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1 /* |
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2 |
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3 Copyright (C) 1996, 1997 John W. Eaton |
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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 2, or (at your option) any |
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10 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, write to the Free |
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19 Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA |
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20 02110-1301, USA. |
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21 |
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22 */ |
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23 |
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24 // Based on Tony Richardson's filter.m. |
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25 // |
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26 // Originally translated to C++ by KH (Kurt.Hornik@wu-wien.ac.at) |
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27 // with help from Fritz Leisch and Andreas Weingessel on Oct 20, 1994. |
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28 // |
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29 // Rewritten to use templates to handle both real and complex cases by |
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30 // jwe, Wed Nov 1 19:15:29 1995. |
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31 |
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32 #ifdef HAVE_CONFIG_H |
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33 #include <config.h> |
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34 #endif |
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35 |
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36 #include "quit.h" |
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37 |
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38 #include "defun-dld.h" |
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39 #include "error.h" |
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40 #include "oct-obj.h" |
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41 |
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42 #if !defined (CXX_NEW_FRIEND_TEMPLATE_DECL) |
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43 extern MArrayN<double> |
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44 filter (MArray<double>&, MArray<double>&, MArrayN<double>&, int dim); |
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45 |
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46 extern MArrayN<Complex> |
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47 filter (MArray<Complex>&, MArray<Complex>&, MArrayN<Complex>&, int dim); |
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48 #endif |
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49 |
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50 template <class T> |
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51 MArrayN<T> |
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52 filter (MArray<T>& b, MArray<T>& a, MArrayN<T>& x, MArrayN<T>& si, |
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53 int dim = 0) |
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54 { |
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55 MArrayN<T> y; |
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56 |
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57 octave_idx_type a_len = a.length (); |
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58 octave_idx_type b_len = b.length (); |
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59 |
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60 octave_idx_type ab_len = a_len > b_len ? a_len : b_len; |
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61 |
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62 b.resize (ab_len, 0.0); |
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63 if (a_len > 1) |
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64 a.resize (ab_len, 0.0); |
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65 |
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66 T norm = a (0); |
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67 |
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68 if (norm == 0.0) |
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69 { |
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70 error ("filter: the first element of a must be non-zero"); |
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71 return y; |
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72 } |
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73 |
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74 dim_vector x_dims = x.dims (); |
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75 if (dim < 0 || dim > x_dims.length ()) |
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76 { |
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77 error ("filter: filtering over invalid dimension"); |
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78 return y; |
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79 } |
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80 |
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81 octave_idx_type x_len = x_dims(dim); |
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82 |
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83 dim_vector si_dims = si.dims (); |
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84 octave_idx_type si_len = si_dims(0); |
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85 |
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86 if (si_len != ab_len - 1) |
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87 { |
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88 error ("filter: first dimension of si must be of length max (length (a), length (b)) - 1"); |
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89 return y; |
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90 } |
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91 |
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92 if (si_dims.length () != x_dims.length ()) |
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93 { |
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94 error ("filter: dimensionality of si and x must agree"); |
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95 return y; |
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96 } |
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97 |
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98 octave_idx_type si_dim = 0; |
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99 for (octave_idx_type i = 0; i < x_dims.length (); i++) |
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100 { |
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101 if (i == dim) |
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102 continue; |
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103 |
