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annotate libinterp/corefcn/ellipj.cc @ 16587:a3fdd6041e64

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Fix ellipj, ellipke, and expint docstrings * ellipj.cc, ellipke.m, expint.m: Fix docstring signatures and wording.
author Mike Miller <mtmiller@ieee.org>
date Sun, 28 Apr 2013 19:25:50 -0400
parents f423873d3275
children 4d2b0104ee05
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
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1 /*
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2
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3 Copyright (C) 2001 Leopoldo Cerbaro <redbliss@libero.it>
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4
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5 This file is part of Octave.
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6
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7 Octave is free software; you can redistribute it and/or modify it
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8 under the terms of the GNU General Public License as published by the
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9 Free Software Foundation; either version 3 of the License, or (at your
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10 option) any later version.
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11
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12 Octave is distributed in the hope that it will be useful, but WITHOUT
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13 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
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14 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
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15 for more details.
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16
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17 You should have received a copy of the GNU General Public License
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18 along with Octave; see the file COPYING. If not, see
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19 <http://www.gnu.org/licenses/>.
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20
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21 */
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22
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23 #ifdef HAVE_CONFIG_H
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24 #include <config.h>
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25 #endif
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26
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27 #include "defun.h"
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28 #include "error.h"
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29 #include "lo-ieee.h"
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30
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31 static void
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32 gripe_ellipj_arg (const char *arg)
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33 {
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34 error ("ellipj: expecting scalar or matrix as %s argument", arg);
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35 }
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36
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37 static void
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38 sncndn (double u, double m, double& sn, double& cn, double& dn, double& err)
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39 {
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40 static const int Nmax = 16;
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41 double m1, t=0, si_u, co_u, se_u, ta_u, b, c[Nmax], a[Nmax], phi;
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42 int n, Nn, ii;
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43
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44 if (m < 0 || m > 1)
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45 {
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46 warning ("ellipj: expecting 0 <= m <= 1"); /* -lc- */
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47 sn = cn = dn = lo_ieee_nan_value ();
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48 return;
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49 }
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50
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51 double sqrt_eps = sqrt (std::numeric_limits<double>::epsilon ());
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52 if (m < sqrt_eps)
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53 {
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54 /* # For small m, ( Abramowitz and Stegun, Section 16.13 ) */
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55 si_u = sin (u);
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56 co_u = cos (u);
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57 t = 0.25*m*(u - si_u*co_u);
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58 sn = si_u - t * co_u;
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59 cn = co_u + t * si_u;
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60 dn = 1 - 0.5*m*si_u*si_u;
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61 }
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62 else if ((1 - m) < sqrt_eps)
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63 {
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64 /* For m1 = (1-m) small ( Abramowitz and Stegun, Section 16.15 ) */
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65 m1 = 1 - m;
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66 si_u = sinh (u);
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67 co_u = cosh (u);
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68 ta_u = tanh (u);
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69 se_u = 1/co_u;
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70 sn = ta_u + 0.25*m1*(si_u*co_u - u)*se_u*se_u;
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71 cn = se_u - 0.25*m1*(si_u*co_u - u)*ta_u*se_u;
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72 dn = se_u + 0.25*m1*(si_u*co_u + u)*ta_u*se_u;
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73 }
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74 else
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75 {
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76 /*
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77 // Arithmetic-Geometric Mean (AGM) algorithm
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78 // ( Abramowitz and Stegun, Section 16.4 )
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79 */
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80
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81 a[0] = 1;
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82 b = sqrt (1 - m);
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83 c[0] = sqrt (m);
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84 for (n = 1; n < Nmax; ++n)
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85 {
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86 a[n] = (a[n - 1] + b)/2;
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87 c[n] = (a[n - 1] - b)/2;
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88 b = sqrt (a[n - 1]*b);
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89 if (c[n]/a[n] < std::numeric_limits<double>::epsilon ()) break;
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90 }
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91 if (n >= Nmax - 1)
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92 {
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93 err = 1;
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94 return;
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95 }
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96 Nn = n;
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97 for (ii = 1; n > 0; ii = ii*2, --n) ; // ii = pow(2,Nn)
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98 phi = ii*a[Nn]*u;
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99 for (n = Nn; n > 0; --n)
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100 {
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101 t = phi;
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102 phi = (asin ((c[n]/a[n])* sin (phi)) + phi)/2;
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103 }
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104 sn = sin (phi);
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105 cn = cos (phi);
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106 dn = cn/cos (t - phi);
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107 }
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108 }
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109
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110 static void
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111 sncndn (Complex& u, double m, Complex& sn, Complex& cn, Complex& dn,
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112 double& err)
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113 {
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114 double m1 = 1 - m, ss1, cc1, dd1;
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115
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116 sncndn (imag (u), m1, ss1, cc1, dd1, err);
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117 if (real (u) == 0)
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118 {
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119 /* u is pure imag: Jacoby imag. transf. */
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120 sn = Complex (0, ss1/cc1);
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121 cn = 1/cc1; // cn.imag = 0;
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122 dn = dd1/cc1; // dn.imag = 0;
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123 }
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124 else
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125 {
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126 /* u is generic complex */
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127 double ss, cc, dd, ddd;
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128
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129 sncndn (real (u), m, ss, cc, dd, err);
