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annotate scripts/general/interpft.m @ 20830:b65888ec820e draft default tip gccjit

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dmalcom gcc jit import
author Stefan Mahr <dac922@gmx.de>
date Fri, 27 Feb 2015 16:59:36 +0100
parents 7503499a252b
children
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4197fc428c7d maint: Update copyright notices for 2015.
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1 ## Copyright (C) 2001-2015 Paul Kienzle
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2 ##
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3 ## This file is part of Octave.
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4 ##
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5 ## Octave is free software; you can redistribute it and/or modify it
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6 ## under the terms of the GNU General Public License as published by
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7 ## the Free Software Foundation; either version 3 of the License, or (at
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8 ## your option) any later version.
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9 ##
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10 ## Octave is distributed in the hope that it will be useful, but
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11 ## WITHOUT ANY WARRANTY; without even the implied warranty of
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12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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13 ## General Public License for more details.
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14 ##
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15 ## You should have received a copy of the GNU General Public License
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16 ## along with Octave; see the file COPYING. If not, see
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17 ## <http://www.gnu.org/licenses/>.
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18
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19 ## -*- texinfo -*-
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20 ## @deftypefn {Function File} {} interpft (@var{x}, @var{n})
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21 ## @deftypefnx {Function File} {} interpft (@var{x}, @var{n}, @var{dim})
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22 ##
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23 ## Fourier interpolation.
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24 ##
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25 ## If @var{x} is a vector then @var{x} is resampled with @var{n} points. The
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26 ## data in @var{x} is assumed to be equispaced. If @var{x} is a matrix or an
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27 ## N-dimensional array, the interpolation is performed on each column of
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28 ## @var{x}.
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29 ##
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30 ## If @var{dim} is specified, then interpolate along the dimension @var{dim}.
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31 ##
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32 ## @code{interpft} assumes that the interpolated function is periodic, and so
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33 ## assumptions are made about the endpoints of the interpolation.
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34 ## @seealso{interp1}
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35 ## @end deftypefn
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36
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37 ## Author: Paul Kienzle
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38 ## 2001-02-11
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39 ## * initial version
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40 ## 2002-03-17 aadler
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41 ## * added code to work on matrices as well
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42 ## 2006-05-25 dbateman
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43 ## * Make it matlab compatiable, cutting out the 2-D interpolation
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44
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45 function z = interpft (x, n, dim)
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46
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47 if (nargin < 2 || nargin > 3)
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48 print_usage ();
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49 endif
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50
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51 if (! (isscalar (n) && n == fix (n)))
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52 error ("interpft: N must be a scalar integer");
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53 endif
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54
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55 if (nargin == 2)
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56 if (isrow (x))
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57 dim = 2;
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58 else
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59 dim = 1;
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60 endif
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61 endif
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62
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63 nd = ndims (x);
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64
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65 if (dim < 1 || dim > nd)
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66 error ("interpft: invalid dimension DIM");
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67 endif
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68
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69 perm = [dim:nd, 1:(dim-1)];
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70 x = permute (x, perm);
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71 m = rows (x);
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72
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73 inc = ceil (m/n);
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74 y = fft (x) / m;
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75 k = ceil (m / 2);
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76 sz = size (x);
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77 sz(1) = n * inc - m;
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78
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79 idx = repmat ({':'}, nd, 1);
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80 idx{1} = 1:k;
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81 z = cat (1, y(idx{:}), zeros (sz));
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82 idx{1} = k+1:m;
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83 z = cat (1, z, y(idx{:}));
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84
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85 ## When m is an even number of rows, the FFT has a single Nyquist bin.
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86 ## If zero-padded above, distribute the value of the Nyquist bin evenly
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87 ## between the new corresponding positive and negative frequency bins.