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104 if (x_dims(i) == 1) |
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105 continue; |
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106 |
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107 if (si_dims(++si_dim) != x_dims(i)) |
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108 { |
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109 error ("filter: dimensionality of si and x must agree"); |
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110 return y; |
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111 } |
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112 } |
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113 |
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114 if (norm != 1.0) |
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115 { |
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116 a = a / norm; |
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117 b = b / norm; |
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118 } |
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119 |
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120 if (a_len <= 1 && si_len <= 0) |
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121 return b(0) * x; |
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122 |
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123 y.resize (x_dims, 0.0); |
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124 |
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125 int x_stride = 1; |
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126 for (int i = 0; i < dim; i++) |
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127 x_stride *= x_dims(i); |
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128 |
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129 octave_idx_type x_num = x_dims.numel () / x_len; |
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130 for (octave_idx_type num = 0; num < x_num; num++) |
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131 { |
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132 octave_idx_type x_offset; |
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133 if (x_stride == 1) |
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134 x_offset = num * x_len; |
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135 else |
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136 { |
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137 octave_idx_type x_offset2 = 0; |
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138 x_offset = num; |
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139 while (x_offset >= x_stride) |
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140 { |
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141 x_offset -= x_stride; |
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142 x_offset2++; |
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143 } |
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144 x_offset += x_offset2 * x_stride * x_len; |
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145 } |
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146 octave_idx_type si_offset = num * si_len; |
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147 |
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148 if (a_len > 1) |
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149 { |
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150 T *py = y.fortran_vec (); |
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151 T *psi = si.fortran_vec (); |
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152 |
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153 const T *pa = a.data (); |
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154 const T *pb = b.data (); |
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155 const T *px = x.data (); |
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156 |
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157 psi += si_offset; |
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158 |
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159 for (octave_idx_type i = 0, idx = x_offset; i < x_len; i++, idx += x_stride) |
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160 { |
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161 py[idx] = psi[0] + pb[0] * px[idx]; |
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162 |
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163 if (si_len > 0) |
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164 { |
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165 for (octave_idx_type j = 0; j < si_len - 1; j++) |
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166 { |
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167 OCTAVE_QUIT; |
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168 |
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169 psi[j] = psi[j+1] - pa[j+1] * py[idx] + pb[j+1] * px[idx]; |
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170 } |
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171 |
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172 psi[si_len-1] = pb[si_len] * px[idx] - pa[si_len] * py[idx]; |
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173 } |
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174 else |
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175 { |
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176 OCTAVE_QUIT; |
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177 |
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178 psi[0] = pb[si_len] * px[idx] - pa[si_len] * py[idx]; |
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179 } |
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180 } |
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181 } |
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182 else if (si_len > 0) |
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183 { |
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184 T *py = y.fortran_vec (); |
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185 T *psi = si.fortran_vec (); |
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186 |
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187 const T *pb = b.data (); |
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188 const T *px = x.data (); |
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189 |
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190 psi += si_offset; |
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191 |
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192 for (octave_idx_type i = 0, idx = x_offset; i < x_len; i++, idx += x_stride) |
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193 { |
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194 py[idx] = psi[0] + pb[0] * px[idx]; |
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195 |
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196 if (si_len > 1) |
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197 { |
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198 for (octave_idx_type j = 0; j < si_len - 1; j++) |