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130 ddd = cc1*cc1 + m*ss*ss*ss1*ss1;
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131 sn = Complex (ss*dd1/ddd, cc*dd*ss1*cc1/ddd);
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132 cn = Complex (cc*cc1/ddd, -ss*dd*ss1*dd1/ddd);
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133 dn = Complex (dd*cc1*dd1/ddd, -m*ss*cc*ss1/ddd);
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134 }
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135 }
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136
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137 DEFUN (ellipj, args, nargout,
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138 "-*- texinfo -*-\n\
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139 @deftypefn {Built-in Function} {[@var{sn}, @var{cn}, @var{dn}, @var{err}] =} ellipj (@var{u}, @var{m})\n\
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140 Compute the Jacobi elliptic functions @var{sn}, @var{cn}, and @var{dn}\n\
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141 of complex argument @var{u} and real parameter @var{m}.\n\
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142 \n\
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143 If @var{m} is a scalar, the results are the same size as @var{u}.\n\
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144 If @var{u} is a scalar, the results are the same size as @var{m}.\n\
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145 If @var{u} is a column vector and @var{m} is a row vector, the\n\
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146 results are matrices with @code{length (@var{u})} rows and\n\
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147 @code{length (@var{m})} columns. Otherwise, @var{u} and\n\
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148 @var{m} must conform and the results will be the same size.\n\
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149 \n\
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150 The value of @var{u} may be complex.\n\
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151 The value of @var{m} must be 0 <= m <= 1.\n\
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152 \n\
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153 If requested, @var{err} contains the following status information\n\
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154 and is the same size as the result.\n\
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155 \n\
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156 @enumerate 0\n\
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157 @item\n\
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158 Normal return.\n\
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159 @item\n\
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160 Error---no computation, algorithm termination condition not met,\n\
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161 return @code{NaN}.\n\
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162 @end enumerate\n\
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163 Ref: Abramowitz, Milton and Stegun, Irene A\n\
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164 Handbook of Mathematical Functions, Dover, 1965\n\
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165 Chapter 16 (Sections 16.4, 16.13 and 16.15)\n\
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166 @seealso{ellipke}\n\
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167 @end deftypefn")
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168 {
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169 octave_value_list retval;
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170
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171 int nargin = args.length ();
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172
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173 if (nargin != 2 )
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174 {
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175 print_usage ();
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176 return retval;
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177 }
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178
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179 octave_value u_arg = args(0);
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180 octave_value m_arg = args(1);
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181
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182 if (m_arg.is_scalar_type ())
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183 {
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184 double m = args(1).double_value ();
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185
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186 if (error_state)
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187 {
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188 gripe_ellipj_arg ("second");
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189 return retval;
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190 }
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191
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192 if (u_arg.is_scalar_type ())
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193 {
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194 if (u_arg.is_real_type ())
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195 { // u real
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196 double u = args(0).double_value ();
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197
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198 if (error_state)
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199 {
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200 gripe_ellipj_arg ("first");
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201 return retval;
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202 }
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203 double sn, cn, dn;
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204 double err = 0;
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205
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206 sncndn (u, m, sn, cn, dn, err);
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207 retval (0) = sn;
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208 retval (1) = cn;
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209 retval (2) = dn;
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210 if (nargout > 3) retval(3) = err;
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211 }
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212 else
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213 { // u complex
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214 Complex u = u_arg.complex_value ();
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215
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216 if (error_state)
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217 {
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218 gripe_ellipj_arg ("second");
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219 return retval;
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220 }
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221
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222 Complex sn, cn, dn;
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223 double err;
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224
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225 sncndn (u, m, sn, cn, dn, err);
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226
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227 retval (0) = sn;
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228 retval (1) = cn;
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229 retval (2) = dn;
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230 if (nargout > 3) retval(3) = err;
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231 }
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232 }
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233 else
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234 { /* u is matrix ( m is scalar ) */
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235 ComplexMatrix u = u_arg.complex_matrix_value ();
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236
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237 if (error_state)
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238 {
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239 gripe_ellipj_arg ("first");
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240 return retval;
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241 }
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242
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243 octave_idx_type nr = u.rows ();
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244 octave_idx_type nc = u.cols ();
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245
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246 ComplexMatrix sn (nr, nc), cn (nr, nc), dn (nr, nc);
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247 Matrix err (nr, nc);
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248
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249 for (octave_idx_type j = 0; j < nc; j++)
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250 for (octave_idx_type i = 0; i < nr; i++)
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251 sncndn (u(i,j), m, sn(i,j), cn(i,j), dn(i,j), err(i,j));
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252
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253 retval (0) = sn;
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254 retval (1) = cn;
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255 retval (2) = dn;
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parents: 16585
diff changeset
256 if (nargout > 3) retval(3) = err;
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
257 }
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
258 }
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
259 else
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
260 {
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
261 Matrix m = args(1).matrix_value ();
