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nextpow2: Fix for input between 0.5 and 1 (bug #62947). * scripts/general/nextpow2.m: Switch to a naïve implementation using log2 with a single output argument and ceil.
author Markus Mützel <markus.muetzel@gmx.de>
date Wed, 24 Aug 2022 17:15:34 +0200
parents 796f54d4ddbf
children 5d3faba0342e
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1 ########################################################################
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2 ##
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3 ## Copyright (C) 2001-2022 The Octave Project Developers
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4 ##
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5 ## See the file COPYRIGHT.md in the top-level directory of this
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6 ## distribution or <https://octave.org/copyright/>.
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7 ##
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8 ## This file is part of Octave.
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9 ##
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10 ## Octave is free software: you can redistribute it and/or modify it
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11 ## under the terms of the GNU General Public License as published by
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12 ## the Free Software Foundation, either version 3 of the License, or
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13 ## (at your option) any later version.
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14 ##
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15 ## Octave is distributed in the hope that it will be useful, but
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16 ## WITHOUT ANY WARRANTY; without even the implied warranty of
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17 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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18 ## GNU General Public License for more details.
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19 ##
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20 ## You should have received a copy of the GNU General Public License
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21 ## along with Octave; see the file COPYING. If not, see
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22 ## <https://www.gnu.org/licenses/>.
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23 ##
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24 ########################################################################
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25
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26 ## -*- texinfo -*-
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27 ## @deftypefn {} {} interpft (@var{x}, @var{n})
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28 ## @deftypefnx {} {} interpft (@var{x}, @var{n}, @var{dim})
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29 ##
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30 ## Fourier interpolation.
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31 ##
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32 ## If @var{x} is a vector then @var{x} is resampled with @var{n} points. The
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33 ## data in @var{x} is assumed to be equispaced. If @var{x} is a matrix or an
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34 ## N-dimensional array, the interpolation is performed on each column of
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35 ## @var{x}.
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36 ##
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37 ## If @var{dim} is specified, then interpolate along the dimension @var{dim}.
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38 ##
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39 ## @code{interpft} assumes that the interpolated function is periodic, and so
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40 ## assumptions are made about the endpoints of the interpolation.
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41 ## @seealso{interp1}
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42 ## @end deftypefn
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43
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44 function z = interpft (x, n, dim)
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45
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46 if (nargin < 2)
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47 print_usage ();
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48 endif
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49
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50 if (! (isscalar (n) && n == fix (n)))
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51 error ("interpft: N must be a scalar integer");
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52 endif
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53
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54 if (nargin == 2)
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55 if (isrow (x))
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56 dim = 2;
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57 else
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58 dim = 1;
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59 endif
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60 endif
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61
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62 nd = ndims (x);
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63
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64 if (dim < 1 || dim > nd)
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65 error ("interpft: invalid dimension DIM");
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66 endif
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67
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68 perm = [dim:nd, 1:(dim-1)];
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69 x = permute (x, perm);
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70 m = rows (x);
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71
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72 inc = ceil (m/n);
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73 y = fft (x) / m;
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74 k = ceil (m / 2);
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75 sz = size (x);
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76 sz(1) = n * inc - m;
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77
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78 idx = repmat ({':'}, nd, 1);
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79 idx{1} = 1:k;
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80 z = cat (1, y(idx{:}), zeros (sz));
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81 idx{1} = k+1:m;
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82 z = cat (1, z, y(idx{:}));
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83
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84 ## When m is an even number of rows, the FFT has a single Nyquist bin.
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85 ## If zero-padded above, distribute the value of the Nyquist bin evenly
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86 ## between the new corresponding positive and negative frequency bins.