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199 { |
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200 OCTAVE_QUIT; |
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201 |
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202 psi[j] = psi[j+1] + pb[j+1] * px[idx]; |
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203 } |
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204 |
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205 psi[si_len-1] = pb[si_len] * px[idx]; |
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206 } |
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207 else |
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208 { |
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209 OCTAVE_QUIT; |
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210 |
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211 psi[0] = pb[1] * px[idx]; |
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212 } |
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213 } |
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214 } |
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215 } |
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216 |
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217 return y; |
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218 } |
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219 |
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220 #if !defined (CXX_NEW_FRIEND_TEMPLATE_DECL) |
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221 extern MArrayN<double> |
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222 filter (MArray<double>&, MArray<double>&, MArrayN<double>&, |
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223 MArrayN<double>&, int dim); |
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224 |
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225 extern MArrayN<Complex> |
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226 filter (MArray<Complex>&, MArray<Complex>&, MArrayN<Complex>&, |
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227 MArrayN<Complex>&, int dim); |
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228 #endif |
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229 |
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230 template <class T> |
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231 MArrayN<T> |
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232 filter (MArray<T>& b, MArray<T>& a, MArrayN<T>& x, int dim = -1) |
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233 { |
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234 dim_vector x_dims = x.dims(); |
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235 |
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236 if (dim < 0) |
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237 { |
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238 // Find first non-singleton dimension |
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239 while (dim < x_dims.length () && x_dims(dim) <= 1) |
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240 dim++; |
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241 |
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242 // All dimensions singleton, pick first dimension |
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243 if (dim == x_dims.length ()) |
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244 dim = 0; |
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245 } |
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246 else |
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247 if (dim < 0 || dim > x_dims.length ()) |
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248 { |
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249 error ("filter: filtering over invalid dimension"); |
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250 return MArrayN<T> (); |
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251 } |
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252 |
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253 octave_idx_type a_len = a.length (); |
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254 octave_idx_type b_len = b.length (); |
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255 |
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256 octave_idx_type si_len = (a_len > b_len ? a_len : b_len) - 1; |
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257 dim_vector si_dims = x.dims (); |
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258 for (int i = dim; i > 0; i--) |
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259 si_dims(i) = si_dims(i-1); |
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260 si_dims(0) = si_len; |
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261 |
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262 MArrayN<T> si (si_dims, T (0.0)); |
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263 |
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264 return filter (b, a, x, si, dim); |
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265 } |
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266 |
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267 DEFUN_DLD (filter, args, nargout, |
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268 "-*- texinfo -*-\n\ |
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269 @deftypefn {Loadable Function} {y =} filter (@var{b}, @var{a}, @var{x})\n\ |
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270 @deftypefnx {Loadable Function} {[@var{y}, @var{sf}] =} filter (@var{b}, @var{a}, @var{x}, @var{si})\n\ |
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271 @deftypefnx {Loadable Function} {[@var{y}, @var{sf}] =} filter (@var{b}, @var{a}, @var{x}, [], @var{dim})\n\ |
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272 @deftypefnx {Loadable Function} {[@var{y}, @var{sf}] =} filter (@var{b}, @var{a}, @var{x}, @var{si}, @var{dim})\n\ |
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273 Return the solution to the following linear, time-invariant difference\n\ |
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274 equation:\n\ |
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275 @iftex\n\ |
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276 @tex\n\ |
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277 $$\n\ |
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278 \\sum_{k=0}^N a_{k+1} y_{n-k} = \\sum_{k=0}^M b_{k+1} x_{n-k}, \\qquad\n\ |
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279 1 \\le n \\le P\n\ |
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280 $$\n\ |
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281 @end tex\n\ |
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282 @end iftex\n\ |
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283 @ifinfo\n\ |
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284 \n\ |
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285 @smallexample\n\ |
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286 N M\n\ |