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
262
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
263 if (error_state)
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
264 {
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
265 gripe_ellipj_arg ("second");
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
266 return retval;
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
267 }
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
268
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
269 octave_idx_type mr = m.rows ();
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
270 octave_idx_type mc = m.cols ();
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
271
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
272 if (u_arg.is_scalar_type ())
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
273 { /* u is scalar */
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
274 octave_idx_type nr = m.rows ();
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
275 octave_idx_type nc = m.cols ();
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
276 Matrix err (nr, nc);
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
277
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
278 if (u_arg.is_real_type ())
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
279 {
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
280 double u = u_arg.double_value ();
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
281
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
282 if (error_state)
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
283 {
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
284 gripe_ellipj_arg ("first");
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
285 return retval;
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
286 }
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
287
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
288 Matrix sn (nr, nc), cn (nr, nc), dn (nr, nc);
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
289 for (octave_idx_type j = 0; j < nc; j++)
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
290 for (octave_idx_type i = 0; i < nr; i++)
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
291 sncndn (u, m(i,j), sn(i,j), cn(i,j), dn(i,j), err(i,j));
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
292
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
293 retval (0) = sn;
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
294 retval (1) = cn;
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
295 retval (2) = dn;
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
296 if (nargout > 3) retval(3) = err;
16584
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
297 }
16586
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
298 else
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
299 {
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
300 Complex u = u_arg.complex_value ();
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
301 if (error_state)
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
302 {
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
303 gripe_ellipj_arg ("first");
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
304 return retval;
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
305 }
16584
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
306
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
307 ComplexMatrix sn (nr, nc), cn (nr, nc), dn (nr, nc);
16586
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
308 for (octave_idx_type j = 0; j < nc; j++)
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
309 for (octave_idx_type i = 0; i < nr; i++)
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
310 sncndn (u, m(i,j), sn(i,j), cn(i,j), dn(i,j), err(i,j));
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
311 retval (0) = sn;
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
312 retval (1) = cn;
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
313 retval (2) = dn;
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
314 if (nargout > 3) retval(3) = err;
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
315 }
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
316 }
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
317 else
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
318 { // u is matrix (m is matrix)
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
319 if (u_arg.is_real_type ())
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
320 { // u real matrix
16584
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
321
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
322 Matrix u = u_arg.matrix_value ();
16586
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
323 if (error_state)
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
324 {
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
325 gripe_ellipj_arg ("first ");
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
326 return retval;
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
327 }
16584
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
328
16586
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
329 octave_idx_type ur = u.rows ();
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
330 octave_idx_type uc = u.cols ();
16584
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
331
16586
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
332 if (mr == 1 && uc == 1)
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
333 { // u column, m row
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
334 RowVector rm = m.row (0);
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
335 ColumnVector cu = u.column (0);
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
336
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
337 Matrix sn (ur, mc), cn (ur, mc), dn (ur, mc);
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
338 Matrix err (ur,mc);
16584
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
339
16586
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
340 for (octave_idx_type j = 0; j < mc; j++)
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
341 for (octave_idx_type i = 0; i < ur; i++)
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
342 sncndn (cu(i), rm(j), sn(i,j), cn(i,j), dn(i,j), err(i,j));
16584
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
343
16586
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
344 retval (0) = sn;
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
345 retval (1) = cn;
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
346 retval (2) = dn;
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
347 if (nargout > 3) retval(3) = err;
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
348 }
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
349 else if (ur == mr && uc == mc)
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
350 {
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
351 Matrix sn (ur, mc), cn (ur, mc), dn (ur, mc);
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
352 Matrix err (ur,mc);
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
353
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
354 for (octave_idx_type j = 0; j < uc; j++)
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
355 for (octave_idx_type i = 0; i < ur; i++)
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
356 sncndn (u(i,j), m(i,j), sn(i,j), cn(i,j), dn(i,j), err(i,j));
16584
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
357
16586
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
358 retval (0) = sn;
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
359 retval (1) = cn;
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
360 retval (2) = dn;
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
361 if (nargout > 3) retval(3) = err;
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
362 }
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
363 else
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
364 error ("u m invalid");
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
365 }
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
366 else
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
367 { // u complex matrix
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
368 ComplexMatrix u = u_arg.complex_matrix_value ();
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
369 if (error_state)
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
370 {
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
371 gripe_ellipj_arg ("second");
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
372 return retval;
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
373 }
16584
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
374
16586
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
375 octave_idx_type ur = u.rows ();
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
376 octave_idx_type uc = u.cols ();
16584
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
377
16586
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
378 if (mr == 1 && uc == 1)
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
379 {
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
380 RowVector rm = m.row (0);
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
381 ComplexColumnVector cu = u.column (0);
16584
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
382
16586
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
383 ComplexMatrix sn (ur, mc), cn (ur, mc), dn (ur, mc);
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
384 Matrix err (ur,mc);
16584
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
385
16586
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
386 for (octave_idx_type j = 0; j < mc; j++)
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
387 for (octave_idx_type i = 0; i < ur; i++)
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
388 sncndn (cu(i), rm(j), sn(i,j), cn(i,j), dn(i,j), err(i,j));
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
389
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
390 retval (0) = sn;
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
391 retval (1) = cn;
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
392 retval (2) = dn;
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
393 if (nargout > 3) retval(3) = err;
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