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87 if (sz(1) > 0 && k == m/2)
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88 idx{1} = n * inc - k + 1;
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89 tmp = z(idx{:}) / 2;
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90 z(idx{:}) = tmp;
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91 idx{1} = k + 1;
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92 z(idx{:}) = tmp;
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93 endif
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94
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95 z = n * ifft (z);
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96
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97 if (inc != 1)
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98 sz(1) = n;
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99 z = inc * reshape (z(1:inc:end), sz);
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100 endif
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101
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102 z = ipermute (z, perm);
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103
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104 endfunction
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105
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106
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107 %!demo
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108 %! clf;
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109 %! t = 0 : 0.3 : pi; dt = t(2)-t(1);
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110 %! n = length (t); k = 100;
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111 %! ti = t(1) + [0 : k-1]*dt*n/k;
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112 %! y = sin (4*t + 0.3) .* cos (3*t - 0.1);
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113 %! yp = sin (4*ti + 0.3) .* cos (3*ti - 0.1);
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114 %! plot (ti, yp, 'g', ti, interp1 (t, y, ti, "spline"), 'b', ...
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115 %! ti, interpft (y, k), 'c', t, y, "r+");
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116 %! legend ("sin (4t+0.3)cos (3t-0.1)", "spline", "interpft", "data");
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117
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118 %!shared n,y
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119 %! x = [0:10]'; y = sin(x); n = length (x);
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120 %!testif HAVE_FFTW
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121 %! assert (interpft (y, n), y, 20*eps);
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122 %!testif HAVE_FFTW
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123 %! assert (interpft (y', n), y', 20*eps);
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124 %!testif HAVE_FFTW
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125 %! assert (interpft ([y,y],n), [y,y], 20*eps);
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126
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127 ## Test case with complex input
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128 %!testif HAVE_FFTW <*39566>
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129 %! x = (1 + j) * [1:4]';
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130 %! y = ifft ([15 + 15*j; -6; -1.5 - 1.5*j; 0; -1.5 - 1.5*j; -6*j]);
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131 %! assert (interpft (x, 6), y, 10*eps);
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132
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133 ## Test for correct spectral symmetry with even/odd lengths
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134 %!testif HAVE_FFTW
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9e43deb9bfc3 maint: Use semicolon after assert statement inside %!test blocks.
Rik <rik@octave.org>
parents: 28912
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135 %! assert (max (abs (imag (interpft ([1:8], 20)))), 0, 20*eps);
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John W. Eaton <jwe@octave.org>
parents: 25054
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136 %!testif HAVE_FFTW
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Rik <rik@octave.org>
parents: 28912
diff changeset
137 %! assert (max (abs (imag (interpft ([1:8], 21)))), 0, 21*eps);
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John W. Eaton <jwe@octave.org>
parents: 25054
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138 %!testif HAVE_FFTW
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Rik <rik@octave.org>
parents: 28912
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139 %! assert (max (abs (imag (interpft ([1:9], 20)))), 0, 20*eps);
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John W. Eaton <jwe@octave.org>
parents: 25054
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140 %!testif HAVE_FFTW
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Rik <rik@octave.org>
parents: 28912
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141 %! assert (max (abs (imag (interpft ([1:9], 21)))), 0, 21*eps);
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3a23cbde59d5 interpft.m: Fix interpolation to preserve spectral symmetry (bug #39566)
Mike Miller <mtmiller@ieee.org>
parents: 17089
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142
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Rik <rik@octave.org>
parents: 19697
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143 ## Test input validation
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d8318c12d903 test: remove unnecessary BIST tests in m-files checking for excessive number of inputs.
Rik <rik@octave.org>
parents: 28789
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144 %!error <Invalid call> interpft ()
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Rik <rik@octave.org>
parents: 28789
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145 %!error <Invalid call> interpft (1)
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Rik <octave@nomad.inbox5.com>
parents: 14138
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146 %!error <N must be a scalar integer> interpft (1,[2,2])
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Rik <octave@nomad.inbox5.com>
parents: 14138
diff changeset
147 %!error <N must be a scalar integer> interpft (1,2.1)
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Rik <octave@nomad.inbox5.com>
parents: 14138
diff changeset
148 %!error <invalid dimension DIM> interpft (1,2,0)
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Rik <octave@nomad.inbox5.com>
parents: 14138
diff changeset
149 %!error <invalid dimension DIM> interpft (1,2,3)