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287 SUM a(k+1) y(n-k) = SUM b(k+1) x(n-k) for 1<=n<=length(x)\n\ |
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288 k=0 k=0\n\ |
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289 @end smallexample\n\ |
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290 @end ifinfo\n\ |
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291 \n\ |
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292 @noindent\n\ |
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293 where\n\ |
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294 @ifinfo\n\ |
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295 N=length(a)-1 and M=length(b)-1.\n\ |
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296 @end ifinfo\n\ |
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297 @iftex\n\ |
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298 @tex\n\ |
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299 $a \\in \\Re^{N-1}$, $b \\in \\Re^{M-1}$, and $x \\in \\Re^P$.\n\ |
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300 @end tex\n\ |
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301 @end iftex\n\ |
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302 over the first non-singleton dimension of @var{x} or over @var{dim} if\n\ |
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303 supplied. An equivalent form of this equation is:\n\ |
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304 @iftex\n\ |
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305 @tex\n\ |
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306 $$\n\ |
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307 y_n = -\\sum_{k=1}^N c_{k+1} y_{n-k} + \\sum_{k=0}^M d_{k+1} x_{n-k}, \\qquad\n\ |
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308 1 \\le n \\le P\n\ |
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309 $$\n\ |
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310 @end tex\n\ |
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311 @end iftex\n\ |
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312 @ifinfo\n\ |
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313 \n\ |
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314 @smallexample\n\ |
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315 N M\n\ |
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316 y(n) = - SUM c(k+1) y(n-k) + SUM d(k+1) x(n-k) for 1<=n<=length(x)\n\ |
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317 k=1 k=0\n\ |
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318 @end smallexample\n\ |
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319 @end ifinfo\n\ |
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320 \n\ |
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321 @noindent\n\ |
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322 where\n\ |
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323 @ifinfo\n\ |
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324 c = a/a(1) and d = b/a(1).\n\ |
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325 @end ifinfo\n\ |
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326 @iftex\n\ |
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327 @tex\n\ |
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328 $c = a/a_1$ and $d = b/a_1$.\n\ |
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329 @end tex\n\ |
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330 @end iftex\n\ |
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331 \n\ |
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332 If the fourth argument @var{si} is provided, it is taken as the\n\ |
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333 initial state of the system and the final state is returned as\n\ |
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334 @var{sf}. The state vector is a column vector whose length is\n\ |
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335 equal to the length of the longest coefficient vector minus one.\n\ |
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336 If @var{si} is not supplied, the initial state vector is set to all\n\ |
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337 zeros.\n\ |
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338 \n\ |
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339 In terms of the z-transform, y is the result of passing the discrete-\n\ |
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340 time signal x through a system characterized by the following rational\n\ |
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341 system function:\n\ |
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342 @iftex\n\ |
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343 @tex\n\ |
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344 $$\n\ |
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345 H(z) = {\\displaystyle\\sum_{k=0}^M d_{k+1} z^{-k}\n\ |
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346 \\over 1 + \\displaystyle\\sum_{k+1}^N c_{k+1} z^{-k}}\n\ |
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347 $$\n\ |
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348 @end tex\n\ |
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349 @end iftex\n\ |
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350 @ifinfo\n\ |
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351 \n\ |
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352 @example\n\ |
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353 M\n\ |
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354 SUM d(k+1) z^(-k)\n\ |
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355 k=0\n\ |
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356 H(z) = ----------------------\n\ |
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357 N\n\ |
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358 1 + SUM c(k+1) z(-k)\n\ |
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359 k=1\n\ |
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360 @end example\n\ |
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361 @end ifinfo\n\ |
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362 @end deftypefn") |
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363 { |
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364 octave_value_list retval; |
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365 |
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366 int nargin = args.length (); |
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367 |
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368 if (nargin < 3 || nargin > 5) |
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369 { |
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370 print_usage (); |
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371 return retval; |
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372 } |
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373 |
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374 const char *errmsg = "filter: arguments a and b must be vectors"; |