394 }
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
395 else if (ur == mr && uc == mc)
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
396 {
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
397 ComplexMatrix sn (ur, mc), cn (ur, mc), dn (ur, mc);
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
398 Matrix err (ur,mc);
16584
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
399
16586
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
400 for (octave_idx_type j = 0; j < uc; j++)
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
401 for (octave_idx_type i = 0; i < ur; i++)
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
402 sncndn (u(i,j), m(i,j), sn(i,j), cn(i,j), dn(i,j), err(i,j));
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
403
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
404 retval (0) = sn;
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
405 retval (1) = cn;
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
406 retval (2) = dn;
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
407 if (nargout > 3) retval(3) = err;
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
408 }
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
409 else
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
410 error ("u m invalid");
16584
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
411 }
16586
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
412 }
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
413 } // m matrix
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
414
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
415 return retval;
16584
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
416 }
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
417
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
418 /*
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
419 ## demos taken from inst/ellipj.m
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
420
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
421 %!demo
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
422 %! N = 150;
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
423 %! % m = [1-logspace(0,log(eps),N-1), 1]; ## m near 1
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
424 %! % m = [0, logspace(log(eps),0,N-1)]; ## m near 0
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
425 %! m = linspace(0,1,N); ## m equally spaced
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
426 %! u = linspace(-20,20,N);
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
427 %! M = ones(length(u),1) * m;
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
428 %! U = u' * ones(1, length(m));
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
429 %! [sn, cn, dn] = ellipj(U,M);
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
430 %!
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
431 %! %% Plotting
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
432 %! c = colormap(hot(64));
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
433 %! data = {sn,cn,dn};
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
434 %! dname = {"sn","cn","dn"};
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
435 %! for i=1:3
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
436 %! subplot(1,3,i);
16585
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
437 %! data{i}(data{i} > 1) = 1;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
438 %! data{i}(data{i} < -1) = -1;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
439 %! image(m,u,32*data{i}+32);
16584
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
440 %! title(dname{i});
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
441 %! end
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
442 %! colormap(c);
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
443
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
444 %!demo
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
445 %! N = 200;
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
446 %! % m = [1-logspace(0,log(eps),N-1), 1]; ## m near 1
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
447 %! % m = [0, logspace(log(eps),0,N-1)]; ## m near 0
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
448 %! m = linspace(0,1,N); ## m equally spaced
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
449 %! u = linspace(0,20,5);
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
450 %! M = ones(length(u),1) * m;
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
451 %! U = u' * ones(1, length(m));
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
452 %! [sn, cn, dn] = ellipj(U,M);
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
453 %!
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
454 %! %% Plotting
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
455 %! data = {sn,cn,dn};
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
456 %! dname = {"sn","cn","dn"};
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
457 %! for i=1:3
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
458 %! subplot(1,3,i);
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
459 %! plot(m, data{i});
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
460 %! title(dname{i});
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
461 %! grid on;
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
462 %! end
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
463 */
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
464
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
465 /*
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
466 ## tests taken from inst/test_sncndn.m
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
467
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
468 %!test
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
469 %! k = (tan(pi/8.))^2; m = k*k;
16586
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents: 16585
diff changeset
470 %! SN = [
16584
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
471 %! -1. + I * 0. , -0.8392965923 + 0. * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
472 %! -1. + I * 0.2 , -0.8559363407 + 0.108250955 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
473 %! -1. + I * 0.4 , -0.906529758 + 0.2204040232 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
474 %! -1. + I * 0.6 , -0.9931306727 + 0.3403783409 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
475 %! -1. + I * 0.8 , -1.119268095 + 0.4720784944 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
476 %! -1. + I * 1. , -1.29010951 + 0.6192468708 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
477 %! -1. + I * 1.2 , -1.512691987 + 0.7850890595 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
478 %! -1. + I * 1.4 , -1.796200374 + 0.9714821804 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
479 %! -1. + I * 1.6 , -2.152201882 + 1.177446413 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
480 %! -1. + I * 1.8 , -2.594547417 + 1.396378892 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
481 %! -1. + I * 2. , -3.138145339 + 1.611394819 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
482 %! -0.8 + I * 0. , -0.7158157937 + 0. * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
483 %! -0.8 + I * 0.2 , -0.7301746722 + 0.1394690862 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
484 %! -0.8 + I * 0.4 , -0.7738940898 + 0.2841710966 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
485 %! -0.8 + I * 0.6 , -0.8489542135 + 0.4394411376 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
486 %! -0.8 + I * 0.8 , -0.9588386397 + 0.6107824358 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
487 %! -0.8 + I * 1. , -1.108848724 + 0.8038415767 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
488 %! -0.8 + I * 1.2 , -1.306629972 + 1.024193359 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
489 %! -0.8 + I * 1.4 , -1.563010199 + 1.276740951 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
490 %! -0.8 + I * 1.6 , -1.893274688 + 1.564345558 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
491 %! -0.8 + I * 1.8 , -2.318944084 + 1.88491973 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
492 %! -0.8 + I * 2. , -2.869716809 + 2.225506523 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
493 %! -0.6 + I * 0. , -0.5638287208 + 0. * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
494 %! -0.6 + I * 0.2 , -0.5752723012 + 0.1654722474 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
495 %! -0.6 + I * 0.4 , -0.610164314 + 0.3374004736 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
496 %! -0.6 + I * 0.6 , -0.6702507087 + 0.5224614298 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
497 %! -0.6 + I * 0.8 , -0.7586657365 + 0.7277663879 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
498 %! -0.6 + I * 1. , -0.8803349115 + 0.9610513652 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
499 %! -0.6 + I * 1.2 , -1.042696526 + 1.230800819 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
500 %! -0.6 + I * 1.4 , -1.256964505 + 1.546195843 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
501 %! -0.6 + I * 1.6 , -1.540333527 + 1.916612621 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
502 %! -0.6 + I * 1.8 , -1.919816065 + 2.349972151 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
503 %! -0.6 + I * 2. , -2.438761841 + 2.848129496 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
504 %! -0.4 + I * 0. , -0.3891382858 + 0. * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
505 %! -0.4 + I * 0.2 , -0.3971152026 + 0.1850563793 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
506 %! -0.4 + I * 0.4 , -0.4214662882 + 0.3775700801 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
507 %! -0.4 + I * 0.6 , -0.4635087491 + 0.5853434119 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
508 %! -0.4 + I * 0.8 , -0.5256432877 + 0.8168992398 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
509 %! -0.4 + I * 1. , -0.611733177 + 1.081923504 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
510 %! -0.4 + I * 1.2 , -0.7278102331 + 1.391822501 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
511 %! -0.4 + I * 1.4 , -0.8833807998 + 1.760456461 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
512 %! -0.4 + I * 1.6 , -1.093891878 + 2.205107766 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
