Mercurial > hg > octave-lyh
annotate scripts/special-matrix/toeplitz.m @ 14868:5d3a684236b0
maint: Use Octave coding conventions for cuddling parentheses in scripts directory
* lin2mu.m, loadaudio.m, wavread.m, accumarray.m, bicubic.m, celldisp.m,
colon.m, cplxpair.m, dblquad.m, divergence.m, genvarname.m, gradient.m,
int2str.m, interp1.m, interp1q.m, interp2.m, interpn.m, loadobj.m, nthargout.m,
__isequal__.m, __splinen__.m, quadgk.m, quadl.m, quadv.m, rat.m, rot90.m,
rotdim.m, saveobj.m, subsindex.m, triplequad.m, delaunay3.m, griddata.m,
inpolygon.m, tsearchn.m, voronoi.m, get_first_help_sentence.m, which.m,
gray2ind.m, pink.m, dlmwrite.m, strread.m, textread.m, textscan.m, housh.m,
ishermitian.m, issymmetric.m, krylov.m, logm.m, null.m, rref.m,
compare_versions.m, copyfile.m, dump_prefs.m, edit.m, fileparts.m,
getappdata.m, isappdata.m, movefile.m, orderfields.m, parseparams.m,
__xzip__.m, rmappdata.m, setappdata.m, swapbytes.m, unpack.m, ver.m, fminbnd.m,
fminunc.m, fsolve.m, glpk.m, lsqnonneg.m, qp.m, sqp.m, configure_make.m,
copy_files.m, describe.m, get_description.m, get_forge_pkg.m, install.m,
installed_packages.m, is_architecture_dependent.m, load_package_dirs.m,
print_package_description.m, rebuild.m, repackage.m, save_order.m, shell.m,
allchild.m, ancestor.m, area.m, axes.m, axis.m, clabel.m, close.m, colorbar.m,
comet.m, comet3.m, contour.m, cylinder.m, ezmesh.m, ezsurf.m, findobj.m,
fplot.m, hist.m, isocolors.m, isonormals.m, isosurface.m, isprop.m, legend.m,
mesh.m, meshz.m, pareto.m, pcolor.m, peaks.m, plot3.m, plotmatrix.m, plotyy.m,
polar.m, print.m, __add_datasource__.m, __add_default_menu__.m,
__axes_limits__.m, __bar__.m, __clabel__.m, __contour__.m, __errcomm__.m,
__errplot__.m, __ezplot__.m, __file_filter__.m, __fltk_print__.m,
__ghostscript__.m, __gnuplot_print__.m, __go_draw_axes__.m,
__go_draw_figure__.m, __interp_cube__.m, __marching_cube__.m, __patch__.m,
__pie__.m, __plt__.m, __print_parse_opts__.m, __quiver__.m, __scatter__.m,
__stem__.m, __tight_eps_bbox__.m, __uigetdir_fltk__.m, __uigetfile_fltk__.m,
__uiputfile_fltk__.m, quiver.m, quiver3.m, rectangle.m, refreshdata.m,
ribbon.m, scatter.m, semilogy.m, shading.m, slice.m, subplot.m, surface.m,
surfl.m, surfnorm.m, text.m, uigetfile.m, uiputfile.m, whitebg.m, deconv.m,
mkpp.m, pchip.m, polyaffine.m, polyder.m, polygcd.m, polyout.m, polyval.m,
ppint.m, ppjumps.m, ppval.m, residue.m, roots.m, spline.m, splinefit.m,
addpref.m, getpref.m, setpref.m, ismember.m, setxor.m, arch_fit.m, arch_rnd.m,
arch_test.m, autoreg_matrix.m, diffpara.m, fftconv.m, filter2.m, hanning.m,
hurst.m, periodogram.m, triangle_sw.m, sinc.m, spectral_xdf.m, spencer.m,
stft.m, synthesis.m, unwrap.m, yulewalker.m, bicgstab.m, gmres.m, pcg.m, pcr.m,
__sprand_impl__.m, speye.m, spfun.m, sprandn.m, spstats.m, svds.m,
treelayout.m, treeplot.m, bessel.m, factor.m, legendre.m, perms.m, primes.m,
magic.m, toeplitz.m, corr.m, cov.m, mean.m, median.m, mode.m, qqplot.m,
quantile.m, ranks.m, zscore.m, logistic_regression_likelihood.m,
bartlett_test.m, chisquare_test_homogeneity.m, chisquare_test_independence.m,
kolmogorov_smirnov_test.m, run_test.m, u_test.m, wilcoxon_test.m, z_test.m,
z_test_2.m, bin2dec.m, dec2base.m, mat2str.m, strcat.m, strchr.m, strjust.m,
strtok.m, substr.m, untabify.m, assert.m, demo.m, example.m, fail.m, speed.m,
test.m, now.m: Use Octave coding conventions for cuddling parentheses in
scripts directory.
