 100*eps)
977 %!assert (besselh (-alpha,2,x), jx - I*yx, 100*eps) 978 %!assert (besselh (-alpha,2,x), jx - I*yx, 100*eps)
978 %! 979 %!
979 %!assert (besselj (-alpha,x,1), jx*exp (-abs (imag (x))), 100*eps) 980 %!assert (besselj (-alpha,x,1), jx* exp (-abs (imag (x))), 100*eps)
980 %!assert (bessely (-alpha,x,1), yx*exp (-abs (imag (x))), 100*eps) 981 %!assert (bessely (-alpha,x,1), yx* exp (-abs (imag (x))), 100*eps)
981 %!assert (besseli (-alpha,x,1), ix*exp (-abs (real (x))), 100*eps) 982 %!assert (besseli (-alpha,x,1), ix* exp (-abs (real (x))), 100*eps)
982 %!assert (besselk (-alpha,x,1), kx*exp (x), 100*eps) 983 %!assert (besselk (-alpha,x,1), kx* exp (x), 100*eps)
983 %!assert (besselh (-alpha,1,x,1), (jx + I*yx)*exp (-I*x), 100*eps) 984 %!assert (besselh (-alpha,1,x,1), (jx + I*yx)* exp (-I*x), 100*eps)
984 %!assert (besselh (-alpha,2,x,1), (jx - I*yx)*exp (I*x), 100*eps) 985 %!assert (besselh (-alpha,2,x,1), (jx - I*yx)* exp (I*x), 100*eps)
985 %! 986 %!
986 %! ## Bessel functions, odd order, complex x 987 %! ## Bessel functions, odd order, complex x
987 %! 988 %!
988 %! alpha = 3; x = 2.5 + 1.875 * I; 989 %! alpha = 3; x = 2.5 + 1.875 * I;
989 %! jx = 0.1330721523048277493333458596 + 0.5386295217249660078754395597*I; 990 %! jx = 0.1330721523048277493333458596 + 0.5386295217249660078754395597*I;
996 %!assert (besseli (alpha,x), ix, 100*eps) 997 %!assert (besseli (alpha,x), ix, 100*eps)
997 %!assert (besselk (alpha,x), kx, 100*eps) 998 %!assert (besselk (alpha,x), kx, 100*eps)
998 %!assert (besselh (alpha,1,x), jx + I*yx, 100*eps) 999 %!assert (besselh (alpha,1,x), jx + I*yx, 100*eps)
999 %!assert (besselh (alpha,2,x), jx - I*yx, 100*eps) 1000 %!assert (besselh (alpha,2,x), jx - I*yx, 100*eps)
1000 %! 1001 %!
1001 %!assert (besselj (alpha,x,1), jx*exp (-abs (imag (x))), 100*eps) 1002 %!assert (besselj (alpha,x,1), jx* exp (-abs (imag (x))), 100*eps)
1002 %!assert (bessely (alpha,x,1), yx*exp (-abs (imag (x))), 100*eps) 1003 %!assert (bessely (alpha,x,1), yx* exp (-abs (imag (x))), 100*eps)
1003 %!assert (besseli (alpha,x,1), ix*exp (-abs (real (x))), 100*eps) 1004 %!assert (besseli (alpha,x,1), ix* exp (-abs (real (x))), 100*eps)
1004 %!assert (besselk (alpha,x,1), kx*exp (x), 100*eps) 1005 %!assert (besselk (alpha,x,1), kx* exp (x), 100*eps)
1005 %!assert (besselh (alpha,1,x,1), (jx + I*yx)*exp (-I*x), 100*eps) 1006 %!assert (besselh (alpha,1,x,1), (jx + I*yx)* exp (-I*x), 100*eps)
1006 %!assert (besselh (alpha,2,x,1), (jx - I*yx)*exp (I*x), 100*eps) 1007 %!assert (besselh (alpha,2,x,1), (jx - I*yx)* exp (I*x), 100*eps)
1007 %! 1008 %!