513 %! -0.4 + I * 1.8 , -1.385545188 + 2.747638761 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
514 %! -0.4 + I * 2. , -1.805081271 + 3.41525351 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
515 %! -0.2 + I * 0. , -0.1986311721 + 0. * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
516 %! -0.2 + I * 0.2 , -0.2027299916 + 0.1972398665 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
517 %! -0.2 + I * 0.4 , -0.2152524522 + 0.402598347 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
518 %! -0.2 + I * 0.6 , -0.2369100139 + 0.6246336356 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
519 %! -0.2 + I * 0.8 , -0.2690115146 + 0.8728455227 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
520 %! -0.2 + I * 1. , -0.3136938773 + 1.158323088 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
521 %! -0.2 + I * 1.2 , -0.3743615191 + 1.494672508 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
522 %! -0.2 + I * 1.4 , -0.4565255082 + 1.899466033 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
523 %! -0.2 + I * 1.6 , -0.5694611346 + 2.39667232 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
524 %! -0.2 + I * 1.8 , -0.7296612675 + 3.020990664 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
525 %! -0.2 + I * 2. , -0.9685726188 + 3.826022536 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
526 %! 0. + I * 0. , 0. + 0. * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
527 %! 0. + I * 0.2 , 0. + 0.201376364 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
528 %! 0. + I * 0.4 , 0. + 0.4111029248 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
529 %! 0. + I * 0.6 , 0. + 0.6380048435 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
530 %! 0. + I * 0.8 , 0. + 0.8919321473 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
531 %! 0. + I * 1. , 0. + 1.184486615 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
532 %! 0. + I * 1.2 , 0. + 1.530096023 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
533 %! 0. + I * 1.4 , 0. + 1.947754612 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
534 %! 0. + I * 1.6 , 0. + 2.464074356 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
535 %! 0. + I * 1.8 , 0. + 3.119049475 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
536 %! 0. + I * 2. , 0. + 3.97786237 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
537 %! 0.2 + I * 0. , 0.1986311721 + 0. * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
538 %! 0.2 + I * 0.2 , 0.2027299916 + 0.1972398665 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
539 %! 0.2 + I * 0.4 , 0.2152524522 + 0.402598347 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
540 %! 0.2 + I * 0.6 , 0.2369100139 + 0.6246336356 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
541 %! 0.2 + I * 0.8 , 0.2690115146 + 0.8728455227 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
542 %! 0.2 + I * 1. , 0.3136938773 + 1.158323088 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
543 %! 0.2 + I * 1.2 , 0.3743615191 + 1.494672508 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
544 %! 0.2 + I * 1.4 , 0.4565255082 + 1.899466033 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
545 %! 0.2 + I * 1.6 , 0.5694611346 + 2.39667232 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
546 %! 0.2 + I * 1.8 , 0.7296612675 + 3.020990664 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
547 %! 0.2 + I * 2. , 0.9685726188 + 3.826022536 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
548 %! 0.4 + I * 0. , 0.3891382858 + 0. * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
549 %! 0.4 + I * 0.2 , 0.3971152026 + 0.1850563793 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
550 %! 0.4 + I * 0.4 , 0.4214662882 + 0.3775700801 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
551 %! 0.4 + I * 0.6 , 0.4635087491 + 0.5853434119 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
552 %! 0.4 + I * 0.8 , 0.5256432877 + 0.8168992398 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
553 %! 0.4 + I * 1. , 0.611733177 + 1.081923504 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
554 %! 0.4 + I * 1.2 , 0.7278102331 + 1.391822501 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
555 %! 0.4 + I * 1.4 , 0.8833807998 + 1.760456461 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
556 %! 0.4 + I * 1.6 , 1.093891878 + 2.205107766 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
557 %! 0.4 + I * 1.8 , 1.385545188 + 2.747638761 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
558 %! 0.4 + I * 2. , 1.805081271 + 3.41525351 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
559 %! 0.6 + I * 0. , 0.5638287208 + 0. * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
560 %! 0.6 + I * 0.2 , 0.5752723012 + 0.1654722474 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
561 %! 0.6 + I * 0.4 , 0.610164314 + 0.3374004736 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
562 %! 0.6 + I * 0.6 , 0.6702507087 + 0.5224614298 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
563 %! 0.6 + I * 0.8 , 0.7586657365 + 0.7277663879 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
564 %! 0.6 + I * 1. , 0.8803349115 + 0.9610513652 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
565 %! 0.6 + I * 1.2 , 1.042696526 + 1.230800819 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
566 %! 0.6 + I * 1.4 , 1.256964505 + 1.546195843 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
567 %! 0.6 + I * 1.6 , 1.540333527 + 1.916612621 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
568 %! 0.6 + I * 1.8 , 1.919816065 + 2.349972151 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
569 %! 0.6 + I * 2. , 2.438761841 + 2.848129496 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
570 %! 0.8 + I * 0. , 0.7158157937 + 0. * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
571 %! 0.8 + I * 0.2 , 0.7301746722 + 0.1394690862 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
572 %! 0.8 + I * 0.4 , 0.7738940898 + 0.2841710966 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
573 %! 0.8 + I * 0.6 , 0.8489542135 + 0.4394411376 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
574 %! 0.8 + I * 0.8 , 0.9588386397 + 0.6107824358 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
575 %! 0.8 + I * 1. , 1.108848724 + 0.8038415767 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
576 %! 0.8 + I * 1.2 , 1.306629972 + 1.024193359 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
577 %! 0.8 + I * 1.4 , 1.563010199 + 1.276740951 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
578 %! 0.8 + I * 1.6 , 1.893274688 + 1.564345558 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
579 %! 0.8 + I * 1.8 , 2.318944084 + 1.88491973 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
580 %! 0.8 + I * 2. , 2.869716809 + 2.225506523 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
581 %! 1. + I * 0. , 0.8392965923 + 0. * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
582 %! 1. + I * 0.2 , 0.8559363407 + 0.108250955 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
583 %! 1. + I * 0.4 , 0.906529758 + 0.2204040232 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
584 %! 1. + I * 0.6 , 0.9931306727 + 0.3403783409 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
585 %! 1. + I * 0.8 , 1.119268095 + 0.4720784944 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
586 %! 1. + I * 1. , 1.29010951 + 0.6192468708 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
587 %! 1. + I * 1.2 , 1.512691987 + 0.7850890595 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
588 %! 1. + I * 1.4 , 1.796200374 + 0.9714821804 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
589 %! 1. + I * 1.6 , 2.152201882 + 1.177446413 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
590 %! 1. + I * 1.8 , 2.594547417 + 1.396378892 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
591 %! 1. + I * 2. , 3.138145339 + 1.611394819 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
592 %! ];
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
593 %! CN = [
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
594 %! -1. + I * 0. , 0.5436738271 + 0. * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
595 %! -1. + I * 0.2 , 0.5541219664 + 0.1672121517 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
596 %! -1. + I * 0.4 , 0.5857703552 + 0.3410940893 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
597 %! -1. + I * 0.6 , 0.6395034233 + 0.5285979063 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
598 %! -1. + I * 0.8 , 0.716688504 + 0.7372552987 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
599 %! -1. + I * 1. , 0.8189576795 + 0.9755037374 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
600 %! -1. + I * 1.2 , 0.9477661951 + 1.253049471 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
601 %! -1. + I * 1.4 , 1.103540657 + 1.581252712 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
602 %! -1. + I * 1.6 , 1.284098214 + 1.973449038 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
603 %! -1. + I * 1.8 , 1.481835651 + 2.4449211 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
604 %! -1. + I * 2. , 1.679032464 + 3.011729224 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
605 %! -0.8 + I * 0. , 0.6982891589 + 0. * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
606 %! -0.8 + I * 0.2 , 0.71187169 + 0.1430549855 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
607 %! -0.8 + I * 0.4 , 0.7530744458 + 0.2920273465 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
608 %! -0.8 + I * 0.6 , 0.8232501212 + 0.4531616768 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
609 %! -0.8 + I * 0.8 , 0.9245978896 + 0.6334016187 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
610 %! -0.8 + I * 1. , 1.060030206 + 0.8408616109 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
611 %! -0.8 + I * 1.2 , 1.232861756 + 1.085475913 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
612 %! -0.8 + I * 1.4 , 1.446126965 + 1.379933558 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
613 %! -0.8 + I * 1.6 , 1.701139468 + 1.741030588 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
614 %! -0.8 + I * 1.8 , 1.994526268 + 2.191509596 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
615 %! -0.8 + I * 2. , 2.312257188 + 2.762051518 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