author | Rik <octave@nomad.inbox5.com> |
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date | Tue, 17 Jul 2012 07:08:39 -0700 |
parents | 72c96de7a403 |
children | b81b9d079515 |
rev | line source |
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1 ## Copyright (C) 1993-2012 John W. Eaton |
9092 | 2 ## Copyright (C) 2009 VZLU Prague |
2313 | 3 ## |
4 ## This file is part of Octave. | |
5 ## | |
6 ## Octave is free software; you can redistribute it and/or modify it | |
7 ## under the terms of the GNU General Public License as published by | |
7016 | 8 ## the Free Software Foundation; either version 3 of the License, or (at |
9 ## your option) any later version. | |
2313 | 10 ## |
11 ## Octave is distributed in the hope that it will be useful, but | |
12 ## WITHOUT ANY WARRANTY; without even the implied warranty of | |
13 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU | |
14 ## General Public License for more details. | |
15 ## | |
16 ## You should have received a copy of the GNU General Public License | |
7016 | 17 ## along with Octave; see the file COPYING. If not, see |
18 ## <http://www.gnu.org/licenses/>. | |
245 | 19 |
3369 | 20 ## -*- texinfo -*- |
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21 ## @deftypefn {Function File} {} toeplitz (@var{c}) |
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22 ## @deftypefnx {Function File} {} toeplitz (@var{c}, @var{r}) |
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23 ## Return the Toeplitz matrix constructed from the first column @var{c}, |
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24 ## and (optionally) the first row @var{r}. If the first element of @var{r} |
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25 ## is not the same as the first element of @var{c}, the first element of |
3369 | 26 ## @var{c} is used. If the second argument is omitted, the first row is |
27 ## taken to be the same as the first column. | |
3426 | 28 ## |
5016 | 29 ## A square Toeplitz matrix has the form: |
3369 | 30 ## @tex |
31 ## $$ | |
5016 | 32 ## \left[\matrix{c_0 & r_1 & r_2 & \cdots & r_n\cr |
33 ## c_1 & c_0 & r_1 & \cdots & r_{n-1}\cr | |
34 ## c_2 & c_1 & c_0 & \cdots & r_{n-2}\cr | |
35 ## \vdots & \vdots & \vdots & \ddots & \vdots\cr | |
36 ## c_n & c_{n-1} & c_{n-2} & \ldots & c_0}\right] | |
3369 | 37 ## $$ |
38 ## @end tex | |
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39 ## @ifnottex |
3426 | 40 ## |
3369 | 41 ## @example |
42 ## @group | |
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43 ## c(0) r(1) r(2) @dots{} r(n) |
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44 ## c(1) c(0) r(1) @dots{} r(n-1) |
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45 ## c(2) c(1) c(0) @dots{} r(n-2) |
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46 ## . . . . . |
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47 ## . . . . . |
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48 ## . . . . . |
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49 ## c(n) c(n-1) c(n-2) @dots{} c(0) |
3369 | 50 ## @end group |
51 ## @end example | |
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52 ## |
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53 ## @end ifnottex |
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54 ## @seealso{hankel} |
3369 | 55 ## @end deftypefn |
4 | 56 |
9092 | 57 ## Author: jwe && jh |
2314 | 58 |
2311 | 59 function retval = toeplitz (c, r) |
4 | 60 |
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61 if (nargin < 1 || nargin > 2) |
6046 | 62 print_usage (); |
4 | 63 endif |
64 | |
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65 if (nargin == 1) |
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66 if (! isvector (c)) |
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67 error ("toeplitz: C must be a vector"); |
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68 endif |
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69 |
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70 r = c; |
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71 nr = length (c); |
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72 nc = nr; |
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73 else |
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74 if (! (isvector (c) && isvector (r))) |
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75 error ("toeplitz: C and R must be vectors"); |
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76 elseif (r(1) != c(1)) |
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77 warning ("toeplitz: column wins anti-diagonal conflict"); |
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78 endif |
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79 |
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80 nr = length (c); |
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81 nc = length (r); |
4 | 82 endif |
83 | |
9092 | 84 if (nr == 0 || nc == 0) |
85 ## Empty matrix. | |
86 retval = zeros (nr, nc, class (c)); | |
87 return; | |
4 | 88 endif |
89 | |
2303 | 90 ## If we have a single complex argument, we want to return a |
91 ## Hermitian-symmetric matrix (actually, this will really only be | |
92 ## Hermitian-symmetric if the first element of the vector is real). | |
9092 | 93 if (nargin == 1 && iscomplex (c)) |
1016 | 94 c = conj (c); |
95 c(1) = conj (c(1)); | |
96 endif | |
97 | |
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98 if (issparse (c) && issparse (r)) |
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99 c = c(:).'; ## enforce row vector |
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100 r = r(:).'; ## enforce row vector |
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101 cidx = find (c); |
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102 ridx = find (r); |
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103 |
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104 ## Ignore the first element in r. |
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105 ridx = ridx(ridx > 1); |
4 | 106 |
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107 ## Form matrix. |
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108 retval = spdiags (repmat (c(cidx),nr,1),1-cidx,nr,nc) + ... |
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109 spdiags (repmat (r(ridx),nr,1),ridx-1,nr,nc); |
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110 else |
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111 ## Concatenate data into a single column vector. |
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112 data = [r(end:-1:2)(:); c(:)]; |
4 | 113 |
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114 ## Get slices. |
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115 slices = cellslices (data, nc:-1:1, nc+nr-1:-1:nr); |
4 | 116 |
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117 ## Form matrix. |
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118 retval = horzcat (slices{:}); |
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119 endif |
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120 |
4 | 121 endfunction |
7411 | 122 |
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123 |
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124 %!assert (toeplitz (1), [1]) |
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125 %!assert (toeplitz ([1, 2, 3], [1; -3; -5]), [1, -3, -5; 2, 1, -3; 3, 2, 1]) |
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126 %!assert (toeplitz ([1, 2, 3], [1; -3i; -5i]), [1, -3i, -5i; 2, 1, -3i; 3, 2, 1]) |
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128 %% Test input validation |
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129 %!error toeplitz () |
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130 %!error toeplitz (1, 2, 3) |
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131 %!error <C must be a vector> toeplitz ([1, 2; 3, 4]) |
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132 %!error <C and R must be vectors> toeplitz ([1, 2; 3, 4], 1) |
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133 %!error <C and R must be vectors> toeplitz (1, [1, 2; 3, 4]) |
7411 | 134 |