1008 %!assert (besselj (-alpha,x), -jx, 100*eps) 1009 %!assert (besselj (-alpha,x), -jx, 100*eps)
1009 %!assert (bessely (-alpha,x), -yx, 100*eps) 1010 %!assert (bessely (-alpha,x), -yx, 100*eps)
1010 %!assert (besseli (-alpha,x), ix, 100*eps) 1011 %!assert (besseli (-alpha,x), ix, 100*eps)
1011 %!assert (besselk (-alpha,x), kx, 100*eps) 1012 %!assert (besselk (-alpha,x), kx, 100*eps)
1012 %!assert (besselh (-alpha,1,x), -(jx + I*yx), 100*eps) 1013 %!assert (besselh (-alpha,1,x), -(jx + I*yx), 100*eps)
1013 %!assert (besselh (-alpha,2,x), -(jx - I*yx), 100*eps) 1014 %!assert (besselh (-alpha,2,x), -(jx - I*yx), 100*eps)
1014 %! 1015 %!
1015 %!assert (besselj (-alpha,x,1), -jx*exp (-abs (imag (x))), 100*eps) 1016 %!assert (besselj (-alpha,x,1), -jx* exp (-abs (imag (x))), 100*eps)
1016 %!assert (bessely (-alpha,x,1), -yx*exp (-abs (imag (x))), 100*eps) 1017 %!assert (bessely (-alpha,x,1), -yx* exp (-abs (imag (x))), 100*eps)
1017 %!assert (besseli (-alpha,x,1), ix*exp (-abs (real (x))), 100*eps) 1018 %!assert (besseli (-alpha,x,1), ix* exp (-abs (real (x))), 100*eps)
1018 %!assert (besselk (-alpha,x,1), kx*exp (x), 100*eps) 1019 %!assert (besselk (-alpha,x,1), kx* exp (x), 100*eps)
1019 %!assert (besselh (-alpha,1,x,1), -(jx + I*yx)*exp (-I*x), 100*eps) 1020 %!assert (besselh (-alpha,1,x,1), -(jx + I*yx)* exp (-I*x), 100*eps)
1020 %!assert (besselh (-alpha,2,x,1), -(jx - I*yx)*exp (I*x), 100*eps) 1021 %!assert (besselh (-alpha,2,x,1), -(jx - I*yx)* exp (I*x), 100*eps)
1021 %! 1022 %!
1022 %! ## Bessel functions, fractional order, complex x 1023 %! ## Bessel functions, fractional order, complex x
1023 %! 1024 %!
1024 %! alpha = 3.5; x = 1.75 + 4.125 * I; 1025 %! alpha = 3.5; x = 1.75 + 4.125 * I;
1025 %! jx = -3.018566131370455929707009100 - 0.7585648436793900607704057611*I; 1026 %! jx = -3.018566131370455929707009100 - 0.7585648436793900607704057611*I;
1032 %!assert (besseli (alpha,x), ix, 100*eps) 1033 %!assert (besseli (alpha,x), ix, 100*eps)
1033 %!assert (besselk (alpha,x), kx, 100*eps) 1034 %!assert (besselk (alpha,x), kx, 100*eps)
1034 %!assert (besselh (alpha,1,x), jx + I*yx, 100*eps) 1035 %!assert (besselh (alpha,1,x), jx + I*yx, 100*eps)
1035 %!assert (besselh (alpha,2,x), jx - I*yx, 100*eps) 1036 %!assert (besselh (alpha,2,x), jx - I*yx, 100*eps)
1036 %! 1037 %!