616 %! -0.6 + I * 0. , 0.8258917445 + 0. * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
617 %! -0.6 + I * 0.2 , 0.842151698 + 0.1130337928 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
618 %! -0.6 + I * 0.4 , 0.8915487431 + 0.2309124769 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
619 %! -0.6 + I * 0.6 , 0.975948103 + 0.3588102098 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
620 %! -0.6 + I * 0.8 , 1.098499209 + 0.5026234141 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
621 %! -0.6 + I * 1. , 1.263676101 + 0.6695125973 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
622 %! -0.6 + I * 1.2 , 1.477275851 + 0.8687285705 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
623 %! -0.6 + I * 1.4 , 1.746262523 + 1.112955966 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
624 %! -0.6 + I * 1.6 , 2.078179075 + 1.420581466 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
625 %! -0.6 + I * 1.8 , 2.479425208 + 1.819580713 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
626 %! -0.6 + I * 2. , 2.950586798 + 2.354077344 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
627 %! -0.4 + I * 0. , 0.9211793498 + 0. * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
628 %! -0.4 + I * 0.2 , 0.9395019377 + 0.07822091534 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
629 %! -0.4 + I * 0.4 , 0.9952345231 + 0.1598950363 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
630 %! -0.4 + I * 0.6 , 1.090715991 + 0.2487465067 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
631 %! -0.4 + I * 0.8 , 1.229998843 + 0.34910407 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
632 %! -0.4 + I * 1. , 1.419103868 + 0.4663848201 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
633 %! -0.4 + I * 1.2 , 1.666426377 + 0.607877235 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
634 %! -0.4 + I * 1.4 , 1.983347336 + 0.7841054404 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
635 %! -0.4 + I * 1.6 , 2.385101684 + 1.01134031 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
636 %! -0.4 + I * 1.8 , 2.89185416 + 1.316448705 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
637 %! -0.4 + I * 2. , 3.529393374 + 1.74670531 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
638 %! -0.2 + I * 0. , 0.9800743122 + 0. * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
639 %! -0.2 + I * 0.2 , 0.9997019476 + 0.03999835809 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
640 %! -0.2 + I * 0.4 , 1.059453907 + 0.08179712295 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
641 %! -0.2 + I * 0.6 , 1.16200643 + 0.1273503824 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
642 %! -0.2 + I * 0.8 , 1.312066413 + 0.1789585449 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
643 %! -0.2 + I * 1. , 1.516804331 + 0.2395555269 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
644 %! -0.2 + I * 1.2 , 1.786613221 + 0.313189147 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
645 %! -0.2 + I * 1.4 , 2.136422971 + 0.405890925 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
646 %! -0.2 + I * 1.6 , 2.588021972 + 0.527357091 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
647 %! -0.2 + I * 1.8 , 3.174302819 + 0.6944201617 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
648 %! -0.2 + I * 2. , 3.947361147 + 0.9387994989 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
649 %! 0. + I * 0. , 1. + 0. * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
650 %! 0. + I * 0.2 , 1.020074723 + 0. * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
651 %! 0. + I * 0.4 , 1.08120563 + 0. * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
652 %! 0. + I * 0.6 , 1.18619146 + 0. * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
653 %! 0. + I * 0.8 , 1.339978715 + 0. * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
654 %! 0. + I * 1. , 1.550164037 + 0. * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
655 %! 0. + I * 1.2 , 1.827893279 + 0. * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
656 %! 0. + I * 1.4 , 2.189462954 + 0. * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
657 %! 0. + I * 1.6 , 2.659259752 + 0. * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
658 %! 0. + I * 1.8 , 3.275434266 + 0. * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
659 %! 0. + I * 2. , 4.101632484 + 0. * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
660 %! 0.2 + I * 0. , 0.9800743122 + 0. * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
661 %! 0.2 + I * 0.2 , 0.9997019476 - 0.03999835809 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
662 %! 0.2 + I * 0.4 , 1.059453907 - 0.08179712295 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
663 %! 0.2 + I * 0.6 , 1.16200643 - 0.1273503824 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
664 %! 0.2 + I * 0.8 , 1.312066413 - 0.1789585449 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
665 %! 0.2 + I * 1. , 1.516804331 - 0.2395555269 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
666 %! 0.2 + I * 1.2 , 1.786613221 - 0.313189147 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
667 %! 0.2 + I * 1.4 , 2.136422971 - 0.405890925 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
668 %! 0.2 + I * 1.6 , 2.588021972 - 0.527357091 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
669 %! 0.2 + I * 1.8 , 3.174302819 - 0.6944201617 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
670 %! 0.2 + I * 2. , 3.947361147 - 0.9387994989 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
671 %! 0.4 + I * 0. , 0.9211793498 + 0. * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
672 %! 0.4 + I * 0.2 , 0.9395019377 - 0.07822091534 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
673 %! 0.4 + I * 0.4 , 0.9952345231 - 0.1598950363 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
674 %! 0.4 + I * 0.6 , 1.090715991 - 0.2487465067 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
675 %! 0.4 + I * 0.8 , 1.229998843 - 0.34910407 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
676 %! 0.4 + I * 1. , 1.419103868 - 0.4663848201 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
677 %! 0.4 + I * 1.2 , 1.666426377 - 0.607877235 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
678 %! 0.4 + I * 1.4 , 1.983347336 - 0.7841054404 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
679 %! 0.4 + I * 1.6 , 2.385101684 - 1.01134031 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
680 %! 0.4 + I * 1.8 , 2.89185416 - 1.316448705 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
681 %! 0.4 + I * 2. , 3.529393374 - 1.74670531 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
682 %! 0.6 + I * 0. , 0.8258917445 + 0. * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
683 %! 0.6 + I * 0.2 , 0.842151698 - 0.1130337928 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
684 %! 0.6 + I * 0.4 , 0.8915487431 - 0.2309124769 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
685 %! 0.6 + I * 0.6 , 0.975948103 - 0.3588102098 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
686 %! 0.6 + I * 0.8 , 1.098499209 - 0.5026234141 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
687 %! 0.6 + I * 1. , 1.263676101 - 0.6695125973 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
688 %! 0.6 + I * 1.2 , 1.477275851 - 0.8687285705 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
689 %! 0.6 + I * 1.4 , 1.746262523 - 1.112955966 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
690 %! 0.6 + I * 1.6 , 2.078179075 - 1.420581466 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
691 %! 0.6 + I * 1.8 , 2.479425208 - 1.819580713 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
692 %! 0.6 + I * 2. , 2.950586798 - 2.354077344 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
693 %! 0.8 + I * 0. , 0.6982891589 + 0. * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
694 %! 0.8 + I * 0.2 , 0.71187169 - 0.1430549855 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
695 %! 0.8 + I * 0.4 , 0.7530744458 - 0.2920273465 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
696 %! 0.8 + I * 0.6 , 0.8232501212 - 0.4531616768 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
697 %! 0.8 + I * 0.8 , 0.9245978896 - 0.6334016187 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
698 %! 0.8 + I * 1. , 1.060030206 - 0.8408616109 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
699 %! 0.8 + I * 1.2 , 1.232861756 - 1.085475913 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
700 %! 0.8 + I * 1.4 , 1.446126965 - 1.379933558 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
701 %! 0.8 + I * 1.6 , 1.701139468 - 1.741030588 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
702 %! 0.8 + I * 1.8 , 1.994526268 - 2.191509596 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
703 %! 0.8 + I * 2. , 2.312257188 - 2.762051518 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
704 %! 1. + I * 0. , 0.5436738271 + 0. * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
705 %! 1. + I * 0.2 , 0.5541219664 - 0.1672121517 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
706 %! 1. + I * 0.4 , 0.5857703552 - 0.3410940893 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
707 %! 1. + I * 0.6 , 0.6395034233 - 0.5285979063 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
708 %! 1. + I * 0.8 , 0.716688504 - 0.7372552987 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
709 %! 1. + I * 1. , 0.8189576795 - 0.9755037374 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
710 %! 1. + I * 1.2 , 0.9477661951 - 1.253049471 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
711 %! 1. + I * 1.4 , 1.103540657 - 1.581252712 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
712 %! 1. + I * 1.6 , 1.284098214 - 1.973449038 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
713 %! 1. + I * 1.8 , 1.481835651 - 2.4449211 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
714 %! 1. + I * 2. , 1.679032464 - 3.011729224 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
715 %! ];
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
716 %! DN = [
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
717 %! -1. + I * 0. , 0.9895776106 + 0. * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
718 %! -1. + I * 0.2 , 0.9893361555 + 0.002756935338 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
719 %! -1. + I * 0.4 , 0.9885716856 + 0.005949639805 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