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88 if (sz(1) > 0 && k == m/2)
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89 idx{1} = n * inc - k + 1;
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90 tmp = z(idx{:}) / 2;
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91 z(idx{:}) = tmp;
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92 idx{1} = k + 1;
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93 z(idx{:}) = tmp;
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94 endif
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95
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96 z = n * ifft (z);
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97
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98 if (inc != 1)
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99 sz(1) = n;
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100 z = inc * reshape (z(1:inc:end), sz);
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101 endif
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102
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103 z = ipermute (z, perm);
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104
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105 endfunction
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106
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107
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108 %!demo
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109 %! clf;
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110 %! t = 0 : 0.3 : pi; dt = t(2)-t(1);
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111 %! n = length (t); k = 100;
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112 %! ti = t(1) + [0 : k-1]*dt*n/k;
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113 %! y = sin (4*t + 0.3) .* cos (3*t - 0.1);
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114 %! yp = sin (4*ti + 0.3) .* cos (3*ti - 0.1);
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115 %! plot (ti, yp, 'g', ti, interp1(t, y, ti, "spline"), 'b', ...
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116 %! ti, interpft (y, k), 'c', t, y, "r+");
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117 %! legend ("sin(4t+0.3)cos(3t-0.1)", "spline", "interpft", "data");
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118
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119 %!shared n,y
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120 %! x = [0:10]'; y = sin(x); n = length (x);
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121 %!assert (interpft (y, n), y, 20*eps);
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122 %!assert (interpft (y', n), y', 20*eps);
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123 %!assert (interpft ([y,y],n), [y,y], 20*eps);
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124
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125 ## Test case with complex input from bug #39566
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126 %!test
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127 %! x = (1 + j) * [1:4]';
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128 %! y = ifft ([15 + 15*j; -6; -1.5 - 1.5*j; 0; -1.5 - 1.5*j; -6*j]);
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129 %! assert (interpft (x, 6), y, 10*eps);
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130
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131 ## Test for correct spectral symmetry with even/odd lengths
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132 %!assert (max (abs (imag (interpft ([1:8], 20)))), 0, 20*eps);
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133 %!assert (max (abs (imag (interpft ([1:8], 21)))), 0, 21*eps);
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134 %!assert (max (abs (imag (interpft ([1:9], 20)))), 0, 20*eps);
011e5d67baf1 interpft.m: Widen tolerance on tests to allow for FFT error
Mike Miller <mtmiller@ieee.org>
parents: 17173
diff changeset
135 %!assert (max (abs (imag (interpft ([1:9], 21)))), 0, 21*eps);
17173
3a23cbde59d5 interpft.m: Fix interpolation to preserve spectral symmetry (bug #39566)
Mike Miller <mtmiller@ieee.org>
parents: 17089
diff changeset
136
20038
9fc020886ae9 maint: Clean up m-files to follow Octave coding conventions.
Rik <rik@octave.org>
parents: 19898
diff changeset
137 ## Test input validation
13768
5f96b91b4e0c interpft.m: Miscellaneous code cleanup. Add more input validation tests.
Rik <octave@nomad.inbox5.com>
parents: 12676
diff changeset
138 %!error interpft ()
5f96b91b4e0c interpft.m: Miscellaneous code cleanup. Add more input validation tests.
Rik <octave@nomad.inbox5.com>
parents: 12676
diff changeset
139 %!error interpft (1)
5f96b91b4e0c interpft.m: Miscellaneous code cleanup. Add more input validation tests.
Rik <octave@nomad.inbox5.com>
parents: 12676
diff changeset
140 %!error interpft (1,2,3)
14237
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc.
Rik <octave@nomad.inbox5.com>
parents: 14138
diff changeset
141 %!error <N must be a scalar integer> interpft (1,[2,2])
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc.
Rik <octave@nomad.inbox5.com>
parents: 14138
diff changeset
142 %!error <N must be a scalar integer> interpft (1,2.1)
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc.
Rik <octave@nomad.inbox5.com>
parents: 14138
diff changeset
143 %!error <invalid dimension DIM> interpft (1,2,0)
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc.
Rik <octave@nomad.inbox5.com>
parents: 14138
diff changeset
144 %!error <invalid dimension DIM> interpft (1,2,3)
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc.
Rik <octave@nomad.inbox5.com>
parents: 14138
diff changeset
145