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Create local repository for matrix toolboxes. Step #0 done.
author Antonio Pino Robles <data.script93@gmail.com>
date Wed, 06 May 2015 14:56:53 +0200
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8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
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1 function [x, y, z, m] = pscont(A, k, npts, ax, levels)
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2 %PSCONT Contours and colour pictures of pseudospectra.
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3 % PSCONT(A, K, NPTS, AX, LEVELS) plots LOG10(1/NORM(R(z))),
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4 % where R(z) = INV(z*I-A) is the resolvent of the square matrix A,
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5 % over an NPTS-by-NPTS grid.
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6 % NPTS defaults to a SIZE(A)-dependent value.
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7 % The limits are AX(1) and AX(2) on the x-axis and
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8 % AX(3) and AX(4) on the y-axis.
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9 % If AX is omitted, suitable limits are guessed based on the
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10 % eigenvalues of A.
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11 % The eigenvalues of A are plotted as crosses `x'.
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12 % K determines the type of plot:
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13 % K = 0 (default) PCOLOR and CONTOUR
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14 % K = 1 PCOLOR only
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15 % K = 2 SURFC (SURF and CONTOUR)
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16 % K = 3 SURF only
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17 % K = 4 CONTOUR only
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18 % The contours levels are specified by the vector LEVELS, which
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19 % defaults to -10:-1 (recall we are plotting log10 of the data).
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20 % Thus, by default, the contour lines trace out the boundaries of
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21 % the epsilon pseudospectra for epsilon = 1e-10, ..., 1e-1.
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22 % [X, Y, Z, NPTS] = PSCONT(A, ...) returns the plot data X, Y, Z
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23 % and the value of NPTS used.
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24 %
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25 % After calling this function you may want to change the
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26 % color map (e.g., type COLORMAP HOT - see HELP COLOR) and the
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27 % shading (e.g., type SHADING INTERP - see HELP INTERP).
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28 % For an explanation of the term `pseudospectra', and references,
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29 % see PS.M.
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30 % When A is real and the grid is symmetric about the x-axis, this
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31 % routine exploits symmetry to halve the computational work.
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32
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33 % Colour pseduospectral pictures of this type are referred to as
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34 % `spectral portraits' by Godunov, Kostin, and colleagues.
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35 % References: see PS.
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36
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37 if diff(size(A)), error('Matrix must be square.'), end
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38 n = length(A);
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39 Areal = ~any(imag(A));
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40
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41 if nargin < 5, levels = -10:-1; end
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42 e = eig(A);
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43 if nargin < 4 | isempty(ax)
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44 ax = cpltaxes(e);
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45 if Areal, ax(3) = -ax(4); end % Make sure region symmetric about x-axis.
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46 end
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47 if nargin < 3 | isempty(npts)
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48 npts = 3*round( min(max(5, sqrt(20^2*10^3/n^3) ), 30));
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49 end
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50 if nargin < 2 | isempty(k), k = 0; end
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51
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52 nptsx = npts; nptsy = npts;
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53 Ysymmetry = (Areal & ax(3) == -ax(4));
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54
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55 x = linspace(ax(1), ax(2), npts);
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56 y = linspace(ax(3), ax(4), npts);
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57 if Ysymmetry % Exploit symmetry about x-axis.
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58 nptsy = ceil(npts/2);
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59 y1 = y;
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60 y = y(1:nptsy);
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61 end
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62
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63 [xx, yy] = meshgrid(x,y);
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64 z = xx + sqrt(-1)*yy;
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65 I = eye(n);
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66 Smin = zeros(nptsy, nptsx);
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67
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68 for j=1:nptsx
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69 for i=1:nptsy
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70 Smin(i,j) = min( svd( z(i,j)*I-A ) );
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71 end
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72 end
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73
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74 z = log10( Smin + eps );
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75 if Ysymmetry
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76 z = [z; z(nptsy-rem(npts,2):-1:1,:)];
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77 y = y1;
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78 end
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79
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80 if k == 0 | k == 1
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81 pcolor(x, y, z); hold on
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82 elseif k == 2
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83 surfc(x, y, z); hold on
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84 elseif k == 3
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85 surf(x, y, z); hold on
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86 end
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87
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88 if k == 0
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89 contour(x, y, z, levels,'-k'); hold on
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90 elseif k == 4
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91 contour(x, y, z, levels); hold on
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92 end
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93
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94 if k ~= 2 & k ~= 3
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95 if k == 0 | k == 1
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96 s = 'w'; % White.
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97 else
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98 s = 'k'; % Black.
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99 end
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100 plot(real(e),imag(e),['x' s]);
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101 end
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102
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103 axis('square')
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104 hold off