720 %! -1. + I * 0.6 , 0.9871564855 + 0.01008044183 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
721 %! -1. + I * 0.8 , 0.9848512162 + 0.01579337596 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
722 %! -1. + I * 1. , 0.9812582484 + 0.02396648455 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
723 %! -1. + I * 1.2 , 0.9757399152 + 0.0358288294 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
724 %! -1. + I * 1.4 , 0.9672786056 + 0.0531049859 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
725 %! -1. + I * 1.6 , 0.954237868 + 0.0781744383 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
726 %! -1. + I * 1.8 , 0.933957524 + 0.1141918269 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
727 %! -1. + I * 2. , 0.9020917489 + 0.1650142936 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
728 %! -0.8 + I * 0. , 0.992429635 + 0. * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
729 %! -0.8 + I * 0.2 , 0.9924147861 + 0.003020708044 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
730 %! -0.8 + I * 0.4 , 0.99236555 + 0.00652359532 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
731 %! -0.8 + I * 0.6 , 0.9922655715 + 0.0110676219 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
732 %! -0.8 + I * 0.8 , 0.9920785856 + 0.01737733806 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
733 %! -0.8 + I * 1. , 0.9917291795 + 0.02645738598 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
734 %! -0.8 + I * 1.2 , 0.9910606387 + 0.03974949378 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
735 %! -0.8 + I * 1.4 , 0.9897435004 + 0.05935252515 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
736 %! -0.8 + I * 1.6 , 0.987077644 + 0.08832675281 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
737 %! -0.8 + I * 1.8 , 0.9815667458 + 0.1310872821 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
738 %! -0.8 + I * 2. , 0.970020127 + 0.1938136793 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
739 %! -0.6 + I * 0. , 0.9953099088 + 0. * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
740 %! -0.6 + I * 0.2 , 0.995526009 + 0.002814772354 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
741 %! -0.6 + I * 0.4 , 0.9962071136 + 0.006083312292 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
742 %! -0.6 + I * 0.6 , 0.9974557125 + 0.01033463525 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
743 %! -0.6 + I * 0.8 , 0.9994560563 + 0.01626207722 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
744 %! -0.6 + I * 1. , 1.00249312 + 0.02484336286 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
745 %! -0.6 + I * 1.2 , 1.006973922 + 0.0375167093 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
746 %! -0.6 + I * 1.4 , 1.013436509 + 0.05645315628 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
747 %! -0.6 + I * 1.6 , 1.022504295 + 0.08499262247 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
748 %! -0.6 + I * 1.8 , 1.034670023 + 0.1283564595 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
749 %! -0.6 + I * 2. , 1.049599899 + 0.194806122 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
750 %! -0.4 + I * 0. , 0.9977686897 + 0. * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
751 %! -0.4 + I * 0.2 , 0.9981836165 + 0.002167241934 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
752 %! -0.4 + I * 0.4 , 0.9994946045 + 0.004686808612 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
753 %! -0.4 + I * 0.6 , 1.001910789 + 0.00797144174 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
754 %! -0.4 + I * 0.8 , 1.005817375 + 0.01256717724 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
755 %! -0.4 + I * 1. , 1.011836374 + 0.01925509038 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
756 %! -0.4 + I * 1.2 , 1.020923572 + 0.02920828367 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
757 %! -0.4 + I * 1.4 , 1.034513743 + 0.04425213602 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
758 %! -0.4 + I * 1.6 , 1.054725746 + 0.06732276244 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
759 %! -0.4 + I * 1.8 , 1.08462027 + 0.1033236812 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
760 %! -0.4 + I * 2. , 1.128407402 + 0.1608240664 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
761 %! -0.2 + I * 0. , 0.9994191176 + 0. * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
762 %! -0.2 + I * 0.2 , 0.9999683719 + 0.001177128019 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
763 %! -0.2 + I * 0.4 , 1.001705496 + 0.00254669712 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
764 %! -0.2 + I * 0.6 , 1.004913944 + 0.004334880912 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
765 %! -0.2 + I * 0.8 , 1.010120575 + 0.006842775622 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
766 %! -0.2 + I * 1. , 1.018189543 + 0.01050520136 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
767 %! -0.2 + I * 1.2 , 1.030482479 + 0.01598431001 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
768 %! -0.2 + I * 1.4 , 1.049126108 + 0.02433134655 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
769 %! -0.2 + I * 1.6 , 1.077466003 + 0.0372877718 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
770 %! -0.2 + I * 1.8 , 1.120863308 + 0.05789156398 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
771 %! -0.2 + I * 2. , 1.188162088 + 0.09181238708 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
772 %! 0. + I * 0. , 1. + 0. * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
773 %! 0. + I * 0.2 , 1.000596698 + 0. * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
774 %! 0. + I * 0.4 , 1.002484444 + 0. * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
775 %! 0. + I * 0.6 , 1.005973379 + 0. * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
776 %! 0. + I * 0.8 , 1.011641536 + 0. * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
777 %! 0. + I * 1. , 1.020441432 + 0. * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
778 %! 0. + I * 1.2 , 1.033885057 + 0. * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
779 %! 0. + I * 1.4 , 1.054361188 + 0. * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
780 %! 0. + I * 1.6 , 1.085694733 + 0. * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
781 %! 0. + I * 1.8 , 1.134186672 + 0. * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
782 %! 0. + I * 2. , 1.210701071 + 0. * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
783 %! 0.2 + I * 0. , 0.9994191176 + 0. * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
784 %! 0.2 + I * 0.2 , 0.9999683719 - 0.001177128019 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
785 %! 0.2 + I * 0.4 , 1.001705496 - 0.00254669712 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
786 %! 0.2 + I * 0.6 , 1.004913944 - 0.004334880912 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
787 %! 0.2 + I * 0.8 , 1.010120575 - 0.006842775622 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
788 %! 0.2 + I * 1. , 1.018189543 - 0.01050520136 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
789 %! 0.2 + I * 1.2 , 1.030482479 - 0.01598431001 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
790 %! 0.2 + I * 1.4 , 1.049126108 - 0.02433134655 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
791 %! 0.2 + I * 1.6 , 1.077466003 - 0.0372877718 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
792 %! 0.2 + I * 1.8 , 1.120863308 - 0.05789156398 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
793 %! 0.2 + I * 2. , 1.188162088 - 0.09181238708 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
794 %! 0.4 + I * 0. , 0.9977686897 + 0. * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
795 %! 0.4 + I * 0.2 , 0.9981836165 - 0.002167241934 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
796 %! 0.4 + I * 0.4 , 0.9994946045 - 0.004686808612 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
797 %! 0.4 + I * 0.6 , 1.001910789 - 0.00797144174 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
798 %! 0.4 + I * 0.8 , 1.005817375 - 0.01256717724 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
799 %! 0.4 + I * 1. , 1.011836374 - 0.01925509038 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
800 %! 0.4 + I * 1.2 , 1.020923572 - 0.02920828367 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
801 %! 0.4 + I * 1.4 , 1.034513743 - 0.04425213602 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
802 %! 0.4 + I * 1.6 , 1.054725746 - 0.06732276244 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
803 %! 0.4 + I * 1.8 , 1.08462027 - 0.1033236812 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
804 %! 0.4 + I * 2. , 1.128407402 - 0.1608240664 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
805 %! 0.6 + I * 0. , 0.9953099088 + 0. * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
806 %! 0.6 + I * 0.2 , 0.995526009 - 0.002814772354 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
807 %! 0.6 + I * 0.4 , 0.9962071136 - 0.006083312292 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
808 %! 0.6 + I * 0.6 , 0.9974557125 - 0.01033463525 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
809 %! 0.6 + I * 0.8 , 0.9994560563 - 0.01626207722 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
810 %! 0.6 + I * 1. , 1.00249312 - 0.02484336286 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
811 %! 0.6 + I * 1.2 , 1.006973922 - 0.0375167093 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
812 %! 0.6 + I * 1.4 , 1.013436509 - 0.05645315628 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
813 %! 0.6 + I * 1.6 , 1.022504295 - 0.08499262247 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
814 %! 0.6 + I * 1.8 , 1.034670023 - 0.1283564595 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
815 %! 0.6 + I * 2. , 1.049599899 - 0.194806122 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
816 %! 0.8 + I * 0. , 0.992429635 + 0. * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
817 %! 0.8 + I * 0.2 , 0.9924147861 - 0.003020708044 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
818 %! 0.8 + I * 0.4 , 0.99236555 - 0.00652359532 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
819 %! 0.8 + I * 0.6 , 0.9922655715 - 0.0110676219 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
820 %! 0.8 + I * 0.8 , 0.9920785856 - 0.01737733806 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