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375 |
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376 int dim; |
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377 dim_vector x_dims = args(2).dims (); |
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378 |
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379 if (nargin == 5) |
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380 { |
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381 dim = args(4).nint_value() - 1; |
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382 if (dim < 0 || dim >= x_dims.length ()) |
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383 { |
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384 error ("filter: filtering over invalid dimension"); |
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385 return retval; |
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386 } |
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387 } |
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388 else |
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389 { |
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390 // Find first non-singleton dimension |
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391 dim = 0; |
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392 while (dim < x_dims.length () && x_dims(dim) <= 1) |
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393 dim++; |
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394 |
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395 // All dimensions singleton, pick first dimension |
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396 if (dim == x_dims.length ()) |
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397 dim = 0; |
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398 } |
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399 |
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400 if (args(0).is_complex_type () |
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401 || args(1).is_complex_type () |
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402 || args(2).is_complex_type () |
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403 || (nargin >= 4 && args(3).is_complex_type ())) |
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404 { |
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405 ComplexColumnVector b (args(0).complex_vector_value ()); |
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406 ComplexColumnVector a (args(1).complex_vector_value ()); |
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407 |
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408 ComplexNDArray x (args(2).complex_array_value ()); |
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409 |
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410 if (! error_state) |
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411 { |
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412 ComplexNDArray si; |
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413 |
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414 if (nargin == 3 || args(3).is_empty ()) |
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415 { |
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416 octave_idx_type a_len = a.length (); |
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417 octave_idx_type b_len = b.length (); |
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418 |
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5275
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419 octave_idx_type si_len = (a_len > b_len ? a_len : b_len) - 1; |
|
3088
|
420 |
|
4844
|
421 dim_vector si_dims = x.dims (); |
|
|
422 for (int i = dim; i > 0; i--) |
|
5059
|
423 si_dims(i) = si_dims(i-1); |
|
|
424 si_dims(0) = si_len; |
|
4844
|
425 |
|
|
426 si.resize (si_dims, 0.0); |
|
3088
|
427 } |
|
|
428 else |
|
4844
|
429 { |
|
|
430 dim_vector si_dims = args (3).dims (); |
|
|
431 bool si_is_vector = true; |
|
5059
|
432 for (int i = 0; i < si_dims.length (); i++) |
|
|
433 if (si_dims(i) != 1 && si_dims(i) < si_dims.numel ()) |
|
4844
|
434 { |
|
|
435 si_is_vector = false; |
|
|
436 break; |
|
|
437 } |
|
|
438 |
|
5059
|
439 si = args(3).complex_array_value (); |
|
|
440 |
|
4844
|
441 if (si_is_vector) |
|
5059
|
442 si = si.reshape (dim_vector (si.numel (), 1)); |
|
4844
|
443 } |
|
3088
|
444 |
|
|
445 if (! error_state) |
|
|
446 { |
|
4844
|
447 ComplexNDArray y (filter (b, a, x, si, dim)); |
|
3088
|
448 |
|
|
449 if (nargout == 2) |
|
4844
|
450 retval(1) = si; |
|
2928
|
451 |
|
4844
|
452 retval(0) = y; |
|
2928
|
453 } |
|
|
454 else |
|
3088
|
455 error (errmsg); |
|
2928
|
456 } |
|
|
457 else |
|
|
458 error (errmsg); |
|
|
459 } |
|
|
460 else |
|
|
461 { |
|
3419
|
462 ColumnVector b (args(0).vector_value ()); |
|
|
463 ColumnVector a (args(1).vector_value ()); |
|
4844
|
464 |
|
|
465 NDArray x (args(2).array_value ()); |
|
2928
|
466 |
|
|
467 if (! error_state) |
|
|
468 { |
|
4844
|
469 NDArray si; |
|
3088
|
470 |
|
4844
|
471 if (nargin == 3 || args(3).is_empty ()) |
|
2928
|
472 { |
|
5275
|
473 octave_idx_type a_len = a.length (); |
|
|
474 octave_idx_type b_len = b.length (); |
|
3088
|
475 |
|
5275
|
476 octave_idx_type si_len = (a_len > b_len ? a_len : b_len) - 1; |
|
3088
|
477 |
|
4844
|
478 dim_vector si_dims = x.dims (); |
|
|
479 for (int i = dim; i > 0; i--) |
|
5059
|
480 si_dims(i) = si_dims(i-1); |
|
|
481 si_dims(0) = si_len; |
|
4844
|
482 |
|
|
483 si.resize (si_dims, 0.0); |
|
3088
|
484 } |
|
|
485 else |
|
4844
|
486 { |
|
|
487 dim_vector si_dims = args (3).dims (); |
|
|
488 bool si_is_vector = true; |
|
5059
|
489 for (int i = 0; i < si_dims.length (); i++) |
|
|
490 if (si_dims(i) != 1 && si_dims(i) < si_dims.numel ()) |
|
4844
|
491 { |
|
|
492 si_is_vector = false; |
|
|
493 break; |
|
|
494 } |
|
|
495 |
|
5059
|
496 si = args(3).array_value (); |
|
|
497 |
|
4844
|
498 if (si_is_vector) |
|
5059
|
499 si = si.reshape (dim_vector (si.numel (), 1)); |
|
4844
|
500 } |
|
3088
|
501 |
|
|
502 if (! error_state) |
|
|
503 { |
|
4844
|
504 NDArray y (filter (b, a, x, si, dim)); |
|
3088
|
505 |
|
|
506 if (nargout == 2) |
|
4844
|
507 retval(1) = si; |
|
2928
|
508 |
|
4844
|
509 retval(0) = y; |
|
2928
|
510 } |
|
|
511 else |
|
3088
|
512 error (errmsg); |
|
2928
|
513 } |
|
|
514 else |
|
|
515 error (errmsg); |
|
|
516 } |
|
|
517 |
|
|
518 return retval; |
|
|
519 } |
|
|
520 |
|
4844
|
521 template MArrayN<double> |
|
|
522 filter (MArray<double>&, MArray<double>&, MArrayN<double>&, |
|
|
523 MArrayN<double>&, int dim); |
|
2928
|
524 |
|
4844
|
525 template MArrayN<double> |
|
|
526 filter (MArray<double>&, MArray<double>&, MArrayN<double>&, int dim); |
|
2928
|
527 |
|
4844
|
528 template MArrayN<Complex> |
|
|
529 filter (MArray<Complex>&, MArray<Complex>&, MArrayN<Complex>&, |
|
|
530 MArrayN<Complex>&, int dim); |
|
2928
|
531 |
|
4844
|
532 template MArrayN<Complex> |
|
|
533 filter (MArray<Complex>&, MArray<Complex>&, MArrayN<Complex>&, int dim); |
|
2928
|
534 |
|
|
535 /* |
|
|
536 ;;; Local Variables: *** |
|
|
537 ;;; mode: C++ *** |
|
|
538 ;;; End: *** |
|
|
539 */ |
