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1 % Numerical Integration Toolbox |
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2 % |
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3 % MATLAB Toolbox for 1-D, 2-D, and n-D Numerical Integration |
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4 % |
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5 % Edited Version for OCTAVE |
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6 % |
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7 % The original 1-D routines were obtained from NETLIB and were |
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8 % written by |
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9 % Howard Wilson |
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10 % Department of Engineering Mechanics |
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11 % University of Alabama |
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12 % Box 870278 |
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13 % Tuscaloosa, Alabama 35487-0278 |
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14 % Phone 205 348-1617 |
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15 % Email address: HWILSON @ UA1VM.UA.EDU |
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16 % |
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17 % The rest of the routines were written by |
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18 % Bryce Gardner |
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19 % Ray W. Herrick Laboratories |
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20 % Purdue University |
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21 % West Lafayette, IN 47906 |
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22 % Phone: 317-494-0231 |
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23 % Fax: 317-494-0787 |
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24 % Email: gardner@ecn.purdue.edu |
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25 % |
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26 % Easy to use routines: (these routines iteratively integrate with |
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27 % higher order quadratures until the integral has |
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28 % converged--use these routine unless you want to |
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29 % specify the order of integration quadrature that |
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30 % is to be used) |
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31 % quadg.m -- High accuracy replacement for QUAD and QUAD8 (1-D) |
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32 % quad2dg.m -- 2-D integration over a rectangular region |
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33 % quad2dggen.m -- 2-D integration over a general region |
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34 % quadndg.m -- n-D integration over a n-D hyper-rectangular region |
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35 % README.nit -- introductory readme file |
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36 % |
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37 % The 1-D routines: |
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38 % README -- The original readme file by Howard Wilson |
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39 % gquad.m -- Integrates a 1-D function with input Gauss |
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40 % points and weights (modified by Bryce Gardner to |
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41 % handle an optional parameter in the function to be |
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42 % integrated and also to calculate the Gauss points |
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43 % and weights on the fly) |
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44 % gquad6.m -- Integrates a 1-D function with a 6-point quadrature |
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45 % grule.m -- Calculates the Gauss points and weights |
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46 % run.log -- File with examples |
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47 % |
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48 % New 1-D routines: |
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49 % quadg.m -- High accuracy replacement for QUAD and QUAD8 |
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50 % quadc.m -- 1-D Gauss-Chebyshev integration routine |
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51 % crule.m -- Calculates the Gauss-Chebyshev points and weights |
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52 % ncrule.m -- Calculates the Newton-Coates points and weights |
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53 % |
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54 % The 2-D routines: |
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55 % quad2dg.m -- 2-D integration over a rectangular region |
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56 % quad2dc.m -- 2-D integration over a rectangular region with |
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57 % a 1/sqrt(1-x.^2)/sqrt(1-y.^2) sinqularity |
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58 % gquad2d.m -- Integrates a 2-D function over a square region |
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59 % gquad2d6.m -- Integrates a 2-D function over a square region with |
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60 % a 6-point quadrature |
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61 % quad2dggen.m -- 2-D integration over a general region |
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62 % quad2dcgen.m -- 2-D integration over a general region with |
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63 % a 1/sqrt(1-x.^2)/sqrt(1-y.^2) sinqularity |
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64 % gquad2dgen.m -- Integrates a 2-D function over a variable region |
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65 % (That is the limits on the inner integration are |
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66 % defined by a function of the variable of integration |
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67 % of the outer integral.) |
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68 % grule2d.m -- Calculates the Gauss points and weights for gquad2d.m |
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69 % grule2dgen.m -- Calculates the Gauss points and weights for |
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70 % gquad2dgen.m |
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71 % crule2d.m -- Calculates the Gauss-Chebyshev points and weights |
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72 % for gquad2d.m |
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73 % crule2dgen.m -- Calculates the Gauss-Chebyshev points and weights |
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74 % for gquad2dgen.m |
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75 % |
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76 % The n-D routines: |
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77 % quadndg.m -- n-D integration over an n-D hyper-rectangular region |
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78 % gquadnd.m -- Integrates a n-D function over |
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79 % an n-D hyper-rectangular |
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80 % region using a Gauss quadrature |
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81 % cquadnd.m -- Integrates a n-D function over |
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82 % an n-D hyper-rectangular |
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83 % region using a Gauss-Chebyshev quadrature |
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84 % innerfun.m -- used internally to gquadnd.m and cquadnd.m |
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85 % |
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86 % Utility routines: |
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87 % count.m -- routine to count the number of function calls |
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88 % zero_count.m -- routine to report the number of function calls and |
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89 % then to reset the counter |
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90 % |
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91 % Test scripts: |
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92 % run2dtests.m -- 2-D examples and 1-D Gauss-Chebyshev examples |
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93 % tests2d.log -- output of run2dtests.m -- Matlab 4.1 on a Sparc 10 |
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94 % test_ncrule.m-- m-file to check the Newton-Coates quadrature |
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95 % testsnc.log -- output of test_ncrule.m -- Matlab 4.1 on a Sparc 10 |
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96 % test_quadg.m -- m-file to check the quadg routine |
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97 % testsqg.log -- output of test_quadg.m -- Matlab 4.1 on a Sparc 10 |
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98 % |
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99 % Test functions: |
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100 % xsquar.m -- xsquar(x)=x.^2 |
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101 % xcubed.m -- xcubed(x)=x.^3 |
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102 % x25.m -- x25(x)=x.^25 |
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103 % fxpow.m -- fxpow(x,y)=x.^y |
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104 % hx.m -- hx(x)=sum(x.^2) |
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105 % gxy.m -- gxy(x,y)=x.^2+y.^2 |
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106 % gxy1.m -- gxy1(x,y)=ones(size(x)) |
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107 % gxy2.m -- gxy2(x,y)=sqrt(x.^2+y.^2) |
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108 % glimh.m -- glimh(y)=3 |
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109 % glimh2.m -- glimh(y)=y |
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110 % gliml.m -- gliml(y)=0 |
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111 % lcrcl.m -- lcrcl(y)=-sqrt(4-y.^2) |
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112 % lcrcu.m -- lcrcu(y)=sqrt(4-y.^2) |
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113 % |