821 %! 0.8 + I * 1. , 0.9917291795 - 0.02645738598 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
822 %! 0.8 + I * 1.2 , 0.9910606387 - 0.03974949378 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
823 %! 0.8 + I * 1.4 , 0.9897435004 - 0.05935252515 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
824 %! 0.8 + I * 1.6 , 0.987077644 - 0.08832675281 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
825 %! 0.8 + I * 1.8 , 0.9815667458 - 0.1310872821 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
826 %! 0.8 + I * 2. , 0.970020127 - 0.1938136793 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
827 %! 1. + I * 0. , 0.9895776106 + 0. * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
828 %! 1. + I * 0.2 , 0.9893361555 - 0.002756935338 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
829 %! 1. + I * 0.4 , 0.9885716856 - 0.005949639805 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
830 %! 1. + I * 0.6 , 0.9871564855 - 0.01008044183 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
831 %! 1. + I * 0.8 , 0.9848512162 - 0.01579337596 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
832 %! 1. + I * 1. , 0.9812582484 - 0.02396648455 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
833 %! 1. + I * 1.2 , 0.9757399152 - 0.0358288294 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
834 %! 1. + I * 1.4 , 0.9672786056 - 0.0531049859 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
835 %! 1. + I * 1.6 , 0.954237868 - 0.0781744383 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
836 %! 1. + I * 1.8 , 0.933957524 - 0.1141918269 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
837 %! 1. + I * 2. , 0.9020917489 - 0.1650142936 * I
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
838 %! ];
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
839 %! tol = 1e-9;
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
840 %! for x = 0:10
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
841 %! for y = 0:10
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
842 %! ur = -1 + x * 0.2;
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
843 %! ui = y * 0.2;
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
844 %! ii = 1 + y + x*11;
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
845 %! [sn, cn, dn] = ellipj (ur + I * ui, m);
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
846 %! assert (SN (ii, 2), sn, tol);
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
847 %! assert (CN (ii, 2), cn, tol);
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
848 %! assert (DN (ii, 2), dn, tol);
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
849 %! endfor
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
850 %! endfor
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
851
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
852 ## tests taken from test_ellipj.m
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
853 %!test
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
854 %! u1 = pi/3; m1 = 0;
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
855 %! res1 = [sin(pi/3), cos(pi/3), 1];
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
856 %! [sn,cn,dn]=ellipj(u1,m1);
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
857 %! assert([sn,cn,dn], res1, 10*eps);
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
858
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
859 %!test
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
860 %! u2 = log(2); m2 = 1;
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
861 %! res2 = [ 3/5, 4/5, 4/5 ];
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
862 %! [sn,cn,dn]=ellipj(u2,m2);
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
863 %! assert([sn,cn,dn], res2, 10*eps);
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
864
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
865 %!test
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
866 %! u3 = log(2)*1i; m3 = 0;
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
867 %! res3 = [3i/4,5/4,1];
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
868 %! [sn,cn,dn]=ellipj(u3,m3);
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
869 %! assert([sn,cn,dn], res3, 10*eps);
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
870
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
871 %!test
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
872 %! u4 = -1; m4 = tan(pi/8)^4;
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
873 %! res4 = [-0.8392965923,0.5436738271,0.9895776106];
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
874 %! [sn,cn,dn]=ellipj(u4, m4);
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
875 %! assert([sn,cn,dn], res4, 1e-10);
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
876
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
877 %!test
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
878 %! u5 = -0.2 + 0.4i; m5 = tan(pi/8)^4;
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
879 %! res5 = [ -0.2152524522 + 0.402598347i, ...
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
880 %! 1.059453907 + 0.08179712295i, ...
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
881 %! 1.001705496 + 0.00254669712i ];
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
882 %! [sn,cn,dn]=ellipj(u5,m5);
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
883 %! assert([sn,cn,dn], res5, 1e-9);
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
884
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
885 %!test
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
886 %! u6 = 0.2 + 0.6i; m6 = tan(pi/8)^4;
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
887 %! res6 = [ 0.2369100139 + 0.624633635i, ...
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
888 %! 1.16200643 - 0.1273503824i, ...
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
889 %! 1.004913944 - 0.004334880912i ];
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
890 %! [sn,cn,dn]=ellipj(u6,m6);
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
891 %! assert([sn,cn,dn], res6, 1e-8);
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
892
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
893 %!test
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
894 %! u7 = 0.8 + 0.8i; m7 = tan(pi/8)^4;
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
895 %! res7 = [0.9588386397 + 0.6107824358i, ...
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
896 %! 0.9245978896 - 0.6334016187i, ...
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
897 %! 0.9920785856 - 0.01737733806i ];
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
898 %! [sn,cn,dn]=ellipj(u7,m7);
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
899 %! assert([sn,cn,dn], res7, 1e-10);
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
900
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
901 %!test
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
902 %! u=[0,pi/6,pi/4,pi/2]; m=0;
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
903 %! res = [0,1/2,1/sqrt(2),1;1,cos(pi/6),1/sqrt(2),0;1,1,1,1];
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
904 %! [sn,cn,dn]=ellipj(u,m);
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
905 %! assert([sn;cn;dn],res, 100*eps);
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
906 %! [sn,cn,dn]=ellipj(u',0);
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
907 %! assert([sn,cn,dn],res', 100*eps);
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
908
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
909 ## XXX FIXME XXX
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
910 ## need to check [real,complex]x[scalar,rowvec,colvec,matrix]x[u,m]
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
911
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
912 %!test
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
913 %! ## Test Jacobi elliptic functions
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
914 %! ## against "exact" solution from Mathematica 3.0
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
915 %! ## David Billinghurst <David.Billinghurst@riotinto.com>
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
916 %! ## 1 February 2001
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
917 %! u = [ 0.25; 0.25; 0.20; 0.20; 0.672; 0.5];
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
918 %! m = [ 0.0; 1.0; 0.19; 0.81; 0.36; 0.9999999999];
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
919 %! S = [ sin(0.25); tanh(0.25);
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
920 %! 0.19842311013970879516;
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
921 %! 0.19762082367187648571;
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
922 %! 0.6095196917919021945;
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
923 %! 0.4621171572617320908 ];
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
924 %! C = [ cos(0.25); sech(0.25);
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
925 %! 0.9801164570409401062;
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
926 %! 0.9802785369736752032;
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
927 %! 0.7927709286533560550;
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
928 %! 0.8868188839691764094 ];
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
929 %! D = [ 1.0; sech(0.25);
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
930 %! 0.9962526643271134302;
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
931 %! 0.9840560289645665155;
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
932 %! 0.9307281387786906491;
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
933 %! 0.8868188839812167635 ];
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
934 %! [sn,cn,dn] = ellipj(u,m);
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
935 %! assert(sn,S,8*eps);
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
936 %! assert(cn,C,8*eps);
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
937 %! assert(dn,D,8*eps);
16585
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
938
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
939 %!error ellipj ()
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
940 %!error ellipj (1)
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
941 %!error ellipj (1,2,3,4)
16584
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff changeset
942 */