1037 %!assert (besselj (alpha,x,1), jx*exp (-abs (imag (x))), 100*eps) 1038 %!assert (besselj (alpha,x,1), jx* exp (-abs (imag (x))), 100*eps)
1038 %!assert (bessely (alpha,x,1), yx*exp (-abs (imag (x))), 100*eps) 1039 %!assert (bessely (alpha,x,1), yx* exp (-abs (imag (x))), 100*eps)
1039 %!assert (besseli (alpha,x,1), ix*exp (-abs (real (x))), 100*eps) 1040 %!assert (besseli (alpha,x,1), ix* exp (-abs (real (x))), 100*eps)
1040 %!assert (besselk (alpha,x,1), kx*exp (x), 100*eps) 1041 %!assert (besselk (alpha,x,1), kx* exp (x), 100*eps)
1041 %!assert (besselh (alpha,1,x,1), (jx + I*yx)*exp (-I*x), 100*eps) 1042 %!assert (besselh (alpha,1,x,1), (jx + I*yx)* exp (-I*x), 100*eps)
1042 %!assert (besselh (alpha,2,x,1), (jx - I*yx)*exp (I*x), 100*eps) 1043 %!assert (besselh (alpha,2,x,1), (jx - I*yx)* exp (I*x), 100*eps)
1043 %! 1044 %!
1044 %! nix = 0.09822388691172060573913739253 - 0.7110230642207380127317227407*I; 1045 %! nix = 0.09822388691172060573913739253 - 0.7110230642207380127317227407*I;
1045 %! 1046 %!
1046 %!assert (besselj (-alpha,x), yx, 100*eps) 1047 %!assert (besselj (-alpha,x), yx, 100*eps)
1047 %!assert (bessely (-alpha,x), -jx, 100*eps) 1048 %!assert (bessely (-alpha,x), -jx, 100*eps)
1048 %!assert (besseli (-alpha,x), nix, 100*eps) 1049 %!assert (besseli (-alpha,x), nix, 100*eps)
1049 %!assert (besselk (-alpha,x), kx, 100*eps) 1050 %!assert (besselk (-alpha,x), kx, 100*eps)
1050 %!assert (besselh (-alpha,1,x), -I*(jx + I*yx), 100*eps) 1051 %!assert (besselh (-alpha,1,x), -I*(jx + I*yx), 100*eps)
1051 %!assert (besselh (-alpha,2,x), I*(jx - I*yx), 100*eps) 1052 %!assert (besselh (-alpha,2,x), I*(jx - I*yx), 100*eps)
1052 %! 1053 %!
1053 %!assert (besselj (-alpha,x,1), yx*exp (-abs (imag (x))), 100*eps) 1054 %!assert (besselj (-alpha,x,1), yx* exp (-abs (imag (x))), 100*eps)
1054 %!assert (bessely (-alpha,x,1), -jx*exp (-abs (imag (x))), 100*eps) 1055 %!assert (bessely (-alpha,x,1), -jx* exp (-abs (imag (x))), 100*eps)
1055 %!assert (besseli (-alpha,x,1), nix*exp (-abs (real (x))), 100*eps) 1056 %!assert (besseli (-alpha,x,1), nix* exp (-abs (real (x))), 100*eps)
1056 %!assert (besselk (-alpha,x,1), kx*exp (x), 100*eps) 1057 %!assert (besselk (-alpha,x,1), kx* exp (x), 100*eps)
1057 %!assert (besselh (-alpha,1,x,1), -I*(jx + I*yx)*exp (-I*x), 100*eps) 1058 %!assert (besselh (-alpha,1,x,1), -I*(jx + I*yx)* exp (-I*x), 100*eps)
1058 %!assert (besselh (-alpha,2,x,1), I*(jx - I*yx)*exp (I*x), 100*eps) 1059 %!assert (besselh (-alpha,2,x,1), I*(jx - I*yx)* exp (I*x), 100*eps)
1059 1060
1060 Tests contributed by Robert T. Short. 1061 Tests contributed by Robert T. Short.
1061 Tests are based on the properties and tables in A&S: 1062 Tests are based on the properties and tables in A&S:
1062 Abramowitz and Stegun, "Handbook of Mathematical Functions", 1063 Abramowitz and Stegun, "Handbook of Mathematical Functions",
1063 1972. 1064 1972.